Finite Group Databasebeta

← #17195111

Subgroups — #17195111

Order 4352.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D17C211yesmaximal, characteristic
2#14531919C211yesmaximal, characteristic, complemented
3#14531917C211yesmaximal, characteristic, complemented
4#14531914C211yesmaximal, characteristic, complemented
5#14531914C211yesmaximal, characteristic, complemented
6#14531783C211yesmaximal, characteristic, complemented
7#14531779C211yesmaximal, characteristic, complemented
8#14531775C211yesmaximal, characteristic, complemented
9#14531771C211yesmaximal, characteristic, complemented
10#14531660C211yesmaximal, characteristic, complemented
11#14531658C211yesmaximal, characteristic, complemented
12#14531632C211yesmaximal, characteristic, complemented
13#14531631C211yesmaximal, characteristic, complemented
14#14531628C211yesmaximal, characteristic, complemented
15#14531628C211yesmaximal, characteristic, complemented
16#14531605C211yesmaximal, characteristic
17#14531602C211yesmaximal, characteristic
18#14531578C211yesmaximal, characteristic, complemented
19#14531574C211yesmaximal, characteristic, complemented
20#14531570C211yesmaximal, characteristic, complemented
21#14531383C211yesmaximal, characteristic, complemented
22#14531378C211yesmaximal, characteristic, complemented
23#14531311C211yesmaximal, characteristic, complemented
24C4×#10587580C211yesmaximal, characteristic, complemented
25#14531305C211yesmaximal, characteristic, complemented
26C4×#10587569C211yesmaximal, characteristic, complemented
27#14531166C211yesmaximal, characteristic, complemented
28#14531138C211yesmaximal, characteristic, complemented
29#14531136C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2335C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587580C2211yescharacteristic
35C2×#10587580C2211yescharacteristic
36C2×#10587572C2211yescharacteristic
37C2×#10587615C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587569C2211yescharacteristic
40C2×#10587621C2211yescharacteristic
41#123×D17C4116yescomplemented
42C2×C4×D68C2211yescharacteristic
43C2×#10587579C2211yescharacteristic
44C2×C4×C22⋊D17C2211yescharacteristic
45C2×#10587567C2211yescharacteristic
46C2×#10587578C2211yescharacteristic
47C2×#10587578C2211yescharacteristic, complemented
48C2×#10587578C2211yescharacteristic, complemented
49C2×#10587558C2211yescharacteristic
50C2×C4⋊C4×D17C2211yescharacteristic
51C2×C4⋊C4×D17C2211yescharacteristic
52C22×#63227C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C42×D17C2211yescharacteristic, complemented
60C2×C42×D17C2211yescharacteristic, complemented
61#11762712C2211yescharacteristic
62#11762709C2211yescharacteristic
63#11762709C2211yescharacteristic
64#11762708C2211yescharacteristic, complemented
65#11762706C2211yescharacteristic, complemented
66#11762704C2211yescharacteristic, complemented
67#11762703C2211yescharacteristic, complemented
68#11762703C2211yescharacteristic, complemented
69#11762703C2211yescharacteristic, complemented
70#11762703C2211yescharacteristic, complemented
71#11762702C2211yescharacteristic, complemented
72#11762702C2211yescharacteristic, complemented
73#11762702C2211yescharacteristic, complemented
74#11762702C2211yescharacteristic, complemented
75#11762701C2211yescharacteristic, complemented
76#11762701C2211yescharacteristic, complemented
77#11762701C2211yescharacteristic, complemented
78#11762700C2211yescharacteristic, complemented
79#11762699C2211yescharacteristic, complemented
80#11762699C2211yescharacteristic, complemented
81#11762699C2211yescharacteristic, complemented
82#11762698C2211yescharacteristic, complemented
83#11762697C2211yescharacteristic, complemented
84#11762697C2211yescharacteristic, complemented
85#11762697C2211yescharacteristic, complemented
86#11762697C2211yescharacteristic, complemented
87#11762696C2211yescharacteristic, complemented
88#11762696C2211yescharacteristic, complemented
89#11762696C2211yescharacteristic, complemented
90#11762695C2211yescharacteristic, complemented
91#11762695C2211yescharacteristic, complemented
92#11762694C2211yescharacteristic, complemented
93#11762694C2211yescharacteristic, complemented
94#11762693C2211yescharacteristic, complemented
95#11762692C2211yescharacteristic, complemented
96#11762692C2211yescharacteristic, complemented
97#11762691C2211yescharacteristic, complemented
98#11762690C2211yescharacteristic, complemented
99#11762690C2211yescharacteristic, complemented
100#11762690C2211yescharacteristic, complemented
101#11762689C2211yescharacteristic
102#11762687C2211yescharacteristic
103#11762687C2211yescharacteristic
104#11762685C2211yescharacteristic
105#11762685C2211yescharacteristic
106#11762685C2211yescharacteristic
107#11762685C2211yescharacteristic
108#11762684C2211yescharacteristic, complemented
109#11762683C2211yescharacteristic, complemented
110#11762683C2211yescharacteristic, complemented
111#11762683C2211yescharacteristic, complemented
112#11762680C2211yescharacteristic, complemented
113#11762680C2211yescharacteristic, complemented
114#11762680C2211yescharacteristic, complemented
115#11762671C2211yescharacteristic
116#11762671C2211yescharacteristic
117#11762671C2211yescharacteristic, complemented
118#11762671C2211yescharacteristic, complemented
119#11762669C2211yescharacteristic, complemented
120#11762668C2211yescharacteristic
121#11762668C2211yescharacteristic
122#11762666C2211yescharacteristic
123#11762666C2211yescharacteristic
124#11762666C2211yescharacteristic
125#11762666C2211yescharacteristic
126#11762664C2211yescharacteristic
127#11762664C2211yescharacteristic
128#11762664C2211yescharacteristic
129#11762664C2211yescharacteristic
130C4⋊C4×Dic17C2211yescharacteristic, complemented
131C4⋊C4×Dic17C2211yescharacteristic, complemented
132C4⋊C4×Dic17C2211yescharacteristic, complemented
133C4×#63225C2211yescharacteristic, complemented
134C4×#63225C2211yescharacteristic, complemented
135C4×#63225C2211yescharacteristic, complemented
136C4×C4⋊Dic17C2211yescharacteristic, complemented
137C4×C4⋊Dic17C2211yescharacteristic, complemented
138#11762660C2211yescharacteristic, complemented
139#11762660C2211yescharacteristic, complemented
140#11762660C2211yescharacteristic, complemented
141C22⋊C4×Dic17C2211yescharacteristic, complemented
142C22⋊C4×Dic17C2211yescharacteristic, complemented
143C22⋊C4×Dic17C2211yescharacteristic, complemented
144C22⋊C4×Dic17C2211yescharacteristic, complemented
145C22⋊C4×Dic17C2211yescharacteristic, complemented
146C22⋊C4×Dic17C2211yescharacteristic, complemented
147C22⋊C4×Dic17C2211yescharacteristic, complemented
148C4×#63227C2211yescharacteristic
149C4×#63227C2211yescharacteristic
150C4×#63227C2211yescharacteristic
151C4×#63227C2211yescharacteristic
152C4×#63227C2211yescharacteristic, complemented
153C4×#63227C2211yescharacteristic, complemented
154C4×#63227C2211yescharacteristic, complemented
155C4×#63227C2211yescharacteristic, complemented
156C4×#63227C2211yescharacteristic, complemented
157C4×C22⋊Dic17C2211yescharacteristic, complemented
158C4×C22⋊Dic17C2211yescharacteristic, complemented
159C4×C22⋊Dic17C2211yescharacteristic, complemented
160#11762656C2211yescharacteristic
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#123C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#389C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#388C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#387C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C17×#380C2211yescharacteristic, complemented
185C4×C4⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C23×Dic17C2311yescharacteristic
196C23×Dic17C2311yescharacteristic
197C2×D4×D17—42no—
198C2×D4×D17—42no—
199C2×D4×D17C2×C418yes—
200C22×D68C2311yescharacteristic
201C22×C4×D17—42no—
202C22×C4×D17—42no—
203C22×C4×D17C2×C418yescomplemented
204C22×C4×D17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C17×#123C2×C418yescomplemented
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250#10587621C2×C418yescomplemented
251#10587615C2×C418yescomplemented
252C4×C22⋊D17—42no—
253C2×#63227—24no—
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×C4×Dic17C2311yescharacteristic
296C2×C4×Dic17C2311yescharacteristic
297C2×C4×Dic17C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314#10587580C2×C418yescomplemented
315#10587580C2×C418yescomplemented
316#10587579—42no—
317#10587578—24no—
318#10587578—42no—
319#10587578—42no—
320C4⋊C4×D17C2×C418yescomplemented
321C4⋊C4×D17C2×C418yescomplemented
322#10587572C2×C418yescomplemented
323#10587569C2×C418yescomplemented
324#10587569C2×C418yescomplemented
325#10587567—42no—
326C22⋊C4×D17—24no—
327C22⋊C4×D17—24no—
328C22⋊C4×D17—24no—
329C22⋊C4×D17C2×C418yescomplemented
330C22⋊C4×D17C2×C418yescomplemented
331C22⋊C4×D17C2×C418yescomplemented
332C4×D68—42no—
333#10587558—24no—
334C42×D17—42no—
335C42×D17—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—22no—
381C23×D17—22no—
382C23×D17—22no—
383C23×D17—22no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17C22×C414yes—
391C23×D17C22×C414yes—
392C23×D17C2411yescharacteristic
393C23×D17C2411yescharacteristic
394C23×D17C2411yescharacteristic
395C2×D4×C17—41no—
396C2×D4×C17—41no—
397C2×D4×C17C22×C414yes—
398C22×C4×C17—22no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17C22×C414yes—
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C2×C22⋊D17—22no—
418C2×C22⋊D17—22no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17C22×C414yes—
422C2×C22⋊D17C22×C414yes—
423C22×Dic17—22no—
424C22×Dic17—41no—
425C22×Dic17—41no—
426C22×Dic17—41no—
427C22×Dic17—41no—
428C22×Dic17C22×C414yes—
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442D4×D17—416no—
443C2×D68—22no—
444C2×D68—22no—
445C2×D68C22×C414yes—
446C2×C4×D17—22no—
447C2×C4×D17—22no—
448C2×C4×D17—22no—
449C2×C4×D17—22no—
450C2×C4×D17—22no—
451C2×C4×D17—22no—
452C2×C4×D17—22no—
453C2×C4×D17—22no—
454C2×C4×D17—22no—
455C2×C4×D17—22no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—416no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17C22×C414yes—
480C2×C4×D17C22×C414yes—
481C2×C4×D17C22×C414yes—
482C2×C4×D17C22×C414yes—
483C2×C4×D17C22×C414yes—
484C2×C4×D17C22×C414yes—
485C2×C4×D17C22×C414yes—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—41no—
488C4⋊C4×C17—41no—
489C4⋊C4×C17—41no—
490C4⋊C4×C17—41no—
491C4⋊C4×C17C22×C414yes—
492C4⋊C4×C17C22×C414yes—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—22no—
495C22⋊C4×C17—22no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17C22×C414yes—
501C22⋊C4×C17C22×C414yes—
502C22⋊C4×C17C22×C414yes—
503C42×C17—22no—
504C42×C17—41no—
505C42×C17—41no—
506C42×C17—41no—
507C42×C17—41no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17C22×C414yes—
516C22⋊Dic17C22×C414yes—
517C22⋊Dic17C22×C414yes—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
524#63227—22no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227C22×C414yes—
535#63227C22×C414yes—
536#63227C22×C414yes—
537#63227C22×C414yes—
538#63227C22×C414yes—
539#63227C22×C414yes—
540#63227#4114yes—
541#63227#4114yes—
542C4⋊Dic17—22no—
543C4⋊Dic17—41no—
544C4⋊Dic17—41no—
545C4⋊Dic17—41no—
546C4⋊Dic17—41no—
547C4⋊Dic17C22×C414yes—
548C4⋊Dic17C22×C414yes—
549#63225—22no—
550#63225—22no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225C22×C414yes—
556#63225C22×C414yes—
557#63225C22×C414yes—
558#63225C22×C414yes—
559C4×Dic17—22no—
560C4×Dic17—22no—
561C4×Dic17—22no—
562C4×Dic17—41no—
563C4×Dic17—41no—
564C4×Dic17—41no—
565C4×Dic17—41no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17—41no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578#34238—171nomaximal, Sylow
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17C23×C412yes—
592C23×C17C23×C412yes—
593C23×C17C2511yescharacteristic
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—28no—
609C22×D17—28no—
610C22×D17—28no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—44no—
618C22×D17—82no—
619C22×D17—82no—
620C22×D17—82no—
621C22×D17—82no—
622C22×D17C23×C412yes—
623C22×D17C23×C412yes—
624C22×D17C23×C412yes—
625C22×D17C2×#4112yes—
626C22×D17C2×#4112yes—
627C22×D17H(5,𝔽2)12yes—
628C22×D17H(5,𝔽2)12yes—
629D4×C17—44no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—44no—
663C2×C4×C17—82no—
664C2×C4×C17C23×C412yes—
665C2×C4×C17C23×C412yes—
666C2×C4×C17C23×C412yes—
667C2×C4×C17C23×C412yes—
668C2×C4×C17C23×C412yes—
669C2×C4×C17C2×#4112yes—
670C2×C4×C17C2×#4112yes—
671C22⋊D17—28no—
672C22⋊D17—44no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—44no—
706C2×Dic17—82no—
707C2×Dic17C23×C412yes—
708C2×Dic17C23×C412yes—
709C2×Dic17C23×C412yes—
710C2×Dic17C23×C412yes—
711C2×Dic17C23×C412yes—
712C2×Dic17C2×#4112yes—
713C2×Dic17C2×#4112yes—
714D68—28no—
715C4×D17—28no—
716C4×D17—28no—
717C4×D17—28no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—44no—
722C4×D17—44no—
723C4×D17—44no—
724C4×D17—44no—
725C4×D17—44no—
726C4×D17—82no—
727C4×D17—82no—
728C22×#123—171no—
729#2374—171no—
730#2374—171no—
731#2374—171no—
732#2374—171no—
733#2359—171no—
734#2359—171no—
735#2359—171no—
736#2359—171no—
737#2345—171no—
738#2345—171no—
739#2342—171no—
740#2342—171no—
741#2342—171no—
742#2342—171no—
743D4×C22⋊C4—171no—
744D4×C22⋊C4—171no—
745#2335—171no—
746#2335—171no—
747#2335—171no—
748#2335D1711yescharacteristic, complemented
749#2313—171no—
750#2312—171no—
751C4×#123—171no—
752C4×#123—171no—
753C4×#123—171no—
754C4×#123—171no—
755#2280—171no—
756#2274—171no—
757#2273—171no—
758C2×C4×C22⋊C4—171no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17C24×C411yescharacteristic
774C22×C17C22×#4111yescharacteristic
775C22×C17C22×#4111yescharacteristic
776C22×C17C2×H(5,𝔽2)11yescharacteristic
777C22×C17C2×H(5,𝔽2)11yescharacteristic
778C22×C17#58511yescharacteristic
779C22×C17#58511yescharacteristic
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—22no—
795C2×D17—416no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—88no—
801C2×D17C4×#4114yes—
802C2×D17#51814yes—
803C4×C17—22no—
804C4×C17—22no—
805C4×C17—22no—
806C4×C17—22no—
807C4×C17—22no—
808C4×C17—22no—
809C4×C17—22no—
810C4×C17—41no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816Dic17—22no—
817Dic17—22no—
818Dic17—22no—
819Dic17—22no—
820Dic17—22no—
821Dic17—22no—
822Dic17—22no—
823Dic17—41no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829C23×D4—171no—
830C24×C4—171no—
831C2×#123—171no—
832C2×#123—171no—
833C2×#123—1716no—
834C2×#123—171no—
835C2×#123—171no—
836C2×#123—171no—
837C2×#123—171no—
838C2×#123—171no—
839C2×#123C2×D1711yescharacteristic
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×#117—171no—
845C2×#117—171no—
846C2×#117—171no—
847C2×#117—171no—
848C22×C4⋊C4—171no—
849C22×C4⋊C4—171no—
850C22×C22⋊C4—171no—
851C22×C22⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4—171no—
855C22×C22⋊C4—171no—
856C22×C22⋊C4—171no—
857C22×C42—171no—
858C22×C42—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390C2×D1711yescharacteristic
863#389—171no—
864#389—171no—
865#389—171no—
866#389C2×D1711yescharacteristic, complemented
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388C2×D1711yescharacteristic, complemented
888#388C2×D1711yescharacteristic, complemented
889#388C2×D1711yescharacteristic, complemented
890#388C2×D1711yescharacteristic, complemented
891#387—171no—
892#387—171no—
893#387—171no—
894#387—171no—
895#387—171no—
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387C2×D1711yescharacteristic, complemented
906#387C2×D1711yescharacteristic, complemented
907#386—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386C2×D1711yescharacteristic
915#385—171no—
916#385—171no—
917#385—171no—
918#385—171no—
919#385—171no—
920#385—171no—
921#385—171no—
922#385C2×D1711yescharacteristic, complemented
923#381—171no—
924#381—171no—
925#381—171no—
926#381—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#380—171no—
931#380—171no—
932#380—171no—
933#380—171no—
934#380C2×D1711yescharacteristic, complemented
935#379—171no—
936#379—171no—
937#379—171no—
938#379—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C4⋊C4—171no—
942C4×C4⋊C4—171no—
943C4×C4⋊C4—171no—
944C4×C4⋊C4—171no—
945C4×C4⋊C4—171no—
946C4×C4⋊C4—171no—
947C4×C4⋊C4—171no—
948C4×C4⋊C4—171no—
949C4×C4⋊C4—171no—
950C4×C4⋊C4C2×D1711yescharacteristic, complemented
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956C4×C22⋊C4—171no—
957C4×C22⋊C4—171no—
958C4×C22⋊C4—171no—
959C4×C22⋊C4—171no—
960C4×C22⋊C4—171no—
961C4×C22⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4—171no—
975C4×C22⋊C4—171no—
976C4×C22⋊C4—171no—
977C4×C22⋊C4—171no—
978C4×C22⋊C4—171no—
979C4×C22⋊C4—171no—
980C4×C22⋊C4—171no—
981C4×C22⋊C4C2×D1711yescharacteristic, complemented
982C4×C22⋊C4C2×D1711yescharacteristic, complemented
983C2×#95—171no—
984C2×#95—171no—
985C2×C17—42no—
986C2×C17—42no—
987C2×C17C2×C4×#4111yescharacteristic
988C2×C17C2×#51811yescharacteristic
989C2×C17#342811yescharacteristic
990C2×C17#351311yescharacteristic
991C2×C17#351311yescharacteristic
992C2×C17#351311yescharacteristic
993C2×C17#351311yescharacteristic
994D17—24no—
995D17—24no—
996D17—42no—
997C25—171no—
998C25—171no—
999C22×D4—171no—
1000C22×D4—171no—
1001C22×D4—178no—
1002C22×D4—171no—
1003C22×D4—682no—
1004C22×D4—682no—
1005C22×D4C22×D1711yescharacteristic
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4—171no—
1010C23×C4—178no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—171no—
1015C23×C4—171no—
1016C23×C4—171no—
1017C23×C4—171no—
1018C23×C4—171no—
1019C23×C4—171no—
1020C23×C4—171no—
1021C23×C4—171no—
1022C23×C4—682no—
1023C23×C4—682no—
1024C23×C4C22×D1711yescharacteristic
1025C23×C4C22×D1711yescharacteristic
1026#123—178no—
1027#123—178no—
1028#123—178no—
1029#123—178no—
1030#123—178no—
1031#123—178no—
1032#123—178no—
1033#123C4×D1718yescomplemented
1034C4×D4—682no—
1035C4×D4—682no—
1036C4×D4—682no—
1037C4×D4—682no—
1038#117—344no—
1039#117—344no—
1040#117—682no—
1041#117—682no—
1042C2×C4⋊C4—171no—
1043C2×C4⋊C4—171no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—178no—
1049C2×C4⋊C4—178no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4C22×D1711yescharacteristic
1062C2×C4⋊C4C22×D1711yescharacteristic
1063C2×C4⋊C4C22×D1711yescharacteristic
1064C2×C4⋊C4C22×D1711yescharacteristic
1065C2×C4⋊C4C22×D1711yescharacteristic
1066C2×C4⋊C4C22×D1711yescharacteristic
1067C2×C4⋊C4C22×D1711yescharacteristic
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—178no—
1080C2×C22⋊C4—178no—
1081C2×C22⋊C4—178no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—344no—
1106C2×C22⋊C4—344no—
1107C2×C22⋊C4—344no—
1108C2×C22⋊C4—344no—
1109C2×C22⋊C4C22×D1711yescharacteristic
1110C2×C22⋊C4C22×D1711yescharacteristic
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C42—171no—
1120C2×C42—171no—
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—171no—
1133C2×C42—171no—
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42—171no—
1137C2×C42—171no—
1138C2×C42—682no—
1139C2×C42—682no—
1140C2×C42C22×D1711yescharacteristic
1141C2×C42C22×D1711yescharacteristic
1142C2×C42C22×D1711yescharacteristic
1143C2×C42C22×D1711yescharacteristic
1144C2×C42C22×D1711yescharacteristic
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179#95C22×D1711yescharacteristic
1180#95C22×D1711yescharacteristic
1181#95C22×D1711yescharacteristic
1182#95C22×D1711yescharacteristic
1183#95C22×D1711yescharacteristic
1184#95C22×D1711yescharacteristic
1185C17#3423811yescharacteristic, complemented, Sylow
1186C24—171no—
1187C24—171no—
1188C24—171no—
1189C24—174no—
1190C24—174no—
1191C24—342no—
1192C24—342no—
1193C24—342no—
1194C24—342no—
1195C24—342no—
1196C24—342no—
1197C24—681no—
1198C24—681no—
1199C24—681no—
1200C24—681no—
1201C24—681no—
1202C24—681no—
1203C24C23×D1711yescharacteristic
1204C24C23×D1711yescharacteristic
1205C2×D4—41no—
1206C2×D4—41no—
1207C2×D4—174no—
1208C2×D4—174no—
1209C2×D4—174no—
1210C2×D4—342no—
1211C2×D4—342no—
1212C2×D4—342no—
1213C2×D4—342no—
1214C2×D4—681no—
1215C2×D4—681no—
1216C2×D4—6816no—
1217C2×D4C2×C4×D1714yes—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—171no—
1224C22×C4—171no—
1225C22×C4—171no—
1226C22×C4—171no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—174no—
1231C22×C4—174no—
1232C22×C4—174no—
1233C22×C4—174no—
1234C22×C4—174no—
1235C22×C4—174no—
1236C22×C4—174no—
1237C22×C4—174no—
1238C22×C4—171no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—342no—
1245C22×C4—342no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—342no—
1255C22×C4—342no—
1256C22×C4—342no—
1257C22×C4—342no—
1258C22×C4—342no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—6816no—
1278C22×C4—681no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4—681no—
1282C22×C4C2×C4×D1714yes—
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C4⋊C4—22no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—41no—
1300C4⋊C4—41no—
1301C4⋊C4—174no—
1302C4⋊C4—174no—
1303C4⋊C4—174no—
1304C4⋊C4—174no—
1305C4⋊C4—174no—
1306C4⋊C4—174no—
1307C4⋊C4—342no—
1308C4⋊C4—342no—
1309C4⋊C4—342no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4C2×C4×D1714yes—
1319C4⋊C4C2×C4×D1714yes—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—174no—
1328C22⋊C4—174no—
1329C22⋊C4—174no—
1330C22⋊C4—174no—
1331C22⋊C4—174no—
1332C22⋊C4—174no—
1333C22⋊C4—174no—
1334C22⋊C4—174no—
1335C22⋊C4—174no—
1336C22⋊C4—174no—
1337C22⋊C4—174no—
1338C22⋊C4—342no—
1339C22⋊C4—342no—
1340C22⋊C4—342no—
1341C22⋊C4—342no—
1342C22⋊C4—342no—
1343C22⋊C4—342no—
1344C22⋊C4—342no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4—681no—
1361C22⋊C4C2×C4×D1714yes—
1362C22⋊C4C2×C4×D1714yes—
1363C22⋊C4C2×C4×D1714yes—
1364C42—22no—
1365C42—41no—
1366C42—41no—
1367C42—41no—
1368C42—41no—
1369C42—342no—
1370C42—342no—
1371C42—342no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42—681no—
1381C42—681no—
1382C42—681no—
1383C42—681no—
1384C42—681no—
1385C42—681no—
1386C42—681no—
1387C42—681no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—172no—
1401C23—172no—
1402C23—172no—
1403C23—172no—
1404C23—172no—
1405C23—172no—
1406C23—172no—
1407C23—348no—
1408C23—348no—
1409C23—348no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—684no—
1425C23—684no—
1426C23—684no—
1427C23—684no—
1428C23—684no—
1429C23—684no—
1430C23—684no—
1431C23—1362no—
1432C23—1362no—
1433C23—1362no—
1434C23—1362no—
1435C23C22×C4×D1712yes—
1436C23C22×C4×D1712yes—
1437C23C24×D1711yescharacteristic
1438D4—44no—
1439D4—348no—
1440D4—348no—
1441D4—684no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—44no—
1475C2×C4—82no—
1476C2×C4—172no—
1477C2×C4—172no—
1478C2×C4—172no—
1479C2×C4—172no—
1480C2×C4—172no—
1481C2×C4—172no—
1482C2×C4—172no—
1483C2×C4—348no—
1484C2×C4—348no—
1485C2×C4—348no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—684no—
1519C2×C4—684no—
1520C2×C4—684no—
1521C2×C4—684no—
1522C2×C4—684no—
1523C2×C4—684no—
1524C2×C4—684no—
1525C2×C4—684no—
1526C2×C4—684no—
1527C2×C4—1362no—
1528C2×C4—1362no—
1529C2×C4—1362no—
1530C2×C4C22×C4×D1712yes—
1531C2×C4C22×C4×D1712yes—
1532C2×C4C22×C4×D1712yes—
1533C2×C4C22×C4×D1712yes—
1534C2×C4C22×C4×D1712yes—
1535C2×C4#41×D1712yes—
1536C2×C4#41×D1712yes—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—174no—
1552C22—174no—
1553C22—342no—
1554C22—342no—
1555C22—342no—
1556C22—342no—
1557C22—342no—
1558C22—342no—
1559C22—342no—
1560C22—342no—
1561C22—342no—
1562C22—342no—
1563C22—342no—
1564C22—342no—
1565C22—342no—
1566C22—342no—
1567C22—342no—
1568C22—6816no—
1569C22—681no—
1570C22—681no—
1571C22—681no—
1572C22—681no—
1573C22—1368no—
1574C22C23×C4×D1711yescharacteristic
1575C22C2×#41×D1711yescharacteristic
1576C22C2×#41×D1711yescharacteristic
1577C22H(5,𝔽2)×D1711yescharacteristic
1578C22H(5,𝔽2)×D1711yescharacteristic
1579C22#1176364411yescharacteristic
1580C22#1176364611yescharacteristic
1581C4—22no—
1582C4—22no—
1583C4—22no—
1584C4—22no—
1585C4—22no—
1586C4—22no—
1587C4—22no—
1588C4—41no—
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—342no—
1595C4—342no—
1596C4—342no—
1597C4—342no—
1598C4—342no—
1599C4—342no—
1600C4—342no—
1601C4—681no—
1602C4—681no—
1603C4—681no—
1604C4—681no—
1605C4—681no—
1606C4—681no—
1607C2—42no—
1608C2—42no—
1609C2—344no—
1610C2—344no—
1611C2—682no—
1612C2C4×#41×D1711yescharacteristic
1613C2D17×#51811yescharacteristic
1614C2#1454198411yescharacteristic
1615C2#1454271411yescharacteristic
1616C2#1454272011yescharacteristic
1617C2#1454272211yescharacteristic
1618C2#1454273011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2335C2
socle, cosocleC23×C17C25
prime radicalC22×D4×D17C22
hypercenter#2335D17
hypocenterC17#34238
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531919C2semidirect
3. #14531917C2semidirect
4. #14531914C2semidirect
5. #14531914C2semidirect
6. #14531783C2semidirect
7. #14531779C2semidirect
8. #14531775C2semidirect
9. #14531771C2semidirect
10. #14531660C2semidirect
11. #14531658C2semidirect
12. #14531632C2semidirect
13. #14531631C2semidirect
14. #14531628C2semidirect
15. #14531628C2semidirect
18. #14531578C2semidirect
19. #14531574C2semidirect
20. #14531570C2semidirect
21. #14531383C2semidirect
22. #14531378C2semidirect
23. #14531311C2semidirect
24. C4×#10587580C2semidirect
25. #14531305C2semidirect
26. C4×#10587569C2semidirect
27. #14531166C2semidirect
28. #14531138C2semidirect
29. #14531136C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2335C2semidirect
41. #123×D17C4semidirect
47. C2×#10587578C22semidirect
48. C2×#10587578C22semidirect
59. C2×C42×D17C22semidirect
60. C2×C42×D17C22semidirect
64. #11762708C22semidirect
65. #11762706C22semidirect
66. #11762704C22semidirect
67. #11762703C22semidirect
68. #11762703C22semidirect
69. #11762703C22semidirect
70. #11762703C22semidirect
71. #11762702C22semidirect
72. #11762702C22semidirect
73. #11762702C22semidirect
74. #11762702C22semidirect
75. #11762701C22semidirect
76. #11762701C22semidirect
77. #11762701C22semidirect
78. #11762700C22semidirect
79. #11762699C22semidirect
80. #11762699C22semidirect
81. #11762699C22semidirect
82. #11762698C22semidirect
83. #11762697C22semidirect
84. #11762697C22semidirect
85. #11762697C22semidirect
86. #11762697C22semidirect
87. #11762696C22semidirect
88. #11762696C22semidirect
89. #11762696C22semidirect
90. #11762695C22semidirect
91. #11762695C22semidirect
92. #11762694C22semidirect
93. #11762694C22semidirect
94. #11762693C22semidirect
95. #11762692C22semidirect
96. #11762692C22semidirect
97. #11762691C22semidirect
98. #11762690C22semidirect
99. #11762690C22semidirect
100. #11762690C22semidirect
108. #11762684C22semidirect
109. #11762683C22semidirect
110. #11762683C22semidirect
111. #11762683C22semidirect
112. #11762680C22semidirect
113. #11762680C22semidirect
114. #11762680C22semidirect
117. #11762671C22semidirect
118. #11762671C22semidirect
119. #11762669C22semidirect
130. C4⋊C4×Dic17C22semidirect
131. C4⋊C4×Dic17C22semidirect
132. C4⋊C4×Dic17C22semidirect
133. C4×#63225C22semidirect
134. C4×#63225C22semidirect
135. C4×#63225C22semidirect
136. C4×C4⋊Dic17C22semidirect
137. C4×C4⋊Dic17C22semidirect
138. #11762660C22semidirect
139. #11762660C22semidirect
140. #11762660C22semidirect
141. C22⋊C4×Dic17C22semidirect
142. C22⋊C4×Dic17C22semidirect
143. C22⋊C4×Dic17C22semidirect
144. C22⋊C4×Dic17C22semidirect
145. C22⋊C4×Dic17C22semidirect
146. C22⋊C4×Dic17C22semidirect
147. C22⋊C4×Dic17C22semidirect
152. C4×#63227C22semidirect
153. C4×#63227C22semidirect
154. C4×#63227C22semidirect
155. C4×#63227C22semidirect
156. C4×#63227C22semidirect
157. C4×C22⋊Dic17C22semidirect
158. C4×C22⋊Dic17C22semidirect
159. C4×C22⋊Dic17C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
171. #95×D17C22semidirect
172. #95×D17C22semidirect
175. C17×#389C22semidirect
176. C17×#388C22semidirect
177. C17×#388C22semidirect
178. C17×#388C22semidirect
179. C17×#388C22semidirect
180. C17×#387C22semidirect
181. C17×#387C22semidirect
183. C17×#385C22semidirect
184. C17×#380C22semidirect
185. C4×C4⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
203. C22×C4×D17C2×C4semidirect
217. C17×#123C2×C4semidirect
250. #10587621C2×C4semidirect
251. #10587615C2×C4semidirect
314. #10587580C2×C4semidirect
315. #10587580C2×C4semidirect
320. C4⋊C4×D17C2×C4semidirect
321. C4⋊C4×D17C2×C4semidirect
322. #10587572C2×C4semidirect
323. #10587569C2×C4semidirect
324. #10587569C2×C4semidirect
329. C22⋊C4×D17C2×C4semidirect
330. C22⋊C4×D17C2×C4semidirect
331. C22⋊C4×D17C2×C4semidirect
748. #2335D17semidirect
866. #389C2×D17semidirect
887. #388C2×D17semidirect
888. #388C2×D17semidirect
889. #388C2×D17semidirect
890. #388C2×D17semidirect
905. #387C2×D17semidirect
906. #387C2×D17semidirect
922. #385C2×D17semidirect
934. #380C2×D17semidirect
950. C4×C4⋊C4C2×D17semidirect
981. C4×C22⋊C4C2×D17semidirect
982. C4×C22⋊C4C2×D17semidirect
1033. #123C4×D17semidirect
1185. C17#34238semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#123×D172
#145319192
#145319172
#145319142
#145317832
#145317792
#145317752
#145317712
#145316602
#145316582
#145316322
#145316312
#145316282
#145316052
#145316022
#145315782
#145315742
#145315702
#145313832
#145313782
#145313112
C4×#105875802
#145313052
C4×#105875692
#145311662
#145311382
#145311362
C4×C22⋊C4×D172
C17×#23352
#3423817