Finite Group Databasebeta

← #17194199

Subgroups — #17194199

Order 4352.

2732 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763482C211yesmaximal, characteristic
2#14531914C211yesmaximal, characteristic, complemented
3#14531909C211yesmaximal, characteristic, complemented
4#14531907C211yesmaximal, characteristic, complemented
5#14531892C211yesmaximal, characteristic, complemented
6#14531866C211yesmaximal, characteristic, complemented
7#14531862C211yesmaximal, characteristic, complemented
8#14531779C211yesmaximal, characteristic, complemented
9#14531761C211yesmaximal, characteristic
10#14531722C211yesmaximal, characteristic, complemented
11#14531719C211yesmaximal, characteristic, complemented
12#14531640C211yesmaximal, characteristic, complemented
13#14531639C211yesmaximal, characteristic, complemented
14#14531634C211yesmaximal, characteristic, complemented
15#14531631C211yesmaximal, characteristic, complemented
16#14531334C211yesmaximal, characteristic, complemented
17#14531334C211yesmaximal, characteristic, complemented
18#14531325C211yesmaximal, characteristic, complemented
19#14531316C211yesmaximal, characteristic, complemented
20#14531314C211yesmaximal, characteristic, complemented
21#14531311C211yesmaximal, characteristic, complemented
22#123×Dic17C211yesmaximal, characteristic, complemented
23#14531303C211yesmaximal, characteristic, complemented
24#14531289C211yesmaximal, characteristic
25C4×D4×Dic17C211yesmaximal, characteristic, complemented
26C4×#10587567C211yesmaximal, characteristic, complemented
27#117×Dic17C211yesmaximal, characteristic, complemented
28C4×#10587578C211yesmaximal, characteristic, complemented
29C2×#11762656C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2359C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33#11763482C4116yescomplemented
34C2×#10587584C2211yescharacteristic
35C2×#10587584C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587572C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587583C2211yescharacteristic
40C2×#10587564C2211yescharacteristic
41C2×#10587623C2211yescharacteristic
42C2×#10587573C2211yescharacteristic, complemented
43C2×D4×Dic17C2211yescharacteristic
44C2×D4×Dic17C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic
46C2×#10587567C2211yescharacteristic
47C2×#10587567C2211yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587612C2211yescharacteristic
50C2×#10587578C2211yescharacteristic
51C2×#10587578C2211yescharacteristic
52C22×#63227C2211yescharacteristic
53C22×#63227C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C22×C4×Dic17C2211yescharacteristic
57C22×C4×Dic17C2211yescharacteristic
58C22×C4×Dic17C2211yescharacteristic, complemented
59C2×C42×D17C2211yescharacteristic
60C2×C42×D17C2211yescharacteristic
61#11762715C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762713C2211yescharacteristic, complemented
64#11762709C2211yescharacteristic
65#11762704C2211yescharacteristic, complemented
66#11762703C2211yescharacteristic, complemented
67#11762702C2211yescharacteristic, complemented
68#11762702C2211yescharacteristic, complemented
69#11762701C2211yescharacteristic
70#11762701C2211yescharacteristic
71#11762700C2211yescharacteristic
72#11762700C2211yescharacteristic
73#11762700C2211yescharacteristic
74#11762699C2211yescharacteristic
75#11762699C2211yescharacteristic
76#11762699C2211yescharacteristic
77#11762699C2211yescharacteristic
78#11762699C2211yescharacteristic
79#11762697C2211yescharacteristic, complemented
80#11762696C2211yescharacteristic, complemented
81#11762696C2211yescharacteristic, complemented
82#11762695C2211yescharacteristic, complemented
83#11762695C2211yescharacteristic, complemented
84#11762694C2211yescharacteristic, complemented
85#11762694C2211yescharacteristic, complemented
86#11762694C2211yescharacteristic, complemented
87#11762694C2211yescharacteristic, complemented
88#11762693C2211yescharacteristic, complemented
89#11762692C2211yescharacteristic, complemented
90#11762692C2211yescharacteristic, complemented
91#11762692C2211yescharacteristic, complemented
92#11762692C2211yescharacteristic, complemented
93#11762690C2211yescharacteristic, complemented
94#11762689C2211yescharacteristic
95#11762688C2211yescharacteristic
96#11762685C2211yescharacteristic
97#11762685C2211yescharacteristic
98#11762685C2211yescharacteristic
99#11762684C2211yescharacteristic
100#11762683C2211yescharacteristic
101#11762683C2211yescharacteristic
102#11762682C2211yescharacteristic
103#11762682C2211yescharacteristic
104#11762680C2211yescharacteristic
105#11762680C2211yescharacteristic
106#11762680C2211yescharacteristic
107#11762676C2211yescharacteristic, complemented
108#11762676C2211yescharacteristic, complemented
109#11762673C2211yescharacteristic, complemented
110#11762672C2211yescharacteristic
111#11762671C2211yescharacteristic
112#11762670C2211yescharacteristic, complemented
113#11762667C2211yescharacteristic
114#11762666C2211yescharacteristic
115#11762664C2211yescharacteristic
116C4⋊C4×Dic17C2211yescharacteristic, complemented
117C4⋊C4×Dic17C2211yescharacteristic, complemented
118C4⋊C4×Dic17C2211yescharacteristic, complemented
119C4⋊C4×Dic17C2211yescharacteristic, complemented
120C4⋊C4×Dic17C2211yescharacteristic, complemented
121C4⋊C4×Dic17C2211yescharacteristic, complemented
122C4⋊C4×Dic17C2211yescharacteristic, complemented
123C4⋊C4×Dic17C2211yescharacteristic, complemented
124C4⋊C4×Dic17C2211yescharacteristic, complemented
125C4×#63225C2211yescharacteristic, complemented
126C4×C4⋊Dic17C2211yescharacteristic, complemented
127C4×C4⋊Dic17C2211yescharacteristic, complemented
128#11762660C2211yescharacteristic, complemented
129#11762660C2211yescharacteristic, complemented
130#11762660C2211yescharacteristic, complemented
131C22⋊C4×Dic17C2211yescharacteristic
132C22⋊C4×Dic17C2211yescharacteristic
133C22⋊C4×Dic17C2211yescharacteristic
134C22⋊C4×Dic17C2211yescharacteristic
135C22⋊C4×Dic17C2211yescharacteristic
136C22⋊C4×Dic17C2211yescharacteristic
137C22⋊C4×Dic17C2211yescharacteristic, complemented
138C22⋊C4×Dic17C2211yescharacteristic, complemented
139C22⋊C4×Dic17C2211yescharacteristic, complemented
140C22⋊C4×Dic17C2211yescharacteristic, complemented
141C22⋊C4×Dic17C2211yescharacteristic, complemented
142C4×#63227C2211yescharacteristic
143C4×#63227C2211yescharacteristic
144C4×#63227C2211yescharacteristic
145C4×#63227C2211yescharacteristic
146C4×#63227C2211yescharacteristic
147C4×C22⋊Dic17C2211yescharacteristic
148C4×C22⋊Dic17C2211yescharacteristic
149C4×C22⋊Dic17C2211yescharacteristic, complemented
150#11762656C2211yescharacteristic
151#11762656C2211yescharacteristic
152#11762656C2211yescharacteristic
153#11762656C2211yescharacteristic
154#11762656C2211yescharacteristic
155#11762656C2211yescharacteristic
156#11762656C2211yescharacteristic
157#11762656C2211yescharacteristic
158#11762656C2211yescharacteristic
159#11762656C2211yescharacteristic
160#11762656C2211yescharacteristic
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762655C2211yescharacteristic, complemented
164#11762655C2211yescharacteristic, complemented
165#11762654C2211yescharacteristic, complemented
166#11762654C2211yescharacteristic, complemented
167C2×#10587502C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170C42×Dic17C2211yescharacteristic, complemented
171C42×Dic17C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C17×#123C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C17×#117C2211yescharacteristic
176C17×#389C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#386C2211yescharacteristic
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C23×Dic17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C22×C4×D17—24no—
202C22×C4×D17—24no—
203C22×C4×D17—42no—
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×Dic34C2311yescharacteristic
213C17×#123C2×C418yescomplemented
214C4×D4×C17—24no—
215C17×#117—24no—
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊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×C42×C17C2311yescharacteristic
232C2×C42×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244#10587623C2×C418yes—
245D4×Dic17—24no—
246D4×Dic17C2×C418yescomplemented
247C4×C22⋊D17—24no—
248C2×#63227—24no—
249C2×#63227C2×C418yescomplemented
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
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
268#10587612C2×C418yescomplemented
269C2×C4⋊Dic17C2311yescharacteristic
270C2×C4⋊Dic17C2311yescharacteristic
271C2×C4⋊Dic17C2311yescharacteristic
272C2×C4⋊Dic17C2311yescharacteristic
273C2×C4⋊Dic17C2311yescharacteristic
274C2×C4⋊Dic17C2311yescharacteristic
275C2×C4⋊Dic17C2311yescharacteristic
276C2×#63225C2311yescharacteristic
277C2×#63225C2311yescharacteristic
278C2×#63225C2311yescharacteristic
279C2×#63225C2311yescharacteristic
280C2×#63225C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×C4×Dic17—24no—
285C2×C4×Dic17—42no—
286C2×C4×Dic17—42no—
287C2×C4×Dic17C2311yescharacteristic
288C2×C4×Dic17C2311yescharacteristic
289C2×C4×Dic17C2311yescharacteristic
290C2×C4×Dic17C2311yescharacteristic
291C2×C4×Dic17C2311yescharacteristic
292C2×C4×Dic17C2311yescharacteristic
293C2×C4×Dic17C2311yescharacteristic
294C2×C4×Dic17C2311yescharacteristic
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
314C2×C4×Dic17C2311yescharacteristic
315#10587584C2×C418yescomplemented
316#10587584C2×C418yescomplemented
317#10587583C2×C418yescomplemented
318#10587578—24no—
319#10587578C2×C418yescomplemented
320#10587573—42no—
321#10587572C2×C418yescomplemented
322#10587571C2×C418yescomplemented
323#10587569C2×C418yescomplemented
324#10587567—24no—
325#10587567—42no—
326#10587567C2×C418yescomplemented
327C22⋊C4×D17—24no—
328C22⋊C4×D17C2×C418yescomplemented
329#10587564C2×C418yescomplemented
330C42×D17—24no—
331C42×D17—42no—
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
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—41no—
383C23×D17—41no—
384C23×D17C22×C414yes—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C2×D4×C17—22no—
388C2×D4×C17—22no—
389C2×D4×C17C22×C414yes—
390C22×C4×C17—22no—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—22no—
394C22×C4×C17—22no—
395C22×C4×C17—22no—
396C22×C4×C17—22no—
397C22×C4×C17—22no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17C22×C414yes—
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
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
415C2×C22⋊D17—22no—
416C2×C22⋊D17—22no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17C22×C414yes—
420C2×C22⋊D17C22×C414yes—
421C22×Dic17—22no—
422C22×Dic17—22no—
423C22×Dic17—22no—
424C22×Dic17—22no—
425C22×Dic17—22no—
426C22×Dic17—22no—
427C22×Dic17—22no—
428C22×Dic17—41no—
429C22×Dic17—41no—
430C22×Dic17—41no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17C22×C414yes—
434C22×Dic17C22×C414yescomplemented
435C22×Dic17#4114yes—
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
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—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—416no—
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×D17C22×C414yes—
473C2×C4×D17C22×C414yes—
474C2×C4×D17#4114yes—
475C2×Dic34—41no—
476C2×Dic34—41no—
477C2×Dic34C22×C414yescomplemented
478C4⋊C4×C17—22no—
479C4⋊C4×C17—22no—
480C4⋊C4×C17—22no—
481C4⋊C4×C17—22no—
482C4⋊C4×C17—41no—
483C4⋊C4×C17C22×C414yescomplemented
484C4⋊C4×C17C22×C414yescomplemented
485C22⋊C4×C17—22no—
486C22⋊C4×C17—22no—
487C22⋊C4×C17—22no—
488C22⋊C4×C17—41no—
489C22⋊C4×C17C22×C414yes—
490C22⋊C4×C17C22×C414yescomplemented
491C22⋊C4×C17C22×C414yescomplemented
492C22⋊C4×C17#4114yes—
493C42×C17—22no—
494C42×C17—22no—
495C42×C17—22no—
496C42×C17—22no—
497C42×C17—41no—
498C22⋊Dic17—22no—
499C22⋊Dic17—22no—
500C22⋊Dic17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—41no—
503C22⋊Dic17C22×C414yes—
504C22⋊Dic17C22×C414yes—
505C22⋊Dic17C22×C414yescomplemented
506#63227—22no—
507#63227—22no—
508#63227—22no—
509#63227—22no—
510#63227—22no—
511#63227—22no—
512#63227—22no—
513#63227—41no—
514#63227—41no—
515#63227C22×C414yes—
516#63227C22×C414yes—
517#63227C22×C414yes—
518#63227C22×C414yes—
519#63227C22×C414yes—
520#63227C22×C414yes—
521#63227C22×C414yes—
522#63227C22×C414yes—
523#63227#4114yes—
524C4⋊Dic17—22no—
525C4⋊Dic17—22no—
526C4⋊Dic17—41no—
527C4⋊Dic17C22×C414yescomplemented
528C4⋊Dic17C22×C414yescomplemented
529C4⋊Dic17C22×C414yescomplemented
530C4⋊Dic17C22×C414yescomplemented
531#63225—22no—
532#63225—22no—
533#63225—41no—
534#63225—41no—
535#63225—41no—
536#63225—41no—
537#63225C22×C414yescomplemented
538#63225C22×C414yescomplemented
539C4×Dic17—22no—
540C4×Dic17—22no—
541C4×Dic17—22no—
542C4×Dic17—22no—
543C4×Dic17—22no—
544C4×Dic17—22no—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—22no—
549C4×Dic17—22no—
550C4×Dic17—22no—
551C4×Dic17—22no—
552C4×Dic17—22no—
553C4×Dic17—22no—
554C4×Dic17—22no—
555C4×Dic17—22no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17—41no—
562C4×Dic17—41no—
563C4×Dic17—41no—
564C4×Dic17C22×C414yescomplemented
565C4×Dic17C22×C414yescomplemented
566C4×Dic17C22×C414yescomplemented
567C4×#551—171nomaximal, Sylow
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17C23×C412yes—
579C23×C17C23×C412yes—
580C23×C17C2×#4112yes—
581C23×C17C2×#4112yes—
582C23×C17C2511yescharacteristic
583C22×D17—21no—
584C22×D17—21no—
585C22×D17—21no—
586C22×D17—21no—
587C22×D17—28no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—28no—
595C22×D17—44no—
596C22×D17—44no—
597C22×D17—44no—
598C22×D17—44no—
599C22×D17—44no—
600C22×D17C23×C412yes—
601C22×D17C23×C412yes—
602C22×D17C2×#4112yes—
603C22×D17C2×#4112yes—
604D4×C17—28no—
605C2×C4×C17—28no—
606C2×C4×C17—21no—
607C2×C4×C17—21no—
608C2×C4×C17—21no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
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—44no—
637C2×C4×C17—44no—
638C2×C4×C17—44no—
639C2×C4×C17C23×C412yes—
640C2×C4×C17C23×C412yes—
641C2×C4×C17C23×C412yes—
642C2×C4×C17C23×C412yes—
643C2×C4×C17C23×C412yes—
644C2×C4×C17C2×#4112yes—
645C2×C4×C17C2×#4112yes—
646C2×C4×C17C2×#4112yes—
647C2×C4×C17C2×#4112yes—
648C22⋊D17—28no—
649C22⋊D17—44no—
650C2×Dic17—21no—
651C2×Dic17—21no—
652C2×Dic17—21no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—28no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
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—44no—
683C2×Dic17—44no—
684C2×Dic17—44no—
685C2×Dic17—44no—
686C2×Dic17C23×C412yes—
687C2×Dic17C23×C412yes—
688C2×Dic17C23×C412yes—
689C2×Dic17C23×C412yes—
690C2×Dic17C23×C412yes—
691C2×Dic17C23×C412yes—
692C2×Dic17C2×#4112yes—
693C2×Dic17C2×#4112yes—
694C2×Dic17C2×#4112yes—
695C2×Dic17C2×#4112yes—
696C2×Dic17H(5,𝔽2)12yes—
697C4×D17—28no—
698C4×D17—28no—
699C4×D17—44no—
700C4×D17—44no—
701C4×D17—44no—
702C4×D17—44no—
703C4×D17—44no—
704C4×D17—44no—
705Dic34—44no—
706C2×#551—171no—
707#2374—171no—
708#2373—171no—
709#2373—171no—
710#2372—171no—
711#2368—171no—
712#2368—171no—
713#2359—171no—
714#2359D1711yescharacteristic, complemented
715#2358—171no—
716#2353—171no—
717#2353—171no—
718#2343—171no—
719#2343—171no—
720#2342—171no—
721#2342—171no—
722C4×#126—171no—
723C4×#126—171no—
724C4×#124—171no—
725C4×C22⋊Q8—171no—
726C4×C22⋊Q8—171no—
727C4×#123—171no—
728C4×#123—171no—
729C4×#123—171no—
730C4×#120—171no—
731C42×D4—171no—
732C42×D4—171no—
733C4×#117—171no—
734C4×#117—171no—
735C2×C4×C22⋊C4—171no—
736C2×C4×C22⋊C4—171no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—41no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17—41no—
750C22×C17C4×#4114yes—
751C22×C17C24×C411yescharacteristic
752C22×C17C22×#4111yescharacteristic
753C22×C17C22×#4111yescharacteristic
754C22×C17C22×#4111yescharacteristic
755C22×C17C22×#4111yescharacteristic
756C22×C17C2×H(5,𝔽2)11yescharacteristic
757C22×C17#58511yescharacteristic
758C2×D17—22no—
759C2×D17—22no—
760C2×D17—22no—
761C2×D17—22no—
762C2×D17—22no—
763C2×D17—22no—
764C2×D17—22no—
765C2×D17—22no—
766C2×D17—22no—
767C2×D17—416no—
768C2×D17—41no—
769C2×D17—41no—
770C2×D17—41no—
771C2×D17—41no—
772C2×D17C4×#4114yes—
773C4×C17—22no—
774C4×C17—22no—
775C4×C17—22no—
776C4×C17—22no—
777C4×C17—22no—
778C4×C17—22no—
779C4×C17—22no—
780C4×C17—22no—
781C4×C17—22no—
782C4×C17—41no—
783C4×C17—41no—
784C4×C17—41no—
785C4×C17—41no—
786Dic17—22no—
787Dic17—22no—
788Dic17—22no—
789Dic17—22no—
790Dic17—22no—
791Dic17—22no—
792Dic17—22no—
793Dic17—22no—
794Dic17—41no—
795Dic17—41no—
796Dic17—41no—
797Dic17—41no—
798Dic17—41no—
799Dic17#55114yescomplemented
800C24×C4—171no—
801#551—1716no—
802C2×#126—171no—
803C2×#126—171no—
804C2×#124—171no—
805C2×#123—171no—
806C2×#123—171no—
807C2×#123C2×D1711yescharacteristic
808C2×C22⋊Q8—171no—
809C2×C22⋊Q8—171no—
810C2×#120—171no—
811C2×C4×Q8—171no—
812C2×C4×D4—171no—
813C2×C4×D4—171no—
814C2×C4×D4—171no—
815C2×C4×D4—171no—
816C2×C4×D4—171no—
817C2×C4×D4—171no—
818C2×C4×D4C2×D1711yescharacteristic
819C2×#117—171no—
820C2×#117—171no—
821C2×#117—171no—
822C2×#117C2×D1711yescharacteristic
823C22×C22⋊C4—171no—
824C22×C22⋊C4—171no—
825C22×C22⋊C4—171no—
826C22×C22⋊C4—171no—
827C22×C42—171no—
828C22×C42—171no—
829C22×C42—171no—
830C22×C42—171no—
831C22×C42—171no—
832#391—171no—
833#391—171no—
834#391—171no—
835#390—171no—
836#389—171no—
837#389C2×D1711yescharacteristic, complemented
838#388—171no—
839#388—171no—
840#388—171no—
841#388—171no—
842#388—171no—
843#388—171no—
844#388—171no—
845#388—171no—
846#388—171no—
847#388—171no—
848#388—171no—
849#388—171no—
850#388—171no—
851#388—171no—
852#388C2×D1711yescharacteristic, complemented
853#388C2×D1711yescharacteristic, complemented
854#387—171no—
855#387—171no—
856#387—171no—
857#387—171no—
858#387—171no—
859#387—171no—
860#387—171no—
861#387—171no—
862#387—171no—
863#387—171no—
864#387—171no—
865#387—171no—
866#387—171no—
867#387—171no—
868#387C2×D1711yescharacteristic, complemented
869#387C2×D1711yescharacteristic, complemented
870#386—171no—
871#386—171no—
872#386—171no—
873#386—171no—
874#386—171no—
875#386C2×D1711yescharacteristic
876#385—171no—
877#385—171no—
878#385—171no—
879#385—171no—
880#385—171no—
881#385—171no—
882#385—171no—
883#385—171no—
884#385C2×D1711yescharacteristic
885#385C2×D1711yescharacteristic, complemented
886#383—171no—
887#383—171no—
888#382—171no—
889#381—171no—
890#381—171no—
891#381—171no—
892#380—171no—
893#380—171no—
894#379—171no—
895C4×C4⋊C4—171no—
896C4×C4⋊C4—171no—
897C4×C4⋊C4—171no—
898C4×C4⋊C4—171no—
899C4×C4⋊C4—171no—
900C4×C4⋊C4—171no—
901C4×C4⋊C4—171no—
902C4×C4⋊C4—171no—
903C4×C4⋊C4—171no—
904C4×C4⋊C4—171no—
905C4×C4⋊C4—171no—
906C4×C4⋊C4—171no—
907C4×C4⋊C4—171no—
908C4×C4⋊C4—171no—
909C4×C4⋊C4—171no—
910C4×C4⋊C4C2×D1711yescharacteristic, complemented
911C4×C22⋊C4—171no—
912C4×C22⋊C4—171no—
913C4×C22⋊C4—171no—
914C4×C22⋊C4—171no—
915C4×C22⋊C4—171no—
916C4×C22⋊C4—171no—
917C4×C22⋊C4—171no—
918C4×C22⋊C4—171no—
919C4×C22⋊C4—171no—
920C4×C22⋊C4—171no—
921C4×C22⋊C4—171no—
922C4×C22⋊C4—171no—
923C4×C22⋊C4—171no—
924C4×C22⋊C4—171no—
925C4×C22⋊C4—171no—
926C4×C22⋊C4—171no—
927C4×C22⋊C4—171no—
928C4×C22⋊C4—171no—
929C4×C22⋊C4—171no—
930C4×C22⋊C4—171no—
931C4×C22⋊C4—171no—
932C4×C22⋊C4—171no—
933C4×C22⋊C4—171no—
934C4×C22⋊C4—171no—
935C4×C22⋊C4—171no—
936C4×C22⋊C4—171no—
937C4×C22⋊C4—171no—
938C4×C22⋊C4—171no—
939C4×C22⋊C4—171no—
940C4×C22⋊C4—171no—
941C4×C22⋊C4—171no—
942C4×C22⋊C4—171no—
943C4×C22⋊C4C2×D1711yescharacteristic
944C4×C22⋊C4C2×D1711yescharacteristic, complemented
945#376—171no—
946#376—171no—
947#376—171no—
948#376—171no—
949C2×#95—171no—
950C2×#95—171no—
951C2×#95—171no—
952C2×#95C2×D1711yescharacteristic
953C43—171no—
954C43—171no—
955C43—171no—
956C2×C17—24no—
957C2×C17—42no—
958C2×C17C2×C4×#4111yescharacteristic
959C2×C17C2×C4×#4111yescharacteristic
960C2×C17C4×H(5,𝔽2)11yescharacteristic
961C2×C17C2×#55111yescharacteristic
962C2×C17#347511yescharacteristic
963C2×C17#347511yescharacteristic
964C2×C17#348111yescharacteristic
965D17—24no—
966D17—42no—
967C25—171no—
968C22×Q8—171no—
969C22×D4—171no—
970C22×D4—171no—
971C22×D4C22×D1711yescharacteristic
972C23×C4—171no—
973C23×C4—171no—
974C23×C4—171no—
975C23×C4—171no—
976C23×C4—171no—
977C23×C4—171no—
978C23×C4—171no—
979C23×C4—171no—
980C23×C4—171no—
981C23×C4—171no—
982C23×C4—171no—
983C23×C4—171no—
984C23×C4—171no—
985C23×C4—344no—
986C23×C4—344no—
987C23×C4—682no—
988C23×C4C22×D1711yescharacteristic
989C23×C4C22×D1711yescharacteristic
990C23×C4C22×D1711yescharacteristic
991C23×C4C22×D1711yescharacteristic
992#126—178no—
993#126—178no—
994#124—178no—
995#123—178no—
996#123—178no—
997#123C4×D1718yescomplemented
998C22⋊Q8—178no—
999C22⋊Q8—178no—
1000#120—178no—
1001C4×Q8—682no—
1002C4×D4—24no—
1003C4×D4—178no—
1004C4×D4—178no—
1005C4×D4—344no—
1006C4×D4—344no—
1007C4×D4—344no—
1008C4×D4—682no—
1009#117—24no—
1010#117—178no—
1011#117—178no—
1012#117—344no—
1013C2×C4⋊C4—171no—
1014C2×C4⋊C4—171no—
1015C2×C4⋊C4—171no—
1016C2×C4⋊C4—171no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4C22×D1711yescharacteristic
1029C2×C4⋊C4C22×D1711yescharacteristic
1030C2×C4⋊C4C22×D1711yescharacteristic
1031C2×C4⋊C4C22×D1711yescharacteristic
1032C2×C4⋊C4C22×D1711yescharacteristic
1033C2×C4⋊C4C22×D1711yescharacteristic
1034C2×C4⋊C4C22×D1711yescharacteristic
1035C2×C22⋊C4—171no—
1036C2×C22⋊C4—171no—
1037C2×C22⋊C4—171no—
1038C2×C22⋊C4—178no—
1039C2×C22⋊C4—171no—
1040C2×C22⋊C4—171no—
1041C2×C22⋊C4—171no—
1042C2×C22⋊C4—171no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—171no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—171no—
1047C2×C22⋊C4—171no—
1048C2×C22⋊C4—178no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—344no—
1064C2×C22⋊C4—344no—
1065C2×C22⋊C4C22×D1711yescharacteristic
1066C2×C22⋊C4C22×D1711yescharacteristic
1067C2×C22⋊C4C22×D1711yescharacteristic
1068C2×C22⋊C4C22×D1711yescharacteristic
1069C2×C22⋊C4C22×D1711yescharacteristic
1070C2×C22⋊C4C22×D1711yescharacteristic
1071C2×C22⋊C4C22×D1711yescharacteristic
1072C2×C22⋊C4C22×D1711yescharacteristic
1073C2×C42—171no—
1074C2×C42—171no—
1075C2×C42—171no—
1076C2×C42—171no—
1077C2×C42—171no—
1078C2×C42—171no—
1079C2×C42—171no—
1080C2×C42—171no—
1081C2×C42—171no—
1082C2×C42—171no—
1083C2×C42—171no—
1084C2×C42—171no—
1085C2×C42—171no—
1086C2×C42—171no—
1087C2×C42—171no—
1088C2×C42—171no—
1089C2×C42—171no—
1090C2×C42—171no—
1091C2×C42—171no—
1092C2×C42—171no—
1093C2×C42—171no—
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—344no—
1102C2×C42—344no—
1103C2×C42—682no—
1104C2×C42—682no—
1105C2×C42—682no—
1106C2×C42C22×D1711yescharacteristic
1107C2×C42C22×D1711yescharacteristic
1108C2×C42C22×D1711yescharacteristic
1109C2×C42C22×D1711yescharacteristic
1110C2×C42C22×D1711yescharacteristic
1111#95—171no—
1112#95—171no—
1113#95—171no—
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95C22×D1711yescharacteristic
1146#95C22×D1711yescharacteristic
1147#95C22×D1711yescharacteristic
1148#95C22×D1711yescharacteristic
1149#95C22×D1711yescharacteristic
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154#95C22×D1711yescharacteristic
1155C17C4×#55111yescharacteristic, complemented, Sylow
1156C24—171no—
1157C24—171no—
1158C24—174no—
1159C24—342no—
1160C24—342no—
1161C24—342no—
1162C24—342no—
1163C24—681no—
1164C24—681no—
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—174no—
1168C2×Q8—681no—
1169C2×Q8—681no—
1170C2×D4—22no—
1171C2×D4—22no—
1172C2×D4—174no—
1173C2×D4—174no—
1174C2×D4—342no—
1175C2×D4—342no—
1176C2×D4—681no—
1177C2×D4—681no—
1178C2×D4C2×C4×D1714yes—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—22no—
1182C22×C4—22no—
1183C22×C4—22no—
1184C22×C4—22no—
1185C22×C4—22no—
1186C22×C4—22no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—171no—
1191C22×C4—174no—
1192C22×C4—171no—
1193C22×C4—171no—
1194C22×C4—171no—
1195C22×C4—171no—
1196C22×C4—171no—
1197C22×C4—171no—
1198C22×C4—171no—
1199C22×C4—171no—
1200C22×C4—174no—
1201C22×C4—174no—
1202C22×C4—174no—
1203C22×C4—174no—
1204C22×C4—174no—
1205C22×C4—171no—
1206C22×C4—171no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—171no—
1210C22×C4—342no—
1211C22×C4—342no—
1212C22×C4—342no—
1213C22×C4—342no—
1214C22×C4—342no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—342no—
1219C22×C4—342no—
1220C22×C4—342no—
1221C22×C4—342no—
1222C22×C4—342no—
1223C22×C4—342no—
1224C22×C4—342no—
1225C22×C4—342no—
1226C22×C4—342no—
1227C22×C4—342no—
1228C22×C4—342no—
1229C22×C4—342no—
1230C22×C4—342no—
1231C22×C4—342no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—6816no—
1239C22×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4—681no—
1244C22×C4C2×C4×D1714yes—
1245C22×C4C23×D1711yescharacteristic
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C22×C4C23×D1711yescharacteristic
1254C22×C4C23×D1711yescharacteristic
1255C22×C4C23×D1711yescharacteristic
1256C22×C4C23×D1711yescharacteristic
1257C22×C4C23×D1711yescharacteristic
1258C4⋊C4—22no—
1259C4⋊C4—22no—
1260C4⋊C4—22no—
1261C4⋊C4—22no—
1262C4⋊C4—41no—
1263C4⋊C4—174no—
1264C4⋊C4—174no—
1265C4⋊C4—174no—
1266C4⋊C4—174no—
1267C4⋊C4—174no—
1268C4⋊C4—174no—
1269C4⋊C4—342no—
1270C4⋊C4—342no—
1271C4⋊C4—342no—
1272C4⋊C4—342no—
1273C4⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4—681no—
1277C4⋊C4—681no—
1278C4⋊C4C2×C4×D1714yescomplemented
1279C4⋊C4C2×C4×D1714yescomplemented
1280C22⋊C4—22no—
1281C22⋊C4—22no—
1282C22⋊C4—22no—
1283C22⋊C4—41no—
1284C22⋊C4—174no—
1285C22⋊C4—174no—
1286C22⋊C4—174no—
1287C22⋊C4—174no—
1288C22⋊C4—174no—
1289C22⋊C4—174no—
1290C22⋊C4—174no—
1291C22⋊C4—174no—
1292C22⋊C4—174no—
1293C22⋊C4—174no—
1294C22⋊C4—174no—
1295C22⋊C4—174no—
1296C22⋊C4—342no—
1297C22⋊C4—342no—
1298C22⋊C4—342no—
1299C22⋊C4—342no—
1300C22⋊C4—342no—
1301C22⋊C4—342no—
1302C22⋊C4—342no—
1303C22⋊C4—342no—
1304C22⋊C4—342no—
1305C22⋊C4—342no—
1306C22⋊C4—342no—
1307C22⋊C4—681no—
1308C22⋊C4—681no—
1309C22⋊C4—681no—
1310C22⋊C4C2×C4×D1714yes—
1311C22⋊C4C2×C4×D1714yescomplemented
1312C22⋊C4C2×C4×D1714yescomplemented
1313C22⋊C4#6325414yes—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—41no—
1319C42—174no—
1320C42—174no—
1321C42—174no—
1322C42—342no—
1323C42—342no—
1324C42—342no—
1325C42—342no—
1326C42—342no—
1327C42—342no—
1328C42—342no—
1329C42—342no—
1330C42—342no—
1331C42—342no—
1332C42—342no—
1333C42—342no—
1334C42—342no—
1335C42—342no—
1336C42—342no—
1337C42—342no—
1338C42—342no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42—681no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—172no—
1358C23—172no—
1359C23—172no—
1360C23—172no—
1361C23—348no—
1362C23—341no—
1363C23—341no—
1364C23—341no—
1365C23—341no—
1366C23—348no—
1367C23—341no—
1368C23—341no—
1369C23—341no—
1370C23—341no—
1371C23—341no—
1372C23—341no—
1373C23—684no—
1374C23—684no—
1375C23—684no—
1376C23—684no—
1377C23—684no—
1378C23C22×C4×D1712yes—
1379C23C22×C4×D1712yes—
1380C23C2×#6325412yes—
1381C23#41×D1712yes—
1382C23C24×D1711yescharacteristic
1383Q8—684no—
1384D4—28no—
1385D4—348no—
1386D4—684no—
1387C2×C4—28no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—172no—
1422C2×C4—172no—
1423C2×C4—172no—
1424C2×C4—172no—
1425C2×C4—172no—
1426C2×C4—172no—
1427C2×C4—172no—
1428C2×C4—172no—
1429C2×C4—172no—
1430C2×C4—172no—
1431C2×C4—172no—
1432C2×C4—348no—
1433C2×C4—348no—
1434C2×C4—348no—
1435C2×C4—341no—
1436C2×C4—341no—
1437C2×C4—341no—
1438C2×C4—341no—
1439C2×C4—341no—
1440C2×C4—341no—
1441C2×C4—341no—
1442C2×C4—341no—
1443C2×C4—341no—
1444C2×C4—341no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—684no—
1467C2×C4—684no—
1468C2×C4—684no—
1469C2×C4—684no—
1470C2×C4—684no—
1471C2×C4—684no—
1472C2×C4—684no—
1473C2×C4—684no—
1474C2×C4—684no—
1475C2×C4—684no—
1476C2×C4C22×C4×D1712yes—
1477C2×C4C22×C4×D1712yes—
1478C2×C4C22×C4×D1712yes—
1479C2×C4C22×C4×D1712yes—
1480C2×C4C22×C4×D1712yes—
1481C2×C4C2×#6325412yes—
1482C2×C4C2×#6325412yes—
1483C2×C4#41×D1712yes—
1484C2×C4#41×D1712yes—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—41no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—174no—
1499C22—342no—
1500C22—342no—
1501C22—342no—
1502C22—342no—
1503C22—342no—
1504C22—342no—
1505C22—342no—
1506C22—342no—
1507C22—342no—
1508C22—6816no—
1509C22—681no—
1510C22—681no—
1511C22—681no—
1512C22—681no—
1513C22C4×#6325414yes—
1514C22C23×C4×D1711yescharacteristic
1515C22C2×#41×D1711yescharacteristic
1516C22C2×#41×D1711yescharacteristic
1517C22C2×#41×D1711yescharacteristic
1518C22C22×#6325411yescharacteristic
1519C22H(5,𝔽2)×D1711yescharacteristic
1520C22#1176364611yescharacteristic
1521C4—22no—
1522C4—22no—
1523C4—22no—
1524C4—22no—
1525C4—22no—
1526C4—22no—
1527C4—22no—
1528C4—22no—
1529C4—22no—
1530C4—41no—
1531C4—41no—
1532C4—41no—
1533C4—41no—
1534C4—174no—
1535C4—342no—
1536C4—342no—
1537C4—342no—
1538C4—342no—
1539C4—342no—
1540C4—342no—
1541C4—342no—
1542C4—342no—
1543C4—681no—
1544C4—681no—
1545C4—681no—
1546C4—681no—
1547C4—681no—
1548C2—24no—
1549C2—42no—
1550C2—344no—
1551C2—682no—
1552C2C4×#41×D1711yescharacteristic
1553C2C2×C4×#6325411yescharacteristic
1554C2#1454199011yescharacteristic
1555C2D17×#55111yescharacteristic
1556C2#1454234711yescharacteristic
1557C2#1454234911yescharacteristic
1558C2#1454238911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2359C2
socle, cosocleC23×C17C25
prime radicalC2×#10587623C22
hypercenter#2359D17
hypocenterC17C4×#551
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #14531914C2semidirect
3. #14531909C2semidirect
4. #14531907C2semidirect
5. #14531892C2semidirect
6. #14531866C2semidirect
7. #14531862C2semidirect
8. #14531779C2semidirect
10. #14531722C2semidirect
11. #14531719C2semidirect
12. #14531640C2semidirect
13. #14531639C2semidirect
14. #14531634C2semidirect
15. #14531631C2semidirect
16. #14531334C2semidirect
17. #14531334C2semidirect
18. #14531325C2semidirect
19. #14531316C2semidirect
20. #14531314C2semidirect
21. #14531311C2semidirect
22. #123×Dic17C2semidirect
23. #14531303C2semidirect
25. C4×D4×Dic17C2semidirect
26. C4×#10587567C2semidirect
27. #117×Dic17C2semidirect
28. C4×#10587578C2semidirect
29. C2×#11762656C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2359C2semidirect
33. #11763482C4semidirect
42. C2×#10587573C22semidirect
58. C22×C4×Dic17C22semidirect
61. #11762715C22semidirect
62. #11762713C22semidirect
63. #11762713C22semidirect
65. #11762704C22semidirect
66. #11762703C22semidirect
67. #11762702C22semidirect
68. #11762702C22semidirect
79. #11762697C22semidirect
80. #11762696C22semidirect
81. #11762696C22semidirect
82. #11762695C22semidirect
83. #11762695C22semidirect
84. #11762694C22semidirect
85. #11762694C22semidirect
86. #11762694C22semidirect
87. #11762694C22semidirect
88. #11762693C22semidirect
89. #11762692C22semidirect
90. #11762692C22semidirect
91. #11762692C22semidirect
92. #11762692C22semidirect
93. #11762690C22semidirect
107. #11762676C22semidirect
108. #11762676C22semidirect
109. #11762673C22semidirect
112. #11762670C22semidirect
116. C4⋊C4×Dic17C22semidirect
117. C4⋊C4×Dic17C22semidirect
118. C4⋊C4×Dic17C22semidirect
119. C4⋊C4×Dic17C22semidirect
120. C4⋊C4×Dic17C22semidirect
121. C4⋊C4×Dic17C22semidirect
122. C4⋊C4×Dic17C22semidirect
123. C4⋊C4×Dic17C22semidirect
124. C4⋊C4×Dic17C22semidirect
125. C4×#63225C22semidirect
126. C4×C4⋊Dic17C22semidirect
127. C4×C4⋊Dic17C22semidirect
128. #11762660C22semidirect
129. #11762660C22semidirect
130. #11762660C22semidirect
137. C22⋊C4×Dic17C22semidirect
138. C22⋊C4×Dic17C22semidirect
139. C22⋊C4×Dic17C22semidirect
140. C22⋊C4×Dic17C22semidirect
141. C22⋊C4×Dic17C22semidirect
149. C4×C22⋊Dic17C22semidirect
163. #11762655C22semidirect
164. #11762655C22semidirect
165. #11762654C22semidirect
166. #11762654C22semidirect
170. C42×Dic17C22semidirect
171. C42×Dic17C22semidirect
172. C42×Dic17C22semidirect
176. C17×#389C22semidirect
177. C17×#388C22semidirect
178. C17×#388C22semidirect
179. C17×#387C22semidirect
180. C17×#387C22semidirect
183. C17×#385C22semidirect
184. C4×C4⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
213. C17×#123C2×C4semidirect
246. D4×Dic17C2×C4semidirect
249. C2×#63227C2×C4semidirect
268. #10587612C2×C4semidirect
315. #10587584C2×C4semidirect
316. #10587584C2×C4semidirect
317. #10587583C2×C4semidirect
319. #10587578C2×C4semidirect
321. #10587572C2×C4semidirect
322. #10587571C2×C4semidirect
323. #10587569C2×C4semidirect
326. #10587567C2×C4semidirect
328. C22⋊C4×D17C2×C4semidirect
329. #10587564C2×C4semidirect
434. C22×Dic17C22×C4semidirect
477. C2×Dic34C22×C4semidirect
483. C4⋊C4×C17C22×C4semidirect
484. C4⋊C4×C17C22×C4semidirect
490. C22⋊C4×C17C22×C4semidirect
491. C22⋊C4×C17C22×C4semidirect
505. C22⋊Dic17C22×C4semidirect
527. C4⋊Dic17C22×C4semidirect
528. C4⋊Dic17C22×C4semidirect
529. C4⋊Dic17C22×C4semidirect
530. C4⋊Dic17C22×C4semidirect
537. #63225C22×C4semidirect
538. #63225C22×C4semidirect
564. C4×Dic17C22×C4semidirect
565. C4×Dic17C22×C4semidirect
566. C4×Dic17C22×C4semidirect
714. #2359D17semidirect
799. Dic17#551semidirect
837. #389C2×D17semidirect
852. #388C2×D17semidirect
853. #388C2×D17semidirect
868. #387C2×D17semidirect
869. #387C2×D17semidirect
885. #385C2×D17semidirect
910. C4×C4⋊C4C2×D17semidirect
944. C4×C22⋊C4C2×D17semidirect
997. #123C4×D17semidirect
1155. C17C4×#551semidirect
1278. C4⋊C4C2×C4×D17semidirect
1279. C4⋊C4C2×C4×D17semidirect
1311. C22⋊C4C2×C4×D17semidirect
1312. C22⋊C4C2×C4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#117634822
#145319142
#145319092
#145319072
#145318922
#145318662
#145318622
#145317792
#145317612
#145317222
#145317192
#145316402
#145316392
#145316342
#145316312
#145313342
#145313252
#145313162
#145313142
#145313112
#123×Dic172
#145313032
#145312892
C4×D4×Dic172
C4×#105875672
#117×Dic172
C4×#105875782
C2×#117626562
C4×C22⋊C4×D172
C17×#23592
C4×#55117