Finite Group Databasebeta

← #17194209

Subgroups — #17194209

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×#11763484C211yesmaximal, characteristic
2#14531918C211yesmaximal, characteristic, complemented
3#14531899C211yesmaximal, characteristic, complemented
4#14531892C211yesmaximal, characteristic, complemented
5#14531868C211yesmaximal, characteristic, complemented
6#14531866C211yesmaximal, characteristic, complemented
7#14531781C211yesmaximal, characteristic, complemented
8#14531771C211yesmaximal, characteristic, complemented
9#14531762C211yesmaximal, characteristic
10#14531725C211yesmaximal, characteristic, complemented
11#14531723C211yesmaximal, characteristic, complemented
12#14531647C211yesmaximal, characteristic, complemented
13#14531639C211yesmaximal, characteristic, complemented
14#14531632C211yesmaximal, characteristic, complemented
15#14531628C211yesmaximal, characteristic, complemented
16#14531338C211yesmaximal, characteristic, complemented
17#126×Dic17C211yesmaximal, characteristic, complemented
18#14531325C211yesmaximal, characteristic, complemented
19#14531318C211yesmaximal, characteristic, complemented
20#14531314C211yesmaximal, characteristic, complemented
21#14531311C211yesmaximal, characteristic, complemented
22#14531305C211yesmaximal, characteristic, complemented
23#14531305C211yesmaximal, characteristic, complemented
24#14531285C211yesmaximal, characteristic
25C4×#10587579C211yesmaximal, characteristic, complemented
26C4×#10587579C211yesmaximal, characteristic, complemented
27C4×#10587578C211yesmaximal, characteristic, complemented
28#14531123C211yesmaximal, characteristic, complemented
29C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2373C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33#11763484C4116yescomplemented
34C2×#10587565C2211yescharacteristic
35C2×#10587571C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587580C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587583C2211yescharacteristic
40C2×#10587582C2211yescharacteristic
41C2×#10587568C2211yescharacteristic
42C2×#10587573C2211yescharacteristic, complemented
43C2×C4×D68C2211yescharacteristic
44C2×C4×D68C2211yescharacteristic
45C2×#10587579C2211yescharacteristic
46C2×#10587579C2211yescharacteristic
47C2×#10587579C2211yescharacteristic
48C2×#10587579C2211yescharacteristic
49C2×#10587567C2211yescharacteristic
50C2×#10587578C2211yescharacteristic
51C2×#10587578C2211yescharacteristic
52C2×#10587558C2211yescharacteristic
53C2×#10587558C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C42×D17C2211yescharacteristic
59C2×C42×D17C2211yescharacteristic
60C2×C42×D17C2211yescharacteristic
61C2×C42×D17C2211yescharacteristic
62C2×C42×D17C2211yescharacteristic, complemented
63#11762715C2211yescharacteristic, complemented
64#11762713C2211yescharacteristic, complemented
65#11762713C2211yescharacteristic, complemented
66#11762709C2211yescharacteristic
67#11762706C2211yescharacteristic, complemented
68#11762703C2211yescharacteristic
69#11762703C2211yescharacteristic
70#11762702C2211yescharacteristic
71#11762702C2211yescharacteristic
72#11762702C2211yescharacteristic
73#11762701C2211yescharacteristic, complemented
74#11762701C2211yescharacteristic, complemented
75#11762700C2211yescharacteristic, complemented
76#11762700C2211yescharacteristic, complemented
77#11762700C2211yescharacteristic, complemented
78#11762699C2211yescharacteristic, complemented
79#11762697C2211yescharacteristic
80#11762697C2211yescharacteristic
81#11762695C2211yescharacteristic, complemented
82#11762695C2211yescharacteristic, complemented
83#11762695C2211yescharacteristic, complemented
84#11762694C2211yescharacteristic, complemented
85#11762693C2211yescharacteristic, complemented
86#11762693C2211yescharacteristic, complemented
87#11762693C2211yescharacteristic, complemented
88#11762692C2211yescharacteristic, complemented
89#11762692C2211yescharacteristic, complemented
90#11762692C2211yescharacteristic, complemented
91#11762690C2211yescharacteristic, complemented
92#11762690C2211yescharacteristic, complemented
93#11762690C2211yescharacteristic, complemented
94#11762688C2211yescharacteristic
95#11762687C2211yescharacteristic
96#11762687C2211yescharacteristic
97#11762687C2211yescharacteristic
98#11762687C2211yescharacteristic
99#11762685C2211yescharacteristic
100#11762683C2211yescharacteristic
101#11762683C2211yescharacteristic
102#11762683C2211yescharacteristic
103#11762680C2211yescharacteristic
104#11762680C2211yescharacteristic
105#11762680C2211yescharacteristic
106#11762680C2211yescharacteristic
107#11762680C2211yescharacteristic
108#11762680C2211yescharacteristic, complemented
109#11762677C2211yescharacteristic, complemented
110#11762676C2211yescharacteristic, complemented
111#11762673C2211yescharacteristic, complemented
112#11762671C2211yescharacteristic
113#11762671C2211yescharacteristic
114#11762671C2211yescharacteristic, complemented
115#11762668C2211yescharacteristic
116#11762666C2211yescharacteristic
117#11762664C2211yescharacteristic
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×C4⋊Dic17C2211yescharacteristic, complemented
126#11762660C2211yescharacteristic, complemented
127#11762660C2211yescharacteristic, 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
136C4×#63227C2211yescharacteristic
137C4×#63227C2211yescharacteristic
138C4×#63227C2211yescharacteristic
139C4×#63227C2211yescharacteristic
140C4×#63227C2211yescharacteristic
141C4×#63227C2211yescharacteristic
142C4×#63227C2211yescharacteristic
143C4×#63227C2211yescharacteristic
144C4×#63227C2211yescharacteristic, complemented
145C4×#63227C2211yescharacteristic, complemented
146C4×C22⋊Dic17C2211yescharacteristic
147C4×C22⋊Dic17C2211yescharacteristic
148#11762656C2211yescharacteristic
149#11762656C2211yescharacteristic
150#11762656C2211yescharacteristic
151#11762656C2211yescharacteristic
152#11762656C2211yescharacteristic
153#11762656C2211yescharacteristic
154#11762656C2211yescharacteristic
155#11762656C2211yescharacteristic
156#11762656C2211yescharacteristic
157#11762656C2211yescharacteristic
158#11762656C2211yescharacteristic, complemented
159#11762656C2211yescharacteristic, complemented
160#11762656C2211yescharacteristic, complemented
161#11762656C2211yescharacteristic, complemented
162#11762656C2211yescharacteristic, complemented
163#11762655C2211yescharacteristic, complemented
164#11762654C2211yescharacteristic, complemented
165#11762654C2211yescharacteristic, complemented
166#95×D17C2211yescharacteristic
167#95×D17C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170C42×Dic17C2211yescharacteristic, complemented
171C42×Dic17C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C17×#126C2211yescharacteristic
174C17×#389C2211yescharacteristic, complemented
175C17×#388C2211yescharacteristic
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#385C2211yescharacteristic
182C4×C4⋊C4×C17C2211yescharacteristic, complemented
183C4×C4⋊C4×C17C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C17×#376C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C22×C22⋊D17C2311yescharacteristic
191C23×Dic17C2311yescharacteristic
192C22×D68C2311yescharacteristic
193C22×D68C2311yescharacteristic
194C22×C4×D17—24no—
195C22×C4×D17—24no—
196C22×C4×D17—42no—
197C22×C4×D17C2311yescharacteristic
198C22×C4×D17C2311yescharacteristic
199C22×C4×D17C2311yescharacteristic
200C22×C4×D17C2311yescharacteristic
201C22×C4×D17C2311yescharacteristic
202C22×C4×D17C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
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×#126C2×C418yescomplemented
214C2×C4⋊C4×C17C2311yescharacteristic
215C2×C4⋊C4×C17C2311yescharacteristic
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×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C42×C17C2311yescharacteristic
229C2×C42×C17C2311yescharacteristic
230C2×C42×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×#63227C2311yescharacteristic
242C2×#63227C2311yescharacteristic
243C2×#63227C2311yescharacteristic
244C2×#63227C2311yescharacteristic
245C2×#63227C2311yescharacteristic
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
265C2×C4⋊Dic17C2311yescharacteristic
266C2×C4⋊Dic17C2311yescharacteristic
267C2×C4⋊Dic17C2311yescharacteristic
268C2×C4⋊Dic17C2311yescharacteristic
269C2×#63225C2311yescharacteristic
270C2×#63225C2311yescharacteristic
271C2×#63225C2311yescharacteristic
272C2×#63225C2311yescharacteristic
273C2×#63225C2311yescharacteristic
274C2×#63225C2311yescharacteristic
275C2×#63225C2311yescharacteristic
276C2×#63225C2311yescharacteristic
277C2×#63225C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279C2×C4×Dic17C2311yescharacteristic
280C2×C4×Dic17C2311yescharacteristic
281C2×C4×Dic17C2311yescharacteristic
282C2×C4×Dic17C2311yescharacteristic
283C2×C4×Dic17C2311yescharacteristic
284C2×C4×Dic17C2311yescharacteristic
285C2×C4×Dic17C2311yescharacteristic
286C2×C4×Dic17C2311yescharacteristic
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
303#10587583C2×C418yescomplemented
304#10587582C2×C418yescomplemented
305#10587580C2×C418yescomplemented
306#10587580C2×C418yescomplemented
307#10587579—24no—
308#10587579—24no—
309#10587579—24no—
310#10587579C2×C418yescomplemented
311#10587578—24no—
312#10587578C2×C418yescomplemented
313#10587573—42no—
314#10587571C2×C418yescomplemented
315#10587569C2×C418yescomplemented
316#10587568C2×C418yes—
317#10587567—42no—
318C22⋊C4×D17—24no—
319C22⋊C4×D17—24no—
320C22⋊C4×D17C2×C418yescomplemented
321C22⋊C4×D17C2×C418yescomplemented
322#10587565C2×C418yescomplemented
323C4×D68—24no—
324C4×D68C2×C418yescomplemented
325#10587558—24no—
326#10587558C2×C418yescomplemented
327C42×D17—24no—
328C42×D17—24no—
329C42×D17—42no—
330C42×D17—42no—
331C42×D17—42no—
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
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
377C23×D17—22no—
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—22no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17C22×C414yes—
384C23×D17C2411yescharacteristic
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C22×C4×C17—22no—
388C22×C4×C17—22no—
389C22×C4×C17—41no—
390C22×C4×C17C2411yescharacteristic
391C22×C4×C17C2411yescharacteristic
392C22×C4×C17C2411yescharacteristic
393C22×C4×C17C2411yescharacteristic
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C2×C22⋊D17—41no—
405C2×C22⋊D17—41no—
406C2×C22⋊D17C22×C414yes—
407C22×Dic17—22no—
408C22×Dic17—22no—
409C22×Dic17—22no—
410C22×Dic17C2411yescharacteristic
411C22×Dic17C2411yescharacteristic
412C22×Dic17C2411yescharacteristic
413C22×Dic17C2411yescharacteristic
414C22×Dic17C2411yescharacteristic
415C22×Dic17C2411yescharacteristic
416C22×Dic17C2411yescharacteristic
417C22×Dic17C2411yescharacteristic
418C22×Dic17C2411yescharacteristic
419C22×Dic17C2411yescharacteristic
420C22×Dic17C2411yescharacteristic
421C22×Dic17C2411yescharacteristic
422C22×Dic17C2411yescharacteristic
423C2×D68—22no—
424C2×D68—22no—
425C2×D68—22no—
426C2×D68—22no—
427C2×D68C22×C414yes—
428C2×D68C22×C414yes—
429C2×C4×D17—22no—
430C2×C4×D17—22no—
431C2×C4×D17—22no—
432C2×C4×D17—22no—
433C2×C4×D17—22no—
434C2×C4×D17—22no—
435C2×C4×D17—22no—
436C2×C4×D17—22no—
437C2×C4×D17—22no—
438C2×C4×D17—22no—
439C2×C4×D17—22no—
440C2×C4×D17—22no—
441C2×C4×D17—22no—
442C2×C4×D17—22no—
443C2×C4×D17—22no—
444C2×C4×D17—22no—
445C2×C4×D17—22no—
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—416no—
455C2×C4×D17—41no—
456C2×C4×D17—41no—
457C2×C4×D17—41no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17C22×C414yes—
469C2×C4×D17C22×C414yes—
470C2×C4×D17C22×C414yes—
471C2×C4×D17C22×C414yes—
472C2×C4×D17C22×C414yescomplemented
473C2×C4×D17#4114yes—
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
485C4⋊C4×C17C22×C414yescomplemented
486C22⋊C4×C17—22no—
487C22⋊C4×C17—22no—
488C22⋊C4×C17—41no—
489C22⋊C4×C17C22×C414yes—
490C22⋊C4×C17C22×C414yes—
491C22⋊C4×C17C22×C414yes—
492C42×C17—22no—
493C42×C17—22no—
494C42×C17—22no—
495C42×C17—22no—
496C42×C17—41no—
497C42×C17—41no—
498C42×C17—41no—
499C42×C17C22×C414yescomplemented
500C22⋊Dic17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—41no—
503C22⋊Dic17C22×C414yes—
504C22⋊Dic17C22×C414yes—
505#63227—22no—
506#63227—22no—
507#63227—22no—
508#63227—22no—
509#63227—22no—
510#63227—22no—
511#63227—22no—
512#63227—22no—
513#63227—22no—
514#63227—22no—
515#63227—41no—
516#63227—41no—
517#63227C22×C414yes—
518#63227C22×C414yes—
519#63227C22×C414yes—
520#63227C22×C414yes—
521#63227C22×C414yes—
522#63227C22×C414yes—
523#63227C22×C414yescomplemented
524#63227C22×C414yescomplemented
525#63227C22×C414yescomplemented
526#63227#4114yes—
527#63227#4114yes—
528C4⋊Dic17—22no—
529C4⋊Dic17—22no—
530C4⋊Dic17—41no—
531C4⋊Dic17C22×C414yescomplemented
532C4⋊Dic17C22×C414yescomplemented
533#63225—22no—
534#63225—22no—
535#63225—41no—
536#63225—41no—
537#63225—41no—
538#63225—41no—
539#63225C22×C414yescomplemented
540#63225C22×C414yescomplemented
541#63225C22×C414yescomplemented
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—22no—
557C4×Dic17—22no—
558C4×Dic17—22no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17—41no—
562C4×Dic17—41no—
563C4×Dic17—41no—
564C4×Dic17—41no—
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×C17C23×C412yes—
575C23×C17C2511yescharacteristic
576C22×D17—21no—
577C22×D17—21no—
578C22×D17—21no—
579C22×D17—21no—
580C22×D17—21no—
581C22×D17—21no—
582C22×D17—21no—
583C22×D17—21no—
584C22×D17—21no—
585C22×D17—21no—
586C22×D17—21no—
587C22×D17—21no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—28no—
591C22×D17—28no—
592C22×D17—44no—
593C22×D17—44no—
594C22×D17—44no—
595C22×D17—44no—
596C22×D17—44no—
597C22×D17C23×C412yes—
598C22×D17C23×C412yes—
599C22×D17C23×C412yes—
600C22×D17C2×#4112yes—
601C22×D17C2×#4112yes—
602C22×D17C2×#4112yes—
603C22×D17C2×#4112yes—
604C2×C4×C17—21no—
605C2×C4×C17—21no—
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×C17C23×C412yes—
638C2×C4×C17C23×C412yes—
639C2×C4×C17C23×C412yes—
640C2×C4×C17C23×C412yes—
641C2×C4×C17C23×C412yes—
642C2×C4×C17C23×C412yes—
643C2×C4×C17C2×#4112yes—
644C2×C4×C17C2×#4112yes—
645C2×C4×C17C2×#4112yes—
646C2×C4×C17C2×#4112yes—
647C22⋊D17—44no—
648C2×Dic17—21no—
649C2×Dic17—21no—
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—21no—
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—44no—
678C2×Dic17C23×C412yes—
679C2×Dic17C23×C412yes—
680C2×Dic17C23×C412yes—
681C2×Dic17C23×C412yes—
682C2×Dic17C23×C412yes—
683C2×Dic17C2×#4112yes—
684C2×Dic17C2×#4112yes—
685C2×Dic17C2×#4112yes—
686C2×Dic17C2×#4112yes—
687C2×Dic17H(5,𝔽2)12yes—
688D68—28no—
689D68—28no—
690C4×D17—28no—
691C4×D17—28no—
692C4×D17—28no—
693C4×D17—28no—
694C4×D17—44no—
695C4×D17—44no—
696C4×D17—44no—
697C4×D17—44no—
698C4×D17—44no—
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#2373D1711yescharacteristic, complemented
710#2372—171no—
711#2368—171no—
712#2368—171no—
713#2359—171no—
714#2359—171no—
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—41no—
741C22×C17—41no—
742C22×C17—41no—
743C22×C17—41no—
744C22×C17C24×C411yescharacteristic
745C22×C17C22×#4111yescharacteristic
746C22×C17C22×#4111yescharacteristic
747C22×C17C22×#4111yescharacteristic
748C22×C17C22×#4111yescharacteristic
749C22×C17C2×H(5,𝔽2)11yescharacteristic
750C22×C17#58511yescharacteristic
751C2×D17—22no—
752C2×D17—22no—
753C2×D17—22no—
754C2×D17—22no—
755C2×D17—22no—
756C2×D17—22no—
757C2×D17—22no—
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—416no—
767C2×D17—41no—
768C2×D17—41no—
769C2×D17—41no—
770C2×D17—41no—
771C2×D17C4×#4114yes—
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—22no—
783C4×C17—41no—
784C4×C17—41no—
785C4×C17—41no—
786C4×C17—41no—
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×#126C2×D1711yescharacteristic
804C2×#124—171no—
805C2×#123—171no—
806C2×#123—171no—
807C2×#123—171no—
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×D4—171no—
819C2×#117—171no—
820C2×#117—171no—
821C2×#117—171no—
822C2×#117—171no—
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#388C2×D1711yescharacteristic
852#388C2×D1711yescharacteristic
853#388C2×D1711yescharacteristic
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#387C2×D1711yescharacteristic, complemented
868#387C2×D1711yescharacteristic, complemented
869#387C2×D1711yescharacteristic, complemented
870#386—171no—
871#386—171no—
872#386—171no—
873#386—171no—
874#386—171no—
875#386—171no—
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#385—171no—
885#385C2×D1711yescharacteristic
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⋊C4C2×D1711yescharacteristic, complemented
909C4×C4⋊C4C2×D1711yescharacteristic, complemented
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
945#376—171no—
946#376—171no—
947#376—171no—
948#376C2×D1711yescharacteristic, complemented
949C2×#95—171no—
950C2×#95—171no—
951C2×#95—171no—
952C2×#95—171no—
953C43—171no—
954C43—171no—
955C43—171no—
956C2×C17—42no—
957C2×C17C2×C4×#4111yescharacteristic
958C2×C17C2×C4×#4111yescharacteristic
959C2×C17C4×H(5,𝔽2)11yescharacteristic
960C2×C17C2×#55111yescharacteristic
961C2×C17#347511yescharacteristic
962C2×C17#347511yescharacteristic
963C2×C17#348111yescharacteristic
964D17—24no—
965D17—24no—
966D17—42no—
967C25—171no—
968C22×Q8—171no—
969C22×D4—171no—
970C22×D4—171no—
971C22×D4—171no—
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—171no—
986C23×C4—171no—
987C23×C4—171no—
988C23×C4—344no—
989C23×C4—344no—
990C23×C4—682no—
991C23×C4C22×D1711yescharacteristic
992#126—178no—
993#126C4×D1718yescomplemented
994#124—178no—
995#123—178no—
996#123—178no—
997#123—178no—
998C22⋊Q8—178no—
999C22⋊Q8—178no—
1000#120—178no—
1001C4×Q8—682no—
1002C4×D4—178no—
1003C4×D4—178no—
1004C4×D4—344no—
1005C4×D4—344no—
1006C4×D4—344no—
1007C4×D4—344no—
1008C4×D4—682no—
1009#117—178no—
1010#117—178no—
1011#117—344no—
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⋊C4C22×D1711yescharacteristic
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—171no—
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—178no—
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—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—344no—
1066C2×C22⋊C4—344no—
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—344no—
1099C2×C42—344no—
1100C2×C42—682no—
1101C2×C42—682no—
1102C2×C42—682no—
1103C2×C42C22×D1711yescharacteristic
1104C2×C42C22×D1711yescharacteristic
1105C2×C42C22×D1711yescharacteristic
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#95C22×D1711yescharacteristic
1144#95C22×D1711yescharacteristic
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—171no—
1159C24—174no—
1160C24—342no—
1161C24—342no—
1162C24—342no—
1163C24—342no—
1164C24—681no—
1165C24—681no—
1166C24C23×D1711yescharacteristic
1167C2×Q8—174no—
1168C2×Q8—681no—
1169C2×Q8—681no—
1170C2×D4—174no—
1171C2×D4—174no—
1172C2×D4—174no—
1173C2×D4—342no—
1174C2×D4—342no—
1175C2×D4—342no—
1176C2×D4—342no—
1177C2×D4—681no—
1178C2×D4—681no—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—41no—
1182C22×C4—171no—
1183C22×C4—171no—
1184C22×C4—171no—
1185C22×C4—171no—
1186C22×C4—171no—
1187C22×C4—171no—
1188C22×C4—171no—
1189C22×C4—171no—
1190C22×C4—174no—
1191C22×C4—174no—
1192C22×C4—174no—
1193C22×C4—174no—
1194C22×C4—174no—
1195C22×C4—174no—
1196C22×C4—174no—
1197C22×C4—171no—
1198C22×C4—171no—
1199C22×C4—171no—
1200C22×C4—171no—
1201C22×C4—171no—
1202C22×C4—342no—
1203C22×C4—342no—
1204C22×C4—342no—
1205C22×C4—342no—
1206C22×C4—342no—
1207C22×C4—342no—
1208C22×C4—342no—
1209C22×C4—342no—
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—681no—
1231C22×C4—681no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4—6816no—
1244C22×C4C23×D1711yescharacteristic
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—342no—
1269C4⋊C4—342no—
1270C4⋊C4—342no—
1271C4⋊C4—342no—
1272C4⋊C4—681no—
1273C4⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4—681no—
1277C4⋊C4C2×C4×D1714yescomplemented
1278C4⋊C4C2×C4×D1714yescomplemented
1279C4⋊C4C2×C4×D1714yescomplemented
1280C22⋊C4—22no—
1281C22⋊C4—22no—
1282C22⋊C4—41no—
1283C22⋊C4—174no—
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—342no—
1308C22⋊C4—681no—
1309C22⋊C4—681no—
1310C22⋊C4—681no—
1311C22⋊C4C2×C4×D1714yes—
1312C22⋊C4C2×C4×D1714yes—
1313C22⋊C4C2×C4×D1714yes—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—41no—
1319C42—41no—
1320C42—41no—
1321C42—174no—
1322C42—174no—
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—342no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42C2×C4×D1714yescomplemented
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—172no—
1354C23—172no—
1355C23—172no—
1356C23—172no—
1357C23—172no—
1358C23—172no—
1359C23—172no—
1360C23—348no—
1361C23—348no—
1362C23—341no—
1363C23—341no—
1364C23—341no—
1365C23—341no—
1366C23—341no—
1367C23—341no—
1368C23—341no—
1369C23—341no—
1370C23—341no—
1371C23—341no—
1372C23—341no—
1373C23—341no—
1374C23—341no—
1375C23—341no—
1376C23—684no—
1377C23—684no—
1378C23—684no—
1379C23—684no—
1380C23—684no—
1381C23C22×C4×D1712yes—
1382C23C24×D1711yescharacteristic
1383Q8—684no—
1384D4—348no—
1385D4—348no—
1386D4—684no—
1387C2×C4—21no—
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—21no—
1419C2×C4—44no—
1420C2×C4—172no—
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—348no—
1431C2×C4—348no—
1432C2×C4—348no—
1433C2×C4—348no—
1434C2×C4—341no—
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—684no—
1464C2×C4—684no—
1465C2×C4—684no—
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×C4C22×C4×D1712yes—
1476C2×C4C22×C4×D1712yes—
1477C2×C4C22×C4×D1712yes—
1478C2×C4C22×C4×D1712yes—
1479C2×C4C22×C4×D1712yes—
1480C2×C4C22×C4×D1712yes—
1481C2×C4#41×D1712yes—
1482C2×C4#41×D1712yes—
1483C2×C4#41×D1712yes—
1484C2×C4#41×D1712yes—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—41no—
1489C22—41no—
1490C22—41no—
1491C22—41no—
1492C22—174no—
1493C22—174no—
1494C22—342no—
1495C22—342no—
1496C22—342no—
1497C22—342no—
1498C22—342no—
1499C22—342no—
1500C22—342no—
1501C22—342no—
1502C22—342no—
1503C22—342no—
1504C22—342no—
1505C22—342no—
1506C22—342no—
1507C22—342no—
1508C22—342no—
1509C22—6816no—
1510C22—681no—
1511C22—681no—
1512C22—681no—
1513C22—681no—
1514C22C23×C4×D1711yescharacteristic
1515C22C2×#41×D1711yescharacteristic
1516C22C2×#41×D1711yescharacteristic
1517C22C2×#41×D1711yescharacteristic
1518C22C2×#41×D1711yescharacteristic
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—22no—
1531C4—41no—
1532C4—41no—
1533C4—41no—
1534C4—41no—
1535C4—174no—
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—42no—
1549C2—344no—
1550C2—344no—
1551C2—682no—
1552C2C4×#41×D1711yescharacteristic
1553C2C4×#41×D1711yescharacteristic
1554C2#1454199011yescharacteristic
1555C2D17×#55111yescharacteristic
1556C2#1454233711yescharacteristic
1557C2#1454234511yescharacteristic
1558C2#1454239111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2373C2
socle, cosocleC23×C17C25
prime radicalC2×#10587568C22
hypercenter#2373D17
hypocenterC17C4×#551
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2373

Complements

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

NH ≅ G/Ntype
2. #14531918C2semidirect
3. #14531899C2semidirect
4. #14531892C2semidirect
5. #14531868C2semidirect
6. #14531866C2semidirect
7. #14531781C2semidirect
8. #14531771C2semidirect
10. #14531725C2semidirect
11. #14531723C2semidirect
12. #14531647C2semidirect
13. #14531639C2semidirect
14. #14531632C2semidirect
15. #14531628C2semidirect
16. #14531338C2semidirect
17. #126×Dic17C2semidirect
18. #14531325C2semidirect
19. #14531318C2semidirect
20. #14531314C2semidirect
21. #14531311C2semidirect
22. #14531305C2semidirect
23. #14531305C2semidirect
25. C4×#10587579C2semidirect
26. C4×#10587579C2semidirect
27. C4×#10587578C2semidirect
28. #14531123C2semidirect
29. C4×C22⋊C4×D17C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2373C2semidirect
33. #11763484C4semidirect
42. C2×#10587573C22semidirect
62. C2×C42×D17C22semidirect
63. #11762715C22semidirect
64. #11762713C22semidirect
65. #11762713C22semidirect
67. #11762706C22semidirect
73. #11762701C22semidirect
74. #11762701C22semidirect
75. #11762700C22semidirect
76. #11762700C22semidirect
77. #11762700C22semidirect
78. #11762699C22semidirect
81. #11762695C22semidirect
82. #11762695C22semidirect
83. #11762695C22semidirect
84. #11762694C22semidirect
85. #11762693C22semidirect
86. #11762693C22semidirect
87. #11762693C22semidirect
88. #11762692C22semidirect
89. #11762692C22semidirect
90. #11762692C22semidirect
91. #11762690C22semidirect
92. #11762690C22semidirect
93. #11762690C22semidirect
108. #11762680C22semidirect
109. #11762677C22semidirect
110. #11762676C22semidirect
111. #11762673C22semidirect
114. #11762671C22semidirect
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×C4⋊Dic17C22semidirect
126. #11762660C22semidirect
127. #11762660C22semidirect
128. #11762660C22semidirect
129. #11762660C22semidirect
130. #11762660C22semidirect
144. C4×#63227C22semidirect
145. C4×#63227C22semidirect
158. #11762656C22semidirect
159. #11762656C22semidirect
160. #11762656C22semidirect
161. #11762656C22semidirect
162. #11762656C22semidirect
163. #11762655C22semidirect
164. #11762654C22semidirect
165. #11762654C22semidirect
170. C42×Dic17C22semidirect
171. C42×Dic17C22semidirect
172. C42×Dic17C22semidirect
174. C17×#389C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
180. C17×#387C22semidirect
182. C4×C4⋊C4×C17C22semidirect
183. C4×C4⋊C4×C17C22semidirect
184. C4×C4⋊C4×C17C22semidirect
187. C17×#376C22semidirect
213. C17×#126C2×C4semidirect
303. #10587583C2×C4semidirect
304. #10587582C2×C4semidirect
305. #10587580C2×C4semidirect
306. #10587580C2×C4semidirect
310. #10587579C2×C4semidirect
312. #10587578C2×C4semidirect
314. #10587571C2×C4semidirect
315. #10587569C2×C4semidirect
320. C22⋊C4×D17C2×C4semidirect
321. C22⋊C4×D17C2×C4semidirect
322. #10587565C2×C4semidirect
324. C4×D68C2×C4semidirect
326. #10587558C2×C4semidirect
472. C2×C4×D17C22×C4semidirect
477. C2×Dic34C22×C4semidirect
483. C4⋊C4×C17C22×C4semidirect
484. C4⋊C4×C17C22×C4semidirect
485. C4⋊C4×C17C22×C4semidirect
499. C42×C17C22×C4semidirect
523. #63227C22×C4semidirect
524. #63227C22×C4semidirect
525. #63227C22×C4semidirect
531. C4⋊Dic17C22×C4semidirect
532. C4⋊Dic17C22×C4semidirect
539. #63225C22×C4semidirect
540. #63225C22×C4semidirect
541. #63225C22×C4semidirect
565. C4×Dic17C22×C4semidirect
566. C4×Dic17C22×C4semidirect
709. #2373D17semidirect
799. Dic17#551semidirect
837. #389C2×D17semidirect
867. #387C2×D17semidirect
868. #387C2×D17semidirect
869. #387C2×D17semidirect
908. C4×C4⋊C4C2×D17semidirect
909. C4×C4⋊C4C2×D17semidirect
910. C4×C4⋊C4C2×D17semidirect
948. #376C2×D17semidirect
993. #126C4×D17semidirect
1155. C17C4×#551semidirect
1277. C4⋊C4C2×C4×D17semidirect
1278. C4⋊C4C2×C4×D17semidirect
1279. C4⋊C4C2×C4×D17semidirect
1346. C42C2×C4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#117634842
#145319182
#145318992
#145318922
#145318682
#145318662
#145317812
#145317712
#145317622
#145317252
#145317232
#145316472
#145316392
#145316322
#145316282
#145313382
#126×Dic172
#145313252
#145313182
#145313142
#145313112
#145313052
#145312852
C4×#105875792
C4×#105875782
#145311232
C4×C22⋊C4×D172
C17×#23732
C4×#55117