Finite Group Databasebeta

← C2×#22592314 #32165313

Subgroups — C2×#22592314 #32165313

Order 18176.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556117C211yesmaximal, characteristic, complemented
2C22×#14556113C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4#22592314C2116yesmaximal, direct product factor
5C2×#17985921C211yesmaximal, characteristic, complemented
6C2×#17985918C211yesmaximal, characteristic, complemented
7C2×#17985915C211yesmaximal, characteristic, complemented
8C2×#17985908C211yesmaximal, characteristic
9C2×#17985899C211yesmaximal, characteristic, complemented
10C2×#17985893C211yesmaximal, characteristic, complemented
11C2×#17985889C211yesmaximal, characteristic, complemented
12C2×#17985889C211yesmaximal, characteristic, complemented
13C2×#17985878C211yesmaximal, characteristic, complemented
14C2×#17985870C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556117—28no—
22C2×#14556117C2218yescomplemented
23C2×#14556113—28no—
24C2×#14556113C2218yescomplemented
25C2×C4×C22⋊D71—28no—
26C2×C4×C22⋊D71C2218yescomplemented
27C22×C4⋊Dic71C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45#17985921C2218yescomplemented
46#17985918C2218yescomplemented
47#17985915C2218yescomplemented
48#17985908C2218yes—
49#17985899C2218yescomplemented
50#17985893C2218yescomplemented
51#17985889C2218yescomplemented
52#17985889C2218yescomplemented
53#17985878C2218yescomplemented
54#17985870C2218yescomplemented
55C4⋊C4×Dic71C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C23×Q8×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C2×C22⋊Q8×C71—28no—
65C2×C22⋊Q8×C71C2218yescomplemented
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C4⋊C4×C71C2211yescharacteristic
68C22×C4⋊C4×C71C2211yescharacteristic
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2211yescharacteristic
71C24×D71C2311yescharacteristic
72C24×D71C2311yescharacteristic
73C22×D284—24no—
74C22×D284—24no—
75C22×D284—42no—
76C22×D284C2314yes—
77C22×C22⋊D71—24no—
78C22×C22⋊D71—24no—
79C22×C22⋊D71—24no—
80C22×C22⋊D71—24no—
81C22×C22⋊D71—24no—
82C22×C22⋊D71—42no—
83C22×C22⋊D71C2314yes—
84C22×C22⋊D71C2314yes—
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—42no—
94C22×C4×D71C2314yes—
95#14556117—232no—
96#14556113—232no—
97C4×C22⋊D71—232no—
98C2×C4⋊Dic71—24no—
99C2×C4⋊Dic71C2314yes—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—42no—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×C22⋊Dic71—24no—
107C2×C22⋊Dic71—24no—
108C2×C22⋊Dic71C2314yes—
109C2×C22⋊Dic71C2314yes—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4—24no—
114C2×(C2×D71)⋊C4—24no—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4D418yescomplemented
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×C4×Dic71—24no—
129C2×C4×Dic71—24no—
130C2×C4×Dic71—24no—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C25×C71C2311yescharacteristic
141C22×Q8×C71—24no—
142C22×Q8×C71—24no—
143C22×Q8×C71—42no—
144C22×Q8×C71C2314yes—
145C23×C4×C71—24no—
146C23×C4×C71—24no—
147C23×C4×C71—42no—
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2314yes—
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2311yescharacteristic
153C23×C4×C71C2311yescharacteristic
154C23×C4×C71C2311yescharacteristic
155C22⋊Q8×C71—232no—
156C2×C4⋊C4×C71—24no—
157C2×C4⋊C4×C71—24no—
158C2×C4⋊C4×C71D418yescomplemented
159C2×C4⋊C4×C71C2314yes—
160C2×C4⋊C4×C71C2314yes—
161C2×C4⋊C4×C71C2314yes—
162C2×C22⋊C4×C71—24no—
163C2×C22⋊C4×C71—24no—
164C2×C22⋊C4×C71C2314yes—
165C2×C22⋊C4×C71C2314yes—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—22no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71C2×D414yes—
180C23×D71C2412yes—
181C23×D71C2412yes—
182C2×D284—28no—
183C2×D284—28no—
184C2×D284—44no—
185C2×D284—416no—
186C2×C22⋊D71—232no—
187C2×C22⋊D71—28no—
188C2×C22⋊D71—28no—
189C2×C22⋊D71—28no—
190C2×C22⋊D71—28no—
191C2×C22⋊D71—28no—
192C2×C22⋊D71—44no—
193C2×C22⋊D71—416no—
194C22×Dic71—22no—
195C22×Dic71—22no—
196C22×Dic71—22no—
197C22×Dic71—22no—
198C22×Dic71—22no—
199C22×Dic71—22no—
200C22×Dic71—22no—
201C22×Dic71—22no—
202C22×Dic71—22no—
203C22×Dic71—22no—
204C22×Dic71—22no—
205C22×Dic71—22no—
206C22×Dic71—22no—
207C22×Dic71—22no—
208C22×Dic71—22no—
209C22×Dic71C2×D414yes—
210C22×Dic71#4114yes—
211C22×Dic71#4114yes—
212C22×Dic71C2412yes—
213C22×Dic71C2412yes—
214C22×Dic71C2412yes—
215C22×Dic71C2412yes—
216C22×Dic71C2412yes—
217C22×Dic71C2412yes—
218C2×C4×D71—28no—
219C2×C4×D71—28no—
220C2×C4×D71—44no—
221C2×C4×D71—416no—
222C4⋊Dic71—28no—
223Dic71⋊C4—28no—
224Dic71⋊C4—28no—
225Dic71⋊C4—44no—
226C22⋊Dic71—28no—
227C22⋊Dic71—28no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4—28no—
232(C2×D71)⋊C4—28no—
233(C2×D71)⋊C4—28no—
234(C2×D71)⋊C4—28no—
235(C2×D71)⋊C4—28no—
236(C2×D71)⋊C4C2×D4116yescomplemented
237C4×Dic71—28no—
238C4×Dic71—28no—
239C4×Dic71—28no—
240C24×C71—22no—
241C24×C71—22no—
242C24×C71—22no—
243C24×C71—22no—
244C24×C71—22no—
245C24×C71—22no—
246C24×C71#4114yes—
247C24×C71C2412yes—
248C24×C71C2411yescharacteristic
249C2×Q8×C71—28no—
250C2×Q8×C71—28no—
251C2×Q8×C71—44no—
252C2×Q8×C71—416no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—28no—
268C22×C4×C71—28no—
269C22×C4×C71—44no—
270C22×C4×C71—416no—
271C22×C4×C71C2×D414yes—
272C22×C4×C71C2×D414yes—
273C22×C4×C71C2×D414yes—
274C22×C4×C71C2×D414yes—
275C22×C4×C71C2412yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C4⋊C4×C71—28no—
282C4⋊C4×C71—28no—
283C4⋊C4×C71C2×D4116yescomplemented
284C22⋊C4×C71—28no—
285C22⋊C4×C71—28no—
286C23×C71—28no—
287C23×C71—28no—
288C23×C71—28no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—44no—
296C23×C71—44no—
297C23×C71—44no—
298C23×C71—44no—
299C23×C71C22×D412yes—
300C23×C71C22×D412yes—
301C23×C71C2×#4112yes—
302C23×C71C2×#4112yes—
303C23×C71C2×#4114yes—
304C23×C71C2×#4112yes—
305C23×C71H(5,𝔽2)12yes—
306C23×C712−1+412yes—
307C23×C71C2511yescharacteristic
308C22×D71—28no—
309C22×D71—28no—
310C22×D71—28no—
311C22×D71—22no—
312C22×D71—22no—
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—22no—
319C22×D71—22no—
320C22×D71—22no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—22no—
324C22×D71—44no—
325C22×D71—44no—
326C22×D71—44no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71—44no—
331C22×D71—44no—
332C22×D71—44no—
333C22×D71—44no—
334C22×D71—44no—
335C22×D71C22×D414yes—
336Q8×C71—416no—
337C2×C4×C71—28no—
338C2×C4×C71—28no—
339C2×C4×C71—28no—
340C2×C4×C71—28no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—416no—
356C2×C4×C71—44no—
357C2×C4×C71—44no—
358C2×C4×C71C22×D414yes—
359C2×C4×C71C22×D414yes—
360C2×C4×C71C22×D414yes—
361C2×C4×C71C22×D414yes—
362C22⋊D71—232no—
363C22⋊D71—416no—
364C2×Dic71—28no—
365C2×Dic71—28no—
366C2×Dic71—28no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—22no—
370C2×Dic71—22no—
371C2×Dic71—22no—
372C2×Dic71—22no—
373C2×Dic71—22no—
374C2×Dic71—22no—
375C2×Dic71—22no—
376C2×Dic71—22no—
377C2×Dic71—22no—
378C2×Dic71—22no—
379C2×Dic71—22no—
380C2×Dic71—22no—
381C2×Dic71—22no—
382C2×Dic71—44no—
383C2×Dic71—44no—
384C2×Dic71—44no—
385C2×Dic71C22×D414yes—
386C2×Dic71C2×#4114yes—
387C2×Dic71C2×#4114yes—
388D284—416no—
389C4×D71—416no—
390C22×C71—24no—
391C22×C71—24no—
392C22×C71—24no—
393C22×C71—42no—
394C22×C71—42no—
395C22×C71—42no—
396C22×C71—42no—
397C22×C71—416no—
398C22×C71#52514yes—
399C22×C71#53214yes—
400C22×C71#54214yes—
401C22×C71D4214yes—
402C22×C71#54714yes—
403C22×C71#54814yes—
404C22×C71#55114yes—
405C22×C71C23×D411yescharacteristic
406C22×C71C23×D411yescharacteristic
407C22×C71C22×#4111yescharacteristic
408C22×C71C22×#4111yescharacteristic
409C22×C71C22×#4111yescharacteristic
410C22×C71C2×H(5,𝔽2)11yescharacteristic
411C22×C71C2×2−1+411yescharacteristic
412C2×D71—24no—
413C2×D71—24no—
414C2×D71—24no—
415C2×D71—42no—
416C2×D71—42no—
417C2×D71—42no—
418C2×D71—42no—
419C2×D71—416no—
420C2×D71—42no—
421C2×D71—42no—
422C2×D71—42no—
423C2×D71—42no—
424C2×D71—42no—
425C2×D71—42no—
426C2×D71—42no—
427C2×D71—88no—
428C4×C71—24no—
429C4×C71—24no—
430C4×C71—24no—
431C4×C71—24no—
432C4×C71—42no—
433C4×C71—42no—
434Dic71—24no—
435Dic71—24no—
436Dic71—24no—
437Dic71—42no—
438Dic71—42no—
439Dic71—42no—
440C2×#2461—711nomaximal, Sylow
441C2×C71—44no—
442C2×C71#246118yescomplemented
443C2×C71C2×#52511yescharacteristic
444C2×C71C2×#53211yescharacteristic
445C2×C71C2×#54211yescharacteristic
446C2×C71C2×D4211yescharacteristic
447C2×C71C2×#54711yescharacteristic
448C2×C71C2×#54811yescharacteristic
449C2×C71C2×#55111yescharacteristic
450D71—44no—
451D71—82no—
452C22×#124—711no—
453C22×#123—711no—
454C22×C22⋊Q8D7111yescharacteristic, complemented
455C22×C4×D4—711no—
456#2461—7116no—
457C2×#396—711no—
458C2×#395—711no—
459C2×#394—711no—
460C2×#392—711no—
461C2×#390—711no—
462C2×#388—711no—
463C2×#388—711no—
464C2×#388—711no—
465C2×#386—711no—
466C2×#385—711no—
467C2×C4×C4⋊C4—711no—
468C71C2×#246111yescharacteristic, complemented, Sylow
469C23×Q8C2×D7111yescharacteristic
470C23×D4—711no—
471C23×D4—711no—
472C23×D4—711no—
473C24×C4—711no—
474C24×C4C2×D7111yescharacteristic
475C2×#124—718no—
476C2×#124—1428no—
477C2×#123—718no—
478C2×#123—1428no—
479C2×C22⋊Q8—28no—
480C2×C22⋊Q8C2×D7118yescomplemented
481C2×C4×D4—718no—
482C2×C4×D4—1428no—
483C22×C4⋊C4—711no—
484C22×C4⋊C4—711no—
485C22×C4⋊C4—711no—
486C22×C4⋊C4—711no—
487C22×C4⋊C4C2×D7111yescharacteristic
488C22×C4⋊C4C2×D7111yescharacteristic
489C22×C4⋊C4C2×D7111yescharacteristic
490C22×C22⋊C4—711no—
491C22×C22⋊C4—711no—
492C22×C22⋊C4—711no—
493C22×C22⋊C4—711no—
494C22×C22⋊C4—711no—
495C22×C22⋊C4—711no—
496C22×C22⋊C4—711no—
497C22×C22⋊C4—711no—
498C22×C22⋊C4—711no—
499C22×C22⋊C4—711no—
500C22×C22⋊C4—711no—
501C22×C22⋊C4C2×D7111yescharacteristic
502C22×C22⋊C4C2×D7111yescharacteristic
503C22×C42—711no—
504C22×C42—711no—
505C22×C42—711no—
506#396—718no—
507#395—718no—
508#394—718no—
509#392—718no—
510#390—718no—
511#388—718no—
512#388—718no—
513#388—718no—
514#386—718no—
515#385—718no—
516C4×C4⋊C4—718no—
517C2×#95—711no—
518C2×#95—711no—
519C2×#95—711no—
520C2×#95—711no—
521C2×#95—711no—
522C2×#95—711no—
523C25—711no—
524C25—711no—
525C25C22×D7111yescharacteristic
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—42no—
529C22×Q8C22×D7114yes—
530C22×D4—2842no—
531C22×D4—2842no—
532C22×D4—714no—
533C22×D4—714no—
534C22×D4—714no—
535C22×D4—1424no—
536C22×D4—1424no—
537C22×D4—1424no—
538C22×D4—1424no—
539C22×D4—1424no—
540C22×D4—1424no—
541C22×D4—1424no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—2842no—
546C23×C4—714no—
547C23×C4—711no—
548C23×C4—711no—
549C23×C4—711no—
550C23×C4—711no—
551C23×C4—711no—
552C23×C4—711no—
553C23×C4—1424no—
554C23×C4—1424no—
555C23×C4C22×D7111yescharacteristic
556C23×C4C22×D7111yescharacteristic
557C23×C4C22×D7114yes—
558C23×C4C22×D7111yescharacteristic
559C23×C4C22×D7111yescharacteristic
560C23×C4C22×D7111yescharacteristic
561C23×C4C22×D7111yescharacteristic
562#124—14232no—
563#123—14232no—
564C22⋊Q8—232no—
565C4×D4—14232no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—2842no—
569C2×C4⋊C4—714no—
570C2×C4⋊C4—714no—
571C2×C4⋊C4—714no—
572C2×C4⋊C4—714no—
573C2×C4⋊C4—1424no—
574C2×C4⋊C4—1424no—
575C2×C4⋊C4—1424no—
576C2×C4⋊C4C22⋊D7118yescomplemented
577C2×C4⋊C4C22×D7114yes—
578C2×C4⋊C4C22×D7114yes—
579C2×C4⋊C4C22×D7114yes—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—718no—
583C2×C22⋊C4—714no—
584C2×C22⋊C4—714no—
585C2×C22⋊C4—714no—
586C2×C22⋊C4—714no—
587C2×C22⋊C4—714no—
588C2×C22⋊C4—714no—
589C2×C22⋊C4—714no—
590C2×C22⋊C4—714no—
591C2×C22⋊C4—714no—
592C2×C22⋊C4—714no—
593C2×C22⋊C4—714no—
594C2×C22⋊C4—1424no—
595C2×C22⋊C4—1424no—
596C2×C22⋊C4—1424no—
597C2×C22⋊C4—1424no—
598C2×C22⋊C4—1424no—
599C2×C22⋊C4—1424no—
600C2×C22⋊C4—1424no—
601C2×C22⋊C4—1424no—
602C2×C22⋊C4—1424no—
603C2×C22⋊C4—1424no—
604C2×C22⋊C4C22×D7114yes—
605C2×C22⋊C4C22×D7114yes—
606C2×C42—714no—
607C2×C42—714no—
608C2×C42—714no—
609C2×C42—1424no—
610C2×C42—1424no—
611C2×C42—1424no—
612#95—714no—
613#95—714no—
614#95—714no—
615#95—714no—
616#95—714no—
617#95—714no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—714no—
625C24—712no—
626C24—712no—
627C24—1422no—
628C24—1422no—
629C24—1422no—
630C24—1422no—
631C24—1422no—
632C24—1422no—
633C24—1422no—
634C24—1422no—
635C24—1422no—
636C24—1422no—
637C24—1422no—
638C24—1422no—
639C24—1422no—
640C24#1176586614yes—
641C24C23×D7112yes—
642C24C23×D7111yescharacteristic
643C2×Q8—28no—
644C2×Q8—28no—
645C2×Q8—44no—
646C2×Q8—416no—
647C2×D4—28416no—
648C2×D4—2844no—
649C2×D4—28416no—
650C2×D4—2844no—
651C2×D4—1428no—
652C2×D4—1428no—
653C2×D4—1428no—
654C2×D4—1428no—
655C2×D4—1428no—
656C2×D4—14232no—
657C2×D4—1428no—
658C2×D4—1428no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—44no—
676C22×C4—416no—
677C22×C4—28416no—
678C22×C4—2844no—
679C22×C4—714no—
680C22×C4—714no—
681C22×C4—714no—
682C22×C4—712no—
683C22×C4—712no—
684C22×C4—712no—
685C22×C4—712no—
686C22×C4—712no—
687C22×C4—712no—
688C22×C4—1428no—
689C22×C4—1422no—
690C22×C4—1422no—
691C22×C4—1422no—
692C22×C4—1422no—
693C22×C4—1422no—
694C22×C4—1422no—
695C22×C4—1422no—
696C22×C4—1422no—
697C22×C4—1422no—
698C22×C4—1428no—
699C22×C4—1422no—
700C22×C4—1422no—
701C22×C4—1422no—
702C22×C4—1422no—
703C22×C4—1422no—
704C22×C4—1422no—
705C22×C4D4×D7114yes—
706C22×C4C2×C22⋊D7114yes—
707C22×C4C2×C22⋊D7114yes—
708C22×C4C2×C22⋊D7114yes—
709C22×C4C23×D7112yes—
710C22×C4C23×D7112yes—
711C22×C4C23×D7112yes—
712C22×C4C23×D7112yes—
713C22×C4C23×D7112yes—
714C22×C4C23×D7112yes—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—2844no—
718C4⋊C4—1428no—
719C4⋊C4—1428no—
720C4⋊C4—1428no—
721C4⋊C4C2×C22⋊D71116yescomplemented
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—7116no—
725C22⋊C4—1428no—
726C22⋊C4—1428no—
727C22⋊C4—1428no—
728C22⋊C4—1428no—
729C22⋊C4—1428no—
730C22⋊C4—1428no—
731C22⋊C4—1428no—
732C22⋊C4—1428no—
733C22⋊C4—1428no—
734C22⋊C4—1428no—
735C42—1428no—
736C42—1428no—
737C42—1428no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—2844no—
752C23—2844no—
753C23—2844no—
754C23—2844no—
755C23—2844no—
756C23—2844no—
757C23—2844no—
758C23—2844no—
759C23—2844no—
760C23—2844no—
761C23—2844no—
762C23—714no—
763C23—1422no—
764C23—1422no—
765C23—1422no—
766C23—1422no—
767C23—1422no—
768C23—1422no—
769C23—1422no—
770C23—1422no—
771C23—1422no—
772C23—1422no—
773C23—1422no—
774C23—1422no—
775C23—1422no—
776C23—1428no—
777C23—1428no—
778C23—1428no—
779C23C2×D4×D7112yes—
780C23C22×C22⋊D7112yes—
781C23#41×D7112yes—
782C23#41×D7112yes—
783C23C2×#1176586614yes—
784C23C2×#1176586612yes—
785C23#1455617312yes—
786C23#1455617612yes—
787C23C24×D7111yescharacteristic
788Q8—416no—
789D4—28416no—
790D4—28416no—
791D4—14232no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—416no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—28416no—
814C2×C4—2844no—
815C2×C4—2844no—
816C2×C4—2844no—
817C2×C4—714no—
818C2×C4—714no—
819C2×C4—714no—
820C2×C4—1422no—
821C2×C4—1422no—
822C2×C4—1422no—
823C2×C4—1422no—
824C2×C4—1422no—
825C2×C4—1422no—
826C2×C4—1422no—
827C2×C4—1422no—
828C2×C4—1422no—
829C2×C4—1422no—
830C2×C4—1422no—
831C2×C4—1422no—
832C2×C4—1422no—
833C2×C4—1422no—
834C2×C4—1422no—
835C2×C4—1428no—
836C2×C4—1428no—
837C2×C4—1428no—
838C2×C4C2×D4×D7114yes—
839C2×C4C22×C22⋊D7114yes—
840C2×C4C22×C22⋊D7114yes—
841C2×C4C22×C22⋊D7114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—416no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—28416no—
851C22—2842no—
852C22—2842no—
853C22—2842no—
854C22—2842no—
855C22—2842no—
856C22—2842no—
857C22—2842no—
858C22—2842no—
859C22—2842no—
860C22—2842no—
861C22—2842no—
862C22—5688no—
863C22—1424no—
864C22—1424no—
865C22—1424no—
866C22#1798651214yes—
867C22#1798654514yes—
868C22#1798661914yes—
869C22D4×C22⋊D7114yes—
870C22#1798665114yes—
871C22#1798666014yes—
872C22#1798667614yes—
873C22C22×D4×D7111yescharacteristic
874C22C23×C22⋊D7111yescharacteristic
875C22C2×#41×D7111yescharacteristic
876C22C2×#41×D7111yescharacteristic
877C22C22×#1176586611yescharacteristic
878C22C2×#1455617311yescharacteristic
879C22C2×#1455617611yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—2842no—
887C4—2842no—
888C4—2842no—
889C4—1424no—
890C4—1424no—
891C4—1424no—
892C2—44no—
893C2—2844no—
894C2—5682no—
895C2#2259231418yesdirect product factor
896C2C2×#1798651211yescharacteristic
897C2C2×#1798654511yescharacteristic
898C2C2×#1798661911yescharacteristic
899C2C2×D4×C22⋊D7111yescharacteristic
900C2C2×#1798665111yescharacteristic
901C2C2×#1798666011yescharacteristic
902C2C2×#1798667611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC2×#17985908C2
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2461
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556117C2semidirect
2. C22×#14556113C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. #22592314C2direct (N × H)
5. C2×#17985921C2semidirect
6. C2×#17985918C2semidirect
7. C2×#17985915C2semidirect
9. C2×#17985899C2semidirect
10. C2×#17985893C2semidirect
11. C2×#17985889C2semidirect
12. C2×#17985889C2semidirect
13. C2×#17985878C2semidirect
14. C2×#17985870C2semidirect
15. C2×C4⋊C4×Dic71C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
22. C2×#14556117C22semidirect
24. C2×#14556113C22semidirect
26. C2×C4×C22⋊D71C22semidirect
45. #17985921C22semidirect
46. #17985918C22semidirect
47. #17985915C22semidirect
49. #17985899C22semidirect
50. #17985893C22semidirect
51. #17985889C22semidirect
52. #17985889C22semidirect
53. #17985878C22semidirect
54. #17985870C22semidirect
55. C4⋊C4×Dic71C22semidirect
65. C2×C22⋊Q8×C71C22semidirect
118. C2×(C2×D71)⋊C4D4semidirect
158. C2×C4⋊C4×C71D4semidirect
236. (C2×D71)⋊C4C2×D4semidirect
283. C4⋊C4×C71C2×D4semidirect
442. C2×C71#2461semidirect
454. C22×C22⋊Q8D71semidirect
468. C71C2×#2461semidirect
480. C2×C22⋊Q8C2×D71semidirect
576. C2×C4⋊C4C22⋊D71semidirect
721. C4⋊C4C2×C22⋊D71semidirect
895. C2#22592314direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561172
C22×#145561132
C22×C4×C22⋊D712
#225923142
C2×#179859212
C2×#179859182
C2×#179859152
C2×#179859082
C2×#179858992
C2×#179858932
C2×#179858892
C2×#179858782
C2×#179858702
C2×C4⋊C4×Dic712
C22×C22⋊Q8×C712
C2×#246171