Finite Group Databasebeta

← C2×#22591386 #32157031

Subgroups — C2×#22591386 #32157031

Order 18176.

4262 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556103C211yesmaximal, characteristic
2C22×C4×D284C211yesmaximal, characteristic, complemented
3C22×#14556090C211yesmaximal, characteristic, complemented
4#22591386C2116yesmaximal, direct product factor
5C2×#17985891C211yesmaximal, characteristic, complemented
6C2×#17985889C211yesmaximal, characteristic, complemented
7C2×#17985885C211yesmaximal, characteristic, complemented
8C2×#17985877C211yesmaximal, characteristic, complemented
9C2×#17985877C211yesmaximal, characteristic, complemented
10C2×#17985877C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
13C2×#17985846C211yesmaximal, characteristic, complemented
14C2×#17985846C211yesmaximal, characteristic, complemented
15C2×#95×D71C211yesmaximal, characteristic, complemented
16C2×#387×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C23×D284C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C23×C4×D71C2211yescharacteristic
24C23×C4×D71C2211yescharacteristic
25C2×#14556103C4116yescomplemented
26C2×#14556103C2218yes—
27C2×C4×D284—28no—
28C2×C4×D284C2218yescomplemented
29C2×#14556090—28no—
30C2×#14556090C2218yescomplemented
31C22×C4⋊Dic71C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
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#17985891C2218yescomplemented
46#17985889C2218yescomplemented
47#17985885C2218yescomplemented
48#17985877C2218yescomplemented
49#17985877C2218yescomplemented
50#17985877C2218yescomplemented
51#17985877C2218yescomplemented
52C4×(C2×D71)⋊C4C2218yescomplemented
53#17985846C2218yescomplemented
54#17985846C2218yescomplemented
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61#95×D71C2218yescomplemented
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C42×C71C2211yescharacteristic
65#387×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C24×D71C2311yescharacteristic
71C24×D71C2311yescharacteristic
72C24×D71C2311yescharacteristic
73C22×D284—24no—
74C22×D284—24no—
75C22×D284—24no—
76C22×D284—24no—
77C22×D284—42no—
78C22×D284—42no—
79C22×D284C2×C418yescomplemented
80C22×D284C2×C418yescomplemented
81C22×D284C2×C418yescomplemented
82C22×D284C2314yes—
83C22×D284C2314yes—
84C22×D284C2314yes—
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C22×C4×D71—24no—
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71—24no—
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—42no—
99C22×C4×D71—42no—
100C22×C4×D71—42no—
101C22×C4×D71—42no—
102C22×C4×D71—42no—
103C22×C4×D71—42no—
104C22×C4×D71C2×C418yescomplemented
105C22×C4×D71C2314yes—
106C22×C4×D71C2314yes—
107C22×C4×D71C2314yes—
108C22×C4×D71C2314yes—
109C22×C4×D71C2314yes—
110#14556103C2×C4164yescomplemented
111C4×D284—232no—
112#14556090—232no—
113C2×C4⋊Dic71—24no—
114C2×C4⋊Dic71C2314yes—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—24no—
120C2×(C2×D71)⋊C4—42no—
121C2×(C2×D71)⋊C4—42no—
122C2×(C2×D71)⋊C4C2×C418yescomplemented
123C2×(C2×D71)⋊C4C2×C418yescomplemented
124C2×(C2×D71)⋊C4D418yescomplemented
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×C4×Dic71—24no—
136C2×C4×Dic71—42no—
137C2×C4×Dic71—42no—
138C2×C4×Dic71C2314yes—
139C2×C4×Dic71C2314yes—
140C2×C4×Dic71C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2311yescharacteristic
153C23×C4×C71C2311yescharacteristic
154C2×C4⋊C4×C71—24no—
155C2×C4⋊C4×C71C2×C418yescomplemented
156C2×C4⋊C4×C71C2314yes—
157C2×C4⋊C4×C71C2314yes—
158C2×C42×C71—24no—
159C2×C42×C71C2314yes—
160#95×C71C2314yes—
161#95×C71C2314yes—
162#95×C71C2314yes—
163#95×C71C2314yes—
164C23×D71—22no—
165C23×D71—22no—
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×D71—22no—
180C23×D71C22×C414yes—
181C23×D71C22×C414yes—
182C23×D71C22×C414yes—
183C23×D71C2×D414yes—
184C23×D71#4114yes—
185C23×D71C2412yes—
186C23×D71C2412yes—
187C23×D71C2412yes—
188C2×D284—232no—
189C2×D284—232no—
190C2×D284—28no—
191C2×D284—28no—
192C2×D284—28no—
193C2×D284—28no—
194C2×D284—416no—
195C2×D284—44no—
196C2×D284—44no—
197C2×D284C22×C4116yescomplemented
198C2×D284C22×C4116yescomplemented
199C2×D284C22×C4116yescomplemented
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×Dic71—22no—
210C22×Dic71—22no—
211C22×Dic71—22no—
212C22×Dic71C22×C414yes—
213C22×Dic71C2×D414yes—
214C22×Dic71#4114yes—
215C22×Dic71C2412yes—
216C22×Dic71C2412yes—
217C22×Dic71C2412yes—
218C22×Dic71C2412yes—
219C22×Dic71C2412yes—
220C2×C4×D71—28no—
221C2×C4×D71—28no—
222C2×C4×D71—28no—
223C2×C4×D71—28no—
224C2×C4×D71—28no—
225C2×C4×D71—28no—
226C2×C4×D71—28no—
227C2×C4×D71—28no—
228C2×C4×D71—416no—
229C2×C4×D71—44no—
230C2×C4×D71—44no—
231C2×C4×D71—44no—
232C2×C4×D71—44no—
233C2×C4×D71—44no—
234C2×C4×D71—44no—
235C2×C4×D71—416no—
236C2×C4×D71—416no—
237C2×C4×D71—416no—
238C2×C4×D71—416no—
239C2×C4×D71C22×C4116yescomplemented
240C4⋊Dic71—28no—
241(C2×D71)⋊C4—28no—
242(C2×D71)⋊C4—28no—
243(C2×D71)⋊C4—28no—
244(C2×D71)⋊C4—28no—
245(C2×D71)⋊C4—28no—
246(C2×D71)⋊C4—44no—
247(C2×D71)⋊C4—44no—
248(C2×D71)⋊C4C22×C4116yescomplemented
249(C2×D71)⋊C4C22×C4116yescomplemented
250(C2×D71)⋊C4C2×D4116yescomplemented
251C4×Dic71—28no—
252C4×Dic71—44no—
253C4×Dic71—44no—
254C24×C71C2411yescharacteristic
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—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71C22×C414yes—
272C22×C4×C71C22×C414yes—
273C22×C4×C71C22×C414yes—
274C22×C4×C71C2×D414yes—
275C22×C4×C71#4114yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C22×C4×C71C2412yes—
282C22×C4×C71C2412yes—
283C4⋊C4×C71—28no—
284C4⋊C4×C71C22×C4116yescomplemented
285C42×C71—28no—
286C23×C71C23×C412yes—
287C23×C71C22×D412yes—
288C23×C71C2×#4112yes—
289C23×C71C2×#4112yes—
290C23×C71C2×#4112yes—
291C23×C71H(5,𝔽2)12yes—
292C23×C71H(5,𝔽2)12yes—
293C23×C71C2511yescharacteristic
294C22×D71—28no—
295C22×D71—28no—
296C22×D71—28no—
297C22×D71—28no—
298C22×D71—28no—
299C22×D71—28no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—28no—
305C22×D71—28no—
306C22×D71—28no—
307C22×D71—28no—
308C22×D71—28no—
309C22×D71—28no—
310C22×D71—22no—
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—44no—
323C22×D71—44no—
324C22×D71—44no—
325C22×D71—44no—
326C22×D71—44no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71C4×D4116yes—
331C22×D71C23×C414yes—
332C22×D71C23×C414yes—
333C22×D71C23×C414yes—
334C22×D71C22×D414yes—
335C22×D71C2×#4114yes—
336C2×C4×C71—28no—
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—22no—
356C2×C4×C71—22no—
357C2×C4×C71—44no—
358C2×C4×C71—44no—
359C2×C4×C71C23×C414yes—
360C2×C4×C71C23×C414yes—
361C2×C4×C71C23×C414yes—
362C2×C4×C71C22×D414yes—
363C2×C4×C71C2×#4114yes—
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—44no—
380C2×Dic71—44no—
381C2×Dic71C23×C414yes—
382C2×Dic71C22×D414yes—
383C2×Dic71C2×#4114yes—
384D284—232no—
385D284—232no—
386D284—416no—
387C4×D71—416no—
388C4×D71—416no—
389C4×D71—416no—
390C4×D71—416no—
391C4×D71—416no—
392C22×C71C2×C4×D414yes—
393C22×C71C4×#4114yes—
394C22×C71#51814yes—
395C22×C71#54614yes—
396C22×C71#54614yes—
397C22×C71#55314yes—
398C22×C71#55314yes—
399C22×C71C24×C411yescharacteristic
400C22×C71C23×D411yescharacteristic
401C22×C71C22×#4111yescharacteristic
402C22×C71C22×#4111yescharacteristic
403C22×C71C22×#4111yescharacteristic
404C22×C71C2×H(5,𝔽2)11yescharacteristic
405C22×C71C2×H(5,𝔽2)11yescharacteristic
406C2×D71—232no—
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—24no—
413C2×D71—24no—
414C2×D71—24no—
415C2×D71—24no—
416C2×D71—24no—
417C2×D71—24no—
418C2×D71—24no—
419C2×D71—416no—
420C2×D71—416no—
421C2×D71—42no—
422C2×D71—42no—
423C2×D71—42no—
424C2×D71—42no—
425C2×D71—42no—
426C2×D71—42no—
427C2×D71—42no—
428C2×D71—42no—
429C2×D71C2×C4×D418yes—
430C4×C71—24no—
431C4×C71—24no—
432C4×C71—24no—
433C4×C71—24no—
434C4×C71—24no—
435C4×C71—42no—
436C4×C71—42no—
437Dic71—24no—
438Dic71—24no—
439Dic71—24no—
440Dic71—42no—
441Dic71—42no—
442C2×#2364—711nomaximal, Sylow
443C2×C71#236418yescomplemented
444C2×C71C22×C4×D411yescharacteristic
445C2×C71C2×C4×#4111yescharacteristic
446C2×C71C2×#51811yescharacteristic
447C2×C71C2×#54611yescharacteristic
448C2×C71C2×#54611yescharacteristic
449C2×C71C2×#55311yescharacteristic
450C2×C71C2×#55311yescharacteristic
451D71—28no—
452D71—44no—
453D71—44no—
454C22×#121—711no—
455C22×C4×D4—711no—
456C22×C4×D4—711no—
457#2364—7116no—
458C2×#388—711no—
459C2×#388—711no—
460C2×#387—711no—
461C2×#387D7111yescharacteristic, complemented
462C2×#386—711no—
463C2×#386—711no—
464C2×#386—711no—
465C2×#386—711no—
466C2×C4×C22⋊C4—711no—
467C2×C4×C22⋊C4—711no—
468C2×C4×C22⋊C4—711no—
469C22×#95—711no—
470C71C2×#236411yescharacteristic, complemented, Sylow
471C23×D4—711no—
472C23×D4—711no—
473C23×D4—711no—
474C24×C4—711no—
475C24×C4—711no—
476C24×C4—711no—
477C24×C4—711no—
478C24×C4—711no—
479C2×#121—7116no—
480C2×#121—718no—
481C2×C4×D4—718no—
482C2×C4×D4—718no—
483C2×C4×D4—1428no—
484C2×C4×D4—1428no—
485C22×C4⋊C4—711no—
486C22×C4⋊C4C2×D7111yescharacteristic
487C22×C4⋊C4C2×D7111yescharacteristic
488C22×C22⋊C4—711no—
489C22×C22⋊C4—711no—
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×C42—711no—
499C22×C42—711no—
500C22×C42—711no—
501C22×C42C2×D7111yescharacteristic
502#388—718no—
503#388—718no—
504#387—718no—
505#387C2×D7118yescomplemented
506#386—718no—
507#386—718no—
508#386—718no—
509#386—718no—
510C4×C22⋊C4—718no—
511C4×C22⋊C4—718no—
512C4×C22⋊C4—718no—
513C2×#95—711no—
514C2×#95—711no—
515C2×#95—711no—
516C2×#95—711no—
517C2×#95—711no—
518C2×#95—711no—
519C2×#95—718no—
520C2×#95C2×D7111yescharacteristic
521C2×#95C2×D7111yescharacteristic
522C2×#95C2×D7111yescharacteristic
523C2×#95C2×D7111yescharacteristic
524C25—711no—
525C25—711no—
526C25—711no—
527C22×D4—2842no—
528C22×D4—2842no—
529C22×D4—718no—
530C22×D4—718no—
531C22×D4—718no—
532C22×D4—714no—
533C22×D4—714no—
534C22×D4—714no—
535C22×D4—1424no—
536C22×D4—1424no—
537C22×D4—1424no—
538C22×D4—1424no—
539C23×C4—2842no—
540C23×C4—2842no—
541C23×C4—2842no—
542C23×C4—2842no—
543C23×C4—2842no—
544C23×C4—2842no—
545C23×C4—718no—
546C23×C4—714no—
547C23×C4—714no—
548C23×C4—714no—
549C23×C4—714no—
550C23×C4—714no—
551C23×C4—711no—
552C23×C4—711no—
553C23×C4—711no—
554C23×C4—711no—
555C23×C4—711no—
556C23×C4—1424no—
557C23×C4—1424no—
558C23×C4—1424no—
559C23×C4—1424no—
560C23×C4—1424no—
561C23×C4—1424no—
562C23×C4—1424no—
563C23×C4—1424no—
564C23×C4C22×D7111yescharacteristic
565C23×C4C22×D7111yescharacteristic
566C23×C4C22×D7111yescharacteristic
567C23×C4C22×D7111yescharacteristic
568C23×C4C22×D7111yescharacteristic
569C23×C4C22×D7111yescharacteristic
570C23×C4C22×D7111yescharacteristic
571#121—7164no—
572C4×D4—14232no—
573C4×D4—14232no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—1424no—
577C2×C4⋊C4C4×D7118yescomplemented
578C2×C4⋊C4C22×D7114yes—
579C2×C4⋊C4C22×D7114yes—
580C2×C22⋊C4—2842no—
581C2×C22⋊C4—2842no—
582C2×C22⋊C4—714no—
583C2×C22⋊C4—714no—
584C2×C22⋊C4—718no—
585C2×C22⋊C4—718no—
586C2×C22⋊C4—718no—
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—714no—
595C2×C22⋊C4—1424no—
596C2×C22⋊C4—1424no—
597C2×C22⋊C4—1424no—
598C2×C22⋊C4—1424no—
599C2×C22⋊C4—1424no—
600C2×C42—24no—
601C2×C42—2842no—
602C2×C42—2842no—
603C2×C42—714no—
604C2×C42—714no—
605C2×C42—714no—
606C2×C42—1424no—
607C2×C42C22×D7114yes—
608#95—714no—
609#95—714no—
610#95—714no—
611#95—714no—
612#95—714no—
613#95—714no—
614#95C22×D7114yes—
615#95C22×D7114yes—
616#95C22×D7114yes—
617#95C22×D7114yes—
618C24—714no—
619C24—714no—
620C24—714no—
621C24—712no—
622C24—714no—
623C24—714no—
624C24—712no—
625C24—712no—
626C24—1422no—
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—1422no—
641C24—1422no—
642C24C23×D7111yescharacteristic
643C2×D4—2844no—
644C2×D4—2844no—
645C2×D4—28416no—
646C2×D4—7116no—
647C2×D4—7116no—
648C2×D4—7116no—
649C2×D4—1428no—
650C2×D4—1428no—
651C2×D4—1428no—
652C2×D4—1428no—
653C2×D4—14232no—
654C2×D4—14232no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
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—28416no—
672C22×C4—28416no—
673C22×C4—28416no—
674C22×C4—2844no—
675C22×C4—2844no—
676C22×C4—2844no—
677C22×C4—2844no—
678C22×C4—2844no—
679C22×C4—28416no—
680C22×C4—2844no—
681C22×C4—28416no—
682C22×C4—7116no—
683C22×C4—714no—
684C22×C4—714no—
685C22×C4—714no—
686C22×C4—712no—
687C22×C4—712no—
688C22×C4—712no—
689C22×C4—712no—
690C22×C4—712no—
691C22×C4—1428no—
692C22×C4—1428no—
693C22×C4—1428no—
694C22×C4—1428no—
695C22×C4—1428no—
696C22×C4—1422no—
697C22×C4—1422no—
698C22×C4—1422no—
699C22×C4—1422no—
700C22×C4—1422no—
701C22×C4—1422no—
702C22×C4—1428no—
703C22×C4—1428no—
704C22×C4—1428no—
705C22×C4—1422no—
706C22×C4—1422no—
707C22×C4—1422no—
708C22×C4—1422no—
709C22×C4—1422no—
710C22×C4—1422no—
711C22×C4C2×C4×D7114yes—
712C22×C4C2×C4×D7114yes—
713C22×C4C2×C4×D7114yes—
714C22×C4D4×D7114yes—
715C22×C4#1176586614yes—
716C22×C4C23×D7112yes—
717C22×C4C23×D7112yes—
718C22×C4C23×D7112yes—
719C22×C4C23×D7112yes—
720C22×C4C23×D7112yes—
721C22×C4C23×D7112yes—
722C22×C4C23×D7112yes—
723C4⋊C4—28no—
724C4⋊C4—1428no—
725C4⋊C4C2×C4×D71116yescomplemented
726C22⋊C4—2844no—
727C22⋊C4—2844no—
728C22⋊C4—7116no—
729C22⋊C4—7116no—
730C22⋊C4—7116no—
731C22⋊C4—1428no—
732C22⋊C4—1428no—
733C22⋊C4—1428no—
734C22⋊C4—1428no—
735C22⋊C4—1428no—
736C42—28no—
737C42—2844no—
738C42—2844no—
739C42—1428no—
740C23—2844no—
741C23—2844no—
742C23—2844no—
743C23—2844no—
744C23—2844no—
745C23—2844no—
746C23—2844no—
747C23—2844no—
748C23—714no—
749C23—714no—
750C23—714no—
751C23—7116no—
752C23—714no—
753C23—714no—
754C23—1422no—
755C23—1422no—
756C23—1422no—
757C23—1422no—
758C23—1422no—
759C23—1422no—
760C23—1422no—
761C23—1422no—
762C23—1422no—
763C23—1422no—
764C23—1422no—
765C23—1422no—
766C23—1428no—
767C23—1428no—
768C23—1428no—
769C23—1428no—
770C23—1428no—
771C23—1428no—
772C23—1422no—
773C23—1422no—
774C23—1422no—
775C23—1422no—
776C23—1428no—
777C23—1428no—
778C23—1428no—
779C23—1428no—
780C23—1428no—
781C23—1428no—
782C23C22×C4×D7112yes—
783C23C2×D4×D7112yes—
784C23#41×D7112yes—
785C23#41×D7112yes—
786C23C2×#1176586612yes—
787C23#1455617412yes—
788C23#1455617412yes—
789C23C24×D7111yescharacteristic
790D4—28416no—
791D4—14232no—
792D4—14232no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—28416no—
817C2×C4—28416no—
818C2×C4—28416no—
819C2×C4—28416no—
820C2×C4—28416no—
821C2×C4—2844no—
822C2×C4—2844no—
823C2×C4—714no—
824C2×C4—714no—
825C2×C4—714no—
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—1422no—
836C2×C4—1422no—
837C2×C4—1422no—
838C2×C4—1428no—
839C2×C4—1428no—
840C2×C4—1428no—
841C2×C4C22×C4×D7114yes—
842C2×C4C22×C4×D7114yes—
843C2×C4C22×C4×D7114yes—
844C2×C4C2×D4×D7114yes—
845C2×C4C2×#1176586614yes—
846C22—2842no—
847C22—2842no—
848C22—2842no—
849C22—2842no—
850C22—2842no—
851C22—2842no—
852C22—2842no—
853C22—2842no—
854C22—28416no—
855C22—28416no—
856C22—718no—
857C22—1424no—
858C22—1424no—
859C22—1424no—
860C22—1424no—
861C22—1424no—
862C22—1424no—
863C22—1424no—
864C22—1424no—
865C22—1424no—
866C22—1424no—
867C22—1424no—
868C22—1424no—
869C22—14232no—
870C22C4×D4×D7114yes—
871C22C4×#1176586614yes—
872C22#1798647314yes—
873C22#1798664014yes—
874C22#1798664114yes—
875C22#1798670014yes—
876C22#1798670214yes—
877C22C23×C4×D7111yescharacteristic
878C22C22×D4×D7111yescharacteristic
879C22C2×#41×D7111yescharacteristic
880C22C2×#41×D7111yescharacteristic
881C22C22×#1176586611yescharacteristic
882C22C2×#1455617411yescharacteristic
883C22C2×#1455617411yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—42no—
891C4—2842no—
892C4—2842no—
893C4—1424no—
894C4—1424no—
895C4—1424no—
896C2—2844no—
897C2—2844no—
898C2—1428no—
899C2#2259138618yesdirect product factor
900C2C2×C4×D4×D7111yescharacteristic
901C2C2×C4×#1176586611yescharacteristic
902C2C2×#1798647311yescharacteristic
903C2C2×#1798664011yescharacteristic
904C2C2×#1798664111yescharacteristic
905C2C2×#1798670011yescharacteristic
906C2C2×#1798670211yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#387×C71C2
socleC24×C71C24
prime radicalC22×#14556103C2
cosocleC23×C71C25
hypercenterC2×#387D71
hypocenterC71C2×#2364
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×D284C2semidirect
3. C22×#14556090C2semidirect
4. #22591386C2direct (N × H)
5. C2×#17985891C2semidirect
6. C2×#17985889C2semidirect
7. C2×#17985885C2semidirect
8. C2×#17985877C2semidirect
9. C2×#17985877C2semidirect
10. C2×#17985877C2semidirect
11. C2×#17985877C2semidirect
12. C2×C4×(C2×D71)⋊C4C2semidirect
13. C2×#17985846C2semidirect
14. C2×#17985846C2semidirect
15. C2×#95×D71C2semidirect
16. C2×#387×C71C2semidirect
25. C2×#14556103C4semidirect
28. C2×C4×D284C22semidirect
30. C2×#14556090C22semidirect
45. #17985891C22semidirect
46. #17985889C22semidirect
47. #17985885C22semidirect
48. #17985877C22semidirect
49. #17985877C22semidirect
50. #17985877C22semidirect
51. #17985877C22semidirect
52. C4×(C2×D71)⋊C4C22semidirect
53. #17985846C22semidirect
54. #17985846C22semidirect
61. #95×D71C22semidirect
65. #387×C71C22semidirect
79. C22×D284C2×C4semidirect
80. C22×D284C2×C4semidirect
81. C22×D284C2×C4semidirect
104. C22×C4×D71C2×C4semidirect
110. #14556103C2×C4semidirect
122. C2×(C2×D71)⋊C4C2×C4semidirect
123. C2×(C2×D71)⋊C4C2×C4semidirect
124. C2×(C2×D71)⋊C4D4semidirect
155. C2×C4⋊C4×C71C2×C4semidirect
197. C2×D284C22×C4semidirect
198. C2×D284C22×C4semidirect
199. C2×D284C22×C4semidirect
239. C2×C4×D71C22×C4semidirect
248. (C2×D71)⋊C4C22×C4semidirect
249. (C2×D71)⋊C4C22×C4semidirect
250. (C2×D71)⋊C4C2×D4semidirect
284. C4⋊C4×C71C22×C4semidirect
443. C2×C71#2364semidirect
461. C2×#387D71semidirect
470. C71C2×#2364semidirect
505. #387C2×D71semidirect
577. C2×C4⋊C4C4×D71semidirect
725. C4⋊C4C2×C4×D71semidirect
899. C2#22591386direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561032
C22×C4×D2842
C22×#145560902
#225913862
C2×#179858912
C2×#179858892
C2×#179858852
C2×#179858772
C2×C4×(C2×D71)⋊C42
C2×#179858462
C2×#95×D712
C2×#387×C712
C2×#236471