Finite Group Databasebeta

← C2×#22591151 #32156369

Subgroups — C2×#22591151 #32156369

Order 18176.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556114C211yesmaximal, characteristic
2#22591151C2116yesmaximal, direct product factor
3C2×#17985904C211yesmaximal, characteristic, complemented
4C2×#17985903C211yesmaximal, characteristic, complemented
5C2×#17985890C211yesmaximal, characteristic, complemented
6C2×#17985888C211yesmaximal, characteristic, complemented
7C2×#17985887C211yesmaximal, characteristic, complemented
8C2×#17985876C211yesmaximal, characteristic
9C2×#17985875C211yesmaximal, characteristic
10C2×#17985871C211yesmaximal, characteristic, complemented
11C2×#17985870C211yesmaximal, characteristic, complemented
12C2×#17985866C211yesmaximal, characteristic, complemented
13C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556114C4116yescomplemented
22C2×#14556114C2218yes—
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×C22⋊Dic71C2211yescharacteristic
27C22×C22⋊Dic71C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×C4×Dic71C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37#17985904C2218yescomplemented
38#17985903C2218yescomplemented
39#17985890C2218yescomplemented
40#17985888C2218yescomplemented
41#17985887C2218yescomplemented
42#17985876C2218yes—
43#17985875C2218yes—
44#17985871C2218yescomplemented
45#17985870C2218yescomplemented
46#17985866C2218yescomplemented
47C4×Dic71⋊C4C2218yescomplemented
48C22⋊C4×Dic71C2218yescomplemented
49#17985846C2218yescomplemented
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C22⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C42×C71C2211yescharacteristic
65#388×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C24×D71C2311yescharacteristic
69C22×Dic142—42no—
70C22×Dic142—42no—
71C22×Dic142C2×C418yescomplemented
72C22×Dic142C2314yes—
73C22×C22⋊D71—42no—
74C22×C22⋊D71—42no—
75C22×C22⋊D71C2×C418yes—
76C22×C22⋊D71C2314yes—
77C23×Dic71—24no—
78C23×Dic71—42no—
79C23×Dic71—42no—
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2314yes—
88C22×C4×D71—24no—
89C22×C4×D71—42no—
90C22×C4×D71—42no—
91C22×C4×D71C2314yes—
92#14556114C2×C4164yescomplemented
93C2×Dic71⋊C4—24no—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—42no—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×Dic71⋊C4C2314yes—
99C2×C22⋊Dic71—24no—
100C2×C22⋊Dic71C2×C418yescomplemented
101C2×C22⋊Dic71C2314yes—
102C2×C22⋊Dic71C2314yes—
103C2×(C2×D71)⋊C4—24no—
104C2×(C2×D71)⋊C4—42no—
105C2×(C2×D71)⋊C4—42no—
106C2×(C2×D71)⋊C4C2×C418yescomplemented
107C2×(C2×D71)⋊C4C2×C418yescomplemented
108C2×(C2×D71)⋊C4C2314yes—
109C2×(C2×D71)⋊C4C2314yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×C4×Dic71—42no—
114C2×C4×Dic71—42no—
115C2×C4×Dic71—42no—
116C2×C4×Dic71C2×C418yescomplemented
117C2×C4×Dic71C2314yes—
118C2×C4×Dic71C2314yes—
119C2×C4×Dic71C2314yes—
120C2×C4×Dic71C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C25×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71—42no—
139C2×C4⋊C4×C71C2314yes—
140C2×C22⋊C4×C71—42no—
141C2×C22⋊C4×C71—42no—
142C2×C22⋊C4×C71C2×C418yescomplemented
143C2×C22⋊C4×C71C2314yes—
144C2×C22⋊C4×C71C2314yes—
145C2×C22⋊C4×C71C2314yes—
146C2×C42×C71—42no—
147C2×C42×C71C2314yes—
148#95×C71C2314yes—
149#95×C71C2314yes—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71C22×C414yes—
157C23×D71C2412yes—
158C2×Dic142—416no—
159C2×Dic142—44no—
160C2×Dic142—44no—
161C2×Dic142C22×C4116yescomplemented
162C2×C22⋊D71—416no—
163C2×C22⋊D71—44no—
164C2×C22⋊D71—44no—
165C2×C22⋊D71C22×C4116yes—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—28no—
183C22×Dic71—44no—
184C22×Dic71—44no—
185C22×Dic71—416no—
186C22×Dic71C22×C414yes—
187C22×Dic71C22×C414yes—
188C22×Dic71C22×C414yes—
189C22×Dic71#4114yes—
190C22×Dic71#4114yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C2×C4×D71—28no—
199C2×C4×D71—44no—
200C2×C4×D71—44no—
201C2×C4×D71—416no—
202Dic71⋊C4—28no—
203Dic71⋊C4—28no—
204Dic71⋊C4—44no—
205C22⋊Dic71—28no—
206C22⋊Dic71C22×C4116yescomplemented
207(C2×D71)⋊C4—28no—
208(C2×D71)⋊C4—44no—
209(C2×D71)⋊C4—44no—
210(C2×D71)⋊C4C22×C4116yescomplemented
211(C2×D71)⋊C4C22×C4116yescomplemented
212C4×Dic71—44no—
213C4×Dic71—44no—
214C4×Dic71—44no—
215C4×Dic71C22×C4116yescomplemented
216C24×C71—22no—
217C24×C71—22no—
218C24×C71—22no—
219C24×C71—22no—
220C24×C71—22no—
221C24×C71—22no—
222C24×C71C22×C414yes—
223C24×C71C2412yes—
224C24×C71C2411yescharacteristic
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71C22×C414yes—
242C22×C4×C71C22×C414yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C4⋊C4×C71—44no—
250C22⋊C4×C71—44no—
251C22⋊C4×C71—44no—
252C22⋊C4×C71C22×C4116yescomplemented
253C42×C71—44no—
254C23×C71—28no—
255C23×C71—28no—
256C23×C71—28no—
257C23×C71—22no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—44no—
264C23×C71—44no—
265C23×C71—44no—
266C23×C71—44no—
267C23×C71C23×C414yes—
268C23×C71C23×C412yes—
269C23×C71C2×#4112yes—
270C23×C71C2×#4112yes—
271C23×C71H(5,𝔽2)12yes—
272C23×C71H(5,𝔽2)12yes—
273C23×C71H(5,𝔽2)12yes—
274C23×C712−1+412yes—
275C23×C71C2511yescharacteristic
276C22×D71—28no—
277C22×D71—28no—
278C22×D71—28no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—22no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71—44no—
288C22×D71—44no—
289C22×D71C23×C414yes—
290C2×C4×C71—28no—
291C2×C4×C71—28no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—44no—
309C2×C4×C71—44no—
310C2×C4×C71—44no—
311C2×C4×C71—44no—
312C2×C4×C71C23×C414yes—
313C2×C4×C71C23×C414yes—
314C22⋊D71—416no—
315C2×Dic71—28no—
316C2×Dic71—28no—
317C2×Dic71—28no—
318C2×Dic71—28no—
319C2×Dic71—28no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—416no—
337C2×Dic71—44no—
338C2×Dic71—44no—
339C2×Dic71C23×C414yes—
340C2×Dic71C23×C414yes—
341C2×Dic71C23×C414yes—
342C2×Dic71C2×#4114yes—
343C2×Dic71C2×#4114yes—
344C4×D71—416no—
345Dic142—416no—
346C22×C71—24no—
347C22×C71—24no—
348C22×C71—24no—
349C22×C71—416no—
350C22×C71—42no—
351C22×C71—42no—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71C4×#4114yes—
355C22×C71#51814yes—
356C22×C71#52014yes—
357C22×C71#53814yes—
358C22×C71#53814yes—
359C22×C71#54214yes—
360C22×C71#54214yes—
361C22×C71C24×C411yescharacteristic
362C22×C71C22×#4111yescharacteristic
363C22×C71C22×#4111yescharacteristic
364C22×C71C2×H(5,𝔽2)11yescharacteristic
365C22×C71C2×H(5,𝔽2)11yescharacteristic
366C22×C71C2×H(5,𝔽2)11yescharacteristic
367C22×C71C2×2−1+411yescharacteristic
368C2×D71—24no—
369C2×D71—24no—
370C2×D71—24no—
371C2×D71—416no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—42no—
376C4×C71—24no—
377C4×C71—24no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71—42no—
381C4×C71—42no—
382Dic71—24no—
383Dic71—24no—
384Dic71—24no—
385Dic71—24no—
386Dic71—24no—
387Dic71—42no—
388Dic71—42no—
389C2×#2337—711nomaximal, Sylow
390C2×C71—44no—
391C2×C71#233718yescomplemented
392C2×C71C2×C4×#4111yescharacteristic
393C2×C71C2×#51811yescharacteristic
394C2×C71C2×#52011yescharacteristic
395C2×C71C2×#53811yescharacteristic
396C2×C71C2×#53811yescharacteristic
397C2×C71C2×#54211yescharacteristic
398C2×C71C2×#54211yescharacteristic
399D71—44no—
400C22×#124—711no—
401#2337—7116no—
402C2×#391—711no—
403C2×#391—711no—
404C2×#388—711no—
405C2×#388—711no—
406C2×#388—711no—
407C2×#388D7111yescharacteristic, complemented
408C2×#386—711no—
409C2×#386—711no—
410C2×#385—711no—
411C2×#385—711no—
412C2×#383—711no—
413C2×C4×C4⋊C4—711no—
414C2×C4×C22⋊C4—711no—
415C2×C4×C22⋊C4—711no—
416C71C2×#233711yescharacteristic, complemented, Sylow
417C23×Q8—711no—
418C23×D4—711no—
419C24×C4—711no—
420C24×C4—711no—
421C2×#124—7116no—
422C2×#124—718no—
423C22×C4⋊C4—711no—
424C22×C4⋊C4—711no—
425C22×C4⋊C4—711no—
426C22×C4⋊C4C2×D7111yescharacteristic
427C22×C22⋊C4—711no—
428C22×C22⋊C4—711no—
429C22×C22⋊C4—711no—
430C22×C22⋊C4—711no—
431C22×C22⋊C4—711no—
432C22×C22⋊C4—711no—
433C22×C22⋊C4—711no—
434C22×C22⋊C4C2×D7111yescharacteristic
435C22×C22⋊C4C2×D7111yescharacteristic
436C22×C22⋊C4C2×D7111yescharacteristic
437C22×C42—711no—
438C22×C42—711no—
439C22×C42—711no—
440C22×C42—711no—
441C22×C42C2×D7111yescharacteristic
442#391—718no—
443#391—718no—
444#388—718no—
445#388—718no—
446#388—718no—
447#388C2×D7118yescomplemented
448#386—718no—
449#386—718no—
450#385—718no—
451#385—718no—
452#383—718no—
453C4×C4⋊C4—718no—
454C4×C22⋊C4—718no—
455C4×C22⋊C4—718no—
456C2×#95—711no—
457C2×#95—711no—
458C2×#95—711no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95C2×D7111yescharacteristic
467C2×#95C2×D7111yescharacteristic
468C25—711no—
469C25C22×D7111yescharacteristic
470C22×Q8—2842no—
471C22×Q8—2842no—
472C22×Q8—718no—
473C22×Q8—714no—
474C22×D4—2842no—
475C22×D4—2842no—
476C22×D4—718no—
477C22×D4—714no—
478C23×C4—2842no—
479C23×C4—2842no—
480C23×C4—2842no—
481C23×C4—2842no—
482C23×C4—714no—
483C23×C4—714no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—711no—
489C23×C4—711no—
490C23×C4—711no—
491C23×C4—1424no—
492C23×C4—1424no—
493C23×C4C22×D7111yescharacteristic
494C23×C4C22×D7111yescharacteristic
495C23×C4C22×D7111yescharacteristic
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C23×C4C22×D7111yescharacteristic
499#124—7164no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—2842no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—1424no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4C22×D7114yes—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—2842no—
511C2×C22⋊C4—2842no—
512C2×C22⋊C4—714no—
513C2×C22⋊C4—714no—
514C2×C22⋊C4—718no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—718no—
517C2×C22⋊C4—718no—
518C2×C22⋊C4—714no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—714no—
521C2×C22⋊C4—714no—
522C2×C22⋊C4—1424no—
523C2×C22⋊C4—1424no—
524C2×C22⋊C4C4×D7118yescomplemented
525C2×C22⋊C4C22×D7114yes—
526C2×C22⋊C4C22×D7114yes—
527C2×C22⋊C4C22×D7114yes—
528C2×C42—42no—
529C2×C42—2842no—
530C2×C42—2842no—
531C2×C42—2842no—
532C2×C42—714no—
533C2×C42—714no—
534C2×C42—714no—
535C2×C42—718no—
536C2×C42—714no—
537C2×C42C22×D7114yes—
538#95—714no—
539#95—714no—
540#95—714no—
541#95—714no—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95—714no—
547#95—714no—
548#95C22×D7114yes—
549#95C22×D7114yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—714no—
557C24—712no—
558C24—1422no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24C2×C4×D7114yes—
565C24C23×D7112yes—
566C24C23×D7111yescharacteristic
567C2×Q8—2844no—
568C2×Q8—2844no—
569C2×Q8—28416no—
570C2×Q8—7116no—
571C2×D4—2844no—
572C2×D4—2844no—
573C2×D4—28416no—
574C2×D4—7116no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—2844no—
592C22×C4—2844no—
593C22×C4—28416no—
594C22×C4—28416no—
595C22×C4—2844no—
596C22×C4—2844no—
597C22×C4—714no—
598C22×C4—714no—
599C22×C4—714no—
600C22×C4—714no—
601C22×C4—714no—
602C22×C4—712no—
603C22×C4—712no—
604C22×C4—712no—
605C22×C4—712no—
606C22×C4—712no—
607C22×C4—712no—
608C22×C4—712no—
609C22×C4—1428no—
610C22×C4—1428no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4C2×C4×D7114yes—
628C22×C4C2×C4×D7114yes—
629C22×C4C23×D7112yes—
630C22×C4C23×D7112yes—
631C22×C4C23×D7112yes—
632C22×C4C23×D7112yes—
633C22×C4C23×D7112yes—
634C22×C4C23×D7112yes—
635C4⋊C4—44no—
636C4⋊C4—2844no—
637C4⋊C4—1428no—
638C4⋊C4—1428no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—2844no—
642C22⋊C4—2844no—
643C22⋊C4—7116no—
644C22⋊C4—7116no—
645C22⋊C4—7116no—
646C22⋊C4—1428no—
647C22⋊C4—1428no—
648C22⋊C4C2×C4×D71116yescomplemented
649C42—44no—
650C42—2844no—
651C42—2844no—
652C42—2844no—
653C42—7116no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—2844no—
668C23—2844no—
669C23—2844no—
670C23—2844no—
671C23—714no—
672C23—1422no—
673C23—1422no—
674C23—1422no—
675C23—1422no—
676C23—1422no—
677C23—1422no—
678C23—1428no—
679C23—1428no—
680C23—1428no—
681C23C22×C4×D7114yes—
682C23C22×C4×D7112yes—
683C23#41×D7112yes—
684C23#41×D7112yes—
685C23#1455617312yes—
686C23#1455617312yes—
687C23#1455617412yes—
688C23#1455617512yes—
689C23C24×D7111yescharacteristic
690Q8—28416no—
691D4—28416no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—28416no—
715C2×C4—2844no—
716C2×C4—2844no—
717C2×C4—28416no—
718C2×C4—714no—
719C2×C4—714no—
720C2×C4—714no—
721C2×C4—714no—
722C2×C4—714no—
723C2×C4—1422no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1428no—
740C2×C4—1428no—
741C2×C4—1428no—
742C2×C4—1428no—
743C2×C4—1428no—
744C2×C4C22×C4×D7114yes—
745C2×C4C22×C4×D7114yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—28416no—
755C22—2842no—
756C22—2842no—
757C22—2842no—
758C22—2842no—
759C22—1424no—
760C22—1424no—
761C22—1424no—
762C22#1798646714yes—
763C22#1798647114yes—
764C22#1798647814yes—
765C22#1798658114yes—
766C22#1798658514yes—
767C22#1798661314yes—
768C22#1798661514yes—
769C22C23×C4×D7111yescharacteristic
770C22C2×#41×D7111yescharacteristic
771C22C2×#41×D7111yescharacteristic
772C22C2×#1455617311yescharacteristic
773C22C2×#1455617311yescharacteristic
774C22C2×#1455617411yescharacteristic
775C22C2×#1455617511yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2842no—
783C4—2842no—
784C4—1424no—
785C4—1424no—
786C4—1424no—
787C4—1424no—
788C4—1424no—
789C2—44no—
790C2—2844no—
791C2#2259115118yesdirect product factor
792C2C2×#1798646711yescharacteristic
793C2C2×#1798647111yescharacteristic
794C2C2×#1798647811yescharacteristic
795C2C2×#1798658111yescharacteristic
796C2C2×#1798658511yescharacteristic
797C2C2×#1798661311yescharacteristic
798C2C2×#1798661511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2337
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #22591151C2direct (N × H)
3. C2×#17985904C2semidirect
4. C2×#17985903C2semidirect
5. C2×#17985890C2semidirect
6. C2×#17985888C2semidirect
7. C2×#17985887C2semidirect
10. C2×#17985871C2semidirect
11. C2×#17985870C2semidirect
12. C2×#17985866C2semidirect
13. C2×C4×Dic71⋊C4C2semidirect
14. C2×C22⋊C4×Dic71C2semidirect
15. C2×#17985846C2semidirect
16. C2×#388×C71C2semidirect
21. C2×#14556114C4semidirect
37. #17985904C22semidirect
38. #17985903C22semidirect
39. #17985890C22semidirect
40. #17985888C22semidirect
41. #17985887C22semidirect
44. #17985871C22semidirect
45. #17985870C22semidirect
46. #17985866C22semidirect
47. C4×Dic71⋊C4C22semidirect
48. C22⋊C4×Dic71C22semidirect
49. #17985846C22semidirect
65. #388×C71C22semidirect
71. C22×Dic142C2×C4semidirect
92. #14556114C2×C4semidirect
100. C2×C22⋊Dic71C2×C4semidirect
106. C2×(C2×D71)⋊C4C2×C4semidirect
107. C2×(C2×D71)⋊C4C2×C4semidirect
116. C2×C4×Dic71C2×C4semidirect
142. C2×C22⋊C4×C71C2×C4semidirect
161. C2×Dic142C22×C4semidirect
206. C22⋊Dic71C22×C4semidirect
210. (C2×D71)⋊C4C22×C4semidirect
211. (C2×D71)⋊C4C22×C4semidirect
215. C4×Dic71C22×C4semidirect
252. C22⋊C4×C71C22×C4semidirect
391. C2×C71#2337semidirect
407. C2×#388D71semidirect
416. C71C2×#2337semidirect
447. #388C2×D71semidirect
524. C2×C22⋊C4C4×D71semidirect
648. C22⋊C4C2×C4×D71semidirect
791. C2#22591151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561142
#225911512
C2×#179859042
C2×#179859032
C2×#179858902
C2×#179858882
C2×#179858872
C2×#179858762
C2×#179858752
C2×#179858712
C2×#179858702
C2×#179858662
C2×C4×Dic71⋊C42
C2×C22⋊C4×Dic712
C2×#179858462
C2×#388×C712
C2×#233771