Finite Group Databasebeta

← C2×#22591069 #32156270

Subgroups — C2×#22591069 #32156270

Order 18176.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556108C211yesmaximal, characteristic
2#22591069C2116yesmaximal, direct product factor
3C2×#17985903C211yesmaximal, characteristic, complemented
4C2×#17985903C211yesmaximal, characteristic, complemented
5C2×#17985897C211yesmaximal, characteristic, complemented
6C2×#17985895C211yesmaximal, characteristic, complemented
7C2×#17985885C211yesmaximal, characteristic, complemented
8C2×#17985884C211yesmaximal, characteristic, complemented
9C2×#17985882C211yesmaximal, characteristic, complemented
10C2×#17985873C211yesmaximal, characteristic
11C2×#17985870C211yesmaximal, characteristic
12C2×#17985858C211yesmaximal, characteristic
13C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
14C2×#17985846C211yesmaximal, characteristic
15C2×#95×D71C211yesmaximal, characteristic
16C2×#387×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556108C4116yescomplemented
22C2×#14556108C2218yes—
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37#17985903C2218yescomplemented
38#17985903C2218yescomplemented
39#17985897C2218yescomplemented
40#17985895C2218yescomplemented
41#17985885C2218yescomplemented
42#17985884C2218yescomplemented
43#17985882C2218yescomplemented
44#17985873C2218yes—
45#17985870C2218yes—
46#17985858C2218yes—
47C4×(C2×D71)⋊C4C2218yes—
48#17985846C2218yes—
49C2×C71⋊#95C2211yescharacteristic
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
59#95×D71C2218yes—
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C42×C71C2211yescharacteristic
63#387×C71C2218yescomplemented
64C2×#95×C71C2211yescharacteristic
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C24×D71C2311yescharacteristic
69C22×Dic142—42no—
70C22×Dic142—42no—
71C22×Dic142C2×C418yescomplemented
72C22×Dic142C2314yes—
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C22×C4×D71—24no—
81C22×C4×D71—42no—
82C22×C4×D71—42no—
83C22×C4×D71—42no—
84C22×C4×D71—42no—
85C22×C4×D71—42no—
86C22×C4×D71—42no—
87C22×C4×D71C2×C418yes—
88C22×C4×D71Q818yescomplemented
89C22×C4×D71C2314yes—
90C22×C4×D71C2314yes—
91C22×C4×D71C2314yes—
92#14556108C2×C4164yescomplemented
93C2×C4⋊Dic71—42no—
94C2×C4⋊Dic71C2×C418yescomplemented
95C2×C4⋊Dic71C2×C418yescomplemented
96C2×C4⋊Dic71C2314yes—
97C2×C4⋊Dic71C2314yes—
98C2×C4⋊Dic71C2314yes—
99C2×Dic71⋊C4—42no—
100C2×Dic71⋊C4—42no—
101C2×Dic71⋊C4—42no—
102C2×Dic71⋊C4—42no—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×(C2×D71)⋊C4—24no—
108C2×(C2×D71)⋊C4—24no—
109C2×(C2×D71)⋊C4C2×C418yes—
110C2×(C2×D71)⋊C4C2×C418yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×C4×Dic71—42no—
116C2×C4×Dic71—42no—
117C2×C4×Dic71—42no—
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—
131C23×C4×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×C71C2×C418yescomplemented
140C2×C4⋊C4×C71C2314yes—
141C2×C4⋊C4×C71C2314yes—
142C2×C42×C71—42no—
143C2×C42×C71C2314yes—
144#95×C71C2314yes—
145#95×C71C2314yes—
146#95×C71C2314yes—
147#95×C71C2314yes—
148C23×D71—22no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71C22×C414yes—
153C23×D71C2×Q814yes—
154C23×D71#4114yes—
155C23×D71C2412yes—
156C2×Dic142—416no—
157C2×Dic142—44no—
158C2×Dic142—44no—
159C2×Dic142C22×C4116yescomplemented
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
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×Dic71C22×C414yes—
178C22×Dic71C22×C414yes—
179C22×Dic71C22×C414yes—
180C22×Dic71C2×Q814yes—
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C2×C4×D71—28no—
189C2×C4×D71—416no—
190C2×C4×D71—416no—
191C2×C4×D71—44no—
192C2×C4×D71—44no—
193C2×C4×D71—44no—
194C2×C4×D71—44no—
195C2×C4×D71—44no—
196C2×C4×D71—44no—
197C2×C4×D71—416no—
198C2×C4×D71C22×C4116yes—
199C2×C4×D71C2×Q8116yescomplemented
200C4⋊Dic71—44no—
201C4⋊Dic71C22×C4116yescomplemented
202C4⋊Dic71C22×C4116yescomplemented
203Dic71⋊C4—44no—
204Dic71⋊C4—44no—
205Dic71⋊C4—44no—
206Dic71⋊C4—44no—
207(C2×D71)⋊C4—28no—
208(C2×D71)⋊C4—28no—
209(C2×D71)⋊C4C22×C4116yes—
210(C2×D71)⋊C4C22×C4116yes—
211C4×Dic71—44no—
212C4×Dic71—44no—
213C4×Dic71—44no—
214C24×C71C2411yescharacteristic
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
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×C71C22×C414yes—
233C22×C4×C71C22×C414yes—
234C22×C4×C71C22×C414yes—
235C22×C4×C71C2×Q814yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C4⋊C4×C71—44no—
244C4⋊C4×C71C22×C4116yescomplemented
245C42×C71—44no—
246C23×C71C23×C412yes—
247C23×C71C22×Q812yes—
248C23×C71C2×#4112yes—
249C23×C71H(5,𝔽2)12yes—
250C23×C71H(5,𝔽2)12yes—
251C23×C71H(5,𝔽2)12yes—
252C23×C712−1+412yes—
253C23×C71C2511yescharacteristic
254C22×D71—28no—
255C22×D71—28no—
256C22×D71—28no—
257C22×D71—28no—
258C22×D71—28no—
259C22×D71—28no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71C4×Q8116yes—
265C22×D71C23×C414yes—
266C22×D71C22×Q814yes—
267C22×D71C2×#4114yes—
268C2×C4×C71—28no—
269C2×C4×C71—28no—
270C2×C4×C71—28no—
271C2×C4×C71—28no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—44no—
290C2×C4×C71—44no—
291C2×C4×C71—44no—
292C2×C4×C71C23×C414yes—
293C2×C4×C71C23×C414yes—
294C2×C4×C71C23×C414yes—
295C2×C4×C71C22×Q814yes—
296C2×Dic71—28no—
297C2×Dic71—28no—
298C2×Dic71—28no—
299C2×Dic71—28no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—44no—
318C2×Dic71—44no—
319C2×Dic71—44no—
320C2×Dic71C23×C414yes—
321C2×Dic71C23×C414yes—
322C2×Dic71C23×C414yes—
323C2×Dic71C22×Q814yes—
324C4×D71—416no—
325C4×D71—416no—
326C4×D71—416no—
327Dic142—416no—
328C22×C71C2×C4×Q814yes—
329C22×C71#51814yes—
330C22×C71#52014yes—
331C22×C71#53814yes—
332C22×C71#53914yes—
333C22×C71#54314yes—
334C22×C71#54414yes—
335C22×C71C24×C411yescharacteristic
336C22×C71C23×Q811yescharacteristic
337C22×C71C22×#4111yescharacteristic
338C22×C71C2×H(5,𝔽2)11yescharacteristic
339C22×C71C2×H(5,𝔽2)11yescharacteristic
340C22×C71C2×H(5,𝔽2)11yescharacteristic
341C22×C71C2×2−1+411yescharacteristic
342C2×D71—232no—
343C2×D71—24no—
344C2×D71—24no—
345C2×D71—24no—
346C2×D71—24no—
347C2×D71—24no—
348C2×D71—24no—
349C2×D71C2×C4×Q818yes—
350C4×C71—24no—
351C4×C71—24no—
352C4×C71—24no—
353C4×C71—24no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71—42no—
357Dic71—24no—
358Dic71—24no—
359Dic71—24no—
360Dic71—24no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#2329—711nomaximal, Sylow
365C2×C71#232918yescomplemented
366C2×C71C22×C4×Q811yescharacteristic
367C2×C71C2×#51811yescharacteristic
368C2×C71C2×#52011yescharacteristic
369C2×C71C2×#53811yescharacteristic
370C2×C71C2×#53911yescharacteristic
371C2×C71C2×#54311yescharacteristic
372C2×C71C2×#54411yescharacteristic
373D71—28no—
374C22×C22⋊Q8—711no—
375#2329—7116no—
376C2×#391—711no—
377C2×#391—711no—
378C2×#389—711no—
379C2×#389—711no—
380C2×#387—711no—
381C2×#387—711no—
382C2×#387—711no—
383C2×#387D7111yescharacteristic, complemented
384C2×#385—711no—
385C2×#385—711no—
386C2×#380—711no—
387C2×C4×C22⋊C4—711no—
388C2×C4×C22⋊C4—711no—
389C22×#95—711no—
390C71C2×#232911yescharacteristic, complemented, Sylow
391C23×Q8—711no—
392C24×C4—711no—
393C24×C4—711no—
394C24×C4—711no—
395C2×C22⋊Q8—7116no—
396C2×C22⋊Q8—718no—
397C22×C4⋊C4—711no—
398C22×C4⋊C4—711no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4C2×D7111yescharacteristic
405C22×C4⋊C4C2×D7111yescharacteristic
406C22×C22⋊C4—711no—
407C22×C22⋊C4—711no—
408C22×C22⋊C4—711no—
409C22×C22⋊C4—711no—
410C22×C42—711no—
411C22×C42—711no—
412C22×C42—711no—
413C22×C42C2×D7111yescharacteristic
414#391—718no—
415#391—718no—
416#389—718no—
417#389—718no—
418#387—718no—
419#387—718no—
420#387—718no—
421#387C2×D7118yescomplemented
422#385—718no—
423#385—718no—
424#380—718no—
425C4×C22⋊C4—718no—
426C4×C22⋊C4—718no—
427C2×#95—711no—
428C2×#95—711no—
429C2×#95—711no—
430C2×#95—711no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—718no—
438C2×#95C2×D7111yescharacteristic
439C2×#95C2×D7111yescharacteristic
440C2×#95C2×D7111yescharacteristic
441C2×#95C2×D7111yescharacteristic
442C25—711no—
443C22×Q8—2842no—
444C22×Q8—2842no—
445C22×Q8—718no—
446C22×Q8—714no—
447C23×C4—2842no—
448C23×C4—2842no—
449C23×C4—2842no—
450C23×C4—2842no—
451C23×C4—2842no—
452C23×C4—2842no—
453C23×C4—718no—
454C23×C4—718no—
455C23×C4—714no—
456C23×C4—714no—
457C23×C4—714no—
458C23×C4—711no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4—711no—
464C23×C4—711no—
465C23×C4—1424no—
466C23×C4C22×D7111yescharacteristic
467C23×C4C22×D7111yescharacteristic
468C23×C4C22×D7111yescharacteristic
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473C22⋊Q8—7164no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—2842no—
476C2×C4⋊C4—2842no—
477C2×C4⋊C4—2842no—
478C2×C4⋊C4—2842no—
479C2×C4⋊C4—2842no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—714no—
485C2×C4⋊C4—718no—
486C2×C4⋊C4—718no—
487C2×C4⋊C4—714no—
488C2×C4⋊C4—714no—
489C2×C4⋊C4C4×D7118yescomplemented
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7114yes—
492C2×C22⋊C4—718no—
493C2×C22⋊C4—718no—
494C2×C22⋊C4—714no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—714no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—1424no—
499C2×C22⋊C4—1424no—
500C2×C42—42no—
501C2×C42—2842no—
502C2×C42—2842no—
503C2×C42—2842no—
504C2×C42—714no—
505C2×C42—714no—
506C2×C42—714no—
507C2×C42C22×D7114yes—
508#95—714no—
509#95—714no—
510#95—714no—
511#95—714no—
512#95—714no—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95—714no—
518#95C22×D7114yes—
519#95C22×D7114yes—
520#95C22×D7114yes—
521#95C22×D7114yes—
522C24—714no—
523C24—714no—
524C24—714no—
525C24—712no—
526C24—1422no—
527C24—1422no—
528C24—1422no—
529C24—1422no—
530C24C23×D7111yescharacteristic
531C2×Q8—2844no—
532C2×Q8—2844no—
533C2×Q8—28416no—
534C2×Q8—7116no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—2844no—
553C22×C4—2844no—
554C22×C4—2844no—
555C22×C4—2844no—
556C22×C4—28416no—
557C22×C4—28416no—
558C22×C4—2844no—
559C22×C4—2844no—
560C22×C4—28416no—
561C22×C4—7116no—
562C22×C4—7116no—
563C22×C4—714no—
564C22×C4—714no—
565C22×C4—714no—
566C22×C4—714no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—712no—
571C22×C4—712no—
572C22×C4—712no—
573C22×C4—712no—
574C22×C4—1428no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4C2×C4×D7114yes—
593C22×C4C2×C4×D7114yes—
594C22×C4C2×C4×D7114yes—
595C22×C4Q8×D7114yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7112yes—
598C22×C4C23×D7112yes—
599C22×C4C23×D7112yes—
600C22×C4C23×D7112yes—
601C22×C4C23×D7112yes—
602C22×C4C23×D7112yes—
603C4⋊C4—44no—
604C4⋊C4—2844no—
605C4⋊C4—2844no—
606C4⋊C4—2844no—
607C4⋊C4—2844no—
608C4⋊C4—2844no—
609C4⋊C4—7116no—
610C4⋊C4—7116no—
611C4⋊C4C2×C4×D71116yescomplemented
612C22⋊C4—7116no—
613C22⋊C4—7116no—
614C22⋊C4—1428no—
615C22⋊C4—1428no—
616C42—44no—
617C42—2844no—
618C42—2844no—
619C42—2844no—
620C23—714no—
621C23—714no—
622C23—714no—
623C23—7116no—
624C23—1422no—
625C23—1422no—
626C23—1422no—
627C23—1422no—
628C23—1428no—
629C23—1428no—
630C23—1428no—
631C23—1428no—
632C23—1428no—
633C23—1428no—
634C23C22×C4×D7112yes—
635C23C2×Q8×D7112yes—
636C23#41×D7112yes—
637C23#1455617312yes—
638C23#1455617412yes—
639C23#1455617412yes—
640C23#1455617512yes—
641C23C24×D7111yescharacteristic
642Q8—28416no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—28416no—
668C2×C4—28416no—
669C2×C4—28416no—
670C2×C4—2844no—
671C2×C4—2844no—
672C2×C4—2844no—
673C2×C4—714no—
674C2×C4—714no—
675C2×C4—714no—
676C2×C4—714no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1428no—
695C2×C4—1428no—
696C2×C4—1428no—
697C2×C4—1428no—
698C2×C4C22×C4×D7114yes—
699C2×C4C22×C4×D7114yes—
700C2×C4C22×C4×D7114yes—
701C2×C4C2×Q8×D7114yes—
702C22—718no—
703C22—1424no—
704C22—1424no—
705C22—1424no—
706C22—1424no—
707C22—14232no—
708C22—1424no—
709C22—1424no—
710C22C4×Q8×D7114yes—
711C22#1798647314yes—
712C22#1798647814yes—
713C22#1798658514yes—
714C22#1798659014yes—
715C22#1798662414yes—
716C22#1798662914yes—
717C22C23×C4×D7111yescharacteristic
718C22C22×Q8×D7111yescharacteristic
719C22C2×#41×D7111yescharacteristic
720C22C2×#1455617311yescharacteristic
721C22C2×#1455617411yescharacteristic
722C22C2×#1455617411yescharacteristic
723C22C2×#1455617511yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2842no—
732C4—2842no—
733C4—2842no—
734C4—1424no—
735C4—1424no—
736C4—1424no—
737C4—1424no—
738C2—1428no—
739C2#2259106918yesdirect product factor
740C2C2×C4×Q8×D7111yescharacteristic
741C2C2×#1798647311yescharacteristic
742C2C2×#1798647811yescharacteristic
743C2C2×#1798658511yescharacteristic
744C2C2×#1798659011yescharacteristic
745C2C2×#1798662411yescharacteristic
746C2C2×#1798662911yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#387×C71C2
socleC24×C71C24
prime radicalC24×D71C23
cosocleC23×C71C25
hypercenterC2×#387D71
hypocenterC71C2×#2329
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22591069C2direct (N × H)
3. C2×#17985903C2semidirect
4. C2×#17985903C2semidirect
5. C2×#17985897C2semidirect
6. C2×#17985895C2semidirect
7. C2×#17985885C2semidirect
8. C2×#17985884C2semidirect
9. C2×#17985882C2semidirect
16. C2×#387×C71C2semidirect
21. C2×#14556108C4semidirect
37. #17985903C22semidirect
38. #17985903C22semidirect
39. #17985897C22semidirect
40. #17985895C22semidirect
41. #17985885C22semidirect
42. #17985884C22semidirect
43. #17985882C22semidirect
63. #387×C71C22semidirect
71. C22×Dic142C2×C4semidirect
88. C22×C4×D71Q8semidirect
92. #14556108C2×C4semidirect
94. C2×C4⋊Dic71C2×C4semidirect
95. C2×C4⋊Dic71C2×C4semidirect
139. C2×C4⋊C4×C71C2×C4semidirect
159. C2×Dic142C22×C4semidirect
199. C2×C4×D71C2×Q8semidirect
201. C4⋊Dic71C22×C4semidirect
202. C4⋊Dic71C22×C4semidirect
244. C4⋊C4×C71C22×C4semidirect
365. C2×C71#2329semidirect
383. C2×#387D71semidirect
390. C71C2×#2329semidirect
421. #387C2×D71semidirect
489. C2×C4⋊C4C4×D71semidirect
611. C4⋊C4C2×C4×D71semidirect
739. C2#22591069direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561082
#225910692
C2×#179859032
C2×#179858972
C2×#179858952
C2×#179858852
C2×#179858842
C2×#179858822
C2×#179858732
C2×#179858702
C2×#179858582
C2×C4×(C2×D71)⋊C42
C2×#179858462
C2×#95×D712
C2×#387×C712
C2×#232971