Finite Group Databasebeta

← C2×#22600910 #32876141

Subgroups — C2×#22600910 #32876141

Order 18176.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986691C211yesmaximal, characteristic
2C2×#17986683C211yesmaximal, characteristic
3#22600910C2116yesmaximal, direct product factor
4C2×#17986399C211yesmaximal, characteristic, complemented
5C2×#17986333C211yesmaximal, characteristic, complemented
6C2×#17986332C211yesmaximal, characteristic, complemented
7C2×#17986338C211yesmaximal, characteristic, complemented
8C2×#17986337C211yesmaximal, characteristic, complemented
9C2×#17986308C211yesmaximal, characteristic, complemented
10C2×#17986304C211yesmaximal, characteristic, complemented
11C2×#17986254C211yesmaximal, characteristic, complemented
12C2×Q16×Dic71C211yesmaximal, characteristic, complemented
13C2×#17986075C211yesmaximal, characteristic
14C2×#17986041C211yesmaximal, characteristic, complemented
15C2×#17986038C211yesmaximal, characteristic, complemented
16C2×#470×C71C211yesmaximal, characteristic, complemented
17C22×#11765848C2211yescharacteristic
18#17986691—24no—
19#17986691C2218yes—
20#17986683—24no—
21#17986683C2218yes—
22C2×#14556123—21no—
23C2×#14556121—21no—
24C2×#14556119—21no—
25C2×#14556119C2211yescharacteristic
26C2×#14556119C2211yescharacteristic
27C2×#14556118—21no—
28C2×#14556112—21no—
29C2×#14556110—21no—
30C2×#14556104C2211yescharacteristic
31C2×#14556104C2211yescharacteristic
32C2×Q8×Dic71C2211yescharacteristic
33C2×Q8×Dic71C2211yescharacteristic
34C2×C4×C22⋊D71C2211yescharacteristic
35C2×#14556087C2211yescharacteristic
36C2×#14556086—21no—
37C2×#14556086C2211yescharacteristic
38C2×#14556084—21no—
39C22×C4⋊Dic71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41#17986399C2218yescomplemented
42#17986338C2218yescomplemented
43#17986337C2218yescomplemented
44#17986333C2218yescomplemented
45#17986332C2218yescomplemented
46#17986308C2218yescomplemented
47#17986304C2218yescomplemented
48#17986254C2218yescomplemented
49Q16×Dic71C2218yescomplemented
50#17986075C2218yes—
51#17986041C2218yescomplemented
52#17986038C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556059C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556052C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C22×Q16×C71C2211yescharacteristic
70C22×M16×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73#470×C71C2218yescomplemented
74C2×#106×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#103×C71C2211yescharacteristic
77C22×C22⋊D71D411yescharacteristic
78C23×Dic71—21no—
79C22×C4×D71—21no—
80C22×C4×D71C2311yescharacteristic
81C2×#11765848—24no—
82C2×#11765848C2314yes—
83C22×C71⋊C8C2311yescharacteristic
84C22×C71⋊C8C2311yescharacteristic
85#14556123—28no—
86#14556121—28no—
87#14556119—28no—
88#14556119—22no—
89#14556119—22no—
90#14556119C2314yes—
91#14556119C2314yes—
92#14556118—28no—
93#14556112—28no—
94#14556110—28no—
95#14556104—22no—
96#14556104—22no—
97#14556104C2314yes—
98#14556104C2314yes—
99Q8×Dic71—22no—
100Q8×Dic71—22no—
101Q8×Dic71C2314yes—
102Q8×Dic71C2314yes—
103C4×C22⋊D71D414yes—
104C4×C22⋊D71C2314yes—
105#14556087—22no—
106#14556087C2314yes—
107#14556086—22no—
108#14556086—28no—
109#14556086C2314yes—
110#14556084—28no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71—21no—
113C2×C4⋊Dic71—21no—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—22no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71C2314yes—
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4D411yescharacteristic
128C4⋊C4×D71—22no—
129C4⋊C4×D71C2314yes—
130C2×C22⋊Dic71—21no—
131C2×C22⋊Dic71D411yescharacteristic
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4D411yescharacteristic
136C2×C4×Dic71—21no—
137C2×C4×Dic71—21no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71C2311yescharacteristic
141#14556062C2314yes—
142#14556062C2314yes—
143#14556061C2314yes—
144#14556061C2314yes—
145#14556061C2314yes—
146#14556060C2314yes—
147#14556060C2314yes—
148#14556059C2314yes—
149Dic71⋊C8C2314yes—
150#14556052C2314yes—
151#14556052C2314yes—
152#14556052C2314yes—
153#14556052C2314yes—
154C22⋊(C71⋊C8)C2314yes—
155(C2×D71)⋊C8C2314yes—
156C8×Dic71C2314yes—
157C22×Q8×C71C2311yescharacteristic
158C22×Q8×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C2×Q16×C71—24no—
161C2×Q16×C71C2314yes—
162C2×M16×C71—24no—
163C2×M16×C71C2314yes—
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22⋊Q8×C71—22no—
167C22⋊Q8×C71—22no—
168C22⋊Q8×C71C2314yes—
169C22⋊Q8×C71C2314yes—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176#106×C71C2314yes—
177#103×C71C2314yes—
178#103×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C2×C22⋊D71—42no—
181C2×C22⋊D71C2×D414yes—
182C22×Dic71—21no—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—24no—
186C22×Dic71—21no—
187C22×Dic71—44no—
188C22×Dic71C2×D411yescharacteristic
189C22×Dic71C2×D411yescharacteristic
190C22×Dic71C2×D411yescharacteristic
191C2×C4×D71—22no—
192C2×C4×D71—22no—
193C2×C4×D71—24no—
194C2×C4×D71—44no—
195C2×C4×D71C2×D412yes—
196C2×C4×D71C2412yes—
197#11765848—28no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8C2412yes—
201C2×C71⋊C8C2412yes—
202C4⋊Dic71—21no—
203C4⋊Dic71—21no—
204C4⋊Dic71—21no—
205C4⋊Dic71—24no—
206C4⋊Dic71—21no—
207C4⋊Dic71—24no—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71—24no—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4C2×D414yes—
221C22⋊Dic71—24no—
222C22⋊Dic71C2×D414yes—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226(C2×D71)⋊C4C2×D414yes—
227C4×Dic71—24no—
228C4×Dic71—24no—
229C4×Dic71—24no—
230C4×Dic71—24no—
231C4×Dic71C2×D412yes—
232C4×Dic71C2412yes—
233C24×C71C2×D411yescharacteristic
234C2×Q8×C71—21no—
235C2×Q8×C71—21no—
236C2×Q8×C71—22no—
237C2×Q8×C71—22no—
238C2×Q8×C71—22no—
239C2×Q8×C71—22no—
240C2×Q8×C71C2412yes—
241C2×Q8×C71C2412yes—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2411yescharacteristic
252Q16×C71—28no—
253M16×C71—28no—
254C2×C8×C71—22no—
255C2×C8×C71#4114yes—
256C2×C8×C71C2412yes—
257C2×C8×C71C2412yes—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71C22×D412yes—
270C23×C71C22×D411yescharacteristic
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71C22×D412yes—
275Q8×C71—22no—
276Q8×C71—22no—
277Q8×C71—22no—
278Q8×C71—22no—
279Q8×C71—42no—
280Q8×C71—42no—
281C2×C4×C71—22no—
282C2×C4×C71—24no—
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—42no—
290C2×C4×C71—42no—
291C2×C4×C71—42no—
292C2×C4×C71—42no—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D411yescharacteristic
295C2×C4×C71C2×#4112yes—
296C2×C4×C712−1+412yes—
297C2×C4×C71C2511yescharacteristic
298C22⋊D71—44no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—48no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71—42no—
310C2×Dic71—42no—
311C2×Dic71C22×D412yes—
312C2×Dic71C22×D412yes—
313C2×Dic71C22×D412yes—
314C4×D71—24no—
315C4×D71—22no—
316C4×D71—22no—
317C4×D71—48no—
318C8×C71—22no—
319C8×C71C2×#4114yes—
320C71⋊C8—22no—
321C71⋊C8—22no—
322C22×C71—22no—
323C22×C71—22no—
324C22×C71—22no—
325C22×C71—44no—
326C22×C71#54712yes—
327C22×C71#57512yes—
328C22×C71#57812yes—
329C22×C71C23×D411yescharacteristic
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—44no—
334C4×C71—22no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71—42no—
339C4×C71#54712yes—
340C4×C71C22×#4111yescharacteristic
341C4×C71C2×2−1+411yescharacteristic
342Dic71—22no—
343Dic71—22no—
344Dic71—22no—
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348Dic71—42no—
349C2×#3352—711nomaximal, Sylow
350C2×C71—42no—
351C2×C71#335214yescomplemented
352C2×C71C2×#54711yescharacteristic
353C2×C71C2×#57511yescharacteristic
354C2×C71C2×#57811yescharacteristic
355D71—42no—
356C2×#552—711no—
357C2×#552—711no—
358#3352—7116no—
359C2×#499—711no—
360C2×#484—711no—
361C2×#484—711no—
362C2×#485—711no—
363C2×#485—711no—
364C2×#479—711no—
365C2×#479—711no—
366C2×#470—711no—
367C2×#470D7111yescharacteristic, complemented
368C2×C4×Q16—711no—
369C2×#436—711no—
370C2×#428—711no—
371C2×#428—711no—
372C71C2×#335211yescharacteristic, complemented, Sylow
373C22×Q16C2×D7111yescharacteristic
374C22×M16—711no—
375C22×M16C2×D7111yescharacteristic
376#552—718no—
377#552—718no—
378#552—1424no—
379#552—1424no—
380C2×#126—1421no—
381C2×#126—1421no—
382C2×#125—711no—
383C2×#125—711no—
384C2×#125—1421no—
385C2×#125—1421no—
386C2×#123—1421no—
387C2×#123—1421no—
388C2×C22⋊Q8—711no—
389C2×C22⋊Q8—711no—
390C2×C22⋊Q8C2×D7111yescharacteristic
391C2×C22⋊Q8C2×D7111yescharacteristic
392C2×C4×Q8—711no—
393C2×C4×Q8—711no—
394C2×C4×D4—711no—
395C2×#117—711no—
396C2×#117—711no—
397C2×#117—1421no—
398C2×#117—1421no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401#499—718no—
402#485—718no—
403#485—718no—
404#484—718no—
405#484—718no—
406#479—718no—
407#479—718no—
408#470—718no—
409#470C2×D7118yescomplemented
410C4×Q16—718no—
411#436—718no—
412#428—718no—
413#428—718no—
414C2×#107—711no—
415C2×#107—711no—
416C2×#107—711no—
417C2×#107—711no—
418C2×#107—711no—
419C2×#106—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106C2×D7111yescharacteristic
423C2×C4⋊C8—711no—
424C2×#103—711no—
425C2×#103—711no—
426C2×#103—711no—
427C2×#103—711no—
428C2×#103C2×D7111yescharacteristic
429C2×#103C2×D7111yescharacteristic
430C2×C22⋊C8—711no—
431C2×C22⋊C8—711no—
432C2×C4×C8—711no—
433C22×Q8C22×D7111yescharacteristic
434C22×Q8C22×D7111yescharacteristic
435C22×D4—711no—
436C23×C4—711no—
437C23×C4—1421no—
438C23×C4—1421no—
439C23×C4C22×D7111yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D7114yes—
442C2×M16—24no—
443C2×M16—714no—
444C2×M16—1424no—
445C2×M16C22×D7114yes—
446C22×C8—711no—
447C22×C8—711no—
448C22×C8C22×D7111yescharacteristic
449C22×C8C22×D7111yescharacteristic
450#126—1428no—
451#126—1428no—
452#125—714no—
453#125—714no—
454#125—1422no—
455#125—1422no—
456#125—1428no—
457#125—1428no—
458#123—1428no—
459#123—1428no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—714no—
463C22⋊Q8—714no—
464C22⋊Q8—1422no—
465C22⋊Q8—1422no—
466C22⋊Q8C22×D7114yes—
467C22⋊Q8C22×D7114yes—
468C4×Q8—714no—
469C4×Q8—714no—
470C4×Q8—1422no—
471C4×Q8—1422no—
472C4×D4—714no—
473C4×D4—714no—
474#117—714no—
475#117—714no—
476#117—1428no—
477#117—1428no—
478#117—1422no—
479#117—1422no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—711no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—714no—
489C2×C4⋊C4—1422no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1421no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1422no—
501C2×C4⋊C4C22×D7111yescharacteristic
502C2×C4⋊C4C22×D7111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—711no—
506C2×C22⋊C4—711no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C42—711no—
512C2×C42—1421no—
513C2×C42—1421no—
514C2×C42—1421no—
515C2×C42—1421no—
516#107—714no—
517#107—714no—
518#107—714no—
519#107—714no—
520#107—714no—
521#106—714no—
522#106—714no—
523#106—714no—
524#106C22×D7114yes—
525C4⋊C8—714no—
526#103—714no—
527#103—714no—
528#103—714no—
529#103—714no—
530#103C22×D7114yes—
531#103C22×D7114yes—
532C22⋊C8—714no—
533C22⋊C8—714no—
534C4×C8—714no—
535C24—711no—
536C24D4×D7111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C23×D7112yes—
544C2×Q8C23×D7112yes—
545C2×D4—2842no—
546C2×D4—714no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—2844no—
554C22×C4—2844no—
555C22×C4—711no—
556C22×C4—711no—
557C22×C4—711no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—1424no—
561C22×C4—1424no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1422no—
567C22×C4—1422no—
568C22×C4D4×D7112yes—
569C22×C4D4×D7111yescharacteristic
570C22×C4C23×D7112yes—
571C22×C4C23×D7111yescharacteristic
572Q16—28no—
573M16—28no—
574M16—1428no—
575C2×C8—22no—
576C2×C8—712no—
577C2×C8—712no—
578C2×C8—1422no—
579C2×C8—1422no—
580C2×C8#1176586414yes—
581C2×C8C23×D7112yes—
582C2×C8C23×D7112yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—714no—
588C4⋊C4—712no—
589C4⋊C4—712no—
590C4⋊C4—712no—
591C4⋊C4—712no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4—1424no—
601C4⋊C4—1421no—
602C4⋊C4—1421no—
603C4⋊C4—1421no—
604C4⋊C4—1424no—
605C4⋊C4—1421no—
606C4⋊C4C23×D7112yes—
607C4⋊C4C23×D7112yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—714no—
611C22⋊C4—714no—
612C22⋊C4—1424no—
613C22⋊C4—1424no—
614C22⋊C4—1424no—
615C22⋊C4—1424no—
616C42—712no—
617C42—712no—
618C42—1424no—
619C42—1424no—
620C42—1424no—
621C42—1424no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—712no—
626C23—1422no—
627C23—1422no—
628C23—1422no—
629C23C2×D4×D7112yes—
630C23C2×D4×D7111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637D4—2844no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—2848no—
651C2×C4—2848no—
652C2×C4—2842no—
653C2×C4—2842no—
654C2×C4—2842no—
655C2×C4—2842no—
656C2×C4—712no—
657C2×C4—712no—
658C2×C4—712no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1424no—
669C2×C4C2×D4×D7112yes—
670C2×C4C2×D4×D7111yescharacteristic
671C2×C4C2×#1176586412yes—
672C2×C4#1455617512yes—
673C2×C4C24×D7111yescharacteristic
674C8—22no—
675C8—1422no—
676C8—1422no—
677C8C2×#1176586414yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—2844no—
683C22—1422no—
684C22—1422no—
685C22—1422no—
686C22#1798664912yes—
687C22#1798679812yes—
688C22#1798681512yes—
689C22C22×D4×D7111yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—2842no—
696C4—2842no—
697C4—2842no—
698C4—2842no—
699C4—1422no—
700C4—1422no—
701C4—1422no—
702C4#1798664912yes—
703C4C22×#1176586411yescharacteristic
704C4C2×#1455617511yescharacteristic
705C2—42no—
706C2—2842no—
707C2#2260091014yesdirect product factor
708C2C2×#1798664911yescharacteristic
709C2C2×#1798679811yescharacteristic
710C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#470×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
hypercenterC2×#470D71
hypocenterC71C2×#3352
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #22600910C2direct (N × H)
4. C2×#17986399C2semidirect
5. C2×#17986333C2semidirect
6. C2×#17986332C2semidirect
7. C2×#17986338C2semidirect
8. C2×#17986337C2semidirect
9. C2×#17986308C2semidirect
10. C2×#17986304C2semidirect
11. C2×#17986254C2semidirect
12. C2×Q16×Dic71C2semidirect
14. C2×#17986041C2semidirect
15. C2×#17986038C2semidirect
16. C2×#470×C71C2semidirect
41. #17986399C22semidirect
42. #17986338C22semidirect
43. #17986337C22semidirect
44. #17986333C22semidirect
45. #17986332C22semidirect
46. #17986308C22semidirect
47. #17986304C22semidirect
48. #17986254C22semidirect
49. Q16×Dic71C22semidirect
51. #17986041C22semidirect
52. #17986038C22semidirect
73. #470×C71C22semidirect
351. C2×C71#3352semidirect
367. C2×#470D71semidirect
372. C71C2×#3352semidirect
409. #470C2×D71semidirect
707. C2#22600910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866912
C2×#179866832
#226009102
C2×#179863992
C2×#179863332
C2×#179863322
C2×#179863382
C2×#179863372
C2×#179863082
C2×#179863042
C2×#179862542
C2×Q16×Dic712
C2×#179860752
C2×#179860412
C2×#179860382
C2×#470×C712
C2×#335271