Finite Group Databasebeta

← C2×#22600797 #32876001

Subgroups — C2×#22600797 #32876001

Order 18176.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986706C211yesmaximal, characteristic
2C2×#17986689C211yesmaximal, characteristic
3#22600797C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986335C211yesmaximal, characteristic, complemented
6C2×#17986341C211yesmaximal, characteristic, complemented
7C2×#17986330C211yesmaximal, characteristic, complemented
8C2×#17986330C211yesmaximal, characteristic, complemented
9C2×#17986307C211yesmaximal, characteristic, complemented
10C2×#17986285C211yesmaximal, characteristic, complemented
11C2×#17986257C211yesmaximal, characteristic, complemented
12C2×#17986240C211yesmaximal, characteristic, complemented
13C2×#17986107C211yesmaximal, characteristic, complemented
14C2×#17986041C211yesmaximal, characteristic, complemented
15C22×#14556060C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic
17C22×Dic284C2211yescharacteristic
18#17986706—24no—
19#17986706C2218yes—
20#17986689—24no—
21#17986689C2218yes—
22C2×#14556128C2211yescharacteristic
23C2×#14556121—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556119—21no—
26C2×#14556118—21no—
27C2×#14556109—21no—
28C2×#14556107C2211yescharacteristic
29C2×#14556107C2211yescharacteristic
30C2×#14556107C2211yescharacteristic
31C2×#14556107C2211yescharacteristic
32C2×#14556105—21no—
33C2×#14556105—21no—
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic
36C2×D4×Dic71—21no—
37C2×#14556087C2211yescharacteristic
38C2×#14556084—21no—
39C22×C4⋊Dic71C2211yescharacteristic
40C22×C4⋊Dic71C2211yescharacteristic
41C22×C4⋊Dic71C2211yescharacteristic
42#17986408C2218yescomplemented
43#17986341C2218yescomplemented
44#17986335C2218yescomplemented
45#17986330C2218yescomplemented
46#17986330C2218yescomplemented
47#17986307C2218yescomplemented
48#17986285C2218yescomplemented
49#17986257C2218yescomplemented
50#17986240C2218yescomplemented
51#17986107C2218yescomplemented
52#17986041C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556060C2211yescharacteristic
62C2×#14556060C2218yescomplemented
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556053C2211yescharacteristic
67C2×#14556053C2211yescharacteristic
68C2×#14556053C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yes—
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×Dic142C2311yescharacteristic
80C23×Dic71—21no—
81C23×Dic71—21no—
82C23×Dic71—21no—
83C2×Dic284—24no—
84C2×Dic284C2314yes—
85#14556128—22no—
86#14556128C2314yes—
87#14556121—28no—
88#14556120—22no—
89#14556120C2314yes—
90#14556119—28no—
91#14556118—28no—
92#14556109—28no—
93#14556107—22no—
94#14556107—22no—
95#14556107—22no—
96#14556107—22no—
97#14556107C2314yes—
98#14556107C2314yes—
99#14556107C2314yes—
100#14556107C2314yes—
101#14556105—28no—
102#14556105—28no—
103C4×Dic142—22no—
104C4×Dic142—22no—
105C4×Dic142C2314yes—
106C4×Dic142C2314yes—
107D4×Dic71—28no—
108#14556087—22no—
109#14556087C2314yes—
110#14556084—28no—
111C2×C4⋊Dic71—22no—
112C2×C4⋊Dic71—22no—
113C2×C4⋊Dic71—22no—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71C2314yes—
119C2×C4⋊Dic71C2314yes—
120C2×C4⋊Dic71C2314yes—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143#14556062C2314yes—
144#14556062C2314yes—
145#14556062C2314yes—
146#14556060C2314yes—
147#14556060C2314yes—
148#14556060C2314yes—
149#14556060C2314yes—
150#14556060C2314yes—
151#14556060C2314yes—
152#14556053C2314yes—
153#14556053C2314yes—
154#14556053C2314yes—
155#14556053C2314yes—
156#14556053C2314yes—
157#14556053C2314yes—
158C22×D4×C71D411yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C2×M16×C71—24no—
162C2×M16×C71C2314yes—
163C22×C8×C71—24no—
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2314yes—
168C22×C8×C71C2311yescharacteristic
169C4×D4×C71D414yes—
170C4×D4×C71C2314yes—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C4⋊C8×C71C2314yes—
176C22⋊C8×C71C2314yes—
177C22⋊C8×C71C2314yes—
178#97×C71C2314yes—
179C2×Dic142—22no—
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—21no—
184C2×Dic142—21no—
185C2×Dic142—24no—
186C2×Dic142—82no—
187C2×Dic142C2412yes—
188C2×Dic142C2412yes—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—24no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—24no—
199C22×Dic71—24no—
200C22×Dic71—44no—
201C22×Dic71—82no—
202C22×Dic71—82no—
203Dic284—28no—
204C4⋊Dic71—21no—
205C4⋊Dic71—21no—
206C4⋊Dic71—24no—
207C4⋊Dic71—24no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71—21no—
211C4⋊Dic71—24no—
212C4⋊Dic71—24no—
213C4⋊Dic71—21no—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228C22⋊Dic71—24no—
229C22⋊Dic71—24no—
230C22⋊Dic71—24no—
231C22⋊Dic71—24no—
232C22⋊Dic71—24no—
233C4×Dic71—24no—
234C4×Dic71—24no—
235C4×Dic71—24no—
236C24×C71C2×D411yescharacteristic
237C24×C71C2×D411yescharacteristic
238C2×D4×C71—24no—
239C2×D4×C71C2×D414yes—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D412yes—
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2412yes—
252C22×C4×C71C2411yescharacteristic
253M16×C71—28no—
254C2×C8×C71—22no—
255C2×C8×C71—22no—
256C2×C8×C71—22no—
257C2×C8×C71—28no—
258C2×C8×C71#4114yes—
259C2×C8×C71C2412yes—
260C2×C8×C71C2412yes—
261C2×C8×C71C2412yes—
262C2×C8×C71C2412yes—
263C4⋊C4×C71C2×D414yes—
264C22⋊C4×C71C2×D414yes—
265C22⋊C4×C71C2×D414yes—
266C42×C71C2×D412yes—
267C42×C71C2412yes—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71#13714yes—
274C23×C71C22×D412yes—
275C23×C71C22×D412yes—
276C23×C71C22×D411yescharacteristic
277D4×C71—28no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—24no—
283C2×C4×C71—24no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71C22×D412yes—
289C2×C4×C71C22×D412yes—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D412yes—
292C2×C4×C71C22×D411yescharacteristic
293C2×C4×C71C2×#4112yes—
294C2×C4×C712−1+412yes—
295C2×C4×C71C2511yescharacteristic
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—42no—
305C2×Dic71—42no—
306C2×Dic71—48no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71—42no—
310C2×Dic71—42no—
311C2×Dic71—42no—
312C2×Dic71—42no—
313C2×Dic71—84no—
314C2×Dic71—84no—
315Dic142—22no—
316Dic142—22no—
317Dic142—22no—
318Dic142—22no—
319Dic142—42no—
320Dic142—42no—
321Dic142—84no—
322C8×C71—22no—
323C8×C71—22no—
324C8×C71—22no—
325C8×C71C2×#4114yes—
326C22×C71—28no—
327C22×C71—22no—
328C22×C71—22no—
329C22×C71—22no—
330C22×C71—22no—
331C22×C71—22no—
332C22×C71—44no—
333C22×C71#54712yes—
334C22×C71C2×#13714yes—
335C22×C71C2×#13712yes—
336C22×C71#57712yes—
337C22×C71C23×D411yescharacteristic
338C4×C71—22no—
339C4×C71—22no—
340C4×C71—22no—
341C4×C71—22no—
342C4×C71#54712yes—
343C4×C71C22×#4111yescharacteristic
344C4×C71C2×2−1+411yescharacteristic
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348Dic71—42no—
349Dic71—42no—
350Dic71—42no—
351Dic71—42no—
352Dic71—42no—
353C2×#3344—711nomaximal, Sylow
354C2×C71—24no—
355C2×C71—42no—
356C2×C71#334414yescomplemented
357C2×C71C2×#54711yescharacteristic
358C2×C71C22×#13711yescharacteristic
359C2×C71C2×#57711yescharacteristic
360C2×#554—711no—
361C2×#552—711no—
362#3344—7116no—
363C2×#501—711no—
364C2×#484—711no—
365C2×#485—711no—
366C2×#483—711no—
367C2×#483—711no—
368C2×#479—711no—
369C2×#475—711no—
370C2×#470—711no—
371C2×#467—711no—
372C2×#441—711no—
373C2×#435D7111yescharacteristic
374C2×#428—711no—
375C22×#106—711no—
376C71C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—711no—
378C22×M16C2×D7111yescharacteristic
379C23×C8C2×D7111yescharacteristic
380#554—718no—
381#554—1424no—
382#552—718no—
383#552—1424no—
384C2×C4⋊Q8—711no—
385C2×#126—1421no—
386C2×#125—711no—
387C2×#125—1421no—
388C2×#125—1421no—
389C2×#123—1421no—
390C2×C22⋊Q8—711no—
391C2×C22⋊Q8—711no—
392C2×C22⋊Q8—711no—
393C2×C22⋊Q8—711no—
394C2×C22⋊Q8—1421no—
395C2×C22⋊Q8—1421no—
396C2×C4×Q8—711no—
397C2×C4×Q8—711no—
398C2×C4×D4—1421no—
399C2×C4×D4C2×D7111yescharacteristic
400C2×#117—711no—
401C2×#117—1421no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405#501—718no—
406#485—718no—
407#484—718no—
408#483—718no—
409#483—718no—
410#479—718no—
411#475—718no—
412#470—718no—
413#467—718no—
414#441—718no—
415#435C2×D7118yes—
416#428—718no—
417C2×#107—711no—
418C2×#107—711no—
419C2×#107—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×#106—711no—
424C2×#106—718no—
425C2×#106—711no—
426C2×#106—711no—
427C2×C4⋊C8C2×D7111yescharacteristic
428C2×#103—711no—
429C2×#103—711no—
430C2×#103—711no—
431C2×#103—711no—
432C2×#103—711no—
433C2×#103—711no—
434C2×C22⋊C8C2×D7111yescharacteristic
435C2×C22⋊C8C2×D7111yescharacteristic
436C2×#97C2×D7111yescharacteristic
437C22×Q8—711no—
438C22×Q8—711no—
439C22×Q8—1421no—
440C22×D4D28411yescharacteristic
441C23×C4—1421no—
442C23×C4—1421no—
443C23×C4—1421no—
444C23×C4C22×D7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C2×Q16—714no—
447C2×Q16—1424no—
448C2×M16—24no—
449C2×M16C22×D7114yes—
450C22×C8—24no—
451C22×C8C22×D7111yescharacteristic
452C22×C8C22×D7114yes—
453C22×C8C22×D7111yescharacteristic
454C22×C8C22×D7111yescharacteristic
455C22×C8C22×D7111yescharacteristic
456C4⋊Q8—714no—
457C4⋊Q8—1422no—
458#126—1428no—
459#125—714no—
460#125—1428no—
461#125—1428no—
462#125—1422no—
463#123—1428no—
464C22⋊Q8—714no—
465C22⋊Q8—714no—
466C22⋊Q8—714no—
467C22⋊Q8—714no—
468C22⋊Q8—1422no—
469C22⋊Q8—1422no—
470C22⋊Q8—1422no—
471C22⋊Q8—1422no—
472C22⋊Q8—1428no—
473C22⋊Q8—1428no—
474C4×Q8—714no—
475C4×Q8—714no—
476C4×Q8—1422no—
477C4×Q8—1422no—
478C4×D4—1428no—
479C4×D4D28414yes—
480C4×D4C22×D7114yes—
481#117—714no—
482#117—1422no—
483#117—1428no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—714no—
490C2×C4⋊C4—714no—
491C2×C4⋊C4—714no—
492C2×C4⋊C4—711no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1422no—
497C2×C4⋊C4—1422no—
498C2×C4⋊C4—1422no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4D28411yescharacteristic
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C22⋊C4—1421no—
513C2×C22⋊C4—1421no—
514C2×C22⋊C4D28411yescharacteristic
515C2×C22⋊C4D28411yescharacteristic
516C2×C42—1421no—
517C2×C42—1421no—
518C2×C42—1421no—
519C2×C42C22×D7111yescharacteristic
520#107—714no—
521#107—714no—
522#107—714no—
523#106—714no—
524#106—714no—
525#106—714no—
526#106—714no—
527#106—714no—
528#106—714no—
529C4⋊C8C22×D7114yes—
530#103—714no—
531#103—714no—
532#103—714no—
533#103—714no—
534#103—714no—
535#103—714no—
536C22⋊C8C22×D7114yes—
537C22⋊C8C22×D7114yes—
538#97C22×D7114yes—
539C24C2×D28411yescharacteristic
540C24C2×D28411yescharacteristic
541C2×Q8—5682no—
542C2×Q8—712no—
543C2×Q8—712no—
544C2×Q8—1422no—
545C2×Q8—1422no—
546C2×Q8—1422no—
547C2×Q8—1422no—
548C2×Q8—1421no—
549C2×Q8—1421no—
550C2×Q8—1424no—
551C2×D4—24no—
552C2×D4C2×D28414yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—2844no—
558C22×C4—5682no—
559C22×C4—5682no—
560C22×C4—1424no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1424no—
570C22×C4—1424no—
571C22×C4C2×D28412yes—
572C22×C4C2×D28412yes—
573C22×C4C2×D28411yescharacteristic
574C22×C4C2×D28411yescharacteristic
575C22×C4C2×D28411yescharacteristic
576C22×C4C2×D28411yescharacteristic
577C22×C4C23×D7112yes—
578C22×C4C23×D7112yes—
579C22×C4C23×D7111yescharacteristic
580Q16—1428no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1176586414yes—
587C2×C8C23×D7112yes—
588C2×C8C23×D7112yes—
589C2×C8C23×D7112yes—
590C2×C8C23×D7112yes—
591C4⋊C4—712no—
592C4⋊C4—712no—
593C4⋊C4—712no—
594C4⋊C4—712no—
595C4⋊C4—712no—
596C4⋊C4—712no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4—1424no—
601C4⋊C4—1424no—
602C4⋊C4—1424no—
603C4⋊C4—1424no—
604C4⋊C4—1424no—
605C4⋊C4—1421no—
606C4⋊C4—1421no—
607C4⋊C4—1424no—
608C4⋊C4—1424no—
609C4⋊C4—1421no—
610C4⋊C4—1421no—
611C4⋊C4—1421no—
612C4⋊C4—1424no—
613C4⋊C4—1421no—
614C4⋊C4—1424no—
615C4⋊C4C2×D28414yes—
616C22⋊C4—1424no—
617C22⋊C4—1424no—
618C22⋊C4—1424no—
619C22⋊C4—1424no—
620C22⋊C4—1424no—
621C22⋊C4C2×D28414yes—
622C22⋊C4C2×D28414yes—
623C42—1424no—
624C42—1424no—
625C42—1424no—
626C42C2×D28412yes—
627C42C23×D7112yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1455616114yes—
634C23C22×D28412yes—
635C23C22×D28412yes—
636C23C22×D28411yescharacteristic
637Q8—2842no—
638Q8—2842no—
639Q8—5684no—
640Q8—1422no—
641Q8—1422no—
642Q8—1422no—
643Q8—1422no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—2842no—
656C2×C4—2842no—
657C2×C4—2848no—
658C2×C4—2842no—
659C2×C4—2842no—
660C2×C4—2842no—
661C2×C4—2842no—
662C2×C4—2842no—
663C2×C4—2842no—
664C2×C4—5684no—
665C2×C4—5684no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1422no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4C22×D28412yes—
675C2×C4C22×D28412yes—
676C2×C4C22×D28412yes—
677C2×C4C22×D28412yes—
678C2×C4C22×D28411yescharacteristic
679C2×C4C2×#1176586412yes—
680C2×C4#1455617512yes—
681C2×C4C24×D7111yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1176586414yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1798665312yes—
694C22C2×#1455616114yes—
695C22C2×#1455616112yes—
696C22#1798681112yes—
697C22C23×D28411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—2842no—
703C4—2842no—
704C4—2842no—
705C4—2842no—
706C4—2842no—
707C4—2842no—
708C4—2842no—
709C4—2842no—
710C4#1798665312yes—
711C4C22×#1176586411yescharacteristic
712C4C2×#1455617511yescharacteristic
713C2—24no—
714C2—42no—
715C2#2260079714yesdirect product factor
716C2C2×#1798665311yescharacteristic
717C2C22×#1455616111yescharacteristic
718C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
hypercenterC2×#435D71
hypocenterC71C2×#3344
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #22600797C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986335C2semidirect
6. C2×#17986341C2semidirect
7. C2×#17986330C2semidirect
8. C2×#17986330C2semidirect
9. C2×#17986307C2semidirect
10. C2×#17986285C2semidirect
11. C2×#17986257C2semidirect
12. C2×#17986240C2semidirect
13. C2×#17986107C2semidirect
14. C2×#17986041C2semidirect
15. C22×#14556060C2semidirect
42. #17986408C22semidirect
43. #17986341C22semidirect
44. #17986335C22semidirect
45. #17986330C22semidirect
46. #17986330C22semidirect
47. #17986307C22semidirect
48. #17986285C22semidirect
49. #17986257C22semidirect
50. #17986240C22semidirect
51. #17986107C22semidirect
52. #17986041C22semidirect
62. C2×#14556060C22semidirect
356. C2×C71#3344semidirect
376. C71C2×#3344semidirect
715. C2#22600797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867062
C2×#179866892
#226007972
C2×#179864082
C2×#179863352
C2×#179863412
C2×#179863302
C2×#179863072
C2×#179862852
C2×#179862572
C2×#179862402
C2×#179861072
C2×#179860412
C22×#145560602
C2×#435×C712
C2×#334471