Finite Group Databasebeta

← C2×#22599632 #32869683

Subgroups — C2×#22599632 #32869683

Order 18176.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986627C211yesmaximal, characteristic, complemented
2#22599632C2116yesmaximal, direct product factor
3C2×#17986405C211yesmaximal, characteristic, complemented
4C2×#17986395C211yesmaximal, characteristic, complemented
5C2×#17986358C211yesmaximal, characteristic, complemented
6C2×#17986353C211yesmaximal, characteristic, complemented
7C2×#17986315C211yesmaximal, characteristic
8C2×#17986337C211yesmaximal, characteristic, complemented
9C2×#17986320C211yesmaximal, characteristic
10C2×#17986327C211yesmaximal, characteristic, complemented
11C2×#17986306C211yesmaximal, characteristic, complemented
12C2×#17986284C211yesmaximal, characteristic, complemented
13C2×#17986299C211yesmaximal, characteristic, complemented
14C2×#17986289C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#542×C71C211yesmaximal, characteristic
17#17986627—24no—
18#17986627C2218yescomplemented
19C2×#14556128C2211yescharacteristic
20C2×#14556128C2211yescharacteristic
21C2×#14556127—21no—
22C2×#14556120C2211yescharacteristic
23C2×#14556120C2211yescharacteristic
24C2×#14556119—21no—
25C2×#14556105—21no—
26C2×#14556105—21no—
27C2×#14556087C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29#17986405C2218yescomplemented
30#17986395C2218yescomplemented
31#17986358C2218yescomplemented
32#17986353C2218yescomplemented
33#17986337C2218yescomplemented
34#17986327C2218yescomplemented
35#17986320C2218yes—
36#17986315C2218yes—
37#17986306C2218yescomplemented
38#17986299C2218yescomplemented
39#17986289C2218yescomplemented
40#17986284C2218yescomplemented
41#17986060C2218yescomplemented
42C2×#14556061C2211yescharacteristic
43C2×#14556061C2211yescharacteristic
44C2×#14556059C2211yescharacteristic
45C2×#14556059C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#542×C71—24no—
65#542×C71C2218yes—
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C23×Dic71—21no—
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84#14556128—22no—
85#14556128—22no—
86#14556128C2314yes—
87#14556128C2314yes—
88#14556127—28no—
89#14556120—22no—
90#14556120—22no—
91#14556120C2314yes—
92#14556120C2314yes—
93#14556119—28no—
94#14556105—28no—
95#14556105—28no—
96#14556087—22no—
97#14556087C2314yes—
98C2×C4⋊Dic71—22no—
99C2×C4⋊Dic71—21no—
100C2×C4⋊Dic71—21no—
101C2×C4⋊Dic71—21no—
102C2×C4⋊Dic71C2314yes—
103C2×C4⋊Dic71C2311yescharacteristic
104C2×C4⋊Dic71C2311yescharacteristic
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2311yescharacteristic
107C2×Dic71⋊C4—21no—
108C2×Dic71⋊C4—21no—
109C2×Dic71⋊C4—21no—
110C2×Dic71⋊C4—21no—
111C2×C22⋊Dic71—21no—
112C2×C4×Dic71—21no—
113#14556061C2314yes—
114#14556061C2314yes—
115#14556059C2314yes—
116#14556059C2314yes—
117#14556059C2314yes—
118#14556059C2314yes—
119#14556059C2314yes—
120#14556059C2314yes—
121C4⋊(C71⋊C8)C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123#14556052C2314yes—
124#14556052C2314yes—
125#14556052C2314yes—
126#14556052C2314yes—
127#14556049C2314yes—
128#14556049C2314yes—
129#14556049C2314yes—
130#14556049C2314yes—
131C22⋊(C71⋊C8)C2314yes—
132C22⋊(C71⋊C8)C2314yes—
133#14556039C2314yes—
134C4×C71⋊C8C2314yes—
135C22×Q8×C71—21no—
136C22×Q8×C71C2311yescharacteristic
137C22×D4×C71—21no—
138C22×D4×C71C2311yescharacteristic
139C23×C4×C71—21no—
140C23×C4×C71C2311yescharacteristic
141C4⋊Q8×C71—22no—
142C4⋊Q8×C71C2314yes—
143#126×C71—28no—
144#124×C71—28no—
145#124×C71—22no—
146#124×C71C2314yes—
147#123×C71—28no—
148C22⋊Q8×C71—22no—
149C22⋊Q8×C71—28no—
150C22⋊Q8×C71C2314yes—
151#121×C71—22no—
152#121×C71C2314yes—
153C4×Q8×C71—22no—
154C4×Q8×C71C2314yes—
155C4×D4×C71—22no—
156C4×D4×C71C2314yes—
157#117×C71D414yes—
158#117×C71C2314yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71D411yescharacteristic
163C2×C4⋊C4×C71D411yescharacteristic
164C2×C4⋊C4×C71C2311yescharacteristic
165C2×C4⋊C4×C71C2311yescharacteristic
166C2×C22⋊C4×C71—21no—
167C2×C22⋊C4×C71—21no—
168C2×C22⋊C4×C71—21no—
169C2×C22⋊C4×C71—21no—
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C2×Dic142—24no—
177C2×Dic142—24no—
178C2×Dic142—82no—
179C2×Dic142—82no—
180C22×Dic71—21no—
181C22×Dic71—21no—
182C22×Dic71—21no—
183C22×Dic71—21no—
184C22×Dic71—24no—
185C22×Dic71—82no—
186C2×C71⋊C8—22no—
187C2×C71⋊C8—22no—
188C2×C71⋊C8—22no—
189C2×C71⋊C8—22no—
190C2×C71⋊C8C2412yes—
191C2×C71⋊C8C2412yes—
192C2×C71⋊C8C2412yes—
193C2×C71⋊C8C2412yes—
194C4⋊Dic71—24no—
195C4⋊Dic71—21no—
196C4⋊Dic71—21no—
197C4⋊Dic71—24no—
198C4⋊Dic71—24no—
199C4⋊Dic71—21no—
200C4⋊Dic71—21no—
201C4⋊Dic71C2412yes—
202C4⋊Dic71C2412yes—
203C4⋊Dic71C2412yes—
204C4⋊Dic71C2412yes—
205Dic71⋊C4—24no—
206Dic71⋊C4—24no—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209C22⋊Dic71—24no—
210C4×Dic71—24no—
211C24×C71—21no—
212C24×C71C2×D411yescharacteristic
213C2×Q8×C71—21no—
214C2×Q8×C71—24no—
215C2×Q8×C71—22no—
216C2×Q8×C71—22no—
217C2×Q8×C71—82no—
218C2×Q8×C71C2412yes—
219C2×D4×C71—24no—
220C2×D4×C71—21no—
221C2×D4×C71—22no—
222C2×D4×C71—22no—
223C2×D4×C71—82no—
224C2×D4×C71C2412yes—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—24no—
231C22×C4×C71—82no—
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2411yescharacteristic
240C4⋊C4×C71—24no—
241C4⋊C4×C71—24no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—21no—
244C4⋊C4×C71—21no—
245C4⋊C4×C71C2×D414yes—
246C4⋊C4×C71C2×D414yes—
247C4⋊C4×C71C2412yes—
248C4⋊C4×C71C2412yes—
249C22⋊C4×C71—24no—
250C22⋊C4×C71—24no—
251C22⋊C4×C71—24no—
252C22⋊C4×C71—24no—
253C22⋊C4×C71—24no—
254C22⋊C4×C71C2×D414yes—
255C22⋊C4×C71C2×D414yes—
256C42×C71—24no—
257C42×C71C2×D412yes—
258C42×C71C2×D412yes—
259C42×C71C2412yes—
260C42×C71C2412yes—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—22no—
264C23×C71—22no—
265C23×C71—42no—
266C23×C71—42no—
267C23×C71—42no—
268C23×C71C22×D412yes—
269C23×C71C22×D411yescharacteristic
270Q8×C71—22no—
271Q8×C71—22no—
272Q8×C71—42no—
273Q8×C71—84no—
274D4×C71—22no—
275D4×C71—22no—
276D4×C71—42no—
277D4×C71—84no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
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—84no—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D412yes—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D411yescharacteristic
299C2×C4×C712−1+412yes—
300C2×C4×C712−1+412yes—
301C2×C4×C71C2511yescharacteristic
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—42no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71—42no—
310C2×Dic71—84no—
311Dic142—84no—
312Dic142—84no—
313C71⋊C8—22no—
314C71⋊C8—22no—
315C71⋊C8—22no—
316C71⋊C8—22no—
317C22×C71—22no—
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—44no—
321C22×C71—42no—
322C22×C71—42no—
323C22×C71—42no—
324C22×C71—84no—
325C22×C71#53612yes—
326C22×C71#57712yes—
327C22×C71#57712yes—
328C22×C71C23×D411yescharacteristic
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71#53612yes—
338C4×C71C2×2−1+411yescharacteristic
339C4×C71C2×2−1+411yescharacteristic
340Dic71—42no—
341Dic71—42no—
342Dic71—42no—
343Dic71—42no—
344C2×#3244—711nomaximal, Sylow
345C2×C71—42no—
346C2×C71—82no—
347C2×C71#324414yescomplemented
348C2×C71C2×#53611yescharacteristic
349C2×C71C2×#57711yescharacteristic
350C2×C71C2×#57711yescharacteristic
351C2×#544—711no—
352C2×#542D7111yescharacteristic
353#3244—7116no—
354C2×#501—711no—
355C2×#498—711no—
356C2×#489—711no—
357C2×#488—711no—
358C2×#481—711no—
359C2×#485—711no—
360C2×#482—711no—
361C2×#483—711no—
362C2×#479—711no—
363C2×#475—711no—
364C2×#478—711no—
365C2×#476—711no—
366C2×#433—711no—
367C71C2×#324411yescharacteristic, complemented, Sylow
368#544—718no—
369#544—1424no—
370#542—24no—
371#542C2×D7118yes—
372C2×C4⋊Q8—711no—
373C2×C4⋊Q8—711no—
374C2×C4⋊Q8—1421no—
375C2×C4⋊Q8C2×D7111yescharacteristic
376C2×#126—21no—
377C2×#125—711no—
378C2×#125—711no—
379C2×#125—1421no—
380C2×#124—21no—
381C2×#124C2×D7111yescharacteristic
382C2×#123—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—1421no—
385C2×C22⋊Q8—1421no—
386C2×C22⋊Q8C2×D7111yescharacteristic
387C2×#121C2×D7111yescharacteristic
388C2×C4×Q8C2×D7111yescharacteristic
389C2×C4×D4C2×D7111yescharacteristic
390C2×#117—711no—
391C2×#117C2×D7111yescharacteristic
392C22×C4⋊C4—711no—
393#501—718no—
394#498—718no—
395#489—718no—
396#488—718no—
397#485—718no—
398#483—718no—
399#482—718no—
400#481—718no—
401#479—718no—
402#478—718no—
403#476—718no—
404#475—718no—
405#433—718no—
406C2×#107—711no—
407C2×#107—711no—
408C2×#106—711no—
409C2×#106—711no—
410C2×#106—711no—
411C2×#106—711no—
412C2×#106—711no—
413C2×#106—711no—
414C2×C4⋊C8—711no—
415C2×C4⋊C8—711no—
416C2×#103—711no—
417C2×#103—711no—
418C2×#103—711no—
419C2×#103—711no—
420C2×#102—711no—
421C2×#102—711no—
422C2×#102—711no—
423C2×#102—711no—
424C2×C22⋊C8—711no—
425C2×C22⋊C8—711no—
426C2×#97—711no—
427C2×C4×C8—711no—
428C22×Q8—21no—
429C22×Q8—1421no—
430C22×Q8—1421no—
431C22×Q8C22×D7111yescharacteristic
432C22×D4—21no—
433C22×D4C22×D7111yescharacteristic
434C23×C4—21no—
435C23×C4—1421no—
436C23×C4C22×D7111yescharacteristic
437C22×C8—711no—
438C22×C8—711no—
439C22×C8—711no—
440C22×C8—711no—
441C4⋊Q8—22no—
442C4⋊Q8—714no—
443C4⋊Q8—714no—
444C4⋊Q8—1428no—
445C4⋊Q8—1422no—
446C4⋊Q8—1422no—
447C4⋊Q8C22×D7114yes—
448#126—28no—
449#125—714no—
450#125—714no—
451#125—1428no—
452#125—1422no—
453#125—1422no—
454#124—28no—
455#124—22no—
456#124C22×D7114yes—
457#123—28no—
458C22⋊Q8—22no—
459C22⋊Q8—28no—
460C22⋊Q8—1428no—
461C22⋊Q8—1428no—
462C22⋊Q8C22×D7114yes—
463#121—22no—
464#121C22×D7114yes—
465C4×Q8—22no—
466C4×Q8C22×D7114yes—
467C4×D4—22no—
468C4×D4C22×D7114yes—
469#117—714no—
470#117—1422no—
471#117C22⋊D7114yes—
472#117C22×D7114yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—711no—
477C2×C4⋊C4—711no—
478C2×C4⋊C4—714no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—711no—
481C2×C4⋊C4—1421no—
482C2×C4⋊C4—1422no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4—1421no—
486C2×C4⋊C4—1421no—
487C2×C4⋊C4—1421no—
488C2×C4⋊C4—1421no—
489C2×C4⋊C4C22⋊D7111yescharacteristic
490C2×C4⋊C4C22⋊D7111yescharacteristic
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1421no—
499C2×C22⋊C4C22⋊D7111yescharacteristic
500C2×C22⋊C4C22⋊D7111yescharacteristic
501C2×C42—21no—
502C2×C42—1421no—
503C2×C42C22×D7111yescharacteristic
504C2×C42C22×D7111yescharacteristic
505#107—714no—
506#107—714no—
507#106—714no—
508#106—714no—
509#106—714no—
510#106—714no—
511#106—714no—
512#106—714no—
513C4⋊C8—714no—
514C4⋊C8—714no—
515#103—714no—
516#103—714no—
517#103—714no—
518#103—714no—
519#102—714no—
520#102—714no—
521#102—714no—
522#102—714no—
523C22⋊C8—714no—
524C22⋊C8—714no—
525#97—714no—
526C4×C8—714no—
527C24—21no—
528C24C2×C22⋊D7111yescharacteristic
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—5682no—
535C2×Q8—5682no—
536C2×Q8—1424no—
537C2×Q8—1424no—
538C2×Q8C23×D7112yes—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—82no—
544C2×D4C23×D7112yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—5682no—
553C22×C4—1421no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1424no—
558C22×C4C2×C22⋊D7112yes—
559C22×C4C2×C22⋊D7111yescharacteristic
560C22×C4C2×C22⋊D7111yescharacteristic
561C22×C4C2×C22⋊D7111yescharacteristic
562C22×C4C2×C22⋊D7111yescharacteristic
563C22×C4C2×C22⋊D7111yescharacteristic
564C22×C4C23×D7112yes—
565C22×C4C23×D7111yescharacteristic
566C2×C8—712no—
567C2×C8—712no—
568C2×C8—712no—
569C2×C8—712no—
570C2×C8—1422no—
571C2×C8—1422no—
572C2×C8—1422no—
573C2×C8—1422no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—712no—
580C4⋊C4—712no—
581C4⋊C4—712no—
582C4⋊C4—712no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4—1424no—
586C4⋊C4—1424no—
587C4⋊C4—1424no—
588C4⋊C4—1421no—
589C4⋊C4—1421no—
590C4⋊C4—1421no—
591C4⋊C4—1421no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4C2×C22⋊D7114yes—
595C4⋊C4C2×C22⋊D7114yes—
596C4⋊C4C23×D7112yes—
597C4⋊C4C23×D7112yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—1424no—
604C22⋊C4C2×C22⋊D7114yes—
605C22⋊C4C2×C22⋊D7114yes—
606C42—24no—
607C42—1424no—
608C42C2×C22⋊D7112yes—
609C42C2×C22⋊D7112yes—
610C42C23×D7112yes—
611C42C23×D7112yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C22⋊D7112yes—
620C23C22×C22⋊D7111yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—5684no—
626Q8—5684no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—84no—
646C2×C4—2842no—
647C2×C4—2842no—
648C2×C4—2842no—
649C2×C4—2842no—
650C2×C4—5684no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4C22×C22⋊D7112yes—
656C2×C4C22×C22⋊D7112yes—
657C2×C4C22×C22⋊D7112yes—
658C2×C4C22×C22⋊D7112yes—
659C2×C4C22×C22⋊D7112yes—
660C2×C4C22×C22⋊D7111yescharacteristic
661C2×C4#1455617512yes—
662C2×C4#1455617512yes—
663C2×C4C24×D7111yescharacteristic
664C8—1422no—
665C8—1422no—
666C8—1422no—
667C8—1422no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#1798657012yes—
677C22#1798680712yes—
678C22#1798681012yes—
679C22C23×C22⋊D7111yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2842no—
689C4—2842no—
690C4—2842no—
691C4—2842no—
692C4#1798657012yes—
693C4C2×#1455617511yescharacteristic
694C4C2×#1455617511yescharacteristic
695C2—42no—
696C2—82no—
697C2#2259963214yesdirect product factor
698C2C2×#1798657011yescharacteristic
699C2C2×#1798680711yescharacteristic
700C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
prime radicalC2×#121×C71C22
hypercenterC2×#542D71
hypocenterC71C2×#3244
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17986627C2semidirect
2. #22599632C2direct (N × H)
3. C2×#17986405C2semidirect
4. C2×#17986395C2semidirect
5. C2×#17986358C2semidirect
6. C2×#17986353C2semidirect
8. C2×#17986337C2semidirect
10. C2×#17986327C2semidirect
11. C2×#17986306C2semidirect
12. C2×#17986284C2semidirect
13. C2×#17986299C2semidirect
14. C2×#17986289C2semidirect
15. C2×#17986060C2semidirect
18. #17986627C22semidirect
29. #17986405C22semidirect
30. #17986395C22semidirect
31. #17986358C22semidirect
32. #17986353C22semidirect
33. #17986337C22semidirect
34. #17986327C22semidirect
37. #17986306C22semidirect
38. #17986299C22semidirect
39. #17986289C22semidirect
40. #17986284C22semidirect
41. #17986060C22semidirect
347. C2×C71#3244semidirect
367. C71C2×#3244semidirect
697. C2#22599632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866272
#225996322
C2×#179864052
C2×#179863952
C2×#179863582
C2×#179863532
C2×#179863152
C2×#179863372
C2×#179863202
C2×#179863272
C2×#179863062
C2×#179862842
C2×#179862992
C2×#179862892
C2×#179860602
C2×#542×C712
C2×#324471