Finite Group Databasebeta

← C2×#22599623 #32869673

Subgroups — C2×#22599623 #32869673

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×#17986620C211yesmaximal, characteristic
2#22599623C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986402C211yesmaximal, characteristic, complemented
5C2×#17986361C211yesmaximal, characteristic, complemented
6C2×#17986356C211yesmaximal, characteristic, complemented
7C2×#17986334C211yesmaximal, characteristic, complemented
8C2×#17986340C211yesmaximal, characteristic, complemented
9C2×#17986323C211yesmaximal, characteristic
10C2×#17986312C211yesmaximal, characteristic
11C2×#17986303C211yesmaximal, characteristic, complemented
12C2×#17986291C211yesmaximal, characteristic, complemented
13C2×#17986296C211yesmaximal, characteristic, complemented
14C2×#17986276C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#544×C71C211yesmaximal, characteristic, complemented
17#17986620—24no—
18#17986620C2218yes—
19C2×#14556128C2211yescharacteristic
20C2×#14556123—21no—
21C2×#14556116C2211yescharacteristic
22C2×#14556114—21no—
23C2×#14556110—21no—
24C2×#14556107C2211yescharacteristic
25C2×#14556106—21no—
26C2×#14556102C2211yescharacteristic
27C2×C4×Dic142C2211yescharacteristic
28C2×C4×D284C2211yescharacteristic
29#17986409C2218yescomplemented
30#17986402C2218yescomplemented
31#17986361C2218yescomplemented
32#17986356C2218yescomplemented
33#17986340C2218yescomplemented
34#17986334C2218yescomplemented
35#17986323C2218yes—
36#17986312C2218yes—
37#17986303C2218yescomplemented
38#17986296C2218yescomplemented
39#17986291C2218yescomplemented
40#17986276C2218yescomplemented
41#17986060C2218yescomplemented
42C2×#14556061C2211yescharacteristic
43C2×#14556061C2211yescharacteristic
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#544×C71—24no—
65#544×C71C2218yescomplemented
66C2×C4⋊Q8×C71—21no—
67C2×C4⋊Q8×C71C2211yescharacteristic
68C2×C4⋊Q8×C71C2211yescharacteristic
69C2×#125×C71—21no—
70C2×#125×C71C2211yescharacteristic
71C2×#125×C71C2211yescharacteristic
72C2×C22⋊Q8×C71—21no—
73C2×C22⋊Q8×C71—21no—
74C2×#117×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84C22×C71⋊C8C2311yescharacteristic
85C22×C71⋊C8C2311yescharacteristic
86#14556128—22no—
87#14556128C2314yes—
88#14556123—28no—
89#14556116—22no—
90#14556116C2314yes—
91#14556114—28no—
92#14556110—28no—
93#14556107—22no—
94#14556107C2314yes—
95#14556106—28no—
96#14556102—22no—
97#14556102C2314yes—
98C4×Dic142—22no—
99C4×Dic142C2314yes—
100C4×D284—22no—
101C4×D284C2314yes—
102C2×C4⋊Dic71—21no—
103C2×C4⋊Dic71C2311yescharacteristic
104C2×C4⋊Dic71C2311yescharacteristic
105C2×Dic71⋊C4—21no—
106C2×Dic71⋊C4—21no—
107C2×C22⋊Dic71—21no—
108C2×(C2×D71)⋊C4—21no—
109C2×(C2×D71)⋊C4—21no—
110C2×(C2×D71)⋊C4—21no—
111C2×(C2×D71)⋊C4—21no—
112C2×C4×Dic71—21no—
113#14556061C2314yes—
114#14556061C2314yes—
115#14556061C2314yes—
116#14556061C2314yes—
117#14556061C2314yes—
118#14556061C2314yes—
119#14556059C2314yes—
120#14556059C2314yes—
121C4⋊(C71⋊C8)C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123#14556051C2314yes—
124#14556051C2314yes—
125#14556051C2314yes—
126#14556051C2314yes—
127#14556048C2314yes—
128#14556048C2314yes—
129#14556048C2314yes—
130#14556048C2314yes—
131C22⋊(C71⋊C8)C2314yes—
132C22⋊(C71⋊C8)C2314yes—
133#14556039C2314yes—
134C4×C71⋊C8C2314yes—
135C22×Q8×C71—21no—
136C22×Q8×C71—21no—
137C23×C4×C71—21no—
138C23×C4×C71C2311yescharacteristic
139C4⋊Q8×C71—28no—
140C4⋊Q8×C71—22no—
141C4⋊Q8×C71—22no—
142C4⋊Q8×C71C2314yes—
143C4⋊Q8×C71C2314yes—
144#125×C71—28no—
145#125×C71—22no—
146#125×C71—22no—
147#125×C71C2314yes—
148#125×C71C2314yes—
149C22⋊Q8×C71—28no—
150C22⋊Q8×C71—28no—
151#117×C71—22no—
152#117×C71D414yes—
153#117×C71C2314yes—
154#117×C71C2314yes—
155C2×C4⋊C4×C71—21no—
156C2×C4⋊C4×C71—22no—
157C2×C4⋊C4×C71—21no—
158C2×C4⋊C4×C71—21no—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71D411yescharacteristic
164C2×C4⋊C4×C71D411yescharacteristic
165C2×C4⋊C4×C71C2314yes—
166C2×C4⋊C4×C71C2311yescharacteristic
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C23×D71—21no—
177C2×Dic142—22no—
178C2×Dic142—22no—
179C2×Dic142—21no—
180C2×Dic142—24no—
181C2×Dic142—82no—
182C2×Dic142C2412yes—
183C2×D284—22no—
184C2×D284—22no—
185C2×D284—21no—
186C2×D284C2412yes—
187C2×C22⋊D71—24no—
188C2×C22⋊D71—82no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C2×C4×D71—24no—
193C2×C4×D71—82no—
194C2×C71⋊C8—22no—
195C2×C71⋊C8—22no—
196C2×C71⋊C8—22no—
197C2×C71⋊C8—22no—
198C2×C71⋊C8C2412yes—
199C2×C71⋊C8C2412yes—
200C2×C71⋊C8C2412yes—
201C2×C71⋊C8C2412yes—
202C4⋊Dic71—24no—
203C4⋊Dic71—21no—
204C4⋊Dic71—21no—
205C4⋊Dic71C2412yes—
206C4⋊Dic71C2412yes—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209C22⋊Dic71—24no—
210(C2×D71)⋊C4—24no—
211(C2×D71)⋊C4—24no—
212(C2×D71)⋊C4—24no—
213(C2×D71)⋊C4—24no—
214C4×Dic71—24no—
215C24×C71C2×D411yescharacteristic
216C2×Q8×C71—24no—
217C2×Q8×C71—24no—
218C2×Q8×C71—82no—
219C2×Q8×C71—82no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71—21no—
226C22×C4×C71—24no—
227C22×C4×C71—82no—
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2×D411yescharacteristic
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D412yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2411yescharacteristic
236C4⋊C4×C71—24no—
237C4⋊C4×C71—21no—
238C4⋊C4×C71—21no—
239C4⋊C4×C71—24no—
240C4⋊C4×C71—24no—
241C4⋊C4×C71—24no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—24no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71—21no—
247C4⋊C4×C71C2×D414yes—
248C4⋊C4×C71C2×D414yes—
249C4⋊C4×C71C2412yes—
250C4⋊C4×C71C2412yes—
251C4⋊C4×C71C2412yes—
252C4⋊C4×C71C2412yes—
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×C71C22×D412yes—
265C23×C71C22×D411yescharacteristic
266C22×D71—22no—
267C22×D71—42no—
268C22×D71—42no—
269C22×D71—42no—
270Q8×C71—84no—
271Q8×C71—84no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—24no—
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—42no—
285C2×C4×C71—42no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71—84no—
289C2×C4×C71C22×D412yes—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D412yes—
292C2×C4×C71C22×D412yes—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D411yescharacteristic
295C2×C4×C712−1+412yes—
296C2×C4×C712−1+412yes—
297C2×C4×C71C2511yescharacteristic
298C22⋊D71—84no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305D284—22no—
306D284—22no—
307D284—42no—
308C4×D71—84no—
309Dic142—22no—
310Dic142—22no—
311Dic142—42no—
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#53612yes—
322C22×C71#57612yes—
323C22×C71#57812yes—
324C22×C71C23×D411yescharacteristic
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—42no—
328C2×D71—84no—
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—42no—
338C4×C71#53612yes—
339C4×C71C2×2−1+411yescharacteristic
340C4×C71C2×2−1+411yescharacteristic
341Dic71—42no—
342Dic71—42no—
343Dic71—42no—
344C2×#3243—711nomaximal, Sylow
345C2×C71—42no—
346C2×C71#324314yescomplemented
347C2×C71C2×#53611yescharacteristic
348C2×C71C2×#57611yescharacteristic
349C2×C71C2×#57811yescharacteristic
350D71—82no—
351C2×#544D7111yescharacteristic, complemented
352C2×#542—711no—
353#3243—7116no—
354C2×#501—711no—
355C2×#500—711no—
356C2×#489—711no—
357C2×#488—711no—
358C2×#484—711no—
359C2×#485—711no—
360C2×#482—711no—
361C2×#480—711no—
362C2×#479—711no—
363C2×#477—711no—
364C2×#478—711no—
365C2×#474—711no—
366C2×#433—711no—
367C71C2×#324311yescharacteristic, complemented, Sylow
368#544—24no—
369#544C2×D7118yescomplemented
370#542—718no—
371#542—1424no—
372C2×C4⋊Q8—21no—
373C2×C4⋊Q8—711no—
374C2×C4⋊Q8C2×D7111yescharacteristic
375C2×C4⋊Q8C2×D7111yescharacteristic
376C2×#126—1421no—
377C2×#125—21no—
378C2×#125C2×D7111yescharacteristic
379C2×#125C2×D7111yescharacteristic
380C2×#124—711no—
381C2×#124—1421no—
382C2×#123—1421no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—711no—
386C2×C22⋊Q8—1421no—
387C2×#121—711no—
388C2×C4×Q8—711no—
389C2×C4×D4—711no—
390C2×#117C2×D7111yescharacteristic
391C2×#117C2×D7111yescharacteristic
392C22×C4⋊C4C2×D7111yescharacteristic
393#501—718no—
394#500—718no—
395#489—718no—
396#488—718no—
397#485—718no—
398#484—718no—
399#482—718no—
400#480—718no—
401#479—718no—
402#478—718no—
403#477—718no—
404#474—718no—
405#433—718no—
406C2×#107—711no—
407C2×#107—711no—
408C2×#107—711no—
409C2×#107—711no—
410C2×#107—711no—
411C2×#107—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—21no—
430C22×Q8—711no—
431C22×Q8—1421no—
432C22×D4—711no—
433C22×D4—1421no—
434C23×C4—21no—
435C23×C4—1421no—
436C23×C4C22×D7111yescharacteristic
437C22×C8—711no—
438C22×C8—711no—
439C22×C8—711no—
440C22×C8—711no—
441C4⋊Q8—28no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—714no—
445C4⋊Q8—1422no—
446C4⋊Q8C22×D7114yes—
447C4⋊Q8C22×D7114yes—
448#126—1428no—
449#125—28no—
450#125—22no—
451#125—22no—
452#125C22×D7114yes—
453#125C22×D7114yes—
454#124—714no—
455#124—1428no—
456#124—1422no—
457#123—1428no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—714no—
461C22⋊Q8—1422no—
462C22⋊Q8—1428no—
463#121—714no—
464#121—1422no—
465C4×Q8—714no—
466C4×Q8—1422no—
467C4×D4—714no—
468C4×D4—1422no—
469#117—22no—
470#117C22⋊D7114yes—
471#117C22×D7114yes—
472#117C22×D7114yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—711no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4—1421no—
486C2×C4⋊C4C22⋊D7111yescharacteristic
487C2×C4⋊C4C22⋊D7111yescharacteristic
488C2×C4⋊C4C22×D7111yescharacteristic
489C2×C4⋊C4C22×D7111yescharacteristic
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1421no—
495C2×C22⋊C4—1421no—
496C2×C22⋊C4—1421no—
497C2×C22⋊C4—1421no—
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#107—714no—
508#107—714no—
509#107—714no—
510#107—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—1421no—
528C24C2×C22⋊D7111yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—5682no—
534C2×Q8—712no—
535C2×Q8—1422no—
536C2×Q8—1422no—
537C2×Q8—1421no—
538C2×Q8—1424no—
539C2×D4—5682no—
540C2×D4—712no—
541C2×D4—1424no—
542C2×D4—1421no—
543C2×D4—1422no—
544C2×D4—1422no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—5682no—
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—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—712no—
586C4⋊C4—712no—
587C4⋊C4—1424no—
588C4⋊C4—1424no—
589C4⋊C4—1421no—
590C4⋊C4—1421no—
591C4⋊C4—1424no—
592C4⋊C4C2×C22⋊D7114yes—
593C4⋊C4C2×C22⋊D7114yes—
594C4⋊C4C23×D7112yes—
595C4⋊C4C23×D7112yes—
596C4⋊C4C23×D7112yes—
597C4⋊C4C23×D7112yes—
598C22⋊C4—24no—
599C22⋊C4—1424no—
600C22⋊C4—1424no—
601C22⋊C4—1424no—
602C22⋊C4—1424no—
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—2842no—
616C23—2842no—
617C23—2842no—
618C23—1422no—
619C23C22×C22⋊D7112yes—
620C23C22×C22⋊D7111yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—2842no—
624Q8—5684no—
625Q8—1422no—
626Q8—1422no—
627D4—2842no—
628D4—5684no—
629D4—1422no—
630D4—1422no—
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—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—2842no—
649C2×C4—2842no—
650C2×C4—2842no—
651C2×C4—5684no—
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#1455617612yes—
662C2×C4#1455617612yes—
663C2×C4C24×D7111yescharacteristic
664C8—1422no—
665C8—1422no—
666C8—1422no—
667C8—1422no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—2842no—
673C22—2842no—
674C22—2842no—
675C22—5684no—
676C22#1798657312yes—
677C22#1798680212yes—
678C22#1798681412yes—
679C22C23×C22⋊D7111yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—2842no—
690C4—2842no—
691C4—2842no—
692C4#1798657312yes—
693C4C2×#1455617611yescharacteristic
694C4C2×#1455617611yescharacteristic
695C2—42no—
696C2—5682no—
697C2#2259962314yesdirect product factor
698C2C2×#1798657311yescharacteristic
699C2C2×#1798680211yescharacteristic
700C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#544×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556102C22
hypercenterC2×#544D71
hypocenterC71C2×#3243
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22599623C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986402C2semidirect
5. C2×#17986361C2semidirect
6. C2×#17986356C2semidirect
7. C2×#17986334C2semidirect
8. C2×#17986340C2semidirect
11. C2×#17986303C2semidirect
12. C2×#17986291C2semidirect
13. C2×#17986296C2semidirect
14. C2×#17986276C2semidirect
15. C2×#17986060C2semidirect
16. C2×#544×C71C2semidirect
29. #17986409C22semidirect
30. #17986402C22semidirect
31. #17986361C22semidirect
32. #17986356C22semidirect
33. #17986340C22semidirect
34. #17986334C22semidirect
37. #17986303C22semidirect
38. #17986296C22semidirect
39. #17986291C22semidirect
40. #17986276C22semidirect
41. #17986060C22semidirect
65. #544×C71C22semidirect
346. C2×C71#3243semidirect
351. C2×#544D71semidirect
367. C71C2×#3243semidirect
369. #544C2×D71semidirect
697. C2#22599623direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225996232
C2×#179864092
C2×#179864022
C2×#179863612
C2×#179863562
C2×#179863342
C2×#179863402
C2×#179863232
C2×#179863122
C2×#179863032
C2×#179862912
C2×#179862962
C2×#179862762
C2×#179860602
C2×#544×C712
C2×#324371