Finite Group Databasebeta

← C2×#22598554 #32865715

Subgroups — C2×#22598554 #32865715

Order 18176.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986611C211yesmaximal, characteristic, complemented
2#22598554C2116yesmaximal, direct product factor
3C2×#17986334C211yesmaximal, characteristic, complemented
4C2×#17986329C211yesmaximal, characteristic, complemented
5C2×#17986306C211yesmaximal, characteristic, complemented
6C2×#17986299C211yesmaximal, characteristic, complemented
7C2×#17986209C211yesmaximal, characteristic, complemented
8C2×#17986204C211yesmaximal, characteristic, complemented
9C2×#17986161C211yesmaximal, characteristic
10C2×#17986161C211yesmaximal, characteristic
11C2×#17986104C211yesmaximal, characteristic, complemented
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×C4×#11765855C211yesmaximal, characteristic, complemented
14C2×C4×#11765853C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#520×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765853C2211yescharacteristic
21#17986611—24no—
22#17986611C2218yescomplemented
23C2×#14556128C2211yescharacteristic
24C2×#14556121—21no—
25C2×#14556121—21no—
26C2×#14556120C2211yescharacteristic
27C2×#14556118—21no—
28C2×#14556118—21no—
29C2×#14556107C2211yescharacteristic
30C2×#14556107C2211yescharacteristic
31C2×C4×Dic142C2211yescharacteristic
32C2×C4×Dic142C2211yescharacteristic
33#17986334C2218yescomplemented
34#17986329C2218yescomplemented
35#17986306C2218yescomplemented
36#17986299C2218yescomplemented
37#17986209C2218yescomplemented
38#17986204C2218yescomplemented
39#17986161C2218yes—
40#17986161C2218yes—
41#17986104C2218yescomplemented
42#17986099C2218yescomplemented
43C4×#11765855C2218yescomplemented
44C4×#11765853C2218yescomplemented
45#17986060C2218yescomplemented
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65#520×C71—24no—
66#520×C71C2218yes—
67C2×C4×Q8×C71C2211yescharacteristic
68C2×C4×Q8×C71C2211yescharacteristic
69C2×C4×D4×C71—21no—
70C2×C4×D4×C71—21no—
71C2×C4×D4×C71C2211yescharacteristic
72C2×C4×D4×C71C2211yescharacteristic
73C2×#117×C71—21no—
74C2×#117×C71C2211yescharacteristic
75C22×C4⋊C4×C71—21no—
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×Dic142C2311yescharacteristic
79C2×#11765855—24no—
80C2×#11765855—24no—
81C2×#11765855C2314yes—
82C2×#11765855C2314yes—
83C2×#11765853—24no—
84C2×#11765853—24no—
85C2×#11765853C2314yes—
86C2×#11765853C2314yes—
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556128—22no—
92#14556128C2314yes—
93#14556121—28no—
94#14556121—28no—
95#14556120—22no—
96#14556120C2314yes—
97#14556118—28no—
98#14556118—28no—
99#14556107—22no—
100#14556107—22no—
101#14556107C2314yes—
102#14556107C2314yes—
103C4×Dic142—22no—
104C4×Dic142—22no—
105C4×Dic142C2314yes—
106C4×Dic142C2314yes—
107C2×C4⋊Dic71—21no—
108C2×C4⋊Dic71—21no—
109C2×C4⋊Dic71C2311yescharacteristic
110C2×C4⋊Dic71C2311yescharacteristic
111C2×Dic71⋊C4—21no—
112C2×Dic71⋊C4—21no—
113C2×Dic71⋊C4—21no—
114C2×Dic71⋊C4—21no—
115C2×Dic71⋊C4—21no—
116C2×Dic71⋊C4—21no—
117C2×C22⋊Dic71—21no—
118C2×C22⋊Dic71—21no—
119C2×C4×Dic71—21no—
120C2×C4×Dic71—21no—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556059C2314yes—
124#14556059C2314yes—
125C4⋊(C71⋊C8)C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556051C2314yes—
132#14556051C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C4×C71⋊C8C2314yes—
139C2×#41×C71—24no—
140C2×#41×C71—24no—
141C2×#41×C71—22no—
142C2×#41×C71C2314yes—
143C22×Q8×C71C2311yescharacteristic
144C22×D4×C71—21no—
145C22×D4×C71C2311yescharacteristic
146C23×C4×C71—21no—
147C23×C4×C71—21no—
148C23×C4×C71—21no—
149C23×C4×C71—21no—
150C23×C4×C71C2311yescharacteristic
151C4×Q8×C71—22no—
152C4×Q8×C71—22no—
153C4×Q8×C71C2314yes—
154C4×Q8×C71C2314yes—
155C4×D4×C71—28no—
156C4×D4×C71—28no—
157C4×D4×C71—22no—
158C4×D4×C71—22no—
159C4×D4×C71C2314yes—
160C4×D4×C71C2314yes—
161#117×C71—28no—
162#117×C71D414yes—
163#117×C71C2314yes—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—22no—
168C2×C4⋊C4×C71—28no—
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71C2314yes—
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C42×C71—21no—
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—22no—
186C2×Dic142—21no—
187C2×Dic142—21no—
188C2×Dic142C2412yes—
189C2×Dic142C2412yes—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194#11765855—28no—
195#11765855—28no—
196#11765853—28no—
197#11765853—28no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C4⋊Dic71—24no—
207C4⋊Dic71—24no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212Dic71⋊C4—24no—
213Dic71⋊C4—24no—
214Dic71⋊C4—24no—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218C22⋊Dic71—24no—
219C22⋊Dic71—24no—
220C4×Dic71—24no—
221C4×Dic71—24no—
222C24×C71—21no—
223C24×C71C2×D411yescharacteristic
224#41×C71—216no—
225#41×C71—28no—
226#41×C71—28no—
227C2×Q8×C71—21no—
228C2×Q8×C71—22no—
229C2×Q8×C71#4114yes—
230C2×Q8×C71C2412yes—
231C2×D4×C71—28no—
232C2×D4×C71—24no—
233C2×D4×C71—21no—
234C2×D4×C71—22no—
235C2×D4×C71#4114yes—
236C2×D4×C71C2412yes—
237C22×C4×C71—28no—
238C22×C4×C71—21no—
239C22×C4×C71—24no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—24no—
245C22×C4×C71—24no—
246C22×C4×C71—24no—
247C22×C4×C71—82no—
248C22×C4×C71—82no—
249C22×C4×C71—82no—
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D412yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2411yescharacteristic
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71C2×D414yes—
264C4⋊C4×C71C2×D414yes—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C22⋊C4×C71—24no—
268C22⋊C4×C71—24no—
269C22⋊C4×C71C2×D414yes—
270C22⋊C4×C71C2×D414yes—
271C42×C71—24no—
272C42×C71—24no—
273C42×C71C2×D412yes—
274C42×C71C2×D412yes—
275C42×C71C2412yes—
276C42×C71C2412yes—
277C23×C71—22no—
278C23×C71—24no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—42no—
283C23×C71—42no—
284C23×C71C22×D412yes—
285C23×C71C22×D411yescharacteristic
286Q8×C71—24no—
287Q8×C71—22no—
288Q8×C71C2×#4114yes—
289D4×C71—216no—
290D4×C71—24no—
291D4×C71—22no—
292D4×C71C2×#4114yes—
293C2×C4×C71—216no—
294C2×C4×C71—22no—
295C2×C4×C71—24no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—24no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—42no—
307C2×C4×C71—42no—
308C2×C4×C71—84no—
309C2×C4×C71—84no—
310C2×C4×C71—84no—
311C2×C4×C71C22×D412yes—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D411yescharacteristic
317C2×C4×C71C2×#4112yes—
318C2×C4×C71C2×#4112yes—
319C2×C4×C71C2511yescharacteristic
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328Dic142—22no—
329Dic142—22no—
330Dic142—22no—
331Dic142—22no—
332Dic142—42no—
333Dic142—42no—
334C71⋊C8—22no—
335C71⋊C8—22no—
336C71⋊C8—22no—
337C71⋊C8—22no—
338C22×C71—22no—
339C22×C71—24no—
340C22×C71—22no—
341C22×C71—22no—
342C22×C71—44no—
343C22×C71—48no—
344C22×C71—42no—
345C22×C71—42no—
346C22×C71#52512yes—
347C22×C71#57712yes—
348C22×C71#57812yes—
349C22×C71C23×D411yescharacteristic
350C4×C71—22no—
351C4×C71—24no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—42no—
357C4×C71—42no—
358C4×C71#52512yes—
359C4×C71C22×#4111yescharacteristic
360C4×C71C22×#4111yescharacteristic
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365C2×#3120—711nomaximal, Sylow
366C2×C71—42no—
367C2×C71—44no—
368C2×C71#312014yescomplemented
369C2×C71C2×#52511yescharacteristic
370C2×C71C2×#57711yescharacteristic
371C2×C71C2×#57811yescharacteristic
372C2×#541—711no—
373C2×#520D7111yescharacteristic
374#3120—7116no—
375C2×#484—711no—
376C2×#483—711no—
377C2×#479—711no—
378C2×#478—711no—
379C2×#462—711no—
380C2×#461—711no—
381C2×#452—711no—
382C2×#452—711no—
383C2×#441—711no—
384C2×#440—711no—
385C2×C4×Q16—711no—
386C2×C4×SD16—711no—
387C2×#433—711no—
388C71C2×#312011yescharacteristic, complemented, Sylow
389C22×#41C2×D7111yescharacteristic
390C22×Q16—711no—
391C22×Q16—711no—
392C22×SD16—711no—
393C22×SD16—711no—
394#541—718no—
395#541—1424no—
396C2×C4⋊Q8—711no—
397C2×#126—1421no—
398C2×#126—1421no—
399C2×#125—711no—
400C2×#125—1421no—
401C2×#125—1421no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—711no—
404#520—24no—
405#520C2×D7118yes—
406C2×C4×Q8—711no—
407C2×C4×Q8—711no—
408C2×C4×Q8C2×D7111yescharacteristic
409C2×C4×Q8C2×D7111yescharacteristic
410C2×C4×D4—21no—
411C2×C4×D4—21no—
412C2×C4×D4C2×D7111yescharacteristic
413C2×C4×D4C2×D7111yescharacteristic
414C2×#117—21no—
415C2×#117C2×D7111yescharacteristic
416C22×C4⋊C4—21no—
417C22×C4⋊C4C2×D7111yescharacteristic
418#484—718no—
419#483—718no—
420#479—718no—
421#478—718no—
422#462—718no—
423#461—718no—
424#452—718no—
425#452—718no—
426#441—718no—
427#440—718no—
428C4×Q16—718no—
429C4×SD16—718no—
430#433—718no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8—711no—
436C2×C4⋊C8—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×C22⋊C8—711no—
446C2×C22⋊C8—711no—
447C2×#97—711no—
448C2×C4×C8—711no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—22no—
452C2×#41C22×D7114yes—
453C22×Q8—711no—
454C22×Q8—711no—
455C22×Q8C22×D7111yescharacteristic
456C22×D4—21no—
457C22×D4C22×D7111yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4C22×D7111yescharacteristic
463C2×Q16—714no—
464C2×Q16—714no—
465C2×Q16—1424no—
466C2×Q16—1424no—
467C2×SD16—714no—
468C2×SD16—714no—
469C2×SD16—1424no—
470C2×SD16—1424no—
471C22×C8—711no—
472C22×C8—711no—
473C22×C8—711no—
474C22×C8—711no—
475C4⋊Q8—714no—
476C4⋊Q8—1422no—
477#126—1428no—
478#126—1428no—
479#125—714no—
480#125—1428no—
481#125—1428no—
482#125—1422no—
483C22⋊Q8—714no—
484C22⋊Q8—714no—
485C22⋊Q8—1422no—
486C22⋊Q8—1422no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—714no—
490C4×Q8—714no—
491C4×Q8—1422no—
492C4×Q8—1422no—
493C4×Q8C22×D7114yes—
494C4×Q8C22×D7114yes—
495C4×D4—28no—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4C22×D7114yes—
500C4×D4C22×D7114yes—
501#117—28no—
502#117C22⋊D7114yes—
503#117C22×D7114yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—28no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4C22⋊D7111yescharacteristic
520C2×C4⋊C4C22⋊D7111yescharacteristic
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7114yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4C22⋊D7111yescharacteristic
529C2×C22⋊C4C22⋊D7111yescharacteristic
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—1421no—
533C2×C42—1421no—
534C2×C42C22×D7111yescharacteristic
535C2×C42C22×D7111yescharacteristic
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540C4⋊C8—714no—
541C4⋊C8—714no—
542#103—714no—
543#103—714no—
544#103—714no—
545#103—714no—
546#103—714no—
547#103—714no—
548#102—714no—
549#102—714no—
550C22⋊C8—714no—
551C22⋊C8—714no—
552#97—714no—
553C4×C8—714no—
554C24—21no—
555C24C2×C22⋊D7111yescharacteristic
556#41—216no—
557#41—28no—
558#41—28no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—712no—
562C2×Q8—712no—
563C2×Q8—1422no—
564C2×Q8—1422no—
565C2×Q8—1422no—
566C2×Q8—1422no—
567C2×Q8—1421no—
568C2×Q8—1421no—
569C2×Q8#1176586514yes—
570C2×Q8C23×D7112yes—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4#1176586514yes—
576C2×D4C23×D7112yes—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4C2×C22⋊D7112yes—
595C22×C4C2×C22⋊D7111yescharacteristic
596C22×C4C2×C22⋊D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C2×C22⋊D7111yescharacteristic
599C22×C4C2×C22⋊D7111yescharacteristic
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602Q16—1428no—
603Q16—1428no—
604SD16—1428no—
605SD16—1428no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—712no—
610C2×C8—1422no—
611C2×C8—1422no—
612C2×C8—1422no—
613C2×C8—1422no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—712no—
620C4⋊C4—712no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1424no—
626C4⋊C4—1424no—
627C4⋊C4—1421no—
628C4⋊C4—1421no—
629C4⋊C4—1424no—
630C4⋊C4—1424no—
631C4⋊C4C2×C22⋊D7114yes—
632C4⋊C4C2×C22⋊D7114yes—
633C4⋊C4C23×D7112yes—
634C4⋊C4C23×D7112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C22⋊C4C2×C22⋊D7114yes—
640C22⋊C4C2×C22⋊D7114yes—
641C42—24no—
642C42—24no—
643C42—1424no—
644C42—1424no—
645C42C2×C22⋊D7112yes—
646C42C2×C22⋊D7112yes—
647C42C23×D7112yes—
648C42C23×D7112yes—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D7112yes—
657C23C22×C22⋊D7111yescharacteristic
658Q8—22no—
659Q8—24no—
660Q8—2842no—
661Q8—2842no—
662Q8—1422no—
663Q8—1422no—
664Q8—1422no—
665Q8—1422no—
666Q8C2×#1176586514yes—
667D4—216no—
668D4—22no—
669D4—24no—
670D4C2×#1176586514yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—2842no—
690C2×C4—2842no—
691C2×C4—2842no—
692C2×C4—2842no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4C22×C22⋊D7112yes—
698C2×C4C22×C22⋊D7112yes—
699C2×C4C22×C22⋊D7112yes—
700C2×C4C22×C22⋊D7112yes—
701C2×C4C22×C22⋊D7112yes—
702C2×C4C22×C22⋊D7111yescharacteristic
703C2×C4C2×#1176586512yes—
704C2×C4C2×#1176586512yes—
705C2×C4C24×D7111yescharacteristic
706C8—1422no—
707C8—1422no—
708C8—1422no—
709C8—1422no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1798651012yes—
719C22#1798681012yes—
720C22#1798681412yes—
721C22C23×C22⋊D7111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4—2842no—
734C4#1798651012yes—
735C4C22×#1176586511yescharacteristic
736C4C22×#1176586511yescharacteristic
737C2—42no—
738C2—44no—
739C2#2259855414yesdirect product factor
740C2C2×#1798651011yescharacteristic
741C2C2×#1798681011yescharacteristic
742C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#520×C71C2
socleC23×C71C22×D4
prime radicalC22×#41×C71C22
hypercenterC2×#520D71
hypocenterC71C2×#3120
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#17986611C2semidirect
2. #22598554C2direct (N × H)
3. C2×#17986334C2semidirect
4. C2×#17986329C2semidirect
5. C2×#17986306C2semidirect
6. C2×#17986299C2semidirect
7. C2×#17986209C2semidirect
8. C2×#17986204C2semidirect
11. C2×#17986104C2semidirect
12. C2×#17986099C2semidirect
13. C2×C4×#11765855C2semidirect
14. C2×C4×#11765853C2semidirect
15. C2×#17986060C2semidirect
22. #17986611C22semidirect
33. #17986334C22semidirect
34. #17986329C22semidirect
35. #17986306C22semidirect
36. #17986299C22semidirect
37. #17986209C22semidirect
38. #17986204C22semidirect
41. #17986104C22semidirect
42. #17986099C22semidirect
43. C4×#11765855C22semidirect
44. C4×#11765853C22semidirect
45. #17986060C22semidirect
368. C2×C71#3120semidirect
388. C71C2×#3120semidirect
739. C2#22598554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866112
#225985542
C2×#179863342
C2×#179863292
C2×#179863062
C2×#179862992
C2×#179862092
C2×#179862042
C2×#179861612
C2×#179861042
C2×#179860992
C2×C4×#117658552
C2×C4×#117658532
C2×#179860602
C2×#520×C712
C2×#312071