Finite Group Databasebeta

← C2×#22598520 #32865679

Subgroups — C2×#22598520 #32865679

Order 18176.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986614C211yesmaximal, characteristic, complemented
2C2×#17986471C211yesmaximal, characteristic, complemented
3#22598520C2116yesmaximal, direct product factor
4C2×#17986342C211yesmaximal, characteristic, complemented
5C2×#17986322C211yesmaximal, characteristic, complemented
6C2×#17986287C211yesmaximal, characteristic, complemented
7C2×#17986278C211yesmaximal, characteristic, complemented
8C2×#17986213C211yesmaximal, characteristic, complemented
9C2×#17986212C211yesmaximal, characteristic, complemented
10C2×#17986151C211yesmaximal, characteristic, complemented
11C2×#17986131C211yesmaximal, characteristic
12C2×#17986109C211yesmaximal, characteristic, complemented
13C2×#17986099C211yesmaximal, characteristic, complemented
14C2×C4×#11765854C211yesmaximal, characteristic, complemented
15C2×#17986058C211yesmaximal, characteristic, complemented
16C2×C4×D8×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765854C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21#17986614—24no—
22#17986614C2218yescomplemented
23C2×#14556127C2211yescharacteristic, complemented
24C2×#14556121—21no—
25C2×#14556115C2211yescharacteristic, complemented
26C2×#14556114—21no—
27C2×#14556111—21no—
28C2×#14556108C2211yescharacteristic
29C2×#14556107—21no—
30C2×#14556099C2211yescharacteristic
31#17986471—24no—
32#17986471C2218yescomplemented
33C2×C4×Dic142C2211yescharacteristic, complemented
34C2×C4×D284C2211yescharacteristic
35C2×D4×Dic71C2211yescharacteristic
36C2×#14556090C2211yescharacteristic
37C2×C4×C22⋊D71—21no—
38C2×(C22⋊D71)⋊C4—21no—
39C2×#14556086C2211yescharacteristic
40C2×#14556085C2211yescharacteristic
41C22×(C2×D71)⋊C4—21no—
42C2×C22⋊C4×D71—21no—
43#17986342C2218yescomplemented
44#17986322C2218yescomplemented
45#17986287C2218yescomplemented
46#17986278C2218yescomplemented
47#17986213C2218yescomplemented
48#17986212C2218yescomplemented
49#17986151C2218yescomplemented
50#17986131C2218yes—
51#17986109C2218yescomplemented
52#17986099C2218yescomplemented
53C4×#11765854C2218yescomplemented
54#17986058C2218yescomplemented
55C2×#14556061C2211yescharacteristic, complemented
56C2×#14556060C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×#14556053C2211yescharacteristic, complemented
61C2×#14556051C2211yescharacteristic, complemented
62C2×#14556050C2211yescharacteristic
63C2×#14556049C2211yescharacteristic
64C2×#14556049C2211yescharacteristic, complemented
65C2×#14556048C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556039C2211yescharacteristic, complemented
69C22×D8×C71C2211yescharacteristic
70C2×C4×D4×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic, complemented
72C4×D8×C71C2218yescomplemented
73C2×#107×C71C2211yescharacteristic, complemented
74C2×#102×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic, complemented
76C2×C4×C8×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C2×D4×D71—24no—
84C2×D4×D71—22no—
85C2×D4×D71—24no—
86C2×D4×D71C2314yes—
87C23×Dic71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C22×C4×D71C2311yescharacteristic
91C2×#11765854—24no—
92C2×#11765854C2314yes—
93C2×#11765853—24no—
94C2×#11765853C2314yes—
95C2×#11765850—24no—
96C2×#11765850C2314yes—
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99#14556127—22no—
100#14556127C2314yescomplemented
101#14556121—28no—
102#14556115—22no—
103#14556115C2314yescomplemented
104#14556114—28no—
105#14556111—28no—
106#14556108—22no—
107#14556108C2314yes—
108#14556107—28no—
109#14556099—22no—
110#14556099C2314yes—
111C4×Dic142—22no—
112C4×Dic142C2314yescomplemented
113C4×D284—22no—
114C4×D284C2314yes—
115D4×Dic71—22no—
116D4×Dic71C2314yes—
117#14556090—22no—
118#14556090C2314yes—
119C4×C22⋊D71—28no—
120(C22⋊D71)⋊C4—28no—
121#14556086—22no—
122#14556086C2314yes—
123#14556085D414yes—
124#14556085C2314yes—
125C2×C4⋊Dic71—21no—
126C2×C4⋊Dic71C2311yescharacteristic
127C2×C4⋊Dic71C2311yescharacteristic
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4D411yescharacteristic
131C2×Dic71⋊C4D411yescharacteristic
132C2×C22⋊Dic71—21no—
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C22⋊Dic71—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—28no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×(C2×D71)⋊C4D411yescharacteristic
143C22⋊C4×D71—28no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71C2311yescharacteristic
147#14556061C2314yescomplemented
148#14556060C2314yescomplemented
149#14556059C2314yescomplemented
150Dic71⋊C8C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152#14556053C2314yescomplemented
153#14556051C2314yescomplemented
154#14556050C2314yes—
155#14556049C2314yes—
156#14556049C2314yescomplemented
157#14556048C2314yes—
158(C2×D71)⋊C8C2314yes—
159(C2×D71)⋊C8C2314yes—
160#14556039C2314yescomplemented
161C22×D4×C71C2311yescharacteristic
162C22×D4×C71C2311yescharacteristic
163C23×C4×C71—21no—
164C23×C4×C71—21no—
165C2×D8×C71—24no—
166C2×D8×C71C2314yes—
167C22×C8×C71C2311yescharacteristic
168C22×C8×C71C2311yescharacteristic
169C4×D4×C71—22no—
170C4×D4×C71—22no—
171C4×D4×C71C2314yes—
172C4×D4×C71C2314yescomplemented
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C42×C71C2311yescharacteristic
178#107×C71C2314yescomplemented
179#102×C71C2314yes—
180#102×C71C2314yescomplemented
181C4×C8×C71C2314yescomplemented
182C23×D71—21no—
183C23×D71—28no—
184C23×D71—24no—
185C23×D71—82no—
186C23×D71—82no—
187C23×D71C2×D411yescharacteristic
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—21no—
191C2×Dic142—24no—
192C2×Dic142—82no—
193C2×Dic142C2412yes—
194C2×D284—21no—
195C2×D284—22no—
196C2×D284#4114yes—
197C2×D284C2412yes—
198C2×C22⋊D71—28no—
199C2×C22⋊D71—24no—
200C2×C22⋊D71—24no—
201C2×C22⋊D71—82no—
202D4×D71—216no—
203D4×D71—28no—
204D4×D71—28no—
205C22×Dic71—21no—
206C22×Dic71—21no—
207C22×Dic71—21no—
208C22×Dic71—24no—
209C22×Dic71—82no—
210C22×Dic71C2×D411yescharacteristic
211C22×Dic71C2×D411yescharacteristic
212C22×Dic71C2×D411yescharacteristic
213C2×C4×D71—22no—
214C2×C4×D71—22no—
215C2×C4×D71—24no—
216C2×C4×D71—24no—
217C2×C4×D71—82no—
218C2×C4×D71—82no—
219C2×C4×D71C2×D412yes—
220C2×C4×D71C2412yes—
221#11765854—28no—
222#11765853—28no—
223#11765850—28no—
224C2×C71⋊C8—22no—
225C2×C71⋊C8—22no—
226C2×C71⋊C8C2412yes—
227C2×C71⋊C8C2412yes—
228C4⋊Dic71—21no—
229C4⋊Dic71—21no—
230C4⋊Dic71—24no—
231C4⋊Dic71C2412yes—
232C4⋊Dic71C2412yes—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4C2×D414yes—
236Dic71⋊C4C2×D414yes—
237C22⋊Dic71—24no—
238C22⋊Dic71—24no—
239C22⋊Dic71—24no—
240C22⋊Dic71—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244(C2×D71)⋊C4—24no—
245(C2×D71)⋊C4C2×D414yes—
246(C2×D71)⋊C4C2×D414yes—
247C4×Dic71—24no—
248C4×Dic71—24no—
249C4×Dic71C2×D412yes—
250C4×Dic71C2412yes—
251C24×C71—21no—
252C24×C71—21no—
253C2×D4×C71—21no—
254C2×D4×C71—21no—
255C2×D4×C71—22no—
256C2×D4×C71—22no—
257C2×D4×C71—22no—
258C2×D4×C71#4114yes—
259C2×D4×C71C2412yes—
260C2×D4×C71C2412yes—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—24no—
264C22×C4×C71—24no—
265C22×C4×C71—82no—
266C22×C4×C71—82no—
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2411yescharacteristic
270D8×C71—28no—
271C2×C8×C71—22no—
272C2×C8×C71—22no—
273C2×C8×C71C2412yes—
274C2×C8×C71C2412yes—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71C2412yes—
278C4⋊C4×C71C2412yes—
279C22⋊C4×C71—24no—
280C22⋊C4×C71—24no—
281C42×C71C2×D412yes—
282C42×C71C2412yes—
283C23×C71—24no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—42no—
287C23×C71—42no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71C22×D411yescharacteristic
292C22×D71—22no—
293C22×D71—24no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—216no—
298C22×D71—42no—
299C22×D71—42no—
300C22×D71—84no—
301C22×D71—84no—
302C22×D71—816no—
303C22×D71C22×D412yes—
304D4×C71—24no—
305D4×C71—22no—
306D4×C71—22no—
307D4×C71—22no—
308D4×C71—42no—
309D4×C71C2×#4114yes—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—42no—
315C2×C4×C71—42no—
316C2×C4×C71—84no—
317C2×C4×C71—84no—
318C2×C4×C71C22×D412yes—
319C2×C4×C71C22×D412yes—
320C2×C4×C71C22×D411yescharacteristic
321C2×C4×C71C2×#4112yes—
322C2×C4×C71C2×#4112yes—
323C2×C4×C71C2511yescharacteristic
324C22⋊D71—216no—
325C22⋊D71—84no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—42no—
333C2×Dic71—42no—
334C2×Dic71—42no—
335C2×Dic71—84no—
336C2×Dic71C22×D412yes—
337C2×Dic71C22×D412yes—
338C2×Dic71C22×D412yes—
339D284—24no—
340D284—22no—
341D284C2×#4114yes—
342C4×D71—24no—
343C4×D71—22no—
344C4×D71—22no—
345C4×D71—84no—
346C4×D71—84no—
347Dic142—22no—
348Dic142—22no—
349Dic142—42no—
350Dic142—84no—
351C8×C71—22no—
352C8×C71—22no—
353C71⋊C8—22no—
354C71⋊C8—22no—
355C22×C71—24no—
356C22×C71—48no—
357C22×C71—42no—
358C22×C71—42no—
359C22×C71—42no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—84no—
363C22×C71#52512yes—
364C22×C71#57612yes—
365C22×C71#57712yes—
366C22×C71C23×D411yescharacteristic
367C2×D71—22no—
368C2×D71—24no—
369C2×D71—22no—
370C2×D71—22no—
371C2×D71—44no—
372C2×D71—48no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—816no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71#52512yes—
381C4×C71C22×#4111yescharacteristic
382C4×C71C22×#4111yescharacteristic
383Dic71—22no—
384Dic71—22no—
385Dic71—22no—
386Dic71—42no—
387Dic71—42no—
388Dic71—42no—
389C2×#3118—711nomaximal, Sylow
390C2×C71—44no—
391C2×C71—82no—
392C2×C71#311814yescomplemented
393C2×C71C2×#52511yescharacteristic
394C2×C71C2×#57611yescharacteristic
395C2×C71C2×#57711yescharacteristic
396D71—42no—
397D71—44no—
398C2×#542—711no—
399C2×#518—711no—
400#3118—7116no—
401C2×#485—711no—
402C2×#482—711no—
403C2×#476—711no—
404C2×#474—711no—
405C2×#463—711no—
406C2×#463—711no—
407C2×#450—711no—
408C2×#447—711no—
409C2×#442—711no—
410C2×#440—711no—
411C2×C4×SD16—711no—
412C2×C4×D8D7111yescharacteristic, complemented
413C2×#433—711no—
414C71C2×#311811yescharacteristic, complemented, Sylow
415C23×D4—711no—
416C22×SD16—711no—
417C22×SD16—711no—
418C22×D8—711no—
419C22×D8C2×D7111yescharacteristic
420#542—718no—
421#542—1424no—
422C2×C4⋊Q8—711no—
423C2×#126—1421no—
424C2×#124—711no—
425C2×#124—1421no—
426C2×#123—1421no—
427C2×C22⋊Q8—711no—
428C2×C22⋊Q8—1421no—
429C2×#121—711no—
430#518—718no—
431#518—1424no—
432C2×C4×Q8—711no—
433C2×C4×D4—711no—
434C2×C4×D4—711no—
435C2×C4×D4—711no—
436C2×C4×D4—1421no—
437C2×C4×D4—1421no—
438C2×C4×D4C2×D7111yescharacteristic
439C2×C4×D4C2×D7111yescharacteristic, complemented
440C2×#117—711no—
441C2×#117—711no—
442C22×C22⋊C4—1421no—
443C22×C22⋊C4—1421no—
444#485—718no—
445#482—718no—
446#476—718no—
447#474—718no—
448#463—718no—
449#463—718no—
450#450—718no—
451#447—718no—
452#442—718no—
453#440—718no—
454C4×SD16—718no—
455C4×D8C2×D7118yescomplemented
456#433—718no—
457C2×#107—711no—
458C2×#107C2×D7111yescharacteristic, complemented
459C2×#106—711no—
460C2×#106—711no—
461C2×C4⋊C8—711no—
462C2×C4⋊C8—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×#102—711no—
469C2×#102C2×D7111yescharacteristic
470C2×#102C2×D7111yescharacteristic, complemented
471C2×C22⋊C8—711no—
472C2×C22⋊C8—711no—
473C2×#97—711no—
474C2×C4×C8C2×D7111yescharacteristic, complemented
475C25—1421no—
476C22×Q8—711no—
477C22×Q8—1421no—
478C22×D4—714no—
479C22×D4—711no—
480C22×D4—1422no—
481C22×D4—1421no—
482C22×D4—1424no—
483C22×D4—1421no—
484C22×D4—1424no—
485C22×D4C22×D7111yescharacteristic
486C22×D4C22×D7111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—711no—
490C23×C4—1421no—
491C23×C4—1421no—
492C23×C4—1421no—
493C2×SD16—714no—
494C2×SD16—714no—
495C2×SD16—1424no—
496C2×SD16—1424no—
497C2×D8—24no—
498C2×D8—714no—
499C2×D8—1424no—
500C2×D8C22×D7114yes—
501C22×C8—711no—
502C22×C8—711no—
503C22×C8C22×D7111yescharacteristic
504C22×C8C22×D7111yescharacteristic
505C4⋊Q8—714no—
506C4⋊Q8—1422no—
507#126—1428no—
508#124—714no—
509#124—1422no—
510#124—1428no—
511#123—1428no—
512C22⋊Q8—714no—
513C22⋊Q8—1422no—
514C22⋊Q8—1428no—
515#121—714no—
516#121—1422no—
517C4×Q8—714no—
518C4×Q8—1422no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—714no—
522C4×D4—714no—
523C4×D4—714no—
524C4×D4—1422no—
525C4×D4—1422no—
526C4×D4—1428no—
527C4×D4—1428no—
528C4×D4—1422no—
529C4×D4C22×D7114yes—
530C4×D4C22×D7114yescomplemented
531#117—714no—
532#117—714no—
533#117—714no—
534#117—1422no—
535C2×C4⋊C4—711no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—711no—
538C2×C4⋊C4—711no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—711no—
547C2×C22⋊C4—711no—
548C2×C22⋊C4—1428no—
549C2×C22⋊C4—1428no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C22⋊C4—1421no—
558C2×C42—711no—
559C2×C42—1421no—
560C2×C42—1421no—
561C2×C42C22×D7111yescharacteristic
562#107—714no—
563#107C22×D7114yescomplemented
564#106—714no—
565#106—714no—
566C4⋊C8—714no—
567C4⋊C8—714no—
568#103—714no—
569#103—714no—
570#102—714no—
571#102—714no—
572#102—714no—
573#102—714no—
574#102C22×D7114yes—
575#102C22×D7114yescomplemented
576C22⋊C8—714no—
577C22⋊C8—714no—
578#97—714no—
579C4×C8C22×D7114yescomplemented
580C24—21no—
581C24—21no—
582C24—5682no—
583C24—5682no—
584C24—711no—
585C24—1424no—
586C24—1428no—
587C24—1421no—
588C2×Q8—5682no—
589C2×Q8—712no—
590C2×Q8—1424no—
591C2×Q8—1422no—
592C2×Q8—1422no—
593C2×Q8—1421no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—5682no—
600C2×D4—714no—
601C2×D4—712no—
602C2×D4—1424no—
603C2×D4—1428no—
604C2×D4—14216no—
605C2×D4—1424no—
606C2×D4—1428no—
607C2×D4—1428no—
608C2×D4—1421no—
609C2×D4—1422no—
610C2×D4#1176586514yes—
611C2×D4C23×D7112yes—
612C2×D4C23×D7112yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—5682no—
620C22×C4—5682no—
621C22×C4—5682no—
622C22×C4—711no—
623C22×C4—711no—
624C22×C4—711no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—1424no—
628C22×C4—1421no—
629C22×C4—1421no—
630C22×C4—1421no—
631C22×C4—1424no—
632C22×C4—1424no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4D4×D7111yescharacteristic
636C22×C4D4×D7111yescharacteristic
637C22×C4C23×D7111yescharacteristic
638SD16—1428no—
639SD16—1428no—
640D8—28no—
641D8—1428no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—712no—
645C2×C8—712no—
646C2×C8—1422no—
647C2×C8—1422no—
648C2×C8C23×D7112yes—
649C2×C8C23×D7112yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—714no—
653C4⋊C4—714no—
654C4⋊C4—712no—
655C4⋊C4—712no—
656C4⋊C4—1424no—
657C4⋊C4—1424no—
658C4⋊C4—1424no—
659C4⋊C4—1421no—
660C4⋊C4—1421no—
661C4⋊C4C23×D7112yes—
662C4⋊C4C23×D7112yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—714no—
666C22⋊C4—714no—
667C22⋊C4—1424no—
668C22⋊C4—1424no—
669C22⋊C4—1424no—
670C22⋊C4—1424no—
671C22⋊C4—1424no—
672C22⋊C4—1424no—
673C22⋊C4—1424no—
674C22⋊C4—1424no—
675C42—712no—
676C42—712no—
677C42—1424no—
678C42—1424no—
679C42D4×D7112yes—
680C42C23×D7112yes—
681C23—22no—
682C23—24no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—2842no—
690C23—2842no—
691C23—56816no—
692C23—5684no—
693C23—5684no—
694C23—712no—
695C23—14216no—
696C23—1422no—
697C23—1422no—
698C23—1424no—
699C23—1422no—
700C23—1422no—
701C23C2×D4×D7111yescharacteristic
702Q8—2842no—
703Q8—5684no—
704Q8—1422no—
705Q8—1422no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—24no—
710D4—42no—
711D4—5684no—
712D4—714no—
713D4—14216no—
714D4—1422no—
715D4—1424no—
716D4C2×#1176586514yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—2842no—
726C2×C4—2842no—
727C2×C4—2842no—
728C2×C4—5684no—
729C2×C4—5684no—
730C2×C4—5684no—
731C2×C4—712no—
732C2×C4—712no—
733C2×C4—712no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1424no—
743C2×C4C2×D4×D7112yes—
744C2×C4C2×D4×D7112yes—
745C2×C4C2×D4×D7111yescharacteristic
746C2×C4#41×D7112yes—
747C2×C4C2×#1176586512yes—
748C2×C4C24×D7111yescharacteristic
749C8—22no—
750C8—22no—
751C8—1422no—
752C8—1422no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—2842no—
762C22—2842no—
763C22—2848no—
764C22—2844no—
765C22—56816no—
766C22—1422no—
767C22—1422no—
768C22—1422no—
769C22—1424no—
770C22#1798650812yes—
771C22#1798680012yes—
772C22#1798680612yes—
773C22C22×D4×D7111yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—2842no—
779C4—2842no—
780C4—2842no—
781C4—1422no—
782C4—1422no—
783C4—1422no—
784C4#1798650812yes—
785C4C2×#41×D7111yescharacteristic
786C4C22×#1176586511yescharacteristic
787C2—44no—
788C2—82no—
789C2—2844no—
790C2—2842no—
791C2#2259852014yesdirect product factor
792C2C2×#1798650811yescharacteristic
793C2C2×#1798680011yescharacteristic
794C2C2×#1798680611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×C4×D8×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986131C2
hypercenterC2×C4×D8D71
hypocenterC71C2×#3118
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#17986614C2semidirect
2. C2×#17986471C2semidirect
3. #22598520C2direct (N × H)
4. C2×#17986342C2semidirect
5. C2×#17986322C2semidirect
6. C2×#17986287C2semidirect
7. C2×#17986278C2semidirect
8. C2×#17986213C2semidirect
9. C2×#17986212C2semidirect
10. C2×#17986151C2semidirect
12. C2×#17986109C2semidirect
13. C2×#17986099C2semidirect
14. C2×C4×#11765854C2semidirect
15. C2×#17986058C2semidirect
16. C2×C4×D8×C71C2semidirect
22. #17986614C22semidirect
23. C2×#14556127C22semidirect
25. C2×#14556115C22semidirect
32. #17986471C22semidirect
33. C2×C4×Dic142C22semidirect
43. #17986342C22semidirect
44. #17986322C22semidirect
45. #17986287C22semidirect
46. #17986278C22semidirect
47. #17986213C22semidirect
48. #17986212C22semidirect
49. #17986151C22semidirect
51. #17986109C22semidirect
52. #17986099C22semidirect
53. C4×#11765854C22semidirect
54. #17986058C22semidirect
55. C2×#14556061C22semidirect
56. C2×#14556060C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×Dic71⋊C8C22semidirect
60. C2×#14556053C22semidirect
61. C2×#14556051C22semidirect
64. C2×#14556049C22semidirect
68. C2×#14556039C22semidirect
71. C2×C4×D4×C71C22semidirect
72. C4×D8×C71C22semidirect
73. C2×#107×C71C22semidirect
75. C2×#102×C71C22semidirect
76. C2×C4×C8×C71C22semidirect
100. #14556127C23semidirect
103. #14556115C23semidirect
112. C4×Dic142C23semidirect
147. #14556061C23semidirect
148. #14556060C23semidirect
149. #14556059C23semidirect
150. Dic71⋊C8C23semidirect
151. Dic71⋊C8C23semidirect
152. #14556053C23semidirect
153. #14556051C23semidirect
156. #14556049C23semidirect
160. #14556039C23semidirect
172. C4×D4×C71C23semidirect
178. #107×C71C23semidirect
180. #102×C71C23semidirect
181. C4×C8×C71C23semidirect
392. C2×C71#3118semidirect
412. C2×C4×D8D71semidirect
414. C71C2×#3118semidirect
439. C2×C4×D4C2×D71semidirect
455. C4×D8C2×D71semidirect
458. C2×#107C2×D71semidirect
470. C2×#102C2×D71semidirect
474. C2×C4×C8C2×D71semidirect
530. C4×D4C22×D71semidirect
563. #107C22×D71semidirect
575. #102C22×D71semidirect
579. C4×C8C22×D71semidirect
791. C2#22598520direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866142
C2×#179864712
#225985202
C2×#179863422
C2×#179863222
C2×#179862872
C2×#179862782
C2×#179862132
C2×#179862122
C2×#179861512
C2×#179861312
C2×#179861092
C2×#179860992
C2×C4×#117658542
C2×#179860582
C2×C4×D8×C712
C2×#311871