Finite Group Databasebeta

← C2×#22601400 #32878452

Subgroups — C2×#22601400 #32878452

Order 18176.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986722C211yesmaximal, characteristic, complemented
2#22601400C2116yesmaximal, direct product factor
3C2×#17986394C211yesmaximal, characteristic, complemented
4C2×#17986386C211yesmaximal, characteristic
5C2×#17986381C211yesmaximal, characteristic, complemented
6C2×#17986221C211yesmaximal, characteristic, complemented
7C2×#17986218C211yesmaximal, characteristic, complemented
8C2×#17986196C211yesmaximal, characteristic, complemented
9C2×#17986214C211yesmaximal, characteristic, complemented
10C2×#17986211C211yesmaximal, characteristic, complemented
11C2×#17986204C211yesmaximal, characteristic, complemented
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986109C211yesmaximal, characteristic, complemented
14C2×#17986104C211yesmaximal, characteristic, complemented
15C2×C4×#11765853C211yesmaximal, characteristic, complemented
16C2×#559×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765853C2211yescharacteristic
21C22×#11765853C2211yescharacteristic
22C22×#11765853C2211yescharacteristic
23C22×#11765852C2211yescharacteristic
24C22×#11765850C2211yescharacteristic
25C22×#11765850C2211yescharacteristic
26#17986722—24no—
27#17986722C2218yescomplemented
28C2×#14556128C2211yescharacteristic
29C2×#14556123—21no—
30C2×#14556123—21no—
31C2×#14556116C2211yescharacteristic
32C2×#14556116C2211yescharacteristic
33C2×#14556104—21no—
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic
36C2×C4×D284C2211yescharacteristic
37C2×#14556086—21no—
38#17986394C2218yescomplemented
39#17986386C2218yes—
40#17986381C2218yescomplemented
41#17986221C2218yescomplemented
42#17986218C2218yescomplemented
43#17986214C2218yescomplemented
44#17986211C2218yescomplemented
45#17986204C2218yescomplemented
46#17986196C2218yescomplemented
47#17986130C2218yescomplemented
48#17986109C2218yescomplemented
49#17986104C2218yescomplemented
50C4×#11765853C2218yescomplemented
51C2×#14556059C2211yescharacteristic
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#559×C71—24no—
65#559×C71C2218yescomplemented
66C2×#127×C71C2211yescharacteristic
67C2×#124×C71—21no—
68C2×#124×C71C2211yescharacteristic
69C2×#124×C71C2211yescharacteristic
70C2×#123×C71—21no—
71C2×#123×C71—21no—
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×Q8×C71C2211yescharacteristic
74C2×C4×D4×C71—21no—
75C2×C4×D4×C71C2211yescharacteristic
76C2×C4×D4×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C4×D71—21no—
81C2×#11765855—24no—
82C2×#11765855—42no—
83C2×#11765855C2314yes—
84C2×#11765855C2314yes—
85C2×#11765853—24no—
86C2×#11765853—42no—
87C2×#11765853—42no—
88C2×#11765853—42no—
89C2×#11765853C2314yes—
90C2×#11765853C2314yes—
91C2×#11765853C2314yes—
92C2×#11765853C2314yes—
93C2×#11765852—42no—
94C2×#11765852C2314yes—
95C2×#11765850—24no—
96C2×#11765850—42no—
97C2×#11765850C2314yes—
98C2×#11765850C2314yes—
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103#14556128—22no—
104#14556128C2314yes—
105#14556123—28no—
106#14556123—28no—
107#14556116—22no—
108#14556116—22no—
109#14556116C2314yes—
110#14556116C2314yes—
111#14556104—28no—
112C4×Dic142—22no—
113C4×Dic142—22no—
114C4×Dic142C2314yes—
115C4×Dic142C2314yes—
116C4×D284—22no—
117C4×D284C2314yes—
118#14556086—28no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×(C2×D71)⋊C4—21no—
127C2×(C2×D71)⋊C4—21no—
128C2×(C2×D71)⋊C4—21no—
129C2×C4×Dic71—21no—
130C2×C4×Dic71—21no—
131#14556059C2314yes—
132C4⋊(C71⋊C8)C2314yes—
133C4⋊(C71⋊C8)C2314yes—
134C4⋊(C71⋊C8)C2314yes—
135#14556052C2314yes—
136#14556051C2314yes—
137#14556051C2314yes—
138#14556049C2314yes—
139#14556049C2314yes—
140#14556048C2314yes—
141#14556039C2314yes—
142#14556039C2314yes—
143C4×C71⋊C8C2314yes—
144C22×Q8×C71D411yescharacteristic
145C22×Q8×C71C2311yescharacteristic
146C22×D4×C71—21no—
147C22×D4×C71—21no—
148C22×D4×C71C2311yescharacteristic
149C22×D4×C71C2311yescharacteristic
150C23×C4×C71—21no—
151C23×C4×C71—21no—
152#127×C71—22no—
153#127×C71C2314yes—
154#124×C71—28no—
155#124×C71—22no—
156#124×C71—22no—
157#124×C71C2314yes—
158#124×C71C2314yes—
159#123×C71—28no—
160#123×C71—28no—
161C4×Q8×C71—22no—
162C4×Q8×C71D414yes—
163C4×Q8×C71C2314yes—
164C4×Q8×C71C2314yes—
165C4×D4×C71—28no—
166C4×D4×C71—22no—
167C4×D4×C71—22no—
168C4×D4×C71C2314yes—
169C4×D4×C71C2314yes—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71D411yescharacteristic
173C2×C4⋊C4×C71D411yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C42×C71—21no—
182C2×C42×C71C2311yescharacteristic
183C2×C42×C71C2311yescharacteristic
184C2×C42×C71C2311yescharacteristic
185C23×D71—21no—
186C2×Dic142—22no—
187C2×Dic142—22no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—21no—
191C2×Dic142—21no—
192C2×Dic142C2412yes—
193C2×Dic142C2412yes—
194C2×D284—22no—
195C2×D284—22no—
196C2×D284—21no—
197C2×D284C2412yes—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C2×C4×D71—24no—
202C2×C4×D71—44no—
203#11765855—28no—
204#11765855—44no—
205#11765853—28no—
206#11765853—44no—
207#11765853—44no—
208#11765853—44no—
209#11765852—44no—
210#11765850—28no—
211#11765850—44no—
212C2×C71⋊C8—22no—
213C2×C71⋊C8—22no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8#4114yes—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C4⋊Dic71—24no—
221C4⋊Dic71—24no—
222C4⋊Dic71—21no—
223C4⋊Dic71C2412yes—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C24×C71—21no—
234C24×C71—21no—
235C2×Q8×C71—21no—
236C2×Q8×C71—22no—
237C2×Q8×C71—22no—
238C2×Q8×C71—42no—
239C2×Q8×C71C2×D414yes—
240C2×Q8×C71C2412yes—
241C2×D4×C71—21no—
242C2×D4×C71—21no—
243C2×D4×C71—24no—
244C2×D4×C71—24no—
245C2×D4×C71—22no—
246C2×D4×C71—22no—
247C2×D4×C71—22no—
248C2×D4×C71—22no—
249C2×D4×C71—44no—
250C2×D4×C71—82no—
251C2×D4×C71C2412yes—
252C2×D4×C71C2412yes—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—24no—
256C22×C4×C71—24no—
257C22×C4×C71—82no—
258C22×C4×C71—82no—
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2411yescharacteristic
266C4⋊C4×C71—24no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71C2×D414yes—
269C4⋊C4×C71C2×D414yes—
270C4⋊C4×C71C2×D414yes—
271C4⋊C4×C71C2412yes—
272C22⋊C4×C71—24no—
273C22⋊C4×C71—24no—
274C22⋊C4×C71—24no—
275C22⋊C4×C71—24no—
276C22⋊C4×C71—24no—
277C22⋊C4×C71—24no—
278C42×C71—24no—
279C42×C71C2×D412yes—
280C42×C71C2×D412yes—
281C42×C71C2×D412yes—
282C42×C71C2412yes—
283C42×C71C2412yes—
284C42×C71C2412yes—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—42no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71—42no—
292C23×C71—42no—
293C23×C71C22×D411yescharacteristic
294C22×D71—22no—
295C22×D71—42no—
296C22×D71—42no—
297C22×D71—42no—
298Q8×C71—22no—
299Q8×C71—22no—
300Q8×C71—44no—
301Q8×C71—42no—
302D4×C71—22no—
303D4×C71—22no—
304D4×C71—22no—
305D4×C71—22no—
306D4×C71—48no—
307D4×C71—42no—
308D4×C71—42no—
309D4×C71—84no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—84no—
321C2×C4×C71—84no—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D412yes—
324C2×C4×C71C22×D412yes—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D412yes—
327C2×C4×C71C22×D412yes—
328C2×C4×C71C22×D411yescharacteristic
329C2×C4×C71C2×#4112yes—
330C2×C4×C71H(5,𝔽2)12yes—
331C2×C4×C71C2511yescharacteristic
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—42no—
336C2×Dic71—42no—
337C2×Dic71—42no—
338D284—22no—
339D284—22no—
340D284—42no—
341C4×D71—48no—
342Dic142—22no—
343Dic142—22no—
344Dic142—22no—
345Dic142—22no—
346Dic142—42no—
347Dic142—42no—
348C71⋊C8—22no—
349C71⋊C8—22no—
350C71⋊C8—22no—
351C71⋊C8C2×#4114yes—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—42no—
357C22×C71—42no—
358C22×C71—84no—
359C22×C71—84no—
360C22×C71#55012yes—
361C22×C71#57512yes—
362C22×C71#57712yes—
363C22×C71C23×D411yescharacteristic
364C2×D71—42no—
365C2×D71—42no—
366C2×D71—42no—
367C2×D71—84no—
368C4×C71—22no—
369C4×C71—22no—
370C4×C71—22no—
371C4×C71—22no—
372C4×C71—22no—
373C4×C71—22no—
374C4×C71—42no—
375C4×C71—42no—
376C4×C71#55012yes—
377C4×C71C22×#4111yescharacteristic
378C4×C71C2×H(5,𝔽2)11yescharacteristic
379Dic71—42no—
380Dic71—42no—
381Dic71—42no—
382C2×#3401—711nomaximal, Sylow
383C2×C71—82no—
384C2×C71—82no—
385C2×C71#340114yescomplemented
386C2×C71C2×#55011yescharacteristic
387C2×C71C2×#57511yescharacteristic
388C2×C71C2×#57711yescharacteristic
389D71—82no—
390C2×#559D7111yescharacteristic, complemented
391C2×#556—711no—
392#3401—7116no—
393C2×#497—711no—
394C2×#496—711no—
395C2×#495—711no—
396C2×#464—711no—
397C2×#464—711no—
398C2×#460—711no—
399C2×#463—711no—
400C2×#463—711no—
401C2×#461—711no—
402C2×#446—711no—
403C2×#442—711no—
404C2×#441—711no—
405C2×C4×SD16—711no—
406C71C2×#340111yescharacteristic, complemented, Sylow
407C22×Q16—711no—
408C22×Q16—711no—
409C22×SD16—711no—
410C22×SD16—711no—
411C22×SD16—711no—
412C22×SD16—711no—
413C22×SD16—711no—
414C22×D8—711no—
415C22×D8—711no—
416#559—24no—
417#559C2×D7118yescomplemented
418#556—718no—
419#556—1424no—
420C2×C4⋊Q8—711no—
421C2×#127C2×D7111yescharacteristic
422C2×#126—1421no—
423C2×#126—1421no—
424C2×#124—21no—
425C2×#124—711no—
426C2×#124—711no—
427C2×#124C2×D7111yescharacteristic
428C2×#124C2×D7111yescharacteristic
429C2×#123—21no—
430C2×#123—21no—
431C2×C22⋊Q8—1421no—
432C2×C4×Q8—711no—
433C2×C4×Q8—711no—
434C2×C4×Q8C2×D7111yescharacteristic
435C2×C4×Q8C2×D7111yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4—711no—
438C2×C4×D4C2×D7111yescharacteristic
439C2×C4×D4C2×D7111yescharacteristic
440C2×#117—1421no—
441#497—718no—
442#496—718no—
443#495—718no—
444#464—718no—
445#464—718no—
446#463—718no—
447#463—718no—
448#461—718no—
449#460—718no—
450#446—718no—
451#442—718no—
452#441—718no—
453C4×SD16—718no—
454C2×#106—711no—
455C2×C4⋊C8—711no—
456C2×C4⋊C8—711no—
457C2×C4⋊C8—711no—
458C2×#103—711no—
459C2×#103—711no—
460C2×#103—711no—
461C2×#102—711no—
462C2×#102—711no—
463C2×#102—711no—
464C2×#97—711no—
465C2×#97—711no—
466C2×C4×C8—711no—
467C22×Q8—711no—
468C22×Q8—711no—
469C22×Q8C22⋊D7111yescharacteristic
470C22×Q8C22×D7111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—711no—
474C22×D4C22×D7111yescharacteristic
475C22×D4C22×D7111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—1421no—
479C2×Q16—2842no—
480C2×Q16—714no—
481C2×Q16—714no—
482C2×Q16—1424no—
483C2×SD16—2842no—
484C2×SD16—2842no—
485C2×SD16—2842no—
486C2×SD16—2842no—
487C2×SD16—714no—
488C2×SD16—714no—
489C2×SD16—714no—
490C2×SD16—714no—
491C2×SD16—714no—
492C2×SD16—1424no—
493C2×D8—2842no—
494C2×D8—714no—
495C2×D8—714no—
496C2×D8—1424no—
497C22×C8—711no—
498C22×C8—711no—
499C22×C8—711no—
500C22×C8—711no—
501C4⋊Q8—714no—
502C4⋊Q8—1422no—
503#127—22no—
504#127C22×D7114yes—
505#126—1428no—
506#126—1428no—
507#124—28no—
508#124—22no—
509#124—22no—
510#124—714no—
511#124—714no—
512#124—1422no—
513#124—1422no—
514#124C22×D7114yes—
515#124C22×D7114yes—
516#123—28no—
517#123—28no—
518C22⋊Q8—1428no—
519C4×Q8—22no—
520C4×Q8—714no—
521C4×Q8—714no—
522C4×Q8—1422no—
523C4×Q8—1422no—
524C4×Q8C22⋊D7114yes—
525C4×Q8C22×D7114yes—
526C4×Q8C22×D7114yes—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—714no—
531C4×D4—1422no—
532C4×D4C22×D7114yes—
533C4×D4C22×D7114yes—
534#117—1428no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—1421no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4C22⋊D7111yescharacteristic
542C2×C4⋊C4C22⋊D7111yescharacteristic
543C2×C4⋊C4C22⋊D7111yescharacteristic
544C2×C4⋊C4C22×D7111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C42—21no—
557C2×C42—1421no—
558C2×C42—1421no—
559C2×C42C22×D7111yescharacteristic
560C2×C42C22×D7111yescharacteristic
561C2×C42C22×D7111yescharacteristic
562#106—714no—
563C4⋊C8—714no—
564C4⋊C8—714no—
565C4⋊C8—714no—
566#103—714no—
567#103—714no—
568#103—714no—
569#102—714no—
570#102—714no—
571#102—714no—
572#97—714no—
573#97—714no—
574C4×C8—714no—
575C24—21no—
576C24—21no—
577C24—1421no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—42no—
582C2×Q8—712no—
583C2×Q8—712no—
584C2×Q8—1422no—
585C2×Q8—1422no—
586C2×Q8—1422no—
587C2×Q8—1422no—
588C2×Q8—1421no—
589C2×Q8—1421no—
590C2×Q8C2×C22⋊D7114yes—
591C2×Q8C23×D7112yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—44no—
601C2×D4—82no—
602C2×D4—712no—
603C2×D4—1421no—
604C2×D4—1422no—
605C2×D4—1422no—
606C2×D4C23×D7112yes—
607C2×D4C23×D7112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—2844no—
615C22×C4—1421no—
616C22×C4—1421no—
617C22×C4—1421no—
618C22×C4—1424no—
619C22×C4C2×C22⋊D7111yescharacteristic
620C22×C4C2×C22⋊D7111yescharacteristic
621C22×C4C2×C22⋊D7111yescharacteristic
622C22×C4C2×C22⋊D7111yescharacteristic
623C22×C4C2×C22⋊D7111yescharacteristic
624C22×C4C2×C22⋊D7111yescharacteristic
625C22×C4C23×D7111yescharacteristic
626Q16—2844no—
627Q16—1428no—
628SD16—2844no—
629SD16—2844no—
630SD16—2844no—
631SD16—2844no—
632SD16—1428no—
633D8—2844no—
634D8—1428no—
635C2×C8—714no—
636C2×C8—712no—
637C2×C8—712no—
638C2×C8—712no—
639C2×C8—712no—
640C2×C8—1422no—
641C2×C8—1422no—
642C2×C8—1422no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—712no—
646C4⋊C4—1424no—
647C4⋊C4—1424no—
648C4⋊C4—1421no—
649C4⋊C4—1424no—
650C4⋊C4—1424no—
651C4⋊C4C2×C22⋊D7114yes—
652C4⋊C4C2×C22⋊D7114yes—
653C4⋊C4C2×C22⋊D7114yes—
654C4⋊C4C23×D7112yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—1424no—
662C22⋊C4—1424no—
663C22⋊C4—1424no—
664C22⋊C4—1424no—
665C22⋊C4—1424no—
666C42—24no—
667C42—1424no—
668C42—1424no—
669C42C2×C22⋊D7112yes—
670C42C2×C22⋊D7112yes—
671C42C2×C22⋊D7112yes—
672C42C23×D7112yes—
673C42C23×D7112yes—
674C42C23×D7112yes—
675C23—22no—
676C23—22no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—2842no—
684C23—2842no—
685C23—2842no—
686C23—1422no—
687C23C22×C22⋊D7111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—44no—
691Q8—42no—
692Q8—2842no—
693Q8—2842no—
694Q8—1422no—
695Q8—1422no—
696Q8—1422no—
697Q8—1422no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—2842no—
707D4—1422no—
708D4—1422no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—2848no—
722C2×C4—2842no—
723C2×C4—2842no—
724C2×C4—2842no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4C22×C22⋊D7112yes—
729C2×C4C22×C22⋊D7112yes—
730C2×C4C22×C22⋊D7112yes—
731C2×C4C22×C22⋊D7112yes—
732C2×C4C22×C22⋊D7112yes—
733C2×C4C22×C22⋊D7112yes—
734C2×C4C22×C22⋊D7111yescharacteristic
735C2×C4#41×D7112yes—
736C2×C4#1455617412yes—
737C2×C4C24×D7111yescharacteristic
738C8—714no—
739C8—1422no—
740C8—1422no—
741C8—1422no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—2842no—
751C22—2842no—
752C22—2842no—
753C22—5684no—
754C22#1798666812yes—
755C22#1798679712yes—
756C22#1798681012yes—
757C22C23×C22⋊D7111yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—2842no—
767C4—2842no—
768C4—2842no—
769C4#1798666812yes—
770C4C2×#41×D7111yescharacteristic
771C4C2×#1455617411yescharacteristic
772C2—82no—
773C2—82no—
774C2—5682no—
775C2#2260140014yesdirect product factor
776C2C2×#1798666811yescharacteristic
777C2C2×#1798679711yescharacteristic
778C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#559×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986386C2
hypercenterC2×#559D71
hypocenterC71C2×#3401
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#17986722C2semidirect
2. #22601400C2direct (N × H)
3. C2×#17986394C2semidirect
5. C2×#17986381C2semidirect
6. C2×#17986221C2semidirect
7. C2×#17986218C2semidirect
8. C2×#17986196C2semidirect
9. C2×#17986214C2semidirect
10. C2×#17986211C2semidirect
11. C2×#17986204C2semidirect
12. C2×#17986130C2semidirect
13. C2×#17986109C2semidirect
14. C2×#17986104C2semidirect
15. C2×C4×#11765853C2semidirect
16. C2×#559×C71C2semidirect
27. #17986722C22semidirect
38. #17986394C22semidirect
40. #17986381C22semidirect
41. #17986221C22semidirect
42. #17986218C22semidirect
43. #17986214C22semidirect
44. #17986211C22semidirect
45. #17986204C22semidirect
46. #17986196C22semidirect
47. #17986130C22semidirect
48. #17986109C22semidirect
49. #17986104C22semidirect
50. C4×#11765853C22semidirect
65. #559×C71C22semidirect
385. C2×C71#3401semidirect
390. C2×#559D71semidirect
406. C71C2×#3401semidirect
417. #559C2×D71semidirect
775. C2#22601400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867222
#226014002
C2×#179863942
C2×#179863862
C2×#179863812
C2×#179862212
C2×#179862182
C2×#179861962
C2×#179862142
C2×#179862112
C2×#179862042
C2×#179861302
C2×#179861092
C2×#179861042
C2×C4×#117658532
C2×#559×C712
C2×#340171