Finite Group Databasebeta

← C2×#22599025 #32867338

Subgroups — C2×#22599025 #32867338

Order 18176.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986620C211yesmaximal, characteristic, complemented
2#22599025C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986386C211yesmaximal, characteristic, complemented
5C2×#17986356C211yesmaximal, characteristic, complemented
6C2×#17986345C211yesmaximal, characteristic, complemented
7C2×#17986250C211yesmaximal, characteristic, complemented
8C2×#17986243C211yesmaximal, characteristic, complemented
9C2×#17986233C211yesmaximal, characteristic, complemented
10C2×#17986226C211yesmaximal, characteristic, complemented
11C2×#17986109C211yesmaximal, characteristic, complemented
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×C4×#11765853C211yesmaximal, characteristic, complemented
14C2×C4×#11765850C211yesmaximal, characteristic, complemented
15C2×#17985955C211yesmaximal, characteristic, complemented
16C2×#540×C71C211yesmaximal, characteristic, complemented
17C22×#11765853C2211yescharacteristic
18C22×#11765853C2211yescharacteristic
19C22×#11765850C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23#17986620—24no—
24#17986620C2218yescomplemented
25C2×#14556128C2211yescharacteristic
26C2×#14556123—21no—
27C2×#14556116C2211yescharacteristic
28C2×#14556114—21no—
29C2×#14556110—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556106—21no—
32C2×#14556102C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×C4×D284C2211yescharacteristic
35#17986409C2218yescomplemented
36#17986386C2218yescomplemented
37#17986356C2218yescomplemented
38#17986345C2218yescomplemented
39#17986250C2218yescomplemented
40#17986243C2218yescomplemented
41#17986233C2218yescomplemented
42#17986226C2218yescomplemented
43#17986109C2218yescomplemented
44#17986099C2218yescomplemented
45C4×#11765853C2218yescomplemented
46C4×#11765850C2218yescomplemented
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556051C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556049C2211yescharacteristic
54C2×#14556049C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59#17985955C2218yescomplemented
60C2×#14556039C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×C4×C71⋊C8C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#540×C71—24no—
65#540×C71C2218yescomplemented
66C2×#127×C71C2211yescharacteristic
67C2×#125×C71C2211yescharacteristic
68C2×#123×C71—21no—
69C2×#123×C71—21no—
70C2×#121×C71—21no—
71C2×#121×C71—21no—
72C2×#121×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765853—24no—
83C2×#11765853—24no—
84C2×#11765853C2314yes—
85C2×#11765853C2314yes—
86C2×#11765850—24no—
87C2×#11765850—24no—
88C2×#11765850C2314yes—
89C2×#11765850C2314yes—
90C2×#11765849—24no—
91C2×#11765849C2314yes—
92C22×C71⋊C8—24no—
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2314yes—
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98#14556128—22no—
99#14556128C2314yes—
100#14556123—28no—
101#14556116—22no—
102#14556116C2314yes—
103#14556114—28no—
104#14556110—28no—
105#14556107—22no—
106#14556107C2314yes—
107#14556106—28no—
108#14556102—22no—
109#14556102C2314yes—
110C4×Dic142—22no—
111C4×Dic142C2314yes—
112C4×D284—22no—
113C4×D284C2314yes—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×Dic71⋊C4—21no—
118C2×Dic71⋊C4—21no—
119C2×C22⋊Dic71—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×(C2×D71)⋊C4—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×C4×Dic71—21no—
125#14556061C2314yes—
126#14556061C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135#14556048C2314yes—
136#14556048C2314yes—
137#14556039C2314yes—
138#14556039C2314yes—
139C4×C71⋊C8C2314yes—
140C4×C71⋊C8C2314yes—
141C22×D4×C71—21no—
142C22×D4×C71—21no—
143C22×D4×C71—21no—
144C22×D4×C71—21no—
145C22×D4×C71C2311yescharacteristic
146C22×D4×C71C2311yescharacteristic
147C23×C4×C71—21no—
148C23×C4×C71—21no—
149C23×C4×C71C2311yescharacteristic
150#127×C71—22no—
151#127×C71C2314yes—
152#125×C71—22no—
153#125×C71C2314yes—
154#123×C71—28no—
155#123×C71—28no—
156#121×C71—22no—
157#121×C71—22no—
158#121×C71—28no—
159#121×C71—28no—
160#121×C71C2314yes—
161#121×C71C2314yes—
162C4×D4×C71—22no—
163C4×D4×C71—22no—
164C4×D4×C71C2314yes—
165C4×D4×C71C2314yes—
166#117×C71D414yes—
167#117×C71C2314yes—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—21no—
186C2×Dic142—24no—
187C2×Dic142—82no—
188C2×Dic142C2412yes—
189C2×D284—22no—
190C2×D284—22no—
191C2×D284—21no—
192C2×D284C2412yes—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—82no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C2×C4×D71—24no—
199C2×C4×D71—82no—
200#11765853—28no—
201#11765853—28no—
202#11765850—28no—
203#11765850—28no—
204#11765849—28no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—28no—
208C2×C71⋊C8#4114yes—
209C2×C71⋊C8#4114yes—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221C22⋊Dic71—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226C4×Dic71—24no—
227C24×C71—21no—
228C24×C71—21no—
229C24×C71C2×D411yescharacteristic
230C2×D4×C71—24no—
231C2×D4×C71—24no—
232C2×D4×C71—21no—
233C2×D4×C71—21no—
234C2×D4×C71—24no—
235C2×D4×C71—24no—
236C2×D4×C71—22no—
237C2×D4×C71—22no—
238C2×D4×C71—22no—
239C2×D4×C71—22no—
240C2×D4×C71—82no—
241C2×D4×C71—82no—
242C2×D4×C71—82no—
243C2×D4×C71—82no—
244C2×D4×C71C2412yes—
245C2×D4×C71C2412yes—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—24no—
251C22×C4×C71—24no—
252C22×C4×C71—82no—
253C22×C4×C71—82no—
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2411yescharacteristic
262C4⋊C4×C71—24no—
263C4⋊C4×C71—24no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71C2×D414yes—
267C4⋊C4×C71C2×D414yes—
268C4⋊C4×C71C2412yes—
269C4⋊C4×C71C2412yes—
270C22⋊C4×C71—24no—
271C22⋊C4×C71—24no—
272C22⋊C4×C71—24no—
273C22⋊C4×C71—24no—
274C22⋊C4×C71C2×D414yes—
275C22⋊C4×C71C2×D414yes—
276C42×C71C2×D412yes—
277C42×C71C2×D412yes—
278C42×C71C2412yes—
279C42×C71C2412yes—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—42no—
286C23×C71—42no—
287C23×C71—42no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71C22×D412yes—
292C23×C71C22×D411yescharacteristic
293C22×D71—22no—
294C22×D71—42no—
295C22×D71—42no—
296C22×D71—42no—
297D4×C71—22no—
298D4×C71—22no—
299D4×C71—22no—
300D4×C71—22no—
301D4×C71—42no—
302D4×C71—42no—
303D4×C71—84no—
304D4×C71—84no—
305D4×C71—84no—
306D4×C71—84no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—24no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—84no—
320C2×C4×C71—84no—
321C2×C4×C71C22×D412yes—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D412yes—
324C2×C4×C71C22×D412yes—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D411yescharacteristic
327C2×C4×C71C2×#4112yes—
328C2×C4×C71C2×#4112yes—
329C2×C4×C71C2511yescharacteristic
330C22⋊D71—84no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—42no—
335C2×Dic71—42no—
336C2×Dic71—42no—
337D284—22no—
338D284—22no—
339D284—42no—
340C4×D71—84no—
341Dic142—22no—
342Dic142—22no—
343Dic142—42no—
344Dic142—84no—
345C71⋊C8—22no—
346C71⋊C8—22no—
347C71⋊C8C2×#4114yes—
348C71⋊C8C2×#4114yes—
349C22×C71—22no—
350C22×C71—22no—
351C22×C71—22no—
352C22×C71—44no—
353C22×C71—42no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—42no—
357C22×C71—42no—
358C22×C71—42no—
359C22×C71—84no—
360C22×C71—84no—
361C22×C71#53212yes—
362C22×C71#57612yes—
363C22×C71#57712yes—
364C22×C71C23×D411yescharacteristic
365C2×D71—42no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71—84no—
369C4×C71—22no—
370C4×C71—22no—
371C4×C71—22no—
372C4×C71—22no—
373C4×C71—22no—
374C4×C71—42no—
375C4×C71—42no—
376C4×C71#53212yes—
377C4×C71C22×#4111yescharacteristic
378C4×C71C22×#4111yescharacteristic
379Dic71—42no—
380Dic71—42no—
381Dic71—42no—
382C2×#3179—711nomaximal, Sylow
383C2×C71—42no—
384C2×C71—82no—
385C2×C71—82no—
386C2×C71#317914yescomplemented
387C2×C71C2×#53211yescharacteristic
388C2×C71C2×#57611yescharacteristic
389C2×C71C2×#57711yescharacteristic
390D71—82no—
391C2×#542—711no—
392C2×#540D7111yescharacteristic, complemented
393#3179—7116no—
394C2×#501—711no—
395C2×#496—711no—
396C2×#488—711no—
397C2×#486—711no—
398C2×#469—711no—
399C2×#468—711no—
400C2×#466—711no—
401C2×#465—711no—
402C2×#442—711no—
403C2×#440—711no—
404C2×C4×SD16—711no—
405C2×C4×D8—711no—
406C2×#405—711no—
407C71C2×#317911yescharacteristic, complemented, Sylow
408C22×SD16—711no—
409C22×SD16—711no—
410C22×D8—711no—
411C22×D8—711no—
412C22×M16—711no—
413C23×C8—711no—
414#542—718no—
415#542—1424no—
416#540—24no—
417#540C2×D7118yescomplemented
418C2×C4⋊Q8—711no—
419C2×#127C2×D7111yescharacteristic
420C2×#126—1421no—
421C2×#125C2×D7111yescharacteristic
422C2×#124—711no—
423C2×#124—1421no—
424C2×#123—21no—
425C2×#123—21no—
426C2×#123—1421no—
427C2×C22⋊Q8—711no—
428C2×C22⋊Q8—1421no—
429C2×#121—21no—
430C2×#121—21no—
431C2×#121—711no—
432C2×#121C2×D7111yescharacteristic
433C2×#121C2×D7111yescharacteristic
434C2×C4×Q8—711no—
435C2×C4×D4—711no—
436C2×C4×D4C2×D7111yescharacteristic
437C2×C4×D4C2×D7111yescharacteristic
438C2×#117C2×D7111yescharacteristic
439#501—718no—
440#496—718no—
441#488—718no—
442#486—718no—
443#469—718no—
444#468—718no—
445#466—718no—
446#465—718no—
447#442—718no—
448#440—718no—
449C4×SD16—718no—
450C4×D8—718no—
451C2×#107—711no—
452C2×#107—711no—
453C2×#106—711no—
454C2×#106—711no—
455C2×#103—711no—
456C2×#103—711no—
457C2×#102—711no—
458C2×#102—711no—
459C2×#102—711no—
460C2×#102—711no—
461C2×#102—711no—
462C2×#102—711no—
463#405—718no—
464C2×#97—711no—
465C2×#97—711no—
466C2×C4×C8—711no—
467C2×C4×C8—711no—
468C22×Q8—711no—
469C22×Q8—1421no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—711no—
475C22×D4—1421no—
476C22×D4C22×D7111yescharacteristic
477C22×D4C22×D7111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—1421no—
481C23×C4C22×D7111yescharacteristic
482C2×SD16—714no—
483C2×SD16—714no—
484C2×SD16—1424no—
485C2×SD16—1424no—
486C2×D8—714no—
487C2×D8—714no—
488C2×D8—1424no—
489C2×D8—1424no—
490C2×M16—714no—
491C2×M16—1424no—
492C22×C8—711no—
493C22×C8—711no—
494C22×C8—711no—
495C22×C8—714no—
496C22×C8—711no—
497C22×C8—1424no—
498C4⋊Q8—714no—
499C4⋊Q8—1422no—
500#127—22no—
501#127C22×D7114yes—
502#126—1428no—
503#125—22no—
504#125C22×D7114yes—
505#124—714no—
506#124—1428no—
507#124—1422no—
508#123—28no—
509#123—28no—
510#123—1428no—
511C22⋊Q8—714no—
512C22⋊Q8—1422no—
513C22⋊Q8—1428no—
514#121—22no—
515#121—22no—
516#121—28no—
517#121—28no—
518#121—714no—
519#121—1422no—
520#121C22×D7114yes—
521#121C22×D7114yes—
522C4×Q8—714no—
523C4×Q8—1422no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—714no—
527C4×D4—1422no—
528C4×D4C22×D7114yes—
529C4×D4C22×D7114yes—
530#117C22⋊D7114yes—
531#117C22×D7114yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—711no—
535C2×C4⋊C4—711no—
536C2×C4⋊C4—1421no—
537C2×C4⋊C4—1421no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4C22⋊D7111yescharacteristic
540C2×C4⋊C4C22⋊D7111yescharacteristic
541C2×C4⋊C4C22×D7111yescharacteristic
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—1421no—
548C2×C22⋊C4—1421no—
549C2×C22⋊C4—1421no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4C22⋊D7111yescharacteristic
553C2×C22⋊C4C22⋊D7111yescharacteristic
554C2×C42—1421no—
555C2×C42C22×D7111yescharacteristic
556C2×C42C22×D7111yescharacteristic
557#107—714no—
558#107—714no—
559#106—714no—
560#106—714no—
561#103—714no—
562#103—714no—
563#102—714no—
564#102—714no—
565#102—714no—
566#102—714no—
567#102—714no—
568#102—714no—
569#97—714no—
570#97—714no—
571C4×C8—714no—
572C4×C8—714no—
573C24—21no—
574C24—21no—
575C24—1421no—
576C24C2×C22⋊D7111yescharacteristic
577C2×Q8—5682no—
578C2×Q8—712no—
579C2×Q8—1422no—
580C2×Q8—1422no—
581C2×Q8—1421no—
582C2×Q8—1424no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—82no—
597C2×D4—5682no—
598C2×D4—712no—
599C2×D4—1424no—
600C2×D4—1421no—
601C2×D4—1422no—
602C2×D4—1422no—
603C2×D4C23×D7112yes—
604C2×D4C23×D7112yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—5682no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1421no—
617C22×C4—1424no—
618C22×C4C2×C22⋊D7112yes—
619C22×C4C2×C22⋊D7111yescharacteristic
620C22×C4C2×C22⋊D7111yescharacteristic
621C22×C4C2×C22⋊D7111yescharacteristic
622C22×C4C2×C22⋊D7111yescharacteristic
623C22×C4C2×C22⋊D7111yescharacteristic
624C22×C4C23×D7112yes—
625C22×C4C23×D7111yescharacteristic
626SD16—1428no—
627SD16—1428no—
628D8—1428no—
629D8—1428no—
630M16—1428no—
631C2×C8—714no—
632C2×C8—714no—
633C2×C8—712no—
634C2×C8—712no—
635C2×C8—712no—
636C2×C8—712no—
637C2×C8—1428no—
638C2×C8—1422no—
639C2×C8—1422no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—712no—
645C4⋊C4—712no—
646C4⋊C4—1424no—
647C4⋊C4—1424no—
648C4⋊C4—1421no—
649C4⋊C4—1421no—
650C4⋊C4—1424no—
651C4⋊C4C2×C22⋊D7114yes—
652C4⋊C4C2×C22⋊D7114yes—
653C4⋊C4C23×D7112yes—
654C4⋊C4C23×D7112yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—1424no—
660C22⋊C4—1424no—
661C22⋊C4—1424no—
662C22⋊C4—1424no—
663C22⋊C4—1424no—
664C22⋊C4C2×C22⋊D7114yes—
665C22⋊C4C2×C22⋊D7114yes—
666C42—1424no—
667C42C2×C22⋊D7112yes—
668C42C2×C22⋊D7112yes—
669C42C23×D7112yes—
670C42C23×D7112yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—2842no—
683C23—2842no—
684C23—2842no—
685C23—1422no—
686C23C22×C22⋊D7112yes—
687C23C22×C22⋊D7111yescharacteristic
688Q8—2842no—
689Q8—5684no—
690Q8—1422no—
691Q8—1422no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—84no—
702D4—2842no—
703D4—5684no—
704D4—1422no—
705D4—1422no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—2842no—
721C2×C4—2842no—
722C2×C4—2842no—
723C2×C4—5684no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4C22×C22⋊D7112yes—
728C2×C4C22×C22⋊D7112yes—
729C2×C4C22×C22⋊D7112yes—
730C2×C4C22×C22⋊D7112yes—
731C2×C4C22×C22⋊D7112yes—
732C2×C4C22×C22⋊D7111yescharacteristic
733C2×C4#41×D7112yes—
734C2×C4#41×D7112yes—
735C2×C4C24×D7111yescharacteristic
736C8—714no—
737C8—714no—
738C8—1422no—
739C8—1422no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—2842no—
753C22—2842no—
754C22—2842no—
755C22—5684no—
756C22#1798654512yes—
757C22#1798680212yes—
758C22#1798681012yes—
759C22C23×C22⋊D7111yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—2842no—
768C4—2842no—
769C4—2842no—
770C4#1798654512yes—
771C4C2×#41×D7111yescharacteristic
772C4C2×#41×D7111yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—5682no—
777C2#2259902514yesdirect product factor
778C2C2×#1798654511yescharacteristic
779C2C2×#1798680211yescharacteristic
780C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#540×C71C2
socleC23×C71C22×D4
hypercenterC2×#540D71
hypocenterC71C2×#3179
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. #22599025C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986386C2semidirect
5. C2×#17986356C2semidirect
6. C2×#17986345C2semidirect
7. C2×#17986250C2semidirect
8. C2×#17986243C2semidirect
9. C2×#17986233C2semidirect
10. C2×#17986226C2semidirect
11. C2×#17986109C2semidirect
12. C2×#17986099C2semidirect
13. C2×C4×#11765853C2semidirect
14. C2×C4×#11765850C2semidirect
15. C2×#17985955C2semidirect
16. C2×#540×C71C2semidirect
24. #17986620C22semidirect
35. #17986409C22semidirect
36. #17986386C22semidirect
37. #17986356C22semidirect
38. #17986345C22semidirect
39. #17986250C22semidirect
40. #17986243C22semidirect
41. #17986233C22semidirect
42. #17986226C22semidirect
43. #17986109C22semidirect
44. #17986099C22semidirect
45. C4×#11765853C22semidirect
46. C4×#11765850C22semidirect
59. #17985955C22semidirect
65. #540×C71C22semidirect
386. C2×C71#3179semidirect
392. C2×#540D71semidirect
407. C71C2×#3179semidirect
417. #540C2×D71semidirect
777. C2#22599025direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225990252
C2×#179864092
C2×#179863862
C2×#179863562
C2×#179863452
C2×#179862502
C2×#179862432
C2×#179862332
C2×#179862262
C2×#179861092
C2×#179860992
C2×C4×#117658532
C2×C4×#117658502
C2×#179859552
C2×#540×C712
C2×#317971