Finite Group Databasebeta

← C31×#18806 #21475565

Subgroups — C31×#18806 #21475565

Order 7936.

1180 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#41×C31C211yesmaximal, characteristic
2C31×#3228C211yesmaximal, characteristic, complemented
3C31×#3110C211yesmaximal, characteristic, complemented
4C31×#3107C211yesmaximal, characteristic, complemented
5C31×#1654C211yesmaximal, characteristic, complemented
6C31×#1651C211yesmaximal, characteristic, complemented
7C31×#1649C211yesmaximal, characteristic, complemented
8C31×#1647C211yesmaximal, characteristic, complemented
9C31×#1642C211yesmaximal, characteristic, complemented
10C31×#1641C211yesmaximal, characteristic, complemented
11C31×#1639C211yesmaximal, characteristic, complemented
12C31×#1639C211yesmaximal, characteristic, complemented
13C31×#1553C211yesmaximal, characteristic, complemented
14C31×#1488C211yesmaximal, characteristic, complemented
15C31×#1478C211yesmaximal, characteristic, complemented
16C22×#41×C31—21no—
17C31×#550C2211yescharacteristic
18D4×Q8×C31C2211yescharacteristic
19C31×#548—21no—
20C31×#547—21no—
21C31×#547C2211yescharacteristic
22C31×#546—22no—
23C31×#546—21no—
24D42×C31—21no—
25D42×C31C2211yescharacteristic
26C31×#533C2211yescharacteristic, complemented
27C31×#532—21no—
28C31×#532C2211yescharacteristic
29C31×#525—22no—
30C31×#525—21no—
31C4×#41×C31C2211yescharacteristic
32C2×C4×D4×C31—21no—
33C2×C4×D4×C31C2211yescharacteristic
34C31×#500C2211yescharacteristic, complemented
35C31×#498C2211yescharacteristic, complemented
36C31×#486C2211yescharacteristic, complemented
37C31×#486C2211yescharacteristic, complemented
38C31×#485—21no—
39C31×#484—21no—
40C31×#482—22no—
41C31×#478—22no—
42C31×#475C2211yescharacteristic, complemented
43C31×#474C2211yescharacteristic
44C31×#474C2211yescharacteristic, complemented
45C31×#474C2211yescharacteristic, complemented
46C31×#462C2211yescharacteristic, complemented
47C31×#461C2211yescharacteristic
48C31×#461C2211yescharacteristic, complemented
49C31×#461C2211yescharacteristic, complemented
50C31×#452—21no—
51C31×#450—21no—
52C31×#440—21no—
53C31×#440—21no—
54C4×Q16×C31—21no—
55C4×SD16×C31—21no—
56C31×#432C2211yescharacteristic, complemented
57C31×#431C2211yescharacteristic, complemented
58C31×#431C2211yescharacteristic, complemented
59C31×#332C2211yescharacteristic, complemented
60C31×#332C2211yescharacteristic, complemented
61C31×#331C2211yescharacteristic, complemented
62C31×#331C2211yescharacteristic, complemented
63C31×Q8⋊C8C2211yescharacteristic, complemented
64C31×Q8⋊C8C2211yescharacteristic, complemented
65C31×D4⋊C8C2211yescharacteristic
66C31×D4⋊C8C2211yescharacteristic
67C31×D4⋊C8C2211yescharacteristic, complemented
68C31×D4⋊C8C2211yescharacteristic, complemented
69C31×D4⋊C8C2211yescharacteristic, complemented
70C31×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—21no—
74C2×#41×C31—21no—
75C2×#41×C31—21no—
76C2×#41×C31—44no—
77C2×#41×C31—44no—
78C2×#41×C31D411yescharacteristic
79C22×Q8×C31—21no—
80C22×D4×C31—22no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31D411yescharacteristic
84C23×C4×C31—22no—
85C23×C4×C31—21no—
86C2×Q16×C31—21no—
87C2×SD16×C31—21no—
88C2×SD16×C31—21no—
89C2×SD16×C31—21no—
90C31×C4⋊Q8—21no—
91C31×C4⋊Q8C2311yescharacteristic
92C31×C4⋊Q8C2311yescharacteristic
93C31×C4⋊Q8C2311yescharacteristic
94C31×#127—21no—
95C31×#127C2311yescharacteristic
96C31×#125—21no—
97C31×#124—22no—
98C31×#124—21no—
99C31×#123—22no—
100C31×#123—22no—
101C31×#123—22no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8—21no—
104C31×C22⋊Q8—22no—
105C31×C22⋊Q8—21no—
106C31×C22⋊Q8—21no—
107C31×C22⋊Q8—21no—
108C31×#121—22no—
109C31×#121—22no—
110C31×#121—22no—
111C31×#121—21no—
112C31×#121—21no—
113C31×#121—21no—
114C31×#121—21no—
115C31×#121—21no—
116C31×#121D412yes—
117C31×#120—22no—
118C31×#120—22no—
119C31×#120—22no—
120C4×Q8×C31—21no—
121C4×Q8×C31—21no—
122C4×Q8×C31D411yescharacteristic
123C4×Q8×C31C2311yescharacteristic
124C4×D4×C31—22no—
125C4×D4×C31—22no—
126C4×D4×C31—22no—
127C4×D4×C31—21no—
128C4×D4×C31—21no—
129C4×D4×C31—21no—
130C4×D4×C31—21no—
131C4×D4×C31—21no—
132C4×D4×C31—21no—
133C4×D4×C31—21no—
134C4×D4×C31D411yescharacteristic
135C4×D4×C31D411yescharacteristic
136C4×D4×C31D411yescharacteristic
137C4×D4×C31D412yes—
138C4×D4×C31C2311yescharacteristic
139C4×D4×C31C2311yescharacteristic
140C4×D4×C31C2311yescharacteristic
141C31×#117—21no—
142C31×#117—21no—
143C31×#117D411yescharacteristic
144C2×C4⋊C4×C31—21no—
145C2×C4⋊C4×C31D411yescharacteristic
146C2×C22⋊C4×C31—22no—
147C2×C22⋊C4×C31—21no—
148C2×C42×C31—21no—
149C2×C42×C31C2311yescharacteristic
150C31×#107—21no—
151C31×#107—21no—
152C31×#107—21no—
153C31×#107—22no—
154C31×#106—21no—
155C31×#106—22no—
156C31×C4⋊C8—21no—
157C31×C4⋊C8C2311yescharacteristic
158C31×C4⋊C8C2311yescharacteristic
159C31×C4⋊C8C2311yescharacteristic
160C31×C4⋊C8C2311yescharacteristic
161C31×#103—21no—
162C31×#103—21no—
163C31×#103—21no—
164C31×#103—21no—
165C31×#103—21no—
166C31×#102—21no—
167C31×#102—21no—
168C31×#102—21no—
169C31×#102—22no—
170C31×#102—22no—
171C31×C22⋊C8—21no—
172C31×C22⋊C8—21no—
173C31×C22⋊C8—21no—
174C31×#97—21no—
175C4×C8×C31—21no—
176C4×C8×C31C2311yescharacteristic
177C4×C8×C31C2311yescharacteristic
178C24×C31—22no—
179C24×C31—21no—
180#41×C31—22no—
181#41×C31—22no—
182#41×C31—48no—
183#41×C31—42no—
184#41×C31—42no—
185#41×C31—48no—
186#41×C31—42no—
187#41×C31—42no—
188#41×C31—42no—
189#41×C31—42no—
190C2×Q8×C31—22no—
191C2×Q8×C31—21no—
192C2×Q8×C31—21no—
193C2×Q8×C31—21no—
194C2×Q8×C31—42no—
195C2×Q8×C31—42no—
196C2×Q8×C31C2×D411yescharacteristic
197C2×D4×C31—21no—
198C2×D4×C31—22no—
199C2×D4×C31—22no—
200C2×D4×C31—22no—
201C2×D4×C31—22no—
202C2×D4×C31—22no—
203C2×D4×C31—22no—
204C2×D4×C31—22no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—41no—
209C2×D4×C31—42no—
210C2×D4×C31—48no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31C2×D411yescharacteristic
215C2×D4×C31C2×D411yescharacteristic
216C2×D4×C31C2×D411yescharacteristic
217C2×D4×C31C2×D412yes—
218C22×C4×C31—21no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—22no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—48no—
231C22×C4×C31—42no—
232C22×C4×C31—42no—
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D411yescharacteristic
235C22×C4×C31C2×D411yescharacteristic
236Q16×C31—42no—
237SD16×C31—42no—
238SD16×C31—42no—
239SD16×C31—42no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—22no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—41no—
257C4⋊C4×C31—41no—
258C4⋊C4×C31C2×D411yescharacteristic
259C4⋊C4×C31C2×D411yescharacteristic
260C4⋊C4×C31C2×D411yescharacteristic
261C4⋊C4×C31C2×D411yescharacteristic
262C4⋊C4×C31C2×D412yes—
263C22⋊C4×C31—22no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—22no—
266C22⋊C4×C31—22no—
267C22⋊C4×C31—21no—
268C22⋊C4×C31—21no—
269C22⋊C4×C31—22no—
270C22⋊C4×C31—21no—
271C22⋊C4×C31—21no—
272C22⋊C4×C31—22no—
273C22⋊C4×C31—21no—
274C22⋊C4×C31—21no—
275C22⋊C4×C31—21no—
276C22⋊C4×C31—41no—
277C42×C31—21no—
278C42×C31—21no—
279C42×C31—21no—
280C42×C31—41no—
281C42×C31C2×D411yescharacteristic
282C42×C31C2×D411yescharacteristic
283C42×C31C2×D411yescharacteristic
284C42×C31C2411yescharacteristic
285#18806C3111yesmaximal, characteristic, direct product factor, Sylow
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—22no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—44no—
293C23×C31—44no—
294C23×C31—81no—
295C23×C31—82no—
296C23×C31#12011yescharacteristic
297Q8×C31—21no—
298Q8×C31—44no—
299Q8×C31—41no—
300Q8×C31—41no—
301Q8×C31—41no—
302Q8×C31—41no—
303Q8×C31—41no—
304Q8×C31—41no—
305Q8×C31AGL(1,ℤ/8)12yes—
306D4×C31—24no—
307D4×C31—21no—
308D4×C31—21no—
309D4×C31—21no—
310D4×C31—21no—
311D4×C31—42no—
312D4×C31—42no—
313D4×C31—44no—
314D4×C31—44no—
315D4×C31—44no—
316D4×C31—44no—
317D4×C31—44no—
318D4×C31—41no—
319D4×C31—41no—
320D4×C31—41no—
321D4×C31—41no—
322D4×C31—82no—
323D4×C31#13512yes—
324D4×C31AGL(1,ℤ/8)12yes—
325C2×C4×C31—24no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—21no—
336C2×C4×C31—41no—
337C2×C4×C31—42no—
338C2×C4×C31—44no—
339C2×C4×C31—44no—
340C2×C4×C31—42no—
341C2×C4×C31—44no—
342C2×C4×C31—42no—
343C2×C4×C31—44no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—81no—
353C2×C4×C31#12011yescharacteristic
354C2×C4×C31#12011yescharacteristic
355C2×C4×C31#12011yescharacteristic
356C2×C4×C31C22×D411yescharacteristic
357C2×C4×C31C22×D411yescharacteristic
358C2×C4×C31C22×D411yescharacteristic
359C8×C31—41no—
360C8×C31—41no—
361C8×C31—41no—
362C8×C31—41no—
363C8×C31—41no—
364C8×C31—41no—
365D4×#41C2×C3111yescharacteristic
366#3228C2×C3111yescharacteristic, complemented
367#3110C2×C3111yescharacteristic, complemented
368#3107C2×C3111yescharacteristic, complemented
369#1654C2×C3111yescharacteristic, complemented
370#1651C2×C3111yescharacteristic, complemented
371#1649C2×C3111yescharacteristic, complemented
372#1647C2×C3111yescharacteristic, complemented
373#1642C2×C3111yescharacteristic, complemented
374#1641C2×C3111yescharacteristic, complemented
375#1639C2×C3111yescharacteristic, complemented
376#1639C2×C3111yescharacteristic, complemented
377#1553C2×C3111yescharacteristic, complemented
378#1488C2×C3111yescharacteristic, complemented
379#1478C2×C3111yescharacteristic, complemented
380C22×C31—21no—
381C22×C31—22no—
382C22×C31—21no—
383C22×C31—22no—
384C22×C31—21no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—41no—
393C22×C31—42no—
394C22×C31—41no—
395C22×C31—84no—
396C22×C31—88no—
397C22×C31C2×#12011yescharacteristic
398C4×C31—21no—
399C4×C31—21no—
400C4×C31—22no—
401C4×C31—21no—
402C4×C31—21no—
403C4×C31—41no—
404C4×C31—41no—
405C4×C31—42no—
406C4×C31—41no—
407C4×C31—41no—
408C4×C31—81no—
409C4×C31—81no—
410C4×C31C2×#13511yescharacteristic
411C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
412C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
413C4×C31#57511yescharacteristic
414C22×#41—21no—
415#550C22×C3111yescharacteristic
416D4×Q8C22×C3111yescharacteristic
417#548—21no—
418#547—21no—
419#547C22×C3111yescharacteristic
420#546—22no—
421#546—21no—
422D42—21no—
423D42C22×C3111yescharacteristic
424#533C22×C3111yescharacteristic, complemented
425#532—21no—
426#532C22×C3111yescharacteristic
427#525—22no—
428#525—21no—
429C4×#41C22×C3111yescharacteristic
430C2×C4×D4—21no—
431C2×C4×D4C22×C3111yescharacteristic
432#500C22×C3111yescharacteristic, complemented
433#498C22×C3111yescharacteristic, complemented
434#486C22×C3111yescharacteristic, complemented
435#486C22×C3111yescharacteristic, complemented
436#485—21no—
437#484—21no—
438#482—22no—
439#478—22no—
440#475C22×C3111yescharacteristic, complemented
441#474C22×C3111yescharacteristic
442#474C22×C3111yescharacteristic, complemented
443#474C22×C3111yescharacteristic, complemented
444#462C22×C3111yescharacteristic, complemented
445#461C22×C3111yescharacteristic
446#461C22×C3111yescharacteristic, complemented
447#461C22×C3111yescharacteristic, complemented
448#452—21no—
449#450—21no—
450#440—21no—
451#440—21no—
452C4×Q16—21no—
453C4×SD16—21no—
454#432C22×C3111yescharacteristic, complemented
455#431C22×C3111yescharacteristic, complemented
456#431C22×C3111yescharacteristic, complemented
457#332C22×C3111yescharacteristic, complemented
458#332C22×C3111yescharacteristic, complemented
459#331C22×C3111yescharacteristic, complemented
460#331C22×C3111yescharacteristic, complemented
461Q8⋊C8C22×C3111yescharacteristic, complemented
462Q8⋊C8C22×C3111yescharacteristic, complemented
463D4⋊C8C22×C3111yescharacteristic
464D4⋊C8C22×C3111yescharacteristic
465D4⋊C8C22×C3111yescharacteristic, complemented
466D4⋊C8C22×C3111yescharacteristic, complemented
467D4⋊C8C22×C3111yescharacteristic, complemented
468D4⋊C8C22×C3111yescharacteristic, complemented
469C2×C31—41no—
470C2×C31—42no—
471C2×C31—42no—
472C2×C31—81no—
473C2×C31—82no—
474C2×C31#300211yescharacteristic
475C2×C31#300311yescharacteristic
476C2×C31#302211yescharacteristic
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—44no—
483C2×#41—44no—
484C2×#41D4×C3111yescharacteristic
485C22×Q8—21no—
486C22×D4—22no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4D4×C3111yescharacteristic
490C23×C4—22no—
491C23×C4—21no—
492C2×Q16—21no—
493C2×SD16—21no—
494C2×SD16—21no—
495C2×SD16—21no—
496C4⋊Q8—21no—
497C4⋊Q8C23×C3111yescharacteristic
498C4⋊Q8C23×C3111yescharacteristic
499C4⋊Q8C23×C3111yescharacteristic
500#127—21no—
501#127C23×C3111yescharacteristic
502#125—21no—
503#124—22no—
504#124—21no—
505#123—22no—
506#123—22no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—22no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121D4×C3112yes—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8D4×C3111yescharacteristic
529C4×Q8C23×C3111yescharacteristic
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4D4×C3111yescharacteristic
541C4×D4D4×C3111yescharacteristic
542C4×D4D4×C3111yescharacteristic
543C4×D4D4×C3112yes—
544C4×D4C23×C3111yescharacteristic
545C4×D4C23×C3111yescharacteristic
546C4×D4C23×C3111yescharacteristic
547#117—21no—
548#117—21no—
549#117D4×C3111yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4D4×C3111yescharacteristic
552C2×C22⋊C4—22no—
553C2×C22⋊C4—21no—
554C2×C42—21no—
555C2×C42C23×C3111yescharacteristic
556#107—21no—
557#107—21no—
558#107—21no—
559#107—22no—
560#106—21no—
561#106—22no—
562C4⋊C8—21no—
563C4⋊C8C23×C3111yescharacteristic
564C4⋊C8C23×C3111yescharacteristic
565C4⋊C8C23×C3111yescharacteristic
566C4⋊C8C23×C3111yescharacteristic
567#103—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—22no—
576#102—22no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580#97—21no—
581C4×C8—21no—
582C4×C8C23×C3111yescharacteristic
583C4×C8C23×C3111yescharacteristic
584C31#1880611yescharacteristic, direct product factor, Sylow
585C24—22no—
586C24—21no—
587#41—22no—
588#41—22no—
589#41—48no—
590#41—42no—
591#41—42no—
592#41—48no—
593#41—42no—
594#41—42no—
595#41—42no—
596#41—42no—
597C2×Q8—22no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8C2×D4×C3111yescharacteristic
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—41no—
616C2×D4—42no—
617C2×D4—48no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C3111yescharacteristic
622C2×D4C2×D4×C3111yescharacteristic
623C2×D4C2×D4×C3111yescharacteristic
624C2×D4C2×D4×C3112yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—48no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643Q16—42no—
644SD16—42no—
645SD16—42no—
646SD16—42no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4C2×D4×C3111yescharacteristic
666C4⋊C4C2×D4×C3111yescharacteristic
667C4⋊C4C2×D4×C3111yescharacteristic
668C4⋊C4C2×D4×C3111yescharacteristic
669C4⋊C4C2×D4×C3112yes—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—22no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—22no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—41no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—41no—
688C42C2×D4×C3111yescharacteristic
689C42C2×D4×C3111yescharacteristic
690C42C2×D4×C3111yescharacteristic
691C42C24×C3111yescharacteristic
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—81no—
701C23—82no—
702C23C31×#12011yescharacteristic
703Q8—21no—
704Q8—44no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8C31×AGL(1,ℤ/8)12yes—
712D4—24no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—42no—
718D4—42no—
719D4—44no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—44no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—82no—
729D4C31×#13512yes—
730D4C31×AGL(1,ℤ/8)12yes—
731C2×C4—24no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—81no—
759C2×C4C31×#12011yescharacteristic
760C2×C4C31×#12011yescharacteristic
761C2×C4C31×#12011yescharacteristic
762C2×C4C22×D4×C3111yescharacteristic
763C2×C4C22×D4×C3111yescharacteristic
764C2×C4C22×D4×C3111yescharacteristic
765C8—41no—
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C22—21no—
772C22—22no—
773C22—21no—
774C22—22no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—84no—
787C22—88no—
788C22C2×C31×#12011yescharacteristic
789C4—21no—
790C4—21no—
791C4—22no—
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—81no—
800C4—81no—
801C4C2×C31×#13511yescharacteristic
802C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
803C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
804C4C31×#57511yescharacteristic
805C2—41no—
806C2—42no—
807C2—42no—
808C2—81no—
809C2—82no—
810C2C31×#300211yescharacteristic
811C2C31×#300311yescharacteristic
812C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalD4×#41×C31C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3228C2semidirect
3. C31×#3110C2semidirect
4. C31×#3107C2semidirect
5. C31×#1654C2semidirect
6. C31×#1651C2semidirect
7. C31×#1649C2semidirect
8. C31×#1647C2semidirect
9. C31×#1642C2semidirect
10. C31×#1641C2semidirect
11. C31×#1639C2semidirect
12. C31×#1639C2semidirect
13. C31×#1553C2semidirect
14. C31×#1488C2semidirect
15. C31×#1478C2semidirect
26. C31×#533C22semidirect
34. C31×#500C22semidirect
35. C31×#498C22semidirect
36. C31×#486C22semidirect
37. C31×#486C22semidirect
42. C31×#475C22semidirect
44. C31×#474C22semidirect
45. C31×#474C22semidirect
46. C31×#462C22semidirect
48. C31×#461C22semidirect
49. C31×#461C22semidirect
56. C31×#432C22semidirect
57. C31×#431C22semidirect
58. C31×#431C22semidirect
59. C31×#332C22semidirect
60. C31×#332C22semidirect
61. C31×#331C22semidirect
62. C31×#331C22semidirect
63. C31×Q8⋊C8C22semidirect
64. C31×Q8⋊C8C22semidirect
67. C31×D4⋊C8C22semidirect
68. C31×D4⋊C8C22semidirect
69. C31×D4⋊C8C22semidirect
70. C31×D4⋊C8C22semidirect
285. #18806C31direct (N × H)
366. #3228C2×C31semidirect
367. #3110C2×C31semidirect
368. #3107C2×C31semidirect
369. #1654C2×C31semidirect
370. #1651C2×C31semidirect
371. #1649C2×C31semidirect
372. #1647C2×C31semidirect
373. #1642C2×C31semidirect
374. #1641C2×C31semidirect
375. #1639C2×C31semidirect
376. #1639C2×C31semidirect
377. #1553C2×C31semidirect
378. #1488C2×C31semidirect
379. #1478C2×C31semidirect
424. #533C22×C31semidirect
432. #500C22×C31semidirect
433. #498C22×C31semidirect
434. #486C22×C31semidirect
435. #486C22×C31semidirect
440. #475C22×C31semidirect
442. #474C22×C31semidirect
443. #474C22×C31semidirect
444. #462C22×C31semidirect
446. #461C22×C31semidirect
447. #461C22×C31semidirect
454. #432C22×C31semidirect
455. #431C22×C31semidirect
456. #431C22×C31semidirect
457. #332C22×C31semidirect
458. #332C22×C31semidirect
459. #331C22×C31semidirect
460. #331C22×C31semidirect
461. Q8⋊C8C22×C31semidirect
462. Q8⋊C8C22×C31semidirect
465. D4⋊C8C22×C31semidirect
466. D4⋊C8C22×C31semidirect
467. D4⋊C8C22×C31semidirect
468. D4⋊C8C22×C31semidirect
584. C31#18806direct (N × H)

Maximal subgroups

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

subgroupindex
D4×#41×C312
C31×#32282
C31×#31102
C31×#31072
C31×#16542
C31×#16512
C31×#16492
C31×#16472
C31×#16422
C31×#16412
C31×#16392
C31×#15532
C31×#14882
C31×#14782
#1880631