Finite Group Databasebeta

← C31×#8488 #21465247

Subgroups — C31×#8488 #21465247

Order 7936.

768 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3535C211yesmaximal, characteristic
2C31×#1899C211yesmaximal, characteristic, complemented
3C31×#1897C211yesmaximal, characteristic, complemented
4C31×#1873C211yesmaximal, characteristic, complemented
5C31×#1516C211yesmaximal, characteristic, complemented
6C31×#1511C211yesmaximal, characteristic, complemented
7C31×#1468C211yesmaximal, characteristic, complemented
8C31×#563—21no—
9C31×#562—21no—
10C31×#554—21no—
11C31×#552—21no—
12C31×#551—21no—
13C31×#551—21no—
14C31×#547—21no—
15C31×#546—21no—
16C31×#544C411yescharacteristic, complemented
17C31×#543C411yescharacteristic, complemented
18C31×#542—21no—
19C31×#539—21no—
20C31×#539—21no—
21C31×#539C411yescharacteristic, complemented
22C31×#538C411yescharacteristic, complemented
23C31×#536—21no—
24C31×#525C2211yescharacteristic
25C2×C31×#123C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#117C2211yescharacteristic
28C2×C31×#104—21no—
29C2×C31×#103—21no—
30C2×C31×#99—21no—
31C31×#407C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C31×#381C2211yescharacteristic
34C31×#342—21no—
35C31×#340—21no—
36C31×#339—21no—
37C31×#328—21no—
38C31×#328—21no—
39C31×#328—21no—
40C31×#327—21no—
41C31×#324—21no—
42C31×#323—21no—
43C2×#41×C31—21no—
44C2×#41×C31D411yescharacteristic
45C22×Q8×C31D411yescharacteristic
46C22×D4×C31D411yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C2×M16×C31—21no—
49C22×C8×C31—21no—
50C31×C4⋊Q8—21no—
51C31×C4⋊Q8—21no—
52C31×C4⋊Q8—21no—
53C31×#126—21no—
54C31×#126—21no—
55C31×#126—21no—
56C31×#126—21no—
57C31×#126—21no—
58C31×#126—21no—
59C31×#125—21no—
60C31×#125—21no—
61C31×#125—21no—
62C31×#125—21no—
63C31×#125—21no—
64C31×#124—21no—
65C31×#124—21no—
66C31×#124—21no—
67C31×#124—21no—
68C31×#123—21no—
69C31×#123—21no—
70C31×#123—21no—
71C31×#123—21no—
72C31×#123—21no—
73C31×#123—21no—
74C31×#123—21no—
75C31×#123—21no—
76C31×#123—21no—
77C31×#123—21no—
78C31×#123—21no—
79C31×#123—21no—
80C31×#123—21no—
81C31×#123—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—21no—
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—21no—
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8C2×C411yescharacteristic
97C31×C22⋊Q8C2×C411yescharacteristic
98C31×C22⋊Q8C2×C411yescharacteristic
99C31×C22⋊Q8D411yescharacteristic
100C31×C22⋊Q8D411yescharacteristic
101C31×C22⋊Q8D411yescharacteristic
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121C2×C411yescharacteristic
107C31×#121D411yescharacteristic
108C31×#120—21no—
109C31×#120—21no—
110C4×Q8×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C31×#117—21no—
119C31×#117—21no—
120C31×#117—21no—
121C31×#117—42no—
122C31×#117D411yescharacteristic
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31C2×C411yescharacteristic
127C2×C4⋊C4×C31D411yescharacteristic
128C2×C4⋊C4×C31D411yescharacteristic
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31C2×C411yescharacteristic
134C2×C22⋊C4×C31D411yescharacteristic
135C2×C22⋊C4×C31D411yescharacteristic
136C2×C42×C31—21no—
137C31×#104—42no—
138C31×#103—42no—
139C31×#99—42no—
140C31×C22⋊C8—21no—
141C31×C22⋊C8—21no—
142C31×C22⋊C8—21no—
143C31×C22⋊C8—21no—
144C31×#95—21no—
145C31×#95—21no—
146C24×C31C22⋊C411yescharacteristic
147C24×C31C2×D411yescharacteristic
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—81no—
151#41×C31—81no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—41no—
156C2×Q8×C31—41no—
157C2×Q8×C31C22⋊C411yescharacteristic
158C2×Q8×C31C22⋊C411yescharacteristic
159C2×Q8×C31C22⋊C411yescharacteristic
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—41no—
168C2×D4×C31—41no—
169C2×D4×C31C22⋊C411yescharacteristic
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—41no—
178C22×C4×C31—41no—
179C22×C4×C31—41no—
180C22×C4×C31—41no—
181C22×C4×C31C22⋊C411yescharacteristic
182C22×C4×C31C22⋊C411yescharacteristic
183C22×C4×C31C22⋊C411yescharacteristic
184C22×C4×C31C22×C411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190M16×C31—41no—
191M16×C31—41no—
192C2×C8×C31—41no—
193C2×C8×C31—41no—
194C2×C8×C31—41no—
195C2×C8×C31—41no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—41no—
221C4⋊C4×C31C22⋊C411yescharacteristic
222C4⋊C4×C31C22⋊C411yescharacteristic
223C4⋊C4×C31C22⋊C411yescharacteristic
224C4⋊C4×C31C22⋊C411yescharacteristic
225C22⋊C4×C31—21no—
226C22⋊C4×C31—21no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—21no—
230C22⋊C4×C31—21no—
231C22⋊C4×C31—21no—
232C22⋊C4×C31—21no—
233C22⋊C4×C31—21no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—21no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—21no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—41no—
250C22⋊C4×C31—41no—
251C22⋊C4×C31—41no—
252C42×C31—21no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—21no—
256C42×C31—21no—
257C42×C31—22no—
258C42×C31—41no—
259#8488C3111yesmaximal, characteristic, direct product factor, Sylow
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31C2×C22⋊C411yescharacteristic
270C23×C31#12011yescharacteristic
271C23×C31#12011yescharacteristic
272Q8×C31—41no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31—81no—
276Q8×C31—81no—
277Q8×C31—81no—
278D4×C31—41no—
279D4×C31—42no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—81no—
285D4×C31—81no—
286D4×C31—81no—
287D4×C31—81no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—42no—
312C2×C4×C31—81no—
313C2×C4×C31—81no—
314C2×C4×C31—81no—
315C2×C4×C31—81no—
316C2×C4×C31—81no—
317C2×C4×C31—81no—
318C2×C4×C31—81no—
319C2×C4×C31—81no—
320C2×C4×C31—81no—
321C2×C4×C31—81no—
322C2×C4×C31—81no—
323C2×C4×C31C2×C22⋊C411yescharacteristic
324C2×C4×C31C2×C22⋊C411yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31#12011yescharacteristic
327C8×C31—81no—
328C8×C31—81no—
329#3535C2×C3111yescharacteristic
330#1899C2×C3111yescharacteristic, complemented
331#1897C2×C3111yescharacteristic, complemented
332#1873C2×C3111yescharacteristic, complemented
333#1516C2×C3111yescharacteristic, complemented
334#1511C2×C3111yescharacteristic, complemented
335#1468C2×C3111yescharacteristic, complemented
336C22×C31—21no—
337C22×C31—21no—
338C22×C31—21no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—21no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31—161no—
353C22×C31#37911yescharacteristic
354C22×C31B(4,𝔽2)11yescharacteristic
355C22×C31#45811yescharacteristic
356C4×C31—21no—
357C4×C31—21no—
358C4×C31—21no—
359C4×C31—21no—
360C4×C31—41no—
361C4×C31—41no—
362C4×C31—41no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—41no—
367C4×C31—41no—
368C4×C31—41no—
369C4×C31—41no—
370C4×C31—82no—
371C4×C31—161no—
372#563—21no—
373#562—21no—
374#554—21no—
375#552—21no—
376#551—21no—
377#551—21no—
378#547—21no—
379#546—21no—
380#544C4×C3111yescharacteristic, complemented
381#543C4×C3111yescharacteristic, complemented
382#542—21no—
383#539—21no—
384#539—21no—
385#539C4×C3111yescharacteristic, complemented
386#538C4×C3111yescharacteristic, complemented
387#536—21no—
388#525C22×C3111yescharacteristic
389C2×#123C22×C3111yescharacteristic
390C2×C22⋊Q8C22×C3111yescharacteristic
391C2×#117C22×C3111yescharacteristic
392C2×#104—21no—
393C2×#103—21no—
394C2×#99—21no—
395#407C22×C3111yescharacteristic
396C2×C22⋊C8C22×C3111yescharacteristic
397#381C22×C3111yescharacteristic
398#342—21no—
399#340—21no—
400#339—21no—
401#328—21no—
402#328—21no—
403#328—21no—
404#327—21no—
405#324—21no—
406#323—21no—
407C2×C31—21no—
408C2×C31—21no—
409C2×C31—41no—
410C2×C31—41no—
411C2×C31—81no—
412C2×C31—81no—
413C2×C31#179011yescharacteristic
414C2×C31#179411yescharacteristic
415C2×C31#179611yescharacteristic
416C2×#41—21no—
417C2×#41D4×C3111yescharacteristic
418C22×Q8D4×C3111yescharacteristic
419C22×D4D4×C3111yescharacteristic
420C23×C4C23×C3111yescharacteristic
421C2×M16—21no—
422C22×C8—21no—
423C4⋊Q8—21no—
424C4⋊Q8—21no—
425C4⋊Q8—21no—
426#126—21no—
427#126—21no—
428#126—21no—
429#126—21no—
430#126—21no—
431#126—21no—
432#125—21no—
433#125—21no—
434#125—21no—
435#125—21no—
436#125—21no—
437#124—21no—
438#124—21no—
439#124—21no—
440#124—21no—
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—21no—
446#123—21no—
447#123—21no—
448#123—21no—
449#123—21no—
450#123—21no—
451#123—21no—
452#123—21no—
453#123—21no—
454#123—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8C2×C4×C3111yescharacteristic
470C22⋊Q8C2×C4×C3111yescharacteristic
471C22⋊Q8C2×C4×C3111yescharacteristic
472C22⋊Q8D4×C3111yescharacteristic
473C22⋊Q8D4×C3111yescharacteristic
474C22⋊Q8D4×C3111yescharacteristic
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121C2×C4×C3111yescharacteristic
480#121D4×C3111yescharacteristic
481#120—21no—
482#120—21no—
483C4×Q8—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491#117—21no—
492#117—21no—
493#117—21no—
494#117—42no—
495#117D4×C3111yescharacteristic
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4C2×C4×C3111yescharacteristic
500C2×C4⋊C4D4×C3111yescharacteristic
501C2×C4⋊C4D4×C3111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4C2×C4×C3111yescharacteristic
507C2×C22⋊C4D4×C3111yescharacteristic
508C2×C22⋊C4D4×C3111yescharacteristic
509C2×C42—21no—
510#104—42no—
511#103—42no—
512#99—42no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517#95—21no—
518#95—21no—
519C31#848811yescharacteristic, direct product factor, Sylow
520C24C22⋊C4×C3111yescharacteristic
521C24C2×D4×C3111yescharacteristic
522#41—41no—
523#41—41no—
524#41—81no—
525#41—81no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8C22⋊C4×C3111yescharacteristic
532C2×Q8C22⋊C4×C3111yescharacteristic
533C2×Q8C22⋊C4×C3111yescharacteristic
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4C22⋊C4×C3111yescharacteristic
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4C22⋊C4×C3111yescharacteristic
556C22×C4C22⋊C4×C3111yescharacteristic
557C22×C4C22⋊C4×C3111yescharacteristic
558C22×C4C22×C4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C2×D4×C3111yescharacteristic
561C22×C4C2×D4×C3111yescharacteristic
562C22×C4C2×D4×C3111yescharacteristic
563C22×C4C2×D4×C3111yescharacteristic
564M16—41no—
565M16—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4C22⋊C4×C3111yescharacteristic
596C4⋊C4C22⋊C4×C3111yescharacteristic
597C4⋊C4C22⋊C4×C3111yescharacteristic
598C4⋊C4C22⋊C4×C3111yescharacteristic
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—22no—
632C42—41no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C2×C22⋊C4×C3111yescharacteristic
643C23C31×#12011yescharacteristic
644C23C31×#12011yescharacteristic
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—81no—
649Q8—81no—
650Q8—81no—
651D4—41no—
652D4—42no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—81no—
658D4—81no—
659D4—81no—
660D4—81no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4C2×C22⋊C4×C3111yescharacteristic
697C2×C4C2×C22⋊C4×C3111yescharacteristic
698C2×C4C31×#12011yescharacteristic
699C2×C4C31×#12011yescharacteristic
700C8—81no—
701C8—81no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—161no—
719C22C31×#37911yescharacteristic
720C22C31×B(4,𝔽2)11yescharacteristic
721C22C31×#45811yescharacteristic
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—82no—
737C4—161no—
738C2—21no—
739C2—21no—
740C2—41no—
741C2—41no—
742C2—81no—
743C2—81no—
744C2C31×#179011yescharacteristic
745C2C31×#179411yescharacteristic
746C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1899C2semidirect
3. C31×#1897C2semidirect
4. C31×#1873C2semidirect
5. C31×#1516C2semidirect
6. C31×#1511C2semidirect
7. C31×#1468C2semidirect
16. C31×#544C4semidirect
17. C31×#543C4semidirect
21. C31×#539C4semidirect
22. C31×#538C4semidirect
259. #8488C31direct (N × H)
330. #1899C2×C31semidirect
331. #1897C2×C31semidirect
332. #1873C2×C31semidirect
333. #1516C2×C31semidirect
334. #1511C2×C31semidirect
335. #1468C2×C31semidirect
380. #544C4×C31semidirect
381. #543C4×C31semidirect
385. #539C4×C31semidirect
386. #538C4×C31semidirect
519. C31#8488direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35352
C31×#18992
C31×#18972
C31×#18732
C31×#15162
C31×#15112
C31×#14682
#848831