Finite Group Databasebeta

← C31×#24141 #21480900

Subgroups — C31×#24141 #21480900

Order 7936.

1200 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
1C31×#3505C211yesmaximal, characteristic
2C31×#2855C211yesmaximal, characteristic, complemented
3C31×#2854C211yesmaximal, characteristic, complemented
4C4×C31×#123C211yesmaximal, characteristic, complemented
5C31×#2044C212yesmaximal, complemented
6C31×#2022C212yesmaximal, complemented
7C31×#1996C211yesmaximal, characteristic, complemented
8C31×#1964C211yesmaximal, characteristic, complemented
9C31×#1890C212yesmaximal, complemented
10C31×#1867C212yesmaximal, complemented
11C31×#1799C211yesmaximal, characteristic, complemented
12C31×#553—22no—
13C31×#553—21no—
14C31×#552—21no—
15C31×#551—22no—
16C31×#548—21no—
17C31×#546—21no—
18C31×#539—21no—
19C31×#538—21no—
20C31×#534C2212yes—
21C31×#529—21no—
22C31×#525—21no—
23C2×C31×#123C2211yescharacteristic
24C2×C31×#123C2212yes—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C31×#518C2212yes—
28C2×C4×D4×C31C2211yescharacteristic
29C22×C42×C31C2211yescharacteristic
30C2×C31×#99C2212yes—
31C2×C31×#99C2212yes—
32C2×C31×#99C2212yes—
33C31×#391—21no—
34C31×#390—21no—
35C31×#389—21no—
36C31×#389—21no—
37C31×#388—22no—
38C31×#388—21no—
39C31×#387—22no—
40C31×#387—21no—
41C31×#386C2212yes—
42C31×#386C2211yescharacteristic
43C31×#385C2212yes—
44C31×#385C2211yescharacteristic
45C31×#381C2212yes—
46C31×#381C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C4×C4⋊C4×C31—21no—
50C4×C22⋊C4×C31—21no—
51C4×C22⋊C4×C31C2211yescharacteristic
52C31×#342C2212yes—
53C31×#342C2212yes—
54C31×#342C2212yes—
55C2×#41×C31—21no—
56C22×Q8×C31D411yescharacteristic
57C22×D4×C31D411yescharacteristic
58C22×D4×C31C2311yescharacteristic
59C22×D4×C31C2312yes—
60C23×C4×C31D411yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C31×#126—22no—
65C31×#126—22no—
66C31×#126—22no—
67C31×#125—21no—
68C31×#125—22no—
69C31×#124—21no—
70C31×#124—22no—
71C31×#123—22no—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—24no—
79C31×#123—42no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—22no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×#121—21no—
87C31×#121—22no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#120—22no—
95C31×#120—22no—
96C4×Q8×C31—21no—
97C4×D4×C31—22no—
98C4×D4×C31—21no—
99C4×D4×C31—21no—
100C4×D4×C31—21no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C31×#117—21no—
108C31×#117—22no—
109C31×#117—22no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31D411yescharacteristic
117C2×C4⋊C4×C31D411yescharacteristic
118C2×C4⋊C4×C31D412yes—
119C2×C4⋊C4×C31D411yescharacteristic
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31D411yescharacteristic
126C2×C22⋊C4×C31D412yes—
127C2×C22⋊C4×C31C2312yes—
128C2×C22⋊C4×C31C2311yescharacteristic
129C2×C22⋊C4×C31C2312yes—
130C2×C22⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31C2312yes—
132C2×C22⋊C4×C31C2311yescharacteristic
133C2×C42×C31—21no—
134C2×C42×C31—21no—
135C2×C42×C31—21no—
136C2×C42×C31—21no—
137C2×C42×C31—21no—
138C2×C42×C31—21no—
139C2×C42×C31—21no—
140C2×C42×C31D411yescharacteristic
141C31×#99—24no—
142C31×#99—42no—
143C31×#99—42no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C24×C31C2×D412yes—
156C24×C31C2×D411yescharacteristic
157C24×C31C2411yescharacteristic
158#41×C31—82no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—42no—
162C2×D4×C31—21no—
163C2×D4×C31—22no—
164C2×D4×C31—21no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—22no—
170C2×D4×C31—21no—
171C2×D4×C31—22no—
172C2×D4×C31—21no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—42no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—42no—
197C22×C4×C31—42no—
198C22×C4×C31—42no—
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D412yes—
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31#4112yescomplemented
212C4⋊C4×C31—24no—
213C4⋊C4×C31—22no—
214C4⋊C4×C31—22no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—22no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—44no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31—44no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—44no—
253C22⋊C4×C31—44no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31#4112yescomplemented
256C42×C31—22no—
257C42×C31—22no—
258C42×C31—21no—
259C42×C31—21no—
260C42×C31—42no—
261C42×C31—41no—
262C42×C31—41no—
263C42×C31—41no—
264C42×C31—41no—
265#24141C3111yesmaximal, characteristic, direct product factor, Sylow
266C23×C31—21no—
267C23×C31—22no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31C22×D411yescharacteristic
279C23×C31C22×D411yescharacteristic
280C23×C31C22×D411yescharacteristic
281C23×C31C2×#4111yescharacteristic
282C23×C31C2×#4111yescharacteristic
283C23×C31H(5,𝔽2)11yescharacteristic
284C23×C312−1+411yescharacteristic
285Q8×C31—42no—
286Q8×C31—81no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—41no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—41no—
295D4×C31—42no—
296D4×C31—81no—
297D4×C31—82no—
298D4×C31—82no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—42no—
333C2×C4×C31—41no—
334C2×C4×C31—42no—
335C2×C4×C31—41no—
336C2×C4×C31—42no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—41no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—81no—
347C2×C4×C31—82no—
348C2×C4×C31—82no—
349C2×C4×C31#12011yescharacteristic
350C2×C4×C31#12011yescharacteristic
351C2×C4×C31#12011yescharacteristic
352C2×C4×C31#12011yescharacteristic
353#3505C2×C3111yescharacteristic
354#2855C2×C3111yescharacteristic, complemented
355#2854C2×C3111yescharacteristic, complemented
356C4×#123C2×C3111yescharacteristic, complemented
357#2044C2×C3112yescomplemented
358#2022C2×C3112yescomplemented
359#1996C2×C3111yescharacteristic, complemented
360#1964C2×C3111yescharacteristic, complemented
361#1890C2×C3112yescomplemented
362#1867C2×C3112yescomplemented
363#1799C2×C3111yescharacteristic, complemented
364C22×C31—21no—
365C22×C31—21no—
366C22×C31—21no—
367C22×C31—21no—
368C22×C31—21no—
369C22×C31—21no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—42no—
375C22×C31—41no—
376C22×C31—42no—
377C22×C31—41no—
378C22×C31—42no—
379C22×C31—42no—
380C22×C31—41no—
381C22×C31—82no—
382C22×C31—81no—
383C22×C31—82no—
384C22×C31C2×#12011yescharacteristic
385C22×C31#52511yescharacteristic
386C22×C31#53711yescharacteristic
387C22×C31#54611yescharacteristic
388C22×C31#54711yescharacteristic
389C22×C31#54811yescharacteristic
390C22×C31#55011yescharacteristic
391C4×C31—21no—
392C4×C31—21no—
393C4×C31—21no—
394C4×C31—42no—
395C4×C31—42no—
396C4×C31—41no—
397C4×C31—42no—
398C4×C31—41no—
399C4×C31—42no—
400C4×C31—42no—
401C4×C31—41no—
402C4×C31—42no—
403C4×C31—82no—
404C4×C31—82no—
405C4×C31—81no—
406C4×C31#45812yes—
407#553—22no—
408#553—21no—
409#552—21no—
410#551—22no—
411#548—21no—
412#546—21no—
413#539—21no—
414#538—21no—
415#534C22×C3112yes—
416#529—21no—
417#525—21no—
418C2×#123C22×C3111yescharacteristic
419C2×#123C22×C3112yes—
420C2×C22⋊Q8C22×C3111yescharacteristic
421C2×#121C22×C3111yescharacteristic
422#518C22×C3112yes—
423C2×C4×D4C22×C3111yescharacteristic
424C22×C42C22×C3111yescharacteristic
425C2×#99C22×C3112yes—
426C2×#99C22×C3112yes—
427C2×#99C22×C3112yes—
428#391—21no—
429#390—21no—
430#389—21no—
431#389—21no—
432#388—22no—
433#388—21no—
434#387—22no—
435#387—21no—
436#386C22×C3112yes—
437#386C22×C3111yescharacteristic
438#385C22×C3112yes—
439#385C22×C3111yescharacteristic
440#381C22×C3112yes—
441#381C22×C3111yescharacteristic
442#380C22×C3111yescharacteristic
443#380C22×C3111yescharacteristic
444C4×C4⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4C22×C3111yescharacteristic
447#342C22×C3112yes—
448#342C22×C3112yes—
449#342C22×C3112yes—
450C2×C31—21no—
451C2×C31—21no—
452C2×C31—21no—
453C2×C31—21no—
454C2×C31—21no—
455C2×C31—21no—
456C2×C31—81no—
457C2×C31—82no—
458C2×C31#240711yescharacteristic
459C2×C31C2×#45811yescharacteristic
460C2×C31#302511yescharacteristic
461C2×#41—21no—
462C22×Q8D4×C3111yescharacteristic
463C22×D4D4×C3111yescharacteristic
464C22×D4C23×C3111yescharacteristic
465C22×D4C23×C3112yes—
466C23×C4D4×C3111yescharacteristic
467C23×C4C23×C3111yescharacteristic
468C23×C4C23×C3111yescharacteristic
469C23×C4C23×C3111yescharacteristic
470#126—22no—
471#126—22no—
472#126—22no—
473#125—21no—
474#125—22no—
475#124—21no—
476#124—22no—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—24no—
485#123—42no—
486C22⋊Q8—21no—
487C22⋊Q8—22no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492#121—21no—
493#121—22no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—22no—
499#121—22no—
500#120—22no—
501#120—22no—
502C4×Q8—21no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513#117—21no—
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4D4×C3111yescharacteristic
523C2×C4⋊C4D4×C3111yescharacteristic
524C2×C4⋊C4D4×C3112yes—
525C2×C4⋊C4D4×C3111yescharacteristic
526C2×C22⋊C4—22no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4D4×C3111yescharacteristic
532C2×C22⋊C4D4×C3112yes—
533C2×C22⋊C4C23×C3112yes—
534C2×C22⋊C4C23×C3111yescharacteristic
535C2×C22⋊C4C23×C3112yes—
536C2×C22⋊C4C23×C3111yescharacteristic
537C2×C22⋊C4C23×C3112yes—
538C2×C22⋊C4C23×C3111yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42D4×C3111yescharacteristic
547#99—24no—
548#99—42no—
549#99—42no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561C31#2414111yescharacteristic, direct product factor, Sylow
562C24C2×D4×C3112yes—
563C24C2×D4×C3111yescharacteristic
564C24C24×C3111yescharacteristic
565#41—82no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—42no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—42no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3112yes—
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3112yes—
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3112yes—
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4#41×C3112yescomplemented
619C4⋊C4—24no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—21no—
632C4⋊C4—44no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—24no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—21no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—42no—
662C22⋊C4#41×C3112yescomplemented
663C42—22no—
664C42—22no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23C22×D4×C3111yescharacteristic
685C23C22×D4×C3111yescharacteristic
686C23C22×D4×C3111yescharacteristic
687C23C2×#41×C3111yescharacteristic
688C23C2×#41×C3111yescharacteristic
689C23C31×H(5,𝔽2)11yescharacteristic
690C23C31×2−1+411yescharacteristic
691Q8—42no—
692Q8—81no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—42no—
702D4—81no—
703D4—82no—
704D4—82no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—81no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4C31×#12011yescharacteristic
756C2×C4C31×#12011yescharacteristic
757C2×C4C31×#12011yescharacteristic
758C2×C4C31×#12011yescharacteristic
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—82no—
777C22—81no—
778C22—82no—
779C22C2×C31×#12011yescharacteristic
780C22C31×#52511yescharacteristic
781C22C31×#53711yescharacteristic
782C22C31×#54611yescharacteristic
783C22C31×#54711yescharacteristic
784C22C31×#54811yescharacteristic
785C22C31×#55011yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—41no—
792C4—42no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—81no—
801C4C31×#45812yes—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—81no—
809C2—82no—
810C2C31×#240711yescharacteristic
811C2C2×C31×#45811yescharacteristic
812C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2855C2semidirect
3. C31×#2854C2semidirect
4. C4×C31×#123C2semidirect
5. C31×#2044C2semidirect
6. C31×#2022C2semidirect
7. C31×#1996C2semidirect
8. C31×#1964C2semidirect
9. C31×#1890C2semidirect
10. C31×#1867C2semidirect
11. C31×#1799C2semidirect
211. C22×C4×C31#41semidirect
255. C22⋊C4×C31#41semidirect
265. #24141C31direct (N × H)
354. #2855C2×C31semidirect
355. #2854C2×C31semidirect
356. C4×#123C2×C31semidirect
357. #2044C2×C31semidirect
358. #2022C2×C31semidirect
359. #1996C2×C31semidirect
360. #1964C2×C31semidirect
361. #1890C2×C31semidirect
362. #1867C2×C31semidirect
363. #1799C2×C31semidirect
561. C31#24141direct (N × H)
618. C22×C4#41×C31semidirect
662. C22⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35052
C31×#28552
C31×#28542
C4×C31×#1232
C31×#20442
C31×#20222
C31×#19962
C31×#19642
C31×#18902
C31×#18672
C31×#17992
#2414131