Finite Group Databasebeta

← C31×#24142 #21480901

Subgroups — C31×#24142 #21480901

Order 7936.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic, complemented
2C31×#2626C211yesmaximal, characteristic, complemented
3C31×#2617C211yesmaximal, characteristic, complemented
4C31×#2321C211yesmaximal, characteristic, complemented
5C31×#2044C212yesmaximal, complemented
6C31×#2021C212yesmaximal, complemented
7C31×#1996C211yesmaximal, characteristic, complemented
8C31×#1964C211yesmaximal, characteristic, complemented
9C31×#1889C212yesmaximal, 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×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120C2211yescharacteristic
26C2×C31×#120C2212yes—
27C31×#518C2212yes—
28C2×C4×D4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C2×C31×#99C2212yes—
31C2×C31×#99C2212yes—
32C2×C31×#99C2212yes—
33C31×#399—21no—
34C31×#397—21no—
35C31×#396—22no—
36C31×#394—22no—
37C31×#393—21no—
38C31×#392—21no—
39C31×#390—21no—
40C31×#388—21no—
41C31×#388—21no—
42C31×#386—21no—
43C31×#386C2211yescharacteristic
44C31×#386C2212yes—
45C31×#385C2211yescharacteristic
46C31×#385C2212yes—
47C31×#380C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#379C2211yescharacteristic
50C31×#379C2212yes—
51C4×C22⋊C4×C31C2211yescharacteristic
52C31×#342C2212yes—
53C31×#342C2212yes—
54C31×#342C2212yes—
55C25×C31C2311yescharacteristic
56C2×#41×C31—21no—
57C22×Q8×C31D411yescharacteristic, complemented
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31D411yescharacteristic, complemented
61C22×D4×C31C2311yescharacteristic
62C22×D4×C31C2312yes—
63C23×C4×C31D411yescharacteristic, complemented
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C31×#126—22no—
67C31×#126—22no—
68C31×#126—22no—
69C31×#125—21no—
70C31×#125—22no—
71C31×#124—21no—
72C31×#124—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×#121—21no—
85C31×#121—22no—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#120—22no—
93C31×#120—22no—
94C31×#120—22no—
95C31×#120—22no—
96C31×#120—24no—
97C31×#120—42no—
98C4×Q8×C31—21no—
99C4×D4×C31—22no—
100C4×D4×C31—21no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31—21no—
104C4×D4×C31—21no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C31×#117—21no—
110C31×#117—22no—
111C31×#117—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31D412yescomplemented
117C2×C4⋊C4×C31D411yescharacteristic, complemented
118C2×C4⋊C4×C31D411yescharacteristic, complemented
119C2×C4⋊C4×C31D411yescharacteristic, complemented
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31D411yescharacteristic, complemented
136C2×C22⋊C4×C31D412yescomplemented
137C2×C22⋊C4×C31C2312yes—
138C2×C22⋊C4×C31C2311yescharacteristic
139C2×C22⋊C4×C31C2312yes—
140C2×C22⋊C4×C31C2311yescharacteristic
141C2×C22⋊C4×C31C2312yes—
142C2×C22⋊C4×C31C2311yescharacteristic
143C2×C42×C31—21no—
144C2×C42×C31D411yescharacteristic, complemented
145C31×#99—24no—
146C31×#99—42no—
147C31×#99—42no—
148C31×#95—22no—
149C31×#95—21no—
150C31×#95—22no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C31×#95—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—81no—
162C24×C31—81no—
163C24×C31C2×D412yes—
164C24×C31C2×D411yescharacteristic
165C24×C31#4112yescomplemented
166C24×C31C2411yescharacteristic
167#41×C31—82no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—81no—
171C2×D4×C31—21no—
172C2×D4×C31—22no—
173C2×D4×C31—21no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—22no—
179C2×D4×C31—21no—
180C2×D4×C31—22no—
181C2×D4×C31—21no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—24no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—44no—
189C2×D4×C31—81no—
190C2×D4×C31—81no—
191C2×D4×C31—81no—
192C2×D4×C31—82no—
193C2×D4×C31—82no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—21no—
205C22×C4×C31—81no—
206C22×C4×C31—81no—
207C22×C4×C31—81no—
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D412yes—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D412yes—
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—22no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—81no—
233C4⋊C4×C31—81no—
234C4⋊C4×C31—81no—
235C4⋊C4×C31—82no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—24no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—21no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—44no—
259C22⋊C4×C31—41no—
260C22⋊C4×C31—41no—
261C22⋊C4×C31—41no—
262C22⋊C4×C31—41no—
263C22⋊C4×C31—81no—
264C22⋊C4×C31—82no—
265C22⋊C4×C31—81no—
266C22⋊C4×C31—82no—
267C22⋊C4×C31—81no—
268C22⋊C4×C31—82no—
269C22⋊C4×C31#4112yescomplemented
270C42×C31—22no—
271C42×C31—22no—
272C42×C31—21no—
273C42×C31—21no—
274C42×C31—81no—
275#24142C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—21no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—21no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—21no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—42no—
290C23×C31—41no—
291C23×C31—42no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—42no—
295C23×C31—41no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—82no—
304C23×C31—82no—
305C23×C31—82no—
306C23×C31—82no—
307C23×C31C22×D411yescharacteristic
308C23×C31C22×D411yescharacteristic
309C23×C31C22×D411yescharacteristic
310C23×C31C2×#4111yescharacteristic
311C23×C31C2×#4111yescharacteristic
312C23×C31H(5,𝔽2)11yescharacteristic
313C23×C312−1+411yescharacteristic
314Q8×C31—42no—
315Q8×C31—81no—
316D4×C31—42no—
317D4×C31—42no—
318D4×C31—42no—
319D4×C31—41no—
320D4×C31—41no—
321D4×C31—41no—
322D4×C31—42no—
323D4×C31—42no—
324D4×C31—41no—
325D4×C31—81no—
326D4×C31—82no—
327D4×C31—84no—
328D4×C31—82no—
329D4×C31—88no—
330C2×C4×C31—21no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—21no—
337C2×C4×C31—22no—
338C2×C4×C31—21no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—42no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—42no—
352C2×C4×C31—41no—
353C2×C4×C31—42no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—41no—
359C2×C4×C31—42no—
360C2×C4×C31—42no—
361C2×C4×C31—42no—
362C2×C4×C31—41no—
363C2×C4×C31—42no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—42no—
367C2×C4×C31—42no—
368C2×C4×C31—81no—
369C2×C4×C31—82no—
370C2×C4×C31—82no—
371C2×C4×C31#12011yescharacteristic
372C2×C4×C31#12011yescharacteristic
373C2×C4×C31#12011yescharacteristic
374C2×C4×C31#12011yescharacteristic
375#3505C2×C3111yescharacteristic, complemented
376#2626C2×C3111yescharacteristic, complemented
377#2617C2×C3111yescharacteristic, complemented
378#2321C2×C3111yescharacteristic, complemented
379#2044C2×C3112yescomplemented
380#2021C2×C3112yescomplemented
381#1996C2×C3111yescharacteristic, complemented
382#1964C2×C3111yescharacteristic, complemented
383#1889C2×C3112yescomplemented
384#1867C2×C3112yescomplemented
385#1799C2×C3111yescharacteristic, complemented
386C22×C31—21no—
387C22×C31—21no—
388C22×C31—21no—
389C22×C31—21no—
390C22×C31—21no—
391C22×C31—21no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—41no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—44no—
399C22×C31—42no—
400C22×C31—44no—
401C22×C31—41no—
402C22×C31—42no—
403C22×C31—42no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—41no—
408C22×C31—82no—
409C22×C31—81no—
410C22×C31—82no—
411C22×C31—82no—
412C22×C31—81no—
413C22×C31—81no—
414C22×C31—82no—
415C22×C31—81no—
416C22×C31—81no—
417C22×C31C2×#12011yescharacteristic
418C22×C31#52511yescharacteristic
419C22×C31#53711yescharacteristic
420C22×C31#54611yescharacteristic
421C22×C31#54711yescharacteristic
422C22×C31#54811yescharacteristic
423C22×C31#55011yescharacteristic
424C4×C31—21no—
425C4×C31—21no—
426C4×C31—21no—
427C4×C31—21no—
428C4×C31—42no—
429C4×C31—41no—
430C4×C31—42no—
431C4×C31—41no—
432C4×C31—42no—
433C4×C31—41no—
434C4×C31—42no—
435C4×C31—82no—
436C4×C31—81no—
437C4×C31—82no—
438C4×C31—81no—
439#553—22no—
440#553—21no—
441#552—21no—
442#551—22no—
443#548—21no—
444#546—21no—
445#539—21no—
446#538—21no—
447#534C22×C3112yes—
448#529—21no—
449#525—21no—
450C2×C22⋊Q8C22×C3111yescharacteristic
451C2×#121C22×C3111yescharacteristic
452C2×#120C22×C3111yescharacteristic
453C2×#120C22×C3112yes—
454#518C22×C3112yes—
455C2×C4×D4C22×C3111yescharacteristic
456C22×C22⋊C4C22×C3111yescharacteristic
457C2×#99C22×C3112yes—
458C2×#99C22×C3112yes—
459C2×#99C22×C3112yes—
460#399—21no—
461#397—21no—
462#396—22no—
463#394—22no—
464#393—21no—
465#392—21no—
466#390—21no—
467#388—21no—
468#388—21no—
469#386—21no—
470#386C22×C3111yescharacteristic
471#386C22×C3112yes—
472#385C22×C3111yescharacteristic
473#385C22×C3112yes—
474#380C22×C3111yescharacteristic
475#380C22×C3111yescharacteristic
476#379C22×C3111yescharacteristic
477#379C22×C3112yes—
478C4×C22⋊C4C22×C3111yescharacteristic
479#342C22×C3112yes—
480#342C22×C3112yes—
481#342C22×C3112yes—
482C2×C31—21no—
483C2×C31—21no—
484C2×C31—21no—
485C2×C31—21no—
486C2×C31—21no—
487C2×C31—21no—
488C2×C31—82no—
489C2×C31—81no—
490C2×C31—82no—
491C2×C31#240711yescharacteristic
492C2×C31#302611yescharacteristic
493C2×C31#302711yescharacteristic
494C25C23×C3111yescharacteristic
495C2×#41—21no—
496C22×Q8D4×C3111yescharacteristic, complemented
497C22×D4—21no—
498C22×D4—22no—
499C22×D4D4×C3111yescharacteristic, complemented
500C22×D4C23×C3111yescharacteristic
501C22×D4C23×C3112yes—
502C23×C4D4×C3111yescharacteristic, complemented
503C23×C4C23×C3111yescharacteristic
504C23×C4C23×C3111yescharacteristic
505#126—22no—
506#126—22no—
507#126—22no—
508#125—21no—
509#125—22no—
510#124—21no—
511#124—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517C22⋊Q8—21no—
518C22⋊Q8—22no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523#121—21no—
524#121—22no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—22no—
530#121—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—24no—
536#120—42no—
537C4×Q8—21no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548#117—21no—
549#117—22no—
550#117—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4D4×C3111yescharacteristic, complemented
556C2×C4⋊C4D4×C3111yescharacteristic, complemented
557C2×C4⋊C4D4×C3112yescomplemented
558C2×C4⋊C4D4×C3111yescharacteristic, complemented
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4D4×C3111yescharacteristic, complemented
575C2×C22⋊C4D4×C3112yescomplemented
576C2×C22⋊C4C23×C3112yes—
577C2×C22⋊C4C23×C3111yescharacteristic
578C2×C22⋊C4C23×C3112yes—
579C2×C22⋊C4C23×C3111yescharacteristic
580C2×C22⋊C4C23×C3112yes—
581C2×C22⋊C4C23×C3111yescharacteristic
582C2×C42—21no—
583C2×C42D4×C3111yescharacteristic, complemented
584#99—24no—
585#99—42no—
586#99—42no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—22no—
592#95—21no—
593#95—22no—
594C31#2414211yescharacteristic, direct product factor, Sylow
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C3112yes—
604C24C2×D4×C3111yescharacteristic
605C24#41×C3112yescomplemented
606C24C24×C3111yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3112yes—
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4C2×D4×C3112yes—
652C22×C4C2×D4×C3111yescharacteristic
653C22×C4C2×D4×C3112yes—
654C22×C4C2×D4×C3111yescharacteristic
655C22×C4C2×D4×C3111yescharacteristic
656C22×C4C2×D4×C3111yescharacteristic
657C22×C4C2×D4×C3111yescharacteristic
658C22×C4C2×D4×C3111yescharacteristic
659C22×C4C2×D4×C3111yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C3112yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C3111yescharacteristic
747C23C22×D4×C3111yescharacteristic
748C23C22×D4×C3111yescharacteristic
749C23C2×#41×C3111yescharacteristic
750C23C2×#41×C3111yescharacteristic
751C23C31×H(5,𝔽2)11yescharacteristic
752C23C31×2−1+411yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—82no—
766D4—84no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4C31×#12011yescharacteristic
811C2×C4C31×#12011yescharacteristic
812C2×C4C31×#12011yescharacteristic
813C2×C4C31×#12011yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×C31×#12011yescharacteristic
846C22C31×#52511yescharacteristic
847C22C31×#53711yescharacteristic
848C22C31×#54611yescharacteristic
849C22C31×#54711yescharacteristic
850C22C31×#54811yescharacteristic
851C22C31×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C31×#240711yescharacteristic
877C2C31×#302611yescharacteristic
878C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
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
1. C31×#3505C2semidirect
2. C31×#2626C2semidirect
3. C31×#2617C2semidirect
4. C31×#2321C2semidirect
5. C31×#2044C2semidirect
6. C31×#2021C2semidirect
7. C31×#1996C2semidirect
8. C31×#1964C2semidirect
9. C31×#1889C2semidirect
10. C31×#1867C2semidirect
11. C31×#1799C2semidirect
57. C22×Q8×C31D4semidirect
60. C22×D4×C31D4semidirect
63. C23×C4×C31D4semidirect
116. C2×C4⋊C4×C31D4semidirect
117. C2×C4⋊C4×C31D4semidirect
118. C2×C4⋊C4×C31D4semidirect
119. C2×C4⋊C4×C31D4semidirect
135. C2×C22⋊C4×C31D4semidirect
136. C2×C22⋊C4×C31D4semidirect
144. C2×C42×C31D4semidirect
165. C24×C31#41semidirect
269. C22⋊C4×C31#41semidirect
275. #24142C31direct (N × H)
375. #3505C2×C31semidirect
376. #2626C2×C31semidirect
377. #2617C2×C31semidirect
378. #2321C2×C31semidirect
379. #2044C2×C31semidirect
380. #2021C2×C31semidirect
381. #1996C2×C31semidirect
382. #1964C2×C31semidirect
383. #1889C2×C31semidirect
384. #1867C2×C31semidirect
385. #1799C2×C31semidirect
496. C22×Q8D4×C31semidirect
499. C22×D4D4×C31semidirect
502. C23×C4D4×C31semidirect
555. C2×C4⋊C4D4×C31semidirect
556. C2×C4⋊C4D4×C31semidirect
557. C2×C4⋊C4D4×C31semidirect
558. C2×C4⋊C4D4×C31semidirect
574. C2×C22⋊C4D4×C31semidirect
575. C2×C22⋊C4D4×C31semidirect
583. C2×C42D4×C31semidirect
594. C31#24142direct (N × H)
605. C24#41×C31semidirect
709. 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×#26262
C31×#26172
C31×#23212
C31×#20442
C31×#20212
C31×#19962
C31×#19642
C31×#18892
C31×#18672
C31×#17992
#2414231