Finite Group Databasebeta

← C31×#25587 #21482346

Subgroups — C31×#25587 #21482346

Order 7936.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic, complemented
2C31×#2561C211yesmaximal, characteristic, complemented
3C31×#2539C211yesmaximal, characteristic, complemented
4C31×#2534C211yesmaximal, characteristic, complemented
5C31×#2022C212yesmaximal, complemented
6C31×#2021C212yesmaximal, complemented
7C31×#1996C211yesmaximal, characteristic, complemented
8C31×#1964C211yesmaximal, characteristic, complemented
9C31×#1890C212yesmaximal, complemented
10C31×#1889C212yesmaximal, complemented
11C4×C31×#99C211yesmaximal, characteristic, complemented
12C31×#553—21no—
13C31×#553—22no—
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×#123C2212yes—
24C2×C31×#123C2211yescharacteristic
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#120C2212yes—
28C2×C31×#120C2211yescharacteristic
29C31×#518C2212yes—
30C2×C4×D4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C2×C31×#99C2212yes—
33C2×C31×#99C2212yes—
34C2×C31×#99C2212yes—
35C31×#399—21no—
36C31×#397—21no—
37C31×#396—21no—
38C31×#394—21no—
39C31×#393—21no—
40C31×#392—21no—
41C31×#390—22no—
42C31×#388—22no—
43C31×#388—21no—
44C31×#386—21no—
45C31×#381C2211yescharacteristic
46C31×#381C2212yes—
47C31×#380C2211yescharacteristic
48C31×#379C2211yescharacteristic
49C31×#379C2212yes—
50C4×C22⋊C4×C31C2211yescharacteristic
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×#123—24no—
79C31×#123—42no—
80C31×#123—42no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—21no—
87C31×#121—21no—
88C31×#121—22no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—21no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#120—22no—
96C31×#120—22no—
97C31×#120—24no—
98C31×#120—42no—
99C31×#120—42no—
100C4×Q8×C31—21no—
101C4×D4×C31—22no—
102C4×D4×C31—21no—
103C4×D4×C31—21no—
104C4×D4×C31—21no—
105C4×D4×C31—21no—
106C4×D4×C31—21no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C31×#117—21no—
112C31×#117—22no—
113C31×#117—22no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31D411yescharacteristic, complemented
118C2×C4⋊C4×C31D411yescharacteristic, complemented
119C2×C4⋊C4×C31D411yescharacteristic, complemented
120C2×C4⋊C4×C31D412yescomplemented
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31D411yescharacteristic, complemented
137C2×C22⋊C4×C31D412yescomplemented
138C2×C22⋊C4×C31C2312yes—
139C2×C22⋊C4×C31C2311yescharacteristic
140C2×C22⋊C4×C31C2311yescharacteristic
141C2×C22⋊C4×C31C2311yescharacteristic
142C2×C22⋊C4×C31C2312yes—
143C2×C22⋊C4×C31C2312yes—
144C2×C42×C31—21no—
145C2×C42×C31—21no—
146C2×C42×C31D411yescharacteristic, complemented
147C31×#99—24no—
148C31×#99—42no—
149C31×#99—42no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—22no—
153C31×#95—21no—
154C31×#95—21no—
155C31×#95—22no—
156C31×#95—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—42no—
163C24×C31—81no—
164C24×C31C2×D412yes—
165C24×C31C2×D411yescharacteristic
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—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—22no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—44no—
186C2×D4×C31—42no—
187C2×D4×C31—44no—
188C2×D4×C31—42no—
189C2×D4×C31—81no—
190C2×D4×C31—82no—
191C2×D4×C31—81no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—22no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—81no—
206C22×C4×C31—81no—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D412yes—
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D412yes—
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—22no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—44no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31—81no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—44no—
254C22⋊C4×C31—44no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—44no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
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#4114yescomplemented
266C42×C31—22no—
267C42×C31—22no—
268C42×C31—21no—
269C42×C31—21no—
270C42×C31—81no—
271C42×C31—81no—
272#25587C3111yesmaximal, characteristic, direct product factor, Sylow
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—42no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—42no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—84no—
301C23×C31—84no—
302C23×C31C22×D411yescharacteristic
303C23×C31C22×D411yescharacteristic
304C23×C31C22×D411yescharacteristic
305C23×C31C2×#4112yes—
306C23×C31H(5,𝔽2)12yes—
307Q8×C31—42no—
308Q8×C31—81no—
309D4×C31—42no—
310D4×C31—42no—
311D4×C31—42no—
312D4×C31—42no—
313D4×C31—42no—
314D4×C31—42no—
315D4×C31—42no—
316D4×C31—81no—
317D4×C31—82no—
318D4×C31—82no—
319D4×C31—88no—
320D4×C31—84no—
321C2×C4×C31—21no—
322C2×C4×C31—22no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—24no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—41no—
342C2×C4×C31—42no—
343C2×C4×C31—41no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—81no—
360C2×C4×C31—82no—
361C2×C4×C31—82no—
362C2×C4×C31#12011yescharacteristic
363C2×C4×C31#12011yescharacteristic
364C2×C4×C31#12011yescharacteristic
365C2×C4×C31#12011yescharacteristic
366#3505C2×C3111yescharacteristic, complemented
367#2561C2×C3111yescharacteristic, complemented
368#2539C2×C3111yescharacteristic, complemented
369#2534C2×C3111yescharacteristic, complemented
370#2022C2×C3112yescomplemented
371#2021C2×C3112yescomplemented
372#1996C2×C3111yescharacteristic, complemented
373#1964C2×C3111yescharacteristic, complemented
374#1890C2×C3112yescomplemented
375#1889C2×C3112yescomplemented
376C4×#99C2×C3111yescharacteristic, complemented
377C22×C31—21no—
378C22×C31—21no—
379C22×C31—21no—
380C22×C31—21no—
381C22×C31—21no—
382C22×C31—21no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—44no—
387C22×C31—42no—
388C22×C31—44no—
389C22×C31—42no—
390C22×C31—41no—
391C22×C31—42no—
392C22×C31—42no—
393C22×C31—41no—
394C22×C31—42no—
395C22×C31—41no—
396C22×C31—42no—
397C22×C31—82no—
398C22×C31—82no—
399C22×C31—81no—
400C22×C31—82no—
401C22×C31—81no—
402C22×C31—82no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31C2×#12011yescharacteristic
407C22×C31#53211yescharacteristic
408C22×C31#53511yescharacteristic
409C22×C31#54612yes—
410C22×C31#55012yes—
411C4×C31—21no—
412C4×C31—21no—
413C4×C31—21no—
414C4×C31—21no—
415C4×C31—44no—
416C4×C31—41no—
417C4×C31—42no—
418C4×C31—41no—
419C4×C31—42no—
420C4×C31—41no—
421C4×C31—42no—
422C4×C31—81no—
423C4×C31—82no—
424C4×C31—81no—
425C4×C31—81no—
426#553—22no—
427#553—21no—
428#552—21no—
429#551—22no—
430#548—21no—
431#546—21no—
432#539—21no—
433#538—21no—
434#534C22×C3112yes—
435#529—21no—
436#525—21no—
437C2×#123C22×C3112yes—
438C2×#123C22×C3111yescharacteristic
439C2×C22⋊Q8C22×C3111yescharacteristic
440C2×#121C22×C3111yescharacteristic
441C2×#120C22×C3112yes—
442C2×#120C22×C3111yescharacteristic
443#518C22×C3112yes—
444C2×C4×D4C22×C3111yescharacteristic
445C22×C22⋊C4C22×C3111yescharacteristic
446C2×#99C22×C3112yes—
447C2×#99C22×C3112yes—
448C2×#99C22×C3112yes—
449#399—21no—
450#397—21no—
451#396—21no—
452#394—21no—
453#393—21no—
454#392—21no—
455#390—22no—
456#388—22no—
457#388—21no—
458#386—21no—
459#381C22×C3112yes—
460#381C22×C3111yescharacteristic
461#380C22×C3111yescharacteristic
462#379C22×C3112yes—
463#379C22×C3111yescharacteristic
464C4×C22⋊C4C22×C3111yescharacteristic
465C4×C22⋊C4C22×C3111yescharacteristic
466#342C22×C3112yes—
467#342C22×C3112yes—
468#342C22×C3112yes—
469C2×C31—22no—
470C2×C31—21no—
471C2×C31—22no—
472C2×C31—21no—
473C2×C31—82no—
474C2×C31—81no—
475C2×C31—82no—
476C2×C31#243111yescharacteristic
477C2×C31#302511yescharacteristic
478C2×C31#302611yescharacteristic
479C25C23×C3111yescharacteristic
480C2×#41—21no—
481C22×Q8D4×C3111yescharacteristic, complemented
482C22×D4—21no—
483C22×D4—22no—
484C22×D4D4×C3111yescharacteristic, complemented
485C22×D4C23×C3111yescharacteristic
486C22×D4C23×C3112yes—
487C23×C4D4×C3111yescharacteristic, complemented
488C23×C4C23×C3111yescharacteristic
489C23×C4C23×C3111yescharacteristic
490#126—22no—
491#126—22no—
492#126—22no—
493#125—21no—
494#125—22no—
495#124—21no—
496#124—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—24no—
503#123—42no—
504#123—42no—
505C22⋊Q8—21no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511#121—21no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121—22no—
519#120—22no—
520#120—22no—
521#120—24no—
522#120—42no—
523#120—42no—
524C4×Q8—21no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535#117—21no—
536#117—22no—
537#117—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C3111yescharacteristic, complemented
542C2×C4⋊C4D4×C3111yescharacteristic, complemented
543C2×C4⋊C4D4×C3112yescomplemented
544C2×C4⋊C4D4×C3111yescharacteristic, complemented
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4D4×C3111yescharacteristic, complemented
561C2×C22⋊C4D4×C3112yescomplemented
562C2×C22⋊C4C23×C3111yescharacteristic
563C2×C22⋊C4C23×C3111yescharacteristic
564C2×C22⋊C4C23×C3112yes—
565C2×C22⋊C4C23×C3111yescharacteristic
566C2×C22⋊C4C23×C3112yes—
567C2×C22⋊C4C23×C3112yes—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42D4×C3111yescharacteristic, complemented
571#99—24no—
572#99—42no—
573#99—42no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—22no—
579#95—21no—
580#95—22no—
581C31#2558711yescharacteristic, direct product factor, Sylow
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C3112yes—
590C24C2×D4×C3111yescharacteristic
591C24C24×C3111yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C3111yescharacteristic
633C22×C4C2×D4×C3112yes—
634C22×C4C2×D4×C3111yescharacteristic
635C22×C4C2×D4×C3112yes—
636C22×C4C2×D4×C3111yescharacteristic
637C22×C4C2×D4×C3112yes—
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C3114yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C3111yescharacteristic
727C23C22×D4×C3111yescharacteristic
728C23C22×D4×C3111yescharacteristic
729C23C2×#41×C3112yes—
730C23C31×H(5,𝔽2)12yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4C31×#12011yescharacteristic
787C2×C4C31×#12011yescharacteristic
788C2×C4C31×#12011yescharacteristic
789C2×C4C31×#12011yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×C31×#12011yescharacteristic
820C22C31×#53211yescharacteristic
821C22C31×#53511yescharacteristic
822C22C31×#54612yes—
823C22C31×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C31×#243111yescharacteristic
847C2C31×#302511yescharacteristic
848C2C31×#302611yescharacteristic
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×#2561C2semidirect
3. C31×#2539C2semidirect
4. C31×#2534C2semidirect
5. C31×#2022C2semidirect
6. C31×#2021C2semidirect
7. C31×#1996C2semidirect
8. C31×#1964C2semidirect
9. C31×#1890C2semidirect
10. C31×#1889C2semidirect
11. C4×C31×#99C2semidirect
57. C22×Q8×C31D4semidirect
60. C22×D4×C31D4semidirect
63. C23×C4×C31D4semidirect
117. C2×C4⋊C4×C31D4semidirect
118. C2×C4⋊C4×C31D4semidirect
119. C2×C4⋊C4×C31D4semidirect
120. C2×C4⋊C4×C31D4semidirect
136. C2×C22⋊C4×C31D4semidirect
137. C2×C22⋊C4×C31D4semidirect
146. C2×C42×C31D4semidirect
265. C22⋊C4×C31#41semidirect
272. #25587C31direct (N × H)
366. #3505C2×C31semidirect
367. #2561C2×C31semidirect
368. #2539C2×C31semidirect
369. #2534C2×C31semidirect
370. #2022C2×C31semidirect
371. #2021C2×C31semidirect
372. #1996C2×C31semidirect
373. #1964C2×C31semidirect
374. #1890C2×C31semidirect
375. #1889C2×C31semidirect
376. C4×#99C2×C31semidirect
481. C22×Q8D4×C31semidirect
484. C22×D4D4×C31semidirect
487. C23×C4D4×C31semidirect
541. C2×C4⋊C4D4×C31semidirect
542. C2×C4⋊C4D4×C31semidirect
543. C2×C4⋊C4D4×C31semidirect
544. C2×C4⋊C4D4×C31semidirect
560. C2×C22⋊C4D4×C31semidirect
561. C2×C22⋊C4D4×C31semidirect
570. C2×C42D4×C31semidirect
581. C31#25587direct (N × H)
690. 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×#25612
C31×#25392
C31×#25342
C31×#20222
C31×#20212
C31×#19962
C31×#19642
C31×#18902
C31×#18892
C4×C31×#992
#2558731