Finite Group Databasebeta

← C31×#15265 #21472024

Subgroups — C31×#15265 #21472024

Order 7936.

2186 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C4⋊Q8C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic
3C2×C31×#395C211yesmaximal, characteristic, complemented
4C2×C31×#393C211yesmaximal, characteristic
5C2×C31×#385C212yesmaximal
6C31×#1446C211yesmaximal, characteristic, complemented
7C31×#1444C212yesmaximal, complemented
8C31×#1441C212yesmaximal, complemented
9C31×#1439C212yesmaximal
10C31×#1437C211yesmaximal, characteristic
11C31×#1436C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×Q8×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C31×C4⋊Q8—24no—
16C2×C31×C4⋊Q8—28no—
17C2×C31×C22⋊Q8—24no—
18C2×C31×C22⋊Q8—24no—
19C2×C31×C22⋊Q8—24no—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2212yes—
23C22×C4⋊C4×C31C2212yes—
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C42×C31C2211yescharacteristic
31C31×#395—24no—
32C31×#393—24no—
33C31×#385—28no—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C25×C31C2311yescharacteristic
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—24no—
47C22×Q8×C31—24no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31—22no—
51C22×Q8×C31—42no—
52C22×Q8×C31—42no—
53C22×Q8×C31D414yes—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—24no—
58C23×C4×C31—42no—
59C23×C4×C31C2312yes—
60C23×C4×C31C2312yes—
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2312yes—
69C31×C4⋊Q8—232no—
70C31×C22⋊Q8—232no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—24no—
82C2×C4⋊C4×C31—24no—
83C2×C4⋊C4×C31—24no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—42no—
87C2×C4⋊C4×C31D414yes—
88C2×C4⋊C4×C31D418yes—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31D414yes—
100C2×C22⋊C4×C31Q818yescomplemented
101C2×C42×C31—22no—
102C2×C42×C31—24no—
103C31×#95—22no—
104C31×#95—24no—
105C31×#95—24no—
106C31×#95—24no—
107C31×#95—24no—
108C31×#95—22no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—42no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31C2×D412yes—
120C24×C31C2×Q814yes—
121C24×C31C2411yescharacteristic
122C2×Q8×C31—28no—
123C2×Q8×C31—28no—
124C2×Q8×C31—28no—
125C2×Q8×C31—44no—
126C2×Q8×C31—48no—
127C2×Q8×C31—48no—
128C2×Q8×C31—48no—
129C2×Q8×C31—48no—
130C2×Q8×C31—44no—
131C2×Q8×C31—44no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—28no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—48no—
178C22×C4×C31—48no—
179C22×C4×C31—44no—
180C22×C4×C31—44no—
181C22×C4×C31C2×D412yes—
182C22×C4×C31C2×D412yes—
183C22×C4×C31C2×D412yes—
184C22×C4×C31C2×D414yes—
185C22×C4×C31C2×D412yes—
186C22×C4×C31C2×D412yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D414yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D414yes—
192C22×C4×C31C2×Q814yes—
193C22×C4×C31C2×Q814yes—
194C22×C4×C31#4114yes—
195C4⋊C4×C31—28no—
196C4⋊C4×C31—28no—
197C4⋊C4×C31—216no—
198C4⋊C4×C31—28no—
199C4⋊C4×C31—216no—
200C4⋊C4×C31—48no—
201C22⋊C4×C31—28no—
202C22⋊C4×C31—28no—
203C22⋊C4×C31—216no—
204C22⋊C4×C31—48no—
205C42×C31—28no—
206#15265C3111yesmaximal, characteristic, direct product factor, Sylow
207C23×C31—22no—
208C23×C31—24no—
209C23×C31—22no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—41no—
218C23×C31—41no—
219C23×C31—41no—
220C23×C31—42no—
221C23×C31—41no—
222C23×C31—42no—
223C23×C31—42no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—42no—
227C23×C31C4⋊Q814yescomplemented
228C23×C31C22×D411yescharacteristic
229C23×C31C22×D412yes—
230C23×C31C22×D411yescharacteristic
231C23×C31C22×D411yescharacteristic
232C23×C31C22×Q812yes—
233C23×C31C2×#4112yes—
234C23×C31H(5,𝔽2)12yes—
235C23×C312−1+412yes—
236C23×C312−1+412yes—
237Q8×C31—416no—
238Q8×C31—416no—
239C2×C4×C31—24no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—24no—
245C2×C4×C31—24no—
246C2×C4×C31—24no—
247C2×C4×C31—24no—
248C2×C4×C31—24no—
249C2×C4×C31—24no—
250C2×C4×C31—24no—
251C2×C4×C31—24no—
252C2×C4×C31—24no—
253C2×C4×C31—22no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—24no—
259C2×C4×C31—24no—
260C2×C4×C31—22no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—24no—
264C2×C4×C31—24no—
265C2×C4×C31—24no—
266C2×C4×C31—24no—
267C2×C4×C31—24no—
268C2×C4×C31—24no—
269C2×C4×C31—416no—
270C2×C4×C31—41no—
271C2×C4×C31—42no—
272C2×C4×C31—41no—
273C2×C4×C31—42no—
274C2×C4×C31—41no—
275C2×C4×C31—42no—
276C2×C4×C31—41no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—42no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31#12014yes—
296C2×C4×C31#12014yes—
297C2×C4×C31C22⋊Q818yescomplemented
298C22×C4⋊Q8C2×C3111yescharacteristic, complemented
299C22×C22⋊Q8C2×C3111yescharacteristic
300C2×#395C2×C3111yescharacteristic, complemented
301C2×#393C2×C3111yescharacteristic
302C2×#385C2×C3112yes—
303#1446C2×C3111yescharacteristic, complemented
304#1444C2×C3112yescomplemented
305#1441C2×C3112yescomplemented
306#1439C2×C3112yes—
307#1437C2×C3111yescharacteristic
308#1436C2×C3111yescharacteristic, complemented
309C22×C31—24no—
310C22×C31—28no—
311C22×C31—42no—
312C22×C31—44no—
313C22×C31—44no—
314C22×C31—44no—
315C22×C31—42no—
316C22×C31—44no—
317C22×C31—44no—
318C22×C31C2×#12011yescharacteristic
319C22×C31C2×#12011yescharacteristic
320C22×C31C2×C22⋊Q812yes—
321C22×C31C2×C4⋊Q811yescharacteristic
322C22×C31#53211yescharacteristic
323C22×C31#53411yescharacteristic
324C22×C31#53612yes—
325C22×C31#53611yescharacteristic
326C22×C31#53611yescharacteristic
327C22×C31#54212yes—
328C22×C31#54412yes—
329C22×C31D4212yes—
330C22×C31D4212yes—
331C22×C31#54712yes—
332C22×C31#54812yes—
333C22×C31#54812yes—
334C22×C31D4×Q812yes—
335C22×C31D4×Q812yes—
336C22×C31D4×Q812yes—
337C22×C31#55412yes—
338C22×C31#56312yes—
339C4×C31—24no—
340C4×C31—24no—
341C4×C31—28no—
342C4×C31—42no—
343C4×C31—42no—
344C4×C31—44no—
345C4×C31—42no—
346C4×C31—42no—
347C4×C31—44no—
348C4×C31—82no—
349C23×Q8C22×C3111yescharacteristic
350C23×Q8C22×C3111yescharacteristic
351C24×C4C22×C3111yescharacteristic
352C2×C4⋊Q8—24no—
353C2×C4⋊Q8—28no—
354C2×C22⋊Q8—24no—
355C2×C22⋊Q8—24no—
356C2×C22⋊Q8—24no—
357C22×C4⋊C4C22×C3111yescharacteristic
358C22×C4⋊C4C22×C3111yescharacteristic
359C22×C4⋊C4C22×C3112yes—
360C22×C4⋊C4C22×C3112yes—
361C22×C4⋊C4C22×C3111yescharacteristic
362C22×C4⋊C4C22×C3112yes—
363C22×C22⋊C4C22×C3111yescharacteristic
364C22×C22⋊C4C22×C3112yes—
365C22×C22⋊C4C22×C3111yescharacteristic
366C22×C22⋊C4C22×C3112yes—
367C22×C42C22×C3111yescharacteristic
368#395—24no—
369#393—24no—
370#385—28no—
371C2×#95C22×C3111yescharacteristic
372C2×#95C22×C3112yes—
373C2×#95C22×C3111yescharacteristic
374C2×#95C22×C3112yes—
375C2×#95C22×C3112yes—
376C2×#95C22×C3112yes—
377C2×#95C22×C3112yes—
378C2×#95C22×C3112yes—
379C2×#95C22×C3112yes—
380C2×C31—44no—
381C2×C31#240311yescharacteristic
382C2×C31#240912yes—
383C2×C31#243211yescharacteristic
384C2×C31#243411yescharacteristic
385C2×C31#244012yes—
386C2×C31#245212yes—
387C2×C31#267412yes—
388C2×C31#267712yes—
389C2×C31#272912yes—
390C25C23×C3111yescharacteristic
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—24no—
394C22×Q8—24no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—42no—
399C22×Q8—42no—
400C22×Q8D4×C3114yes—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—42no—
406C23×C4C23×C3112yes—
407C23×C4C23×C3112yes—
408C23×C4C23×C3111yescharacteristic
409C23×C4C23×C3111yescharacteristic
410C23×C4C23×C3111yescharacteristic
411C23×C4C23×C3111yescharacteristic
412C23×C4C23×C3112yes—
413C23×C4C23×C3111yescharacteristic
414C23×C4C23×C3111yescharacteristic
415C23×C4C23×C3112yes—
416C4⋊Q8—232no—
417C22⋊Q8—232no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4D4×C3114yes—
435C2×C4⋊C4D4×C3118yes—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4D4×C3114yes—
447C2×C22⋊C4Q8×C3118yescomplemented
448C2×C42—22no—
449C2×C42—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—22no—
454#95—22no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—42no—
459C31#1526511yescharacteristic, direct product factor, Sylow
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24C2×D4×C3112yes—
468C24C2×Q8×C3114yes—
469C24C24×C3111yescharacteristic
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—44no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—44no—
479C2×Q8—44no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—28no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4C2×D4×C3112yes—
530C22×C4C2×D4×C3112yes—
531C22×C4C2×D4×C3112yes—
532C22×C4C2×D4×C3114yes—
533C22×C4C2×D4×C3112yes—
534C22×C4C2×D4×C3112yes—
535C22×C4C2×D4×C3112yes—
536C22×C4C2×D4×C3114yes—
537C22×C4C2×D4×C3112yes—
538C22×C4C2×D4×C3112yes—
539C22×C4C2×D4×C3114yes—
540C22×C4C2×Q8×C3114yes—
541C22×C4C2×Q8×C3114yes—
542C22×C4#41×C3114yes—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—216no—
546C4⋊C4—28no—
547C4⋊C4—216no—
548C4⋊C4—48no—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—216no—
552C22⋊C4—48no—
553C42—28no—
554C23—22no—
555C23—24no—
556C23—22no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—42no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23C31×C4⋊Q814yescomplemented
575C23C22×D4×C3111yescharacteristic
576C23C22×D4×C3112yes—
577C23C22×D4×C3111yescharacteristic
578C23C22×D4×C3111yescharacteristic
579C23C22×Q8×C3112yes—
580C23C2×#41×C3112yes—
581C23C31×H(5,𝔽2)12yes—
582C23C31×2−1+412yes—
583C23C31×2−1+412yes—
584Q8—416no—
585Q8—416no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—416no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4C31×#12014yes—
643C2×C4C31×#12014yes—
644C2×C4C31×C22⋊Q818yescomplemented
645C22—24no—
646C22—28no—
647C22—42no—
648C22—44no—
649C22—44no—
650C22—44no—
651C22—42no—
652C22—44no—
653C22—44no—
654C22C2×C31×#12011yescharacteristic
655C22C2×C31×#12011yescharacteristic
656C22C2×C31×C22⋊Q812yes—
657C22C2×C31×C4⋊Q811yescharacteristic
658C22C31×#53211yescharacteristic
659C22C31×#53411yescharacteristic
660C22C31×#53612yes—
661C22C31×#53611yescharacteristic
662C22C31×#53611yescharacteristic
663C22C31×#54212yes—
664C22C31×#54412yes—
665C22D42×C3112yes—
666C22D42×C3112yes—
667C22C31×#54712yes—
668C22C31×#54812yes—
669C22C31×#54812yes—
670C22D4×Q8×C3112yes—
671C22D4×Q8×C3112yes—
672C22D4×Q8×C3112yes—
673C22C31×#55412yes—
674C22C31×#56312yes—
675C4—24no—
676C4—24no—
677C4—28no—
678C4—42no—
679C4—42no—
680C4—44no—
681C4—42no—
682C4—42no—
683C4—44no—
684C4—82no—
685C2—44no—
686C2C31×#240311yescharacteristic
687C2C31×#240912yes—
688C2C31×#243211yescharacteristic
689C2C31×#243411yescharacteristic
690C2C31×#244012yes—
691C2C31×#245212yes—
692C2C31×#267412yes—
693C2C31×#267712yes—
694C2C31×#272912yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C4⋊Q8C2semidirect
3. C2×C31×#395C2semidirect
6. C31×#1446C2semidirect
7. C31×#1444C2semidirect
8. C31×#1441C2semidirect
11. C31×#1436C2semidirect
100. C2×C22⋊C4×C31Q8semidirect
206. #15265C31direct (N × H)
227. C23×C31C4⋊Q8semidirect
297. C2×C4×C31C22⋊Q8semidirect
298. C22×C4⋊Q8C2×C31semidirect
300. C2×#395C2×C31semidirect
303. #1446C2×C31semidirect
304. #1444C2×C31semidirect
305. #1441C2×C31semidirect
308. #1436C2×C31semidirect
447. C2×C22⋊C4Q8×C31semidirect
459. C31#15265direct (N × H)
574. C23C31×C4⋊Q8semidirect
644. C2×C4C31×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C4⋊Q82
C22×C31×C22⋊Q82
C2×C31×#3952
C2×C31×#3932
C2×C31×#3852
C31×#14462
C31×#14442
C31×#14412
C31×#14392
C31×#14372
C31×#14362
#1526531