Finite Group Databasebeta

← C31×#14726 #21471485

Subgroups — C31×#14726 #21471485

Order 7936.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#396C212yesmaximal, complemented
3C2×C31×#385C211yesmaximal, characteristic, complemented
4C2×C31×#385C211yesmaximal, characteristic, complemented
5C2×C31×#380C211yesmaximal, characteristic, complemented
6C2×C31×#379C211yesmaximal, characteristic
7C2×C31×#379C211yesmaximal, characteristic
8C31×#1439C212yesmaximal, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1439C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic, complemented
16C22×C4⋊C4×C31C2212yescomplemented
17C22×C4⋊C4×C31C2212yescomplemented
18C22×C4⋊C4×C31C2211yescharacteristic, complemented
19C22×C22⋊C4×C31—24no—
20C22×C22⋊C4×C31—28no—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C31×#396—28no—
32C31×#385—24no—
33C31×#385—24no—
34C31×#380—24no—
35C31×#379—24no—
36C31×#379—24no—
37C2×C31×#95C2212yescomplemented
38C2×C31×#95C2212yescomplemented
39C2×C31×#95C2211yescharacteristic, complemented
40C2×C31×#95C2211yescharacteristic, complemented
41C2×C31×#95C2212yescomplemented
42C2×C31×#95C2212yescomplemented
43C25×C31—24no—
44C25×C31—22no—
45C25×C31—24no—
46C25×C31—22no—
47C25×C31—22no—
48C25×C31—22no—
49C25×C31—22no—
50C25×C31—22no—
51C25×C31—42no—
52C25×C31—42no—
53C25×C31Q814yes—
54C25×C31C2312yes—
55C25×C31C2311yescharacteristic
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—24no—
60C23×C4×C31—24no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—42no—
64C23×C4×C31—42no—
65C23×C4×C31D414yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—42no—
83C2×C4⋊C4×C31—42no—
84C2×C4⋊C4×C31—42no—
85C2×C22⋊C4×C31—232no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—24no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31D418yes—
114C2×C22⋊C4×C31D414yes—
115C2×C22⋊C4×C31D414yes—
116C31×#95—24no—
117C31×#95—24no—
118C31×#95—24no—
119C31×#95—22no—
120C31×#95—22no—
121C31×#95—42no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—28no—
127C24×C31—28no—
128C24×C31—216no—
129C24×C31—216no—
130C24×C31—28no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—28no—
144C24×C31—28no—
145C24×C31—48no—
146C24×C31—48no—
147C24×C31—48no—
148C24×C31—48no—
149C24×C31—48no—
150C24×C31—48no—
151C24×C31—48no—
152C24×C31—48no—
153C24×C31—48no—
154C24×C31—44no—
155C24×C31—44no—
156C24×C31—48no—
157C24×C31—44no—
158C24×C31—44no—
159C24×C31—44no—
160C24×C31—44no—
161C24×C31C2×D414yes—
162C24×C31C2×D412yes—
163C24×C31C2×D412yes—
164C24×C31C2×D412yes—
165C24×C31C2×Q814yes—
166C24×C31C2×Q812yes—
167C24×C31#4114yes—
168C24×C31#4112yes—
169C24×C31#4112yes—
170C24×C31#4112yes—
171C24×C31C2411yescharacteristic
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—22no—
175C22×C4×C31—28no—
176C22×C4×C31—28no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—28no—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—22no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—44no—
220C22×C4×C31—48no—
221C22×C4×C31—48no—
222C22×C4×C31—48no—
223C22×C4×C31—48no—
224C22×C4×C31—44no—
225C22×C4×C31—44no—
226C22×C4×C31C2×D412yes—
227C22×C4×C31C2×D414yes—
228C22×C4×C31C2×D412yes—
229C22×C4×C31C2×D414yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D414yes—
233C4⋊C4×C31—48no—
234C4⋊C4×C31—48no—
235C4⋊C4×C31—44no—
236C4⋊C4×C31—44no—
237C22⋊C4×C31—216no—
238C22⋊C4×C31—28no—
239C22⋊C4×C31—28no—
240C22⋊C4×C31—216no—
241C22⋊C4×C31—48no—
242C22⋊C4×C31—48no—
243C22⋊C4×C31—48no—
244C22⋊C4×C31—48no—
245C22⋊C4×C31—44no—
246C22⋊C4×C31—44no—
247#14726C3111yesmaximal, characteristic, direct product factor, Sylow
248C23×C31—22no—
249C23×C31—24no—
250C23×C31—22no—
251C23×C31—24no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—232no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—24no—
276C23×C31—24no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—24no—
283C23×C31—432no—
284C23×C31—432no—
285C23×C31—416no—
286C23×C31—416no—
287C23×C31—416no—
288C23×C31—416no—
289C23×C31—432no—
290C23×C31—432no—
291C23×C31—416no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—416no—
309C23×C31#12114yes—
310C23×C31#12114yes—
311C23×C31#12114yes—
312C23×C31C22⋊Q818yes—
313C23×C31C22⋊Q814yes—
314C23×C31C22⋊Q814yes—
315C23×C31C22⋊Q814yes—
316C23×C31#12614yes—
317C23×C31C22×D411yescharacteristic
318C23×C31C22×D412yes—
319C23×C31C22×D411yescharacteristic
320C23×C31C22×D411yescharacteristic
321C23×C31C22×Q811yescharacteristic
322C23×C31C2×#4111yescharacteristic
323C23×C31C2×#4111yescharacteristic
324C23×C31C2×#4111yescharacteristic
325C23×C31C2×#4112yes—
326C23×C31H(5,𝔽2)12yes—
327C23×C31H(5,𝔽2)12yes—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—24no—
331C2×C4×C31—24no—
332C2×C4×C31—24no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—24no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—24no—
340C2×C4×C31—24no—
341C2×C4×C31—24no—
342C2×C4×C31—24no—
343C2×C4×C31—24no—
344C2×C4×C31—24no—
345C2×C4×C31—416no—
346C2×C4×C31—416no—
347C2×C4×C31—41no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—42no—
354C2×C4×C31—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—42no—
360C2×C4×C31—42no—
361C2×C4×C31—42no—
362C2×C4×C31—42no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—42no—
367C2×C4×C31—41no—
368C2×C4×C31—42no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—42no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31#12014yes—
381C23×C22⋊C4C2×C3111yescharacteristic
382C2×#396C2×C3112yescomplemented
383C2×#385C2×C3111yescharacteristic, complemented
384C2×#385C2×C3111yescharacteristic, complemented
385C2×#380C2×C3111yescharacteristic, complemented
386C2×#379C2×C3111yescharacteristic
387C2×#379C2×C3111yescharacteristic
388#1439C2×C3112yescomplemented
389#1439C2×C3112yescomplemented
390#1439C2×C3112yescomplemented
391C22⋊#95C2×C3111yescharacteristic, complemented
392C22×C31—24no—
393C22×C31—24no—
394C22×C31—24no—
395C22×C31—24no—
396C22×C31—24no—
397C22×C31—28no—
398C22×C31—28no—
399C22×C31—28no—
400C22×C31—28no—
401C22×C31—24no—
402C22×C31—28no—
403C22×C31—28no—
404C22×C31—28no—
405C22×C31—464no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—44no—
409C22×C31—44no—
410C22×C31—44no—
411C22×C31—44no—
412C22×C31—44no—
413C22×C31—44no—
414C22×C31—44no—
415C22×C31—44no—
416C22×C31—44no—
417C22×C31—44no—
418C22×C31#39618yescomplemented
419C22×C31C2×#12011yescharacteristic
420C22×C31C2×#12111yescharacteristic
421C22×C31C2×#12111yescharacteristic
422C22×C31C2×#12111yescharacteristic
423C22×C31C2×C22⋊Q811yescharacteristic
424C22×C31C2×C22⋊Q812yes—
425C22×C31C2×C22⋊Q811yescharacteristic
426C22×C31C2×C22⋊Q811yescharacteristic
427C22×C31#52511yescharacteristic
428C22×C31#52512yes—
429C22×C31C2×#12611yescharacteristic
430C22×C31#53411yescharacteristic
431C22×C31#53511yescharacteristic
432C22×C31#53812yes—
433C22×C31#54312yes—
434C22×C31D4212yes—
435C22×C31D4212yes—
436C22×C31#54612yes—
437C22×C31#54612yes—
438C22×C31#54612yes—
439C22×C31#54612yes—
440C22×C31#55112yes—
441C22×C31#55112yes—
442C4×C31—24no—
443C4×C31—42no—
444C4×C31—44no—
445C4×C31—42no—
446C4×C31—44no—
447C4×C31—42no—
448C4×C31—81no—
449C4×C31—81no—
450C4×C31—82no—
451C26C22×C3111yescharacteristic
452C24×C4C22×C3111yescharacteristic
453C24×C4C22×C3111yescharacteristic
454C22×C4⋊C4C22×C3111yescharacteristic, complemented
455C22×C4⋊C4C22×C3112yescomplemented
456C22×C4⋊C4C22×C3112yescomplemented
457C22×C4⋊C4C22×C3111yescharacteristic, complemented
458C22×C22⋊C4—24no—
459C22×C22⋊C4—28no—
460C22×C22⋊C4C22×C3112yes—
461C22×C22⋊C4C22×C3111yescharacteristic
462C22×C22⋊C4C22×C3111yescharacteristic
463C22×C22⋊C4C22×C3112yes—
464C22×C22⋊C4C22×C3112yes—
465C22×C22⋊C4C22×C3112yes—
466C22×C22⋊C4C22×C3112yes—
467C22×C22⋊C4C22×C3112yes—
468C22×C22⋊C4C22×C3111yescharacteristic
469C22×C22⋊C4C22×C3111yescharacteristic
470#396—28no—
471#385—24no—
472#385—24no—
473#380—24no—
474#379—24no—
475#379—24no—
476C2×#95C22×C3112yescomplemented
477C2×#95C22×C3112yescomplemented
478C2×#95C22×C3111yescharacteristic, complemented
479C2×#95C22×C3111yescharacteristic, complemented
480C2×#95C22×C3112yescomplemented
481C2×#95C22×C3112yescomplemented
482C2×C31—28no—
483C2×C31—48no—
484C2×C31C2×#39611yescharacteristic
485C2×C31#240811yescharacteristic
486C2×C31#241011yescharacteristic
487C2×C31#241111yescharacteristic
488C2×C31#242412yes—
489C2×C31#243712yes—
490C2×C31#243712yes—
491C2×C31#248012yes—
492C2×C31#253411yescharacteristic
493C2×C31#262611yescharacteristic
494C2×C31#284811yescharacteristic
495C25—24no—
496C25—22no—
497C25—24no—
498C25—22no—
499C25—22no—
500C25—22no—
501C25—22no—
502C25—22no—
503C25—42no—
504C25—42no—
505C25Q8×C3114yes—
506C25C23×C3112yes—
507C25C23×C3111yescharacteristic
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—42no—
516C23×C4—42no—
517C23×C4D4×C3114yes—
518C23×C4C23×C3111yescharacteristic
519C23×C4C23×C3112yes—
520C23×C4C23×C3111yescharacteristic
521C23×C4C23×C3111yescharacteristic
522C23×C4C23×C3112yes—
523C23×C4C23×C3111yescharacteristic
524C23×C4C23×C3111yescharacteristic
525C23×C4C23×C3112yes—
526C23×C4C23×C3111yescharacteristic
527C2×C4⋊C4—24no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—42no—
537C2×C22⋊C4—232no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4D4×C3118yes—
566C2×C22⋊C4D4×C3114yes—
567C2×C22⋊C4D4×C3114yes—
568#95—24no—
569#95—24no—
570#95—22no—
571#95—22no—
572#95—24no—
573#95—42no—
574C31#1472611yescharacteristic, direct product factor, Sylow
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—28no—
580C24—28no—
581C24—216no—
582C24—216no—
583C24—28no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—28no—
597C24—28no—
598C24—48no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—44no—
608C24—44no—
609C24—48no—
610C24—44no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24C2×D4×C3114yes—
615C24C2×D4×C3112yes—
616C24C2×D4×C3112yes—
617C24C2×D4×C3112yes—
618C24C2×Q8×C3114yes—
619C24C2×Q8×C3112yes—
620C24#41×C3114yes—
621C24#41×C3112yes—
622C24#41×C3112yes—
623C24#41×C3112yes—
624C24C24×C3111yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—44no—
673C22×C4—48no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4C2×D4×C3112yes—
680C22×C4C2×D4×C3114yes—
681C22×C4C2×D4×C3112yes—
682C22×C4C2×D4×C3114yes—
683C22×C4C2×D4×C3112yes—
684C22×C4C2×D4×C3112yes—
685C22×C4C2×D4×C3114yes—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C22⋊C4—216no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—216no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—232no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—432no—
736C23—432no—
737C23—416no—
738C23—416no—
739C23—416no—
740C23—416no—
741C23—432no—
742C23—432no—
743C23—416no—
744C23—416no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23C31×#12114yes—
762C23C31×#12114yes—
763C23C31×#12114yes—
764C23C31×C22⋊Q818yes—
765C23C31×C22⋊Q814yes—
766C23C31×C22⋊Q814yes—
767C23C31×C22⋊Q814yes—
768C23C31×#12614yes—
769C23C22×D4×C3111yescharacteristic
770C23C22×D4×C3112yes—
771C23C22×D4×C3111yescharacteristic
772C23C22×D4×C3111yescharacteristic
773C23C22×Q8×C3111yescharacteristic
774C23C2×#41×C3111yescharacteristic
775C23C2×#41×C3111yescharacteristic
776C23C2×#41×C3111yescharacteristic
777C23C2×#41×C3112yes—
778C23C31×H(5,𝔽2)12yes—
779C23C31×H(5,𝔽2)12yes—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—416no—
798C2×C4—416no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4C31×#12014yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—28no—
842C22—24no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—464no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22C31×#39618yescomplemented
860C22C2×C31×#12011yescharacteristic
861C22C2×C31×#12111yescharacteristic
862C22C2×C31×#12111yescharacteristic
863C22C2×C31×#12111yescharacteristic
864C22C2×C31×C22⋊Q811yescharacteristic
865C22C2×C31×C22⋊Q812yes—
866C22C2×C31×C22⋊Q811yescharacteristic
867C22C2×C31×C22⋊Q811yescharacteristic
868C22C31×#52511yescharacteristic
869C22C31×#52512yes—
870C22C2×C31×#12611yescharacteristic
871C22C31×#53411yescharacteristic
872C22C31×#53511yescharacteristic
873C22C31×#53812yes—
874C22C31×#54312yes—
875C22D42×C3112yes—
876C22D42×C3112yes—
877C22C31×#54612yes—
878C22C31×#54612yes—
879C22C31×#54612yes—
880C22C31×#54612yes—
881C22C31×#55112yes—
882C22C31×#55112yes—
883C4—24no—
884C4—44no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—81no—
890C4—81no—
891C4—82no—
892C2—28no—
893C2—48no—
894C2C2×C31×#39611yescharacteristic
895C2C31×#240811yescharacteristic
896C2C31×#241011yescharacteristic
897C2C31×#241111yescharacteristic
898C2C31×#242412yes—
899C2C31×#243712yes—
900C2C31×#243712yes—
901C2C31×#248012yes—
902C2C31×#253411yescharacteristic
903C2C31×#262611yescharacteristic
904C2C31×#284811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#396C2semidirect
3. C2×C31×#385C2semidirect
4. C2×C31×#385C2semidirect
5. C2×C31×#380C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×C22⋊#95C2semidirect
15. C22×C4⋊C4×C31C22semidirect
16. C22×C4⋊C4×C31C22semidirect
17. C22×C4⋊C4×C31C22semidirect
18. C22×C4⋊C4×C31C22semidirect
37. C2×C31×#95C22semidirect
38. C2×C31×#95C22semidirect
39. C2×C31×#95C22semidirect
40. C2×C31×#95C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
247. #14726C31direct (N × H)
382. C2×#396C2×C31semidirect
383. C2×#385C2×C31semidirect
384. C2×#385C2×C31semidirect
385. C2×#380C2×C31semidirect
388. #1439C2×C31semidirect
389. #1439C2×C31semidirect
390. #1439C2×C31semidirect
391. C22⋊#95C2×C31semidirect
418. C22×C31#396semidirect
454. C22×C4⋊C4C22×C31semidirect
455. C22×C4⋊C4C22×C31semidirect
456. C22×C4⋊C4C22×C31semidirect
457. C22×C4⋊C4C22×C31semidirect
476. C2×#95C22×C31semidirect
477. C2×#95C22×C31semidirect
478. C2×#95C22×C31semidirect
479. C2×#95C22×C31semidirect
480. C2×#95C22×C31semidirect
481. C2×#95C22×C31semidirect
574. C31#14726direct (N × H)
859. C22C31×#396semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3962
C2×C31×#3852
C2×C31×#3802
C2×C31×#3792
C31×#14392
C31×C22⋊#952
#1472631