Finite Group Databasebeta

← C31×#24880 #21481639

Subgroups — C31×#24880 #21481639

Order 7936.

972 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic, complemented
2C2×C31×#419C211yesmaximal, characteristic, complemented
3C31×#2409C211yesmaximal, characteristic
4C31×#2352C211yesmaximal, characteristic
5C31×#2097C211yesmaximal, characteristic, complemented
6C31×#2074C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1928C211yesmaximal, characteristic, complemented
10C31×#1927C211yesmaximal, characteristic, complemented
11C31×#1872C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1809C211yesmaximal, characteristic, complemented
15C31×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#484—24no—
24C2×C31×#107C2211yescharacteristic
25C2×C31×#107C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C31×#419—24no—
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C31×#395—21no—
41C31×#393—21no—
42C31×#391C2211yescharacteristic
43C31×#391C2211yescharacteristic
44C31×#388—21no—
45C31×#387—21no—
46C31×#386—21no—
47C31×#386—21no—
48C31×#385—21no—
49C31×#382C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31—21no—
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—21no—
62C22×Q8×C31—22no—
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—41no—
67C22×Q8×C31—41no—
68C22×Q8×C31C2311yescharacteristic
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31D411yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×M16×C31—22no—
76C2×M16×C31—22no—
77C2×M16×C31—41no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—41no—
85C31×C22⋊Q8—41no—
86C4×D4×C31—22no—
87C4×D4×C31—22no—
88C31×#117—22no—
89C31×#117—41no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31D411yescharacteristic
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31C2311yescharacteristic
113C31×#107—22no—
114C31×#107—22no—
115C31×#106—41no—
116C31×#106—41no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#103—41no—
123C31×#103—41no—
124C31×#103D414yescomplemented
125C31×C22⋊C8—22no—
126C31×C22⋊C8—22no—
127C31×C22⋊C8—41no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C24×C31C2×D411yescharacteristic
139C24×C31C2×D411yescharacteristic
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—28no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—42no—
152C2×Q8×C31—42no—
153C2×Q8×C31—44no—
154C2×Q8×C31—44no—
155C2×Q8×C31—44no—
156C2×Q8×C31—42no—
157C2×Q8×C31C2×D412yes—
158C2×Q8×C31#4112yes—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—41no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—42no—
181C22×C4×C31—42no—
182C22×C4×C31—42no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—81no—
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31#4112yes—
191C22×C4×C31#4112yes—
192C22×C4×C31C2411yescharacteristic
193M16×C31—44no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31C2×D412yes—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—42no—
220C4⋊C4×C31—42no—
221C4⋊C4×C31C2×D412yes—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—81no—
230C42×C31—21no—
231C42×C31—21no—
232C42×C31—42no—
233C42×C31—81no—
234#24880C3111yesmaximal, characteristic, direct product factor, Sylow
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31#12312yes—
248C23×C31#13712yes—
249C23×C31C22×D411yescharacteristic
250Q8×C31—22no—
251Q8×C31—22no—
252Q8×C31—22no—
253Q8×C31—22no—
254Q8×C31—48no—
255Q8×C31—41no—
256Q8×C31—41no—
257Q8×C31—41no—
258Q8×C31—41no—
259D4×C31—44no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—21no—
272C2×C4×C31—22no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—48no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—84no—
305C2×C4×C31#12312yes—
306C2×C4×C31C22×D411yescharacteristic
307C2×C4×C31C2×#4111yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31H(5,𝔽2)11yescharacteristic
311C2×C4×C31H(5,𝔽2)11yescharacteristic
312C8×C31—22no—
313C8×C31—41no—
314C8×C31—41no—
315C8×C31—41no—
316C2×#484C2×C3111yescharacteristic, complemented
317C2×#419C2×C3111yescharacteristic, complemented
318#2409C2×C3111yescharacteristic
319#2352C2×C3111yescharacteristic
320#2097C2×C3111yescharacteristic, complemented
321#2074C2×C3111yescharacteristic, complemented
322#2035C2×C3111yescharacteristic, complemented
323#2035C2×C3111yescharacteristic, complemented
324#1928C2×C3111yescharacteristic, complemented
325#1927C2×C3111yescharacteristic, complemented
326#1872C2×C3111yescharacteristic, complemented
327#1870C2×C3111yescharacteristic
328#1854C2×C3111yescharacteristic, complemented
329#1809C2×C3111yescharacteristic, complemented
330#1787C2×C3111yescharacteristic, complemented
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—22no—
336C22×C31—22no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31C2×#12311yescharacteristic
346C22×C31D4211yescharacteristic
347C22×C31#54611yescharacteristic
348C22×C31C2×#13711yescharacteristic
349C22×C31#57511yescharacteristic
350C22×C31#57711yescharacteristic
351C22×C31#57811yescharacteristic
352C4×C31—22no—
353C4×C31—41no—
354C4×C31—41no—
355C4×C31—41no—
356C4×C31—42no—
357C4×C31—42no—
358C4×C31—42no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31—81no—
362C4×C31—81no—
363C4×C31—81no—
364C4×C31#52511yescharacteristic
365C4×C31#53811yescharacteristic
366C4×C31#54611yescharacteristic
367C4×C31#55111yescharacteristic
368C23×Q8C22×C3111yescharacteristic
369C22×M16C22×C3111yescharacteristic
370C2×C22⋊Q8C22×C3111yescharacteristic
371C2×C22⋊Q8C22×C3111yescharacteristic
372C2×C4×D4C22×C3111yescharacteristic
373C2×#117C22×C3111yescharacteristic
374C22×C4⋊C4C22×C3111yescharacteristic
375#484—24no—
376C2×#107C22×C3111yescharacteristic
377C2×#107C22×C3111yescharacteristic
378C2×#106C22×C3111yescharacteristic
379C2×#106C22×C3111yescharacteristic
380#419—24no—
381C2×#103C22×C3111yescharacteristic
382C2×#103C22×C3111yescharacteristic
383C2×#103C22×C3111yescharacteristic
384C2×#103C22×C3111yescharacteristic
385C2×#103C22×C3111yescharacteristic
386C2×#103C22×C3111yescharacteristic
387C2×#103C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×C22⋊C8C22×C3111yescharacteristic
390C2×C22⋊C8C22×C3111yescharacteristic
391C2×C22⋊C8C22×C3111yescharacteristic
392#395—21no—
393#393—21no—
394#391C22×C3111yescharacteristic
395#391C22×C3111yescharacteristic
396#388—21no—
397#387—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#382C22×C3111yescharacteristic
402#380C22×C3111yescharacteristic
403#380C22×C3111yescharacteristic
404#380C22×C3111yescharacteristic
405C4×C4⋊C4C22×C3111yescharacteristic
406C4×C22⋊C4—21no—
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#336C22×C3111yescharacteristic
412#336C22×C3111yescharacteristic
413C2×C31—42no—
414C2×C31—42no—
415C2×C31#241811yescharacteristic
416C2×C31#309511yescharacteristic
417C2×C31#309711yescharacteristic
418C2×C31#327011yescharacteristic
419C2×C31#327511yescharacteristic
420C2×C31#332011yescharacteristic
421C2×C31#332711yescharacteristic
422C22×Q8—21no—
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—41no—
428C22×Q8—41no—
429C22×Q8C23×C3111yescharacteristic
430C22×Q8C23×C3111yescharacteristic
431C22×D4D4×C3111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C3111yescharacteristic
435C23×C4C23×C3111yescharacteristic
436C2×M16—22no—
437C2×M16—22no—
438C2×M16—41no—
439C22×C8C23×C3111yescharacteristic
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442C22×C8C23×C3111yescharacteristic
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—41no—
446C22⋊Q8—41no—
447C4×D4—22no—
448C4×D4—22no—
449#117—22no—
450#117—41no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4D4×C3111yescharacteristic
457C2×C4⋊C4C23×C3111yescharacteristic
458C2×C4⋊C4C23×C3111yescharacteristic
459C2×C4⋊C4C23×C3111yescharacteristic
460C2×C4⋊C4C23×C3111yescharacteristic
461C2×C4⋊C4C23×C3111yescharacteristic
462C2×C4⋊C4C23×C3111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C3111yescharacteristic
470C2×C22⋊C4D4×C3111yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C3111yescharacteristic
474#107—22no—
475#107—22no—
476#106—41no—
477#106—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#103D4×C3114yescomplemented
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C31#2488011yescharacteristic, direct product factor, Sylow
500C24C2×D4×C3111yescharacteristic
501C24C2×D4×C3111yescharacteristic
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—28no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—42no—
519C2×Q8C2×D4×C3112yes—
520C2×Q8#41×C3112yes—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—41no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4C2×D4×C3111yescharacteristic
549C22×C4C2×D4×C3111yescharacteristic
550C22×C4C2×D4×C3111yescharacteristic
551C22×C4C2×D4×C3111yescharacteristic
552C22×C4#41×C3112yes—
553C22×C4#41×C3112yes—
554C22×C4C24×C3111yescharacteristic
555M16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8C2×D4×C3112yes—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4C2×D4×C3112yes—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—81no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23C31×#12312yes—
609C23C31×#13712yes—
610C23C22×D4×C3111yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—48no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—44no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4C31×#12312yes—
667C2×C4C22×D4×C3111yescharacteristic
668C2×C4C2×#41×C3111yescharacteristic
669C2×C4C2×#41×C3111yescharacteristic
670C2×C4C2×#41×C3111yescharacteristic
671C2×C4C31×H(5,𝔽2)11yescharacteristic
672C2×C4C31×H(5,𝔽2)11yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C2×C31×#12311yescharacteristic
692C22D42×C3111yescharacteristic
693C22C31×#54611yescharacteristic
694C22C2×C31×#13711yescharacteristic
695C22C31×#57511yescharacteristic
696C22C31×#57711yescharacteristic
697C22C31×#57811yescharacteristic
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C31×#52511yescharacteristic
711C4C31×#53811yescharacteristic
712C4C31×#54611yescharacteristic
713C4C31×#55111yescharacteristic
714C2—42no—
715C2—42no—
716C2C31×#241811yescharacteristic
717C2C31×#309511yescharacteristic
718C2C31×#309711yescharacteristic
719C2C31×#327011yescharacteristic
720C2C31×#327511yescharacteristic
721C2C31×#332011yescharacteristic
722C2C31×#332711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#484C2semidirect
2. C2×C31×#419C2semidirect
5. C31×#2097C2semidirect
6. C31×#2074C2semidirect
7. C31×#2035C2semidirect
8. C31×#2035C2semidirect
9. C31×#1928C2semidirect
10. C31×#1927C2semidirect
11. C31×#1872C2semidirect
13. C31×#1854C2semidirect
14. C31×#1809C2semidirect
15. C31×#1787C2semidirect
124. C31×#103D4semidirect
234. #24880C31direct (N × H)
316. C2×#484C2×C31semidirect
317. C2×#419C2×C31semidirect
320. #2097C2×C31semidirect
321. #2074C2×C31semidirect
322. #2035C2×C31semidirect
323. #2035C2×C31semidirect
324. #1928C2×C31semidirect
325. #1927C2×C31semidirect
326. #1872C2×C31semidirect
328. #1854C2×C31semidirect
329. #1809C2×C31semidirect
330. #1787C2×C31semidirect
485. #103D4×C31semidirect
499. C31#24880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4842
C2×C31×#4192
C31×#24092
C31×#23522
C31×#20972
C31×#20742
C31×#20352
C31×#19282
C31×#19272
C31×#18722
C31×#18702
C31×#18542
C31×#18092
C31×#17872
#2488031