Finite Group Databasebeta

← C31×#22499 #21479258

Subgroups — C31×#22499 #21479258

Order 7936.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#552C211yesmaximal, characteristic
2C2×C31×#436C211yesmaximal, characteristic
3C31×#2352C211yesmaximal, characteristic
4C31×#1991C211yesmaximal, characteristic, complemented
5C31×#1989C211yesmaximal, characteristic, complemented
6C31×#1894C211yesmaximal, characteristic, complemented
7C31×#1894C211yesmaximal, characteristic, complemented
8C31×#1873C211yesmaximal, characteristic, complemented
9C31×#1872C211yesmaximal, characteristic, complemented
10C31×#1825C211yesmaximal, characteristic, complemented
11C31×#1824C211yesmaximal, characteristic, complemented
12C31×#1805C211yesmaximal, characteristic, complemented
13C4×C31×#103C211yesmaximal, characteristic, complemented
14C31×#1736C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C31×#552—24no—
19C31×#552C418yescomplemented
20C2×C31×#126—21no—
21C2×C31×#125—21no—
22C2×C31×#125C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117—21no—
29C2×C31×#117C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C31×#436—24no—
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#388—21no—
43C31×#387—21no—
44C31×#386—21no—
45C31×#382C2211yescharacteristic
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C4×C4⋊C4×C31C2211yescharacteristic
49C4×C22⋊C4×C31—21no—
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31D411yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C2×M16×C31—22no—
69C2×M16×C31—22no—
70C2×M16×C31—22no—
71C2×M16×C31—22no—
72C2×M16×C31—41no—
73C2×M16×C31—41no—
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C31×#126—28no—
79C31×#125—28no—
80C31×#125—22no—
81C31×#125C2×C414yescomplemented
82C31×#123—28no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8C2×C414yes—
86C31×C22⋊Q8C2×C414yescomplemented
87C4×Q8×C31—22no—
88C4×Q8×C31C2×C414yescomplemented
89C4×D4×C31C2×C414yes—
90C4×D4×C31D414yes—
91C31×#117—22no—
92C31×#117—28no—
93C31×#117—22no—
94C31×#117—41no—
95C31×#117C2×C414yes—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—41no—
106C2×C4⋊C4×C31C2×C414yescomplemented
107C2×C4⋊C4×C31D411yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31D411yescharacteristic
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C42×C31—21no—
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31—21no—
127C2×C42×C31C2311yescharacteristic
128C31×C4⋊C8—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—41no—
132C31×#103—41no—
133C31×C22⋊C8—22no—
134C31×C22⋊C8—22no—
135C4×C8×C31—22no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C24×C31C2×D411yescharacteristic
142C24×C31C2×D411yescharacteristic
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31C22×C412yes—
149C2×D4×C31—41no—
150C2×D4×C31—41no—
151C2×D4×C31C22⋊C414yes—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—24no—
161C22×C4×C31—21no—
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—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—81no—
174C22×C4×C31C22×C412yes—
175C22×C4×C31C22×C412yes—
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D412yes—
181C22×C4×C31C2×D412yes—
182C22×C4×C31C2411yescharacteristic
183M16×C31—44no—
184M16×C31—44no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31#4112yes—
197C4⋊C4×C31—24no—
198C4⋊C4×C31—24no—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—24no—
202C4⋊C4×C31—24no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
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—42no—
214C4⋊C4×C31C22⋊C414yes—
215C4⋊C4×C31C22×C412yes—
216C4⋊C4×C31C22×C412yes—
217C4⋊C4×C31C22×C412yes—
218C4⋊C4×C31#4112yes—
219C22⋊C4×C31—24no—
220C22⋊C4×C31—24no—
221C22⋊C4×C31—24no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—81no—
225C22⋊C4×C31C22⋊C414yes—
226C22⋊C4×C31C22⋊C414yes—
227C42×C31—24no—
228C42×C31—24no—
229C42×C31—42no—
230C42×C31—81no—
231C42×C31C22×C412yes—
232C42×C31C2×D412yes—
233#22499C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—21no—
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×C31C2×C22⋊C412yes—
247C23×C31C2×C22⋊C412yes—
248C23×C31C22×D411yescharacteristic
249Q8×C31—22no—
250Q8×C31—22no—
251Q8×C31—41no—
252Q8×C31—41no—
253D4×C31—44no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
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—22no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—48no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
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—84no—
296C2×C4×C31C2×C22⋊C412yes—
297C2×C4×C31C2×C22⋊C412yes—
298C2×C4×C31C2×C22⋊C412yes—
299C2×C4×C31C2×C22⋊C412yes—
300C2×C4×C31C23×C411yescharacteristic
301C2×C4×C31C22×D411yescharacteristic
302C2×C4×C31C2×#4111yescharacteristic
303C2×C4×C31C2×#4111yescharacteristic
304C2×C4×C31H(5,𝔽2)11yescharacteristic
305C2×C4×C312−1+411yescharacteristic
306C8×C31—22no—
307C8×C31—41no—
308C8×C31—41no—
309C8×C31—41no—
310C2×#552C2×C3111yescharacteristic
311C2×#436C2×C3111yescharacteristic
312#2352C2×C3111yescharacteristic
313#1991C2×C3111yescharacteristic, complemented
314#1989C2×C3111yescharacteristic, complemented
315#1894C2×C3111yescharacteristic, complemented
316#1894C2×C3111yescharacteristic, complemented
317#1873C2×C3111yescharacteristic, complemented
318#1872C2×C3111yescharacteristic, complemented
319#1825C2×C3111yescharacteristic, complemented
320#1824C2×C3111yescharacteristic, complemented
321#1805C2×C3111yescharacteristic, complemented
322C4×#103C2×C3111yescharacteristic, complemented
323#1736C2×C3111yescharacteristic, complemented
324#1736C2×C3111yescharacteristic, complemented
325C22×C31—22no—
326C22×C31—22no—
327C22×C31—22no—
328C22×C31—22no—
329C22×C31—22no—
330C22×C31—22no—
331C22×C31—41no—
332C22×C31—41no—
333C22×C31—41no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31C22×C22⋊C411yescharacteristic
340C22×C31#54611yescharacteristic
341C22×C31#54711yescharacteristic
342C22×C31#57511yescharacteristic
343C22×C31#57511yescharacteristic
344C22×C31#57711yescharacteristic
345C22×C31#57811yescharacteristic
346C4×C31—22no—
347C4×C31—22no—
348C4×C31—22no—
349C4×C31—22no—
350C4×C31—42no—
351C4×C31—42no—
352C4×C31—42no—
353C4×C31—42no—
354C4×C31—42no—
355C4×C31—81no—
356C4×C31—81no—
357C4×C31—81no—
358C4×C31C4×#4111yescharacteristic
359C4×C31#52011yescharacteristic
360C4×C31#54611yescharacteristic
361C4×C31#54711yescharacteristic
362C22×M16C22×C3111yescharacteristic
363C22×M16C22×C3111yescharacteristic
364#552—24no—
365#552C4×C3118yescomplemented
366C2×#126—21no—
367C2×#125—21no—
368C2×#125C22×C3111yescharacteristic
369C2×#123—21no—
370C2×C22⋊Q8C22×C3111yescharacteristic
371C2×C22⋊Q8C22×C3111yescharacteristic
372C2×C4×Q8C22×C3111yescharacteristic
373C2×C4×D4C22×C3111yescharacteristic
374C2×#117—21no—
375C2×#117C22×C3111yescharacteristic
376C2×#117C22×C3111yescharacteristic
377C22×C4⋊C4C22×C3111yescharacteristic
378C22×C4⋊C4C22×C3111yescharacteristic
379#436—24no—
380C2×C4⋊C8C22×C3111yescharacteristic
381C2×#103C22×C3111yescharacteristic
382C2×#103C22×C3111yescharacteristic
383C2×#103C22×C3111yescharacteristic
384C2×#103C22×C3111yescharacteristic
385C2×C22⋊C8C22×C3111yescharacteristic
386C2×C22⋊C8C22×C3111yescharacteristic
387C2×C4×C8C22×C3111yescharacteristic
388#388—21no—
389#387—21no—
390#386—21no—
391#382C22×C3111yescharacteristic
392#380C22×C3111yescharacteristic
393#380C22×C3111yescharacteristic
394C4×C4⋊C4C22×C3111yescharacteristic
395C4×C22⋊C4—21no—
396#340C22×C3111yescharacteristic
397#340C22×C3111yescharacteristic
398#340C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408C2×C31—42no—
409C2×C31—42no—
410C2×C31#233911yescharacteristic
411C2×C31#289611yescharacteristic
412C2×C31#289811yescharacteristic
413C2×C31#332311yescharacteristic
414C2×C31#332711yescharacteristic
415C2×C31#335111yescharacteristic
416C2×C31#335211yescharacteristic
417C22×Q8C23×C3111yescharacteristic
418C22×D4D4×C3111yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C23×C3111yescharacteristic
422C23×C4C23×C3111yescharacteristic
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—22no—
427C2×M16—41no—
428C2×M16—41no—
429C22×C8C23×C3111yescharacteristic
430C22×C8C23×C3111yescharacteristic
431C22×C8C23×C3111yescharacteristic
432C22×C8C23×C3111yescharacteristic
433#126—28no—
434#125—28no—
435#125—22no—
436#125C2×C4×C3114yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8C2×C4×C3114yes—
441C22⋊Q8C2×C4×C3114yescomplemented
442C4×Q8—22no—
443C4×Q8C2×C4×C3114yescomplemented
444C4×D4C2×C4×C3114yes—
445C4×D4D4×C3114yes—
446#117—22no—
447#117—28no—
448#117—22no—
449#117—41no—
450#117C2×C4×C3114yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4C2×C4×C3114yescomplemented
462C2×C4⋊C4D4×C3111yescharacteristic
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4D4×C3111yescharacteristic
477C2×C22⋊C4D4×C3111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C3111yescharacteristic
483C4⋊C8—22no—
484#103—22no—
485#103—22no—
486#103—41no—
487#103—41no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C4×C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C31#2249911yescharacteristic, direct product factor, Sylow
497C24C2×D4×C3111yescharacteristic
498C24C2×D4×C3111yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C22×C4×C3112yes—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4C22⋊C4×C3114yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4C22×C4×C3112yes—
531C22×C4C22×C4×C3112yes—
532C22×C4C2×D4×C3111yescharacteristic
533C22×C4C2×D4×C3111yescharacteristic
534C22×C4C2×D4×C3111yescharacteristic
535C22×C4C2×D4×C3111yescharacteristic
536C22×C4C2×D4×C3112yes—
537C22×C4C2×D4×C3112yes—
538C22×C4C24×C3111yescharacteristic
539M16—44no—
540M16—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8#41×C3112yes—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4C22⋊C4×C3114yes—
571C4⋊C4C22×C4×C3112yes—
572C4⋊C4C22×C4×C3112yes—
573C4⋊C4C22×C4×C3112yes—
574C4⋊C4#41×C3112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4C22⋊C4×C3114yes—
582C22⋊C4C22⋊C4×C3114yes—
583C42—24no—
584C42—24no—
585C42—42no—
586C42—81no—
587C42C22×C4×C3112yes—
588C42C2×D4×C3112yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C22⋊C4×C3112yes—
602C23C2×C22⋊C4×C3112yes—
603C23C22×D4×C3111yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—48no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
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—84no—
651C2×C4C2×C22⋊C4×C3112yes—
652C2×C4C2×C22⋊C4×C3112yes—
653C2×C4C2×C22⋊C4×C3112yes—
654C2×C4C2×C22⋊C4×C3112yes—
655C2×C4C23×C4×C3111yescharacteristic
656C2×C4C22×D4×C3111yescharacteristic
657C2×C4C2×#41×C3111yescharacteristic
658C2×C4C2×#41×C3111yescharacteristic
659C2×C4C31×H(5,𝔽2)11yescharacteristic
660C2×C4C31×2−1+411yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×C22⋊C4×C3111yescharacteristic
680C22C31×#54611yescharacteristic
681C22C31×#54711yescharacteristic
682C22C31×#57511yescharacteristic
683C22C31×#57511yescharacteristic
684C22C31×#57711yescharacteristic
685C22C31×#57811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C4×#41×C3111yescharacteristic
699C4C31×#52011yescharacteristic
700C4C31×#54611yescharacteristic
701C4C31×#54711yescharacteristic
702C2—42no—
703C2—42no—
704C2C31×#233911yescharacteristic
705C2C31×#289611yescharacteristic
706C2C31×#289811yescharacteristic
707C2C31×#332311yescharacteristic
708C2C31×#332711yescharacteristic
709C2C31×#335111yescharacteristic
710C2C31×#335211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×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
4. C31×#1991C2semidirect
5. C31×#1989C2semidirect
6. C31×#1894C2semidirect
7. C31×#1894C2semidirect
8. C31×#1873C2semidirect
9. C31×#1872C2semidirect
10. C31×#1825C2semidirect
11. C31×#1824C2semidirect
12. C31×#1805C2semidirect
13. C4×C31×#103C2semidirect
14. C31×#1736C2semidirect
15. C31×#1736C2semidirect
19. C31×#552C4semidirect
81. C31×#125C2×C4semidirect
86. C31×C22⋊Q8C2×C4semidirect
88. C4×Q8×C31C2×C4semidirect
106. C2×C4⋊C4×C31C2×C4semidirect
233. #22499C31direct (N × H)
313. #1991C2×C31semidirect
314. #1989C2×C31semidirect
315. #1894C2×C31semidirect
316. #1894C2×C31semidirect
317. #1873C2×C31semidirect
318. #1872C2×C31semidirect
319. #1825C2×C31semidirect
320. #1824C2×C31semidirect
321. #1805C2×C31semidirect
322. C4×#103C2×C31semidirect
323. #1736C2×C31semidirect
324. #1736C2×C31semidirect
365. #552C4×C31semidirect
436. #125C2×C4×C31semidirect
441. C22⋊Q8C2×C4×C31semidirect
443. C4×Q8C2×C4×C31semidirect
461. C2×C4⋊C4C2×C4×C31semidirect
496. C31#22499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5522
C2×C31×#4362
C31×#23522
C31×#19912
C31×#19892
C31×#18942
C31×#18732
C31×#18722
C31×#18252
C31×#18242
C31×#18052
C4×C31×#1032
C31×#17362
#2249931