Finite Group Databasebeta

← C31×#26247 #21483006

Subgroups — C31×#26247 #21483006

Order 7936.

870 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#485C211yesmaximal, characteristic, complemented
2C2×C31×#483C211yesmaximal, characteristic, complemented
3C31×#2542C211yesmaximal, characteristic
4C31×#2352C211yesmaximal, characteristic
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2036C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1981C211yesmaximal, characteristic, complemented
10C31×#1960C211yesmaximal, characteristic, complemented
11C31×#1955C211yesmaximal, characteristic
12C31×#1949C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C31×#1776C211yesmaximal, characteristic, complemented
16C2×C31×C4⋊Q8C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#485—24no—
25C31×#483—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic
41C2×C31×C22⋊C8C2211yescharacteristic
42C2×C31×C22⋊C8C2211yescharacteristic
43C2×C31×#97C2211yescharacteristic
44C31×#399—21no—
45C31×#399—21no—
46C31×#390—21no—
47C31×#388—21no—
48C31×#387—21no—
49C31×#386—21no—
50C31×#384—21no—
51C31×#382C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C4×C4⋊C4×C31C2211yescharacteristic
55C4×C4⋊C4×C31C2211yescharacteristic
56C4×C22⋊C4×C31—21no—
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31D411yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C22×C8×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C31×C4⋊Q8—22no—
72C31×C4⋊Q8—22no—
73C31×C22⋊Q8—22no—
74C31×C22⋊Q8—22no—
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8—41no—
78C31×C22⋊Q8—41no—
79C31×C22⋊Q8—41no—
80C31×C22⋊Q8—41no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C31×#117—22no—
84C31×#117—41no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C22⋊C4×C31—21no—
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×C31—21no—
113C2×C42×C31C2311yescharacteristic
114C31×#107—22no—
115C31×#107—22no—
116C31×#106—22no—
117C31×#106D414yescomplemented
118C31×C4⋊C8—22no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#103—22no—
123C31×#103—41no—
124C31×#103—41no—
125C31×#103—41no—
126C31×#103—41no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—41no—
130C31×C22⋊C8—41no—
131C31×#97—22no—
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—21no—
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—21no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—41no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
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—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—42no—
176C22×C4×C31—42no—
177C22×C4×C31—81no—
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2411yescharacteristic
183C2×C8×C31—21no—
184C2×C8×C31—21no—
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×C31C2×D412yes—
195C4⋊C4×C31—22no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31C2×D412yes—
213C4⋊C4×C31C2×D412yes—
214C4⋊C4×C31#4112yes—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—42no—
221C22⋊C4×C31—42no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—81no—
224C42×C31—42no—
225C42×C31—42no—
226C42×C31—81no—
227C42×C31#4112yes—
228C42×C31#4112yes—
229#26247C3111yesmaximal, characteristic, direct product factor, Sylow
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
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#13712yes—
244C23×C31C22×D411yescharacteristic
245Q8×C31—41no—
246Q8×C31—41no—
247Q8×C31—41no—
248Q8×C31—41no—
249Q8×C31—41no—
250Q8×C31—41no—
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—22no—
262C2×C4×C31—22no—
263C2×C4×C31—21no—
264C2×C4×C31—22no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
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—41no—
296C2×C4×C31—84no—
297C2×C4×C31#12312yes—
298C2×C4×C31#12312yes—
299C2×C4×C31C22×D411yescharacteristic
300C2×C4×C31C2×#4111yescharacteristic
301C2×C4×C31C2×#4111yescharacteristic
302C2×C4×C31C2×#4111yescharacteristic
303C2×C4×C31H(5,𝔽2)11yescharacteristic
304C2×C4×C31H(5,𝔽2)11yescharacteristic
305C8×C31—22no—
306C8×C31—41no—
307C8×C31—41no—
308C8×C31—41no—
309C2×#485C2×C3111yescharacteristic, complemented
310C2×#483C2×C3111yescharacteristic, complemented
311#2542C2×C3111yescharacteristic
312#2352C2×C3111yescharacteristic
313#2036C2×C3111yescharacteristic, complemented
314#2036C2×C3111yescharacteristic, complemented
315#2036C2×C3111yescharacteristic, complemented
316#2035C2×C3111yescharacteristic, complemented
317#1981C2×C3111yescharacteristic, complemented
318#1960C2×C3111yescharacteristic, complemented
319#1955C2×C3111yescharacteristic
320#1949C2×C3111yescharacteristic, complemented
321#1873C2×C3111yescharacteristic, complemented
322#1872C2×C3111yescharacteristic, complemented
323#1776C2×C3111yescharacteristic, complemented
324C22×C31—22no—
325C22×C31—22no—
326C22×C31—22no—
327C22×C31—41no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—41no—
333C22×C31—41no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—41no—
338C22×C31C2×#12311yescharacteristic
339C22×C31D4211yescharacteristic
340C22×C31#54611yescharacteristic
341C22×C31C2×#13711yescharacteristic
342C22×C31#57511yescharacteristic
343C22×C31#57711yescharacteristic
344C22×C31#57811yescharacteristic
345C4×C31—22no—
346C4×C31—22no—
347C4×C31—41no—
348C4×C31—41no—
349C4×C31—42no—
350C4×C31—42no—
351C4×C31—42no—
352C4×C31—81no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31—81no—
356C4×C31—81no—
357C4×C31#53211yescharacteristic
358C4×C31#54011yescharacteristic
359C4×C31#55011yescharacteristic
360C4×C31#55911yescharacteristic
361C2×C4⋊Q8C22×C3111yescharacteristic
362C2×C22⋊Q8C22×C3111yescharacteristic
363C2×C22⋊Q8C22×C3111yescharacteristic
364C2×C22⋊Q8C22×C3111yescharacteristic
365C2×C22⋊Q8C22×C3111yescharacteristic
366C2×C4×D4C22×C3111yescharacteristic
367C2×#117C22×C3111yescharacteristic
368C22×C4⋊C4C22×C3111yescharacteristic
369#485—24no—
370#483—24no—
371C2×#107C22×C3111yescharacteristic
372C2×#107C22×C3111yescharacteristic
373C2×#106C22×C3111yescharacteristic
374C2×#106C22×C3111yescharacteristic
375C2×C4⋊C8C22×C3111yescharacteristic
376C2×#103C22×C3111yescharacteristic
377C2×#103C22×C3111yescharacteristic
378C2×#103C22×C3111yescharacteristic
379C2×#103C22×C3111yescharacteristic
380C2×#103C22×C3111yescharacteristic
381C2×#103C22×C3111yescharacteristic
382C2×#103C22×C3111yescharacteristic
383C2×#103C22×C3111yescharacteristic
384C2×C22⋊C8C22×C3111yescharacteristic
385C2×C22⋊C8C22×C3111yescharacteristic
386C2×C22⋊C8C22×C3111yescharacteristic
387C2×C22⋊C8C22×C3111yescharacteristic
388C2×#97C22×C3111yescharacteristic
389#399—21no—
390#399—21no—
391#390—21no—
392#388—21no—
393#387—21no—
394#386—21no—
395#384—21no—
396#382C22×C3111yescharacteristic
397#380C22×C3111yescharacteristic
398#380C22×C3111yescharacteristic
399C4×C4⋊C4C22×C3111yescharacteristic
400C4×C4⋊C4C22×C3111yescharacteristic
401C4×C22⋊C4—21no—
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406C2×C31—42no—
407C2×C31—81no—
408C2×C31#244511yescharacteristic
409C2×C31#309511yescharacteristic
410C2×C31#309711yescharacteristic
411C2×C31#326611yescharacteristic
412C2×C31#326911yescharacteristic
413C2×C31#330711yescharacteristic
414C2×C31#331211yescharacteristic
415C22×Q8C23×C3111yescharacteristic
416C22×Q8C23×C3111yescharacteristic
417C22×D4D4×C3111yescharacteristic
418C23×C4—21no—
419C23×C4C23×C3111yescharacteristic
420C23×C4C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C22×C8C23×C3111yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—41no—
432C22⋊Q8—41no—
433C22⋊Q8—41no—
434C22⋊Q8—41no—
435C4×D4—22no—
436C4×D4—22no—
437#117—22no—
438#117—41no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4D4×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C4⋊C4C23×C3111yescharacteristic
452C2×C4⋊C4C23×C3111yescharacteristic
453C2×C4⋊C4C23×C3111yescharacteristic
454C2×C4⋊C4C23×C3111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C3111yescharacteristic
463C2×C22⋊C4D4×C3111yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C3111yescharacteristic
468#107—22no—
469#107—22no—
470#106—22no—
471#106D4×C3114yescomplemented
472C4⋊C8—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—41no—
478#103—41no—
479#103—41no—
480#103—41no—
481C22⋊C8—22no—
482C22⋊C8—22no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485#97—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492C31#2624711yescharacteristic, direct product factor, Sylow
493C24C2×D4×C3111yescharacteristic
494C24C2×D4×C3111yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—41no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
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—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4C2×D4×C3111yescharacteristic
534C22×C4C2×D4×C3111yescharacteristic
535C22×C4C2×D4×C3111yescharacteristic
536C22×C4C2×D4×C3111yescharacteristic
537C22×C4C24×C3111yescharacteristic
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
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×C8C2×D4×C3112yes—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4C2×D4×C3112yes—
568C4⋊C4C2×D4×C3112yes—
569C4⋊C4#41×C3112yes—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C42—42no—
580C42—42no—
581C42—81no—
582C42#41×C3112yes—
583C42#41×C3112yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23C31×#13712yes—
598C23C22×D4×C3111yescharacteristic
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
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×C4C31×#12312yes—
652C2×C4C31×#12312yes—
653C2×C4C22×D4×C3111yescharacteristic
654C2×C4C2×#41×C3111yescharacteristic
655C2×C4C2×#41×C3111yescharacteristic
656C2×C4C2×#41×C3111yescharacteristic
657C2×C4C31×H(5,𝔽2)11yescharacteristic
658C2×C4C31×H(5,𝔽2)11yescharacteristic
659C8—22no—
660C8—41no—
661C8—41no—
662C8—41no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22C2×C31×#12311yescharacteristic
678C22D42×C3111yescharacteristic
679C22C31×#54611yescharacteristic
680C22C2×C31×#13711yescharacteristic
681C22C31×#57511yescharacteristic
682C22C31×#57711yescharacteristic
683C22C31×#57811yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4C31×#53211yescharacteristic
697C4C31×#54011yescharacteristic
698C4C31×#55011yescharacteristic
699C4C31×#55911yescharacteristic
700C2—42no—
701C2—81no—
702C2C31×#244511yescharacteristic
703C2C31×#309511yescharacteristic
704C2C31×#309711yescharacteristic
705C2C31×#326611yescharacteristic
706C2C31×#326911yescharacteristic
707C2C31×#330711yescharacteristic
708C2C31×#331211yescharacteristic
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×#485C2semidirect
2. C2×C31×#483C2semidirect
5. C31×#2036C2semidirect
6. C31×#2036C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#1981C2semidirect
10. C31×#1960C2semidirect
12. C31×#1949C2semidirect
13. C31×#1873C2semidirect
14. C31×#1872C2semidirect
15. C31×#1776C2semidirect
117. C31×#106D4semidirect
229. #26247C31direct (N × H)
309. C2×#485C2×C31semidirect
310. C2×#483C2×C31semidirect
313. #2036C2×C31semidirect
314. #2036C2×C31semidirect
315. #2036C2×C31semidirect
316. #2035C2×C31semidirect
317. #1981C2×C31semidirect
318. #1960C2×C31semidirect
320. #1949C2×C31semidirect
321. #1873C2×C31semidirect
322. #1872C2×C31semidirect
323. #1776C2×C31semidirect
471. #106D4×C31semidirect
492. C31#26247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4852
C2×C31×#4832
C31×#25422
C31×#23522
C31×#20362
C31×#20352
C31×#19812
C31×#19602
C31×#19552
C31×#19492
C31×#18732
C31×#18722
C31×#17762
#2624731