Finite Group Databasebeta

← C31×#26988 #21483747

Subgroups — C31×#26988 #21483747

Order 7936.

840 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#470C211yesmaximal, characteristic
2C2×C31×#441C211yesmaximal, characteristic, complemented
3C31×#2429C211yesmaximal, characteristic
4C31×#2423C211yesmaximal, characteristic
5C31×#2084C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic
7C31×#2016C211yesmaximal, characteristic, complemented
8C31×#2001C211yesmaximal, characteristic
9C31×#1956C211yesmaximal, characteristic, complemented
10C31×#1935C211yesmaximal, characteristic, complemented
11C31×#1933C211yesmaximal, characteristic, complemented
12C31×#1894C211yesmaximal, characteristic
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1865C211yesmaximal, characteristic, complemented
15C31×#1753C211yesmaximal, characteristic
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C31×#470—24no—
26C31×#441—24no—
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
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×#97C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#399—21no—
41C31×#398—21no—
42C31×#398—21no—
43C31×#396—21no—
44C31×#391C2211yescharacteristic
45C31×#391C2211yescharacteristic
46C31×#389—21no—
47C31×#389C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#388—21no—
50C31×#388—21no—
51C31×#387—21no—
52C31×#384C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C2×Q16×C31—22no—
66C2×Q16×C31—22no—
67C2×Q16×C31—22no—
68C2×Q16×C31—22no—
69C2×Q16×C31—22no—
70C2×Q16×C31—41no—
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—41no—
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C31×C4⋊Q8—22no—
79C31×C4⋊Q8—41no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—22no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—41no—
84C31×C22⋊Q8—41no—
85C31×C22⋊Q8—41no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31—41no—
89C4×Q8×C31—41no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31D411yescharacteristic
111C2×C22⋊C4×C31D411yescharacteristic
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×#106—22no—
117C31×#106—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#103—41no—
123C31×#103—41no—
124C31×#103—41no—
125C31×#103D414yes—
126C31×C22⋊C8—22no—
127C31×#97—22no—
128C4×C8×C31—41no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95D411yescharacteristic
137C31×#95D411yescharacteristic
138C24×C31C2×D411yescharacteristic
139C2×Q8×C31—21no—
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×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31C2×D412yes—
156C2×Q8×C31#4112yes—
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×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2411yescharacteristic
177Q16×C31—28no—
178Q16×C31—44no—
179M16×C31—44no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
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×C31C2×D412yes—
190C2×C8×C31#4112yes—
191C2×C8×C31#4112yes—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—81no—
211C4⋊C4×C31—81no—
212C4⋊C4×C31C2×D412yes—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—81no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—42no—
224C42×C31—42no—
225#26988C3111yesmaximal, characteristic, direct product factor, Sylow
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31C22×D411yescharacteristic
234Q8×C31—22no—
235Q8×C31—22no—
236Q8×C31—22no—
237Q8×C31—22no—
238Q8×C31—41no—
239Q8×C31—41no—
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—41no—
244Q8×C31—41no—
245Q8×C31—41no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—22no—
254C2×C4×C31—22no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
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#13712yes—
288C2×C4×C31#13712yes—
289C2×C4×C31C22×D411yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31C2×#4111yescharacteristic
292C2×C4×C31C2×#4111yescharacteristic
293C2×C4×C31H(5,𝔽2)11yescharacteristic
294C2×C4×C31H(5,𝔽2)11yescharacteristic
295C8×C31—22no—
296C8×C31—22no—
297C8×C31—22no—
298C8×C31—41no—
299C2×#470C2×C3111yescharacteristic
300C2×#441C2×C3111yescharacteristic, complemented
301#2429C2×C3111yescharacteristic
302#2423C2×C3111yescharacteristic
303#2084C2×C3111yescharacteristic, complemented
304#2035C2×C3111yescharacteristic
305#2016C2×C3111yescharacteristic, complemented
306#2001C2×C3111yescharacteristic
307#1956C2×C3111yescharacteristic, complemented
308#1935C2×C3111yescharacteristic, complemented
309#1933C2×C3111yescharacteristic, complemented
310#1894C2×C3111yescharacteristic
311#1878C2×C3111yescharacteristic, complemented
312#1865C2×C3111yescharacteristic, complemented
313#1753C2×C3111yescharacteristic
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31—41no—
321C22×C31#53211yescharacteristic
322C22×C31D4211yescharacteristic
323C22×C31#54611yescharacteristic
324C22×C31C2×#13711yescharacteristic
325C22×C31C2×#13711yescharacteristic
326C22×C31#57711yescharacteristic
327C22×C31#57811yescharacteristic
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—41no—
331C4×C31—42no—
332C4×C31—42no—
333C4×C31—41no—
334C4×C31—42no—
335C4×C31—41no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31—81no—
341C4×C31#52511yescharacteristic
342C4×C31#54011yescharacteristic
343C4×C31#54611yescharacteristic
344C4×C31#55311yescharacteristic
345C22×Q16C22×C3111yescharacteristic
346C22×Q16C22×C3111yescharacteristic
347C22×M16C22×C3111yescharacteristic
348C2×C4⋊Q8C22×C3111yescharacteristic
349C2×C22⋊Q8C22×C3111yescharacteristic
350C2×C22⋊Q8C22×C3111yescharacteristic
351C2×C22⋊Q8C22×C3111yescharacteristic
352C2×C4×Q8C22×C3111yescharacteristic
353C2×C4×Q8C22×C3111yescharacteristic
354#470—24no—
355#441—24no—
356C2×#106C22×C3111yescharacteristic
357C2×#106C22×C3111yescharacteristic
358C2×#103C22×C3111yescharacteristic
359C2×#103C22×C3111yescharacteristic
360C2×#103C22×C3111yescharacteristic
361C2×#103C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×#103C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×C22⋊C8C22×C3111yescharacteristic
367C2×#97C22×C3111yescharacteristic
368C2×C4×C8C22×C3111yescharacteristic
369#399—21no—
370#398—21no—
371#398—21no—
372#396—21no—
373#391C22×C3111yescharacteristic
374#391C22×C3111yescharacteristic
375#389—21no—
376#389C22×C3111yescharacteristic
377#389C22×C3111yescharacteristic
378#388—21no—
379#388—21no—
380#387—21no—
381#384C22×C3111yescharacteristic
382#380C22×C3111yescharacteristic
383C4×C22⋊C4C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#336C22×C3111yescharacteristic
389#336C22×C3111yescharacteristic
390C2×C31—81no—
391C2×C31#246411yescharacteristic
392C2×C31#317811yescharacteristic
393C2×C31#318511yescharacteristic
394C2×C31#327611yescharacteristic
395C2×C31#327811yescharacteristic
396C2×C31#331211yescharacteristic
397C2×C31#331611yescharacteristic
398C22×Q8C23×C3111yescharacteristic
399C22×Q8C23×C3111yescharacteristic
400C22×Q8C23×C3111yescharacteristic
401C23×C4C23×C3111yescharacteristic
402C2×Q16—22no—
403C2×Q16—22no—
404C2×Q16—22no—
405C2×Q16—22no—
406C2×Q16—22no—
407C2×Q16—41no—
408C2×M16—22no—
409C2×M16—22no—
410C2×M16—41no—
411C22×C8C23×C3111yescharacteristic
412C22×C8C23×C3111yescharacteristic
413C22×C8C23×C3111yescharacteristic
414C22×C8C23×C3111yescharacteristic
415C4⋊Q8—22no—
416C4⋊Q8—41no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421C22⋊Q8—41no—
422C22⋊Q8—41no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—41no—
426C4×Q8—41no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C4⋊C4C23×C3111yescharacteristic
440C2×C4⋊C4C23×C3111yescharacteristic
441C2×C4⋊C4C23×C3111yescharacteristic
442C2×C4⋊C4C23×C3111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C3111yescharacteristic
448C2×C22⋊C4D4×C3111yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C3111yescharacteristic
452C2×C42C23×C3111yescharacteristic
453#106—22no—
454#106—22no—
455#103—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—41no—
460#103—41no—
461#103—41no—
462#103D4×C3114yes—
463C22⋊C8—22no—
464#97—22no—
465C4×C8—41no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95D4×C3111yescharacteristic
474#95D4×C3111yescharacteristic
475C31#2698811yescharacteristic, direct product factor, Sylow
476C24C2×D4×C3111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8C2×D4×C3112yes—
494C2×Q8#41×C3112yes—
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—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C2×D4×C3111yescharacteristic
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C2×D4×C3111yescharacteristic
514C22×C4C24×C3111yescharacteristic
515Q16—28no—
516Q16—44no—
517M16—44no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×D4×C3112yes—
528C2×C8#41×C3112yes—
529C2×C8#41×C3112yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4C2×D4×C3112yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C42—42no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23C22×D4×C3111yescharacteristic
571Q8—22no—
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4C31×#13712yes—
625C2×C4C31×#13712yes—
626C2×C4C22×D4×C3111yescharacteristic
627C2×C4C2×#41×C3111yescharacteristic
628C2×C4C2×#41×C3111yescharacteristic
629C2×C4C2×#41×C3111yescharacteristic
630C2×C4C31×H(5,𝔽2)11yescharacteristic
631C2×C4C31×H(5,𝔽2)11yescharacteristic
632C8—22no—
633C8—22no—
634C8—22no—
635C8—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C31×#53211yescharacteristic
644C22D42×C3111yescharacteristic
645C22C31×#54611yescharacteristic
646C22C2×C31×#13711yescharacteristic
647C22C2×C31×#13711yescharacteristic
648C22C31×#57711yescharacteristic
649C22C31×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—42no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4C31×#52511yescharacteristic
664C4C31×#54011yescharacteristic
665C4C31×#54611yescharacteristic
666C4C31×#55311yescharacteristic
667C2—81no—
668C2C31×#246411yescharacteristic
669C2C31×#317811yescharacteristic
670C2C31×#318511yescharacteristic
671C2C31×#327611yescharacteristic
672C2C31×#327811yescharacteristic
673C2C31×#331211yescharacteristic
674C2C31×#331611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#441C2semidirect
5. C31×#2084C2semidirect
7. C31×#2016C2semidirect
9. C31×#1956C2semidirect
10. C31×#1935C2semidirect
11. C31×#1933C2semidirect
13. C31×#1878C2semidirect
14. C31×#1865C2semidirect
225. #26988C31direct (N × H)
300. C2×#441C2×C31semidirect
303. #2084C2×C31semidirect
305. #2016C2×C31semidirect
307. #1956C2×C31semidirect
308. #1935C2×C31semidirect
309. #1933C2×C31semidirect
311. #1878C2×C31semidirect
312. #1865C2×C31semidirect
475. C31#26988direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4702
C2×C31×#4412
C31×#24292
C31×#24232
C31×#20842
C31×#20352
C31×#20162
C31×#20012
C31×#19562
C31×#19352
C31×#19332
C31×#18942
C31×#18782
C31×#18652
C31×#17532
#2698831