Finite Group Databasebeta

← C31×#24982 #21481741

Subgroups — C31×#24982 #21481741

Order 7936.

862 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
1C31×#2537C211yesmaximal, characteristic
2C31×#2352C211yesmaximal, characteristic, complemented
3C31×#2077C211yesmaximal, characteristic, complemented
4C31×#2077C211yesmaximal, characteristic, complemented
5C31×#2034C211yesmaximal, characteristic, complemented
6C31×#2034C211yesmaximal, characteristic, complemented
7C31×#1955C211yesmaximal, characteristic, complemented
8C31×#1948C211yesmaximal, characteristic, complemented
9C31×#1875C211yesmaximal, characteristic, complemented
10C31×#1874C211yesmaximal, characteristic, complemented
11C31×#1836C211yesmaximal, characteristic, complemented
12C31×#1825C211yesmaximal, characteristic, complemented
13C31×#1823C211yesmaximal, characteristic, complemented
14C31×#1804C211yesmaximal, characteristic, complemented
15C31×#1762C211yesmaximal, characteristic, complemented
16C2×C31×#121—21no—
17C2×C31×#121C2211yescharacteristic
18C2×C31×#121C2211yescharacteristic
19C2×C4×D4×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C2×C31×#106C2211yescharacteristic
24C2×C31×#106C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C2×C31×#102C2211yescharacteristic
27C2×C31×#102C2211yescharacteristic
28C2×C31×#102C2211yescharacteristic
29C2×C31×#102C2211yescharacteristic
30C2×C31×C22⋊C8C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×#97C2211yescharacteristic
35C31×#394—21no—
36C31×#394—21no—
37C31×#388—21no—
38C31×#387—21no—
39C31×#386—21no—
40C31×#384C2211yescharacteristic
41C31×#382C2211yescharacteristic
42C31×#380—21no—
43C31×#380C2211yescharacteristic
44C31×#380C2211yescharacteristic
45C31×#380C2211yescharacteristic
46C31×#380C2211yescharacteristic
47C4×C4⋊C4×C31C2211yescharacteristic
48C4×C22⋊C4×C31—21no—
49C31×#340C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31D411yescharacteristic
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C22×C8×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C31×#121—22no—
72C31×#121—22no—
73C31×#121—41no—
74C31×#121—41no—
75C31×#121—44no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C4×D4×C31—22no—
79C4×D4×C31—22no—
80C31×#117—22no—
81C31×#117—41no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31D411yescharacteristic
88C2×C4⋊C4×C31C2311yescharacteristic
89C2×C4⋊C4×C31C2311yescharacteristic
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31C2311yescharacteristic
108C31×#106—41no—
109C31×#106—41no—
110C31×C4⋊C8—22no—
111C31×#102—22no—
112C31×#102—22no—
113C31×#102—41no—
114C31×#102—41no—
115C31×C22⋊C8—41no—
116C31×C22⋊C8—41no—
117C31×C22⋊C8—41no—
118C31×C22⋊C8—41no—
119C31×#97—22no—
120C31×#95—21no—
121C31×#95—21no—
122C31×#95—21no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C24×C31—21no—
128C24×C31C2×D411yescharacteristic
129C24×C31C2×D411yescharacteristic
130C2×D4×C31—22no—
131C2×D4×C31—22no—
132C2×D4×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—21no—
137C2×D4×C31—41no—
138C2×D4×C31—42no—
139C2×D4×C31—42no—
140C2×D4×C31—42no—
141C2×D4×C31—42no—
142C2×D4×C31—81no—
143C2×D4×C31—81no—
144C2×D4×C31#4112yes—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
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—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—81no—
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2411yescharacteristic
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
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—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
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—81no—
204C4⋊C4×C31#4112yes—
205C22⋊C4×C31—22no—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—81no—
215C42×C31—42no—
216C42×C31—81no—
217C42×C31#4112yes—
218C42×C31#4112yes—
219#24982C3111yesmaximal, characteristic, direct product factor, Sylow
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—22no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31AGL(1,ℤ/8)12yes—
241C23×C31C22×D411yescharacteristic
242D4×C31—22no—
243D4×C31—22no—
244D4×C31—44no—
245D4×C31—41no—
246D4×C31—41no—
247D4×C31—84no—
248D4×C31—84no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
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—41no—
288C2×C4×C31—84no—
289C2×C4×C31—84no—
290C2×C4×C31#12312yes—
291C2×C4×C31#12312yes—
292C2×C4×C31C2×#4111yescharacteristic
293C2×C4×C31C2×#4111yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31H(5,𝔽2)11yescharacteristic
297C2×C4×C31H(5,𝔽2)11yescharacteristic
298C8×C31—41no—
299C8×C31—41no—
300C8×C31—41no—
301C8×C31—41no—
302#2537C2×C3111yescharacteristic
303#2352C2×C3111yescharacteristic, complemented
304#2077C2×C3111yescharacteristic, complemented
305#2077C2×C3111yescharacteristic, complemented
306#2034C2×C3111yescharacteristic, complemented
307#2034C2×C3111yescharacteristic, complemented
308#1955C2×C3111yescharacteristic, complemented
309#1948C2×C3111yescharacteristic, complemented
310#1875C2×C3111yescharacteristic, complemented
311#1874C2×C3111yescharacteristic, complemented
312#1836C2×C3111yescharacteristic, complemented
313#1825C2×C3111yescharacteristic, complemented
314#1823C2×C3111yescharacteristic, complemented
315#1804C2×C3111yescharacteristic, complemented
316#1762C2×C3111yescharacteristic, complemented
317C22×C31—22no—
318C22×C31—22no—
319C22×C31—22no—
320C22×C31—41no—
321C22×C31—41no—
322C22×C31—41no—
323C22×C31—41no—
324C22×C31—41no—
325C22×C31—41no—
326C22×C31—41no—
327C22×C31—42no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31—42no—
331C22×C31—41no—
332C22×C31—42no—
333C22×C31—41no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—81no—
337C22×C31—81no—
338C22×C31C2×#12311yescharacteristic
339C22×C31#54611yescharacteristic
340C22×C31#54611yescharacteristic
341C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C31#57511yescharacteristic
343C22×C31#57711yescharacteristic
344C22×C31#57711yescharacteristic
345C4×C31—22no—
346C4×C31—22no—
347C4×C31—41no—
348C4×C31—41no—
349C4×C31—42no—
350C4×C31—81no—
351C4×C31—81no—
352C4×C31—81no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31—81no—
356C4×C31#52911yescharacteristic
357C4×C31#54011yescharacteristic
358C4×C31#55311yescharacteristic
359C4×C31#55511yescharacteristic
360C2×#121—21no—
361C2×#121C22×C3111yescharacteristic
362C2×#121C22×C3111yescharacteristic
363C2×C4×D4C22×C3111yescharacteristic
364C2×C4×D4C22×C3111yescharacteristic
365C2×#117C22×C3111yescharacteristic
366C22×C4⋊C4C22×C3111yescharacteristic
367C2×#106C22×C3111yescharacteristic
368C2×#106C22×C3111yescharacteristic
369C2×C4⋊C8C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×C22⋊C8C22×C3111yescharacteristic
375C2×C22⋊C8C22×C3111yescharacteristic
376C2×C22⋊C8C22×C3111yescharacteristic
377C2×C22⋊C8C22×C3111yescharacteristic
378C2×#97C22×C3111yescharacteristic
379#394—21no—
380#394—21no—
381#388—21no—
382#387—21no—
383#386—21no—
384#384C22×C3111yescharacteristic
385#382C22×C3111yescharacteristic
386#380—21no—
387#380C22×C3111yescharacteristic
388#380C22×C3111yescharacteristic
389#380C22×C3111yescharacteristic
390#380C22×C3111yescharacteristic
391C4×C4⋊C4C22×C3111yescharacteristic
392C4×C22⋊C4—21no—
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#340C22×C3111yescharacteristic
398#340C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403C2×C31—42no—
404C2×C31—81no—
405C2×C31—82no—
406C2×C31#242011yescharacteristic
407C2×C31#309411yescharacteristic
408C2×C31#309911yescharacteristic
409C2×C31#330611yescharacteristic
410C2×C31#330711yescharacteristic
411C2×C31#331011yescharacteristic
412C2×C31#332111yescharacteristic
413C22×D4—21no—
414C22×D4—21no—
415C22×D4D4×C3111yescharacteristic
416C22×D4C23×C3111yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4C23×C3111yescharacteristic
420C23×C4C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C22×C8C23×C3111yescharacteristic
425#121—22no—
426#121—22no—
427#121—41no—
428#121—41no—
429#121—44no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434#117—22no—
435#117—41no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4D4×C3111yescharacteristic
442C2×C4⋊C4C23×C3111yescharacteristic
443C2×C4⋊C4C23×C3111yescharacteristic
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C3111yescharacteristic
458C2×C22⋊C4D4×C3111yescharacteristic
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C3111yescharacteristic
462#106—41no—
463#106—41no—
464C4⋊C8—22no—
465#102—22no—
466#102—22no—
467#102—41no—
468#102—41no—
469C22⋊C8—41no—
470C22⋊C8—41no—
471C22⋊C8—41no—
472C22⋊C8—41no—
473#97—22no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481C31#2498211yescharacteristic, direct product factor, Sylow
482C24—21no—
483C24C2×D4×C3111yescharacteristic
484C24C2×D4×C3111yescharacteristic
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—41no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4#41×C3112yes—
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×C4—21no—
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—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3111yescharacteristic
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4C2×D4×C3111yescharacteristic
529C22×C4C24×C3111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4#41×C3112yes—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C42—42no—
571C42—81no—
572C42#41×C3112yes—
573C42#41×C3112yes—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C31×AGL(1,ℤ/8)12yes—
595C23C22×D4×C3111yescharacteristic
596D4—22no—
597D4—22no—
598D4—44no—
599D4—41no—
600D4—41no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
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×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—84no—
643C2×C4—84no—
644C2×C4C31×#12312yes—
645C2×C4C31×#12312yes—
646C2×C4C2×#41×C3111yescharacteristic
647C2×C4C2×#41×C3111yescharacteristic
648C2×C4C2×#41×C3111yescharacteristic
649C2×C4C2×#41×C3111yescharacteristic
650C2×C4C31×H(5,𝔽2)11yescharacteristic
651C2×C4C31×H(5,𝔽2)11yescharacteristic
652C8—41no—
653C8—41no—
654C8—41no—
655C8—41no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—42no—
672C22—41no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×C31×#12311yescharacteristic
678C22C31×#54611yescharacteristic
679C22C31×#54611yescharacteristic
680C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
681C22C31×#57511yescharacteristic
682C22C31×#57711yescharacteristic
683C22C31×#57711yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C31×#52911yescharacteristic
696C4C31×#54011yescharacteristic
697C4C31×#55311yescharacteristic
698C4C31×#55511yescharacteristic
699C2—42no—
700C2—81no—
701C2—82no—
702C2C31×#242011yescharacteristic
703C2C31×#309411yescharacteristic
704C2C31×#309911yescharacteristic
705C2C31×#330611yescharacteristic
706C2C31×#330711yescharacteristic
707C2C31×#331011yescharacteristic
708C2C31×#332111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2537C2
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
2. C31×#2352C2semidirect
3. C31×#2077C2semidirect
4. C31×#2077C2semidirect
5. C31×#2034C2semidirect
6. C31×#2034C2semidirect
7. C31×#1955C2semidirect
8. C31×#1948C2semidirect
9. C31×#1875C2semidirect
10. C31×#1874C2semidirect
11. C31×#1836C2semidirect
12. C31×#1825C2semidirect
13. C31×#1823C2semidirect
14. C31×#1804C2semidirect
15. C31×#1762C2semidirect
219. #24982C31direct (N × H)
303. #2352C2×C31semidirect
304. #2077C2×C31semidirect
305. #2077C2×C31semidirect
306. #2034C2×C31semidirect
307. #2034C2×C31semidirect
308. #1955C2×C31semidirect
309. #1948C2×C31semidirect
310. #1875C2×C31semidirect
311. #1874C2×C31semidirect
312. #1836C2×C31semidirect
313. #1825C2×C31semidirect
314. #1823C2×C31semidirect
315. #1804C2×C31semidirect
316. #1762C2×C31semidirect
481. C31#24982direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25372
C31×#23522
C31×#20772
C31×#20342
C31×#19552
C31×#19482
C31×#18752
C31×#18742
C31×#18362
C31×#18252
C31×#18232
C31×#18042
C31×#17622
#2498231