Finite Group Databasebeta

← C31×#25957 #21482716

Subgroups — C31×#25957 #21482716

Order 7936.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#479C211yesmaximal, characteristic, complemented
2C22×C31×#103C211yesmaximal, characteristic
3C31×#2442C211yesmaximal, characteristic
4Q8×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#2097C211yesmaximal, characteristic, complemented
6C31×#2068C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2026C211yesmaximal, characteristic, complemented
9C31×#1865C211yesmaximal, characteristic, complemented
10C31×#1863C211yesmaximal, characteristic, complemented
11C31×#1852C211yesmaximal, characteristic
12C31×#1850C211yesmaximal, characteristic
13C31×#1807C211yesmaximal, characteristic
14C31×#1805C211yesmaximal, characteristic, complemented
15C31×#1787C211yesmaximal, characteristic
16C23×Q8×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×#125C2211yescharacteristic
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C31×#479—24no—
23C2×C31×#107C2211yescharacteristic
24C2×C31×#107C2211yescharacteristic
25C2×C31×#106C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×C4⋊C8C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103—24no—
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C31×#400—21no—
40C31×#398—21no—
41C31×#391—21no—
42C31×#391—21no—
43C31×#391C2211yescharacteristic
44C31×#391C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#385—21no—
48C31×#382C2211yescharacteristic
49C31×#380—21no—
50C31×#380—21no—
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C4×C22⋊C4×C31—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
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—41no—
66C22×Q8×C31—41no—
67C22×Q8×C31Q814yes—
68C22×Q8×C31C2311yescharacteristic
69C22×Q8×C31C2311yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31C2311yescharacteristic
73C22×C8×C31—22no—
74C22×C8×C31—22no—
75C22×C8×C31—41no—
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C31×#125—22no—
81C31×#125—41no—
82C4×Q8×C31—22no—
83C4×Q8×C31—22no—
84C4×Q8×C31—41no—
85C4×Q8×C31—41no—
86C2×C4⋊C4×C31—22no—
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—21no—
94C2×C4⋊C4×C31—41no—
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×C31D411yescharacteristic
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31C2311yescharacteristic
108C2×C42×C31C2311yescharacteristic
109C31×#107—22no—
110C31×#107—41no—
111C31×#106—22no—
112C31×#106—41no—
113C31×C4⋊C8—22no—
114C31×C4⋊C8—41no—
115C31×#103—22no—
116C31×#103—22no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103—41no—
121C31×#103—41no—
122C31×#103D414yes—
123C31×C22⋊C8—22no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95D411yescharacteristic
135C31×#95D411yescharacteristic
136C24×C31C2×D411yescharacteristic
137C2×Q8×C31—24no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
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—42no—
148C2×Q8×C31—42no—
149C2×Q8×C31—44no—
150C2×Q8×C31—44no—
151C2×Q8×C31—44no—
152C2×Q8×C31C2×D412yes—
153C2×Q8×C31C2×Q812yes—
154C2×Q8×C31C2×Q812yes—
155C2×Q8×C31#4112yes—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—24no—
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×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×Q812yes—
180C22×C4×C31#4112yes—
181C22×C4×C31C2411yescharacteristic
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×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—44no—
194C2×C8×C31C2×D412yes—
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—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—81no—
212C4⋊C4×C31—81no—
213C4⋊C4×C31C2×D412yes—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—42no—
223C42×C31—42no—
224#25957C3111yesmaximal, characteristic, direct product factor, Sylow
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31C22⋊Q812yes—
230C23×C31#13512yes—
231C23×C31#13712yes—
232C23×C31C22×D411yescharacteristic
233Q8×C31—22no—
234Q8×C31—22no—
235Q8×C31—22no—
236Q8×C31—22no—
237Q8×C31—22no—
238Q8×C31—48no—
239Q8×C31—41no—
240Q8×C31—41no—
241Q8×C31C22⋊Q814yes—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—21no—
245C2×C4×C31—22no—
246C2×C4×C31—21no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
251C2×C4×C31—22no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—22no—
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—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—48no—
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—84no—
286C2×C4×C31C22⋊Q812yes—
287C2×C4×C31C22×D411yescharacteristic
288C2×C4×C31C22×Q811yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31H(5,𝔽2)11yescharacteristic
292C2×C4×C31H(5,𝔽2)11yescharacteristic
293C8×C31—22no—
294C8×C31—41no—
295C8×C31—41no—
296C8×C31—41no—
297C2×#479C2×C3111yescharacteristic, complemented
298C22×#103C2×C3111yescharacteristic
299#2442C2×C3111yescharacteristic
300Q8×C22⋊C4C2×C3111yescharacteristic
301#2097C2×C3111yescharacteristic, complemented
302#2068C2×C3111yescharacteristic, complemented
303#2066C2×C3111yescharacteristic, complemented
304#2026C2×C3111yescharacteristic, complemented
305#1865C2×C3111yescharacteristic, complemented
306#1863C2×C3111yescharacteristic, complemented
307#1852C2×C3111yescharacteristic
308#1850C2×C3111yescharacteristic
309#1807C2×C3111yescharacteristic
310#1805C2×C3111yescharacteristic, complemented
311#1787C2×C3111yescharacteristic
312C22×C31—22no—
313C22×C31—22no—
314C22×C31—22no—
315C22×C31—22no—
316C22×C31—22no—
317C22×C31—22no—
318C22×C31#47914yescomplemented
319C22×C31C2×C22⋊Q811yescharacteristic
320C22×C31D4211yescharacteristic
321C22×C31#54611yescharacteristic
322C22×C31C2×#13511yescharacteristic
323C22×C31C2×#13711yescharacteristic
324C22×C31#57711yescharacteristic
325C22×C31#57811yescharacteristic
326C4×C31—22no—
327C4×C31—24no—
328C4×C31—42no—
329C4×C31—41no—
330C4×C31—41no—
331C4×C31—42no—
332C4×C31—41no—
333C4×C31—41no—
334C4×C31—81no—
335C4×C31—81no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31C2×C22⋊Q811yescharacteristic
340C4×C31#54311yescharacteristic
341C4×C31#54611yescharacteristic
342C4×C31#55111yescharacteristic
343C23×Q8C22×C3111yescharacteristic
344C23×C8C22×C3111yescharacteristic
345C2×#125C22×C3111yescharacteristic
346C2×C4×Q8C22×C3111yescharacteristic
347C2×C4×Q8C22×C3111yescharacteristic
348C22×C4⋊C4C22×C3111yescharacteristic
349#479—24no—
350C2×#107C22×C3111yescharacteristic
351C2×#107C22×C3111yescharacteristic
352C2×#106C22×C3111yescharacteristic
353C2×#106C22×C3111yescharacteristic
354C2×C4⋊C8C22×C3111yescharacteristic
355C2×C4⋊C8C22×C3111yescharacteristic
356C2×#103—24no—
357C2×#103C22×C3111yescharacteristic
358C2×#103C22×C3111yescharacteristic
359C2×#103C22×C3111yescharacteristic
360C2×#103C22×C3111yescharacteristic
361C2×#103C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×#103C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×C22⋊C8C22×C3111yescharacteristic
366#400—21no—
367#398—21no—
368#391—21no—
369#391—21no—
370#391C22×C3111yescharacteristic
371#391C22×C3111yescharacteristic
372#389C22×C3111yescharacteristic
373#389C22×C3111yescharacteristic
374#385—21no—
375#382C22×C3111yescharacteristic
376#380—21no—
377#380—21no—
378#380C22×C3111yescharacteristic
379#380C22×C3111yescharacteristic
380C4×C22⋊C4—21no—
381C4×C22⋊C4C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#336C22×C3111yescharacteristic
387#336C22×C3111yescharacteristic
388C2×C31—24no—
389C2×C31#243711yescharacteristic
390C2×C31C2×#47911yescharacteristic
391C2×C31#308211yescharacteristic
392C2×C31#327011yescharacteristic
393C2×C31#328211yescharacteristic
394C2×C31#330011yescharacteristic
395C2×C31#332011yescharacteristic
396C22×Q8—21no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—41no—
401C22×Q8—41no—
402C22×Q8Q8×C3114yes—
403C22×Q8C23×C3111yescharacteristic
404C22×Q8C23×C3111yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4C23×C3111yescharacteristic
408C22×C8—22no—
409C22×C8—22no—
410C22×C8—41no—
411C22×C8C23×C3111yescharacteristic
412C22×C8C23×C3111yescharacteristic
413C22×C8C23×C3111yescharacteristic
414C22×C8C23×C3111yescharacteristic
415#125—22no—
416#125—41no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—41no—
420C4×Q8—41no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C4⋊C4C23×C3111yescharacteristic
432C2×C4⋊C4C23×C3111yescharacteristic
433C2×C4⋊C4C23×C3111yescharacteristic
434C2×C4⋊C4C23×C3111yescharacteristic
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C3111yescharacteristic
439C2×C22⋊C4D4×C3111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42C23×C3111yescharacteristic
443C2×C42C23×C3111yescharacteristic
444#107—22no—
445#107—41no—
446#106—22no—
447#106—41no—
448C4⋊C8—22no—
449C4⋊C8—41no—
450#103—22no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103—41no—
456#103—41no—
457#103D4×C3114yes—
458C22⋊C8—22no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95D4×C3111yescharacteristic
470#95D4×C3111yescharacteristic
471C31#2595711yescharacteristic, direct product factor, Sylow
472C24C2×D4×C3111yescharacteristic
473C2×Q8—24no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—28no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8C2×D4×C3112yes—
489C2×Q8C2×Q8×C3112yes—
490C2×Q8C2×Q8×C3112yes—
491C2×Q8#41×C3112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C2×D4×C3111yescharacteristic
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×Q8×C3112yes—
516C22×C4#41×C3112yes—
517C22×C4C24×C3111yescharacteristic
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×C8—21no—
528C2×C8—21no—
529C2×C8—44no—
530C2×C8C2×D4×C3112yes—
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—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4C2×D4×C3112yes—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23C31×C22⋊Q812yes—
565C23C31×#13512yes—
566C23C31×#13712yes—
567C23C22×D4×C3111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8C31×C22⋊Q814yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—48no—
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—84no—
621C2×C4C31×C22⋊Q812yes—
622C2×C4C22×D4×C3111yescharacteristic
623C2×C4C22×Q8×C3111yescharacteristic
624C2×C4C2×#41×C3111yescharacteristic
625C2×C4C2×#41×C3111yescharacteristic
626C2×C4C31×H(5,𝔽2)11yescharacteristic
627C2×C4C31×H(5,𝔽2)11yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22C31×#47914yescomplemented
639C22C2×C31×C22⋊Q811yescharacteristic
640C22D42×C3111yescharacteristic
641C22C31×#54611yescharacteristic
642C22C2×C31×#13511yescharacteristic
643C22C2×C31×#13711yescharacteristic
644C22C31×#57711yescharacteristic
645C22C31×#57811yescharacteristic
646C4—22no—
647C4—24no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C31×C22⋊Q811yescharacteristic
660C4C31×#54311yescharacteristic
661C4C31×#54611yescharacteristic
662C4C31×#55111yescharacteristic
663C2—24no—
664C2C31×#243711yescharacteristic
665C2C2×C31×#47911yescharacteristic
666C2C31×#308211yescharacteristic
667C2C31×#327011yescharacteristic
668C2C31×#328211yescharacteristic
669C2C31×#330011yescharacteristic
670C2C31×#332011yescharacteristic
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
1. C2×C31×#479C2semidirect
5. C31×#2097C2semidirect
6. C31×#2068C2semidirect
7. C31×#2066C2semidirect
8. C31×#2026C2semidirect
9. C31×#1865C2semidirect
10. C31×#1863C2semidirect
14. C31×#1805C2semidirect
224. #25957C31direct (N × H)
297. C2×#479C2×C31semidirect
301. #2097C2×C31semidirect
302. #2068C2×C31semidirect
303. #2066C2×C31semidirect
304. #2026C2×C31semidirect
305. #1865C2×C31semidirect
306. #1863C2×C31semidirect
310. #1805C2×C31semidirect
318. C22×C31#479semidirect
471. C31#25957direct (N × H)
638. C22C31×#479semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4792
C22×C31×#1032
C31×#24422
Q8×C22⋊C4×C312
C31×#20972
C31×#20682
C31×#20662
C31×#20262
C31×#18652
C31×#18632
C31×#18522
C31×#18502
C31×#18072
C31×#18052
C31×#17872
#2595731