Finite Group Databasebeta

← C31×#14142 #21470901

Subgroups — C31×#14142 #21470901

Order 7936.

1490 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#391C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic
4C2×C31×#389C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
6C31×#1443C212yesmaximal
7C31×#1442C212yesmaximal
8C31×#1436C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic
10C31×#1434C212yesmaximal
11C4×C31×#95C211yesmaximal, characteristic
12C23×Q8×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2212yes—
20C22×C42×C31C2211yescharacteristic
21C31×#391—24no—
22C31×#391—24no—
23C31×#391C418yescomplemented
24C31×#389—24no—
25C4×C4⋊C4×C31—24no—
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C22×Q8×C31—22no—
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31C2×C414yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—42no—
67C2×C4⋊C4×C31C2×C414yes—
68C2×C4⋊C4×C31D414yes—
69C2×C4⋊C4×C31D414yes—
70C2×C42×C31—22no—
71C2×C42×C31—22no—
72C2×C42×C31—24no—
73C2×C42×C31—22no—
74C2×C42×C31—22no—
75C2×C42×C31—22no—
76C2×C42×C31—24no—
77C2×C42×C31—22no—
78C2×C42×C31—22no—
79C2×C42×C31—22no—
80C2×C42×C31—42no—
81C2×C42×C31C2×C414yes—
82C31×#95—24no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—24no—
88C31×#95—22no—
89C31×#95—24no—
90C31×#95—22no—
91C31×#95—22no—
92C31×#95—42no—
93C31×#95C2×C418yes—
94C31×#95C2×C418yes—
95C31×#95Q814yescomplemented
96C24×C31C2411yescharacteristic
97C2×Q8×C31—28no—
98C2×Q8×C31—28no—
99C2×Q8×C31—28no—
100C2×Q8×C31—44no—
101C2×Q8×C31—44no—
102C2×Q8×C31—44no—
103C2×Q8×C31—44no—
104C22×C4×C31—21no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—21no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—22no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
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×C31C22×C412yes—
163C22×C4×C31C22×C414yes—
164C22×C4×C31C22×C414yes—
165C22×C4×C31C22×C412yes—
166C22×C4×C31C22×C412yes—
167C22×C4×C31C2×D414yes—
168C22×C4×C31C2×D414yes—
169C22×C4×C31C2×D412yes—
170C22×C4×C31C2×D412yes—
171C22×C4×C31C2×Q812yes—
172C22×C4×C31C2×Q812yes—
173C22×C4×C31C2×Q812yes—
174C22×C4×C31#4112yes—
175C22×C4×C31#4112yes—
176C22×C4×C31#4112yes—
177C22×C4×C31#4112yes—
178C22×C4×C31#4112yes—
179C22×C4×C31#4112yes—
180C22×C4×C31#4112yes—
181C4⋊C4×C31—28no—
182C4⋊C4×C31—28no—
183C4⋊C4×C31—28no—
184C4⋊C4×C31—48no—
185C42×C31—28no—
186C42×C31—48no—
187C42×C31—44no—
188C42×C31—44no—
189#14142C3111yesmaximal, characteristic, direct product factor, Sylow
190C23×C31C23×C411yescharacteristic
191C23×C31C22×D411yescharacteristic
192C23×C31C22×D411yescharacteristic
193C23×C31C22×Q811yescharacteristic
194C23×C31C2×#4111yescharacteristic
195C23×C31C2×#4111yescharacteristic
196C23×C31C2×#4111yescharacteristic
197C23×C31C2×#4111yescharacteristic
198C23×C31C2×#4111yescharacteristic
199C23×C31C2×#4111yescharacteristic
200C23×C31C2×#4111yescharacteristic
201C23×C31H(5,𝔽2)11yescharacteristic
202C23×C312−1+411yescharacteristic
203C23×C312−1+411yescharacteristic
204C23×C312−1+411yescharacteristic
205Q8×C31—416no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—24no—
213C2×C4×C31—22no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—24no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—22no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—24no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—24no—
228C2×C4×C31—22no—
229C2×C4×C31—24no—
230C2×C4×C31—24no—
231C2×C4×C31—24no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—41no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—41no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31#11714yes—
276C2×C4×C31C4×D414yes—
277C2×C4×C31C4×D414yes—
278C2×C4×C31C4×Q814yes—
279C2×C4×C31#12114yes—
280C2×C4×C31#12314yes—
281C2×C4×C31#12414yes—
282C2×C4×C31#12614yes—
283C2×#391C2×C3111yescharacteristic
284C2×#391C2×C3111yescharacteristic
285C2×#391C2×C3111yescharacteristic
286C2×#389C2×C3111yescharacteristic
287C2×C4×C4⋊C4C2×C3111yescharacteristic
288#1443C2×C3112yes—
289#1442C2×C3112yes—
290#1436C2×C3112yes—
291C4⋊#95C2×C3111yescharacteristic
292#1434C2×C3112yes—
293C4×#95C2×C3111yescharacteristic
294C22×C31C2×#11711yescharacteristic
295C22×C31C2×C4×D411yescharacteristic
296C22×C31C2×C4×D411yescharacteristic
297C22×C31C2×C4×Q811yescharacteristic
298C22×C31C4×#4111yescharacteristic
299C22×C31#51911yescharacteristic
300C22×C31#52011yescharacteristic
301C22×C31C2×#12111yescharacteristic
302C22×C31C2×#12311yescharacteristic
303C22×C31C2×#12411yescharacteristic
304C22×C31C2×#12611yescharacteristic
305C22×C31#52911yescharacteristic
306C22×C31#52911yescharacteristic
307C22×C31#53311yescharacteristic
308C22×C31#53311yescharacteristic
309C22×C31#54111yescharacteristic
310C22×C31#54111yescharacteristic
311C22×C31#54211yescharacteristic
312C22×C31#54211yescharacteristic
313C22×C31#54611yescharacteristic
314C22×C31#54611yescharacteristic
315C22×C31#54711yescharacteristic
316C22×C31#54711yescharacteristic
317C22×C31#54811yescharacteristic
318C22×C31#54811yescharacteristic
319C22×C31D4×Q811yescharacteristic
320C22×C31D4×Q811yescharacteristic
321C22×C31#55211yescharacteristic
322C22×C31#55211yescharacteristic
323C22×C31#55411yescharacteristic
324C22×C31#55611yescharacteristic
325C22×C31#55611yescharacteristic
326C22×C31#55611yescharacteristic
327C22×C31#55711yescharacteristic
328C22×C31#55911yescharacteristic
329C4×C31—24no—
330C4×C31—42no—
331C4×C31—44no—
332C4×C31—44no—
333C4×C31—42no—
334C4×C31—42no—
335C4×C31—44no—
336C4×C31—42no—
337C4×C31—42no—
338C4×C31—44no—
339C4×C31#38818yes—
340C23×Q8C22×C3111yescharacteristic
341C22×C4⋊C4C22×C3112yes—
342C22×C4⋊C4C22×C3111yescharacteristic
343C22×C4⋊C4C22×C3111yescharacteristic
344C22×C4⋊C4C22×C3111yescharacteristic
345C22×C42C22×C3111yescharacteristic
346C22×C42C22×C3111yescharacteristic
347C22×C42C22×C3112yes—
348C22×C42C22×C3111yescharacteristic
349#391—24no—
350#391—24no—
351#391C4×C3118yescomplemented
352#389—24no—
353C4×C4⋊C4—24no—
354C2×#95C22×C3111yescharacteristic
355C2×#95C22×C3111yescharacteristic
356C2×#95C22×C3111yescharacteristic
357C2×#95C22×C3112yes—
358C2×#95C22×C3112yes—
359C2×#95C22×C3112yes—
360C2×#95C22×C3112yes—
361C2×#95C22×C3112yes—
362C2×#95C22×C3112yes—
363C2×#95C22×C3112yes—
364C2×#95C22×C3112yes—
365C2×#95C22×C3112yes—
366C2×#95C22×C3112yes—
367C2×#95C22×C3111yescharacteristic
368C2×C31C2×#38811yescharacteristic
369C2×C31#229511yescharacteristic
370C2×C31#232011yescharacteristic
371C2×C31#236011yescharacteristic
372C2×C31#236211yescharacteristic
373C2×C31#236511yescharacteristic
374C2×C31#236711yescharacteristic
375C2×C31#242711yescharacteristic
376C2×C31#242911yescharacteristic
377C2×C31#244611yescharacteristic
378C2×C31#244711yescharacteristic
379C2×C31#248911yescharacteristic
380C2×C31#249211yescharacteristic
381C2×C31#251111yescharacteristic
382C2×C31#251411yescharacteristic
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8C2×C4×C3114yes—
390C23×C4C23×C3112yes—
391C23×C4C23×C3112yes—
392C23×C4C23×C3111yescharacteristic
393C23×C4C23×C3112yes—
394C23×C4C23×C3112yes—
395C23×C4C23×C3111yescharacteristic
396C23×C4C23×C3111yescharacteristic
397C23×C4C23×C3111yescharacteristic
398C23×C4C23×C3111yescharacteristic
399C23×C4C23×C3111yescharacteristic
400C23×C4C23×C3111yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4C2×C4×C3114yes—
411C2×C4⋊C4D4×C3114yes—
412C2×C4⋊C4D4×C3114yes—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—42no—
424C2×C42C2×C4×C3114yes—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—22no—
432#95—24no—
433#95—22no—
434#95—22no—
435#95—42no—
436#95C2×C4×C3118yes—
437#95C2×C4×C3118yes—
438#95Q8×C3114yescomplemented
439C31#1414211yescharacteristic, direct product factor, Sylow
440C24C24×C3111yescharacteristic
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4C22×C4×C3112yes—
507C22×C4C22×C4×C3114yes—
508C22×C4C22×C4×C3114yes—
509C22×C4C22×C4×C3112yes—
510C22×C4C22×C4×C3112yes—
511C22×C4C2×D4×C3114yes—
512C22×C4C2×D4×C3114yes—
513C22×C4C2×D4×C3112yes—
514C22×C4C2×D4×C3112yes—
515C22×C4C2×Q8×C3112yes—
516C22×C4C2×Q8×C3112yes—
517C22×C4C2×Q8×C3112yes—
518C22×C4#41×C3112yes—
519C22×C4#41×C3112yes—
520C22×C4#41×C3112yes—
521C22×C4#41×C3112yes—
522C22×C4#41×C3112yes—
523C22×C4#41×C3112yes—
524C22×C4#41×C3112yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—48no—
529C42—28no—
530C42—48no—
531C42—44no—
532C42—44no—
533C23C23×C4×C3111yescharacteristic
534C23C22×D4×C3111yescharacteristic
535C23C22×D4×C3111yescharacteristic
536C23C22×Q8×C3111yescharacteristic
537C23C2×#41×C3111yescharacteristic
538C23C2×#41×C3111yescharacteristic
539C23C2×#41×C3111yescharacteristic
540C23C2×#41×C3111yescharacteristic
541C23C2×#41×C3111yescharacteristic
542C23C2×#41×C3111yescharacteristic
543C23C2×#41×C3111yescharacteristic
544C23C31×H(5,𝔽2)11yescharacteristic
545C23C31×2−1+411yescharacteristic
546C23C31×2−1+411yescharacteristic
547C23C31×2−1+411yescharacteristic
548Q8—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C31×#11714yes—
619C2×C4C4×D4×C3114yes—
620C2×C4C4×D4×C3114yes—
621C2×C4C4×Q8×C3114yes—
622C2×C4C31×#12114yes—
623C2×C4C31×#12314yes—
624C2×C4C31×#12414yes—
625C2×C4C31×#12614yes—
626C22C2×C31×#11711yescharacteristic
627C22C2×C4×D4×C3111yescharacteristic
628C22C2×C4×D4×C3111yescharacteristic
629C22C2×C4×Q8×C3111yescharacteristic
630C22C4×#41×C3111yescharacteristic
631C22C31×#51911yescharacteristic
632C22C31×#52011yescharacteristic
633C22C2×C31×#12111yescharacteristic
634C22C2×C31×#12311yescharacteristic
635C22C2×C31×#12411yescharacteristic
636C22C2×C31×#12611yescharacteristic
637C22C31×#52911yescharacteristic
638C22C31×#52911yescharacteristic
639C22C31×#53311yescharacteristic
640C22C31×#53311yescharacteristic
641C22C31×#54111yescharacteristic
642C22C31×#54111yescharacteristic
643C22C31×#54211yescharacteristic
644C22C31×#54211yescharacteristic
645C22C31×#54611yescharacteristic
646C22C31×#54611yescharacteristic
647C22C31×#54711yescharacteristic
648C22C31×#54711yescharacteristic
649C22C31×#54811yescharacteristic
650C22C31×#54811yescharacteristic
651C22D4×Q8×C3111yescharacteristic
652C22D4×Q8×C3111yescharacteristic
653C22C31×#55211yescharacteristic
654C22C31×#55211yescharacteristic
655C22C31×#55411yescharacteristic
656C22C31×#55611yescharacteristic
657C22C31×#55611yescharacteristic
658C22C31×#55611yescharacteristic
659C22C31×#55711yescharacteristic
660C22C31×#55911yescharacteristic
661C4—24no—
662C4—42no—
663C4—44no—
664C4—44no—
665C4—42no—
666C4—42no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—44no—
671C4C31×#38818yes—
672C2C2×C31×#38811yescharacteristic
673C2C31×#229511yescharacteristic
674C2C31×#232011yescharacteristic
675C2C31×#236011yescharacteristic
676C2C31×#236211yescharacteristic
677C2C31×#236511yescharacteristic
678C2C31×#236711yescharacteristic
679C2C31×#242711yescharacteristic
680C2C31×#242911yescharacteristic
681C2C31×#244611yescharacteristic
682C2C31×#244711yescharacteristic
683C2C31×#248911yescharacteristic
684C2C31×#249211yescharacteristic
685C2C31×#251111yescharacteristic
686C2C31×#251411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
23. C31×#391C4semidirect
95. C31×#95Q8semidirect
189. #14142C31direct (N × H)
351. #391C4×C31semidirect
438. #95Q8×C31semidirect
439. C31#14142direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3912
C2×C31×#3892
C2×C4×C4⋊C4×C312
C31×#14432
C31×#14422
C31×#14362
C31×C4⋊#952
C31×#14342
C4×C31×#952
#1414231