Finite Group Databasebeta

← C31×#14054 #21470813

Subgroups — C31×#14054 #21470813

Order 7936.

1566 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#125C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
4C31×#1445C212yesmaximal
5C31×#1441C212yesmaximal
6C31×#1436C212yesmaximal
7C31×C4⋊#95C211yesmaximal, characteristic
8C31×C4⋊#95C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic
10C31×C4⋊#95C211yesmaximal, characteristic
11C4×C31×#95C211yesmaximal, characteristic
12C2×C31×#125—24no—
13C2×C31×#125—24no—
14C2×C31×#125C418yescomplemented
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2212yes—
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C31×#389—24no—
27C4×C4⋊C4×C31—24no—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C31×#125—232no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—42no—
66C2×C4⋊C4×C31C2×C418yes—
67C2×C4⋊C4×C31C2×C418yes—
68C2×C4⋊C4×C31C2×C414yes—
69C2×C4⋊C4×C31C2×C414yes—
70C2×C4⋊C4×C31D414yes—
71C2×C4⋊C4×C31D414yes—
72C2×C4⋊C4×C31Q814yes—
73C2×C42×C31—22no—
74C2×C42×C31—22no—
75C2×C42×C31—22no—
76C2×C42×C31—22no—
77C2×C42×C31—24no—
78C2×C42×C31—22no—
79C2×C42×C31—24no—
80C2×C42×C31—22no—
81C2×C42×C31—22no—
82C2×C42×C31—42no—
83C2×C42×C31C2×C414yes—
84C2×C42×C31Q814yes—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—22no—
88C31×#95—24no—
89C31×#95—22no—
90C31×#95—22no—
91C31×#95—22no—
92C31×#95—24no—
93C31×#95—42no—
94C31×#95—42no—
95C31×#95—42no—
96C31×#95—42no—
97C24×C31C2411yescharacteristic
98C22×C4×C31—21no—
99C22×C4×C31—22no—
100C22×C4×C31—21no—
101C22×C4×C31—22no—
102C22×C4×C31—21no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
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—21no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
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—21no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31C22×C412yes—
156C22×C4×C31C22×C412yes—
157C22×C4×C31C22×C414yes—
158C22×C4×C31C22×C414yes—
159C22×C4×C31C22×C412yes—
160C22×C4×C31C2×D414yes—
161C22×C4×C31C2×D414yes—
162C22×C4×C31C2×D412yes—
163C22×C4×C31C2×D412yes—
164C22×C4×C31C2×Q812yes—
165C22×C4×C31C2×Q814yes—
166C22×C4×C31C2×Q812yes—
167C22×C4×C31C2×Q812yes—
168C22×C4×C31C2×Q812yes—
169C22×C4×C31#4112yes—
170C22×C4×C31#4112yes—
171C22×C4×C31#4112yes—
172C22×C4×C31#4112yes—
173C22×C4×C31#4112yes—
174C22×C4×C31#4112yes—
175C4⋊C4×C31—216no—
176C4⋊C4×C31—216no—
177C4⋊C4×C31—28no—
178C4⋊C4×C31—28no—
179C4⋊C4×C31—48no—
180C4⋊C4×C31—44no—
181C4⋊C4×C31C22⋊C4116yes—
182C42×C31—28no—
183C42×C31—28no—
184C42×C31—48no—
185C42×C31—44no—
186#14054C3111yesmaximal, characteristic, direct product factor, Sylow
187C23×C31C23×C411yescharacteristic
188C23×C31C22×D411yescharacteristic
189C23×C31C22×D411yescharacteristic
190C23×C31C22×Q811yescharacteristic
191C23×C31C22×Q811yescharacteristic
192C23×C31C2×#4111yescharacteristic
193C23×C31C2×#4111yescharacteristic
194C23×C31C2×#4111yescharacteristic
195C23×C31C2×#4111yescharacteristic
196C23×C31C2×#4111yescharacteristic
197C23×C31C2×#4111yescharacteristic
198C23×C31H(5,𝔽2)11yescharacteristic
199C23×C31H(5,𝔽2)11yescharacteristic
200C23×C312−1+411yescharacteristic
201C23×C312−1+411yescharacteristic
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—24no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—24no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—24no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—24no—
223C2×C4×C31—22no—
224C2×C4×C31—24no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—22no—
233C2×C4×C31—24no—
234C2×C4×C31—24no—
235C2×C4×C31—41no—
236C2×C4×C31—41no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—42no—
242C2×C4×C31—41no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—42no—
250C2×C4×C31—41no—
251C2×C4×C31—42no—
252C2×C4×C31—41no—
253C2×C4×C31—42no—
254C2×C4×C31—41no—
255C2×C4×C31—42no—
256C2×C4×C31—41no—
257C2×C4×C31—42no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31C2×C22⋊C418yes—
271C2×C4×C31C2×C22⋊C414yes—
272C2×C4×C31C4×Q814yes—
273C2×C4×C31C4×Q814yes—
274C2×C4×C31C22⋊Q814yes—
275C2×C4×C31C22⋊Q814yes—
276C2×C4×C31#12414yes—
277C2×C4×C31#12514yescomplemented
278C2×C4×C31C4⋊Q814yes—
279C22×#125C2×C3111yescharacteristic
280C2×#389C2×C3111yescharacteristic
281C2×C4×C4⋊C4C2×C3111yescharacteristic
282#1445C2×C3112yes—
283#1441C2×C3112yes—
284#1436C2×C3112yes—
285C4⋊#95C2×C3111yescharacteristic
286C4⋊#95C2×C3111yescharacteristic
287C4⋊#95C2×C3112yes—
288C4⋊#95C2×C3111yescharacteristic
289C4×#95C2×C3111yescharacteristic
290C22×C31C22×C22⋊C411yescharacteristic
291C22×C31C2×C4×Q811yescharacteristic
292C22×C31C2×C4×Q811yescharacteristic
293C22×C31C4×#4111yescharacteristic
294C22×C31C4×#4111yescharacteristic
295C22×C31#52011yescharacteristic
296C22×C31#52011yescharacteristic
297C22×C31C2×C22⋊Q811yescharacteristic
298C22×C31C2×C22⋊Q811yescharacteristic
299C22×C31C2×#12411yescharacteristic
300C22×C31C2×#12511yescharacteristic
301C22×C31#52911yescharacteristic
302C22×C31#52911yescharacteristic
303C22×C31C2×C4⋊Q811yescharacteristic
304C22×C31#53311yescharacteristic
305C22×C31#54011yescharacteristic
306C22×C31#54111yescharacteristic
307C22×C31#54411yescharacteristic
308C22×C31#54411yescharacteristic
309C22×C31#54611yescharacteristic
310C22×C31#54611yescharacteristic
311C22×C31#54711yescharacteristic
312C22×C31#54711yescharacteristic
313C22×C31#54811yescharacteristic
314C22×C31#54811yescharacteristic
315C22×C31#55011yescharacteristic
316C22×C31#55011yescharacteristic
317C22×C31#55211yescharacteristic
318C22×C31#55211yescharacteristic
319C22×C31#55311yescharacteristic
320C22×C31#55311yescharacteristic
321C22×C31#55411yescharacteristic
322C22×C31#55411yescharacteristic
323C22×C31#55711yescharacteristic
324C22×C31#55711yescharacteristic
325C4×C31—28no—
326C4×C31—24no—
327C4×C31—42no—
328C4×C31—42no—
329C4×C31—44no—
330C4×C31—42no—
331C4×C31—44no—
332C4×C31—42no—
333C4×C31—42no—
334C4×C31—82no—
335C4×C31#39118yes—
336C2×#125—24no—
337C2×#125—24no—
338C2×#125C4×C3118yescomplemented
339C22×C4⋊C4C22×C3111yescharacteristic
340C22×C4⋊C4C22×C3112yes—
341C22×C4⋊C4C22×C3111yescharacteristic
342C22×C4⋊C4C22×C3112yes—
343C22×C4⋊C4C22×C3112yes—
344C22×C4⋊C4C22×C3111yescharacteristic
345C22×C4⋊C4C22×C3111yescharacteristic
346C22×C42C22×C3111yescharacteristic
347C22×C42C22×C3112yes—
348C22×C42C22×C3111yescharacteristic
349C22×C42C22×C3111yescharacteristic
350#389—24no—
351C4×C4⋊C4—24no—
352C2×#95C22×C3111yescharacteristic
353C2×#95C22×C3111yescharacteristic
354C2×#95C22×C3111yescharacteristic
355C2×#95C22×C3111yescharacteristic
356C2×#95C22×C3112yes—
357C2×#95C22×C3112yes—
358C2×#95C22×C3112yes—
359C2×#95C22×C3112yes—
360C2×#95C22×C3112yes—
361C2×#95C22×C3112yes—
362C2×#95C22×C3112yes—
363C2×#95C22×C3112yes—
364C2×C31C2×#39111yescharacteristic
365C2×C31C4×#12511yescharacteristic
366C2×C31#233011yescharacteristic
367C2×C31#233911yescharacteristic
368C2×C31#234111yescharacteristic
369C2×C31#237011yescharacteristic
370C2×C31#237011yescharacteristic
371C2×C31#244111yescharacteristic
372C2×C31#244211yescharacteristic
373C2×C31#245311yescharacteristic
374C2×C31#245411yescharacteristic
375C2×C31#248911yescharacteristic
376C2×C31#249011yescharacteristic
377C2×C31#255011yescharacteristic
378C2×C31#255211yescharacteristic
379C23×C4C23×C3112yes—
380C23×C4C23×C3112yes—
381C23×C4C23×C3111yescharacteristic
382C23×C4C23×C3111yescharacteristic
383C23×C4C23×C3112yes—
384C23×C4C23×C3111yescharacteristic
385C23×C4C23×C3111yescharacteristic
386C23×C4C23×C3111yescharacteristic
387C23×C4C23×C3112yes—
388C23×C4C23×C3111yescharacteristic
389C23×C4C23×C3111yescharacteristic
390#125—232no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4C2×C4×C3118yes—
406C2×C4⋊C4C2×C4×C3118yes—
407C2×C4⋊C4C2×C4×C3114yes—
408C2×C4⋊C4C2×C4×C3114yes—
409C2×C4⋊C4D4×C3114yes—
410C2×C4⋊C4D4×C3114yes—
411C2×C4⋊C4Q8×C3114yes—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—42no—
422C2×C42C2×C4×C3114yes—
423C2×C42Q8×C3114yes—
424#95—24no—
425#95—24no—
426#95—22no—
427#95—24no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—24no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436C31#1405411yescharacteristic, direct product factor, Sylow
437C24C24×C3111yescharacteristic
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4C22×C4×C3112yes—
496C22×C4C22×C4×C3112yes—
497C22×C4C22×C4×C3114yes—
498C22×C4C22×C4×C3114yes—
499C22×C4C22×C4×C3112yes—
500C22×C4C2×D4×C3114yes—
501C22×C4C2×D4×C3114yes—
502C22×C4C2×D4×C3112yes—
503C22×C4C2×D4×C3112yes—
504C22×C4C2×Q8×C3112yes—
505C22×C4C2×Q8×C3114yes—
506C22×C4C2×Q8×C3112yes—
507C22×C4C2×Q8×C3112yes—
508C22×C4C2×Q8×C3112yes—
509C22×C4#41×C3112yes—
510C22×C4#41×C3112yes—
511C22×C4#41×C3112yes—
512C22×C4#41×C3112yes—
513C22×C4#41×C3112yes—
514C22×C4#41×C3112yes—
515C4⋊C4—216no—
516C4⋊C4—216no—
517C4⋊C4—28no—
518C4⋊C4—28no—
519C4⋊C4—48no—
520C4⋊C4—44no—
521C4⋊C4C22⋊C4×C31116yes—
522C42—28no—
523C42—28no—
524C42—48no—
525C42—44no—
526C23C23×C4×C3111yescharacteristic
527C23C22×D4×C3111yescharacteristic
528C23C22×D4×C3111yescharacteristic
529C23C22×Q8×C3111yescharacteristic
530C23C22×Q8×C3111yescharacteristic
531C23C2×#41×C3111yescharacteristic
532C23C2×#41×C3111yescharacteristic
533C23C2×#41×C3111yescharacteristic
534C23C2×#41×C3111yescharacteristic
535C23C2×#41×C3111yescharacteristic
536C23C2×#41×C3111yescharacteristic
537C23C31×H(5,𝔽2)11yescharacteristic
538C23C31×H(5,𝔽2)11yescharacteristic
539C23C31×2−1+411yescharacteristic
540C23C31×2−1+411yescharacteristic
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C3118yes—
610C2×C4C2×C22⋊C4×C3114yes—
611C2×C4C4×Q8×C3114yes—
612C2×C4C4×Q8×C3114yes—
613C2×C4C31×C22⋊Q814yes—
614C2×C4C31×C22⋊Q814yes—
615C2×C4C31×#12414yes—
616C2×C4C31×#12514yescomplemented
617C2×C4C31×C4⋊Q814yes—
618C22C22×C22⋊C4×C3111yescharacteristic
619C22C2×C4×Q8×C3111yescharacteristic
620C22C2×C4×Q8×C3111yescharacteristic
621C22C4×#41×C3111yescharacteristic
622C22C4×#41×C3111yescharacteristic
623C22C31×#52011yescharacteristic
624C22C31×#52011yescharacteristic
625C22C2×C31×C22⋊Q811yescharacteristic
626C22C2×C31×C22⋊Q811yescharacteristic
627C22C2×C31×#12411yescharacteristic
628C22C2×C31×#12511yescharacteristic
629C22C31×#52911yescharacteristic
630C22C31×#52911yescharacteristic
631C22C2×C31×C4⋊Q811yescharacteristic
632C22C31×#53311yescharacteristic
633C22C31×#54011yescharacteristic
634C22C31×#54111yescharacteristic
635C22C31×#54411yescharacteristic
636C22C31×#54411yescharacteristic
637C22C31×#54611yescharacteristic
638C22C31×#54611yescharacteristic
639C22C31×#54711yescharacteristic
640C22C31×#54711yescharacteristic
641C22C31×#54811yescharacteristic
642C22C31×#54811yescharacteristic
643C22C31×#55011yescharacteristic
644C22C31×#55011yescharacteristic
645C22C31×#55211yescharacteristic
646C22C31×#55211yescharacteristic
647C22C31×#55311yescharacteristic
648C22C31×#55311yescharacteristic
649C22C31×#55411yescharacteristic
650C22C31×#55411yescharacteristic
651C22C31×#55711yescharacteristic
652C22C31×#55711yescharacteristic
653C4—28no—
654C4—24no—
655C4—42no—
656C4—42no—
657C4—44no—
658C4—42no—
659C4—44no—
660C4—42no—
661C4—42no—
662C4—82no—
663C4C31×#39118yes—
664C2C2×C31×#39111yescharacteristic
665C2C4×C31×#12511yescharacteristic
666C2C31×#233011yescharacteristic
667C2C31×#233911yescharacteristic
668C2C31×#234111yescharacteristic
669C2C31×#237011yescharacteristic
670C2C31×#237011yescharacteristic
671C2C31×#244111yescharacteristic
672C2C31×#244211yescharacteristic
673C2C31×#245311yescharacteristic
674C2C31×#245411yescharacteristic
675C2C31×#248911yescharacteristic
676C2C31×#249011yescharacteristic
677C2C31×#255011yescharacteristic
678C2C31×#255211yescharacteristic
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
14. C2×C31×#125C4semidirect
186. #14054C31direct (N × H)
277. C2×C4×C31#125semidirect
338. C2×#125C4×C31semidirect
436. C31#14054direct (N × H)
616. C2×C4C31×#125semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1252
C2×C31×#3892
C2×C4×C4⋊C4×C312
C31×#14452
C31×#14412
C31×#14362
C31×C4⋊#952
C4×C31×#952
#1405431