Finite Group Databasebeta

← C31×#13814 #21470573

Subgroups — C31×#13814 #21470573

Order 7936.

2298 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#385C212yesmaximal
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C31C212yesmaximal
4C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
5C22×C31×#95C211yesmaximal, characteristic
6C31×#1436C212yesmaximal, complemented
7C31×#1436C212yesmaximal, complemented
8C31×C4⋊#95C211yesmaximal, characteristic, complemented
9C31×#1434C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C211yesmaximal, characteristic
11C4×C31×#95C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C24×C4×C31C2212yes—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C42×C31C2212yes—
20C22×C42×C31C2212yes—
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C31×#385C4116yescomplemented
24C4×C4⋊C4×C31—24no—
25C4×C22⋊C4×C31—28no—
26C4×C22⋊C4×C31C418yescomplemented
27C2×C31×#95—24no—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C25×C31C2311yescharacteristic
41C23×C4×C31—24no—
42C23×C4×C31—24no—
43C23×C4×C31—24no—
44C23×C4×C31—22no—
45C23×C4×C31—24no—
46C23×C4×C31—22no—
47C23×C4×C31—24no—
48C23×C4×C31—42no—
49C23×C4×C31—42no—
50C23×C4×C31—42no—
51C23×C4×C31C2×C414yes—
52C23×C4×C31C2×C418yes—
53C23×C4×C31C2312yes—
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—42no—
66C2×C4⋊C4×C31—42no—
67C2×C4⋊C4×C31C2×C418yescomplemented
68C2×C4⋊C4×C31C2×C418yescomplemented
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31C2×C418yes—
72C2×C22⋊C4×C31C2×C414yes—
73C2×C22⋊C4×C31C2×C418yes—
74C2×C22⋊C4×C31C2×C414yes—
75C2×C22⋊C4×C31D414yes—
76C2×C22⋊C4×C31Q814yes—
77C2×C42×C31—22no—
78C2×C42×C31—22no—
79C2×C42×C31—24no—
80C2×C42×C31—24no—
81C2×C42×C31—24no—
82C2×C42×C31—24no—
83C2×C42×C31—42no—
84C2×C42×C31—42no—
85C2×C42×C31—42no—
86C2×C42×C31C2×C414yescomplemented
87C2×C42×C31C2×C414yescomplemented
88C31×#95—22no—
89C31×#95—24no—
90C31×#95—24no—
91C31×#95—24no—
92C31×#95—22no—
93C31×#95—22no—
94C31×#95—42no—
95C31×#95C2×C414yescomplemented
96C31×#95C2×C414yescomplemented
97C31×#95C2×C418yescomplemented
98C31×#95C2×C418yescomplemented
99C31×#95D414yes—
100C24×C31—21no—
101C24×C31—22no—
102C24×C31—21no—
103C24×C31—21no—
104C24×C31—22no—
105C24×C31—21no—
106C24×C31C22×C412yes—
107C24×C31C22×C414yes—
108C24×C31C2×D412yes—
109C24×C31C2×Q812yes—
110C24×C31#4114yes—
111C24×C31C2411yescharacteristic
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—21no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—28no—
131C22×C4×C31—216no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—22no—
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—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—28no—
155C22×C4×C31—216no—
156C22×C4×C31—44no—
157C22×C4×C31—48no—
158C22×C4×C31—48no—
159C22×C4×C31—48no—
160C22×C4×C31—48no—
161C22×C4×C31—48no—
162C22×C4×C31—48no—
163C22×C4×C31—48no—
164C22×C4×C31C22×C414yes—
165C22×C4×C31C22×C412yes—
166C22×C4×C31C22×C414yes—
167C22×C4×C31C22×C414yes—
168C22×C4×C31C22×C412yes—
169C22×C4×C31C22×C412yes—
170C22×C4×C31C22×C414yes—
171C22×C4×C31C22×C414yes—
172C22×C4×C31C22×C412yes—
173C22×C4×C31C22×C412yes—
174C22×C4×C31C22×C414yes—
175C22×C4×C31C22×C412yes—
176C22×C4×C31C2×D412yes—
177C22×C4×C31C2×D412yes—
178C22×C4×C31C2×D412yes—
179C22×C4×C31C2×D414yes—
180C22×C4×C31C2×Q812yes—
181C22×C4×C31C2×Q812yes—
182C22×C4×C31#4112yes—
183C22×C4×C31#4114yes—
184C4⋊C4×C31—216no—
185C4⋊C4×C31—48no—
186C22⋊C4×C31—216no—
187C22⋊C4×C31C42116yescomplemented
188C22⋊C4×C31C4⋊C4116yescomplemented
189C42×C31—28no—
190C42×C31—44no—
191C42×C31—48no—
192C42×C31—48no—
193#13814C3111yesmaximal, characteristic, direct product factor, Sylow
194C23×C31—22no—
195C23×C31—24no—
196C23×C31—22no—
197C23×C31—24no—
198C23×C31—22no—
199C23×C31—24no—
200C23×C31—22no—
201C23×C31—24no—
202C23×C31—22no—
203C23×C31—24no—
204C23×C31—24no—
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—22no—
211C23×C31—24no—
212C23×C31C2×C4214yes—
213C23×C31C2×C4⋊C414yes—
214C23×C31#11714yes—
215C23×C31C4×D418yes—
216C23×C31C4×Q818yes—
217C23×C31C23×C411yescharacteristic
218C23×C31C23×C412yes—
219C23×C31C22×D411yescharacteristic
220C23×C31C22×D411yescharacteristic
221C23×C31C22×Q811yescharacteristic
222C23×C31C2×#4112yes—
223C23×C31C2×#4112yes—
224C23×C31C2×#4111yescharacteristic
225C23×C31H(5,𝔽2)11yescharacteristic
226C23×C31H(5,𝔽2)12yes—
227C23×C312−1+411yescharacteristic
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—24no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—24no—
240C2×C4×C31—24no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—24no—
244C2×C4×C31—22no—
245C2×C4×C31—24no—
246C2×C4×C31—24no—
247C2×C4×C31—24no—
248C2×C4×C31—24no—
249C2×C4×C31—24no—
250C2×C4×C31—22no—
251C2×C4×C31—22no—
252C2×C4×C31—24no—
253C2×C4×C31—24no—
254C2×C4×C31—22no—
255C2×C4×C31—24no—
256C2×C4×C31—22no—
257C2×C4×C31—24no—
258C2×C4×C31—24no—
259C2×C4×C31—24no—
260C2×C4×C31—22no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—24no—
264C2×C4×C31—24no—
265C2×C4×C31—24no—
266C2×C4×C31—22no—
267C2×C4×C31—24no—
268C2×C4×C31—416no—
269C2×C4×C31—432no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—42no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—42no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31C2×C4214yes—
285C2×C4×C31C2×C4214yes—
286C2×C4×C31C2×C4⋊C414yes—
287C2×C4×C31C2×C4⋊C414yes—
288C2×C4×C31C4×D414yes—
289C2×C4×C31C4×D418yes—
290C2×#385C2×C3112yes—
291C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
292C2×C4×C22⋊C4C2×C3112yes—
293C2×C4×C22⋊C4C2×C3111yescharacteristic
294C22×#95C2×C3111yescharacteristic
295#1436C2×C3112yescomplemented
296#1436C2×C3112yescomplemented
297C4⋊#95C2×C3111yescharacteristic, complemented
298#1434C2×C3111yescharacteristic, complemented
299C22⋊#95C2×C3111yescharacteristic
300C4×#95C2×C3111yescharacteristic, complemented
301C22×C31—24no—
302C22×C31—24no—
303C22×C31—24no—
304C22×C31—24no—
305C22×C31—28no—
306C22×C31—28no—
307C22×C31—28no—
308C22×C31—28no—
309C22×C31—24no—
310C22×C31—24no—
311C22×C31C4×C4⋊C418yescomplemented
312C22×C31C22×C4211yescharacteristic
313C22×C31C22×C4⋊C411yescharacteristic
314C22×C31C2×#11711yescharacteristic
315C22×C31C2×C4×D411yescharacteristic
316C22×C31C2×C4×D412yes—
317C22×C31C2×C4×D412yes—
318C22×C31C2×C4×Q812yes—
319C22×C31C4×#4111yescharacteristic
320C22×C31C4×#4112yes—
321C22×C31#51811yescharacteristic
322C22×C31#51812yes—
323C22×C31#52011yescharacteristic
324C22×C31#52012yes—
325C22×C31D4211yescharacteristic
326C22×C31#54612yes—
327C22×C31#54612yes—
328C22×C31#54711yescharacteristic
329C22×C31D4×Q811yescharacteristic
330C22×C31#55112yes—
331C22×C31#55112yes—
332C22×C31#55212yes—
333C22×C31#55411yescharacteristic
334C22×C31#55412yes—
335C4×C31—24no—
336C4×C31—24no—
337C4×C31—24no—
338C4×C31—28no—
339C4×C31—24no—
340C4×C31—24no—
341C4×C31—42no—
342C4×C31—44no—
343C4×C31—44no—
344C4×C31—44no—
345C24×C4C22×C3111yescharacteristic
346C24×C4C22×C3112yes—
347C22×C4⋊C4C22×C3112yes—
348C22×C4⋊C4C22×C3112yes—
349C22×C22⋊C4C22×C3112yes—
350C22×C22⋊C4C22×C3111yescharacteristic
351C22×C22⋊C4C22×C3111yescharacteristic
352C22×C42C22×C3112yes—
353C22×C42C22×C3112yes—
354C22×C42C22×C3111yescharacteristic
355C22×C42C22×C3111yescharacteristic
356#385C4×C31116yescomplemented
357C4×C4⋊C4—24no—
358C4×C22⋊C4—28no—
359C4×C22⋊C4C4×C3118yescomplemented
360C2×#95—24no—
361C2×#95C22×C3111yescharacteristic
362C2×#95C22×C3111yescharacteristic
363C2×#95C22×C3111yescharacteristic
364C2×#95C22×C3112yes—
365C2×#95C22×C3112yes—
366C2×#95C22×C3112yes—
367C2×#95C22×C3112yes—
368C2×#95C22×C3112yes—
369C2×#95C22×C3112yes—
370C2×#95C22×C3111yescharacteristic
371C2×#95C22×C3111yescharacteristic
372C2×#95C22×C3111yescharacteristic
373C2×C31—28no—
374C2×C31C2×C4×C4⋊C411yescharacteristic
375C2×C31C42×D411yescharacteristic
376C2×C31#227511yescharacteristic
377C2×C31#234211yescharacteristic
378C2×C31#234311yescharacteristic
379C2×C31D4×C4⋊C411yescharacteristic
380C2×C31#234911yescharacteristic
381C2×C31#235812yes—
382C2×C31#235912yes—
383C2×C31#236012yes—
384C2×C31#236812yes—
385C25C23×C3111yescharacteristic
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4C2×C4×C3114yes—
397C23×C4C2×C4×C3118yes—
398C23×C4C23×C3112yes—
399C23×C4C23×C3112yes—
400C23×C4C23×C3112yes—
401C23×C4C23×C3111yescharacteristic
402C23×C4C23×C3111yescharacteristic
403C23×C4C23×C3111yescharacteristic
404C23×C4C23×C3111yescharacteristic
405C23×C4C23×C3111yescharacteristic
406C23×C4C23×C3112yes—
407C23×C4C23×C3111yescharacteristic
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4C2×C4×C3118yescomplemented
413C2×C4⋊C4C2×C4×C3118yescomplemented
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4C2×C4×C3118yes—
417C2×C22⋊C4C2×C4×C3114yes—
418C2×C22⋊C4C2×C4×C3118yes—
419C2×C22⋊C4C2×C4×C3114yes—
420C2×C22⋊C4D4×C3114yes—
421C2×C22⋊C4Q8×C3114yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42C2×C4×C3114yescomplemented
432C2×C42C2×C4×C3114yescomplemented
433#95—22no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—22no—
438#95—22no—
439#95—42no—
440#95C2×C4×C3114yescomplemented
441#95C2×C4×C3114yescomplemented
442#95C2×C4×C3118yescomplemented
443#95C2×C4×C3118yescomplemented
444#95D4×C3114yes—
445C31#1381411yescharacteristic, direct product factor, Sylow
446C24—21no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—21no—
452C24C22×C4×C3112yes—
453C24C22×C4×C3114yes—
454C24C2×D4×C3112yes—
455C24C2×Q8×C3112yes—
456C24#41×C3114yes—
457C24C24×C3111yescharacteristic
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—28no—
477C22×C4—216no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
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—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—216no—
502C22×C4—44no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4C22×C4×C3114yes—
511C22×C4C22×C4×C3112yes—
512C22×C4C22×C4×C3114yes—
513C22×C4C22×C4×C3114yes—
514C22×C4C22×C4×C3112yes—
515C22×C4C22×C4×C3112yes—
516C22×C4C22×C4×C3114yes—
517C22×C4C22×C4×C3114yes—
518C22×C4C22×C4×C3112yes—
519C22×C4C22×C4×C3112yes—
520C22×C4C22×C4×C3114yes—
521C22×C4C22×C4×C3112yes—
522C22×C4C2×D4×C3112yes—
523C22×C4C2×D4×C3112yes—
524C22×C4C2×D4×C3112yes—
525C22×C4C2×D4×C3114yes—
526C22×C4C2×Q8×C3112yes—
527C22×C4C2×Q8×C3112yes—
528C22×C4#41×C3112yes—
529C22×C4#41×C3114yes—
530C4⋊C4—216no—
531C4⋊C4—48no—
532C22⋊C4—216no—
533C22⋊C4C42×C31116yescomplemented
534C22⋊C4C4⋊C4×C31116yescomplemented
535C42—28no—
536C42—44no—
537C42—48no—
538C42—48no—
539C23—22no—
540C23—24no—
541C23—22no—
542C23—24no—
543C23—22no—
544C23—24no—
545C23—22no—
546C23—24no—
547C23—22no—
548C23—24no—
549C23—24no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—22no—
556C23—24no—
557C23C2×C42×C3114yes—
558C23C2×C4⋊C4×C3114yes—
559C23C31×#11714yes—
560C23C4×D4×C3118yes—
561C23C4×Q8×C3118yes—
562C23C23×C4×C3111yescharacteristic
563C23C23×C4×C3112yes—
564C23C22×D4×C3111yescharacteristic
565C23C22×D4×C3111yescharacteristic
566C23C22×Q8×C3111yescharacteristic
567C23C2×#41×C3112yes—
568C23C2×#41×C3112yes—
569C23C2×#41×C3111yescharacteristic
570C23C31×H(5,𝔽2)11yescharacteristic
571C23C31×H(5,𝔽2)12yes—
572C23C31×2−1+411yescharacteristic
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—416no—
614C2×C4—432no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4C2×C42×C3114yes—
630C2×C4C2×C42×C3114yes—
631C2×C4C2×C4⋊C4×C3114yes—
632C2×C4C2×C4⋊C4×C3114yes—
633C2×C4C4×D4×C3114yes—
634C2×C4C4×D4×C3118yes—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—28no—
640C22—28no—
641C22—28no—
642C22—28no—
643C22—24no—
644C22—24no—
645C22C4×C4⋊C4×C3118yescomplemented
646C22C22×C42×C3111yescharacteristic
647C22C22×C4⋊C4×C3111yescharacteristic
648C22C2×C31×#11711yescharacteristic
649C22C2×C4×D4×C3111yescharacteristic
650C22C2×C4×D4×C3112yes—
651C22C2×C4×D4×C3112yes—
652C22C2×C4×Q8×C3112yes—
653C22C4×#41×C3111yescharacteristic
654C22C4×#41×C3112yes—
655C22C31×#51811yescharacteristic
656C22C31×#51812yes—
657C22C31×#52011yescharacteristic
658C22C31×#52012yes—
659C22D42×C3111yescharacteristic
660C22C31×#54612yes—
661C22C31×#54612yes—
662C22C31×#54711yescharacteristic
663C22D4×Q8×C3111yescharacteristic
664C22C31×#55112yes—
665C22C31×#55112yes—
666C22C31×#55212yes—
667C22C31×#55411yescharacteristic
668C22C31×#55412yes—
669C4—24no—
670C4—24no—
671C4—24no—
672C4—28no—
673C4—24no—
674C4—24no—
675C4—42no—
676C4—44no—
677C4—44no—
678C4—44no—
679C2—28no—
680C2C2×C4×C4⋊C4×C3111yescharacteristic
681C2C42×D4×C3111yescharacteristic
682C2C31×#227511yescharacteristic
683C2C31×#234211yescharacteristic
684C2C31×#234311yescharacteristic
685C2D4×C4⋊C4×C3111yescharacteristic
686C2C31×#234911yescharacteristic
687C2C31×#235812yes—
688C2C31×#235912yes—
689C2C31×#236012yes—
690C2C31×#236812yes—
subgroupG/H
center, socleC24×C31C24
commutatorC22C22×C42×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊C4×C31C2semidirect
6. C31×#1436C2semidirect
7. C31×#1436C2semidirect
8. C31×C4⋊#95C2semidirect
9. C31×#1434C2semidirect
11. C4×C31×#95C2semidirect
23. C31×#385C4semidirect
26. C4×C22⋊C4×C31C4semidirect
67. C2×C4⋊C4×C31C2×C4semidirect
68. C2×C4⋊C4×C31C2×C4semidirect
86. C2×C42×C31C2×C4semidirect
87. C2×C42×C31C2×C4semidirect
95. C31×#95C2×C4semidirect
96. C31×#95C2×C4semidirect
97. C31×#95C2×C4semidirect
98. C31×#95C2×C4semidirect
187. C22⋊C4×C31C42semidirect
188. C22⋊C4×C31C4⋊C4semidirect
193. #13814C31direct (N × H)
291. C2×C4×C4⋊C4C2×C31semidirect
295. #1436C2×C31semidirect
296. #1436C2×C31semidirect
297. C4⋊#95C2×C31semidirect
298. #1434C2×C31semidirect
300. C4×#95C2×C31semidirect
311. C22×C31C4×C4⋊C4semidirect
356. #385C4×C31semidirect
359. C4×C22⋊C4C4×C31semidirect
412. C2×C4⋊C4C2×C4×C31semidirect
413. C2×C4⋊C4C2×C4×C31semidirect
431. C2×C42C2×C4×C31semidirect
432. C2×C42C2×C4×C31semidirect
440. #95C2×C4×C31semidirect
441. #95C2×C4×C31semidirect
442. #95C2×C4×C31semidirect
443. #95C2×C4×C31semidirect
445. C31#13814direct (N × H)
533. C22⋊C4C42×C31semidirect
534. C22⋊C4C4⋊C4×C31semidirect
645. C22C4×C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3852
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C22×C31×#952
C31×#14362
C31×C4⋊#952
C31×#14342
C31×C22⋊#952
C4×C31×#952
#1381431