Finite Group Databasebeta

← C31×#25974 #21482733

Subgroups — C31×#25974 #21482733

Order 7936.

1144 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#476C211yesmaximal, characteristic, complemented
2C2×C31×#418C211yesmaximal, characteristic
3C31×#2439C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#2092C211yesmaximal, characteristic, complemented
6C31×#2067C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2023C211yesmaximal, characteristic, complemented
9C31×#1862C211yesmaximal, characteristic, complemented
10C31×#1862C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1851C211yesmaximal, characteristic, complemented
13C31×#1809C211yesmaximal, characteristic, complemented
14C31×#1804C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic
16C23×D4×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic, complemented
19C2×C4×D4×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C22⋊C4×C31—21no—
23C31×#476—24no—
24C2×C31×#107C2211yescharacteristic, complemented
25C2×C31×#107C2211yescharacteristic, complemented
26C2×C31×#106C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×C4⋊C8C2211yescharacteristic, complemented
29C2×C31×C4⋊C8C2211yescharacteristic, complemented
30C31×#418—24no—
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C31×#396—21no—
41C31×#393—21no—
42C31×#391—21no—
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic, complemented
46C31×#389C2211yescharacteristic, complemented
47C31×#387—21no—
48C31×#386—21no—
49C31×#386—21no—
50C31×#382C2211yescharacteristic, complemented
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×Q8×C31—21no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—21no—
66C22×D4×C31—22no—
67C22×D4×C31—41no—
68C22×D4×C31—41no—
69C22×D4×C31Q814yescomplemented
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C2×M16×C31—22no—
76C2×M16×C31—22no—
77C2×M16×C31—41no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×C4⋊Q8—22no—
83C31×C4⋊Q8—41no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—41no—
87C4×D4×C31—41no—
88C31×#117—22no—
89C31×#117—41no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—44no—
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C22⋊C4×C31D411yescharacteristic
111C2×C42×C31—21no—
112C2×C42×C31C2311yescharacteristic
113C2×C42×C31C2311yescharacteristic
114C31×#107—41no—
115C31×#107—41no—
116C31×#106—22no—
117C31×#106—22no—
118C31×C4⋊C8—22no—
119C31×C4⋊C8—41no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—41no—
126C31×#102—41no—
127C31×#102D414yes—
128C31×C22⋊C8—22no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95D411yescharacteristic
136C31×#95D411yescharacteristic
137C24×C31—21no—
138C24×C31—21no—
139C24×C31—24no—
140C24×C31—42no—
141C24×C31—42no—
142C24×C31—42no—
143C24×C31—42no—
144C24×C31—81no—
145C24×C31—81no—
146C24×C31C2×D411yescharacteristic
147C2×Q8×C31—42no—
148C2×Q8×C31—42no—
149C2×Q8×C31—81no—
150C2×D4×C31—28no—
151C2×D4×C31—24no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—44no—
161C2×D4×C31—44no—
162C2×D4×C31—44no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31C2×D412yes—
166C2×D4×C31C2×Q812yes—
167C2×D4×C31C2×Q812yes—
168C2×D4×C31#4112yes—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—42no—
180C22×C4×C31—42no—
181C22×C4×C31—42no—
182C22×C4×C31—42no—
183C22×C4×C31—81no—
184C22×C4×C31—81no—
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×Q812yes—
191C22×C4×C31#4112yes—
192C22×C4×C31C2411yescharacteristic
193M16×C31—44no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31C2×D412yes—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—81no—
220C4⋊C4×C31C2×D412yes—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—41no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—81no—
230C22⋊C4×C31—81no—
231C22⋊C4×C31—81no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—42no—
237#25974C3111yesmaximal, characteristic, direct product factor, Sylow
238C23×C31—22no—
239C23×C31—21no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—22no—
248C23×C31—48no—
249C23×C31—48no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—84no—
261C23×C31—84no—
262C23×C31—84no—
263C23×C31—84no—
264C23×C31—84no—
265C23×C31C22⋊Q812yes—
266C23×C31C22×D411yescharacteristic
267Q8×C31—84no—
268D4×C31—22no—
269D4×C31—22no—
270D4×C31—22no—
271D4×C31—22no—
272D4×C31—22no—
273D4×C31—48no—
274D4×C31—41no—
275D4×C31—41no—
276D4×C31C22⋊Q814yes—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—21no—
286C2×C4×C31—22no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—84no—
313C2×C4×C31—84no—
314C2×C4×C31C22⋊Q812yes—
315C2×C4×C31AGL(1,ℤ/8)12yes—
316C2×C4×C31C22×D411yescharacteristic
317C2×C4×C31C22×Q811yescharacteristic
318C2×C4×C31C2×#4111yescharacteristic
319C2×C4×C31C2×#4111yescharacteristic
320C2×C4×C31H(5,𝔽2)11yescharacteristic
321C2×C4×C31H(5,𝔽2)11yescharacteristic
322C8×C31—22no—
323C8×C31—41no—
324C8×C31—41no—
325C8×C31—41no—
326C2×#476C2×C3111yescharacteristic, complemented
327C2×#418C2×C3111yescharacteristic
328#2439C2×C3111yescharacteristic, complemented
329D4×C22⋊C4C2×C3111yescharacteristic
330#2092C2×C3111yescharacteristic, complemented
331#2067C2×C3111yescharacteristic, complemented
332#2065C2×C3111yescharacteristic, complemented
333#2023C2×C3111yescharacteristic, complemented
334#1862C2×C3111yescharacteristic, complemented
335#1862C2×C3111yescharacteristic, complemented
336#1854C2×C3111yescharacteristic, complemented
337#1851C2×C3111yescharacteristic, complemented
338#1809C2×C3111yescharacteristic, complemented
339#1804C2×C3111yescharacteristic, complemented
340#1786C2×C3111yescharacteristic
341C22×C31—22no—
342C22×C31—22no—
343C22×C31—22no—
344C22×C31—24no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—41no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—816no—
359C22×C31—81no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31C2×C22⋊Q811yescharacteristic
364C22×C31D4211yescharacteristic
365C22×C31#54611yescharacteristic
366C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C31#57511yescharacteristic
368C22×C31#57611yescharacteristic
369C22×C31#57711yescharacteristic
370C4×C31—22no—
371C4×C31—22no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—41no—
375C4×C31—41no—
376C4×C31—81no—
377C4×C31—81no—
378C4×C31—81no—
379C4×C31—81no—
380C4×C31—81no—
381C4×C31C2×C22⋊Q811yescharacteristic
382C4×C31#54311yescharacteristic
383C4×C31#54611yescharacteristic
384C4×C31#55111yescharacteristic
385C23×D4C22×C3111yescharacteristic
386C22×M16C22×C3111yescharacteristic
387C2×C4⋊Q8C22×C3111yescharacteristic, complemented
388C2×C4×D4C22×C3111yescharacteristic
389C2×C4×D4C22×C3111yescharacteristic
390C2×#117C22×C3111yescharacteristic
391C22×C22⋊C4—21no—
392#476—24no—
393C2×#107C22×C3111yescharacteristic, complemented
394C2×#107C22×C3111yescharacteristic, complemented
395C2×#106C22×C3111yescharacteristic, complemented
396C2×#106C22×C3111yescharacteristic, complemented
397C2×C4⋊C8C22×C3111yescharacteristic, complemented
398C2×C4⋊C8C22×C3111yescharacteristic, complemented
399#418—24no—
400C2×#102C22×C3111yescharacteristic
401C2×#102C22×C3111yescharacteristic
402C2×#102C22×C3111yescharacteristic
403C2×#102C22×C3111yescharacteristic
404C2×#102C22×C3111yescharacteristic
405C2×#102C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×#102C22×C3111yescharacteristic
408C2×C22⋊C8C22×C3111yescharacteristic
409#396—21no—
410#393—21no—
411#391—21no—
412#390C22×C3111yescharacteristic
413#390C22×C3111yescharacteristic
414#389C22×C3111yescharacteristic, complemented
415#389C22×C3111yescharacteristic, complemented
416#387—21no—
417#386—21no—
418#386—21no—
419#382C22×C3111yescharacteristic, complemented
420#380C22×C3111yescharacteristic
421#380C22×C3111yescharacteristic
422#379—21no—
423C4×C22⋊C4C22×C3111yescharacteristic
424#340C22×C3111yescharacteristic, complemented
425#340C22×C3111yescharacteristic, complemented
426#340C22×C3111yescharacteristic, complemented
427#340C22×C3111yescharacteristic, complemented
428#336C22×C3111yescharacteristic, complemented
429#336C22×C3111yescharacteristic, complemented
430C2×C31—42no—
431C2×C31—44no—
432C2×C31—82no—
433C2×C31#243711yescharacteristic
434C2×C31#307711yescharacteristic
435C2×C31#308111yescharacteristic
436C2×C31#326511yescharacteristic
437C2×C31#327311yescharacteristic
438C2×C31#331111yescharacteristic
439C2×C31#332511yescharacteristic
440C25—21no—
441C22×Q8—21no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—41no—
447C22×D4—41no—
448C22×D4Q8×C3114yescomplemented
449C22×D4C23×C3111yescharacteristic
450C22×D4C23×C3111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4C23×C3111yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C23×C3111yescharacteristic
458C22×C8C23×C3111yescharacteristic
459C22×C8C23×C3111yescharacteristic
460C22×C8C23×C3111yescharacteristic
461C4⋊Q8—22no—
462C4⋊Q8—41no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—41no—
466C4×D4—41no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4C23×C3111yescharacteristic
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C4⋊C4C23×C3111yescharacteristic
476C2×C4⋊C4C23×C3111yescharacteristic
477C2×C4⋊C4C23×C3111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—44no—
488C2×C22⋊C4D4×C3111yescharacteristic
489C2×C22⋊C4D4×C3111yescharacteristic
490C2×C42—21no—
491C2×C42C23×C3111yescharacteristic
492C2×C42C23×C3111yescharacteristic
493#107—41no—
494#107—41no—
495#106—22no—
496#106—22no—
497C4⋊C8—22no—
498C4⋊C8—41no—
499#102—22no—
500#102—22no—
501#102—22no—
502#102—22no—
503#102—22no—
504#102—41no—
505#102—41no—
506#102D4×C3114yes—
507C22⋊C8—22no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95D4×C3111yescharacteristic
515#95D4×C3111yescharacteristic
516C31#2597411yescharacteristic, direct product factor, Sylow
517C24—21no—
518C24—21no—
519C24—24no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24C2×D4×C3111yescharacteristic
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—81no—
530C2×D4—28no—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4C2×D4×C3112yes—
546C2×D4C2×Q8×C3112yes—
547C2×D4C2×Q8×C3112yes—
548C2×D4#41×C3112yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×Q8×C3112yes—
571C22×C4#41×C3112yes—
572C22×C4C24×C3111yescharacteristic
573M16—44no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8C2×D4×C3112yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4C2×D4×C3112yes—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—22no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—48no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23C31×C22⋊Q812yes—
645C23C22×D4×C3111yescharacteristic
646Q8—84no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—41no—
654D4—41no—
655D4C31×C22⋊Q814yes—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4C31×C22⋊Q812yes—
694C2×C4C31×AGL(1,ℤ/8)12yes—
695C2×C4C22×D4×C3111yescharacteristic
696C2×C4C22×Q8×C3111yescharacteristic
697C2×C4C2×#41×C3111yescharacteristic
698C2×C4C2×#41×C3111yescharacteristic
699C2×C4C31×H(5,𝔽2)11yescharacteristic
700C2×C4C31×H(5,𝔽2)11yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—816no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C2×C31×C22⋊Q811yescharacteristic
728C22D42×C3111yescharacteristic
729C22C31×#54611yescharacteristic
730C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
731C22C31×#57511yescharacteristic
732C22C31×#57611yescharacteristic
733C22C31×#57711yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C2×C31×C22⋊Q811yescharacteristic
746C4C31×#54311yescharacteristic
747C4C31×#54611yescharacteristic
748C4C31×#55111yescharacteristic
749C2—42no—
750C2—44no—
751C2—82no—
752C2C31×#243711yescharacteristic
753C2C31×#307711yescharacteristic
754C2C31×#308111yescharacteristic
755C2C31×#326511yescharacteristic
756C2C31×#327311yescharacteristic
757C2C31×#331111yescharacteristic
758C2C31×#332511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
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×#476C2semidirect
3. C31×#2439C2semidirect
5. C31×#2092C2semidirect
6. C31×#2067C2semidirect
7. C31×#2065C2semidirect
8. C31×#2023C2semidirect
9. C31×#1862C2semidirect
10. C31×#1862C2semidirect
11. C31×#1854C2semidirect
12. C31×#1851C2semidirect
13. C31×#1809C2semidirect
14. C31×#1804C2semidirect
18. C2×C31×C4⋊Q8C22semidirect
24. C2×C31×#107C22semidirect
25. C2×C31×#107C22semidirect
26. C2×C31×#106C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×C4⋊C8C22semidirect
29. C2×C31×C4⋊C8C22semidirect
45. C31×#389C22semidirect
46. C31×#389C22semidirect
50. C31×#382C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
69. C22×D4×C31Q8semidirect
237. #25974C31direct (N × H)
326. C2×#476C2×C31semidirect
328. #2439C2×C31semidirect
330. #2092C2×C31semidirect
331. #2067C2×C31semidirect
332. #2065C2×C31semidirect
333. #2023C2×C31semidirect
334. #1862C2×C31semidirect
335. #1862C2×C31semidirect
336. #1854C2×C31semidirect
337. #1851C2×C31semidirect
338. #1809C2×C31semidirect
339. #1804C2×C31semidirect
387. C2×C4⋊Q8C22×C31semidirect
393. C2×#107C22×C31semidirect
394. C2×#107C22×C31semidirect
395. C2×#106C22×C31semidirect
396. C2×#106C22×C31semidirect
397. C2×C4⋊C8C22×C31semidirect
398. C2×C4⋊C8C22×C31semidirect
414. #389C22×C31semidirect
415. #389C22×C31semidirect
419. #382C22×C31semidirect
424. #340C22×C31semidirect
425. #340C22×C31semidirect
426. #340C22×C31semidirect
427. #340C22×C31semidirect
428. #336C22×C31semidirect
429. #336C22×C31semidirect
448. C22×D4Q8×C31semidirect
516. C31#25974direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4762
C2×C31×#4182
C31×#24392
D4×C22⋊C4×C312
C31×#20922
C31×#20672
C31×#20652
C31×#20232
C31×#18622
C31×#18542
C31×#18512
C31×#18092
C31×#18042
C31×#17862
#2597431