Finite Group Databasebeta

← C31×#26257 #21483016

Subgroups — C31×#26257 #21483016

Order 7936.

946 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#496C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C31×#2448C211yesmaximal, characteristic, complemented
4C31×#2445C211yesmaximal, characteristic, complemented
5C31×#2055C211yesmaximal, characteristic, complemented
6C31×#2054C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2041C211yesmaximal, characteristic, complemented
9C31×#1973C211yesmaximal, characteristic, complemented
10C31×#1972C211yesmaximal, characteristic, complemented
11C31×#1970C211yesmaximal, characteristic, complemented
12C31×#1943C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1879C211yesmaximal, characteristic, complemented
15C31×#1771C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C2×C31×#127C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C31×#496—24no—
26C4×SD16×C31—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#97C2211yescharacteristic
39C2×C31×#97C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic
41C31×#399—21no—
42C31×#397—21no—
43C31×#394—21no—
44C31×#394—21no—
45C31×#391C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#388—21no—
55C31×#386—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31C2311yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C2×SD16×C31—22no—
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31—41no—
73C2×SD16×C31D414yes—
74C2×D8×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—41no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×#127—22no—
85C31×#127—41no—
86C31×#124—22no—
87C31×#124—41no—
88C31×#123—44no—
89C4×Q8×C31—22no—
90C4×Q8×C31—41no—
91C4×D4×C31—22no—
92C4×D4×C31—41no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C42×C31—21no—
116C2×C42×C31C2311yescharacteristic
117C2×C42×C31C2311yescharacteristic
118C2×C42×C31C2311yescharacteristic
119C31×#107—22no—
120C31×#106—22no—
121C31×C4⋊C8—22no—
122C31×#103—22no—
123C31×#103—41no—
124C31×#102—22no—
125C31×#102—41no—
126C31×#102—41no—
127C31×#102—41no—
128C31×#102—41no—
129C31×#102—41no—
130C31×#97—22no—
131C31×#97—22no—
132C4×C8×C31—22no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95D411yescharacteristic
138C31×#95D411yescharacteristic
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31C2×D412yes—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
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—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—81no—
170C2×D4×C31—81no—
171C2×D4×C31C2×D412yes—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—42no—
178C22×C4×C31—42no—
179C22×C4×C31—81no—
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2411yescharacteristic
187SD16×C31—28no—
188SD16×C31—44no—
189D8×C31—44no—
190D8×C31—44no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31C2×D412yes—
200C2×C8×C31#4112yes—
201C2×C8×C31#4112yes—
202C2×C8×C31#4112yes—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
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—41no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31—81no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—42no—
221C22⋊C4×C31—42no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—81no—
225C22⋊C4×C31—81no—
226C22⋊C4×C31—81no—
227C22⋊C4×C31—81no—
228C22⋊C4×C31—81no—
229C42×C31—21no—
230C42×C31—21no—
231C42×C31—21no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—42no—
236#26257C3111yesmaximal, characteristic, direct product factor, Sylow
237C23×C31—22no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
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×C31C22×D411yescharacteristic
259Q8×C31—22no—
260Q8×C31—22no—
261Q8×C31—41no—
262Q8×C31—41no—
263D4×C31—22no—
264D4×C31—22no—
265D4×C31—41no—
266D4×C31—41no—
267D4×C31—41no—
268D4×C31—41no—
269D4×C31—41no—
270D4×C31—41no—
271D4×C31—41no—
272D4×C31—41no—
273D4×C31—41no—
274D4×C31—41no—
275D4×C31—84no—
276D4×C31—84no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—22no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
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—84no—
310C2×C4×C31AGL(1,ℤ/8)12yes—
311C2×C4×C31C22×D411yescharacteristic
312C2×C4×C31C2×#4111yescharacteristic
313C2×C4×C31C2×#4111yescharacteristic
314C2×C4×C31C2×#4111yescharacteristic
315C2×C4×C31H(5,𝔽2)11yescharacteristic
316C2×C4×C31H(5,𝔽2)11yescharacteristic
317C8×C31—22no—
318C8×C31—41no—
319C8×C31—41no—
320C8×C31#12314yescomplemented
321C2×#496C2×C3111yescharacteristic
322C2×C4×SD16C2×C3111yescharacteristic, complemented
323#2448C2×C3111yescharacteristic, complemented
324#2445C2×C3111yescharacteristic, complemented
325#2055C2×C3111yescharacteristic, complemented
326#2054C2×C3111yescharacteristic, complemented
327#2042C2×C3111yescharacteristic, complemented
328#2041C2×C3111yescharacteristic, complemented
329#1973C2×C3111yescharacteristic, complemented
330#1972C2×C3111yescharacteristic, complemented
331#1970C2×C3111yescharacteristic, complemented
332#1943C2×C3111yescharacteristic, complemented
333#1880C2×C3111yescharacteristic, complemented
334#1879C2×C3111yescharacteristic, complemented
335#1771C2×C3111yescharacteristic, complemented
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31#53211yescharacteristic
358C22×C31D4211yescharacteristic
359C22×C31#55011yescharacteristic
360C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C31#57511yescharacteristic
362C22×C31#57611yescharacteristic
363C22×C31#57711yescharacteristic
364C4×C31—22no—
365C4×C31—41no—
366C4×C31—41no—
367C4×C31—42no—
368C4×C31—41no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—81no—
372C4×C31—81no—
373C4×C31—81no—
374C4×C31—81no—
375C4×C31C2×#12311yescharacteristic
376C4×C31#54011yescharacteristic
377C4×C31#54611yescharacteristic
378C4×C31#55911yescharacteristic
379C22×SD16C22×C3111yescharacteristic
380C22×SD16C22×C3111yescharacteristic
381C22×D8C22×C3111yescharacteristic
382C22×D8C22×C3111yescharacteristic
383C2×#127C22×C3111yescharacteristic
384C2×#124C22×C3111yescharacteristic
385C2×#123—21no—
386C2×C4×Q8C22×C3111yescharacteristic
387C2×C4×D4C22×C3111yescharacteristic
388#496—24no—
389C4×SD16—24no—
390C2×#107C22×C3111yescharacteristic
391C2×#106C22×C3111yescharacteristic
392C2×C4⋊C8C22×C3111yescharacteristic
393C2×#103C22×C3111yescharacteristic
394C2×#103C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396C2×#102C22×C3111yescharacteristic
397C2×#102C22×C3111yescharacteristic
398C2×#102C22×C3111yescharacteristic
399C2×#102C22×C3111yescharacteristic
400C2×#102C22×C3111yescharacteristic
401C2×#97C22×C3111yescharacteristic
402C2×#97C22×C3111yescharacteristic
403C2×C4×C8C22×C3111yescharacteristic
404#399—21no—
405#397—21no—
406#394—21no—
407#394—21no—
408#391C22×C3111yescharacteristic
409#390C22×C3111yescharacteristic
410#390C22×C3111yescharacteristic
411#390C22×C3111yescharacteristic
412#390C22×C3111yescharacteristic
413#390C22×C3111yescharacteristic
414#389C22×C3111yescharacteristic
415#389C22×C3111yescharacteristic
416#388—21no—
417#388—21no—
418#386—21no—
419C4×C4⋊C4C22×C3111yescharacteristic
420#340C22×C3111yescharacteristic
421#340C22×C3111yescharacteristic
422#336C22×C3111yescharacteristic
423#336C22×C3111yescharacteristic
424C2×C31—82no—
425C2×C31—161no—
426C2×C31—161no—
427C2×C31#244511yescharacteristic
428C2×C31#317111yescharacteristic
429C2×C31#317911yescharacteristic
430C2×C31#326511yescharacteristic
431C2×C31#326811yescharacteristic
432C2×C31#339911yescharacteristic
433C2×C31#340111yescharacteristic
434C22×Q8C23×C3111yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4C23×C3111yescharacteristic
438C22×D4C23×C3111yescharacteristic
439C22×D4C23×C3111yescharacteristic
440C23×C4—21no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C2×SD16D4×C3114yes—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8—22no—
451C2×D8—22no—
452C2×D8—41no—
453C22×C8C23×C3111yescharacteristic
454C22×C8C23×C3111yescharacteristic
455C22×C8C23×C3111yescharacteristic
456C22×C8C23×C3111yescharacteristic
457#127—22no—
458#127—41no—
459#124—22no—
460#124—41no—
461#123—44no—
462C4×Q8—22no—
463C4×Q8—41no—
464C4×D4—22no—
465C4×D4—41no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4D4×C3111yescharacteristic
470C2×C4⋊C4D4×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C4⋊C4C23×C3111yescharacteristic
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
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—21no—
488C2×C42—21no—
489C2×C42C23×C3111yescharacteristic
490C2×C42C23×C3111yescharacteristic
491C2×C42C23×C3111yescharacteristic
492#107—22no—
493#106—22no—
494C4⋊C8—22no—
495#103—22no—
496#103—41no—
497#102—22no—
498#102—41no—
499#102—41no—
500#102—41no—
501#102—41no—
502#102—41no—
503#97—22no—
504#97—22no—
505C4×C8—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95D4×C3111yescharacteristic
511#95D4×C3111yescharacteristic
512C31#2625711yescharacteristic, direct product factor, Sylow
513C24—21no—
514C24—21no—
515C24—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8C2×D4×C3112yes—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C2×D4×C3112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4C2×D4×C3111yescharacteristic
555C22×C4C2×D4×C3111yescharacteristic
556C22×C4C2×D4×C3111yescharacteristic
557C22×C4C2×D4×C3111yescharacteristic
558C22×C4C2×D4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C24×C3111yescharacteristic
561SD16—28no—
562SD16—44no—
563D8—44no—
564D8—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8C2×D4×C3112yes—
574C2×C8#41×C3112yes—
575C2×C8#41×C3112yes—
576C2×C8#41×C3112yes—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—41no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—42no—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C22×D4×C3111yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—84no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
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—84no—
683C2×C4C31×AGL(1,ℤ/8)12yes—
684C2×C4C22×D4×C3111yescharacteristic
685C2×C4C2×#41×C3111yescharacteristic
686C2×C4C2×#41×C3111yescharacteristic
687C2×C4C2×#41×C3111yescharacteristic
688C2×C4C31×H(5,𝔽2)11yescharacteristic
689C2×C4C31×H(5,𝔽2)11yescharacteristic
690C8—22no—
691C8—41no—
692C8—41no—
693C8C31×#12314yescomplemented
694C22—42no—
695C22—42no—
696C22—42no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C31×#53211yescharacteristic
716C22D42×C3111yescharacteristic
717C22C31×#55011yescharacteristic
718C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
719C22C31×#57511yescharacteristic
720C22C31×#57611yescharacteristic
721C22C31×#57711yescharacteristic
722C4—22no—
723C4—41no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4C2×C31×#12311yescharacteristic
734C4C31×#54011yescharacteristic
735C4C31×#54611yescharacteristic
736C4C31×#55911yescharacteristic
737C2—82no—
738C2—161no—
739C2—161no—
740C2C31×#244511yescharacteristic
741C2C31×#317111yescharacteristic
742C2C31×#317911yescharacteristic
743C2C31×#326511yescharacteristic
744C2C31×#326811yescharacteristic
745C2C31×#339911yescharacteristic
746C2C31×#340111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#496C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C31C2semidirect
3. C31×#2448C2semidirect
4. C31×#2445C2semidirect
5. C31×#2055C2semidirect
6. C31×#2054C2semidirect
7. C31×#2042C2semidirect
8. C31×#2041C2semidirect
9. C31×#1973C2semidirect
10. C31×#1972C2semidirect
11. C31×#1970C2semidirect
12. C31×#1943C2semidirect
13. C31×#1880C2semidirect
14. C31×#1879C2semidirect
15. C31×#1771C2semidirect
236. #26257C31direct (N × H)
320. C8×C31#123semidirect
322. C2×C4×SD16C2×C31semidirect
323. #2448C2×C31semidirect
324. #2445C2×C31semidirect
325. #2055C2×C31semidirect
326. #2054C2×C31semidirect
327. #2042C2×C31semidirect
328. #2041C2×C31semidirect
329. #1973C2×C31semidirect
330. #1972C2×C31semidirect
331. #1970C2×C31semidirect
332. #1943C2×C31semidirect
333. #1880C2×C31semidirect
334. #1879C2×C31semidirect
335. #1771C2×C31semidirect
512. C31#26257direct (N × H)
693. C8C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4962
C2×C4×SD16×C312
C31×#24482
C31×#24452
C31×#20552
C31×#20542
C31×#20422
C31×#20412
C31×#19732
C31×#19722
C31×#19702
C31×#19432
C31×#18802
C31×#18792
C31×#17712
#2625731