Finite Group Databasebeta

← C31×#26834 #21483593

Subgroups — C31×#26834 #21483593

Order 7936.

960 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#486C211yesmaximal, characteristic, complemented
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C31×#2452C211yesmaximal, characteristic, complemented
4C31×#2445C211yesmaximal, characteristic, complemented
5C31×#2065C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2054C211yesmaximal, characteristic, complemented
8C31×#2011C211yesmaximal, characteristic
9C31×#1972C211yesmaximal, characteristic, complemented
10C31×#1936C211yesmaximal, characteristic, complemented
11C31×#1936C211yesmaximal, characteristic, complemented
12C31×#1934C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1771C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#127C2211yescharacteristic
20C2×C31×#123—21no—
21C2×C31×C22⋊Q8—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#486—24no—
25C31×#442—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#102C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#97C2211yescharacteristic
38C2×C31×#97C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#396—21no—
41C31×#394—21no—
42C31×#394—21no—
43C31×#393—21no—
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#386—21no—
53C31×#385—21no—
54C4×C4⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31C2311yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C2×D8×C31—22no—
70C2×D8×C31—22no—
71C2×D8×C31—22no—
72C2×D8×C31—22no—
73C2×D8×C31—22no—
74C2×D8×C31—41no—
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×C4⋊Q8—22no—
80C31×C4⋊Q8—41no—
81C31×#127—22no—
82C31×#127—41no—
83C31×#123—44no—
84C31×C22⋊Q8—44no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—41no—
88C4×D4×C31—41no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31D411yescharacteristic
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C42×C31C2311yescharacteristic
113C2×C42×C31C2311yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C31×#106—22no—
116C31×#106—41no—
117C31×C4⋊C8—22no—
118C31×#102—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102D414yes—
126C31×#97—22no—
127C31×#97—22no—
128C4×C8×C31—22no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95D411yescharacteristic
133C31×#95D411yescharacteristic
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C2×Q8×C31—42no—
138C2×Q8×C31—42no—
139C2×Q8×C31—81no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
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—42no—
157C2×D4×C31—42no—
158C2×D4×C31—42no—
159C2×D4×C31—42no—
160C2×D4×C31—81no—
161C2×D4×C31—81no—
162C2×D4×C31C2×D412yes—
163C2×D4×C31#4112yes—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—81no—
174C22×C4×C31—81no—
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2411yescharacteristic
182D8×C31—28no—
183D8×C31—44no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31C2×D412yes—
194C2×C8×C31#4112yes—
195C2×C8×C31#4112yes—
196C4⋊C4×C31—22no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31C2×D412yes—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—81no—
221C22⋊C4×C31—81no—
222C22⋊C4×C31—81no—
223C22⋊C4×C31—81no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31—21no—
230#26834C3111yesmaximal, characteristic, direct product factor, Sylow
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
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×C31C22×D411yescharacteristic
253Q8×C31—84no—
254D4×C31—22no—
255D4×C31—22no—
256D4×C31—22no—
257D4×C31—22no—
258D4×C31—41no—
259D4×C31—41no—
260D4×C31—41no—
261D4×C31—41no—
262D4×C31—41no—
263D4×C31—41no—
264D4×C31—41no—
265D4×C31—41no—
266D4×C31—84no—
267D4×C31—84no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—22no—
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—21no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—84no—
300C2×C4×C31—84no—
301C2×C4×C31AGL(1,ℤ/8)12yes—
302C2×C4×C31AGL(1,ℤ/8)12yes—
303C2×C4×C31C22×D411yescharacteristic
304C2×C4×C31C2×#4111yescharacteristic
305C2×C4×C31C2×#4111yescharacteristic
306C2×C4×C31C2×#4111yescharacteristic
307C2×C4×C31H(5,𝔽2)11yescharacteristic
308C2×C4×C312−1+411yescharacteristic
309C8×C31—22no—
310C8×C31—22no—
311C8×C31—22no—
312C8×C31—41no—
313C2×#486C2×C3111yescharacteristic, complemented
314C2×#442C2×C3111yescharacteristic, complemented
315#2452C2×C3111yescharacteristic, complemented
316#2445C2×C3111yescharacteristic, complemented
317#2065C2×C3111yescharacteristic, complemented
318#2058C2×C3111yescharacteristic, complemented
319#2054C2×C3111yescharacteristic, complemented
320#2011C2×C3111yescharacteristic
321#1972C2×C3111yescharacteristic, complemented
322#1936C2×C3111yescharacteristic, complemented
323#1936C2×C3111yescharacteristic, complemented
324#1934C2×C3111yescharacteristic, complemented
325#1879C2×C3111yescharacteristic, complemented
326#1864C2×C3111yescharacteristic, complemented
327#1771C2×C3111yescharacteristic, complemented
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—81no—
337C22×C31—81no—
338C22×C31—81no—
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#53211yescharacteristic
350C22×C31D4211yescharacteristic
351C22×C31#54811yescharacteristic
352C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C31#57611yescharacteristic
355C22×C31#57711yescharacteristic
356C4×C31—22no—
357C4×C31—22no—
358C4×C31—41no—
359C4×C31—41no—
360C4×C31—41no—
361C4×C31—42no—
362C4×C31—41no—
363C4×C31—81no—
364C4×C31—81no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31#52511yescharacteristic
368C4×C31#54211yescharacteristic
369C4×C31#54711yescharacteristic
370C4×C31#55111yescharacteristic
371C22×D8C22×C3111yescharacteristic
372C22×D8C22×C3111yescharacteristic
373C2×C4⋊Q8C22×C3111yescharacteristic
374C2×#127C22×C3111yescharacteristic
375C2×#123—21no—
376C2×C22⋊Q8—21no—
377C2×C4×D4C22×C3111yescharacteristic
378C2×C4×D4C22×C3111yescharacteristic
379#486—24no—
380#442—24no—
381C2×#106C22×C3111yescharacteristic
382C2×#106C22×C3111yescharacteristic
383C2×C4⋊C8C22×C3111yescharacteristic
384C2×#102C22×C3111yescharacteristic
385C2×#102C22×C3111yescharacteristic
386C2×#102C22×C3111yescharacteristic
387C2×#102C22×C3111yescharacteristic
388C2×#102C22×C3111yescharacteristic
389C2×#102C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#97C22×C3111yescharacteristic
393C2×#97C22×C3111yescharacteristic
394C2×C4×C8C22×C3111yescharacteristic
395#396—21no—
396#394—21no—
397#394—21no—
398#393—21no—
399#390C22×C3111yescharacteristic
400#390C22×C3111yescharacteristic
401#390C22×C3111yescharacteristic
402#390C22×C3111yescharacteristic
403#390C22×C3111yescharacteristic
404#389C22×C3111yescharacteristic
405#389C22×C3111yescharacteristic
406#389C22×C3111yescharacteristic
407#386—21no—
408#385—21no—
409C4×C4⋊C4C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#336C22×C3111yescharacteristic
415#336C22×C3111yescharacteristic
416C2×C31—82no—
417C2×C31—82no—
418C2×C31—161no—
419C2×C31#246111yescharacteristic
420C2×C31#317911yescharacteristic
421C2×C31#318411yescharacteristic
422C2×C31#326411yescharacteristic
423C2×C31#326511yescharacteristic
424C2×C31#336611yescharacteristic
425C2×C31#337311yescharacteristic
426C22×Q8—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4C23×C3111yescharacteristic
430C22×D4C23×C3111yescharacteristic
431C22×D4C23×C3111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C2×D8—22no—
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—22no—
439C2×D8—41no—
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442C22×C8C23×C3111yescharacteristic
443C22×C8C23×C3111yescharacteristic
444C4⋊Q8—22no—
445C4⋊Q8—41no—
446#127—22no—
447#127—41no—
448#123—44no—
449C22⋊Q8—44no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—41no—
453C4×D4—41no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4D4×C3111yescharacteristic
459C2×C4⋊C4D4×C3111yescharacteristic
460C2×C4⋊C4C23×C3111yescharacteristic
461C2×C4⋊C4C23×C3111yescharacteristic
462C2×C4⋊C4C23×C3111yescharacteristic
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C42C23×C3111yescharacteristic
478C2×C42C23×C3111yescharacteristic
479C2×C42C23×C3111yescharacteristic
480#106—22no—
481#106—41no—
482C4⋊C8—22no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102D4×C3114yes—
491#97—22no—
492#97—22no—
493C4×C8—22no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95D4×C3111yescharacteristic
498#95D4×C3111yescharacteristic
499C31#2683411yescharacteristic, direct product factor, Sylow
500C24—21no—
501C24—21no—
502C24—21no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—81no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4C2×D4×C3112yes—
529C2×D4#41×C3112yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3111yescharacteristic
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4C2×D4×C3111yescharacteristic
545C22×C4C2×D4×C3111yescharacteristic
546C22×C4C2×D4×C3111yescharacteristic
547C22×C4C24×C3111yescharacteristic
548D8—28no—
549D8—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8C2×D4×C3112yes—
560C2×C8#41×C3112yes—
561C2×C8#41×C3112yes—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4C2×D4×C3112yes—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—21no—
596C23—22no—
597C23—22no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C3111yescharacteristic
618Q8—84no—
619D4—22no—
620D4—22no—
621D4—22no—
622D4—22no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—84no—
632D4—84no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4C31×AGL(1,ℤ/8)12yes—
667C2×C4C31×AGL(1,ℤ/8)12yes—
668C2×C4C22×D4×C3111yescharacteristic
669C2×C4C2×#41×C3111yescharacteristic
670C2×C4C2×#41×C3111yescharacteristic
671C2×C4C2×#41×C3111yescharacteristic
672C2×C4C31×H(5,𝔽2)11yescharacteristic
673C2×C4C31×2−1+411yescharacteristic
674C8—22no—
675C8—22no—
676C8—22no—
677C8—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22C31×#53211yescharacteristic
700C22D42×C3111yescharacteristic
701C22C31×#54811yescharacteristic
702C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
703C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
704C22C31×#57611yescharacteristic
705C22C31×#57711yescharacteristic
706C4—22no—
707C4—22no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4—81no—
717C4C31×#52511yescharacteristic
718C4C31×#54211yescharacteristic
719C4C31×#54711yescharacteristic
720C4C31×#55111yescharacteristic
721C2—82no—
722C2—82no—
723C2—161no—
724C2C31×#246111yescharacteristic
725C2C31×#317911yescharacteristic
726C2C31×#318411yescharacteristic
727C2C31×#326411yescharacteristic
728C2C31×#326511yescharacteristic
729C2C31×#336611yescharacteristic
730C2C31×#337311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2011C2
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
1. C2×C31×#486C2semidirect
2. C2×C31×#442C2semidirect
3. C31×#2452C2semidirect
4. C31×#2445C2semidirect
5. C31×#2065C2semidirect
6. C31×#2058C2semidirect
7. C31×#2054C2semidirect
9. C31×#1972C2semidirect
10. C31×#1936C2semidirect
11. C31×#1936C2semidirect
12. C31×#1934C2semidirect
13. C31×#1879C2semidirect
14. C31×#1864C2semidirect
15. C31×#1771C2semidirect
230. #26834C31direct (N × H)
313. C2×#486C2×C31semidirect
314. C2×#442C2×C31semidirect
315. #2452C2×C31semidirect
316. #2445C2×C31semidirect
317. #2065C2×C31semidirect
318. #2058C2×C31semidirect
319. #2054C2×C31semidirect
321. #1972C2×C31semidirect
322. #1936C2×C31semidirect
323. #1936C2×C31semidirect
324. #1934C2×C31semidirect
325. #1879C2×C31semidirect
326. #1864C2×C31semidirect
327. #1771C2×C31semidirect
499. C31#26834direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4862
C2×C31×#4422
C31×#24522
C31×#24452
C31×#20652
C31×#20582
C31×#20542
C31×#20112
C31×#19722
C31×#19362
C31×#19342
C31×#18792
C31×#18642
C31×#17712
#2683431