Finite Group Databasebeta

← C31×#17615 #21474374

Subgroups — C31×#17615 #21474374

Order 7936.

1038 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic
2C31×#2972C211yesmaximal, characteristic, complemented
3C31×#2353C211yesmaximal, characteristic, complemented
4C31×#1521C212yesmaximal, complemented
5C31×#1520C211yesmaximal, characteristic, complemented
6C31×#1519C211yesmaximal, characteristic, complemented
7C31×#1516C212yesmaximal, complemented
8C31×#1501C212yesmaximal, complemented
9C31×#1500C212yesmaximal, complemented
10C2×C31×#328C211yesmaximal, characteristic, complemented
11C2×C31×#327C211yesmaximal, characteristic, complemented
12C31×#553—22no—
13C31×#553C412yescomplemented
14C31×#552C412yescomplemented
15C31×#551—22no—
16C31×#548C412yescomplemented
17C31×#546C412yescomplemented
18C31×#539—21no—
19C31×#538—21no—
20C31×#534—21no—
21C31×#529C2212yes—
22C31×#525C2212yes—
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C31×#518—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C8×D4×C31—22no—
28C8×D4×C31—22no—
29C31×#431C2212yescomplemented
30C2×C31×C22⋊C8C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2212yescomplemented
33C31×#388—21no—
34C31×#387—21no—
35C31×#386—21no—
36C31×#383C2211yescharacteristic, complemented
37C31×#381C2211yescharacteristic, complemented
38C31×#380C2211yescharacteristic
39C4×C22⋊C4×C31—21no—
40C4×C22⋊C4×C31C2211yescharacteristic, complemented
41C31×#376C2211yescharacteristic, complemented
42C2×C31×#95C2211yescharacteristic
43C31×#328C2212yescomplemented
44C31×#328C2212yescomplemented
45C31×#328C2212yescomplemented
46C31×#328C2212yescomplemented
47C31×#327C2212yes—
48C31×#327C2212yes—
49C31×#327C2212yes—
50C31×#327C2212yes—
51C2×#41×C31C2×C412yescomplemented
52C22×Q8×C31C2×C411yescharacteristic
53C22×D4×C31—21no—
54C22×D4×C31C2×C411yescharacteristic
55C22×D4×C31D411yescharacteristic
56C23×C4×C31—21no—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C22×C8×C31—21no—
60C22×C8×C31—21no—
61C22×C8×C31—22no—
62C31×#126—22no—
63C31×#126—22no—
64C31×#126—22no—
65C31×#125—22no—
66C31×#125C2×C412yescomplemented
67C31×#124—22no—
68C31×#124C2×C412yescomplemented
69C31×#123—22no—
70C31×#123—22no—
71C31×#123—22no—
72C31×#123—22no—
73C31×#123—22no—
74C31×C22⋊Q8—21no—
75C31×C22⋊Q8—21no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8C2×C412yes—
78C31×C22⋊Q8C2×C412yescomplemented
79C31×C22⋊Q8C2312yes—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—21no—
83C31×#121—21no—
84C31×#121—22no—
85C31×#121C2×C412yes—
86C31×#121C2×C412yescomplemented
87C31×#121C2312yes—
88C31×#120—22no—
89C31×#120—22no—
90C4×Q8×C31C2×C412yescomplemented
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31C2×C412yes—
97C4×D4×C31C2×C412yes—
98C4×D4×C31C2×C412yescomplemented
99C4×D4×C31D412yes—
100C4×D4×C31D412yes—
101C31×#117—22no—
102C31×#117—22no—
103C31×#117C2×C412yescomplemented
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31C2×C411yescharacteristic
107C2×C4⋊C4×C31C2×C411yescharacteristic
108C2×C4⋊C4×C31D411yescharacteristic
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31D411yescharacteristic
116C2×C22⋊C4×C31D411yescharacteristic
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31C2311yescharacteristic
120C31×C4⋊C8—22no—
121C31×C22⋊C8—21no—
122C31×C22⋊C8—21no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8C2312yes—
125C31×C22⋊C8C2312yes—
126C4×C8×C31—22no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95C2311yescharacteristic
133C31×#95C2311yescharacteristic
134C31×#95C2311yescharacteristic
135C31×#95C2311yescharacteristic
136C24×C31—21no—
137C24×C31C2×D411yescharacteristic
138C24×C31C2×D411yescharacteristic
139#41×C31—82no—
140C2×Q8×C31—21no—
141C2×Q8×C31—81no—
142C2×Q8×C31C22×C412yes—
143C2×D4×C31—22no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—22no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—21no—
150C2×D4×C31—42no—
151C2×D4×C31—42no—
152C2×D4×C31—81no—
153C2×D4×C31C22⋊C412yes—
154C2×D4×C31C22⋊C412yes—
155C2×D4×C31C22×C412yes—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—81no—
168C22×C4×C31—81no—
169C22×C4×C31—81no—
170C22×C4×C31C22×C411yescharacteristic
171C22×C4×C31C22×C411yescharacteristic
172C22×C4×C31C22×C412yes—
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D412yes—
180C22×C4×C31C2411yescharacteristic
181C2×C8×C31—22no—
182C2×C8×C31—22no—
183C2×C8×C31—81no—
184C2×C8×C31—81no—
185C2×C8×C31—82no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—81no—
195C4⋊C4×C31C22⋊C412yes—
196C4⋊C4×C31C22⋊C412yes—
197C4⋊C4×C31C22×C412yes—
198C4⋊C4×C31C22×C412yes—
199C22⋊C4×C31—22no—
200C22⋊C4×C31—22no—
201C22⋊C4×C31—22no—
202C22⋊C4×C31—22no—
203C22⋊C4×C31—22no—
204C22⋊C4×C31—22no—
205C22⋊C4×C31—22no—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—22no—
208C22⋊C4×C31—22no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—81no—
212C22⋊C4×C31C22⋊C412yes—
213C22⋊C4×C31C22⋊C412yes—
214C22⋊C4×C31C22⋊C412yes—
215C22⋊C4×C31C22⋊C412yes—
216C42×C31—22no—
217C42×C31—22no—
218C42×C31—42no—
219C42×C31—81no—
220C42×C31C22×C412yes—
221C42×C31C2×D412yes—
222#17615C3111yesmaximal, characteristic, direct product factor, Sylow
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—22no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—42no—
231C23×C31—81no—
232C23×C31—81no—
233C23×C31C2×C22⋊C412yes—
234C23×C31C2×C22⋊C411yescharacteristic
235C23×C31C2×C22⋊C411yescharacteristic
236C23×C31#13512yes—
237C23×C31#13512yes—
238C23×C31C22×D411yescharacteristic
239Q8×C31—42no—
240Q8×C31—81no—
241D4×C31—24no—
242D4×C31—24no—
243D4×C31—42no—
244D4×C31—42no—
245D4×C31—42no—
246D4×C31—44no—
247D4×C31—81no—
248D4×C31—82no—
249D4×C31—82no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—22no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—41no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—42no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—42no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—42no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—82no—
279C2×C4×C31—82no—
280C2×C4×C31—81no—
281C2×C4×C31—81no—
282C2×C4×C31—84no—
283C2×C4×C31C2×C22⋊C412yes—
284C2×C4×C31C2×C22⋊C412yes—
285C2×C4×C31C2×C22⋊C412yes—
286C2×C4×C31C2×C22⋊C411yescharacteristic
287C2×C4×C31C2×C22⋊C411yescharacteristic
288C2×C4×C31C23×C411yescharacteristic
289C2×C4×C31C22×D411yescharacteristic
290C8×C31—42no—
291C8×C31—42no—
292#3505C2×C3111yescharacteristic
293#2972C2×C3111yescharacteristic, complemented
294#2353C2×C3111yescharacteristic, complemented
295#1521C2×C3112yescomplemented
296#1520C2×C3111yescharacteristic, complemented
297#1519C2×C3111yescharacteristic, complemented
298#1516C2×C3112yescomplemented
299#1501C2×C3112yescomplemented
300#1500C2×C3112yescomplemented
301C2×#328C2×C3111yescharacteristic, complemented
302C2×#327C2×C3111yescharacteristic, complemented
303C22×C31—21no—
304C22×C31—21no—
305C22×C31—21no—
306C22×C31—21no—
307C22×C31—21no—
308C22×C31—21no—
309C22×C31—22no—
310C22×C31—22no—
311C22×C31—22no—
312C22×C31—42no—
313C22×C31—42no—
314C22×C31—42no—
315C22×C31—42no—
316C22×C31—42no—
317C22×C31—81no—
318C22×C31—81no—
319C22×C31—162no—
320C22×C31#41612yes—
321C22×C31#41612yes—
322C22×C31C22×C22⋊C411yescharacteristic
323C22×C31C2×#13511yescharacteristic
324C22×C31C2×#13511yescharacteristic
325C4×C31—21no—
326C4×C31—21no—
327C4×C31—22no—
328C4×C31—21no—
329C4×C31—21no—
330C4×C31—22no—
331C4×C31—22no—
332C4×C31—42no—
333C4×C31—42no—
334C4×C31—42no—
335C4×C31—42no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339#553—22no—
340#553C4×C3112yescomplemented
341#552C4×C3112yescomplemented
342#551—22no—
343#548C4×C3112yescomplemented
344#546C4×C3112yescomplemented
345#539—21no—
346#538—21no—
347#534—21no—
348#529C22×C3112yes—
349#525C22×C3112yes—
350C2×C22⋊Q8C22×C3111yescharacteristic
351C2×#121C22×C3111yescharacteristic
352#518—21no—
353C2×C4×D4C22×C3111yescharacteristic
354C8×D4—22no—
355C8×D4—22no—
356#431C22×C3112yescomplemented
357C2×C22⋊C8C22×C3111yescharacteristic
358C2×C22⋊C8C22×C3111yescharacteristic
359C2×C22⋊C8C22×C3112yescomplemented
360#388—21no—
361#387—21no—
362#386—21no—
363#383C22×C3111yescharacteristic, complemented
364#381C22×C3111yescharacteristic, complemented
365#380C22×C3111yescharacteristic
366C4×C22⋊C4—21no—
367C4×C22⋊C4C22×C3111yescharacteristic, complemented
368#376C22×C3111yescharacteristic, complemented
369C2×#95C22×C3111yescharacteristic
370#328C22×C3112yescomplemented
371#328C22×C3112yescomplemented
372#328C22×C3112yescomplemented
373#328C22×C3112yescomplemented
374#327C22×C3112yes—
375#327C22×C3112yes—
376#327C22×C3112yes—
377#327C22×C3112yes—
378C2×C31—21no—
379C2×C31—21no—
380C2×C31—22no—
381C2×C31—22no—
382C2×C31—42no—
383C2×C31—82no—
384C2×C31#288311yescharacteristic
385C2×C31C2×#41611yescharacteristic
386C2×C31#290111yescharacteristic
387C2×#41C2×C4×C3112yescomplemented
388C22×Q8C2×C4×C3111yescharacteristic
389C22×D4—21no—
390C22×D4C2×C4×C3111yescharacteristic
391C22×D4D4×C3111yescharacteristic
392C23×C4—21no—
393C23×C4C23×C3111yescharacteristic
394C23×C4C23×C3111yescharacteristic
395C22×C8—21no—
396C22×C8—21no—
397C22×C8—22no—
398#126—22no—
399#126—22no—
400#126—22no—
401#125—22no—
402#125C2×C4×C3112yescomplemented
403#124—22no—
404#124C2×C4×C3112yescomplemented
405#123—22no—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8C2×C4×C3112yes—
414C22⋊Q8C2×C4×C3112yescomplemented
415C22⋊Q8C23×C3112yes—
416#121—22no—
417#121—22no—
418#121—21no—
419#121—21no—
420#121—22no—
421#121C2×C4×C3112yes—
422#121C2×C4×C3112yescomplemented
423#121C23×C3112yes—
424#120—22no—
425#120—22no—
426C4×Q8C2×C4×C3112yescomplemented
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4C2×C4×C3112yes—
433C4×D4C2×C4×C3112yes—
434C4×D4C2×C4×C3112yescomplemented
435C4×D4D4×C3112yes—
436C4×D4D4×C3112yes—
437#117—22no—
438#117—22no—
439#117C2×C4×C3112yescomplemented
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4C2×C4×C3111yescharacteristic
443C2×C4⋊C4C2×C4×C3111yescharacteristic
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4D4×C3111yescharacteristic
452C2×C22⋊C4D4×C3111yescharacteristic
453C2×C42—21no—
454C2×C42—21no—
455C2×C42C23×C3111yescharacteristic
456C4⋊C8—22no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—22no—
460C22⋊C8C23×C3112yes—
461C22⋊C8C23×C3112yes—
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95C23×C3111yescharacteristic
469#95C23×C3111yescharacteristic
470#95C23×C3111yescharacteristic
471#95C23×C3111yescharacteristic
472C31#1761511yescharacteristic, direct product factor, Sylow
473C24—21no—
474C24C2×D4×C3111yescharacteristic
475C24C2×D4×C3111yescharacteristic
476#41—82no—
477C2×Q8—21no—
478C2×Q8—81no—
479C2×Q8C22×C4×C3112yes—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—81no—
490C2×D4C22⋊C4×C3112yes—
491C2×D4C22⋊C4×C3112yes—
492C2×D4C22×C4×C3112yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4C22×C4×C3111yescharacteristic
508C22×C4C22×C4×C3111yescharacteristic
509C22×C4C22×C4×C3112yes—
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C2×D4×C3111yescharacteristic
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3112yes—
517C22×C4C24×C3111yescharacteristic
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—81no—
521C2×C8—81no—
522C2×C8—82no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—81no—
532C4⋊C4C22⋊C4×C3112yes—
533C4⋊C4C22⋊C4×C3112yes—
534C4⋊C4C22×C4×C3112yes—
535C4⋊C4C22×C4×C3112yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4C22⋊C4×C3112yes—
550C22⋊C4C22⋊C4×C3112yes—
551C22⋊C4C22⋊C4×C3112yes—
552C22⋊C4C22⋊C4×C3112yes—
553C42—22no—
554C42—22no—
555C42—42no—
556C42—81no—
557C42C22×C4×C3112yes—
558C42C2×D4×C3112yes—
559C23—21no—
560C23—21no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—42no—
567C23—81no—
568C23—81no—
569C23C2×C22⋊C4×C3112yes—
570C23C2×C22⋊C4×C3111yescharacteristic
571C23C2×C22⋊C4×C3111yescharacteristic
572C23C31×#13512yes—
573C23C31×#13512yes—
574C23C22×D4×C3111yescharacteristic
575Q8—42no—
576Q8—81no—
577D4—24no—
578D4—24no—
579D4—42no—
580D4—44no—
581D4—42no—
582D4—42no—
583D4—81no—
584D4—82no—
585D4—82no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—84no—
619C2×C4C2×C22⋊C4×C3112yes—
620C2×C4C2×C22⋊C4×C3112yes—
621C2×C4C2×C22⋊C4×C3112yes—
622C2×C4C2×C22⋊C4×C3111yescharacteristic
623C2×C4C2×C22⋊C4×C3111yescharacteristic
624C2×C4C23×C4×C3111yescharacteristic
625C2×C4C22×D4×C3111yescharacteristic
626C8—42no—
627C8—42no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—162no—
645C22C31×#41612yes—
646C22C31×#41612yes—
647C22C22×C22⋊C4×C3111yescharacteristic
648C22C2×C31×#13511yescharacteristic
649C22C2×C31×#13511yescharacteristic
650C4—21no—
651C4—21no—
652C4—22no—
653C4—21no—
654C4—21no—
655C4—22no—
656C4—22no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C2—21no—
665C2—21no—
666C2—22no—
667C2—22no—
668C2—42no—
669C2—82no—
670C2C31×#288311yescharacteristic
671C2C2×C31×#41611yescharacteristic
672C2C31×#290111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3505C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2972C2semidirect
3. C31×#2353C2semidirect
4. C31×#1521C2semidirect
5. C31×#1520C2semidirect
6. C31×#1519C2semidirect
7. C31×#1516C2semidirect
8. C31×#1501C2semidirect
9. C31×#1500C2semidirect
10. C2×C31×#328C2semidirect
11. C2×C31×#327C2semidirect
13. C31×#553C4semidirect
14. C31×#552C4semidirect
16. C31×#548C4semidirect
17. C31×#546C4semidirect
29. C31×#431C22semidirect
32. C2×C31×C22⋊C8C22semidirect
36. C31×#383C22semidirect
37. C31×#381C22semidirect
40. C4×C22⋊C4×C31C22semidirect
41. C31×#376C22semidirect
43. C31×#328C22semidirect
44. C31×#328C22semidirect
45. C31×#328C22semidirect
46. C31×#328C22semidirect
51. C2×#41×C31C2×C4semidirect
66. C31×#125C2×C4semidirect
68. C31×#124C2×C4semidirect
78. C31×C22⋊Q8C2×C4semidirect
86. C31×#121C2×C4semidirect
90. C4×Q8×C31C2×C4semidirect
98. C4×D4×C31C2×C4semidirect
103. C31×#117C2×C4semidirect
222. #17615C31direct (N × H)
293. #2972C2×C31semidirect
294. #2353C2×C31semidirect
295. #1521C2×C31semidirect
296. #1520C2×C31semidirect
297. #1519C2×C31semidirect
298. #1516C2×C31semidirect
299. #1501C2×C31semidirect
300. #1500C2×C31semidirect
301. C2×#328C2×C31semidirect
302. C2×#327C2×C31semidirect
340. #553C4×C31semidirect
341. #552C4×C31semidirect
343. #548C4×C31semidirect
344. #546C4×C31semidirect
356. #431C22×C31semidirect
359. C2×C22⋊C8C22×C31semidirect
363. #383C22×C31semidirect
364. #381C22×C31semidirect
367. C4×C22⋊C4C22×C31semidirect
368. #376C22×C31semidirect
370. #328C22×C31semidirect
371. #328C22×C31semidirect
372. #328C22×C31semidirect
373. #328C22×C31semidirect
387. C2×#41C2×C4×C31semidirect
402. #125C2×C4×C31semidirect
404. #124C2×C4×C31semidirect
414. C22⋊Q8C2×C4×C31semidirect
422. #121C2×C4×C31semidirect
426. C4×Q8C2×C4×C31semidirect
434. C4×D4C2×C4×C31semidirect
439. #117C2×C4×C31semidirect
472. C31#17615direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35052
C31×#29722
C31×#23532
C31×#15212
C31×#15202
C31×#15192
C31×#15162
C31×#15012
C31×#15002
C2×C31×#3282
C2×C31×#3272
#1761531