Finite Group Databasebeta

← C31×#18252 #21475011

Subgroups — C31×#18252 #21475011

Order 7936.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic, complemented
2C31×#3006C211yesmaximal, characteristic, complemented
3C31×#3002C211yesmaximal, characteristic, complemented
4C31×#2430C211yesmaximal, characteristic, complemented
5C31×#1606C211yesmaximal, characteristic, complemented
6C31×#1604C211yesmaximal, characteristic, complemented
7C31×#1603C211yesmaximal, characteristic, complemented
8C31×#1601C211yesmaximal, characteristic, complemented
9C31×#1600C211yesmaximal, characteristic, complemented
10C31×#1598C211yesmaximal, characteristic, complemented
11C31×#1597C211yesmaximal, characteristic, complemented
12C31×#1595C211yesmaximal, characteristic, complemented
13C31×#1504C211yesmaximal, characteristic, complemented
14C2×C31×#327C211yesmaximal, characteristic, complemented
15C31×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic, complemented
17C2×C31×AGL(1,ℤ/8)—21no—
18C2×C31×#135—21no—
19C31×#562—21no—
20C31×#560—21no—
21C31×#553—21no—
22C31×#551—21no—
23C31×#546—21no—
24C31×#546—21no—
25C31×#546—21no—
26D42×C31—21no—
27C31×#540—21no—
28C31×#539—21no—
29C31×#539C2211yescharacteristic
30C31×#538—21no—
31C31×#538C2211yescharacteristic
32C31×#537C2211yescharacteristic
33C31×#534—21no—
34C31×#534C2211yescharacteristic
35C31×#525C2211yescharacteristic
36C2×C31×#123C2211yescharacteristic
37C2×C31×#121—21no—
38C2×C31×#121C2211yescharacteristic
39C31×#452—21no—
40C31×#451C2211yescharacteristic, complemented
41C31×#450C2211yescharacteristic, complemented
42C31×#449—21no—
43C31×#449—21no—
44C31×#449—21no—
45C31×#448C2211yescharacteristic
46C31×#448C2211yescharacteristic, complemented
47C31×#448C2211yescharacteristic, complemented
48C31×#447C2211yescharacteristic
49C31×#447C2211yescharacteristic, complemented
50C31×#447C2211yescharacteristic, complemented
51C31×#417—21no—
52C31×#416—21no—
53C31×#407C2211yescharacteristic, complemented
54C2×C31×C22⋊C8C2211yescharacteristic, complemented
55C31×#395C2211yescharacteristic, complemented
56C31×#394C2211yescharacteristic, complemented
57C31×#393C2211yescharacteristic, complemented
58C31×#392C2211yescharacteristic, complemented
59C31×#386—21no—
60C31×#386—21no—
61C31×#385—21no—
62C2×C31×#95C2211yescharacteristic, complemented
63C31×#328C2211yescharacteristic, complemented
64C31×#328C2211yescharacteristic, complemented
65C31×#327C2211yescharacteristic
66C31×#327C2211yescharacteristic
67C31×#327C2211yescharacteristic, complemented
68C31×#327C2211yescharacteristic, complemented
69C31×#327C2211yescharacteristic, complemented
70C31×#327C2211yescharacteristic, complemented
71C31×#324C2211yescharacteristic, complemented
72C31×#324C2211yescharacteristic, complemented
73C31×#323C2211yescharacteristic, complemented
74C31×#323C2211yescharacteristic, complemented
75C2×#41×C31—21no—
76C2×#41×C31—21no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—44no—
81C2×#41×C31D411yescharacteristic, complemented
82C22×Q8×C31C2311yescharacteristic
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31—21no—
86C22×D4×C31—21no—
87C22×D4×C31—21no—
88C22×D4×C31D411yescharacteristic
89C22×D4×C31D411yescharacteristic, complemented
90C22×D4×C31C2311yescharacteristic
91C23×C4×C31—21no—
92C23×C4×C31—21no—
93C23×C4×C31C2311yescharacteristic
94C31×AGL(1,ℤ/8)—44no—
95C31×#135—44no—
96C2×Q16×C31—21no—
97C2×SD16×C31—21no—
98C2×SD16×C31—21no—
99C2×SD16×C31—21no—
100C2×SD16×C31—21no—
101C2×D8×C31—21no—
102C2×D8×C31—21no—
103C2×D8×C31—21no—
104C2×M16×C31—21no—
105C22×C8×C31—21no—
106C31×#127—21no—
107C31×#126—21no—
108C31×#126—21no—
109C31×#126—21no—
110C31×#126—21no—
111C31×#125—21no—
112C31×#125—21no—
113C31×#124—21no—
114C31×#124—21no—
115C31×#124—21no—
116C31×#123—21no—
117C31×#123—21no—
118C31×#123—21no—
119C31×#123—21no—
120C31×#123—21no—
121C31×#123—21no—
122C31×#123—21no—
123C31×#123—21no—
124C31×#123—21no—
125C31×#123—21no—
126C31×#123—21no—
127C31×#123—21no—
128C31×#123—21no—
129C31×#123—21no—
130C31×C22⋊Q8—21no—
131C31×C22⋊Q8—21no—
132C31×C22⋊Q8—21no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8D411yescharacteristic, complemented
136C31×C22⋊Q8C2311yescharacteristic
137C31×#121—21no—
138C31×#121—21no—
139C31×#121—21no—
140C31×#121—21no—
141C31×#121—21no—
142C31×#121—21no—
143C31×#121—21no—
144C31×#121—21no—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—21no—
149C31×#121—21no—
150C31×#121—21no—
151C31×#121—21no—
152C31×#121—44no—
153C31×#121D411yescharacteristic, complemented
154C31×#121D411yescharacteristic, complemented
155C31×#121D411yescharacteristic, complemented
156C31×#121C2311yescharacteristic
157C31×#121C2311yescharacteristic
158C31×#121C2311yescharacteristic
159C31×#120—21no—
160C31×#120—21no—
161C31×#120—21no—
162C31×#120—21no—
163C31×#120—21no—
164C31×#120—21no—
165C31×#120—21no—
166C31×#120—21no—
167C4×D4×C31—21no—
168C4×D4×C31—21no—
169C4×D4×C31—21no—
170C4×D4×C31—21no—
171C4×D4×C31—21no—
172C4×D4×C31—21no—
173C4×D4×C31—21no—
174C4×D4×C31—21no—
175C31×#117—21no—
176C31×#117D411yescharacteristic, complemented
177C2×C4⋊C4×C31—21no—
178C2×C4⋊C4×C31D411yescharacteristic
179C2×C4⋊C4×C31D411yescharacteristic, complemented
180C2×C4⋊C4×C31C2311yescharacteristic
181C2×C22⋊C4×C31—21no—
182C2×C22⋊C4×C31—21no—
183C2×C22⋊C4×C31—21no—
184C2×C22⋊C4×C31—21no—
185C2×C22⋊C4×C31—21no—
186C2×C22⋊C4×C31—21no—
187C2×C22⋊C4×C31—21no—
188C2×C22⋊C4×C31D411yescharacteristic
189C2×C22⋊C4×C31D411yescharacteristic
190C2×C22⋊C4×C31C2311yescharacteristic
191C31×#103—21no—
192C31×#103—21no—
193C31×#103—21no—
194C31×#103—21no—
195C31×#102—21no—
196C31×#102—21no—
197C31×#102—21no—
198C31×#102—21no—
199C31×C22⋊C8—21no—
200C31×C22⋊C8—21no—
201C31×C22⋊C8C2311yescharacteristic
202C31×C22⋊C8C2311yescharacteristic
203C31×C22⋊C8C2311yescharacteristic
204C31×C22⋊C8C2311yescharacteristic
205C31×#95—21no—
206C31×#95—21no—
207C31×#95—21no—
208C31×#95C2311yescharacteristic
209C31×#95C2311yescharacteristic
210C24×C31—21no—
211C24×C31—21no—
212C24×C31—21no—
213C24×C31C2×D411yescharacteristic
214C24×C31C2×D411yescharacteristic
215#41×C31—24no—
216#41×C31—24no—
217#41×C31—42no—
218#41×C31—42no—
219#41×C31—42no—
220#41×C31—42no—
221#41×C31—42no—
222#41×C31—42no—
223#41×C31—42no—
224#41×C31—81no—
225#41×C31—81no—
226C2×Q8×C31—21no—
227C2×Q8×C31—21no—
228C2×Q8×C31—21no—
229C2×Q8×C31—42no—
230C2×Q8×C31C2×D411yescharacteristic
231C2×D4×C31—24no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—21no—
239C2×D4×C31—21no—
240C2×D4×C31—21no—
241C2×D4×C31—21no—
242C2×D4×C31—21no—
243C2×D4×C31—21no—
244C2×D4×C31—21no—
245C2×D4×C31—21no—
246C2×D4×C31—21no—
247C2×D4×C31—21no—
248C2×D4×C31—21no—
249C2×D4×C31—21no—
250C2×D4×C31—21no—
251C2×D4×C31—42no—
252C2×D4×C31—42no—
253C2×D4×C31—42no—
254C2×D4×C31—42no—
255C2×D4×C31—41no—
256C2×D4×C31—41no—
257C2×D4×C31—42no—
258C2×D4×C31—42no—
259C2×D4×C31—81no—
260C2×D4×C31—81no—
261C2×D4×C31—81no—
262C2×D4×C31—81no—
263C2×D4×C31—81no—
264C2×D4×C31—82no—
265C2×D4×C31C2×D411yescharacteristic
266C2×D4×C31C2×D411yescharacteristic
267C2×D4×C31C2×D411yescharacteristic
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—42no—
279C22×C4×C31—42no—
280C22×C4×C31—42no—
281C22×C4×C31—42no—
282C22×C4×C31—41no—
283C22×C4×C31—41no—
284C22×C4×C31—42no—
285C22×C4×C31—81no—
286C22×C4×C31C2×D411yescharacteristic
287C22×C4×C31C2×D411yescharacteristic
288C22×C4×C31C2×D411yescharacteristic
289C22×C4×C31C2×D411yescharacteristic
290C22×C4×C31C2×D411yescharacteristic
291C22×C4×C31C2×D411yescharacteristic
292C22×C4×C31C2×D411yescharacteristic
293C22×C4×C31C2×D411yescharacteristic
294C22×C4×C31C2411yescharacteristic
295Q16×C31—42no—
296SD16×C31—42no—
297SD16×C31—42no—
298SD16×C31—42no—
299SD16×C31—42no—
300D8×C31—42no—
301D8×C31—42no—
302D8×C31—42no—
303M16×C31—42no—
304C2×C8×C31—21no—
305C2×C8×C31—21no—
306C2×C8×C31—21no—
307C2×C8×C31—21no—
308C2×C8×C31—42no—
309C4⋊C4×C31—21no—
310C4⋊C4×C31—21no—
311C4⋊C4×C31—21no—
312C4⋊C4×C31—21no—
313C4⋊C4×C31—21no—
314C4⋊C4×C31—21no—
315C4⋊C4×C31—21no—
316C4⋊C4×C31—21no—
317C4⋊C4×C31—21no—
318C4⋊C4×C31—21no—
319C4⋊C4×C31—21no—
320C4⋊C4×C31—21no—
321C4⋊C4×C31—21no—
322C4⋊C4×C31—42no—
323C4⋊C4×C31C2×D411yescharacteristic
324C4⋊C4×C31C2×D411yescharacteristic
325C4⋊C4×C31C2×D411yescharacteristic
326C4⋊C4×C31C2×D411yescharacteristic
327C22⋊C4×C31—21no—
328C22⋊C4×C31—21no—
329C22⋊C4×C31—21no—
330C22⋊C4×C31—21no—
331C22⋊C4×C31—21no—
332C22⋊C4×C31—21no—
333C22⋊C4×C31—21no—
334C22⋊C4×C31—21no—
335C22⋊C4×C31—21no—
336C22⋊C4×C31—21no—
337C22⋊C4×C31—21no—
338C22⋊C4×C31—21no—
339C22⋊C4×C31—21no—
340C22⋊C4×C31—21no—
341C22⋊C4×C31—21no—
342C22⋊C4×C31—21no—
343C22⋊C4×C31—21no—
344C22⋊C4×C31—21no—
345C22⋊C4×C31—21no—
346C22⋊C4×C31—21no—
347C22⋊C4×C31—21no—
348C22⋊C4×C31—21no—
349C22⋊C4×C31—21no—
350C22⋊C4×C31—21no—
351C22⋊C4×C31—21no—
352C22⋊C4×C31—42no—
353C22⋊C4×C31—42no—
354C22⋊C4×C31—42no—
355C22⋊C4×C31—81no—
356C42×C31—21no—
357C42×C31—21no—
358C42×C31—21no—
359#18252C3111yesmaximal, characteristic, direct product factor, Sylow
360C23×C31—21no—
361C23×C31—21no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—21no—
365C23×C31—21no—
366C23×C31—21no—
367C23×C31—21no—
368C23×C31—21no—
369C23×C31—21no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—42no—
380C23×C31—81no—
381C23×C31—81no—
382C23×C31—81no—
383C23×C31—81no—
384C23×C31—81no—
385C23×C31#12011yescharacteristic
386C23×C31#12011yescharacteristic
387C23×C31C22×D411yescharacteristic
388Q8×C31—22no—
389Q8×C31—22no—
390Q8×C31—41no—
391Q8×C31—41no—
392Q8×C31—41no—
393Q8×C31—81no—
394D4×C31—22no—
395D4×C31—22no—
396D4×C31—41no—
397D4×C31—41no—
398D4×C31—41no—
399D4×C31—41no—
400D4×C31—41no—
401D4×C31—44no—
402D4×C31—41no—
403D4×C31—41no—
404D4×C31—41no—
405D4×C31—41no—
406D4×C31—41no—
407D4×C31—41no—
408D4×C31—44no—
409D4×C31—42no—
410D4×C31—42no—
411D4×C31—81no—
412D4×C31—81no—
413D4×C31—81no—
414D4×C31—81no—
415D4×C31—81no—
416D4×C31—81no—
417D4×C31—81no—
418D4×C31—81no—
419D4×C31—81no—
420D4×C31—81no—
421D4×C31—81no—
422D4×C31—81no—
423D4×C31—84no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—21no—
429C2×C4×C31—21no—
430C2×C4×C31—21no—
431C2×C4×C31—21no—
432C2×C4×C31—21no—
433C2×C4×C31—21no—
434C2×C4×C31—21no—
435C2×C4×C31—21no—
436C2×C4×C31—21no—
437C2×C4×C31—21no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—44no—
443C2×C4×C31—44no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—81no—
454C2×C4×C31—81no—
455C2×C4×C31—81no—
456C2×C4×C31—81no—
457C2×C4×C31—81no—
458C2×C4×C31—81no—
459C2×C4×C31—81no—
460C2×C4×C31—84no—
461C2×C4×C31#12011yescharacteristic
462C2×C4×C31#12011yescharacteristic
463C2×C4×C31C22×D411yescharacteristic
464C2×C4×C31C22×D411yescharacteristic
465C8×C31—41no—
466C8×C31—41no—
467C8×C31—41no—
468C8×C31—41no—
469#3534C2×C3111yescharacteristic, complemented
470#3006C2×C3111yescharacteristic, complemented
471#3002C2×C3111yescharacteristic, complemented
472#2430C2×C3111yescharacteristic, complemented
473#1606C2×C3111yescharacteristic, complemented
474#1604C2×C3111yescharacteristic, complemented
475#1603C2×C3111yescharacteristic, complemented
476#1601C2×C3111yescharacteristic, complemented
477#1600C2×C3111yescharacteristic, complemented
478#1598C2×C3111yescharacteristic, complemented
479#1597C2×C3111yescharacteristic, complemented
480#1595C2×C3111yescharacteristic, complemented
481#1504C2×C3111yescharacteristic, complemented
482C2×#327C2×C3111yescharacteristic, complemented
483#1468C2×C3111yescharacteristic, complemented
484C22×C31—21no—
485C22×C31—21no—
486C22×C31—21no—
487C22×C31—21no—
488C22×C31—21no—
489C22×C31—21no—
490C22×C31—21no—
491C22×C31—42no—
492C22×C31—42no—
493C22×C31—42no—
494C22×C31—42no—
495C22×C31—41no—
496C22×C31—41no—
497C22×C31—41no—
498C22×C31—41no—
499C22×C31—41no—
500C22×C31—41no—
501C22×C31—41no—
502C22×C31—41no—
503C22×C31—42no—
504C22×C31—41no—
505C22×C31—41no—
506C22×C31—41no—
507C22×C31—41no—
508C22×C31—81no—
509C22×C31—81no—
510C22×C31—81no—
511C22×C31—81no—
512C22×C31—81no—
513C22×C31—81no—
514C22×C31—162no—
515C22×C31—162no—
516C22×C31B(4,𝔽2)12yes—
517C22×C31C2×#12011yescharacteristic
518C22×C31#57611yescharacteristic
519C22×C31#57711yescharacteristic
520C4×C31—21no—
521C4×C31—21no—
522C4×C31—21no—
523C4×C31—21no—
524C4×C31—42no—
525C4×C31—41no—
526C4×C31—41no—
527C4×C31—41no—
528C4×C31—41no—
529C4×C31—41no—
530C4×C31—41no—
531C4×C31—42no—
532C4×C31—41no—
533C4×C31—41no—
534C4×C31—81no—
535C22×#41C22×C3111yescharacteristic, complemented
536C2×AGL(1,ℤ/8)—21no—
537C2×#135—21no—
538#562—21no—
539#560—21no—
540#553—21no—
541#551—21no—
542#546—21no—
543#546—21no—
544#546—21no—
545D42—21no—
546#540—21no—
547#539—21no—
548#539C22×C3111yescharacteristic
549#538—21no—
550#538C22×C3111yescharacteristic
551#537C22×C3111yescharacteristic
552#534—21no—
553#534C22×C3111yescharacteristic
554#525C22×C3111yescharacteristic
555C2×#123C22×C3111yescharacteristic
556C2×#121—21no—
557C2×#121C22×C3111yescharacteristic
558#452—21no—
559#451C22×C3111yescharacteristic, complemented
560#450C22×C3111yescharacteristic, complemented
561#449—21no—
562#449—21no—
563#449—21no—
564#448C22×C3111yescharacteristic
565#448C22×C3111yescharacteristic, complemented
566#448C22×C3111yescharacteristic, complemented
567#447C22×C3111yescharacteristic
568#447C22×C3111yescharacteristic, complemented
569#447C22×C3111yescharacteristic, complemented
570#417—21no—
571#416—21no—
572#407C22×C3111yescharacteristic, complemented
573C2×C22⋊C8C22×C3111yescharacteristic, complemented
574#395C22×C3111yescharacteristic, complemented
575#394C22×C3111yescharacteristic, complemented
576#393C22×C3111yescharacteristic, complemented
577#392C22×C3111yescharacteristic, complemented
578#386—21no—
579#386—21no—
580#385—21no—
581C2×#95C22×C3111yescharacteristic, complemented
582#328C22×C3111yescharacteristic, complemented
583#328C22×C3111yescharacteristic, complemented
584#327C22×C3111yescharacteristic
585#327C22×C3111yescharacteristic
586#327C22×C3111yescharacteristic, complemented
587#327C22×C3111yescharacteristic, complemented
588#327C22×C3111yescharacteristic, complemented
589#327C22×C3111yescharacteristic, complemented
590#324C22×C3111yescharacteristic, complemented
591#324C22×C3111yescharacteristic, complemented
592#323C22×C3111yescharacteristic, complemented
593#323C22×C3111yescharacteristic, complemented
594C2×C31—21no—
595C2×C31—21no—
596C2×C31—22no—
597C2×C31—41no—
598C2×C31—82no—
599C2×C31—81no—
600C2×C31—81no—
601C2×C31—81no—
602C2×C31—81no—
603C2×C31#301211yescharacteristic
604C2×C31#301811yescharacteristic
605C2×C31C2×B(4,𝔽2)11yescharacteristic
606C2×#41—21no—
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—44no—
612C2×#41D4×C3111yescharacteristic, complemented
613C22×Q8C23×C3111yescharacteristic
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C3111yescharacteristic
620C22×D4D4×C3111yescharacteristic, complemented
621C22×D4C23×C3111yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4C23×C3111yescharacteristic
625AGL(1,ℤ/8)—44no—
626#135—44no—
627C2×Q16—21no—
628C2×SD16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×D8—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×M16—21no—
636C22×C8—21no—
637#127—21no—
638#126—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#125—21no—
643#125—21no—
644#124—21no—
645#124—21no—
646#124—21no—
647#123—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8D4×C3111yescharacteristic, complemented
667C22⋊Q8C23×C3111yescharacteristic
668#121—21no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—44no—
684#121D4×C3111yescharacteristic, complemented
685#121D4×C3111yescharacteristic, complemented
686#121D4×C3111yescharacteristic, complemented
687#121C23×C3111yescharacteristic
688#121C23×C3111yescharacteristic
689#121C23×C3111yescharacteristic
690#120—21no—
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706#117—21no—
707#117D4×C3111yescharacteristic, complemented
708C2×C4⋊C4—21no—
709C2×C4⋊C4D4×C3111yescharacteristic
710C2×C4⋊C4D4×C3111yescharacteristic, complemented
711C2×C4⋊C4C23×C3111yescharacteristic
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4D4×C3111yescharacteristic
720C2×C22⋊C4D4×C3111yescharacteristic
721C2×C22⋊C4C23×C3111yescharacteristic
722#103—21no—
723#103—21no—
724#103—21no—
725#103—21no—
726#102—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730C22⋊C8—21no—
731C22⋊C8—21no—
732C22⋊C8C23×C3111yescharacteristic
733C22⋊C8C23×C3111yescharacteristic
734C22⋊C8C23×C3111yescharacteristic
735C22⋊C8C23×C3111yescharacteristic
736#95—21no—
737#95—21no—
738#95—21no—
739#95C23×C3111yescharacteristic
740#95C23×C3111yescharacteristic
741C31#1825211yescharacteristic, direct product factor, Sylow
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C3111yescharacteristic
746C24C2×D4×C3111yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C3111yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C3111yescharacteristic
798C2×D4C2×D4×C3111yescharacteristic
799C2×D4C2×D4×C3111yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C3111yescharacteristic
819C22×C4C2×D4×C3111yescharacteristic
820C22×C4C2×D4×C3111yescharacteristic
821C22×C4C2×D4×C3111yescharacteristic
822C22×C4C2×D4×C3111yescharacteristic
823C22×C4C2×D4×C3111yescharacteristic
824C22×C4C2×D4×C3111yescharacteristic
825C22×C4C2×D4×C3111yescharacteristic
826C22×C4C24×C3111yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C3111yescharacteristic
856C4⋊C4C2×D4×C3111yescharacteristic
857C4⋊C4C2×D4×C3111yescharacteristic
858C4⋊C4C2×D4×C3111yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23C31×#12011yescharacteristic
917C23C31×#12011yescharacteristic
918C23C22×D4×C3111yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4C31×#12011yescharacteristic
993C2×C4C31×#12011yescharacteristic
994C2×C4C22×D4×C3111yescharacteristic
995C2×C4C22×D4×C3111yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C31×B(4,𝔽2)12yes—
1033C22C2×C31×#12011yescharacteristic
1034C22C31×#57611yescharacteristic
1035C22C31×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C31×#301211yescharacteristic
1061C2C31×#301811yescharacteristic
1062C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3534C2semidirect
2. C31×#3006C2semidirect
3. C31×#3002C2semidirect
4. C31×#2430C2semidirect
5. C31×#1606C2semidirect
6. C31×#1604C2semidirect
7. C31×#1603C2semidirect
8. C31×#1601C2semidirect
9. C31×#1600C2semidirect
10. C31×#1598C2semidirect
11. C31×#1597C2semidirect
12. C31×#1595C2semidirect
13. C31×#1504C2semidirect
14. C2×C31×#327C2semidirect
15. C31×#1468C2semidirect
16. C22×#41×C31C22semidirect
40. C31×#451C22semidirect
41. C31×#450C22semidirect
46. C31×#448C22semidirect
47. C31×#448C22semidirect
49. C31×#447C22semidirect
50. C31×#447C22semidirect
53. C31×#407C22semidirect
54. C2×C31×C22⋊C8C22semidirect
55. C31×#395C22semidirect
56. C31×#394C22semidirect
57. C31×#393C22semidirect
58. C31×#392C22semidirect
62. C2×C31×#95C22semidirect
63. C31×#328C22semidirect
64. C31×#328C22semidirect
67. C31×#327C22semidirect
68. C31×#327C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#324C22semidirect
72. C31×#324C22semidirect
73. C31×#323C22semidirect
74. C31×#323C22semidirect
81. C2×#41×C31D4semidirect
89. C22×D4×C31D4semidirect
135. C31×C22⋊Q8D4semidirect
153. C31×#121D4semidirect
154. C31×#121D4semidirect
155. C31×#121D4semidirect
176. C31×#117D4semidirect
179. C2×C4⋊C4×C31D4semidirect
359. #18252C31direct (N × H)
469. #3534C2×C31semidirect
470. #3006C2×C31semidirect
471. #3002C2×C31semidirect
472. #2430C2×C31semidirect
473. #1606C2×C31semidirect
474. #1604C2×C31semidirect
475. #1603C2×C31semidirect
476. #1601C2×C31semidirect
477. #1600C2×C31semidirect
478. #1598C2×C31semidirect
479. #1597C2×C31semidirect
480. #1595C2×C31semidirect
481. #1504C2×C31semidirect
482. C2×#327C2×C31semidirect
483. #1468C2×C31semidirect
535. C22×#41C22×C31semidirect
559. #451C22×C31semidirect
560. #450C22×C31semidirect
565. #448C22×C31semidirect
566. #448C22×C31semidirect
568. #447C22×C31semidirect
569. #447C22×C31semidirect
572. #407C22×C31semidirect
573. C2×C22⋊C8C22×C31semidirect
574. #395C22×C31semidirect
575. #394C22×C31semidirect
576. #393C22×C31semidirect
577. #392C22×C31semidirect
581. C2×#95C22×C31semidirect
582. #328C22×C31semidirect
583. #328C22×C31semidirect
586. #327C22×C31semidirect
587. #327C22×C31semidirect
588. #327C22×C31semidirect
589. #327C22×C31semidirect
590. #324C22×C31semidirect
591. #324C22×C31semidirect
592. #323C22×C31semidirect
593. #323C22×C31semidirect
612. C2×#41D4×C31semidirect
620. C22×D4D4×C31semidirect
666. C22⋊Q8D4×C31semidirect
684. #121D4×C31semidirect
685. #121D4×C31semidirect
686. #121D4×C31semidirect
707. #117D4×C31semidirect
710. C2×C4⋊C4D4×C31semidirect
741. C31#18252direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35342
C31×#30062
C31×#30022
C31×#24302
C31×#16062
C31×#16042
C31×#16032
C31×#16012
C31×#16002
C31×#15982
C31×#15972
C31×#15952
C31×#15042
C2×C31×#3272
C31×#14682
#1825231