Finite Group Databasebeta

← C31×#8442 #21465201

Subgroups — C31×#8442 #21465201

Order 7936.

794 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3482C211yesmaximal, characteristic
2C31×#1994C211yesmaximal, characteristic, complemented
3C4×C31×#104C211yesmaximal, characteristic, complemented
4C4×C31×#104C211yesmaximal, characteristic, complemented
5C31×#1526C211yesmaximal, characteristic, complemented
6C31×#1489C211yesmaximal, characteristic, complemented
7C31×#1489C211yesmaximal, characteristic, complemented
8C31×#557C411yescharacteristic, complemented
9C31×#556—21no—
10C31×#556C411yescharacteristic, complemented
11C31×#552—22no—
12C31×#552—21no—
13D4×Q8×C31C411yescharacteristic, complemented
14C31×#548—21no—
15C31×#547—21no—
16C31×#547C411yescharacteristic, complemented
17C31×#533—21no—
18C31×#533C2211yescharacteristic
19C31×#529—21no—
20C31×#529—22no—
21C4×#41×C31—21no—
22C4×#41×C31C2211yescharacteristic
23C4×#41×C31C2211yescharacteristic
24C2×C4×Q8×C31—21no—
25C31×#423C2211yescharacteristic
26C2×C31×#104—21no—
27C2×C31×#104—21no—
28C4×M16×C31C2211yescharacteristic
29C4×M16×C31C2211yescharacteristic
30C43×C31C2211yescharacteristic
31C31×#339—22no—
32C31×#339—21no—
33C31×#339—21no—
34C31×#330—22no—
35C31×Q8⋊C8—21no—
36C31×Q8⋊C8—21no—
37C31×D4⋊C8—21no—
38C31×D4⋊C8—21no—
39C2×#41×C31—21no—
40C2×#41×C31D411yescharacteristic
41C2×#41×C31D411yescharacteristic
42C22×Q8×C31—21no—
43C2×M16×C31—21no—
44C2×M16×C31—21no—
45C2×M16×C31—21no—
46C31×C4⋊Q8—21no—
47C31×C4⋊Q8—21no—
48C31×C4⋊Q8C2×C411yescharacteristic
49C31×C4⋊Q8C2×C411yescharacteristic
50C31×#126—22no—
51C31×#126—22no—
52C31×#126—22no—
53C31×#125—22no—
54C31×#125—22no—
55C31×#125—21no—
56C31×#125D412yes—
57C31×#124—22no—
58C31×#124—21no—
59C31×#123—22no—
60C31×#123—22no—
61C31×#123—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—21no—
64C31×C22⋊Q8—21no—
65C31×C22⋊Q8—21no—
66C31×C22⋊Q8—21no—
67C31×C22⋊Q8—22no—
68C31×C22⋊Q8—21no—
69C31×#121—22no—
70C31×#121—21no—
71C4×Q8×C31—22no—
72C4×Q8×C31—22no—
73C4×Q8×C31—21no—
74C4×Q8×C31—21no—
75C4×Q8×C31—21no—
76C4×Q8×C31—21no—
77C4×Q8×C31—21no—
78C4×Q8×C31C2×C411yescharacteristic
79C4×Q8×C31C2×C411yescharacteristic
80C4×Q8×C31D411yescharacteristic
81C4×Q8×C31D411yescharacteristic
82C4×D4×C31—22no—
83C4×D4×C31—22no—
84C4×D4×C31—21no—
85C4×D4×C31—21no—
86C4×D4×C31—21no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C4×D4×C31C2×C411yescharacteristic
90C4×D4×C31C2×C411yescharacteristic
91C4×D4×C31D411yescharacteristic
92C4×D4×C31D411yescharacteristic
93C31×#117—22no—
94C31×#117—22no—
95C31×#117—21no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117D411yescharacteristic
99C31×#117D411yescharacteristic
100C31×#117D412yes—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—21no—
103C2×C42×C31—22no—
104C2×C42×C31—21no—
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C31×C4⋊C8—21no—
111C31×C4⋊C8—21no—
112C31×#104—24no—
113C31×#104—24no—
114C31×#97—21no—
115C31×#97—21no—
116C4×C8×C31—21no—
117C4×C8×C31—21no—
118#41×C31—22no—
119#41×C31—22no—
120#41×C31—41no—
121#41×C31—41no—
122#41×C31—42no—
123#41×C31—42no—
124C2×Q8×C31—22no—
125C2×Q8×C31—21no—
126C2×Q8×C31—21no—
127C2×Q8×C31—42no—
128C2×Q8×C31—42no—
129C2×Q8×C31C22⋊C411yescharacteristic
130C2×Q8×C31C22⋊C411yescharacteristic
131C2×D4×C31—22no—
132C2×D4×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31C22⋊C411yescharacteristic
135C2×D4×C31C22⋊C411yescharacteristic
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—41no—
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148M16×C31—22no—
149M16×C31—22no—
150M16×C31—41no—
151M16×C31—41no—
152M16×C31—42no—
153C2×C8×C31—41no—
154C2×C8×C31—41no—
155C2×C8×C31—41no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31C22⋊C411yescharacteristic
171C4⋊C4×C31C22⋊C411yescharacteristic
172C4⋊C4×C31C22⋊C411yescharacteristic
173C4⋊C4×C31C22⋊C411yescharacteristic
174C4⋊C4×C31C22⋊C412yes—
175C4⋊C4×C31C22⋊C412yes—
176C22⋊C4×C31—22no—
177C22⋊C4×C31—22no—
178C22⋊C4×C31—22no—
179C22⋊C4×C31—22no—
180C22⋊C4×C31—21no—
181C22⋊C4×C31—21no—
182C22⋊C4×C31—22no—
183C22⋊C4×C31—21no—
184C22⋊C4×C31—21no—
185C22⋊C4×C31—21no—
186C22⋊C4×C31—21no—
187C42×C31—22no—
188C42×C31—22no—
189C42×C31—21no—
190C42×C31—21no—
191C42×C31—21no—
192C42×C31—21no—
193C42×C31—21no—
194C42×C31—21no—
195C42×C31—22no—
196C42×C31—22no—
197C42×C31—22no—
198C42×C31—22no—
199C42×C31—41no—
200C42×C31—41no—
201C42×C31—41no—
202C42×C31C22×C411yescharacteristic
203C42×C31C2×D411yescharacteristic
204C42×C31C2×D411yescharacteristic
205C42×C31C2×D411yescharacteristic
206#8442C3111yesmaximal, characteristic, direct product factor, Sylow
207C23×C31—21no—
208C23×C31—21no—
209C23×C31#12011yescharacteristic
210Q8×C31—21no—
211Q8×C31—21no—
212Q8×C31—21no—
213Q8×C31—44no—
214Q8×C31—41no—
215Q8×C31—41no—
216Q8×C31—41no—
217Q8×C31—41no—
218Q8×C31#10412yescomplemented
219D4×C31—21no—
220D4×C31—21no—
221D4×C31—21no—
222D4×C31—42no—
223D4×C31—42no—
224D4×C31—44no—
225D4×C31#10412yescomplemented
226C2×C4×C31—21no—
227C2×C4×C31—21no—
228C2×C4×C31—21no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—22no—
237C2×C4×C31—21no—
238C2×C4×C31—21no—
239C2×C4×C31—22no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—44no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—44no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31C2×C22⋊C411yescharacteristic
256C2×C4×C31C2×C22⋊C411yescharacteristic
257C2×C4×C31C2×C22⋊C411yescharacteristic
258C2×C4×C31#12011yescharacteristic
259C2×C4×C31#12011yescharacteristic
260C2×C4×C31#12011yescharacteristic
261C8×C31—42no—
262C8×C31—42no—
263C8×C31—81no—
264#3482C2×C3111yescharacteristic
265#1994C2×C3111yescharacteristic, complemented
266C4×#104C2×C3111yescharacteristic, complemented
267C4×#104C2×C3111yescharacteristic, complemented
268#1526C2×C3111yescharacteristic, complemented
269#1489C2×C3111yescharacteristic, complemented
270#1489C2×C3111yescharacteristic, complemented
271C22×C31—21no—
272C22×C31—21no—
273C22×C31—21no—
274C22×C31—22no—
275C22×C31—41no—
276C22×C31—41no—
277C22×C31—41no—
278C22×C31—41no—
279C22×C31—41no—
280C22×C31#37911yescharacteristic
281C4×C31—21no—
282C4×C31—21no—
283C4×C31—21no—
284C4×C31—22no—
285C4×C31—44no—
286C4×C31—41no—
287C4×C31—41no—
288C4×C31—41no—
289C4×C31—41no—
290C4×C31—42no—
291C4×C31—42no—
292C4×C31—41no—
293C4×C31C2×#10411yescharacteristic
294C4×C31C2×#10411yescharacteristic
295C4×C31#42111yescharacteristic
296C4×C31#42111yescharacteristic
297C4×C31#45411yescharacteristic
298C4×C31#45611yescharacteristic
299#557C4×C3111yescharacteristic, complemented
300#556—21no—
301#556C4×C3111yescharacteristic, complemented
302#552—22no—
303#552—21no—
304D4×Q8C4×C3111yescharacteristic, complemented
305#548—21no—
306#547—21no—
307#547C4×C3111yescharacteristic, complemented
308#533—21no—
309#533C22×C3111yescharacteristic
310#529—21no—
311#529—22no—
312C4×#41—21no—
313C4×#41C22×C3111yescharacteristic
314C4×#41C22×C3111yescharacteristic
315C2×C4×Q8—21no—
316#423C22×C3111yescharacteristic
317C2×#104—21no—
318C2×#104—21no—
319C4×M16C22×C3111yescharacteristic
320C4×M16C22×C3111yescharacteristic
321C43C22×C3111yescharacteristic
322#339—22no—
323#339—21no—
324#339—21no—
325#330—22no—
326Q8⋊C8—21no—
327Q8⋊C8—21no—
328D4⋊C8—21no—
329D4⋊C8—21no—
330C2×C31—41no—
331C2×C31—42no—
332C2×C31—81no—
333C2×C31#178911yescharacteristic
334C2×C31#178911yescharacteristic
335C2×C31#179311yescharacteristic
336C2×#41—21no—
337C2×#41D4×C3111yescharacteristic
338C2×#41D4×C3111yescharacteristic
339C22×Q8—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8C2×C4×C3111yescharacteristic
346C4⋊Q8C2×C4×C3111yescharacteristic
347#126—22no—
348#126—22no—
349#126—22no—
350#125—22no—
351#125—22no—
352#125—21no—
353#125D4×C3112yes—
354#124—22no—
355#124—21no—
356#123—22no—
357#123—22no—
358#123—22no—
359C22⋊Q8—22no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366#121—22no—
367#121—21no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C2×C4×C3111yescharacteristic
376C4×Q8C2×C4×C3111yescharacteristic
377C4×Q8D4×C3111yescharacteristic
378C4×Q8D4×C3111yescharacteristic
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C2×C4×C3111yescharacteristic
387C4×D4C2×C4×C3111yescharacteristic
388C4×D4D4×C3111yescharacteristic
389C4×D4D4×C3111yescharacteristic
390#117—22no—
391#117—22no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117D4×C3111yescharacteristic
396#117D4×C3111yescharacteristic
397#117D4×C3112yes—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C42—22no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42C23×C3111yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409#104—24no—
410#104—24no—
411#97—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C31#844211yescharacteristic, direct product factor, Sylow
416#41—22no—
417#41—22no—
418#41—41no—
419#41—41no—
420#41—42no—
421#41—42no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8C22⋊C4×C3111yescharacteristic
428C2×Q8C22⋊C4×C3111yescharacteristic
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C22⋊C4×C3111yescharacteristic
433C2×D4C22⋊C4×C3111yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4C2×D4×C3111yescharacteristic
444C22×C4C2×D4×C3111yescharacteristic
445C22×C4C2×D4×C3111yescharacteristic
446M16—22no—
447M16—22no—
448M16—41no—
449M16—41no—
450M16—42no—
451C2×C8—41no—
452C2×C8—41no—
453C2×C8—41no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4C22⋊C4×C3111yescharacteristic
469C4⋊C4C22⋊C4×C3111yescharacteristic
470C4⋊C4C22⋊C4×C3111yescharacteristic
471C4⋊C4C22⋊C4×C3111yescharacteristic
472C4⋊C4C22⋊C4×C3112yes—
473C4⋊C4C22⋊C4×C3112yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C42—22no—
486C42—22no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—22no—
493C42—21no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—41no—
498C42—41no—
499C42—41no—
500C42C22×C4×C3111yescharacteristic
501C42C2×D4×C3111yescharacteristic
502C42C2×D4×C3111yescharacteristic
503C42C2×D4×C3111yescharacteristic
504C23—21no—
505C23—21no—
506C23C31×#12011yescharacteristic
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—44no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8C31×#10412yescomplemented
516D4—21no—
517D4—21no—
518D4—21no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4C31×#10412yescomplemented
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4C2×C22⋊C4×C3111yescharacteristic
553C2×C4C2×C22⋊C4×C3111yescharacteristic
554C2×C4C2×C22⋊C4×C3111yescharacteristic
555C2×C4C31×#12011yescharacteristic
556C2×C4C31×#12011yescharacteristic
557C2×C4C31×#12011yescharacteristic
558C8—42no—
559C8—42no—
560C8—81no—
561C22—21no—
562C22—21no—
563C22—22no—
564C22—21no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22C31×#37911yescharacteristic
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—44no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4C2×C31×#10411yescharacteristic
584C4C2×C31×#10411yescharacteristic
585C4C31×#42111yescharacteristic
586C4C31×#42111yescharacteristic
587C4C31×#45411yescharacteristic
588C4C31×#45611yescharacteristic
589C2—41no—
590C2—42no—
591C2—81no—
592C2C31×#178911yescharacteristic
593C2C31×#178911yescharacteristic
594C2C31×#179311yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#379
prime radicalC31×#3482C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1994C2semidirect
3. C4×C31×#104C2semidirect
4. C4×C31×#104C2semidirect
5. C31×#1526C2semidirect
6. C31×#1489C2semidirect
7. C31×#1489C2semidirect
8. C31×#557C4semidirect
10. C31×#556C4semidirect
13. D4×Q8×C31C4semidirect
16. C31×#547C4semidirect
206. #8442C31direct (N × H)
218. Q8×C31#104semidirect
225. D4×C31#104semidirect
265. #1994C2×C31semidirect
266. C4×#104C2×C31semidirect
267. C4×#104C2×C31semidirect
268. #1526C2×C31semidirect
269. #1489C2×C31semidirect
270. #1489C2×C31semidirect
299. #557C4×C31semidirect
301. #556C4×C31semidirect
304. D4×Q8C4×C31semidirect
307. #547C4×C31semidirect
415. C31#8442direct (N × H)
515. Q8C31×#104semidirect
522. D4C31×#104semidirect

Maximal subgroups

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

subgroupindex
C31×#34822
C31×#19942
C4×C31×#1042
C31×#15262
C31×#14892
#844231