Finite Group Databasebeta

← C31×#13976 #21470735

Subgroups — C31×#13976 #21470735

Order 7936.

1838 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic
4C2×C31×#389C211yesmaximal, characteristic
5C2×C31×#384C211yesmaximal, characteristic
6C31×#1444C214yesmaximal
7C31×#1436C214yesmaximal
8C31×C4⋊#95C211yesmaximal, characteristic
9C4×C31×#95C211yesmaximal, characteristic
10C23×Q8×C31C2211yescharacteristic
11C2×C4×Q8×C31—24no—
12C2×C4×Q8×C31—24no—
13C2×C4×Q8×C31—24no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2214yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C42×C31C2212yes—
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C31×#391—24no—
25C31×#391C418yescomplemented
26C31×#389—24no—
27C31×#384—24no—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2214yes—
31C2×C31×#95C2214yes—
32C2×C31×#95C2214yes—
33C2×C31×#95C2212yes—
34C22×Q8×C31—22no—
35C22×Q8×C31—22no—
36C22×Q8×C31—22no—
37C22×Q8×C31—22no—
38C22×Q8×C31C2×C414yes—
39C22×Q8×C31D414yes—
40C22×Q8×C31Q814yes—
41C23×C4×C31C2312yes—
42C23×C4×C31C2312yes—
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C4×Q8×C31—232no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—28no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—28no—
64C2×C4⋊C4×C31—44no—
65C2×C4⋊C4×C31—44no—
66C2×C4⋊C4×C31C2×C414yes—
67C2×C4⋊C4×C31D414yes—
68C2×C42×C31—24no—
69C2×C42×C31—24no—
70C2×C42×C31—24no—
71C2×C42×C31—22no—
72C2×C42×C31—22no—
73C2×C42×C31—22no—
74C2×C42×C31—22no—
75C2×C42×C31—22no—
76C2×C42×C31—22no—
77C2×C42×C31—22no—
78C2×C42×C31C2×C414yes—
79C2×C42×C31D414yes—
80C31×#95—24no—
81C31×#95—28no—
82C31×#95—24no—
83C31×#95—44no—
84C31×#95C2×C4116yes—
85C31×#95Q818yescomplemented
86C24×C31C2411yescharacteristic
87C2×Q8×C31—28no—
88C2×Q8×C31—28no—
89C2×Q8×C31—28no—
90C2×Q8×C31—28no—
91C2×Q8×C31—28no—
92C2×Q8×C31—28no—
93C2×Q8×C31C4⋊C4116yescomplemented
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—24no—
117C22×C4×C31—22no—
118C22×C4×C31—24no—
119C22×C4×C31—24no—
120C22×C4×C31—22no—
121C22×C4×C31—24no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31C22×C414yes—
129C22×C4×C31C22×C414yes—
130C22×C4×C31C22×C414yes—
131C22×C4×C31C22×C412yes—
132C22×C4×C31C2×D414yes—
133C22×C4×C31C2×D412yes—
134C22×C4×C31C2×D414yes—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D412yes—
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×Q814yes—
140C22×C4×C31C2×Q814yes—
141C22×C4×C31C2×Q814yes—
142C22×C4×C31C2×Q814yes—
143C22×C4×C31C2×Q812yes—
144C22×C4×C31#4114yes—
145C22×C4×C31#4112yes—
146C22×C4×C31#4112yes—
147C4⋊C4×C31—216no—
148C4⋊C4×C31—28no—
149C4⋊C4×C31—28no—
150C4⋊C4×C31—416no—
151C4⋊C4×C31—48no—
152C4⋊C4×C31—44no—
153C42×C31—216no—
154C42×C31—28no—
155C42×C31—28no—
156C42×C31—44no—
157#13976C3111yesmaximal, characteristic, direct product factor, Sylow
158C23×C31C23×C411yescharacteristic
159C23×C31C22×D411yescharacteristic
160C23×C31C22×D411yescharacteristic
161C23×C31C22×D411yescharacteristic
162C23×C31C22×Q811yescharacteristic
163C23×C31C22×Q812yes—
164C23×C31C2×#4111yescharacteristic
165C23×C31C2×#4111yescharacteristic
166C23×C31C2×#4112yes—
167C23×C31H(5,𝔽2)12yes—
168C23×C312−1+412yes—
169Q8×C31—232no—
170C2×C4×C31—24no—
171C2×C4×C31—24no—
172C2×C4×C31—24no—
173C2×C4×C31—24no—
174C2×C4×C31—22no—
175C2×C4×C31—24no—
176C2×C4×C31—24no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—22no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—24no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—28no—
188C2×C4×C31—24no—
189C2×C4×C31—22no—
190C2×C4×C31—22no—
191C2×C4×C31—24no—
192C2×C4×C31—22no—
193C2×C4×C31—28no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—44no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—44no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—44no—
212C2×C4×C31—44no—
213C2×C4×C31C2×C4⋊C418yes—
214C2×C4×C31C2×C4⋊C414yes—
215C2×C4×C31C4×D414yes—
216C2×C4×C31C4×D414yes—
217C2×C4×C31C4×Q818yescomplemented
218C2×C4×C31#12014yes—
219C2×C4×C31C22⋊Q814yes—
220C2×C4×C31C22⋊Q814yes—
221C2×C4×C31#12314yes—
222C2×C4×C31C4⋊Q814yes—
223C22×C4×Q8C2×C3111yescharacteristic
224C2×#391C2×C3111yescharacteristic
225C2×#391C2×C3111yescharacteristic
226C2×#389C2×C3111yescharacteristic
227C2×#384C2×C3111yescharacteristic
228#1444C2×C3114yes—
229#1436C2×C3114yes—
230C4⋊#95C2×C3111yescharacteristic
231C4×#95C2×C3111yescharacteristic
232C22×C31C22×C4⋊C411yescharacteristic
233C22×C31C2×C4×D411yescharacteristic
234C22×C31C2×C4×D411yescharacteristic
235C22×C31C2×C4×Q812yes—
236C22×C31#52012yes—
237C22×C31C2×#12011yescharacteristic
238C22×C31C2×C22⋊Q811yescharacteristic
239C22×C31C2×C22⋊Q811yescharacteristic
240C22×C31C2×#12311yescharacteristic
241C22×C31C2×C4⋊Q811yescharacteristic
242C22×C31#53211yescharacteristic
243C22×C31#53312yes—
244C22×C31#53511yescharacteristic
245C22×C31#53611yescharacteristic
246C22×C31#54212yes—
247C22×C31#54612yes—
248C22×C31D4×Q812yes—
249C22×C31D4×Q812yes—
250C22×C31#55012yes—
251C22×C31#55212yes—
252C22×C31#55412yes—
253C22×C31#55712yes—
254C22×C31Q8212yes—
255C4×C31—28no—
256C4×C31—24no—
257C4×C31—28no—
258C4×C31—44no—
259C4×C31—44no—
260C4×C31—42no—
261C4×C31—44no—
262C4×C31—82no—
263C4×C31#38518yes—
264C23×Q8C22×C3111yescharacteristic
265C2×C4×Q8—24no—
266C2×C4×Q8—24no—
267C2×C4×Q8—24no—
268C22×C4⋊C4C22×C3112yes—
269C22×C4⋊C4C22×C3111yescharacteristic
270C22×C4⋊C4C22×C3114yes—
271C22×C4⋊C4C22×C3111yescharacteristic
272C22×C4⋊C4C22×C3111yescharacteristic
273C22×C4⋊C4C22×C3112yes—
274C22×C42C22×C3112yes—
275C22×C42C22×C3111yescharacteristic
276C22×C42C22×C3111yescharacteristic
277C22×C42C22×C3111yescharacteristic
278#391—24no—
279#391C4×C3118yescomplemented
280#389—24no—
281#384—24no—
282C2×#95C22×C3112yes—
283C2×#95C22×C3112yes—
284C2×#95C22×C3114yes—
285C2×#95C22×C3114yes—
286C2×#95C22×C3114yes—
287C2×#95C22×C3112yes—
288C2×C31C2×#38511yescharacteristic
289C2×C31C4×C4⋊Q811yescharacteristic
290C2×C31#232611yescharacteristic
291C2×C31Q8×C4⋊C412yes—
292C2×C31#236012yes—
293C2×C31#242312yes—
294C2×C31#243111yescharacteristic
295C2×C31#243411yescharacteristic
296C2×C31#245112yes—
297C2×C31#256511yescharacteristic
298C2×C31#256711yescharacteristic
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8C2×C4×C3114yes—
304C22×Q8D4×C3114yes—
305C22×Q8Q8×C3114yes—
306C23×C4C23×C3112yes—
307C23×C4C23×C3112yes—
308C23×C4C23×C3111yescharacteristic
309C23×C4C23×C3112yes—
310C23×C4C23×C3112yes—
311C23×C4C23×C3112yes—
312C23×C4C23×C3112yes—
313C23×C4C23×C3111yescharacteristic
314C23×C4C23×C3111yescharacteristic
315C4×Q8—232no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×C4×C3114yes—
332C2×C4⋊C4D4×C3114yes—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42C2×C4×C3114yes—
344C2×C42D4×C3114yes—
345#95—24no—
346#95—28no—
347#95—24no—
348#95—44no—
349#95C2×C4×C31116yes—
350#95Q8×C3118yescomplemented
351C31#1397611yescharacteristic, direct product factor, Sylow
352C24C24×C3111yescharacteristic
353C2×Q8—28no—
354C2×Q8—28no—
355C2×Q8—28no—
356C2×Q8—28no—
357C2×Q8—28no—
358C2×Q8—28no—
359C2×Q8C4⋊C4×C31116yescomplemented
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4C22×C4×C3114yes—
395C22×C4C22×C4×C3114yes—
396C22×C4C22×C4×C3114yes—
397C22×C4C22×C4×C3112yes—
398C22×C4C2×D4×C3114yes—
399C22×C4C2×D4×C3112yes—
400C22×C4C2×D4×C3114yes—
401C22×C4C2×D4×C3112yes—
402C22×C4C2×D4×C3112yes—
403C22×C4C2×D4×C3112yes—
404C22×C4C2×D4×C3112yes—
405C22×C4C2×Q8×C3114yes—
406C22×C4C2×Q8×C3114yes—
407C22×C4C2×Q8×C3114yes—
408C22×C4C2×Q8×C3114yes—
409C22×C4C2×Q8×C3112yes—
410C22×C4#41×C3114yes—
411C22×C4#41×C3112yes—
412C22×C4#41×C3112yes—
413C4⋊C4—216no—
414C4⋊C4—28no—
415C4⋊C4—28no—
416C4⋊C4—416no—
417C4⋊C4—48no—
418C4⋊C4—44no—
419C42—216no—
420C42—28no—
421C42—28no—
422C42—44no—
423C23C23×C4×C3111yescharacteristic
424C23C22×D4×C3111yescharacteristic
425C23C22×D4×C3111yescharacteristic
426C23C22×D4×C3111yescharacteristic
427C23C22×Q8×C3111yescharacteristic
428C23C22×Q8×C3112yes—
429C23C2×#41×C3111yescharacteristic
430C23C2×#41×C3111yescharacteristic
431C23C2×#41×C3112yes—
432C23C31×H(5,𝔽2)12yes—
433C23C31×2−1+412yes—
434Q8—232no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—28no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—28no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4C2×C4⋊C4×C3118yes—
479C2×C4C2×C4⋊C4×C3114yes—
480C2×C4C4×D4×C3114yes—
481C2×C4C4×D4×C3114yes—
482C2×C4C4×Q8×C3118yescomplemented
483C2×C4C31×#12014yes—
484C2×C4C31×C22⋊Q814yes—
485C2×C4C31×C22⋊Q814yes—
486C2×C4C31×#12314yes—
487C2×C4C31×C4⋊Q814yes—
488C22C22×C4⋊C4×C3111yescharacteristic
489C22C2×C4×D4×C3111yescharacteristic
490C22C2×C4×D4×C3111yescharacteristic
491C22C2×C4×Q8×C3112yes—
492C22C31×#52012yes—
493C22C2×C31×#12011yescharacteristic
494C22C2×C31×C22⋊Q811yescharacteristic
495C22C2×C31×C22⋊Q811yescharacteristic
496C22C2×C31×#12311yescharacteristic
497C22C2×C31×C4⋊Q811yescharacteristic
498C22C31×#53211yescharacteristic
499C22C31×#53312yes—
500C22C31×#53511yescharacteristic
501C22C31×#53611yescharacteristic
502C22C31×#54212yes—
503C22C31×#54612yes—
504C22D4×Q8×C3112yes—
505C22D4×Q8×C3112yes—
506C22C31×#55012yes—
507C22C31×#55212yes—
508C22C31×#55412yes—
509C22C31×#55712yes—
510C22Q82×C3112yes—
511C4—28no—
512C4—24no—
513C4—28no—
514C4—44no—
515C4—44no—
516C4—42no—
517C4—44no—
518C4—82no—
519C4C31×#38518yes—
520C2C2×C31×#38511yescharacteristic
521C2C4×C31×C4⋊Q811yescharacteristic
522C2C31×#232611yescharacteristic
523C2Q8×C4⋊C4×C3112yes—
524C2C31×#236012yes—
525C2C31×#242312yes—
526C2C31×#243111yescharacteristic
527C2C31×#243411yescharacteristic
528C2C31×#245112yes—
529C2C31×#256511yescharacteristic
530C2C31×#256711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
25. C31×#391C4semidirect
85. C31×#95Q8semidirect
93. C2×Q8×C31C4⋊C4semidirect
157. #13976C31direct (N × H)
217. C2×C4×C31C4×Q8semidirect
279. #391C4×C31semidirect
350. #95Q8×C31semidirect
351. C31#13976direct (N × H)
359. C2×Q8C4⋊C4×C31semidirect
482. C2×C4C4×Q8×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#3912
C2×C31×#3892
C2×C31×#3842
C31×#14442
C31×#14362
C31×C4⋊#952
C4×C31×#952
#1397631