Finite Group Databasebeta

← C31×#8324 #21465083

Subgroups — C31×#8324 #21465083

Order 7936.

1006 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#520C211yesmaximal, characteristic
2C31×#1479C212yesmaximal, complemented
3C31×#1478C212yesmaximal, complemented
4C31×#1458C211yesmaximal, characteristic, complemented
5C31×#1458C211yesmaximal, characteristic, complemented
6C22×#41×C31C411yescharacteristic
7C31×#520—24no—
8C31×#520—24no—
9C2×C4×Q8×C31C411yescharacteristic
10C2×C4×Q8×C31C2211yescharacteristic
11C2×C4×D4×C31—21no—
12C2×C4×D4×C31—21no—
13C2×C4×D4×C31C411yescharacteristic
14C2×C4×D4×C31C2211yescharacteristic
15C2×C31×#117—21no—
16C2×C31×#117C2211yescharacteristic
17C22×C4⋊C4×C31—21no—
18C22×C4⋊C4×C31C411yescharacteristic
19C31×#431C2212yes—
20C31×#431C2212yes—
21C31×Q8⋊C8—24no—
22C31×D4⋊C8—24no—
23C31×#324—21no—
24C31×#324—21no—
25C31×#323—21no—
26C31×#323—21no—
27C2×#41×C31—22no—
28C2×#41×C31—22no—
29C2×#41×C31—22no—
30C2×#41×C31—22no—
31C2×#41×C31—22no—
32C2×#41×C31C814yescomplemented
33C22×Q8×C31C2×C411yescharacteristic
34C22×D4×C31—21no—
35C22×D4×C31C2×C411yescharacteristic
36C23×C4×C31—21no—
37C23×C4×C31—21no—
38C23×C4×C31—21no—
39C23×C4×C31—21no—
40C23×C4×C31C2×C411yescharacteristic
41C4×Q8×C31—22no—
42C4×Q8×C31—22no—
43C4×Q8×C31—22no—
44C4×Q8×C31D414yes—
45C4×D4×C31—28no—
46C4×D4×C31—28no—
47C4×D4×C31—22no—
48C4×D4×C31—22no—
49C4×D4×C31—22no—
50C4×D4×C31D414yes—
51C31×#117—28no—
52C31×#117—22no—
53C31×#117—22no—
54C2×C4⋊C4×C31—28no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31C2×C411yescharacteristic
61C2×C4⋊C4×C31C2×C411yescharacteristic
62C2×C4⋊C4×C31D411yescharacteristic
63C2×C4⋊C4×C31D411yescharacteristic
64C2×C22⋊C4×C31—21no—
65C2×C22⋊C4×C31—21no—
66C2×C22⋊C4×C31D411yescharacteristic
67C2×C22⋊C4×C31D411yescharacteristic
68C2×C42×C31—21no—
69C2×C42×C31—21no—
70C2×C42×C31C2×C411yescharacteristic
71C2×C42×C31C2311yescharacteristic
72C31×C4⋊C8—22no—
73C31×C4⋊C8—22no—
74C31×C22⋊C8—22no—
75C31×C22⋊C8—22no—
76C4×C8×C31—22no—
77C4×C8×C31—22no—
78C24×C31—21no—
79C24×C31C22⋊C411yescharacteristic
80#41×C31—28no—
81#41×C31—28no—
82#41×C31—28no—
83#41×C31—28no—
84C2×Q8×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31C22⋊C412yes—
88C2×Q8×C31C2×C812yes—
89C2×Q8×C31M1612yes—
90C2×D4×C31—24no—
91C2×D4×C31—24no—
92C2×D4×C31—24no—
93C2×D4×C31—21no—
94C2×D4×C31—21no—
95C2×D4×C31—21no—
96C2×D4×C31C22⋊C412yes—
97C2×D4×C31C2×C812yes—
98C2×D4×C31M1612yes—
99C22×C4×C31—24no—
100C22×C4×C31—24no—
101C22×C4×C31—21no—
102C22×C4×C31—24no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—24no—
110C22×C4×C31—24no—
111C22×C4×C31—24no—
112C22×C4×C31—82no—
113C22×C4×C31—82no—
114C22×C4×C31—82no—
115C22×C4×C31C22⋊C411yescharacteristic
116C22×C4×C31C22⋊C411yescharacteristic
117C22×C4×C31C22⋊C411yescharacteristic
118C22×C4×C31C2×C812yes—
119C22×C4×C31M1612yes—
120C22×C4×C31C22×C411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C2×C8×C31—42no—
124C2×C8×C31—42no—
125C4⋊C4×C31—24no—
126C4⋊C4×C31—24no—
127C4⋊C4×C31—21no—
128C4⋊C4×C31—21no—
129C4⋊C4×C31—22no—
130C4⋊C4×C31—24no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31C22⋊C412yes—
133C4⋊C4×C31C22⋊C412yes—
134C22⋊C4×C31—24no—
135C22⋊C4×C31—24no—
136C22⋊C4×C31—22no—
137C22⋊C4×C31—22no—
138C42×C31—24no—
139C42×C31—21no—
140C42×C31—21no—
141C42×C31—24no—
142C42×C31C2×D412yes—
143C42×C31C2×D412yes—
144#8324C3111yesmaximal, characteristic, direct product factor, Sylow
145C23×C31—21no—
146C23×C31—22no—
147C23×C31—22no—
148C23×C31—21no—
149C23×C31—22no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—42no—
153C23×C31—42no—
154C23×C31C22⋊C812yes—
155C23×C31C2×C22⋊C411yescharacteristic
156Q8×C31—22no—
157Q8×C31—22no—
158Q8×C31—22no—
159Q8×C31C22⋊C814yes—
160D4×C31—216no—
161D4×C31—22no—
162D4×C31—22no—
163D4×C31—22no—
164D4×C31C22⋊C814yes—
165C2×C4×C31—216no—
166C2×C4×C31—22no—
167C2×C4×C31—21no—
168C2×C4×C31—22no—
169C2×C4×C31—21no—
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—21no—
176C2×C4×C31—21no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—42no—
182C2×C4×C31—42no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—84no—
186C2×C4×C31—84no—
187C2×C4×C31—84no—
188C2×C4×C31C22⋊C812yes—
189C2×C4×C31C2×C22⋊C411yescharacteristic
190C2×C4×C31C2×C22⋊C411yescharacteristic
191C2×C4×C31#12012yes—
192C2×C4×C31#12012yes—
193C2×C4×C31C22×C811yescharacteristic
194C2×C4×C31C2×M1611yescharacteristic
195C2×C4×C31C2×M1611yescharacteristic
196C2×C4×C31C2×M1611yescharacteristic
197C8×C31—82no—
198C8×C31—82no—
199C2×#520C2×C3111yescharacteristic
200#1479C2×C3112yescomplemented
201#1478C2×C3112yescomplemented
202#1458C2×C3111yescharacteristic, complemented
203#1458C2×C3111yescharacteristic, complemented
204C22×C31—21no—
205C22×C31—21no—
206C22×C31—22no—
207C22×C31—24no—
208C22×C31—42no—
209C22×C31—44no—
210C22×C31—42no—
211C22×C31—44no—
212C22×C31—41no—
213C22×C31—42no—
214C22×C31—41no—
215C22×C31—42no—
216C22×C31#37911yescharacteristic
217C22×C31C2×C22⋊C811yescharacteristic
218C22×C31#40711yescharacteristic
219C4×C31—22no—
220C4×C31—22no—
221C4×C31—22no—
222C4×C31—24no—
223C4×C31—42no—
224C4×C31—42no—
225C4×C31—41no—
226C4×C31—41no—
227C4×C31C2×C22⋊C811yescharacteristic
228C4×C31C2×C22⋊C811yescharacteristic
229C4×C31#40711yescharacteristic
230C4×C31#40711yescharacteristic
231C22×#41C4×C3111yescharacteristic
232#520—24no—
233#520—24no—
234C2×C4×Q8C4×C3111yescharacteristic
235C2×C4×Q8C22×C3111yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C4×C3111yescharacteristic
239C2×C4×D4C22×C3111yescharacteristic
240C2×#117—21no—
241C2×#117C22×C3111yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4C4×C3111yescharacteristic
244#431C22×C3112yes—
245#431C22×C3112yes—
246Q8⋊C8—24no—
247D4⋊C8—24no—
248#324—21no—
249#324—21no—
250#323—21no—
251#323—21no—
252C2×C31—21no—
253C2×C31—21no—
254C2×C31—42no—
255C2×C31—44no—
256C2×C31#177911yescharacteristic
257C2×C31#179511yescharacteristic
258C2×C31#179611yescharacteristic
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41C8×C3114yescomplemented
265C22×Q8C2×C4×C3111yescharacteristic
266C22×D4—21no—
267C22×D4C2×C4×C3111yescharacteristic
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4C2×C4×C3111yescharacteristic
273C4×Q8—22no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8D4×C3114yes—
277C4×D4—28no—
278C4×D4—28no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4D4×C3114yes—
283#117—28no—
284#117—22no—
285#117—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4C2×C4×C3111yescharacteristic
293C2×C4⋊C4C2×C4×C3111yescharacteristic
294C2×C4⋊C4D4×C3111yescharacteristic
295C2×C4⋊C4D4×C3111yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4D4×C3111yescharacteristic
299C2×C22⋊C4D4×C3111yescharacteristic
300C2×C42—21no—
301C2×C42—21no—
302C2×C42C2×C4×C3111yescharacteristic
303C2×C42C23×C3111yescharacteristic
304C4⋊C8—22no—
305C4⋊C8—22no—
306C22⋊C8—22no—
307C22⋊C8—22no—
308C4×C8—22no—
309C4×C8—22no—
310C31#832411yescharacteristic, direct product factor, Sylow
311C24—21no—
312C24C22⋊C4×C3111yescharacteristic
313#41—28no—
314#41—28no—
315#41—28no—
316#41—28no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8C22⋊C4×C3112yes—
321C2×Q8C2×C8×C3112yes—
322C2×Q8M16×C3112yes—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4C22⋊C4×C3112yes—
330C2×D4C2×C8×C3112yes—
331C2×D4M16×C3112yes—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4—82no—
348C22×C4C22⋊C4×C3111yescharacteristic
349C22×C4C22⋊C4×C3111yescharacteristic
350C22×C4C22⋊C4×C3111yescharacteristic
351C22×C4C2×C8×C3112yes—
352C22×C4M16×C3112yes—
353C22×C4C22×C4×C3111yescharacteristic
354C22×C4C2×D4×C3111yescharacteristic
355C22×C4C2×D4×C3111yescharacteristic
356C2×C8—42no—
357C2×C8—42no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4C22⋊C4×C3112yes—
366C4⋊C4C22⋊C4×C3112yes—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42—24no—
372C42—21no—
373C42—21no—
374C42—24no—
375C42C2×D4×C3112yes—
376C42C2×D4×C3112yes—
377C23—22no—
378C23—21no—
379C23—22no—
380C23—21no—
381C23—22no—
382C23—41no—
383C23—41no—
384C23—42no—
385C23—42no—
386C23C31×C22⋊C812yes—
387C23C2×C22⋊C4×C3111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—22no—
391Q8C31×C22⋊C814yes—
392D4—216no—
393D4—22no—
394D4—22no—
395D4—22no—
396D4C31×C22⋊C814yes—
397C2×C4—216no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—84no—
420C2×C4C31×C22⋊C812yes—
421C2×C4C2×C22⋊C4×C3111yescharacteristic
422C2×C4C2×C22⋊C4×C3111yescharacteristic
423C2×C4C31×#12012yes—
424C2×C4C31×#12012yes—
425C2×C4C22×C8×C3111yescharacteristic
426C2×C4C2×M16×C3111yescharacteristic
427C2×C4C2×M16×C3111yescharacteristic
428C2×C4C2×M16×C3111yescharacteristic
429C8—82no—
430C8—82no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—24no—
435C22—42no—
436C22—44no—
437C22—44no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—42no—
442C22—41no—
443C22C31×#37911yescharacteristic
444C22C2×C31×C22⋊C811yescharacteristic
445C22C31×#40711yescharacteristic
446C4—22no—
447C4—22no—
448C4—22no—
449C4—24no—
450C4—42no—
451C4—42no—
452C4—41no—
453C4—41no—
454C4C2×C31×C22⋊C811yescharacteristic
455C4C2×C31×C22⋊C811yescharacteristic
456C4C31×#40711yescharacteristic
457C4C31×#40711yescharacteristic
458C2—21no—
459C2—21no—
460C2—44no—
461C2—42no—
462C2C31×#177911yescharacteristic
463C2C31×#179511yescharacteristic
464C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×#41×C31C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1479C2semidirect
3. C31×#1478C2semidirect
4. C31×#1458C2semidirect
5. C31×#1458C2semidirect
32. C2×#41×C31C8semidirect
144. #8324C31direct (N × H)
200. #1479C2×C31semidirect
201. #1478C2×C31semidirect
202. #1458C2×C31semidirect
203. #1458C2×C31semidirect
264. C2×#41C8×C31semidirect
310. C31#8324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5202
C31×#14792
C31×#14782
C31×#14582
#832431