Finite Group Databasebeta

← C31×#8776 #21465535

Subgroups — C31×#8776 #21465535

Order 7936.

480 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2353C211yesmaximal, characteristic
2C4×C31×#99C211yesmaximal, characteristic
3C31×#1465C211yesmaximal, characteristic
4C31×#1297C212yesmaximal, complemented
5C31×#1284C212yesmaximal, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C2×C31×#99—21no—
8C31×#407C2212yes—
9C31×#388—21no—
10C31×#387—21no—
11C31×#386—21no—
12C31×#383C411yescharacteristic, complemented
13C31×#381C2211yescharacteristic
14C31×#380C411yescharacteristic, complemented
15C4×C22⋊C4×C31—21no—
16C4×C22⋊C4×C31C2212yes—
17C4×C22⋊C4×C31C2211yescharacteristic
18C31×#376C411yescharacteristic, complemented
19C2×C31×#95C411yescharacteristic, complemented
20C31×#342—21no—
21C31×#324—21no—
22C31×#323—21no—
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C2×M16×C31—22no—
28C4×D4×C31—22no—
29C4×D4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31D411yescharacteristic
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—21no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31D411yescharacteristic
38C2×C42×C31—21no—
39C2×C42×C31—21no—
40C2×C42×C31—22no—
41C2×C42×C31C2×C411yescharacteristic
42C31×#99—24no—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—22no—
45C31×#95—21no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—22no—
51C31×#95C2×C411yescharacteristic
52C31×#95C2×C411yescharacteristic
53C31×#95C2×C411yescharacteristic
54C31×#95C2×C411yescharacteristic
55C24×C31C22⋊C411yescharacteristic
56C24×C31C2×D411yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—22no—
59C2×D4×C31—41no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—81no—
70C22×C4×C31—81no—
71C22×C4×C31—81no—
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22×C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31#4112yes—
78C22×C4×C31#4112yes—
79M16×C31—82no—
80C2×C8×C31—42no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—81no—
83C22⋊C4×C31—22no—
84C22⋊C4×C31—22no—
85C22⋊C4×C31—24no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—81no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—42no—
93C42×C31—81no—
94C42×C31—82no—
95#8776C3111yesmaximal, characteristic, direct product factor, Sylow
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—21no—
99C23×C31—21no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31#10412yes—
105C23×C31C2×C22⋊C411yescharacteristic
106C23×C31#12312yes—
107D4×C31—44no—
108C2×C4×C31—22no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—41no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—44no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—81no—
133C2×C4×C31—81no—
134C2×C4×C31—84no—
135C2×C4×C31—82no—
136C2×C4×C31—82no—
137C2×C4×C31#11711yescharacteristic
138C2×C4×C31#11711yescharacteristic
139C2×C4×C31#12312yes—
140C8×C31—82no—
141#2353C2×C3111yescharacteristic
142C4×#99C2×C3111yescharacteristic
143#1465C2×C3111yescharacteristic
144#1297C2×C3112yescomplemented
145#1284C2×C3112yescomplemented
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—22no—
149C22×C31—22no—
150C22×C31—22no—
151C22×C31—22no—
152C22×C31—42no—
153C22×C31—42no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—81no—
157C22×C31—81no—
158C22×C31#38111yescharacteristic
159C22×C31C2×#10411yescharacteristic
160C22×C31#42111yescharacteristic
161C4×C31—22no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—42no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31—81no—
169C4×C31—81no—
170C4×C31—81no—
171C4×C31—84no—
172C2×C4×D4C22×C3111yescharacteristic
173C2×#99—21no—
174#407C22×C3112yes—
175#388—21no—
176#387—21no—
177#386—21no—
178#383C4×C3111yescharacteristic, complemented
179#381C22×C3111yescharacteristic
180#380C4×C3111yescharacteristic, complemented
181C4×C22⋊C4—21no—
182C4×C22⋊C4C22×C3112yes—
183C4×C22⋊C4C22×C3111yescharacteristic
184#376C4×C3111yescharacteristic, complemented
185C2×#95C4×C3111yescharacteristic, complemented
186#342—21no—
187#324—21no—
188#323—21no—
189C2×C31—21no—
190C2×C31—21no—
191C2×C31—42no—
192C2×C31—42no—
193C2×C31#182611yescharacteristic
194C2×C31#182711yescharacteristic
195C2×C31#182811yescharacteristic
196C22×D4D4×C3111yescharacteristic
197C23×C4—21no—
198C23×C4C2×C4×C3111yescharacteristic
199C23×C4C23×C3111yescharacteristic
200C2×M16—22no—
201C4×D4—22no—
202C4×D4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4D4×C3111yescharacteristic
205C2×C22⋊C4—22no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4D4×C3111yescharacteristic
210C2×C22⋊C4D4×C3111yescharacteristic
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—22no—
214C2×C42C2×C4×C3111yescharacteristic
215#99—24no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—22no—
224#95C2×C4×C3111yescharacteristic
225#95C2×C4×C3111yescharacteristic
226#95C2×C4×C3111yescharacteristic
227#95C2×C4×C3111yescharacteristic
228C31#877611yescharacteristic, direct product factor, Sylow
229C24C22⋊C4×C3111yescharacteristic
230C24C2×D4×C3111yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4C22⋊C4×C3111yescharacteristic
247C22×C4C22⋊C4×C3111yescharacteristic
248C22×C4C22⋊C4×C3111yescharacteristic
249C22×C4C22×C4×C3111yescharacteristic
250C22×C4C2×D4×C3111yescharacteristic
251C22×C4#41×C3112yes—
252C22×C4#41×C3112yes—
253M16—82no—
254C2×C8—42no—
255C4⋊C4—22no—
256C4⋊C4—81no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—24no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—81no—
264C42—21no—
265C42—21no—
266C42—42no—
267C42—81no—
268C42—82no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C31×#10412yes—
278C23C2×C22⋊C4×C3111yescharacteristic
279C23C31×#12312yes—
280D4—44no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—44no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—84no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4C31×#11711yescharacteristic
311C2×C4C31×#11711yescharacteristic
312C2×C4C31×#12312yes—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22C31×#38111yescharacteristic
327C22C2×C31×#10411yescharacteristic
328C22C31×#42111yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—84no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2C31×#182611yescharacteristic
345C2C31×#182711yescharacteristic
346C2C31×#182811yescharacteristic
subgroupG/H
center, socleC22×C31#381
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31D4
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
4. C31×#1297C2semidirect
5. C31×#1284C2semidirect
12. C31×#383C4semidirect
14. C31×#380C4semidirect
18. C31×#376C4semidirect
19. C2×C31×#95C4semidirect
95. #8776C31direct (N × H)
144. #1297C2×C31semidirect
145. #1284C2×C31semidirect
178. #383C4×C31semidirect
180. #380C4×C31semidirect
184. #376C4×C31semidirect
185. C2×#95C4×C31semidirect
228. C31#8776direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23532
C4×C31×#992
C31×#14652
C31×#12972
C31×#12842
#877631