Finite Group Databasebeta

← C31×#11763 #21468522

Subgroups — C31×#11763 #21468522

Order 7936.

428 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2599C211yesmaximal, characteristic
2C31×#1742C211yesmaximal, characteristic
3C31×#1464C211yesmaximal, characteristic
4C31×#1354C212yesmaximal, complemented
5C31×#1346C212yesmaximal, complemented
6C22×M16×C31—21no—
7C2×C4×Q8×C31C411yescharacteristic
8C2×C31×#117C2211yescharacteristic
9C31×#432—21no—
10C31×#398C2211yescharacteristic
11C31×#397C411yescharacteristic
12C31×#395C2211yescharacteristic
13C31×#393C411yescharacteristic
14C31×#388—21no—
15C31×#387—21no—
16C31×#387—21no—
17C31×#385—21no—
18C31×#383C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×Q8×C31C2×C411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C2×M16×C31—24no—
26C2×M16×C31—22no—
27C2×M16×C31—41no—
28C2×M16×C31—42no—
29C22×C8×C31—41no—
30C4×Q8×C31—41no—
31C4×Q8×C31—41no—
32C31×#117—41no—
33C31×#117—41no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31C2311yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C42×C31—21no—
45C2×C42×C31C2×C411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C31×C4⋊C8—41no—
48C31×C22⋊C8—22no—
49C31×#97—41no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31C22⋊C411yescharacteristic
59C2×Q8×C31—42no—
60C2×Q8×C31—41no—
61C22×C4×C31—22no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22×C411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76M16×C31—24no—
77M16×C31—44no—
78M16×C31—42no—
79C2×C8×C31—44no—
80C2×C8×C31—42no—
81C2×C8×C31—42no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—42no—
99#11763C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—21no—
101C23×C31—21no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31#10412yes—
105C23×C31C2×C22⋊C411yescharacteristic
106Q8×C31—42no—
107Q8×C31—42no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—22no—
111C2×C4×C31—22no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—22no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
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—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31#9911yescharacteristic
137C2×C4×C31#9911yescharacteristic
138C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C31#13711yescharacteristic
140C8×C31—44no—
141C8×C31—82no—
142#2599C2×C3111yescharacteristic
143#1742C2×C3111yescharacteristic
144#1464C2×C3111yescharacteristic
145#1354C2×C3112yescomplemented
146#1346C2×C3112yescomplemented
147C22×C31—21no—
148C22×C31—21no—
149C22×C31—22no—
150C22×C31—42no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—81no—
154C22×C31C2×#9911yescharacteristic
155C22×C31#41711yescharacteristic
156C22×C31C2×#10411yescharacteristic
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—42no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—81no—
167C4×C31—81no—
168C4×C31—81no—
169C22×M16—21no—
170C2×C4×Q8C4×C3111yescharacteristic
171C2×#117C22×C3111yescharacteristic
172#432—21no—
173#398C22×C3111yescharacteristic
174#397C4×C3111yescharacteristic
175#395C22×C3111yescharacteristic
176#393C4×C3111yescharacteristic
177#388—21no—
178#387—21no—
179#387—21no—
180#385—21no—
181#383C4×C3111yescharacteristic
182#343—21no—
183#343C22×C3112yes—
184#324C22×C3112yes—
185#323—21no—
186C2×C31—21no—
187C2×C31—21no—
188C2×C31—42no—
189C2×C31#150411yescharacteristic
190C2×C31#212011yescharacteristic
191C2×C31#213511yescharacteristic
192C22×Q8C2×C4×C3111yescharacteristic
193C23×C4D4×C3111yescharacteristic
194C2×M16—24no—
195C2×M16—22no—
196C2×M16—41no—
197C2×M16—42no—
198C22×C8—41no—
199C4×Q8—41no—
200C4×Q8—41no—
201#117—41no—
202#117—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×C4×C3111yescharacteristic
207C2×C4⋊C4D4×C3111yescharacteristic
208C2×C4⋊C4C23×C3111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4C2×C4×C3111yescharacteristic
212C2×C22⋊C4D4×C3111yescharacteristic
213C2×C42—21no—
214C2×C42C2×C4×C3111yescharacteristic
215C2×C42D4×C3111yescharacteristic
216C4⋊C8—41no—
217C22⋊C8—22no—
218#97—41no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C2×C4×C3111yescharacteristic
226#95C2×C4×C3111yescharacteristic
227C31#1176311yescharacteristic, direct product factor, Sylow
228C24C22⋊C4×C3111yescharacteristic
229C2×Q8—42no—
230C2×Q8—41no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C22⋊C4×C3111yescharacteristic
241C22×C4C22⋊C4×C3111yescharacteristic
242C22×C4C22⋊C4×C3111yescharacteristic
243C22×C4C22×C4×C3111yescharacteristic
244C22×C4C2×D4×C3111yescharacteristic
245C22×C4C2×D4×C3111yescharacteristic
246M16—24no—
247M16—44no—
248M16—42no—
249C2×C8—44no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—42no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23C31×#10412yes—
274C23C2×C22⋊C4×C3111yescharacteristic
275Q8—42no—
276Q8—42no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4C31×#9911yescharacteristic
306C2×C4C31×#9911yescharacteristic
307C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
308C2×C4C31×#13711yescharacteristic
309C8—44no—
310C8—82no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×C31×#9911yescharacteristic
319C22C31×#41711yescharacteristic
320C22C2×C31×#10411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2C31×#150411yescharacteristic
337C2C31×#212011yescharacteristic
338C2C31×#213511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1354C2semidirect
5. C31×#1346C2semidirect
99. #11763C31direct (N × H)
145. #1354C2×C31semidirect
146. #1346C2×C31semidirect
227. C31#11763direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25992
C31×#17422
C31×#14642
C31×#13542
C31×#13462
#1176331