Finite Group Databasebeta

← C31×#11767 #21468526

Subgroups — C31×#11767 #21468526

Order 7936.

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

normal subgroups only

This group has 420 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×#2611C211yesmaximal, characteristic
2C31×#1742C211yesmaximal, characteristic
3C31×#1464C211yesmaximal, characteristic
4C31×#1353C212yesmaximal, complemented
5C31×#1346C212yesmaximal, complemented
6C22×M16×C31—21no—
7C2×C31×#125C411yescharacteristic
8C2×C31×#117C2211yescharacteristic
9C31×#432—21no—
10C31×#400C2211yescharacteristic
11C31×#399C411yescharacteristic
12C31×#398C2211yescharacteristic
13C31×#397C411yescharacteristic
14C31×#389—21no—
15C31×#388—21no—
16C31×#387—21no—
17C31×#385—21no—
18C31×#376C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C23×C4×C31D411yescharacteristic
24C2×M16×C31—24no—
25C2×M16×C31—22no—
26C2×M16×C31—41no—
27C2×M16×C31—42no—
28C22×C8×C31—41no—
29C31×#125—41no—
30C31×#125—41no—
31C31×#117—41no—
32C31×#117—41no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C4⋊C4×C31C2311yescharacteristic
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31C2×C411yescharacteristic
44C2×C22⋊C4×C31D411yescharacteristic
45C2×C42×C31—21no—
46C2×C42×C31C2×C411yescharacteristic
47C2×C42×C31D411yescharacteristic
48C31×C4⋊C8—41no—
49C31×C22⋊C8—22no—
50C31×#97—41no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31C22⋊C411yescharacteristic
59C22×C4×C31—22no—
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—21no—
67C22×C4×C31—21no—
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74M16×C31—24no—
75M16×C31—44no—
76M16×C31—42no—
77C2×C8×C31—44no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—41no—
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#11767C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—21no—
101C23×C31—21no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31#10412yes—
105C23×C31C2×C22⋊C411yescharacteristic
106C2×C4×C31—22no—
107C2×C4×C31—22no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—22no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
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#9911yescharacteristic
135C2×C4×C31#9911yescharacteristic
136C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C31#13711yescharacteristic
138C8×C31—44no—
139C8×C31—82no—
140#2611C2×C3111yescharacteristic
141#1742C2×C3111yescharacteristic
142#1464C2×C3111yescharacteristic
143#1353C2×C3112yescomplemented
144#1346C2×C3112yescomplemented
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—22no—
148C22×C31—42no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—81no—
152C22×C31C2×#9911yescharacteristic
153C22×C31#41711yescharacteristic
154C22×C31C2×#10411yescharacteristic
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—42no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—81no—
165C4×C31—81no—
166C4×C31—81no—
167C22×M16—21no—
168C2×#125C4×C3111yescharacteristic
169C2×#117C22×C3111yescharacteristic
170#432—21no—
171#400C22×C3111yescharacteristic
172#399C4×C3111yescharacteristic
173#398C22×C3111yescharacteristic
174#397C4×C3111yescharacteristic
175#389—21no—
176#388—21no—
177#387—21no—
178#385—21no—
179#376C4×C3111yescharacteristic
180#343—21no—
181#343C22×C3112yes—
182#324C22×C3112yes—
183#323—21no—
184C2×C31—21no—
185C2×C31—21no—
186C2×C31—42no—
187C2×C31#150411yescharacteristic
188C2×C31#212311yescharacteristic
189C2×C31#213211yescharacteristic
190C23×C4D4×C3111yescharacteristic
191C2×M16—24no—
192C2×M16—22no—
193C2×M16—41no—
194C2×M16—42no—
195C22×C8—41no—
196#125—41no—
197#125—41no—
198#117—41no—
199#117—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C3111yescharacteristic
205C2×C4⋊C4C2×C4×C3111yescharacteristic
206C2×C4⋊C4D4×C3111yescharacteristic
207C2×C4⋊C4C23×C3111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4C2×C4×C3111yescharacteristic
211C2×C22⋊C4D4×C3111yescharacteristic
212C2×C42—21no—
213C2×C42C2×C4×C3111yescharacteristic
214C2×C42D4×C3111yescharacteristic
215C4⋊C8—41no—
216C22⋊C8—22no—
217#97—41no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95C2×C4×C3111yescharacteristic
224#95C2×C4×C3111yescharacteristic
225C31#1176711yescharacteristic, direct product factor, Sylow
226C24C22⋊C4×C3111yescharacteristic
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C22⋊C4×C3111yescharacteristic
239C22×C4C22×C4×C3111yescharacteristic
240C22×C4C2×D4×C3111yescharacteristic
241C22×C4C2×D4×C3111yescharacteristic
242M16—24no—
243M16—44no—
244M16—42no—
245C2×C8—44no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—42no—
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23C31×#10412yes—
272C23C2×C22⋊C4×C3111yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
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×C4C31×#9911yescharacteristic
302C2×C4C31×#9911yescharacteristic
303C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
304C2×C4C31×#13711yescharacteristic
305C8—44no—
306C8—82no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—81no—
314C22C2×C31×#9911yescharacteristic
315C22C31×#41711yescharacteristic
316C22C2×C31×#10411yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4—81no—
329C2—21no—
330C2—21no—
331C2—42no—
332C2C31×#150411yescharacteristic
333C2C31×#212311yescharacteristic
334C2C31×#213211yescharacteristic
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×#1353C2semidirect
5. C31×#1346C2semidirect
99. #11767C31direct (N × H)
143. #1353C2×C31semidirect
144. #1346C2×C31semidirect
225. C31#11767direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26112
C31×#17422
C31×#14642
C31×#13532
C31×#13462
#1176731