Finite Group Databasebeta

← C31×#11740 #21468499

Subgroups — C31×#11740 #21468499

Order 7936.

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

normal subgroups only

This group has 358 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×#2634C211yesmaximal, characteristic
2C4×C31×#101C211yesmaximal, characteristic
3C31×#1461C211yesmaximal, characteristic
4C31×#1353C212yesmaximal
5C31×#1346C212yesmaximal
6C2×C31×#125C411yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#431—21no—
9C2×C31×#101—21no—
10C4×M16×C31—21no—
11C31×#400—21no—
12C31×#400C411yescharacteristic
13C31×#400C2211yescharacteristic
14C31×#398C411yescharacteristic
15C31×#398C2211yescharacteristic
16C31×#395—21no—
17C31×#387—21no—
18C31×#387—21no—
19C31×#383C411yescharacteristic
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C22×Q8×C31D411yescharacteristic
24C2×M16×C31—22no—
25C31×#125—41no—
26C31×#125—41no—
27C4×Q8×C31—41no—
28C4×Q8×C31—41no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C4⋊C4×C31C2311yescharacteristic
38C2×C42×C31C2×C411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C31×C4⋊C8—41no—
42C31×#101—24no—
43C31×C22⋊C8—22no—
44C31×#97—41no—
45C4×C8×C31—41no—
46C4×C8×C31—41no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C2×Q8×C31—22no—
58C2×Q8×C31—22no—
59C2×Q8×C31—41no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22×C411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C22×C4×C31C2×D411yescharacteristic
71M16×C31—24no—
72M16×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—41no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C42×C31—21no—
86C42×C31—21no—
87C42×C31—21no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—21no—
91#11740C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31C2×C22⋊C411yescharacteristic
93Q8×C31—44no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—41no—
105C2×C4×C31—41no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—42no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31#9911yescharacteristic
120C2×C4×C31#9911yescharacteristic
121C2×C4×C31#10412yes—
122C2×C4×C31#13512yes—
123C8×C31—44no—
124C8×C31—82no—
125#2634C2×C3111yescharacteristic
126C4×#101C2×C3111yescharacteristic
127#1461C2×C3111yescharacteristic
128#1353C2×C3112yes—
129#1346C2×C3112yes—
130C22×C31—21no—
131C22×C31—21no—
132C22×C31C2×#9911yescharacteristic
133C22×C31#41611yescharacteristic
134C22×C31C2×#10411yescharacteristic
135C4×C31—21no—
136C4×C31—21no—
137C4×C31—22no—
138C4×C31—22no—
139C4×C31—41no—
140C4×C31—41no—
141C4×C31—41no—
142C4×C31—41no—
143C4×C31—81no—
144C4×C31—81no—
145C4×C31—81no—
146C4×C31—81no—
147C2×#125C4×C3111yescharacteristic
148C2×C4×Q8C22×C3111yescharacteristic
149#431—21no—
150C2×#101—21no—
151C4×M16—21no—
152#400—21no—
153#400C4×C3111yescharacteristic
154#400C22×C3111yescharacteristic
155#398C4×C3111yescharacteristic
156#398C22×C3111yescharacteristic
157#395—21no—
158#387—21no—
159#387—21no—
160#383C4×C3111yescharacteristic
161#343C22×C3112yes—
162#324—21no—
163#324C22×C3112yes—
164C2×C31—21no—
165C2×C31—21no—
166C2×C31#150111yescharacteristic
167C2×C31#212311yescharacteristic
168C2×C31#213311yescharacteristic
169C22×Q8D4×C3111yescharacteristic
170C2×M16—22no—
171#125—41no—
172#125—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×C4×C3111yescharacteristic
180C2×C4⋊C4C2×C4×C3111yescharacteristic
181C2×C4⋊C4C2×C4×C3111yescharacteristic
182C2×C4⋊C4D4×C3111yescharacteristic
183C2×C4⋊C4C23×C3111yescharacteristic
184C2×C42C2×C4×C3111yescharacteristic
185C2×C42D4×C3111yescharacteristic
186C2×C42D4×C3111yescharacteristic
187C4⋊C8—41no—
188#101—24no—
189C22⋊C8—22no—
190#97—41no—
191C4×C8—41no—
192C4×C8—41no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95C2×C4×C3111yescharacteristic
202#95C2×C4×C3111yescharacteristic
203C31#1174011yescharacteristic, direct product factor, Sylow
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C22⋊C4×C3111yescharacteristic
212C22×C4C22⋊C4×C3111yescharacteristic
213C22×C4C22⋊C4×C3111yescharacteristic
214C22×C4C22⋊C4×C3111yescharacteristic
215C22×C4C22×C4×C3111yescharacteristic
216C22×C4C2×D4×C3111yescharacteristic
217C22×C4C2×D4×C3111yescharacteristic
218M16—24no—
219M16—42no—
220C2×C8—42no—
221C2×C8—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×C22⋊C4×C3111yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4C31×#9911yescharacteristic
266C2×C4C31×#9911yescharacteristic
267C2×C4C31×#10412yes—
268C2×C4C31×#13512yes—
269C8—44no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22C2×C31×#9911yescharacteristic
274C22C31×#41611yescharacteristic
275C22C2×C31×#10411yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2C31×#150111yescharacteristic
291C2C31×#212311yescharacteristic
292C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
91. #11740C31direct (N × H)
203. C31#11740direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26342
C4×C31×#1012
C31×#14612
C31×#13532
C31×#13462
#1174031