Finite Group Databasebeta

← C31×#7493 #21464252

Subgroups — C31×#7493 #21464252

Order 7936.

334 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×C31×#353C211yesmaximal, characteristic
2C31×#1887C211yesmaximal, characteristic
3C31×#1555C211yesmaximal, characteristic
4C2×C31×#127C2211yescharacteristic
5C31×#518C411yescharacteristic, complemented
6C31×#432—21no—
7C31×#418—21no—
8C2×C31×#100C411yescharacteristic, complemented
9C2×C31×#99—21no—
10C31×#353—21no—
11C31×#353C412yescomplemented
12C31×#339—21no—
13C31×#331—21no—
14C31×#331C412yescomplemented
15C22×D4×C31—41no—
16C22×D4×C31C2×C411yescharacteristic
17C22×D4×C31D411yescharacteristic
18C2×M16×C31—21no—
19C31×#127—41no—
20C31×#127C2×C411yescharacteristic
21C31×#127C2×C411yescharacteristic
22C31×#127D411yescharacteristic
23C31×#127Q811yescharacteristic
24C4×D4×C31—42no—
25C31×#117—21no—
26C2×C22⋊C4×C31—41no—
27C2×C22⋊C4×C31—41no—
28C2×C42×C31D411yescharacteristic
29C31×C4⋊C8—22no—
30C31×#102—42no—
31C31×#100—41no—
32C31×#99—22no—
33C31×#99—41no—
34C31×C22⋊C8—41no—
35C31×#97—41no—
36C24×C31—21no—
37C24×C31—21no—
38C2×D4×C31—21no—
39C2×D4×C31—21no—
40C2×D4×C31—41no—
41C2×D4×C31—41no—
42C2×D4×C31—41no—
43C2×D4×C31—41no—
44C2×D4×C31—41no—
45C2×D4×C31—41no—
46C2×D4×C31—41no—
47C2×D4×C31—41no—
48C2×D4×C31—84no—
49C2×D4×C31C4211yescharacteristic
50C2×D4×C31C22⋊C411yescharacteristic
51C2×D4×C31C4⋊C411yescharacteristic
52C2×D4×C31C4⋊C411yescharacteristic
53C22×C4×C31—21no—
54C22×C4×C31—42no—
55C22×C4×C31—81no—
56C22×C4×C31C22⋊C411yescharacteristic
57M16×C31—41no—
58M16×C31—41no—
59C2×C8×C31—42no—
60C2×C8×C31—41no—
61C4⋊C4×C31—22no—
62C22⋊C4×C31—41no—
63C22⋊C4×C31—42no—
64C22⋊C4×C31—42no—
65C22⋊C4×C31—81no—
66C42×C31—21no—
67C42×C31—41no—
68C42×C31C22⋊C411yescharacteristic
69C42×C31C4⋊C411yescharacteristic
70#7493C3111yesmaximal, characteristic, direct product factor, Sylow
71C23×C31—21no—
72C23×C31—21no—
73C23×C31—21no—
74C23×C31—21no—
75C23×C31—41no—
76C23×C31—41no—
77C23×C31—41no—
78C23×C31—41no—
79C23×C31—82no—
80C23×C31—82no—
81C23×C31#9911yescharacteristic
82D4×C31—41no—
83D4×C31—41no—
84D4×C31—41no—
85D4×C31—41no—
86D4×C31—42no—
87D4×C31—81no—
88D4×C31—82no—
89D4×C31—82no—
90D4×C31—82no—
91D4×C31—82no—
92C2×C4×C31—21no—
93C2×C4×C31—21no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31—82no—
99C2×C4×C31—162no—
100C2×C4×C31—162no—
101C2×C4×C31#9511yescharacteristic
102C2×C4×C31#9911yescharacteristic
103C8×C31—82no—
104C8×C31—81no—
105C2×#353C2×C3111yescharacteristic
106#1887C2×C3111yescharacteristic
107#1555C2×C3111yescharacteristic
108C22×C31—41no—
109C22×C31—41no—
110C22×C31—41no—
111C22×C31—41no—
112C22×C31—41no—
113C22×C31—81no—
114C22×C31—81no—
115C22×C31—81no—
116C22×C31—81no—
117C22×C31—82no—
118C22×C31—82no—
119C22×C31—161no—
120C22×C31—161no—
121C22×C31#34211yescharacteristic
122C22×C31AΣL(1,𝔽16)11yescharacteristic
123C22×C31#35211yescharacteristic
124C4×C31—22no—
125C4×C31—21no—
126C4×C31—21no—
127C4×C31—41no—
128C4×C31—82no—
129C4×C31—162no—
130C2×#127C22×C3111yescharacteristic
131#518C4×C3111yescharacteristic, complemented
132#432—21no—
133#418—21no—
134C2×#100C4×C3111yescharacteristic, complemented
135C2×#99—21no—
136#353—21no—
137#353C4×C3112yescomplemented
138#339—21no—
139#331—21no—
140#331C4×C3112yescomplemented
141C2×C31—21no—
142C2×C31—21no—
143C2×C31—21no—
144C2×C31—81no—
145C2×C31—81no—
146C2×C31—81no—
147C2×C31—81no—
148C2×C31#139011yescharacteristic
149C22×D4—41no—
150C22×D4C2×C4×C3111yescharacteristic
151C22×D4D4×C3111yescharacteristic
152C2×M16—21no—
153#127—41no—
154#127C2×C4×C3111yescharacteristic
155#127C2×C4×C3111yescharacteristic
156#127D4×C3111yescharacteristic
157#127Q8×C3111yescharacteristic
158C4×D4—42no—
159#117—21no—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C42D4×C3111yescharacteristic
163C4⋊C8—22no—
164#102—42no—
165#100—41no—
166#99—22no—
167#99—41no—
168C22⋊C8—41no—
169#97—41no—
170C31#749311yescharacteristic, direct product factor, Sylow
171C24—21no—
172C24—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4—84no—
184C2×D4C42×C3111yescharacteristic
185C2×D4C22⋊C4×C3111yescharacteristic
186C2×D4C4⋊C4×C3111yescharacteristic
187C2×D4C4⋊C4×C3111yescharacteristic
188C22×C4—21no—
189C22×C4—42no—
190C22×C4—81no—
191C22×C4C22⋊C4×C3111yescharacteristic
192M16—41no—
193M16—41no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—22no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—81no—
201C42—21no—
202C42—41no—
203C42C22⋊C4×C3111yescharacteristic
204C42C4⋊C4×C3111yescharacteristic
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23—41no—
212C23—41no—
213C23—82no—
214C23—82no—
215C23C31×#9911yescharacteristic
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220D4—42no—
221D4—81no—
222D4—82no—
223D4—82no—
224D4—82no—
225D4—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—162no—
234C2×C4—162no—
235C2×C4C31×#9511yescharacteristic
236C2×C4C31×#9911yescharacteristic
237C8—82no—
238C8—81no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—82no—
249C22—82no—
250C22—161no—
251C22—161no—
252C22C31×#34211yescharacteristic
253C22C31×AΣL(1,𝔽16)11yescharacteristic
254C22C31×#35211yescharacteristic
255C4—22no—
256C4—21no—
257C4—21no—
258C4—41no—
259C4—82no—
260C4—162no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—81no—
265C2—81no—
266C2—81no—
267C2—81no—
268C2C31×#139011yescharacteristic
subgroupG/H
center, socleC2×C31#1390
commutatorC2×D4C42×C31
Frattini, cosocleC2×#127C22×C31
prime radicalC2×C31×#127C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×#127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C31×#518C4semidirect
8. C2×C31×#100C4semidirect
11. C31×#353C4semidirect
14. C31×#331C4semidirect
70. #7493C31direct (N × H)
131. #518C4×C31semidirect
134. C2×#100C4×C31semidirect
137. #353C4×C31semidirect
140. #331C4×C31semidirect
170. C31#7493direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3532
C31×#18872
C31×#15552
#749331