Finite Group Databasebeta

← C31×#9004 #21465763

Subgroups — C31×#9004 #21465763

Order 7936.

458 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 134 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×#491C211yesmaximal, characteristic
2C31×#2382C211yesmaximal, characteristic
3C31×#1993C212yesmaximal
4C2×C31×#330C211yesmaximal, characteristic
5C31×#1295C212yesmaximal
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C31×#125C2211yescharacteristic
8C31×#491—22no—
9C31×#491C414yescomplemented
10C2×C31×#103—22no—
11C2×C31×#97C2212yes—
12C2×C31×#97C2211yescharacteristic
13C31×#389—22no—
14C31×#387—22no—
15C31×#387—22no—
16C31×#382C2212yes—
17C31×#340—22no—
18C31×#340—22no—
19C31×#330—22no—
20C22×Q8×C31—21no—
21C22×C8×C31—21no—
22C22×C8×C31—22no—
23C31×C4⋊Q8—21no—
24C31×C4⋊Q8—22no—
25C31×C4⋊Q8C2×C412yes—
26C31×#125—22no—
27C31×#125C2×C412yes—
28C31×#125D412yes—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31D412yes—
33C2×C4⋊C4×C31D412yes—
34C2×C4⋊C4×C31D412yes—
35C2×C42×C31—22no—
36C2×C42×C31C2311yescharacteristic
37C31×#103—28no—
38C31×#97—21no—
39C31×#97—22no—
40C31×#97—22no—
41C31×#97C2×C412yes—
42C31×#95—22no—
43C31×#95—22no—
44C31×#95—22no—
45C31×#95—22no—
46C2×Q8×C31—22no—
47C2×Q8×C31—42no—
48C2×Q8×C31—42no—
49C2×Q8×C31—41no—
50C22×C4×C31—22no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—41no—
54C22×C4×C31C2×D411yescharacteristic
55C22×C4×C31C2×D412yes—
56C2×C8×C31—24no—
57C2×C8×C31—22no—
58C2×C8×C31—41no—
59C2×C8×C31—41no—
60C2×C8×C31—42no—
61C2×C8×C31—42no—
62C4⋊C4×C31—24no—
63C4⋊C4×C31—24no—
64C4⋊C4×C31—22no—
65C4⋊C4×C31—24no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—82no—
70C4⋊C4×C31C22⋊C414yes—
71C42×C31—82no—
72C42×C31C22×C411yescharacteristic
73C42×C31C2×D411yescharacteristic
74C42×C31#4112yes—
75#9004C3111yesmaximal, characteristic, direct product factor, Sylow
76C23×C31#12011yescharacteristic
77Q8×C31—44no—
78Q8×C31—82no—
79C2×C4×C31—21no—
80C2×C4×C31—21no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—24no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—81no—
94C2×C4×C31—81no—
95C2×C4×C31C2×C22⋊C411yescharacteristic
96C2×C4×C31C4×D412yes—
97C2×C4×C31#12112yes—
98C2×C4×C31#12311yescharacteristic
99C8×C31—44no—
100C8×C31—42no—
101C2×#491C2×C3111yescharacteristic
102#2382C2×C3111yescharacteristic
103#1993C2×C3112yes—
104C2×#330C2×C3111yescharacteristic
105#1295C2×C3112yes—
106C22×C31#38611yescharacteristic
107C22×C31#45411yescharacteristic
108C22×C31#45411yescharacteristic
109C22×C31#45512yes—
110C22×C31#45612yes—
111C4×C31—22no—
112C4×C31—22no—
113C4×C31—21no—
114C4×C31—21no—
115C4×C31—44no—
116C4×C31—82no—
117C4×C31—82no—
118C4×C31—82no—
119C2×C4⋊Q8C22×C3111yescharacteristic
120C2×#125C22×C3111yescharacteristic
121#491—22no—
122#491C4×C3114yescomplemented
123C2×#103—22no—
124C2×#97C22×C3112yes—
125C2×#97C22×C3111yescharacteristic
126#389—22no—
127#387—22no—
128#387—22no—
129#382C22×C3112yes—
130#340—22no—
131#340—22no—
132#330—22no—
133C2×C31#166211yescharacteristic
134C2×C31#166311yescharacteristic
135C2×C31#166412yes—
136C2×C31#188212yes—
137C2×C31#188811yescharacteristic
138C22×Q8—21no—
139C22×C8—22no—
140C22×C8—21no—
141C4⋊Q8—21no—
142C4⋊Q8—22no—
143C4⋊Q8C2×C4×C3112yes—
144#125—22no—
145#125C2×C4×C3112yes—
146#125D4×C3112yes—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4D4×C3112yes—
151C2×C4⋊C4D4×C3112yes—
152C2×C4⋊C4D4×C3112yes—
153C2×C42—22no—
154C2×C42C23×C3111yescharacteristic
155#103—28no—
156#97—21no—
157#97—22no—
158#97—22no—
159#97C2×C4×C3112yes—
160#95—22no—
161#95—22no—
162#95—22no—
163#95—22no—
164C31#900411yescharacteristic, direct product factor, Sylow
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—41no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4C2×D4×C3111yescharacteristic
174C22×C4C2×D4×C3112yes—
175C2×C8—24no—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—82no—
189C4⋊C4C22⋊C4×C3114yes—
190C42—82no—
191C42C22×C4×C3111yescharacteristic
192C42C2×D4×C3111yescharacteristic
193C42#41×C3112yes—
194C23C31×#12011yescharacteristic
195Q8—44no—
196Q8—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4C2×C22⋊C4×C3111yescharacteristic
214C2×C4C4×D4×C3112yes—
215C2×C4C31×#12112yes—
216C2×C4C31×#12311yescharacteristic
217C8—44no—
218C8—42no—
219C22C31×#38611yescharacteristic
220C22C31×#45411yescharacteristic
221C22C31×#45411yescharacteristic
222C22C31×#45512yes—
223C22C31×#45612yes—
224C4—22no—
225C4—22no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—82no—
230C4—82no—
231C4—82no—
232C2C31×#166211yescharacteristic
233C2C31×#166311yescharacteristic
234C2C31×#166412yes—
235C2C31×#188212yes—
236C2C31×#188811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#491C4semidirect
75. #9004C31direct (N × H)
122. #491C4×C31semidirect
164. C31#9004direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4912
C31×#23822
C31×#19932
C2×C31×#3302
C31×#12952
#900431