Finite Group Databasebeta

← C31×#8913 #21465672

Subgroups — C31×#8913 #21465672

Order 7936.

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

normal subgroups only

This group has 428 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
1C31×#2382C211yesmaximal, characteristic
2C31×#1992C211yesmaximal, characteristic
3C31×#1847C212yesmaximal
4C2×C31×#330C211yesmaximal, characteristic
5C31×#1295C212yesmaximal
6C2×C31×#125C2211yescharacteristic
7C2×C31×#107—22no—
8C2×C31×#106—22no—
9C2×C31×#97C2211yescharacteristic
10C2×C31×#97C2212yes—
11C31×#389—22no—
12C31×#387—22no—
13C31×#387—22no—
14C31×#384C2211yescharacteristic
15C31×#382C2212yes—
16C31×#340—22no—
17C31×#330C414yescomplemented
18C22×C8×C31—22no—
19C22×C8×C31—21no—
20C31×#125—22no—
21C31×#125C2×C412yes—
22C31×#125Q812yes—
23C2×C4⋊C4×C31—22no—
24C2×C4⋊C4×C31—22no—
25C2×C4⋊C4×C31—21no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31D412yes—
28C2×C4⋊C4×C31D412yes—
29C2×C4⋊C4×C31D412yes—
30C2×C42×C31—22no—
31C2×C42×C31C2311yescharacteristic
32C31×#107—44no—
33C31×#106—44no—
34C31×#97—22no—
35C31×#97—22no—
36C31×#97C2×C414yes—
37C31×#95—22no—
38C31×#95—22no—
39C31×#95—22no—
40C31×#95—22no—
41C22×C4×C31—22no—
42C22×C4×C31—22no—
43C22×C4×C31—22no—
44C22×C4×C31—41no—
45C22×C4×C31C2×D411yescharacteristic
46C22×C4×C31C2×D412yes—
47C2×C8×C31—24no—
48C2×C8×C31—24no—
49C2×C8×C31—24no—
50C2×C8×C31—22no—
51C2×C8×C31—41no—
52C2×C8×C31—41no—
53C4⋊C4×C31—24no—
54C4⋊C4×C31—24no—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—42no—
57C4⋊C4×C31—42no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—42no—
61C4⋊C4×C31—82no—
62C4⋊C4×C31C4⋊C414yes—
63C42×C31—82no—
64C42×C31C22×C411yescharacteristic
65C42×C31C2×Q811yescharacteristic
66C42×C31#4112yes—
67#8913C3111yesmaximal, characteristic, direct product factor, Sylow
68C23×C31#12011yescharacteristic
69C2×C4×C31—22no—
70C2×C4×C31—21no—
71C2×C4×C31—21no—
72C2×C4×C31—22no—
73C2×C4×C31—24no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—42no—
80C2×C4×C31—42no—
81C2×C4×C31—42no—
82C2×C4×C31—82no—
83C2×C4×C31—81no—
84C2×C4×C31C2×C4⋊C411yescharacteristic
85C2×C4×C31C4×D412yes—
86C2×C4×C31C22⋊Q812yes—
87C2×C4×C31#12311yescharacteristic
88C8×C31—28no—
89C8×C31—42no—
90#2382C2×C3111yescharacteristic
91#1992C2×C3111yescharacteristic
92#1847C2×C3112yes—
93C2×#330C2×C3111yescharacteristic
94#1295C2×C3112yes—
95C22×C31#38511yescharacteristic
96C22×C31#45312yes—
97C22×C31#45411yescharacteristic
98C22×C31#45611yescharacteristic
99C22×C31#45612yes—
100C4×C31—21no—
101C4×C31—21no—
102C4×C31—22no—
103C4×C31—22no—
104C4×C31—44no—
105C4×C31—82no—
106C4×C31—82no—
107C4×C31—161no—
108C2×#125C22×C3111yescharacteristic
109C2×#107—22no—
110C2×#106—22no—
111C2×#97C22×C3111yescharacteristic
112C2×#97C22×C3112yes—
113#389—22no—
114#387—22no—
115#387—22no—
116#384C22×C3111yescharacteristic
117#382C22×C3112yes—
118#340—22no—
119#330C4×C3114yescomplemented
120C2×C31#165611yescharacteristic
121C2×C31#166012yes—
122C2×C31#166311yescharacteristic
123C2×C31#185711yescharacteristic
124C2×C31#185912yes—
125C22×C8—22no—
126C22×C8—21no—
127#125—22no—
128#125C2×C4×C3112yes—
129#125Q8×C3112yes—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4D4×C3112yes—
135C2×C4⋊C4D4×C3112yes—
136C2×C4⋊C4D4×C3112yes—
137C2×C42—22no—
138C2×C42C23×C3111yescharacteristic
139#107—44no—
140#106—44no—
141#97—22no—
142#97—22no—
143#97C2×C4×C3114yes—
144#95—22no—
145#95—22no—
146#95—22no—
147#95—22no—
148C31#891311yescharacteristic, direct product factor, Sylow
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—41no—
153C22×C4C2×D4×C3111yescharacteristic
154C22×C4C2×D4×C3112yes—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—22no—
159C2×C8—41no—
160C2×C8—41no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—82no—
170C4⋊C4C4⋊C4×C3114yes—
171C42—82no—
172C42C22×C4×C3111yescharacteristic
173C42C2×Q8×C3111yescharacteristic
174C42#41×C3112yes—
175C23C31×#12011yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C2×C4⋊C4×C3111yescharacteristic
192C2×C4C4×D4×C3112yes—
193C2×C4C31×C22⋊Q812yes—
194C2×C4C31×#12311yescharacteristic
195C8—28no—
196C8—42no—
197C22C31×#38511yescharacteristic
198C22C31×#45312yes—
199C22C31×#45411yescharacteristic
200C22C31×#45611yescharacteristic
201C22C31×#45612yes—
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C31×#165611yescharacteristic
211C2C31×#166012yes—
212C2C31×#166311yescharacteristic
213C2C31×#185711yescharacteristic
214C2C31×#185912yes—
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
17. C31×#330C4semidirect
67. #8913C31direct (N × H)
119. #330C4×C31semidirect
148. C31#8913direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23822
C31×#19922
C31×#18472
C2×C31×#3302
C31×#12952
#891331