Finite Group Databasebeta

← C31×#8915 #21465674

Subgroups — C31×#8915 #21465674

Order 7936.

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

normal subgroups only

This group has 396 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×#1836C212yesmaximal
4C2×C31×#330C211yesmaximal, characteristic
5C31×#1295C212yesmaximal
6C2×C31×#125C2211yescharacteristic
7C2×C31×#97C2211yescharacteristic
8C2×C31×#97C2212yes—
9C31×#389—22no—
10C31×#387—22no—
11C31×#387—22no—
12C31×#384C2211yescharacteristic
13C31×#382C2212yes—
14C31×#340—22no—
15C31×#340—22no—
16C31×#340—22no—
17C31×#330C414yescomplemented
18C22×C8×C31—21no—
19C22×C8×C31—22no—
20C31×#125—22no—
21C31×#125C2×C412yes—
22C31×#125Q812yes—
23C2×C4⋊C4×C31—22no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31—22no—
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×#97—22no—
33C31×#97—22no—
34C31×#97C2×C414yes—
35C31×#95—22no—
36C31×#95—22no—
37C31×#95—22no—
38C31×#95—22no—
39C22×C4×C31—22no—
40C22×C4×C31—22no—
41C22×C4×C31—22no—
42C22×C4×C31—41no—
43C22×C4×C31C2×D411yescharacteristic
44C22×C4×C31C2×D412yes—
45C2×C8×C31—22no—
46C2×C8×C31—24no—
47C2×C8×C31—41no—
48C2×C8×C31—42no—
49C2×C8×C31—42no—
50C2×C8×C31—41no—
51C4⋊C4×C31—24no—
52C4⋊C4×C31—24no—
53C4⋊C4×C31—22no—
54C4⋊C4×C31—42no—
55C4⋊C4×C31—42no—
56C4⋊C4×C31—42no—
57C4⋊C4×C31—44no—
58C4⋊C4×C31—82no—
59C4⋊C4×C31C4⋊C414yes—
60C42×C31—82no—
61C42×C31C22×C411yescharacteristic
62C42×C31C2×Q811yescharacteristic
63C42×C31#4112yes—
64#8915C3111yesmaximal, characteristic, direct product factor, Sylow
65C23×C31#12011yescharacteristic
66C2×C4×C31—21no—
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—21no—
70C2×C4×C31—24no—
71C2×C4×C31—42no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—81no—
80C2×C4×C31—82no—
81C2×C4×C31C2×C4⋊C411yescharacteristic
82C2×C4×C31C4×D412yes—
83C2×C4×C31C22⋊Q812yes—
84C2×C4×C31#12311yescharacteristic
85C8×C31—42no—
86C8×C31—44no—
87#2382C2×C3111yescharacteristic
88#1992C2×C3111yescharacteristic
89#1836C2×C3112yes—
90C2×#330C2×C3111yescharacteristic
91#1295C2×C3112yes—
92C22×C31#38511yescharacteristic
93C22×C31#45411yescharacteristic
94C22×C31#45412yes—
95C22×C31#45512yes—
96C22×C31#45611yescharacteristic
97C4×C31—21no—
98C4×C31—21no—
99C4×C31—22no—
100C4×C31—22no—
101C4×C31—44no—
102C4×C31—82no—
103C4×C31—82no—
104C4×C31—161no—
105C2×#125C22×C3111yescharacteristic
106C2×#97C22×C3111yescharacteristic
107C2×#97C22×C3112yes—
108#389—22no—
109#387—22no—
110#387—22no—
111#384C22×C3111yescharacteristic
112#382C22×C3112yes—
113#340—22no—
114#340—22no—
115#340—22no—
116#330C4×C3114yescomplemented
117C2×C31#165811yescharacteristic
118C2×C31#166211yescharacteristic
119C2×C31#166412yes—
120C2×C31#185711yescharacteristic
121C2×C31#186012yes—
122C22×C8—21no—
123C22×C8—22no—
124#125—22no—
125#125C2×C4×C3112yes—
126#125Q8×C3112yes—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4D4×C3112yes—
132C2×C4⋊C4D4×C3112yes—
133C2×C4⋊C4D4×C3112yes—
134C2×C42—22no—
135C2×C42C23×C3111yescharacteristic
136#97—22no—
137#97—22no—
138#97C2×C4×C3114yes—
139#95—22no—
140#95—22no—
141#95—22no—
142#95—22no—
143C31#891511yescharacteristic, direct product factor, Sylow
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—41no—
148C22×C4C2×D4×C3111yescharacteristic
149C22×C4C2×D4×C3112yes—
150C2×C8—22no—
151C2×C8—24no—
152C2×C8—41no—
153C2×C8—42no—
154C2×C8—42no—
155C2×C8—41no—
156C4⋊C4—24no—
157C4⋊C4—24no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—44no—
163C4⋊C4—82no—
164C4⋊C4C4⋊C4×C3114yes—
165C42—82no—
166C42C22×C4×C3111yescharacteristic
167C42C2×Q8×C3111yescharacteristic
168C42#41×C3112yes—
169C23C31×#12011yescharacteristic
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—82no—
185C2×C4C2×C4⋊C4×C3111yescharacteristic
186C2×C4C4×D4×C3112yes—
187C2×C4C31×C22⋊Q812yes—
188C2×C4C31×#12311yescharacteristic
189C8—42no—
190C8—44no—
191C22C31×#38511yescharacteristic
192C22C31×#45411yescharacteristic
193C22C31×#45412yes—
194C22C31×#45512yes—
195C22C31×#45611yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—82no—
202C4—82no—
203C4—161no—
204C2C31×#165811yescharacteristic
205C2C31×#166211yescharacteristic
206C2C31×#166412yes—
207C2C31×#185711yescharacteristic
208C2C31×#186012yes—
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
64. #8915C31direct (N × H)
116. #330C4×C31semidirect
143. C31#8915direct (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×#18362
C2×C31×#3302
C31×#12952
#891531