Finite Group Databasebeta

← C31×#7568 #21464327

Subgroups — C31×#7568 #21464327

Order 7936.

444 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 170 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
1C4×C31×#125C211yesmaximal, characteristic
2C31×#1744C212yesmaximal
3C31×#1271C214yesmaximal
4C2×C31×#125C411yescharacteristic
5C2×C4×C8×C31—22no—
6C31×#389C2212yes—
7C31×#387—22no—
8C31×#382C411yescharacteristic
9C4×C4⋊C4×C31—22no—
10C4×C4⋊C4×C31C412yes—
11C43×C31C2211yescharacteristic
12C31×#336—22no—
13C31×#336C2214yes—
14C22×C8×C31—24no—
15C31×#125—22no—
16C31×#125C814yescomplemented
17C2×C4⋊C4×C31—22no—
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31C2×C412yes—
20C2×C4⋊C4×C31C2×C412yes—
21C2×C42×C31—22no—
22C2×C42×C31C2×C411yescharacteristic
23C2×C42×C31C2×C411yescharacteristic
24C2×C42×C31D412yes—
25C2×C42×C31D412yes—
26C2×C42×C31C2311yescharacteristic
27C4×C8×C31—28no—
28C31×#95—22no—
29C31×#95—22no—
30C31×#95—22no—
31C22×C4×C31—22no—
32C22×C4×C31—22no—
33C22×C4×C31C22⋊C411yescharacteristic
34C22×C4×C31C22⋊C412yes—
35C22×C4×C31C22⋊C411yescharacteristic
36C22×C4×C31C22×C411yescharacteristic
37C22×C4×C31C2×D412yes—
38C2×C8×C31—28no—
39C2×C8×C31—44no—
40C2×C8×C31—44no—
41C4⋊C4×C31—28no—
42C4⋊C4×C31—22no—
43C4⋊C4×C31—42no—
44C4⋊C4×C31—44no—
45C4⋊C4×C31C2×C814yes—
46C42×C31—22no—
47C42×C31—24no—
48C42×C31—24no—
49C42×C31—41no—
50C42×C31—44no—
51C42×C31C2×C812yes—
52C42×C31M1612yes—
53#7568C3111yesmaximal, characteristic, direct product factor, Sylow
54C23×C31C2×C22⋊C411yescharacteristic
55C2×C4×C31—21no—
56C2×C4×C31—22no—
57C2×C4×C31—21no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—24no—
62C2×C4×C31—21no—
63C2×C4×C31—22no—
64C2×C4×C31—42no—
65C2×C4×C31—42no—
66C2×C4×C31—42no—
67C2×C4×C31—42no—
68C2×C4×C31—42no—
69C2×C4×C31C22⋊C814yes—
70C2×C4×C31#10112yes—
71C2×C4×C31#10414yes—
72C2×C4×C31C22×C811yescharacteristic
73C2×C4×C31C2×M1611yescharacteristic
74C2×C4×C31#13514yes—
75C8×C31—48no—
76C4×#125C2×C3111yescharacteristic
77#1744C2×C3112yes—
78#1271C2×C3114yes—
79C22×C31C2×C22⋊C811yescharacteristic
80C22×C31#41011yescharacteristic
81C22×C31C2×#10111yescharacteristic
82C22×C31#41612yes—
83C22×C31C2×#10412yes—
84C4×C31—21no—
85C4×C31—21no—
86C4×C31—24no—
87C4×C31—24no—
88C4×C31—41no—
89C4×C31—44no—
90C4×C31—82no—
91C4×C31#33014yes—
92C2×#125C4×C3111yescharacteristic
93C2×C4×C8—22no—
94#389C22×C3112yes—
95#387—22no—
96#382C4×C3111yescharacteristic
97C4×C4⋊C4—22no—
98C4×C4⋊C4C4×C3112yes—
99C43C22×C3111yescharacteristic
100#336—22no—
101#336C22×C3114yes—
102C2×C31#146111yescharacteristic
103C2×C31#147612yes—
104C2×C31#150012yes—
105C2×C31C2×#33011yescharacteristic
106C2×C31#154411yescharacteristic
107C22×C8—24no—
108#125—22no—
109#125C8×C3114yescomplemented
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4C2×C4×C3112yes—
113C2×C4⋊C4C2×C4×C3112yes—
114C2×C42—22no—
115C2×C42C2×C4×C3111yescharacteristic
116C2×C42C2×C4×C3111yescharacteristic
117C2×C42D4×C3112yes—
118C2×C42D4×C3112yes—
119C2×C42C23×C3111yescharacteristic
120C4×C8—28no—
121#95—22no—
122#95—22no—
123#95—22no—
124C31#756811yescharacteristic, direct product factor, Sylow
125C22×C4—22no—
126C22×C4—22no—
127C22×C4C22⋊C4×C3111yescharacteristic
128C22×C4C22⋊C4×C3112yes—
129C22×C4C22⋊C4×C3111yescharacteristic
130C22×C4C22×C4×C3111yescharacteristic
131C22×C4C2×D4×C3112yes—
132C2×C8—28no—
133C2×C8—44no—
134C2×C8—44no—
135C4⋊C4—28no—
136C4⋊C4—22no—
137C4⋊C4—42no—
138C4⋊C4—44no—
139C4⋊C4C2×C8×C3114yes—
140C42—22no—
141C42—24no—
142C42—24no—
143C42—41no—
144C42—44no—
145C42C2×C8×C3112yes—
146C42M16×C3112yes—
147C23C2×C22⋊C4×C3111yescharacteristic
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4C31×C22⋊C814yes—
163C2×C4C31×#10112yes—
164C2×C4C31×#10414yes—
165C2×C4C22×C8×C3111yescharacteristic
166C2×C4C2×M16×C3111yescharacteristic
167C2×C4C31×#13514yes—
168C8—48no—
169C22C2×C31×C22⋊C811yescharacteristic
170C22C31×#41011yescharacteristic
171C22C2×C31×#10111yescharacteristic
172C22C31×#41612yes—
173C22C2×C31×#10412yes—
174C4—21no—
175C4—21no—
176C4—24no—
177C4—24no—
178C4—41no—
179C4—44no—
180C4—82no—
181C4C31×#33014yes—
182C2C31×#146111yescharacteristic
183C2C31×#147612yes—
184C2C31×#150012yes—
185C2C2×C31×#33011yescharacteristic
186C2C31×#154411yescharacteristic
subgroupG/H
centerC22×C4×C31C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
socle, prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
16. C31×#125C8semidirect
53. #7568C31direct (N × H)
109. #125C8×C31semidirect
124. C31#7568direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1252
C31×#17442
C31×#12712
#756831