Finite Group Databasebeta

← C31×#7504 #21464263

Subgroups — C31×#7504 #21464263

Order 7936.

336 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 70 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×#353C212yesmaximal
2C31×#1961C211yesmaximal, characteristic
3C2×C31×#127C2211yescharacteristic
4C2×C31×#102—22no—
5C2×C31×#99—22no—
6C2×C31×#97C411yescharacteristic, complemented
7C31×#382C411yescharacteristic, complemented
8C31×#353—22no—
9C31×#353C414yescomplemented
10C22×D4×C31—41no—
11C22×D4×C31D412yes—
12C22×C8×C31—21no—
13C31×#127—41no—
14C31×#127C2×C412yes—
15C31×#127D411yescharacteristic
16C31×#127Q811yescharacteristic
17C2×C4⋊C4×C31—21no—
18C2×C22⋊C4×C31—42no—
19C2×C42×C31C2×C411yescharacteristic
20C31×#102—44no—
21C31×#99—24no—
22C31×#99—42no—
23C31×#97—41no—
24C31×#95—41no—
25C24×C31—22no—
26C2×D4×C31—22no—
27C2×D4×C31—42no—
28C2×D4×C31—42no—
29C2×D4×C31—42no—
30C2×D4×C31—41no—
31C2×D4×C31—41no—
32C2×D4×C31—84no—
33C2×D4×C31C22⋊C412yes—
34C2×D4×C31C4⋊C412yes—
35C22×C4×C31—21no—
36C22×C4×C31—41no—
37C22×C4×C31—82no—
38C22×C4×C31C22⋊C411yescharacteristic
39C2×C8×C31—22no—
40C2×C8×C31—41no—
41C2×C8×C31—41no—
42C4⋊C4×C31—42no—
43C22⋊C4×C31—44no—
44C22⋊C4×C31—82no—
45C42×C31—21no—
46C42×C31C4211yescharacteristic
47C42×C31C4⋊C411yescharacteristic
48#7504C3111yesmaximal, characteristic, direct product factor, Sylow
49C23×C31—22no—
50C23×C31—22no—
51C23×C31—42no—
52C23×C31—42no—
53C23×C31—84no—
54C23×C31#9911yescharacteristic
55D4×C31—42no—
56D4×C31—42no—
57D4×C31—82no—
58D4×C31—84no—
59D4×C31—82no—
60D4×C31—82no—
61C2×C4×C31—21no—
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—21no—
65C2×C4×C31—42no—
66C2×C4×C31—82no—
67C2×C4×C31—84no—
68C2×C4×C31—81no—
69C2×C4×C31—164no—
70C2×C4×C31#9511yescharacteristic
71C2×C4×C31#9911yescharacteristic
72C8×C31—42no—
73C2×#353C2×C3112yes—
74#1961C2×C3111yescharacteristic
75C22×C31—22no—
76C22×C31—42no—
77C22×C31—42no—
78C22×C31—82no—
79C22×C31—82no—
80C22×C31—84no—
81C22×C31—162no—
82C22×C31#34211yescharacteristic
83C22×C31#35311yescharacteristic
84C22×C31#35411yescharacteristic
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—41no—
88C4×C31—41no—
89C4×C31—161no—
90C4×C31—164no—
91C2×#127C22×C3111yescharacteristic
92C2×#102—22no—
93C2×#99—22no—
94C2×#97C4×C3111yescharacteristic, complemented
95#382C4×C3111yescharacteristic, complemented
96#353—22no—
97#353C4×C3114yescomplemented
98C2×C31—21no—
99C2×C31—21no—
100C2×C31—82no—
101C2×C31—82no—
102C2×C31#139311yescharacteristic
103C2×C31#141212yes—
104C22×D4—41no—
105C22×D4D4×C3112yes—
106C22×C8—21no—
107#127—41no—
108#127C2×C4×C3112yes—
109#127D4×C3111yescharacteristic
110#127Q8×C3111yescharacteristic
111C2×C4⋊C4—21no—
112C2×C22⋊C4—42no—
113C2×C42C2×C4×C3111yescharacteristic
114#102—44no—
115#99—24no—
116#99—42no—
117#97—41no—
118#95—41no—
119C31#750411yescharacteristic, direct product factor, Sylow
120C24—22no—
121C2×D4—22no—
122C2×D4—42no—
123C2×D4—42no—
124C2×D4—42no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4—84no—
128C2×D4C22⋊C4×C3112yes—
129C2×D4C4⋊C4×C3112yes—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—82no—
133C22×C4C22⋊C4×C3111yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C4⋊C4—42no—
138C22⋊C4—44no—
139C22⋊C4—82no—
140C42—21no—
141C42C42×C3111yescharacteristic
142C42C4⋊C4×C3111yescharacteristic
143C23—22no—
144C23—22no—
145C23—42no—
146C23—42no—
147C23—84no—
148C23C31×#9911yescharacteristic
149D4—42no—
150D4—42no—
151D4—82no—
152D4—84no—
153D4—82no—
154D4—82no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—82no—
161C2×C4—84no—
162C2×C4—81no—
163C2×C4—164no—
164C2×C4C31×#9511yescharacteristic
165C2×C4C31×#9911yescharacteristic
166C8—42no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—82no—
171C22—82no—
172C22—84no—
173C22—162no—
174C22C31×#34211yescharacteristic
175C22C31×#35311yescharacteristic
176C22C31×#35411yescharacteristic
177C4—21no—
178C4—21no—
179C4—41no—
180C4—41no—
181C4—161no—
182C4—164no—
183C2—21no—
184C2—21no—
185C2—82no—
186C2—82no—
187C2C31×#139311yescharacteristic
188C2C31×#141212yes—
subgroupG/H
center, socleC22×C31#354
commutatorC42C42×C31
Frattini, cosocleC2×#127C22×C31
prime radicalC2×C31×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×#127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C31×#97C4semidirect
7. C31×#382C4semidirect
9. C31×#353C4semidirect
48. #7504C31direct (N × H)
94. C2×#97C4×C31semidirect
95. #382C4×C31semidirect
97. #353C4×C31semidirect
119. C31#7504direct (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×#19612
#750431