Finite Group Databasebeta

← C31×#7376 #21464135

Subgroups — C31×#7376 #21464135

Order 7936.

202 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1857C211yesmaximal, characteristic
2C31×#1319C211yesmaximal, characteristic
3C31×#1272C211yesmaximal, characteristic
4C31×#519C411yescharacteristic
5C31×#428—21no—
6C2×C31×#101C411yescharacteristic
7C31×#391C2211yescharacteristic
8C31×#339—21no—
9C31×#336—21no—
10C31×#324—21no—
11C22×Q8×C31C2×C411yescharacteristic
12C2×M16×C31—21no—
13C22×C8×C31—41no—
14C4×Q8×C31—41no—
15C4×Q8×C31—41no—
16C31×#117—21no—
17C31×#117—41no—
18C2×C4⋊C4×C31D411yescharacteristic
19C2×C42×C31D411yescharacteristic
20C31×#107—41no—
21C31×#106—41no—
22C31×#101—21no—
23C31×#101C812yescomplemented
24C31×C22⋊C8—41no—
25C31×#95—41no—
26C2×Q8×C31—21no—
27C2×Q8×C31—41no—
28C2×Q8×C31—41no—
29C2×Q8×C31C2×C811yescharacteristic
30C2×Q8×C31M1611yescharacteristic
31C22×C4×C31—21no—
32C22×C4×C31—21no—
33C22×C4×C31—21no—
34C22×C4×C31C22⋊C411yescharacteristic
35M16×C31—22no—
36M16×C31—41no—
37C2×C8×C31—41no—
38C2×C8×C31—42no—
39C2×C8×C31—81no—
40C2×C8×C31—81no—
41C2×C8×C31—81no—
42C4⋊C4×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—41no—
45C4⋊C4×C31—41no—
46C4⋊C4×C31—41no—
47C22⋊C4×C31—41no—
48C42×C31—41no—
49C42×C31—41no—
50C42×C31—42no—
51#7376C3111yesmaximal, characteristic, direct product factor, Sylow
52C23×C31#9911yescharacteristic
53Q8×C31—41no—
54Q8×C31—41no—
55Q8×C31—42no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31—81no—
70C2×C4×C31C22⋊C811yescharacteristic
71C2×C4×C31#10111yescharacteristic
72C8×C31—42no—
73C8×C31—82no—
74C8×C31—161no—
75#1857C2×C3111yescharacteristic
76#1319C2×C3111yescharacteristic
77#1272C2×C3111yescharacteristic
78C22×C31—21no—
79C22×C31—21no—
80C22×C31#32411yescharacteristic
81C22×C31AΣL(1,𝔽16)11yescharacteristic
82C22×C31#35211yescharacteristic
83C4×C31—21no—
84C4×C31—21no—
85C4×C31—41no—
86C4×C31—41no—
87C4×C31—41no—
88C4×C31—41no—
89C4×C31—81no—
90C4×C31—81no—
91C4×C31—81no—
92#519C4×C3111yescharacteristic
93#428—21no—
94C2×#101C4×C3111yescharacteristic
95#391C22×C3111yescharacteristic
96#339—21no—
97#336—21no—
98#324—21no—
99C2×C31—21no—
100C2×C31—21no—
101C2×C31#132611yescharacteristic
102C2×C31#140411yescharacteristic
103C2×C31#140511yescharacteristic
104C22×Q8C2×C4×C3111yescharacteristic
105C2×M16—21no—
106C22×C8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109#117—21no—
110#117—41no—
111C2×C4⋊C4D4×C3111yescharacteristic
112C2×C42D4×C3111yescharacteristic
113#107—41no—
114#106—41no—
115#101—21no—
116#101C8×C3112yescomplemented
117C22⋊C8—41no—
118#95—41no—
119C31#737611yescharacteristic, direct product factor, Sylow
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C2×C8×C3111yescharacteristic
124C2×Q8M16×C3111yescharacteristic
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4C22⋊C4×C3111yescharacteristic
129M16—22no—
130M16—41no—
131C2×C8—41no—
132C2×C8—42no—
133C2×C8—81no—
134C2×C8—81no—
135C2×C8—81no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C22⋊C4—41no—
142C42—41no—
143C42—41no—
144C42—42no—
145C23C31×#9911yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4C31×C22⋊C811yescharacteristic
164C2×C4C31×#10111yescharacteristic
165C8—42no—
166C8—82no—
167C8—161no—
168C22—21no—
169C22—21no—
170C22C31×#32411yescharacteristic
171C22C31×AΣL(1,𝔽16)11yescharacteristic
172C22C31×#35211yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—81no—
182C2—21no—
183C2—21no—
184C2C31×#132611yescharacteristic
185C2C31×#140411yescharacteristic
186C2C31×#140511yescharacteristic
subgroupG/H
center, socleC22×C31AΣL(1,𝔽16)
commutatorC2×Q8C2×C8×C31
Frattini, cosocle#391C22×C31
prime radicalC23×C31#99
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#391 ◁ G

Complements

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

NH ≅ G/Ntype
23. C31×#101C8semidirect
51. #7376C31direct (N × H)
116. #101C8×C31semidirect
119. C31#7376direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#18572
C31×#13192
C31×#12722
#737631