Finite Group Databasebeta

← C31×#11989 #21468748

Subgroups — C31×#11989 #21468748

Order 7936.

292 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3176C211yesmaximal, characteristic
2C31×#2166C211yesmaximal, characteristic, complemented
3C31×#2153C211yesmaximal, characteristic, complemented
4C31×#1366C212yesmaximal, complemented
5C31×#1357C212yesmaximal, complemented
6C31×#540C412yes—
7C2×C31×M32—21no—
8C31×#499C2211yescharacteristic
9C31×#493C2211yescharacteristic
10C31×#490C412yes—
11C31×#469—21no—
12C31×#466—21no—
13C31×#442—21no—
14C4×D8×C31—21no—
15C31×#405C2211yescharacteristic
16C31×#364—21no—
17C31×#364C2212yes—
18C31×#364C2212yes—
19C31×#349—21no—
20C31×#347—21no—
21C2×D8×C31—21no—
22C2×D8×C31—21no—
23C2×M16×C31D411yescharacteristic
24C22×C8×C31D411yescharacteristic
25C31×#127C2×C412yes—
26C31×#125C2×C412yes—
27C31×#123—42no—
28C31×#121—22no—
29C31×#121—42no—
30C4×D4×C31—22no—
31C31×#117C2×C411yescharacteristic
32C31×M32—22no—
33C31×M32—22no—
34C31×M32—41no—
35C2×C16×C31—41no—
36C31×#107—21no—
37C31×#106—21no—
38C31×#102—22no—
39C31×#102—22no—
40C31×#97C2×C411yescharacteristic
41C31×#97D411yescharacteristic
42C4×C8×C31D411yescharacteristic
43C4×C8×C31C2311yescharacteristic
44C2×D4×C31—22no—
45C2×D4×C31—42no—
46C2×D4×C31—42no—
47C22×C4×C31—42no—
48C22×C4×C31C22⋊C411yescharacteristic
49D8×C31—42no—
50D8×C31—41no—
51D8×C31—41no—
52M16×C31—22no—
53C2×C8×C31—21no—
54C2×C8×C31—21no—
55C2×C8×C31C22⋊C411yescharacteristic
56C2×C8×C31C22⋊C411yescharacteristic
57C2×C8×C31C2×D411yescharacteristic
58C2×C8×C31C2×D411yescharacteristic
59C4⋊C4×C31—21no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—42no—
62C22⋊C4×C31—21no—
63C22⋊C4×C31—42no—
64C22⋊C4×C31—42no—
65C42×C31C22⋊C411yescharacteristic
66C42×C31C22×C411yescharacteristic
67C16×C31—42no—
68C16×C31—42no—
69#11989C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—42no—
71C23×C31#10011yescharacteristic
72D4×C31—42no—
73D4×C31—42no—
74D4×C31—162no—
75D4×C31—162no—
76C2×C4×C31—21no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—42no—
81C2×C4×C31—162no—
82C2×C4×C31#10011yescharacteristic
83C2×C4×C31C2×C22⋊C411yescharacteristic
84C8×C31—21no—
85C8×C31—21no—
86C8×C31#13512yes—
87C8×C31AGL(1,ℤ/8)11yescharacteristic
88C8×C31#13711yescharacteristic
89#3176C2×C3111yescharacteristic
90#2166C2×C3111yescharacteristic, complemented
91#2153C2×C3111yescharacteristic, complemented
92#1366C2×C3112yescomplemented
93#1357C2×C3112yescomplemented
94C22×C31—21no—
95C22×C31—41no—
96C22×C31—82no—
97C22×C31—82no—
98C22×C31—82no—
99C22×C31C2×#10011yescharacteristic
100C4×C31—21no—
101C4×C31—41no—
102C4×C31—41no—
103C4×C31—82no—
104C4×C31#41611yescharacteristic
105C4×C31#41711yescharacteristic
106#540C4×C3112yes—
107C2×M32—21no—
108#499C22×C3111yescharacteristic
109#493C22×C3111yescharacteristic
110#490C4×C3112yes—
111#469—21no—
112#466—21no—
113#442—21no—
114C4×D8—21no—
115#405C22×C3111yescharacteristic
116#364—21no—
117#364C22×C3112yes—
118#364C22×C3112yes—
119#349—21no—
120#347—21no—
121C2×C31—21no—
122C2×C31—41no—
123C2×C31—162no—
124C2×C31#155111yescharacteristic
125C2×D8—21no—
126C2×D8—21no—
127C2×M16D4×C3111yescharacteristic
128C22×C8D4×C3111yescharacteristic
129#127C2×C4×C3112yes—
130#125C2×C4×C3112yes—
131#123—42no—
132#121—22no—
133#121—42no—
134C4×D4—22no—
135#117C2×C4×C3111yescharacteristic
136M32—22no—
137M32—22no—
138M32—41no—
139C2×C16—41no—
140#107—21no—
141#106—21no—
142#102—22no—
143#102—22no—
144#97C2×C4×C3111yescharacteristic
145#97D4×C3111yescharacteristic
146C4×C8D4×C3111yescharacteristic
147C4×C8C23×C3111yescharacteristic
148C31#1198911yescharacteristic, direct product factor, Sylow
149C2×D4—22no—
150C2×D4—42no—
151C2×D4—42no—
152C22×C4—42no—
153C22×C4C22⋊C4×C3111yescharacteristic
154D8—42no—
155D8—41no—
156D8—41no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8C22⋊C4×C3111yescharacteristic
161C2×C8C22⋊C4×C3111yescharacteristic
162C2×C8C2×D4×C3111yescharacteristic
163C2×C8C2×D4×C3111yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—42no—
167C22⋊C4—21no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42C22⋊C4×C3111yescharacteristic
171C42C22×C4×C3111yescharacteristic
172C16—42no—
173C16—42no—
174C23—42no—
175C23C31×#10011yescharacteristic
176D4—42no—
177D4—42no—
178D4—162no—
179D4—162no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—42no—
185C2×C4—162no—
186C2×C4C31×#10011yescharacteristic
187C2×C4C2×C22⋊C4×C3111yescharacteristic
188C8—21no—
189C8—21no—
190C8C31×#13512yes—
191C8C31×AGL(1,ℤ/8)11yescharacteristic
192C8C31×#13711yescharacteristic
193C22—21no—
194C22—41no—
195C22—82no—
196C22—82no—
197C22—82no—
198C22C2×C31×#10011yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—82no—
203C4C31×#41611yescharacteristic
204C4C31×#41711yescharacteristic
205C2—21no—
206C2—41no—
207C2—162no—
208C2C31×#155111yescharacteristic
subgroupG/H
center, socleC2×C31#1551
commutatorC42C22×C4×C31
Frattini, cosocleC4×C8C23×C31
prime radicalC31×#3176C2
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C31×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2166C2semidirect
3. C31×#2153C2semidirect
4. C31×#1366C2semidirect
5. C31×#1357C2semidirect
69. #11989C31direct (N × H)
90. #2166C2×C31semidirect
91. #2153C2×C31semidirect
92. #1366C2×C31semidirect
93. #1357C2×C31semidirect
148. C31#11989direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31762
C31×#21662
C31×#21532
C31×#13662
C31×#13572
#1198931