Finite Group Databasebeta

← C2×C31×#1412 #21470352

Subgroups — C2×C31×#1412 #21470352

Order 7936.

390 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 94 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×#490C211yesmaximal, characteristic
2C2×C31×#353C212yesmaximal
3C31×#1412C214yesmaximal, direct product factor
4C2×C31×#127C2211yescharacteristic
5C2×C31×#125C411yescharacteristic, complemented
6C31×#490—22no—
7C31×#490C412yescomplemented
8C31×#490C2212yes—
9C2×C31×#102—22no—
10C2×C31×#99—22no—
11C2×C31×#97C411yescharacteristic, complemented
12C31×#353—22no—
13C31×#353C2214yes—
14C22×D4×C31—41no—
15C22×D4×C31D412yes—
16C22×C8×C31—21no—
17C31×#127—41no—
18C31×#127C2×C411yescharacteristic
19C31×#127D412yes—
20C31×#127C2311yescharacteristic
21C31×#125—21no—
22C31×#125—41no—
23C31×#125C2×C412yescomplemented
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31—41no—
26C2×C22⋊C4×C31—42no—
27C2×C42×C31C2×C411yescharacteristic
28C31×#102—24no—
29C31×#102—24no—
30C31×#99—24no—
31C31×#99—42no—
32C31×#97—21no—
33C31×#97C2×C412yescomplemented
34C24×C31—22no—
35C2×D4×C31—22no—
36C2×D4×C31—42no—
37C2×D4×C31—42no—
38C2×D4×C31—41no—
39C2×D4×C31—42no—
40C2×D4×C31—41no—
41C2×D4×C31—84no—
42C2×D4×C31C22⋊C412yes—
43C2×D4×C31C2×D412yes—
44C22×C4×C31—21no—
45C22×C4×C31—41no—
46C22×C4×C31—82no—
47C22×C4×C31C22⋊C411yescharacteristic
48C2×C8×C31—22no—
49C2×C8×C31—41no—
50C2×C8×C31—41no—
51C4⋊C4×C31—22no—
52C4⋊C4×C31—42no—
53C4⋊C4×C31—42no—
54C4⋊C4×C31—41no—
55C22⋊C4×C31—44no—
56C22⋊C4×C31—82no—
57C42×C31—21no—
58C42×C31C22⋊C411yescharacteristic
59C42×C31C22×C411yescharacteristic
60C2×#1412C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—22no—
62C23×C31—22no—
63C23×C31—42no—
64C23×C31—42no—
65C23×C31—84no—
66C23×C31#9911yescharacteristic
67D4×C31—42no—
68D4×C31—42no—
69D4×C31—82no—
70D4×C31—82no—
71D4×C31—84no—
72D4×C31—82no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—82no—
80C2×C4×C31—84no—
81C2×C4×C31—164no—
82C2×C4×C31#9911yescharacteristic
83C2×C4×C31C2×C22⋊C411yescharacteristic
84C8×C31—42no—
85C2×#490C2×C3111yescharacteristic
86C2×#353C2×C3112yes—
87#1412C2×C3114yesdirect product factor
88C22×C31—22no—
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—82no—
92C22×C31—82no—
93C22×C31—84no—
94C22×C31—162no—
95C22×C31#35411yescharacteristic
96C22×C31#35411yescharacteristic
97C22×C31C2×#9911yescharacteristic
98C4×C31—21no—
99C4×C31—21no—
100C4×C31—41no—
101C4×C31—41no—
102C4×C31—82no—
103C4×C31—164no—
104C2×#127C22×C3111yescharacteristic
105C2×#125C4×C3111yescharacteristic, complemented
106#490—22no—
107#490C4×C3112yescomplemented
108#490C22×C3112yes—
109C2×#102—22no—
110C2×#99—22no—
111C2×#97C4×C3111yescharacteristic, complemented
112#353—22no—
113#353C22×C3114yes—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31—82no—
117C2×C31—82no—
118C2×C31#141212yesdirect product factor
119C2×C31C2×#35411yescharacteristic
120C22×D4—41no—
121C22×D4D4×C3112yes—
122C22×C8—21no—
123#127—41no—
124#127C2×C4×C3111yescharacteristic
125#127D4×C3112yes—
126#127C23×C3111yescharacteristic
127#125—21no—
128#125—41no—
129#125C2×C4×C3112yescomplemented
130C2×C4⋊C4—21no—
131C2×C4⋊C4—41no—
132C2×C22⋊C4—42no—
133C2×C42C2×C4×C3111yescharacteristic
134#102—24no—
135#102—24no—
136#99—24no—
137#99—42no—
138#97—21no—
139#97C2×C4×C3112yescomplemented
140C31C2×#141211yescharacteristic, direct product factor, Sylow
141C24—22no—
142C2×D4—22no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4—41no—
146C2×D4—42no—
147C2×D4—41no—
148C2×D4—84no—
149C2×D4C22⋊C4×C3112yes—
150C2×D4C2×D4×C3112yes—
151C22×C4—21no—
152C22×C4—41no—
153C22×C4—82no—
154C22×C4C22⋊C4×C3111yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—41no—
162C22⋊C4—44no—
163C22⋊C4—82no—
164C42—21no—
165C42C22⋊C4×C3111yescharacteristic
166C42C22×C4×C3111yescharacteristic
167C23—22no—
168C23—22no—
169C23—42no—
170C23—42no—
171C23—84no—
172C23C31×#9911yescharacteristic
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178D4—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—84no—
187C2×C4—164no—
188C2×C4C31×#9911yescharacteristic
189C2×C4C2×C22⋊C4×C3111yescharacteristic
190C8—42no—
191C22—22no—
192C22—42no—
193C22—42no—
194C22—82no—
195C22—82no—
196C22—84no—
197C22—162no—
198C22C31×#35411yescharacteristic
199C22C31×#35411yescharacteristic
200C22C2×C31×#9911yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—164no—
207C2—21no—
208C2—21no—
209C2—82no—
210C2—82no—
211C2C31×#141212yesdirect product factor
212C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC22×C31#354
commutatorC42C22×C4×C31
Frattini, cosocle#127C23×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
3. C31×#1412C2direct (N × H)
5. C2×C31×#125C4semidirect
7. C31×#490C4semidirect
11. C2×C31×#97C4semidirect
23. C31×#125C2×C4semidirect
33. C31×#97C2×C4semidirect
60. C2×#1412C31direct (N × H)
87. #1412C2×C31direct (N × H)
105. C2×#125C4×C31semidirect
107. #490C4×C31semidirect
111. C2×#97C4×C31semidirect
118. C2×C31#1412direct (N × H)
129. #125C2×C4×C31semidirect
139. #97C2×C4×C31semidirect
140. C31C2×#1412direct (N × H)
211. C2C31×#1412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4902
C2×C31×#3532
C31×#14122
C2×#141231