Finite Group Databasebeta

← C31×#1495 #16841428

Subgroups — C31×#1495 #16841428

Order 3968.

216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 92 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×#529C211yesmaximal, characteristic
2C31×#431C211yesmaximal, characteristic, complemented
3C31×#423C211yesmaximal, characteristic, complemented
4C31×Q8⋊C8C212yesmaximal, complemented
5C31×D4⋊C8C212yesmaximal, complemented
6C2×M16×C31—21no—
7C31×#126—21no—
8C31×#125C411yescharacteristic
9C31×#124C411yescharacteristic
10C31×#123—21no—
11C31×C22⋊Q8C411yescharacteristic
12C31×#121C411yescharacteristic
13C4×Q8×C31C2211yescharacteristic
14C4×D4×C31—21no—
15C4×D4×C31C2211yescharacteristic
16C31×#117—21no—
17C2×C42×C31C2211yescharacteristic
18C31×C4⋊C8—21no—
19C31×C4⋊C8—21no—
20C31×C4⋊C8C2212yes—
21C31×C22⋊C8—21no—
22C4×C8×C31C2212yes—
23C2×Q8×C31C2×C411yescharacteristic
24C2×D4×C31—21no—
25C2×D4×C31C2×C411yescharacteristic
26C22×C4×C31—21no—
27C22×C4×C31C2×C411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30M16×C31—42no—
31C2×C8×C31—22no—
32C2×C8×C31—22no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31C2×C411yescharacteristic
38C4⋊C4×C31C2×C411yescharacteristic
39C22⋊C4×C31—21no—
40C22⋊C4×C31—21no—
41C22⋊C4×C31—21no—
42C22⋊C4×C31—21no—
43C22⋊C4×C31—21no—
44C42×C31—21no—
45C42×C31C2×C411yescharacteristic
46C42×C31D411yescharacteristic
47C42×C31D411yescharacteristic
48C42×C31C2311yescharacteristic
49C23×C31—21no—
50C23×C31C22⋊C411yescharacteristic
51Q8×C31—22no—
52D4×C31—22no—
53D4×C31—42no—
54C2×C4×C31—22no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C22⋊C411yescharacteristic
64C2×C4×C31C22⋊C411yescharacteristic
65C2×C4×C31C22⋊C411yescharacteristic
66C2×C4×C31C22×C411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C8×C31—42no—
70C8×C31—42no—
71#1495C3111yesmaximal, characteristic, direct product factor, Sylow
72C22×C31—21no—
73C22×C31—21no—
74C22×C31—21no—
75C22×C31—41no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31C2×C22⋊C411yescharacteristic
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—41no—
84C4×C31—41no—
85C4×C31—41no—
86C4×C31#13112yes—
87C4×C31AGL(1,ℤ/8)11yescharacteristic
88C4×C31#13711yescharacteristic
89#529C2×C3111yescharacteristic
90#431C2×C3111yescharacteristic, complemented
91#423C2×C3111yescharacteristic, complemented
92Q8⋊C8C2×C3112yescomplemented
93D4⋊C8C2×C3112yescomplemented
94C2×C31—41no—
95C2×C31—81no—
96C2×C31#40811yescharacteristic
97C2×C31#41711yescharacteristic
98C2×C31#42111yescharacteristic
99C2×M16—21no—
100#126—21no—
101#125C4×C3111yescharacteristic
102#124C4×C3111yescharacteristic
103#123—21no—
104C22⋊Q8C4×C3111yescharacteristic
105#121C4×C3111yescharacteristic
106C4×Q8C22×C3111yescharacteristic
107C4×D4—21no—
108C4×D4C22×C3111yescharacteristic
109#117—21no—
110C2×C42C22×C3111yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8C22×C3112yes—
114C22⋊C8—21no—
115C4×C8C22×C3112yes—
116C31#149511yescharacteristic, direct product factor, Sylow
117C2×Q8C2×C4×C3111yescharacteristic
118C2×D4—21no—
119C2×D4C2×C4×C3111yescharacteristic
120C22×C4—21no—
121C22×C4C2×C4×C3111yescharacteristic
122C22×C4D4×C3111yescharacteristic
123C22×C4D4×C3111yescharacteristic
124M16—42no—
125C2×C8—22no—
126C2×C8—22no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4C2×C4×C3111yescharacteristic
132C4⋊C4C2×C4×C3111yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—21no—
138C42—21no—
139C42C2×C4×C3111yescharacteristic
140C42D4×C3111yescharacteristic
141C42D4×C3111yescharacteristic
142C42C23×C3111yescharacteristic
143C23—21no—
144C23C22⋊C4×C3111yescharacteristic
145Q8—22no—
146D4—22no—
147D4—42no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4C22⋊C4×C3111yescharacteristic
158C2×C4C22⋊C4×C3111yescharacteristic
159C2×C4C22⋊C4×C3111yescharacteristic
160C2×C4C22×C4×C3111yescharacteristic
161C2×C4C2×D4×C3111yescharacteristic
162C2×C4C2×D4×C3111yescharacteristic
163C8—42no—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×C22⋊C4×C3111yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4C31×#13112yes—
180C4C31×AGL(1,ℤ/8)11yescharacteristic
181C4C31×#13711yescharacteristic
182C2—41no—
183C2—81no—
184C2C31×#40811yescharacteristic
185C2C31×#41711yescharacteristic
186C2C31×#42111yescharacteristic
subgroupG/H
centerC2×C4×C31C2×D4
commutatorC2×C4C22×C4×C31
Frattini, cosocleC42C23×C31
socleC22×C31C2×C22⋊C4
prime radicalC31×#121C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#431C2semidirect
3. C31×#423C2semidirect
4. C31×Q8⋊C8C2semidirect
5. C31×D4⋊C8C2semidirect
71. #1495C31direct (N × H)
90. #431C2×C31semidirect
91. #423C2×C31semidirect
92. Q8⋊C8C2×C31semidirect
93. D4⋊C8C2×C31semidirect
116. C31#1495direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#5292
C31×#4312
C31×#4232
C31×Q8⋊C82
C31×D4⋊C82
#149531