Finite Group Databasebeta

← C31×#32794 #21489553

Subgroups — C31×#32794 #21489553

Order 7936.

600 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 206 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×#2628C212yesmaximal
2C31×#2101C214yesmaximal, complemented
3C31×#2077C214yesmaximal
4C31×#2058C214yesmaximal, complemented
5C31×#1818C211yesmaximal, characteristic
6C2×C31×C4⋊Q8C2212yes—
7C2×C31×#117C2211yescharacteristic
8C2×C31×#106C2214yes—
9C2×C31×C22⋊C8C2212yes—
10C31×#400—22no—
11C31×#399—22no—
12C31×#395—22no—
13C31×#393—22no—
14C31×#389C2214yes—
15C31×#382C2212yes—
16C31×#380C2214yes—
17C31×#340C2218yes—
18C31×#340C2214yes—
19C31×#336C2214yes—
20C22×Q8×C31—22no—
21C23×C4×C31C2311yescharacteristic
22C22×C8×C31C2314yes—
23C31×C4⋊Q8—44no—
24C31×#117—42no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—24no—
27C2×C4⋊C4×C31D412yes—
28C2×C4⋊C4×C31C2314yes—
29C2×C4⋊C4×C31C2314yes—
30C2×C22⋊C4×C31—24no—
31C2×C22⋊C4×C31D411yescharacteristic
32C2×C22⋊C4×C31D411yescharacteristic
33C2×C42×C31C2312yes—
34C31×#106—44no—
35C31×C22⋊C8—42no—
36C31×#95—24no—
37C31×#95—22no—
38C31×#95—22no—
39C31×#95—24no—
40C24×C31C2×D411yescharacteristic
41C2×Q8×C31—44no—
42C2×Q8×C31—84no—
43C22×C4×C31—22no—
44C22×C4×C31—24no—
45C22×C4×C31—24no—
46C22×C4×C31—24no—
47C22×C4×C31C2×D411yescharacteristic
48C22×C4×C31C2×D412yes—
49C22×C4×C31C2×D412yes—
50C22×C4×C31C2411yescharacteristic
51C2×C8×C31—24no—
52C2×C8×C31—28no—
53C4⋊C4×C31—28no—
54C4⋊C4×C31—28no—
55C4⋊C4×C31—42no—
56C4⋊C4×C31—44no—
57C4⋊C4×C31—84no—
58C22⋊C4×C31—41no—
59C22⋊C4×C31—41no—
60C22⋊C4×C31—84no—
61C42×C31—24no—
62#32794C3111yesmaximal, characteristic, direct product factor, Sylow
63C23×C31—21no—
64C23×C31—22no—
65C23×C31—24no—
66C23×C31C22×D411yescharacteristic
67Q8×C31—88no—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—21no—
71C2×C4×C31—22no—
72C2×C4×C31—24no—
73C2×C4×C31—24no—
74C2×C4×C31—44no—
75C2×C4×C31—44no—
76C2×C4×C31—44no—
77C2×C4×C31—44no—
78C2×C4×C31—44no—
79C2×C4×C31—44no—
80C2×C4×C31—44no—
81C2×C4×C31H(5,𝔽2)12yes—
82C2×C4×C312−1+414yes—
83C8×C31—44no—
84#2628C2×C3112yes—
85#2101C2×C3114yescomplemented
86#2077C2×C3114yes—
87#2058C2×C3114yescomplemented
88#1818C2×C3111yescharacteristic
89C22×C31—41no—
90C22×C31—42no—
91C22×C31—44no—
92C22×C31#53411yescharacteristic
93C22×C31#53612yes—
94C22×C31#57714yes—
95C4×C31—41no—
96C4×C31—42no—
97C4×C31—42no—
98C4×C31—84no—
99C4×C31—84no—
100C4×C31#56314yes—
101C2×C4⋊Q8C22×C3112yes—
102C2×#117C22×C3111yescharacteristic
103C2×#106C22×C3114yes—
104C2×C22⋊C8C22×C3112yes—
105#400—22no—
106#399—22no—
107#395—22no—
108#393—22no—
109#389C22×C3114yes—
110#382C22×C3112yes—
111#380C22×C3114yes—
112#340C22×C3118yes—
113#340C22×C3114yes—
114#336C22×C3114yes—
115C2×C31—81no—
116C2×C31#281711yescharacteristic
117C2×C31#320012yes—
118C2×C31#324414yes—
119C22×Q8—22no—
120C23×C4C23×C3111yescharacteristic
121C22×C8C23×C3114yes—
122C4⋊Q8—44no—
123#117—42no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4D4×C3112yes—
127C2×C4⋊C4C23×C3114yes—
128C2×C4⋊C4C23×C3114yes—
129C2×C22⋊C4—24no—
130C2×C22⋊C4D4×C3111yescharacteristic
131C2×C22⋊C4D4×C3111yescharacteristic
132C2×C42C23×C3112yes—
133#106—44no—
134C22⋊C8—42no—
135#95—24no—
136#95—22no—
137#95—22no—
138#95—24no—
139C31#3279411yescharacteristic, direct product factor, Sylow
140C24C2×D4×C3111yescharacteristic
141C2×Q8—44no—
142C2×Q8—84no—
143C22×C4—22no—
144C22×C4—24no—
145C22×C4—24no—
146C22×C4—24no—
147C22×C4C2×D4×C3111yescharacteristic
148C22×C4C2×D4×C3112yes—
149C22×C4C2×D4×C3112yes—
150C22×C4C24×C3111yescharacteristic
151C2×C8—24no—
152C2×C8—28no—
153C4⋊C4—28no—
154C4⋊C4—28no—
155C4⋊C4—42no—
156C4⋊C4—44no—
157C4⋊C4—84no—
158C22⋊C4—41no—
159C22⋊C4—41no—
160C22⋊C4—84no—
161C42—24no—
162C23—21no—
163C23—22no—
164C23—24no—
165C23C22×D4×C3111yescharacteristic
166Q8—88no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4C31×H(5,𝔽2)12yes—
181C2×C4C31×2−1+414yes—
182C8—44no—
183C22—42no—
184C22—44no—
185C22—41no—
186C22C31×#53411yescharacteristic
187C22C31×#53612yes—
188C22C31×#57714yes—
189C4—42no—
190C4—42no—
191C4—41no—
192C4—84no—
193C4—84no—
194C4C31×#56314yes—
195C2—81no—
196C2C31×#281711yescharacteristic
197C2C31×#320012yes—
198C2C31×#324414yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2101C2semidirect
4. C31×#2058C2semidirect
62. #32794C31direct (N × H)
85. #2101C2×C31semidirect
87. #2058C2×C31semidirect
139. C31#32794direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26282
C31×#21012
C31×#20772
C31×#20582
C31×#18182
#3279431