Finite Group Databasebeta

← C31×#10037 #21466796

Subgroups — C31×#10037 #21466796

Order 7936.

476 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3162C211yesmaximal, characteristic
2C31×#3104C212yesmaximal
3C31×#1985C211yesmaximal, characteristic
4C31×#1481C212yesmaximal
5C31×#1275C211yesmaximal, characteristic
6C31×#533C2212yes—
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#501—22no—
9C31×#501—22no—
10C31×#484—22no—
11C31×#477—22no—
12C31×#462—22no—
13C31×#451—22no—
14C4×Q16×C31—24no—
15C31×#431C2212yes—
16C31×#427—22no—
17C2×C31×C4⋊C8C2211yescharacteristic
18C2×C31×#97C2211yescharacteristic
19C31×#336—22no—
20C31×Q8⋊C8—24no—
21C22×Q8×C31D411yescharacteristic
22C2×Q16×C31—24no—
23C22×C8×C31—21no—
24C22×C8×C31D412yes—
25C31×C4⋊Q8D412yes—
26C31×C4⋊Q8D412yes—
27C31×#125—22no—
28C31×C22⋊Q8—22no—
29C31×C22⋊Q8—22no—
30C4×Q8×C31—22no—
31C4×Q8×C31—22no—
32C4×Q8×C31—22no—
33C4×Q8×C31—22no—
34C31×#117—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C42×C31—21no—
38C2×C42×C31C2311yescharacteristic
39C31×#107—22no—
40C31×#107—22no—
41C31×#107—24no—
42C31×#106—24no—
43C31×C4⋊C8—22no—
44C31×C4⋊C8—22no—
45C31×#103—24no—
46C31×#103—24no—
47C31×C22⋊C8—22no—
48C31×#97—22no—
49C4×C8×C31D414yes—
50C2×Q8×C31—22no—
51C2×Q8×C31—22no—
52C2×Q8×C31—22no—
53C2×Q8×C31—42no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31C2×D411yescharacteristic
57C22×C4×C31C2×D411yescharacteristic
58C22×C4×C31#4111yescharacteristic
59Q16×C31—48no—
60C2×C8×C31—22no—
61C2×C8×C31—22no—
62C2×C8×C31—24no—
63C2×C8×C31—41no—
64C2×C8×C31—42no—
65C2×C8×C31Q1614yescomplemented
66C4⋊C4×C31—22no—
67C4⋊C4×C31—22no—
68C4⋊C4×C31—22no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—42no—
74C22⋊C4×C31—42no—
75C42×C31—41no—
76C42×C31—41no—
77C42×C31—42no—
78C42×C31C2×D412yes—
79C42×C31C2×D412yes—
80#10037C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31#12111yescharacteristic
82Q8×C31—24no—
83Q8×C31—42no—
84Q8×C31—44no—
85Q8×C31—44no—
86C2×C4×C31—22no—
87C2×C4×C31—41no—
88C2×C4×C31—41no—
89C2×C4×C31—41no—
90C2×C4×C31—41no—
91C2×C4×C31—42no—
92C2×C4×C31—41no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31#12012yes—
96C2×C4×C31#12011yescharacteristic
97C2×C4×C31#12112yes—
98C2×C4×C31#12711yescharacteristic
99C2×C4×C31C2×Q1612yes—
100C2×C4×C31#13712yes—
101C8×C31—24no—
102C8×C31—44no—
103C8×C31—81no—
104#3162C2×C3111yescharacteristic
105#3104C2×C3112yes—
106#1985C2×C3111yescharacteristic
107#1481C2×C3112yes—
108#1275C2×C3111yescharacteristic
109C22×C31—21no—
110C22×C31—21no—
111C22×C31#39211yescharacteristic
112C22×C31#46212yes—
113C4×C31—22no—
114C4×C31—22no—
115C4×C31—42no—
116C4×C31—82no—
117C4×C31—81no—
118C4×C31—82no—
119C4×C31#45112yes—
120C4×C31#49411yescharacteristic
121C4×C31#49711yescharacteristic
122#533C22×C3112yes—
123C2×C4×Q8C22×C3111yescharacteristic
124#501—22no—
125#501—22no—
126#484—22no—
127#477—22no—
128#462—22no—
129#451—22no—
130C4×Q16—24no—
131#431C22×C3112yes—
132#427—22no—
133C2×C4⋊C8C22×C3111yescharacteristic
134C2×#97C22×C3111yescharacteristic
135#336—22no—
136Q8⋊C8—24no—
137C2×C31—22no—
138C2×C31#201011yescharacteristic
139C2×C31#201611yescharacteristic
140C2×C31#201711yescharacteristic
141C22×Q8D4×C3111yescharacteristic
142C2×Q16—24no—
143C22×C8—21no—
144C22×C8D4×C3112yes—
145C4⋊Q8D4×C3112yes—
146C4⋊Q8D4×C3112yes—
147#125—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154#117—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4D4×C3111yescharacteristic
157C2×C42—21no—
158C2×C42C23×C3111yescharacteristic
159#107—22no—
160#107—22no—
161#107—24no—
162#106—24no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165#103—24no—
166#103—24no—
167C22⋊C8—22no—
168#97—22no—
169C4×C8D4×C3114yes—
170C31#1003711yescharacteristic, direct product factor, Sylow
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—42no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D4×C3111yescharacteristic
178C22×C4C2×D4×C3111yescharacteristic
179C22×C4#41×C3111yescharacteristic
180Q16—48no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—24no—
184C2×C8—41no—
185C2×C8—42no—
186C2×C8Q16×C3114yescomplemented
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C22⋊C4—42no—
196C42—41no—
197C42—41no—
198C42—42no—
199C42C2×D4×C3112yes—
200C42C2×D4×C3112yes—
201C23C31×#12111yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—44no—
205Q8—44no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4C31×#12012yes—
216C2×C4C31×#12011yescharacteristic
217C2×C4C31×#12112yes—
218C2×C4C31×#12711yescharacteristic
219C2×C4C2×Q16×C3112yes—
220C2×C4C31×#13712yes—
221C8—24no—
222C8—44no—
223C8—81no—
224C22—21no—
225C22—21no—
226C22C31×#39211yescharacteristic
227C22C31×#46212yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—82no—
232C4—81no—
233C4—82no—
234C4C31×#45112yes—
235C4C31×#49411yescharacteristic
236C4C31×#49711yescharacteristic
237C2—22no—
238C2C31×#201011yescharacteristic
239C2C31×#201611yescharacteristic
240C2C31×#201711yescharacteristic
subgroupG/H
centerC2×C4×C31#127
commutator, Frattini, cosocleC2×C42C23×C31
socleC22×C31#392
prime radicalC23×C31#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
65. C2×C8×C31Q16semidirect
80. #10037C31direct (N × H)
170. C31#10037direct (N × H)
186. C2×C8Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#31622
C31×#31042
C31×#19852
C31×#14812
C31×#12752
#1003731