Finite Group Databasebeta

← C31×#7496 #21464255

Subgroups — C31×#7496 #21464255

Order 7936.

274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2132C211yesmaximal, characteristic
2C31×#1884C211yesmaximal, characteristic
3C31×#1560C211yesmaximal, characteristic
4C31×#568C411yescharacteristic
5C31×#532C2211yescharacteristic
6C31×#423—21no—
7C31×#421—21no—
8C31×#413—21no—
9C31×#410C411yescharacteristic
10C31×#356—21no—
11C31×#355C412yescomplemented
12C31×#339—21no—
13C31×#333—21no—
14C31×#331C412yescomplemented
15C2×#41×C31C2×C411yescharacteristic
16C2×#41×C31D411yescharacteristic
17C31×#131—42no—
18C2×M16×C31—21no—
19C2×M16×C31—41no—
20C2×M16×C31—41no—
21C2×M16×C31—41no—
22C31×C4⋊Q8D411yescharacteristic
23C31×#127C2×C411yescharacteristic
24C31×#124C2×C411yescharacteristic
25C31×#124Q811yescharacteristic
26C31×#121—41no—
27C4×D4×C31—41no—
28C31×#117—21no—
29C2×C42×C31D411yescharacteristic
30C31×C4⋊C8—22no—
31C31×C4⋊C8—41no—
32C31×#104—42no—
33C31×#101—22no—
34C31×#100—41no—
35C31×#99—41no—
36#41×C31—41no—
37#41×C31—41no—
38#41×C31—41no—
39#41×C31—41no—
40C2×Q8×C31C22⋊C411yescharacteristic
41C2×Q8×C31C4⋊C411yescharacteristic
42C2×D4×C31—21no—
43C2×D4×C31—21no—
44C2×D4×C31—41no—
45C2×D4×C31C4211yescharacteristic
46C2×D4×C31C4⋊C411yescharacteristic
47C22×C4×C31—21no—
48C22×C4×C31—21no—
49C22×C4×C31—21no—
50C22×C4×C31C22⋊C411yescharacteristic
51M16×C31—22no—
52M16×C31—41no—
53M16×C31—42no—
54M16×C31—42no—
55M16×C31—82no—
56M16×C31—81no—
57C2×C8×C31—41no—
58C2×C8×C31—42no—
59C2×C8×C31—42no—
60C2×C8×C31—81no—
61C4⋊C4×C31—41no—
62C4⋊C4×C31—41no—
63C22⋊C4×C31—41no—
64C22⋊C4×C31—41no—
65C22⋊C4×C31—41no—
66C42×C31—21no—
67C42×C31—41no—
68C42×C31C22⋊C411yescharacteristic
69C42×C31C4⋊C411yescharacteristic
70#7496C3111yesmaximal, characteristic, direct product factor, Sylow
71C23×C31—21no—
72C23×C31—21no—
73C23×C31#9911yescharacteristic
74Q8×C31—41no—
75Q8×C31—41no—
76D4×C31—41no—
77D4×C31—41no—
78D4×C31—42no—
79D4×C31—81no—
80D4×C31—81no—
81D4×C31—81no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—41no—
89C2×C4×C31—41no—
90C2×C4×C31—41no—
91C2×C4×C31—41no—
92C2×C4×C31—41no—
93C2×C4×C31—41no—
94C2×C4×C31—81no—
95C2×C4×C31#9511yescharacteristic
96C2×C4×C31#9911yescharacteristic
97C8×C31—42no—
98C8×C31—82no—
99C8×C31—82no—
100#2132C2×C3111yescharacteristic
101#1884C2×C3111yescharacteristic
102#1560C2×C3111yescharacteristic
103C22×C31—21no—
104C22×C31—41no—
105C22×C31—41no—
106C22×C31—41no—
107C22×C31—81no—
108C22×C31—81no—
109C22×C31#34211yescharacteristic
110C4×C31—21no—
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—41no—
114C4×C31—41no—
115C4×C31—41no—
116C4×C31—161no—
117C4×C31AΣL(1,𝔽16)11yescharacteristic
118C4×C31#35211yescharacteristic
119#568C4×C3111yescharacteristic
120#532C22×C3111yescharacteristic
121#423—21no—
122#421—21no—
123#413—21no—
124#410C4×C3111yescharacteristic
125#356—21no—
126#355C4×C3112yescomplemented
127#339—21no—
128#333—21no—
129#331C4×C3112yescomplemented
130C2×C31—21no—
131C2×C31—41no—
132C2×C31—81no—
133C2×C31—81no—
134C2×C31#139011yescharacteristic
135C2×#41C2×C4×C3111yescharacteristic
136C2×#41D4×C3111yescharacteristic
137#131—42no—
138C2×M16—21no—
139C2×M16—41no—
140C2×M16—41no—
141C2×M16—41no—
142C4⋊Q8D4×C3111yescharacteristic
143#127C2×C4×C3111yescharacteristic
144#124C2×C4×C3111yescharacteristic
145#124Q8×C3111yescharacteristic
146#121—41no—
147C4×D4—41no—
148#117—21no—
149C2×C42D4×C3111yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—41no—
152#104—42no—
153#101—22no—
154#100—41no—
155#99—41no—
156C31#749611yescharacteristic, direct product factor, Sylow
157#41—41no—
158#41—41no—
159#41—41no—
160#41—41no—
161C2×Q8C22⋊C4×C3111yescharacteristic
162C2×Q8C4⋊C4×C3111yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4C42×C3111yescharacteristic
167C2×D4C4⋊C4×C3111yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4C22⋊C4×C3111yescharacteristic
172M16—22no—
173M16—41no—
174M16—42no—
175M16—42no—
176M16—82no—
177M16—81no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—81no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C42—21no—
188C42—41no—
189C42C22⋊C4×C3111yescharacteristic
190C42C4⋊C4×C3111yescharacteristic
191C23—21no—
192C23—21no—
193C23C31×#9911yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—42no—
199D4—81no—
200D4—81no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4C31×#9511yescharacteristic
216C2×C4C31×#9911yescharacteristic
217C8—42no—
218C8—82no—
219C8—82no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22C31×#34211yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—161no—
234C4C31×AΣL(1,𝔽16)11yescharacteristic
235C4C31×#35211yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2C31×#139011yescharacteristic
subgroupG/H
center, socleC2×C31#1390
commutatorC2×D4C42×C31
Frattini, cosocle#532C22×C31
prime radicalC31×#532C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

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

NH ≅ G/Ntype
11. C31×#355C4semidirect
14. C31×#331C4semidirect
70. #7496C31direct (N × H)
126. #355C4×C31semidirect
129. #331C4×C31semidirect
156. C31#7496direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#21322
C31×#18842
C31×#15602
#749631