Finite Group Databasebeta

← C31×#7345 #21464104

Subgroups — C31×#7345 #21464104

Order 7936.

342 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1793C211yesmaximal, characteristic
2C31×#1319C211yesmaximal, characteristic, complemented
3C31×#1272C211yesmaximal, characteristic, complemented
4C2×C31×2−1+4C411yescharacteristic
5C2×C31×#104—21no—
6C31×#417—21no—
7C2×C31×#101C411yescharacteristic
8C31×#391C2211yescharacteristic
9C31×#336—21no—
10C31×#324—21no—
11C31×2−1+4—21no—
12C31×2−1+4—41no—
13C31×2−1+4—42no—
14C31×2−1+4C812yescomplemented
15C2×#41×C31—21no—
16C2×#41×C31—41no—
17C2×#41×C31—41no—
18C22×Q8×C31—41no—
19C22×Q8×C31C2×C411yescharacteristic
20C2×M16×C31—21no—
21C22×C8×C31—41no—
22C2×C4⋊C4×C31D411yescharacteristic
23C2×C42×C31D411yescharacteristic
24C31×#104—42no—
25C31×#103—41no—
26C31×#102—41no—
27C31×#101—41no—
28C31×C22⋊C8—41no—
29C31×#95—41no—
30#41×C31—22no—
31#41×C31—22no—
32#41×C31—41no—
33#41×C31—42no—
34#41×C31—42no—
35#41×C31—42no—
36#41×C31—42no—
37#41×C31—44no—
38#41×C31—42no—
39#41×C31—42no—
40#41×C31—41no—
41C2×Q8×C31—21no—
42C2×Q8×C31—21no—
43C2×Q8×C31—41no—
44C2×Q8×C31—41no—
45C2×Q8×C31—42no—
46C2×Q8×C31—42no—
47C2×Q8×C31—44no—
48C2×Q8×C31—41no—
49C2×Q8×C31C2×C811yescharacteristic
50C2×Q8×C31M1611yescharacteristic
51C2×D4×C31—21no—
52C2×D4×C31—41no—
53C2×D4×C31—41no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—41no—
58C22×C4×C31—42no—
59C22×C4×C31C22⋊C411yescharacteristic
60M16×C31—41no—
61M16×C31—41no—
62C2×C8×C31—41no—
63C2×C8×C31—42no—
64C2×C8×C31—81no—
65C2×C8×C31—81no—
66C2×C8×C31—81no—
67C4⋊C4×C31—41no—
68C42×C31—41no—
69#7345C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—41no—
71C23×C31#9911yescharacteristic
72Q8×C31—22no—
73Q8×C31—41no—
74Q8×C31—41no—
75Q8×C31—42no—
76Q8×C31—41no—
77Q8×C31—42no—
78Q8×C31—42no—
79D4×C31—22no—
80D4×C31—41no—
81D4×C31—42no—
82D4×C31—42no—
83D4×C31—42no—
84D4×C31—42no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—41no—
94C2×C4×C31—44no—
95C2×C4×C31—44no—
96C2×C4×C31—41no—
97C2×C4×C31—41no—
98C2×C4×C31—41no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—81no—
102C2×C4×C31C22⋊C811yescharacteristic
103C2×C4×C31#10011yescharacteristic
104C8×C31—81no—
105C8×C31—82no—
106C8×C31—161no—
107#1793C2×C3111yescharacteristic
108#1319C2×C3111yescharacteristic, complemented
109#1272C2×C3111yescharacteristic, complemented
110C22×C31—21no—
111C22×C31—21no—
112C22×C31—42no—
113C22×C31—81no—
114C22×C31—81no—
115C22×C31#32311yescharacteristic
116C22×C31AΣL(1,𝔽16)11yescharacteristic
117C22×C31AΣL(1,𝔽16)11yescharacteristic
118C4×C31—21no—
119C4×C31—21no—
120C4×C31—41no—
121C4×C31—41no—
122C4×C31—41no—
123C4×C31—41no—
124C4×C31—42no—
125C4×C31—81no—
126C2×2−1+4C4×C3111yescharacteristic
127C2×#104—21no—
128#417—21no—
129C2×#101C4×C3111yescharacteristic
130#391C22×C3111yescharacteristic
131#336—21no—
132#324—21no—
133C2×C31—21no—
134C2×C31—21no—
135C2×C31—82no—
136C2×C31#131611yescharacteristic
137C2×C31#140411yescharacteristic
138C2×C31#140511yescharacteristic
1392−1+4—21no—
1402−1+4—41no—
1412−1+4—42no—
1422−1+4C8×C3112yescomplemented
143C2×#41—21no—
144C2×#41—41no—
145C2×#41—41no—
146C22×Q8—41no—
147C22×Q8C2×C4×C3111yescharacteristic
148C2×M16—21no—
149C22×C8—41no—
150C2×C4⋊C4D4×C3111yescharacteristic
151C2×C42D4×C3111yescharacteristic
152#104—42no—
153#103—41no—
154#102—41no—
155#101—41no—
156C22⋊C8—41no—
157#95—41no—
158C31#734511yescharacteristic, direct product factor, Sylow
159#41—22no—
160#41—22no—
161#41—41no—
162#41—42no—
163#41—42no—
164#41—42no—
165#41—42no—
166#41—44no—
167#41—42no—
168#41—42no—
169#41—41no—
170C2×Q8—21no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—44no—
177C2×Q8—41no—
178C2×Q8C2×C8×C3111yescharacteristic
179C2×Q8M16×C3111yescharacteristic
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4C22⋊C4×C3111yescharacteristic
189M16—41no—
190M16—41no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C4⋊C4—41no—
197C42—41no—
198C23—41no—
199C23C31×#9911yescharacteristic
200Q8—22no—
201Q8—41no—
202Q8—41no—
203Q8—42no—
204Q8—41no—
205Q8—42no—
206Q8—42no—
207D4—22no—
208D4—41no—
209D4—42no—
210D4—42no—
211D4—42no—
212D4—42no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4C31×C22⋊C811yescharacteristic
231C2×C4C31×#10011yescharacteristic
232C8—81no—
233C8—82no—
234C8—161no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—81no—
239C22—81no—
240C22C31×#32311yescharacteristic
241C22C31×AΣL(1,𝔽16)11yescharacteristic
242C22C31×AΣL(1,𝔽16)11yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—42no—
250C4—81no—
251C2—21no—
252C2—21no—
253C2—82no—
254C2C31×#131611yescharacteristic
255C2C31×#140411yescharacteristic
256C2C31×#140511yescharacteristic
subgroupG/H
center, socleC22×C31AΣL(1,𝔽16)
commutatorC2×Q8C2×C8×C31
Frattini, cosocle#391C22×C31
prime radicalC2×C31×2−1+4C4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#391 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1319C2semidirect
3. C31×#1272C2semidirect
14. C31×2−1+4C8semidirect
69. #7345C31direct (N × H)
108. #1319C2×C31semidirect
109. #1272C2×C31semidirect
142. 2−1+4C8×C31semidirect
158. C31#7345direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17932
C31×#13192
C31×#12722
#734531