Finite Group Databasebeta

← C31×#7346 #21464105

Subgroups — C31×#7346 #21464105

Order 7936.

318 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1794C211yesmaximal, characteristic
2C31×#1321C211yesmaximal, characteristic, complemented
3C31×#1315C211yesmaximal, characteristic, complemented
4C31×#585C411yescharacteristic
5C31×#421—21no—
6C31×#416—21no—
7C31×#410C411yescharacteristic
8C31×#408C2211yescharacteristic
9C31×#349—21no—
10C31×C22⋊C16—21no—
11C31×2−1+4—21no—
12C31×2−1+4—41no—
13C31×H(5,𝔽2)—41no—
14C31×H(5,𝔽2)—41no—
15C31×H(5,𝔽2)C812yes—
16C2×#41×C31—21no—
17C2×#41×C31—41no—
18C2×#41×C31—42no—
19C2×#41×C31C2×C411yescharacteristic
20C2×M16×C31D411yescharacteristic
21C22×C8×C31D411yescharacteristic
22C31×#117—21no—
23C31×M32—41no—
24C2×C16×C31—41no—
25C31×#104—42no—
26C31×#103—41no—
27C31×#102—41no—
28C31×#99—41no—
29C31×C22⋊C8—41no—
30#41×C31—22no—
31#41×C31—22no—
32#41×C31—41no—
33#41×C31—42no—
34#41×C31—41no—
35#41×C31—41no—
36#41×C31—42no—
37#41×C31—42no—
38#41×C31—44no—
39#41×C31—42no—
40#41×C31—41no—
41#41×C31—42no—
42C2×Q8×C31—21no—
43C2×Q8×C31—42no—
44C2×Q8×C31—41no—
45C2×Q8×C31M1611yescharacteristic
46C2×D4×C31—21no—
47C2×D4×C31—21no—
48C2×D4×C31—42no—
49C2×D4×C31—44no—
50C2×D4×C31—41no—
51C2×D4×C31—42no—
52C2×D4×C31—41no—
53C2×D4×C31C2×C811yescharacteristic
54C22×C4×C31—21no—
55C22×C4×C31—41no—
56C22×C4×C31—42no—
57C22×C4×C31C22⋊C411yescharacteristic
58M16×C31—41no—
59C2×C8×C31—21no—
60C2×C8×C31—21no—
61C2×C8×C31—41no—
62C4⋊C4×C31—41no—
63C22⋊C4×C31—41no—
64C42×C31—41no—
65C16×C31—81no—
66C16×C31—81no—
67#7346C3111yesmaximal, characteristic, direct product factor, Sylow
68C23×C31—21no—
69C23×C31—41no—
70C23×C31—42no—
71C23×C31#10011yescharacteristic
72Q8×C31—22no—
73Q8×C31—41no—
74Q8×C31—42no—
75Q8×C31—41no—
76D4×C31—22no—
77D4×C31—41no—
78D4×C31—42no—
79D4×C31—42no—
80D4×C31—42no—
81D4×C31—44no—
82D4×C31—42no—
83D4×C31—41no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—42no—
88C2×C4×C31—41no—
89C2×C4×C31—44no—
90C2×C4×C31—41no—
91C2×C4×C31—41no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—81no—
95C2×C4×C31C22⋊C811yescharacteristic
96C2×C4×C31#9911yescharacteristic
97C8×C31—41no—
98C8×C31—41no—
99#1794C2×C3111yescharacteristic
100#1321C2×C3111yescharacteristic, complemented
101#1315C2×C3111yescharacteristic, complemented
102C22×C31—21no—
103C22×C31—41no—
104C22×C31—42no—
105C22×C31—41no—
106C22×C31—81no—
107C22×C31—161no—
108C22×C31—162no—
109C22×C31#32311yescharacteristic
110C4×C31—21no—
111C4×C31—41no—
112C4×C31—42no—
113C4×C31—161no—
114C4×C31AΣL(1,𝔽16)11yescharacteristic
115C4×C31AΣL(1,𝔽16)11yescharacteristic
116#585C4×C3111yescharacteristic
117#421—21no—
118#416—21no—
119#410C4×C3111yescharacteristic
120#408C22×C3111yescharacteristic
121#349—21no—
122C22⋊C16—21no—
123C2×C31—21no—
124C2×C31—41no—
125C2×C31—81no—
126C2×C31—82no—
127C2×C31#131611yescharacteristic
1282−1+4—21no—
1292−1+4—41no—
130H(5,𝔽2)—41no—
131H(5,𝔽2)—41no—
132H(5,𝔽2)C8×C3112yes—
133C2×#41—21no—
134C2×#41—41no—
135C2×#41—42no—
136C2×#41C2×C4×C3111yescharacteristic
137C2×M16D4×C3111yescharacteristic
138C22×C8D4×C3111yescharacteristic
139#117—21no—
140M32—41no—
141C2×C16—41no—
142#104—42no—
143#103—41no—
144#102—41no—
145#99—41no—
146C22⋊C8—41no—
147C31#734611yescharacteristic, direct product factor, Sylow
148#41—22no—
149#41—22no—
150#41—41no—
151#41—42no—
152#41—41no—
153#41—41no—
154#41—42no—
155#41—42no—
156#41—44no—
157#41—42no—
158#41—41no—
159#41—42no—
160C2×Q8—21no—
161C2×Q8—42no—
162C2×Q8—41no—
163C2×Q8M16×C3111yescharacteristic
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—42no—
167C2×D4—44no—
168C2×D4—41no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4C2×C8×C3111yescharacteristic
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4C22⋊C4×C3111yescharacteristic
176M16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—41no—
180C4⋊C4—41no—
181C22⋊C4—41no—
182C42—41no—
183C16—81no—
184C16—81no—
185C23—21no—
186C23—41no—
187C23—42no—
188C23C31×#10011yescharacteristic
189Q8—22no—
190Q8—41no—
191Q8—42no—
192Q8—41no—
193D4—22no—
194D4—41no—
195D4—42no—
196D4—42no—
197D4—42no—
198D4—44no—
199D4—42no—
200D4—41no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—44no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4C31×C22⋊C811yescharacteristic
213C2×C4C31×#9911yescharacteristic
214C8—41no—
215C8—41no—
216C22—21no—
217C22—41no—
218C22—42no—
219C22—41no—
220C22—81no—
221C22—161no—
222C22—162no—
223C22C31×#32311yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—161no—
228C4C31×AΣL(1,𝔽16)11yescharacteristic
229C4C31×AΣL(1,𝔽16)11yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—82no—
234C2C31×#131611yescharacteristic
subgroupG/H
centerC4×C31AΣL(1,𝔽16)
commutatorC2×D4C2×C8×C31
Frattini, cosocle#408C22×C31
socleC2×C31#1316
prime radicalC31×#585C4
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#408 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1321C2semidirect
3. C31×#1315C2semidirect
67. #7346C31direct (N × H)
100. #1321C2×C31semidirect
101. #1315C2×C31semidirect
147. C31#7346direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17942
C31×#13212
C31×#13152
#734631