Finite Group Databasebeta

← C31×#7489 #21464248

Subgroups — C31×#7489 #21464248

Order 7936.

302 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C31×#354C211yesmaximal, characteristic
2C31×#1888C211yesmaximal, characteristic
3C2×C31×#329C211yesmaximal, characteristic
4C2×C31×#124C2211yescharacteristic
5C31×#519C411yescharacteristic, complemented
6C31×#418—21no—
7C2×C31×#101C411yescharacteristic, complemented
8C2×C31×#99—21no—
9C2×C31×#97—21no—
10C31×#354—21no—
11C31×#354C412yescomplemented
12C31×#339—21no—
13C31×#329—21no—
14C31×#329C412yescomplemented
15C22×Q8×C31C2×C411yescharacteristic
16C22×D4×C31D411yescharacteristic
17C2×M16×C31—21no—
18C22×C8×C31—41no—
19C31×#124—41no—
20C31×#124C2×C411yescharacteristic
21C31×#124C2×C411yescharacteristic
22C31×#124D411yescharacteristic
23C31×#124Q811yescharacteristic
24C4×Q8×C31—42no—
25C31×#117—21no—
26C31×#117—41no—
27C2×C22⋊C4×C31—41no—
28C2×C22⋊C4×C31—41no—
29C2×C42×C31D411yescharacteristic
30C31×#102—42no—
31C31×#101—41no—
32C31×#99—22no—
33C31×#99—41no—
34C31×#97—22no—
35C31×#97—41no—
36C24×C31—21no—
37C2×Q8×C31—21no—
38C2×Q8×C31—41no—
39C2×Q8×C31—41no—
40C2×Q8×C31C4211yescharacteristic
41C2×Q8×C31C4⋊C411yescharacteristic
42C2×D4×C31—21no—
43C2×D4×C31—41no—
44C2×D4×C31—41no—
45C2×D4×C31C22⋊C411yescharacteristic
46C2×D4×C31C4⋊C411yescharacteristic
47C22×C4×C31—21no—
48C22×C4×C31—21no—
49C22×C4×C31—81no—
50C22×C4×C31C22⋊C411yescharacteristic
51M16×C31—41no—
52M16×C31—41no—
53C2×C8×C31—42no—
54C2×C8×C31—44no—
55C2×C8×C31—41no—
56C4⋊C4×C31—22no—
57C4⋊C4×C31—42no—
58C22⋊C4×C31—41no—
59C22⋊C4×C31—41no—
60C22⋊C4×C31—41no—
61C22⋊C4×C31—41no—
62C22⋊C4×C31—41no—
63C22⋊C4×C31—42no—
64C22⋊C4×C31—81no—
65C42×C31—21no—
66C42×C31—41no—
67C42×C31—42no—
68C42×C31C22⋊C411yescharacteristic
69C42×C31C4⋊C411yescharacteristic
70#7489C3111yesmaximal, characteristic, direct product factor, Sylow
71C23×C31—21no—
72C23×C31—21no—
73C23×C31—41no—
74C23×C31—41no—
75C23×C31—82no—
76C23×C31#9911yescharacteristic
77Q8×C31—41no—
78Q8×C31—41no—
79Q8×C31—42no—
80D4×C31—41no—
81D4×C31—41no—
82D4×C31—81no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
89C2×C4×C31—42no—
90C2×C4×C31—41no—
91C2×C4×C31—41no—
92C2×C4×C31—42no—
93C2×C4×C31—82no—
94C2×C4×C31—162no—
95C2×C4×C31#9511yescharacteristic
96C2×C4×C31#9911yescharacteristic
97C8×C31—44no—
98C8×C31—81no—
99C2×#354C2×C3111yescharacteristic
100#1888C2×C3111yescharacteristic
101C2×#329C2×C3111yescharacteristic
102C22×C31—22no—
103C22×C31—41no—
104C22×C31—41no—
105C22×C31—81no—
106C22×C31—81no—
107C22×C31—82no—
108C22×C31—161no—
109C22×C31#34211yescharacteristic
110C22×C31AΣL(1,𝔽16)11yescharacteristic
111C22×C31#35211yescharacteristic
112C4×C31—21no—
113C4×C31—21no—
114C4×C31—41no—
115C4×C31—41no—
116C4×C31—41no—
117C4×C31—41no—
118C4×C31—82no—
119C4×C31—162no—
120C2×#124C22×C3111yescharacteristic
121#519C4×C3111yescharacteristic, complemented
122#418—21no—
123C2×#101C4×C3111yescharacteristic, complemented
124C2×#99—21no—
125C2×#97—21no—
126#354—21no—
127#354C4×C3112yescomplemented
128#339—21no—
129#329—21no—
130#329C4×C3112yescomplemented
131C2×C31—21no—
132C2×C31—21no—
133C2×C31—81no—
134C2×C31—81no—
135C2×C31#139011yescharacteristic
136C2×C31#140412yes—
137C22×Q8C2×C4×C3111yescharacteristic
138C22×D4D4×C3111yescharacteristic
139C2×M16—21no—
140C22×C8—41no—
141#124—41no—
142#124C2×C4×C3111yescharacteristic
143#124C2×C4×C3111yescharacteristic
144#124D4×C3111yescharacteristic
145#124Q8×C3111yescharacteristic
146C4×Q8—42no—
147#117—21no—
148#117—41no—
149C2×C22⋊C4—41no—
150C2×C22⋊C4—41no—
151C2×C42D4×C3111yescharacteristic
152#102—42no—
153#101—41no—
154#99—22no—
155#99—41no—
156#97—22no—
157#97—41no—
158C31#748911yescharacteristic, direct product factor, Sylow
159C24—21no—
160C2×Q8—21no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8C42×C3111yescharacteristic
164C2×Q8C4⋊C4×C3111yescharacteristic
165C2×D4—21no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4C22⋊C4×C3111yescharacteristic
169C2×D4C4⋊C4×C3111yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—81no—
173C22×C4C22⋊C4×C3111yescharacteristic
174M16—41no—
175M16—41no—
176C2×C8—42no—
177C2×C8—44no—
178C2×C8—41no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—42no—
187C22⋊C4—81no—
188C42—21no—
189C42—41no—
190C42—42no—
191C42C22⋊C4×C3111yescharacteristic
192C42C4⋊C4×C3111yescharacteristic
193C23—21no—
194C23—21no—
195C23—41no—
196C23—41no—
197C23—82no—
198C23C31×#9911yescharacteristic
199Q8—41no—
200Q8—41no—
201Q8—42no—
202D4—41no—
203D4—41no—
204D4—81no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—162no—
217C2×C4C31×#9511yescharacteristic
218C2×C4C31×#9911yescharacteristic
219C8—44no—
220C8—81no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22—82no—
227C22—161no—
228C22C31×#34211yescharacteristic
229C22C31×AΣL(1,𝔽16)11yescharacteristic
230C22C31×#35211yescharacteristic
231C4—21no—
232C4—21no—
233C4—41no—
234C4—41no—
235C4—41no—
236C4—41no—
237C4—82no—
238C4—162no—
239C2—21no—
240C2—21no—
241C2—81no—
242C2—81no—
243C2C31×#139011yescharacteristic
244C2C31×#140412yes—
subgroupG/H
center, socleC22×C31AΣL(1,𝔽16)
commutatorC2×Q8C42×C31
Frattini, cosocleC2×#124C22×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×#124 ◁ G

Complements

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

NH ≅ G/Ntype
5. C31×#519C4semidirect
7. C2×C31×#101C4semidirect
11. C31×#354C4semidirect
14. C31×#329C4semidirect
70. #7489C31direct (N × H)
121. #519C4×C31semidirect
123. C2×#101C4×C31semidirect
127. #354C4×C31semidirect
130. #329C4×C31semidirect
158. C31#7489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3542
C31×#18882
C2×C31×#3292
#748931