Finite Group Databasebeta

← C31×#7481 #21464240

Subgroups — C31×#7481 #21464240

Order 7936.

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

normal subgroups only

This group has 284 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
1C2×C31×#354C211yesmaximal, characteristic
2C31×#1888C211yesmaximal, characteristic
3C31×#1533C211yesmaximal, characteristic
4C2×C31×#124C2211yescharacteristic
5C31×#519C411yescharacteristic, complemented
6C31×#432—21no—
7C31×#418—21no—
8C2×C31×#101C411yescharacteristic, complemented
9C2×C31×#99—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—
18C31×#124—41no—
19C31×#124C2×C411yescharacteristic
20C31×#124C2×C411yescharacteristic
21C31×#124D411yescharacteristic
22C31×#124Q811yescharacteristic
23C4×Q8×C31—42no—
24C31×#117—21no—
25C31×#117—41no—
26C2×C22⋊C4×C31—41no—
27C2×C22⋊C4×C31—41no—
28C2×C42×C31D411yescharacteristic
29C31×C4⋊C8—41no—
30C31×#102—42no—
31C31×#101—41no—
32C31×#99—22no—
33C31×#99—41no—
34C31×C22⋊C8—41no—
35C31×#97—22no—
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—41no—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—42no—
57C22⋊C4×C31—41no—
58C22⋊C4×C31—41no—
59C22⋊C4×C31—41no—
60C22⋊C4×C31—41no—
61C22⋊C4×C31—41no—
62C22⋊C4×C31—42no—
63C22⋊C4×C31—81no—
64C42×C31—21no—
65C42×C31—41no—
66C42×C31—42no—
67C42×C31C22⋊C411yescharacteristic
68C42×C31C4⋊C411yescharacteristic
69#7481C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—21no—
71C23×C31—21no—
72C23×C31—41no—
73C23×C31—41no—
74C23×C31—82no—
75C23×C31#9911yescharacteristic
76Q8×C31—41no—
77Q8×C31—41no—
78Q8×C31—42no—
79D4×C31—41no—
80D4×C31—41no—
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—42no—
91C2×C4×C31—81no—
92C2×C4×C31—82no—
93C2×C4×C31—162no—
94C2×C4×C31#9511yescharacteristic
95C2×C4×C31#9911yescharacteristic
96C8×C31—81no—
97C8×C31—82no—
98C2×#354C2×C3111yescharacteristic
99#1888C2×C3111yescharacteristic
100#1533C2×C3111yescharacteristic
101C22×C31—41no—
102C22×C31—41no—
103C22×C31—41no—
104C22×C31—81no—
105C22×C31—81no—
106C22×C31—82no—
107C22×C31—161no—
108C22×C31#34211yescharacteristic
109C22×C31AΣL(1,𝔽16)11yescharacteristic
110C22×C31#35211yescharacteristic
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—41no—
114C4×C31—41no—
115C4×C31—41no—
116C4×C31—41no—
117C4×C31—82no—
118C4×C31—162no—
119C2×#124C22×C3111yescharacteristic
120#519C4×C3111yescharacteristic, complemented
121#432—21no—
122#418—21no—
123C2×#101C4×C3111yescharacteristic, complemented
124C2×#99—21no—
125#354—21no—
126#354C4×C3112yescomplemented
127#339—21no—
128#329—21no—
129#329C4×C3112yescomplemented
130C2×C31—21no—
131C2×C31—21no—
132C2×C31—21no—
133C2×C31—81no—
134C2×C31—81no—
135C2×C31#139011yescharacteristic
136C22×Q8C2×C4×C3111yescharacteristic
137C22×D4D4×C3111yescharacteristic
138C2×M16—21no—
139#124—41no—
140#124C2×C4×C3111yescharacteristic
141#124C2×C4×C3111yescharacteristic
142#124D4×C3111yescharacteristic
143#124Q8×C3111yescharacteristic
144C4×Q8—42no—
145#117—21no—
146#117—41no—
147C2×C22⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C42D4×C3111yescharacteristic
150C4⋊C8—41no—
151#102—42no—
152#101—41no—
153#99—22no—
154#99—41no—
155C22⋊C8—41no—
156#97—22no—
157C31#748111yescharacteristic, direct product factor, Sylow
158C24—21no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8C42×C3111yescharacteristic
163C2×Q8C4⋊C4×C3111yescharacteristic
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4C22⋊C4×C3111yescharacteristic
168C2×D4C4⋊C4×C3111yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—81no—
172C22×C4C22⋊C4×C3111yescharacteristic
173M16—41no—
174M16—41no—
175C2×C8—42no—
176C2×C8—41no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—42no—
185C22⋊C4—81no—
186C42—21no—
187C42—41no—
188C42—42no—
189C42C22⋊C4×C3111yescharacteristic
190C42C4⋊C4×C3111yescharacteristic
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23—82no—
196C23C31×#9911yescharacteristic
197Q8—41no—
198Q8—41no—
199Q8—42no—
200D4—41no—
201D4—41no—
202D4—81no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—81no—
213C2×C4—82no—
214C2×C4—162no—
215C2×C4C31×#9511yescharacteristic
216C2×C4C31×#9911yescharacteristic
217C8—81no—
218C8—82no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22—81no—
224C22—82no—
225C22—161no—
226C22C31×#34211yescharacteristic
227C22C31×AΣL(1,𝔽16)11yescharacteristic
228C22C31×#35211yescharacteristic
229C4—21no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—41no—
235C4—82no—
236C4—162no—
237C2—21no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—81no—
242C2C31×#139011yescharacteristic
subgroupG/H
center, socleC2×C31#1390
commutatorC2×Q8C42×C31
Frattini, cosocleC2×#124C22×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×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
8. C2×C31×#101C4semidirect
11. C31×#354C4semidirect
14. C31×#329C4semidirect
69. #7481C31direct (N × H)
120. #519C4×C31semidirect
123. C2×#101C4×C31semidirect
126. #354C4×C31semidirect
129. #329C4×C31semidirect
157. C31#7481direct (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
C31×#15332
#748131