Finite Group Databasebeta

← C31×#8769 #21465528

Subgroups — C31×#8769 #21465528

Order 7936.

378 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2356C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic
3C31×#1461C211yesmaximal, characteristic
4C31×#1303C212yesmaximal
5C31×#1286C212yesmaximal
6C2×C4×Q8×C31C2211yescharacteristic
7C31×#431C2212yes—
8C31×#423C2212yes—
9C2×C31×#101—21no—
10C31×#391—21no—
11C31×#387—22no—
12C31×#383C412yes—
13C31×#382C2211yescharacteristic
14C4×C4⋊C4×C31—21no—
15C4×C4⋊C4×C31C2211yescharacteristic
16C31×#376C412yes—
17C31×#343—21no—
18C31×#324—22no—
19C22×Q8×C31D411yescharacteristic
20C2×M16×C31—22no—
21C4×Q8×C31—22no—
22C4×Q8×C31—22no—
23C2×C4⋊C4×C31—21no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31D412yes—
26C2×C4⋊C4×C31D411yescharacteristic
27C2×C42×C31—22no—
28C2×C42×C31—21no—
29C2×C42×C31C2×C412yes—
30C2×C42×C31C2311yescharacteristic
31C31×C4⋊C8—22no—
32C31×C4⋊C8—22no—
33C31×C4⋊C8—22no—
34C31×#101—42no—
35C31×C22⋊C8—22no—
36C4×C8×C31—22no—
37C31×#95—22no—
38C31×#95—22no—
39C31×#95—22no—
40C31×#95—21no—
41C31×#95C2×C411yescharacteristic
42C31×#95C2×C412yes—
43C31×#95C2×C411yescharacteristic
44C2×Q8×C31—22no—
45C2×Q8×C31—22no—
46C2×Q8×C31—21no—
47C2×Q8×C31—21no—
48C22×C4×C31—21no—
49C22×C4×C31—22no—
50C22×C4×C31—21no—
51C22×C4×C31C22⋊C412yes—
52C22×C4×C31C22⋊C412yes—
53C22×C4×C31C22×C411yescharacteristic
54C22×C4×C31C2×D411yescharacteristic
55C22×C4×C31C2×D411yescharacteristic
56M16×C31—42no—
57M16×C31—42no—
58C2×C8×C31—42no—
59C2×C8×C31—42no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—24no—
62C4⋊C4×C31—42no—
63C4⋊C4×C31—41no—
64C4⋊C4×C31—41no—
65C42×C31—22no—
66C42×C31—22no—
67C42×C31—44no—
68C42×C31—42no—
69C42×C31#4112yes—
70C42×C31#4112yes—
71#8769C3111yesmaximal, characteristic, direct product factor, Sylow
72C23×C31C2×C22⋊C411yescharacteristic
73Q8×C31—42no—
74Q8×C31—42no—
75C2×C4×C31—22no—
76C2×C4×C31—22no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—41no—
81C2×C4×C31—41no—
82C2×C4×C31—41no—
83C2×C4×C31—41no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31—41no—
87C2×C4×C31—41no—
88C2×C4×C31—42no—
89C2×C4×C31—41no—
90C2×C4×C31—42no—
91C2×C4×C31#11711yescharacteristic
92C2×C4×C31#11711yescharacteristic
93C2×C4×C31#12312yes—
94C2×C4×C31#12312yes—
95C2×C4×C31#13512yes—
96C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C31#13711yescharacteristic
98C8×C31—82no—
99C8×C31—82no—
100#2356C2×C3111yescharacteristic
101#1801C2×C3111yescharacteristic
102#1461C2×C3111yescharacteristic
103#1303C2×C3112yes—
104#1286C2×C3112yes—
105C22×C31—21no—
106C22×C31—21no—
107C22×C31#38111yescharacteristic
108C22×C31#41611yescharacteristic
109C22×C31#41711yescharacteristic
110C4×C31—22no—
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—42no—
114C4×C31—42no—
115C4×C31—42no—
116C4×C31—81no—
117C4×C31—82no—
118C4×C31#48212yes—
119C4×C31#48512yes—
120C2×C4×Q8C22×C3111yescharacteristic
121#431C22×C3112yes—
122#423C22×C3112yes—
123C2×#101—21no—
124#391—21no—
125#387—22no—
126#383C4×C3112yes—
127#382C22×C3111yescharacteristic
128C4×C4⋊C4—21no—
129C4×C4⋊C4C22×C3111yescharacteristic
130#376C4×C3112yes—
131#343—21no—
132#324—22no—
133C2×C31—21no—
134C2×C31—21no—
135C2×C31#182511yescharacteristic
136C2×C31#182711yescharacteristic
137C2×C31#183011yescharacteristic
138C22×Q8D4×C3111yescharacteristic
139C2×M16—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4D4×C3112yes—
145C2×C4⋊C4D4×C3111yescharacteristic
146C2×C42—22no—
147C2×C42—21no—
148C2×C42C2×C4×C3112yes—
149C2×C42C23×C3111yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153#101—42no—
154C22⋊C8—22no—
155C4×C8—22no—
156#95—22no—
157#95—22no—
158#95—22no—
159#95—21no—
160#95C2×C4×C3111yescharacteristic
161#95C2×C4×C3112yes—
162#95C2×C4×C3111yescharacteristic
163C31#876911yescharacteristic, direct product factor, Sylow
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4C22⋊C4×C3112yes—
172C22×C4C22⋊C4×C3112yes—
173C22×C4C22×C4×C3111yescharacteristic
174C22×C4C2×D4×C3111yescharacteristic
175C22×C4C2×D4×C3111yescharacteristic
176M16—42no—
177M16—42no—
178C2×C8—42no—
179C2×C8—42no—
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C42—22no—
186C42—22no—
187C42—44no—
188C42—42no—
189C42#41×C3112yes—
190C42#41×C3112yes—
191C23C2×C22⋊C4×C3111yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4C31×#11711yescharacteristic
211C2×C4C31×#11711yescharacteristic
212C2×C4C31×#12312yes—
213C2×C4C31×#12312yes—
214C2×C4C31×#13512yes—
215C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
216C2×C4C31×#13711yescharacteristic
217C8—82no—
218C8—82no—
219C22—21no—
220C22—21no—
221C22C31×#38111yescharacteristic
222C22C31×#41611yescharacteristic
223C22C31×#41711yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4C31×#48212yes—
233C4C31×#48512yes—
234C2—21no—
235C2—21no—
236C2C31×#182511yescharacteristic
237C2C31×#182711yescharacteristic
238C2C31×#183011yescharacteristic
subgroupG/H
center, socleC22×C31#381
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
71. #8769C31direct (N × H)
163. C31#8769direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23562
C31×#18012
C31×#14612
C31×#13032
C31×#12862
#876931