Finite Group Databasebeta

← C31×#9067 #21465826

Subgroups — C31×#9067 #21465826

Order 7936.

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

normal subgroups only

This group has 444 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×#3131C211yesmaximal, characteristic
2C31×#2979C211yesmaximal, characteristic
3C31×#1525C211yesmaximal, characteristic
4C31×#1485C212yesmaximal, complemented
5C31×#1278C212yesmaximal, complemented
6C31×#533C2211yescharacteristic
7C31×#532C2211yescharacteristic
8C31×#488—22no—
9C31×#487C412yes—
10C31×#486C412yes—
11C31×#436—22no—
12C8×D4×C31—22no—
13C31×#431C2212yes—
14C31×#416—22no—
15C31×#408—22no—
16C4×M16×C31C2212yes—
17C2×C4×C8×C31C2211yescharacteristic
18C31×#329—22no—
19C31×Q8⋊C8—22no—
20C31×Q8⋊C8—22no—
21C2×#41×C31D412yes—
22C2×M16×C31—22no—
23C2×M16×C31—22no—
24C22×C8×C31—21no—
25C22×C8×C31—22no—
26C31×C4⋊Q8C2×C412yes—
27C31×C4⋊Q8C2×C411yescharacteristic
28C31×#127C2×C411yescharacteristic
29C31×#125—21no—
30C31×#124D412yes—
31C31×C22⋊Q8—22no—
32C31×#121—22no—
33C4×Q8×C31—22no—
34C4×D4×C31—22no—
35C31×#117—21no—
36C2×C42×C31C2311yescharacteristic
37C31×C4⋊C8D412yes—
38C31×C4⋊C8D412yes—
39C31×#103—24no—
40C31×#102—24no—
41C31×C22⋊C8—24no—
42C31×C22⋊C8—22no—
43C31×#97—22no—
44C4×C8×C31—21no—
45C4×C8×C31—22no—
46C4×C8×C31—22no—
47C4×C8×C31C2×C412yes—
48#41×C31—42no—
49#41×C31—42no—
50C2×Q8×C31—22no—
51C2×Q8×C31C22⋊C412yes—
52C2×D4×C31—22no—
53C2×D4×C31—22no—
54C2×D4×C31C22⋊C412yes—
55C22×C4×C31—22no—
56C22×C4×C31C2×D411yescharacteristic
57C22×C4×C31#4112yes—
58M16×C31—24no—
59M16×C31—42no—
60M16×C31—82no—
61C2×C8×C31—22no—
62C2×C8×C31—22no—
63C2×C8×C31—22no—
64C2×C8×C31—41no—
65C2×C8×C31—41no—
66C2×C8×C31—42no—
67C2×C8×C31—82no—
68C4⋊C4×C31—22no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—42no—
72C22⋊C4×C31—24no—
73C22⋊C4×C31—41no—
74C42×C31—41no—
75C42×C31C22×C411yescharacteristic
76C42×C31C2×D411yescharacteristic
77C42×C31C2×D412yes—
78#9067C3111yesmaximal, characteristic, direct product factor, Sylow
79C23×C31—22no—
80C23×C31#12311yescharacteristic
81Q8×C31—42no—
82Q8×C31—42no—
83Q8×C31—42no—
84D4×C31—42no—
85D4×C31—42no—
86D4×C31—42no—
87D4×C31—82no—
88C2×C4×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—22no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31C2×C22⋊C411yescharacteristic
97C2×C4×C31C4×D412yes—
98C2×C4×C31#12011yescharacteristic
99C2×C4×C31#12112yes—
100C8×C31—42no—
101C8×C31—44no—
102C8×C31—42no—
103C8×C31—42no—
104#3131C2×C3111yescharacteristic
105#2979C2×C3111yescharacteristic
106#1525C2×C3111yescharacteristic
107#1485C2×C3112yescomplemented
108#1278C2×C3112yescomplemented
109C22×C31—22no—
110C22×C31—21no—
111C22×C31—44no—
112C22×C31—42no—
113C22×C31#38611yescharacteristic
114C4×C31—22no—
115C4×C31—21no—
116C4×C31—42no—
117C4×C31—82no—
118C4×C31#44312yes—
119C4×C31#44412yes—
120C4×C31#45511yescharacteristic
121C4×C31#45511yescharacteristic
122#533C22×C3111yescharacteristic
123#532C22×C3111yescharacteristic
124#488—22no—
125#487C4×C3112yes—
126#486C4×C3112yes—
127#436—22no—
128C8×D4—22no—
129#431C22×C3112yes—
130#416—22no—
131#408—22no—
132C4×M16C22×C3112yes—
133C2×C4×C8C22×C3111yescharacteristic
134#329—22no—
135Q8⋊C8—22no—
136Q8⋊C8—22no—
137C2×C31—41no—
138C2×C31—82no—
139C2×C31#187612yes—
140C2×C31#188511yescharacteristic
141C2×#41D4×C3112yes—
142C2×M16—22no—
143C2×M16—22no—
144C22×C8—21no—
145C22×C8—22no—
146C4⋊Q8C2×C4×C3112yes—
147C4⋊Q8C2×C4×C3111yescharacteristic
148#127C2×C4×C3111yescharacteristic
149#125—21no—
150#124D4×C3112yes—
151C22⋊Q8—22no—
152#121—22no—
153C4×Q8—22no—
154C4×D4—22no—
155#117—21no—
156C2×C42C23×C3111yescharacteristic
157C4⋊C8D4×C3112yes—
158C4⋊C8D4×C3112yes—
159#103—24no—
160#102—24no—
161C22⋊C8—24no—
162C22⋊C8—22no—
163#97—22no—
164C4×C8—21no—
165C4×C8—22no—
166C4×C8—22no—
167C4×C8C2×C4×C3112yes—
168C31#906711yescharacteristic, direct product factor, Sylow
169#41—42no—
170#41—42no—
171C2×Q8—22no—
172C2×Q8C22⋊C4×C3112yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4C22⋊C4×C3112yes—
176C22×C4—22no—
177C22×C4C2×D4×C3111yescharacteristic
178C22×C4#41×C3112yes—
179M16—24no—
180M16—42no—
181M16—82no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—42no—
188C2×C8—82no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C22⋊C4—24no—
194C22⋊C4—41no—
195C42—41no—
196C42C22×C4×C3111yescharacteristic
197C42C2×D4×C3111yescharacteristic
198C42C2×D4×C3112yes—
199C23—22no—
200C23C31×#12311yescharacteristic
201Q8—42no—
202Q8—42no—
203Q8—42no—
204D4—42no—
205D4—42no—
206D4—42no—
207D4—82no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4C2×C22⋊C4×C3111yescharacteristic
217C2×C4C4×D4×C3112yes—
218C2×C4C31×#12011yescharacteristic
219C2×C4C31×#12112yes—
220C8—42no—
221C8—44no—
222C8—42no—
223C8—42no—
224C22—22no—
225C22—21no—
226C22—44no—
227C22—42no—
228C22C31×#38611yescharacteristic
229C4—22no—
230C4—21no—
231C4—42no—
232C4—82no—
233C4C31×#44312yes—
234C4C31×#44412yes—
235C4C31×#45511yescharacteristic
236C4C31×#45511yescharacteristic
237C2—41no—
238C2—82no—
239C2C31×#187612yes—
240C2C31×#188511yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#386
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1485C2semidirect
5. C31×#1278C2semidirect
78. #9067C31direct (N × H)
107. #1485C2×C31semidirect
108. #1278C2×C31semidirect
168. C31#9067direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31312
C31×#29792
C31×#15252
C31×#14852
C31×#12782
#906731