Finite Group Databasebeta

← C31×#8584 #21465343

Subgroups — C31×#8584 #21465343

Order 7936.

456 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 154 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
1C4×C31×#125C211yesmaximal, characteristic
2C31×#1767C212yesmaximal
3C2×C31×#330C212yesmaximal
4C31×#1295C212yesmaximal
5C2×C31×#125C2211yescharacteristic
6C2×C31×C4⋊C8—22no—
7C2×C31×#97C2214yes—
8C31×#389C412yes—
9C31×#387—22no—
10C31×#382C2211yescharacteristic
11C4×C4⋊C4×C31—22no—
12C4×C4⋊C4×C31C412yes—
13C43×C31C2211yescharacteristic
14C31×#336—22no—
15C31×#330—24no—
16C22×C8×C31—24no—
17C31×#125—22no—
18C31×#125D412yes—
19C31×#125Q812yes—
20C2×C4⋊C4×C31—22no—
21C2×C4⋊C4×C31—22no—
22C2×C4⋊C4×C31C2×C412yes—
23C2×C4⋊C4×C31C2×C412yes—
24C2×C42×C31—22no—
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31C2×C411yescharacteristic
27C2×C42×C31D412yes—
28C2×C42×C31D412yes—
29C2×C42×C31C2311yescharacteristic
30C31×C4⋊C8—28no—
31C31×#97—24no—
32C31×#97—24no—
33C31×#95—22no—
34C31×#95—22no—
35C31×#95—22no—
36C22×C4×C31—22no—
37C22×C4×C31—22no—
38C22×C4×C31C22⋊C411yescharacteristic
39C22×C4×C31C22⋊C411yescharacteristic
40C22×C4×C31C22⋊C412yes—
41C22×C4×C31C22×C411yescharacteristic
42C22×C4×C31C2×D412yes—
43C2×C8×C31—28no—
44C2×C8×C31—44no—
45C2×C8×C31—44no—
46C4⋊C4×C31—22no—
47C4⋊C4×C31—24no—
48C4⋊C4×C31—24no—
49C4⋊C4×C31—42no—
50C4⋊C4×C31—44no—
51C4⋊C4×C31C4⋊C414yes—
52C42×C31—22no—
53C42×C31—24no—
54C42×C31—41no—
55C42×C31—42no—
56C42×C31—44no—
57C42×C31C2×D411yescharacteristic
58C42×C31C2×Q811yescharacteristic
59C42×C31#4112yes—
60#8584C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31C2×C22⋊C411yescharacteristic
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—24no—
70C2×C4×C31—21no—
71C2×C4×C31—22no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31—42no—
77C2×C4×C31#10112yes—
78C2×C4×C31#10414yes—
79C2×C4×C31C2×C4⋊C411yescharacteristic
80C2×C4×C31#11711yescharacteristic
81C2×C4×C31#12112yes—
82C2×C4×C31C22⋊Q812yes—
83C8×C31—48no—
84C4×#125C2×C3111yescharacteristic
85#1767C2×C3112yes—
86C2×#330C2×C3112yes—
87#1295C2×C3112yes—
88C22×C31#38011yescharacteristic
89C22×C31C2×#10111yescharacteristic
90C22×C31#41311yescharacteristic
91C22×C31C2×#10412yes—
92C22×C31#42112yes—
93C4×C31—21no—
94C4×C31—21no—
95C4×C31—22no—
96C4×C31—22no—
97C4×C31—24no—
98C4×C31—22no—
99C4×C31—44no—
100C4×C31—41no—
101C4×C31—82no—
102C2×#125C22×C3111yescharacteristic
103C2×C4⋊C8—22no—
104C2×#97C22×C3114yes—
105#389C4×C3112yes—
106#387—22no—
107#382C22×C3111yescharacteristic
108C4×C4⋊C4—22no—
109C4×C4⋊C4C4×C3112yes—
110C43C22×C3111yescharacteristic
111#336—22no—
112#330—24no—
113C2×C31#152611yescharacteristic
114C2×C31#153212yes—
115C2×C31#153411yescharacteristic
116C2×C31#180111yescharacteristic
117C2×C31#180612yes—
118C22×C8—24no—
119#125—22no—
120#125D4×C3112yes—
121#125Q8×C3112yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4C2×C4×C3112yes—
125C2×C4⋊C4C2×C4×C3112yes—
126C2×C42—22no—
127C2×C42C2×C4×C3111yescharacteristic
128C2×C42C2×C4×C3111yescharacteristic
129C2×C42D4×C3112yes—
130C2×C42D4×C3112yes—
131C2×C42C23×C3111yescharacteristic
132C4⋊C8—28no—
133#97—24no—
134#97—24no—
135#95—22no—
136#95—22no—
137#95—22no—
138C31#858411yescharacteristic, direct product factor, Sylow
139C22×C4—22no—
140C22×C4—22no—
141C22×C4C22⋊C4×C3111yescharacteristic
142C22×C4C22⋊C4×C3111yescharacteristic
143C22×C4C22⋊C4×C3112yes—
144C22×C4C22×C4×C3111yescharacteristic
145C22×C4C2×D4×C3112yes—
146C2×C8—28no—
147C2×C8—44no—
148C2×C8—44no—
149C4⋊C4—22no—
150C4⋊C4—24no—
151C4⋊C4—24no—
152C4⋊C4—42no—
153C4⋊C4—44no—
154C4⋊C4C4⋊C4×C3114yes—
155C42—22no—
156C42—24no—
157C42—41no—
158C42—42no—
159C42—44no—
160C42C2×D4×C3111yescharacteristic
161C42C2×Q8×C3111yescharacteristic
162C42#41×C3112yes—
163C23C2×C22⋊C4×C3111yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4C31×#10112yes—
180C2×C4C31×#10414yes—
181C2×C4C2×C4⋊C4×C3111yescharacteristic
182C2×C4C31×#11711yescharacteristic
183C2×C4C31×#12112yes—
184C2×C4C31×C22⋊Q812yes—
185C8—48no—
186C22C31×#38011yescharacteristic
187C22C2×C31×#10111yescharacteristic
188C22C31×#41311yescharacteristic
189C22C2×C31×#10412yes—
190C22C31×#42112yes—
191C4—21no—
192C4—21no—
193C4—22no—
194C4—22no—
195C4—24no—
196C4—22no—
197C4—44no—
198C4—41no—
199C4—82no—
200C2C31×#152611yescharacteristic
201C2C31×#153212yes—
202C2C31×#153411yescharacteristic
203C2C31×#180111yescharacteristic
204C2C31×#180612yes—
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
60. #8584C31direct (N × H)
138. C31#8584direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1252
C31×#17672
C2×C31×#3302
C31×#12952
#858431