Finite Group Databasebeta

← C31×#7349 #21464108

Subgroups — C31×#7349 #21464108

Order 7936.

302 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1819C211yesmaximal, characteristic
2C31×#1316C212yesmaximal
3C22×C22⋊C4×C31C411yescharacteristic
4C31×#379C411yescharacteristic
5C31×#379C2211yescharacteristic
6C31×#342—22no—
7C31×#323—22no—
8C25×C31C2×C411yescharacteristic
9C23×C4×C31—21no—
10C2×C22⋊C4×C31—21no—
11C2×C22⋊C4×C31—21no—
12C2×C22⋊C4×C31—41no—
13C2×C22⋊C4×C31—41no—
14C2×C22⋊C4×C31—41no—
15C2×C22⋊C4×C31—41no—
16C2×C22⋊C4×C31C812yescomplemented
17C2×C22⋊C4×C31D412yes—
18C31×C22⋊C8—42no—
19C24×C31—21no—
20C24×C31—21no—
21C24×C31—42no—
22C24×C31—82no—
23C24×C31C22⋊C411yescharacteristic
24C24×C31C2×C811yescharacteristic
25C24×C31M1611yescharacteristic
26C22×C4×C31—22no—
27C22×C4×C31—22no—
28C22×C4×C31—41no—
29C22×C4×C31—41no—
30C22×C4×C31—41no—
31C22×C4×C31—82no—
32C2×C8×C31—82no—
33C22⋊C4×C31—41no—
34C22⋊C4×C31—41no—
35C22⋊C4×C31—42no—
36C22⋊C4×C31—42no—
37C22⋊C4×C31—42no—
38C22⋊C4×C31—82no—
39C22⋊C4×C31—82no—
40#7349C3111yesmaximal, characteristic, direct product factor, Sylow
41C23×C31—21no—
42C23×C31—22no—
43C23×C31—21no—
44C23×C31—42no—
45C23×C31—41no—
46C23×C31—42no—
47C23×C31—42no—
48C23×C31—42no—
49C23×C31—41no—
50C23×C31—42no—
51C23×C31—81no—
52C23×C31—81no—
53C23×C31—81no—
54C23×C31—81no—
55C23×C31—84no—
56C23×C31—84no—
57C23×C31C22⋊C811yescharacteristic
58C23×C31#9911yescharacteristic
59C23×C31#10011yescharacteristic
60C2×C4×C31—42no—
61C2×C4×C31—42no—
62C2×C4×C31—82no—
63C2×C4×C31—82no—
64C2×C4×C31—82no—
65C2×C4×C31—82no—
66C2×C4×C31—81no—
67C2×C4×C31—82no—
68C8×C31—162no—
69#1819C2×C3111yescharacteristic
70#1316C2×C3112yes—
71C22×C31—22no—
72C22×C31—21no—
73C22×C31—21no—
74C22×C31—41no—
75C22×C31—41no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31—41no—
79C22×C31—41no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—41no—
83C22×C31—41no—
84C22×C31—82no—
85C22×C31—84no—
86C22×C31—84no—
87C22×C31—82no—
88C22×C31#32311yescharacteristic
89C22×C31#35212yes—
90C4×C31—82no—
91C4×C31—82no—
92C4×C31—161no—
93C22×C22⋊C4C4×C3111yescharacteristic
94#379C4×C3111yescharacteristic
95#379C22×C3111yescharacteristic
96#342—22no—
97#323—22no—
98C2×C31—21no—
99C2×C31—22no—
100C2×C31—41no—
101C2×C31—42no—
102C2×C31—41no—
103C2×C31—81no—
104C2×C31#131711yescharacteristic
105C25C2×C4×C3111yescharacteristic
106C23×C4—21no—
107C2×C22⋊C4—21no—
108C2×C22⋊C4—21no—
109C2×C22⋊C4—41no—
110C2×C22⋊C4—41no—
111C2×C22⋊C4—41no—
112C2×C22⋊C4—41no—
113C2×C22⋊C4C8×C3112yescomplemented
114C2×C22⋊C4D4×C3112yes—
115C22⋊C8—42no—
116C31#734911yescharacteristic, direct product factor, Sylow
117C24—21no—
118C24—21no—
119C24—42no—
120C24—82no—
121C24C22⋊C4×C3111yescharacteristic
122C24C2×C8×C3111yescharacteristic
123C24M16×C3111yescharacteristic
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4—82no—
130C2×C8—82no—
131C22⋊C4—41no—
132C22⋊C4—41no—
133C22⋊C4—42no—
134C22⋊C4—42no—
135C22⋊C4—42no—
136C22⋊C4—82no—
137C22⋊C4—82no—
138C23—21no—
139C23—22no—
140C23—21no—
141C23—42no—
142C23—41no—
143C23—42no—
144C23—42no—
145C23—42no—
146C23—41no—
147C23—42no—
148C23—81no—
149C23—81no—
150C23—81no—
151C23—81no—
152C23—84no—
153C23—84no—
154C23C31×C22⋊C811yescharacteristic
155C23C31×#9911yescharacteristic
156C23C31×#10011yescharacteristic
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—82no—
160C2×C4—82no—
161C2×C4—82no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—82no—
165C8—162no—
166C22—22no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22—82no—
180C22—84no—
181C22—84no—
182C22—82no—
183C22C31×#32311yescharacteristic
184C22C31×#35212yes—
185C4—82no—
186C4—82no—
187C4—161no—
188C2—21no—
189C2—22no—
190C2—41no—
191C2—42no—
192C2—41no—
193C2—81no—
194C2C31×#131711yescharacteristic
subgroupG/H
center, socleC2×C31#1317
commutatorC24C2×C8×C31
Frattini, cosocle#379C22×C31
prime radicalC25×C31C2×C4
LCSG ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C24×C31 ◁ C31×#379 ◁ G

Complements

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

NH ≅ G/Ntype
16. C2×C22⋊C4×C31C8semidirect
40. #7349C31direct (N × H)
113. C2×C22⋊C4C8×C31semidirect
116. C31#7349direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#18192
C31×#13162
#734931