Finite Group Databasebeta

← #1462×C179 #37504684

Subgroups — #1462×C179 #37504684

Order 22912.

440 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C22×C22⋊C4×C179C211yesmaximal, characteristic
2#407×C179C212yesmaximal, complemented
3#323×C179C214yesmaximal, complemented
4C25×C179C411yescharacteristic
5C23×C4×C179C411yescharacteristic
6C23×C4×C179C2211yescharacteristic
7C2×M16×C179—22no—
8C2×C22⋊C4×C179—22no—
9C2×C22⋊C4×C179—22no—
10C2×C22⋊C4×C179C412yes—
11C2×C22⋊C4×C179C2212yes—
12C22⋊C8×C179—22no—
13C22⋊C8×C179C2214yescomplemented
14C24×C179—21no—
15C24×C179—21no—
16C24×C179—24no—
17C24×C179—42no—
18C24×C179—42no—
19C24×C179C2×C411yescharacteristic
20C24×C179C2×C412yes—
21C22×C4×C179—21no—
22C22×C4×C179—21no—
23C22×C4×C179—42no—
24C22×C4×C179—42no—
25C22×C4×C179C2×C412yes—
26C22×C4×C179C2×C411yescharacteristic
27C22×C4×C179D412yes—
28C22×C4×C179D412yes—
29C22×C4×C179C2311yescharacteristic
30M16×C179—44no—
31C2×C8×C179—24no—
32C22⋊C4×C179—24no—
33C22⋊C4×C179—24no—
34C23×C179—22no—
35C23×C179—22no—
36C23×C179—22no—
37C23×C179—24no—
38C23×C179—24no—
39C23×C179—22no—
40C23×C179—22no—
41C23×C179—42no—
42C23×C179—42no—
43C23×C179—416no—
44C23×C179—42no—
45C23×C179—42no—
46C23×C179—42no—
47C23×C179—42no—
48C23×C179C22⋊C411yescharacteristic
49C23×C179C22⋊C411yescharacteristic
50C23×C179M1614yescomplemented
51C23×C179C22×C411yescharacteristic
52C2×C4×C179—24no—
53C2×C4×C179—22no—
54C2×C4×C179—41no—
55C2×C4×C179—42no—
56C2×C4×C179—41no—
57C2×C4×C179—42no—
58C2×C4×C179—42no—
59C2×C4×C179—42no—
60C2×C4×C179C22⋊C412yes—
61C2×C4×C179C2×D412yes—
62C8×C179—44no—
63C22×C179—28no—
64C22×C179—21no—
65C22×C179—21no—
66C22×C179—21no—
67C22×C179—21no—
68C22×C179—21no—
69C22×C179—21no—
70C22×C179—24no—
71C22×C179—44no—
72C22×C179—48no—
73C22×C179—48no—
74C22×C179—44no—
75C22×C179—42no—
76C22×C179—42no—
77C22×C179#9912yes—
78C22×C179#10012yes—
79C22×C179C2×C22⋊C411yescharacteristic
80C22×C179C2×M1612yes—
81C4×C179—22no—
82C4×C179—22no—
83C4×C179—42no—
84C2×C179—22no—
85C2×C179—22no—
86C2×C179—22no—
87C2×C179—44no—
88C2×C179#40711yescharacteristic
89C2×C179C2×#9911yescharacteristic
90C2×C179C2×#10011yescharacteristic
91C179#146211yescharacteristic, direct product factor, Sylow
92#1462C17911yesmaximal, characteristic, direct product factor, Sylow
93C22×C22⋊C4C2×C17911yescharacteristic
94#407C2×C17912yescomplemented
95#323C2×C17914yescomplemented
96C25C4×C17911yescharacteristic
97C23×C4C4×C17911yescharacteristic
98C23×C4C22×C17911yescharacteristic
99C2×M16—22no—
100C2×C22⋊C4—22no—
101C2×C22⋊C4—22no—
102C2×C22⋊C4C4×C17912yes—
103C2×C22⋊C4C22×C17912yes—
104C22⋊C8—22no—
105C22⋊C8C22×C17914yescomplemented
106C24—24no—
107C24—21no—
108C24—21no—
109C24—42no—
110C24—42no—
111C24C2×C4×C17911yescharacteristic
112C24C2×C4×C17912yes—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—42no—
116C22×C4—42no—
117C22×C4C2×C4×C17912yes—
118C22×C4C2×C4×C17911yescharacteristic
119C22×C4D4×C17912yes—
120C22×C4D4×C17912yes—
121C22×C4C23×C17911yescharacteristic
122M16—44no—
123C2×C8—24no—
124C22⋊C4—24no—
125C22⋊C4—24no—
126C23—22no—
127C23—22no—
128C23—22no—
129C23—24no—
130C23—24no—
131C23—22no—
132C23—22no—
133C23—42no—
134C23—42no—
135C23—416no—
136C23—42no—
137C23—42no—
138C23—42no—
139C23—42no—
140C23C22⋊C4×C17911yescharacteristic
141C23C22⋊C4×C17911yescharacteristic
142C23M16×C17914yescomplemented
143C23C22×C4×C17911yescharacteristic
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4C22⋊C4×C17912yes—
153C2×C4C2×D4×C17912yes—
154C8—44no—
155C22—28no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—24no—
163C22—44no—
164C22—48no—
165C22—48no—
166C22—44no—
167C22—42no—
168C22—42no—
169C22#99×C17912yes—
170C22#100×C17912yes—
171C22C2×C22⋊C4×C17911yescharacteristic
172C22C2×M16×C17912yes—
173C4—22no—
174C4—22no—
175C4—42no—
176C2—22no—
177C2—22no—
178C2—22no—
179C2—44no—
180C2#407×C17911yescharacteristic
181C2C2×#99×C17911yescharacteristic
182C2C2×#100×C17911yescharacteristic
subgroupG/H
center, socleC22×C179C2×C22⋊C4
commutatorC23C22×C4×C179
Frattini, cosocleC22×C4C23×C179
prime radicalC25×C179C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C179 ◁ C23×C4×C179 ◁ G

Complements

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

NH ≅ G/Ntype
2. #407×C179C2semidirect
3. #323×C179C2semidirect
13. C22⋊C8×C179C22semidirect
50. C23×C179M16semidirect
91. C179#1462direct (N × H)
92. #1462C179direct (N × H)
94. #407C2×C179semidirect
95. #323C2×C179semidirect
105. C22⋊C8C22×C179semidirect
142. C23M16×C179semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×C1792
#407×C1792
#323×C1792
#1462179