Finite Group Databasebeta

← #37507331

Subgroups — #37507331

Order 22912.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#19153069C211yesmaximal, characteristic
2#26038493C212yesmaximal, complemented
3#26038164C212yesmaximal, complemented
4#26038163C211yesmaximal, characteristic
5#323×C179C211yesmaximal, characteristic
6C23×Dic179C411yescharacteristic
7#19153069—22no—
8#19153069—22no—
9C2×Dic179⋊C4C411yescharacteristic
10C2×Dic179⋊C4C2211yescharacteristic
11C2×C22⋊Dic179C411yescharacteristic
12C2×C4×Dic179C411yescharacteristic
13C2×C4×Dic179C2211yescharacteristic
14Dic179⋊C8—22no—
15C22⋊(C179⋊C8)C2212yes—
16#19153023—22no—
17C2×C22⋊C4×C179C2211yescharacteristic
18C22⋊C8×C179C2212yes—
19C22×Dic179—21no—
20C22×Dic179—21no—
21C22×Dic179—22no—
22C22×Dic179—22no—
23C22×Dic179C2×C411yescharacteristic
24C22×Dic179C2×C411yescharacteristic
25C22×Dic179C2×C411yescharacteristic
26C22×Dic179C2×C411yescharacteristic
27C2×C179⋊C8—22no—
28Dic179⋊C4—22no—
29Dic179⋊C4—22no—
30C22⋊Dic179—22no—
31C4×Dic179—21no—
32C4×Dic179—21no—
33C4×Dic179D412yes—
34C4×Dic179D412yes—
35C24×C179C2×C411yescharacteristic
36C22×C4×C179C2×C411yescharacteristic
37C22×C4×C179C2311yescharacteristic
38C2×C8×C179—22no—
39C22⋊C4×C179—22no—
40C2×Dic179—24no—
41C2×Dic179—24no—
42C2×Dic179—21no—
43C2×Dic179—21no—
44C2×Dic179—21no—
45C2×Dic179—21no—
46C2×Dic179—21no—
47C2×Dic179—41no—
48C2×Dic179—41no—
49C2×Dic179C22⋊C411yescharacteristic
50C2×Dic179C22⋊C411yescharacteristic
51C2×Dic179C22⋊C412yes—
52C2×Dic179M1612yes—
53C179⋊C8—42no—
54C23×C179—21no—
55C23×C179—21no—
56C23×C179—41no—
57C23×C179—41no—
58C23×C179M1612yes—
59C23×C179C22×C411yescharacteristic
60C2×C4×C179—21no—
61C2×C4×C179—41no—
62C2×C4×C179—41no—
63C2×C4×C179C2×D412yes—
64C8×C179—42no—
65C22×C179—21no—
66C22×C179—21no—
67C22×C179—22no—
68C22×C179—42no—
69C22×C179—42no—
70C22×C179—41no—
71C22×C179—41no—
72C22×C179C2×C22⋊C411yescharacteristic
73C22×C179C2×M1611yescharacteristic
74C22×C179C2×M1611yescharacteristic
75C4×C179—22no—
76C4×C179—41no—
77Dic179—21no—
78Dic179—21no—
79Dic179—22no—
80Dic179—22no—
81Dic179—41no—
82C2×C179—21no—
83C2×C179—21no—
84C2×C179—42no—
85C2×C179#40711yescharacteristic
86C2×C179#41011yescharacteristic
87C2×C179#41311yescharacteristic
88C179#146411yescharacteristic, complemented, Sylow
89#1464—1791nomaximal, Sylow
90C2×#117—1791no—
91#432—1792no—
92#324—1792no—
93#323—1791no—
94#323D17911yescharacteristic
95C23×C4—1791no—
96#117—3582no—
97#117—3582no—
98C2×C4⋊C4—1791no—
99C2×C4⋊C4—1791no—
100C2×C22⋊C4—1791no—
101C2×C22⋊C4C2×D17911yescharacteristic
102C2×C42—1791no—
103C2×C42—1791no—
104C4⋊C8—3582no—
105C22⋊C8—1792no—
106C22⋊C8C2×D17912yes—
107#97—3582no—
108C24C4×D17911yescharacteristic
109C22×C4—3582no—
110C22×C4—3581no—
111C22×C4—3581no—
112C22×C4—3582no—
113C22×C4—1791no—
114C22×C4—1791no—
115C22×C4—1791no—
116C22×C4—1791no—
117C22×C4C4×D17911yescharacteristic
118C22×C4C22×D17911yescharacteristic
119C2×C8—22no—
120C2×C8—3582no—
121C4⋊C4—3582no—
122C4⋊C4—3582no—
123C22⋊C4—22no—
124C22⋊C4—3582no—
125C42—3581no—
126C42—3581no—
127C42—1792no—
128C42—1792no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23#1566824212yes—
134C23C2×C4×D17911yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—3584no—
139C2×C4—3584no—
140C2×C4—3581no—
141C2×C4—3581no—
142C2×C4—3581no—
143C2×C4—3581no—
144C2×C4—3581no—
145C2×C4—1791no—
146C2×C4—1791no—
147C2×C4—1792no—
148C2×C4—1792no—
149C2×C4—7161no—
150C2×C4—7161no—
151C2×C4D4×D17912yes—
152C8—42no—
153C8—7162no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D17911yescharacteristic
162C22M16×D17911yescharacteristic
163C22C2×#1566824211yescharacteristic
164C4—22no—
165C4—41no—
166C4—3582no—
167C4—3581no—
168C4—3581no—
169C4—3582no—
170C4—7161no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2#2603840111yescharacteristic
175C2#2603841111yescharacteristic
176C2#2603842011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D179
commutatorC23×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#323×C179C2
socleC22×C179C2×C22⋊C4
prime radicalC24×C179C2×C4
cosocleC22×C4×C179C23
hypercenter#323D179
hypocenterC179#1464
LCSG ▷ C23×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #26038493C2semidirect
3. #26038164C2semidirect
88. C179#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#191530692
#260384932
#260381642
#260381632
#323×C1792
#1464179