Finite Group Databasebeta

← #37507578

Subgroups — #37507578

Order 22912.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#26038973C211yesmaximal, characteristic
2#26038307C211yesmaximal, characteristic, complemented
3#26038177C212yesmaximal, complemented
4#26038174C212yesmaximal
5#431×C179C211yesmaximal, characteristic, complemented
6#19153107—21no—
7#19153105C411yescharacteristic, complemented
8#19153101C411yescharacteristic, complemented
9#19153096—21no—
10#19153092C2211yescharacteristic
11#19153087C2211yescharacteristic
12C4×Dic358C411yescharacteristic, complemented
13C4×D716C411yescharacteristic, complemented
14C4×C22⋊D179—21no—
15#19153070—21no—
16C179⋊#95—21no—
17C179⋊#95—21no—
18C179⋊#95C2212yes—
19C2×C42×C179C2211yescharacteristic
20C4⋊C8×C179—21no—
21C22⋊C8×C179C2212yes—
22C4×C8×C179—21no—
23C2×Dic358C2×C411yescharacteristic
24C2×D716C2×C411yescharacteristic
25C2×C22⋊D179—21no—
26C22×Dic179—22no—
27C2×C4×D179—21no—
28C4⋊Dic179C2×C411yescharacteristic
29C4⋊Dic179C2×C411yescharacteristic
30Dic179⋊C4—21no—
31Dic179⋊C4—21no—
32Dic179⋊C4—21no—
33Dic179⋊C4—21no—
34C22⋊Dic179—21no—
35(C2×D179)⋊C4—21no—
36(C2×D179)⋊C4—21no—
37(C2×D179)⋊C4—21no—
38(C2×D179)⋊C4—21no—
39C4×Dic179—21no—
40C22×C4×C179D411yescharacteristic
41C22×C4×C179D411yescharacteristic
42C22×C4×C179C2311yescharacteristic
43C2×C8×C179—22no—
44C42×C179C2×C411yescharacteristic
45C42×C179C2×C411yescharacteristic
46C42×C179D411yescharacteristic
47C42×C179D411yescharacteristic
48C22×D179—21no—
49Dic358—41no—
50D716—41no—
51C22⋊D179—42no—
52C2×Dic179—21no—
53C2×Dic179—21no—
54C2×Dic179—21no—
55C2×Dic179—42no—
56C2×Dic179—42no—
57C2×Dic179—42no—
58C4×D179—42no—
59C23×C179C2×D411yescharacteristic
60C2×C4×C179—22no—
61C2×C4×C179—41no—
62C2×C4×C179—41no—
63C2×C4×C179C22⋊C411yescharacteristic
64C2×C4×C179C22⋊C411yescharacteristic
65C2×C4×C179C22⋊C411yescharacteristic
66C2×C4×C179C22⋊C411yescharacteristic
67C2×C4×C179C22×C411yescharacteristic
68C2×C4×C179C2×D411yescharacteristic
69C8×C179—42no—
70C22×C179—21no—
71C22×C179—21no—
72C22×C179C2×C22⋊C411yescharacteristic
73C22×C179#13512yes—
74C2×D179—41no—
75C2×D179—41no—
76C2×D179—41no—
77C4×C179—21no—
78C4×C179—21no—
79C4×C179—21no—
80C4×C179—21no—
81C4×C179—21no—
82C4×C179—21no—
83Dic179—41no—
84Dic179—41no—
85Dic179—41no—
86Dic179—82no—
87C2×C179—22no—
88C2×C179#41011yescharacteristic
89C2×C179#41611yescharacteristic
90C2×C179#42111yescharacteristic
91D179—81no—
92C179#152111yescharacteristic, complemented, Sylow
93#1521—1791nomaximal, Sylow
94#529—1791no—
95#431D17911yescharacteristic, complemented
96#383—1791no—
97#328—1792no—
98#327—1792no—
99#126—3581no—
100#125—1791no—
101#124—1791no—
102#123—3581no—
103C22⋊Q8—1791no—
104#121—1791no—
105C4×Q8—1791no—
106C4×D4—3581no—
107C4×D4—1791no—
108#117—3581no—
109C2×C42C2×D17911yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D17912yes—
112C4×C8—21no—
113#95—3581no—
114#95—3581no—
115#95—1792no—
116C2×Q8—1791no—
117C2×D4—3581no—
118C2×D4—1791no—
119C22×C4—3581no—
120C22×C4—3582no—
121C22×C4D71611yescharacteristic
122C22×C4D71611yescharacteristic
123C22×C4C22×D17911yescharacteristic
124C2×C8—22no—
125C4⋊C4—3581no—
126C4⋊C4—3581no—
127C4⋊C4—3581no—
128C4⋊C4—3581no—
129C4⋊C4—1791no—
130C4⋊C4—1791no—
131C22⋊C4—3581no—
132C22⋊C4—3581no—
133C22⋊C4—3581no—
134C22⋊C4—3581no—
135C22⋊C4—3581no—
136C42—3581no—
137C42C4×D17911yescharacteristic
138C42C4×D17911yescharacteristic
139C42C22⋊D17911yescharacteristic
140C42C22⋊D17911yescharacteristic
141C23—3581no—
142C23C2×D71611yescharacteristic
143Q8—7161no—
144D4—7161no—
145D4—7162no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3581no—
150C2×C4—3581no—
151C2×C4—3581no—
152C2×C4—7162no—
153C2×C4—7162no—
154C2×C4—7162no—
155C2×C4—7162no—
156C2×C4(C2×D179)⋊C411yescharacteristic
157C2×C4(C2×D179)⋊C411yescharacteristic
158C2×C4(C2×D179)⋊C411yescharacteristic
159C2×C4(C2×D179)⋊C411yescharacteristic
160C2×C4C2×C4×D17911yescharacteristic
161C2×C4C2×C22⋊D17911yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—7161no—
166C22—7161no—
167C22—7161no—
168C22C2×(C2×D179)⋊C411yescharacteristic
169C22#1915313512yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—14322no—
177C4—7161no—
178C4—7161no—
179C4—7161no—
180C2—22no—
181C2—14321no—
182C2#2603841211yescharacteristic
183C2#2603843611yescharacteristic
184C2#2603845511yescharacteristic
subgroupG/H
centerC22C2×(C2×D179)⋊C4
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#431×C179C2
socleC22×C179C2×C22⋊C4
prime radical#19153087C22
cosocleC22×C4×C179C23
hypercenter#431D179
hypocenterC179#1521
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #26038307C2semidirect
3. #26038177C2semidirect
5. #431×C179C2semidirect
7. #19153105C4semidirect
8. #19153101C4semidirect
12. C4×Dic358C4semidirect
13. C4×D716C4semidirect
92. C179#1521semidirect
95. #431D179semidirect

Maximal subgroups

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

subgroupindex
#260389732
#260383072
#260381772
#260381742
#431×C1792
#1521179