Finite Group Databasebeta

← #37508334

Subgroups — #37508334

Order 22912.

184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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#26038849C211yesmaximal, characteristic, complemented
2#26038809C211yesmaximal, characteristic, complemented
3#26038798C211yesmaximal, characteristic
4#26038181C211yesmaximal, characteristic, complemented
5#26038181C211yesmaximal, characteristic, complemented
6#26038179C211yesmaximal, characteristic
7#563×C179C211yesmaximal, characteristic
8#19153113C2211yescharacteristic
9#19153046—21no—
10#19153044—21no—
11#19153037—21no—
12#19153036—21no—
13#19153036—21no—
14#19153034—21no—
15#19153024C2211yescharacteristic
16#19153024C2211yescharacteristic
17#19153024C2211yescharacteristic
18C4⋊Q8×C179—21no—
19#126×C179—21no—
20#126×C179—21no—
21#125×C179C2211yescharacteristic
22#125×C179C2211yescharacteristic
23#124×C179C2211yescharacteristic
24#123×C179—21no—
25C22⋊Q8×C179—21no—
26C22⋊Q8×C179—21no—
27C2×Dic358—21no—
28C2×C179⋊C8—21no—
29C2×C179⋊C8—21no—
30C2×C179⋊C8—21no—
31C4⋊Dic179—21no—
32C4⋊Dic179—21no—
33C2×Q8×C179—21no—
34C2×Q8×C179D411yescharacteristic
35C2×D4×C179D411yescharacteristic
36C22×C4×C179—21no—
37C4⋊C4×C179—21no—
38C4⋊C4×C179—21no—
39C4⋊C4×C179—21no—
40C4⋊C4×C179—21no—
41C4⋊C4×C179—21no—
42C4⋊C4×C179—21no—
43C4⋊C4×C179D411yescharacteristic
44C4⋊C4×C179D411yescharacteristic
45C4⋊C4×C179D411yescharacteristic
46C4⋊C4×C179D411yescharacteristic
47C22⋊C4×C179—21no—
48C22⋊C4×C179—21no—
49C22⋊C4×C179—21no—
50C22⋊C4×C179—21no—
51C22⋊C4×C179—21no—
52C42×C179—21no—
53C42×C179C2311yescharacteristic
54Dic358—42no—
55C2×Dic179—41no—
56C179⋊C8—22no—
57C179⋊C8—41no—
58C179⋊C8—41no—
59C23×C179—21no—
60Q8×C179—41no—
61Q8×C179—81no—
62D4×C179—41no—
63C2×C4×C179—21no—
64C2×C4×C179—21no—
65C2×C4×C179—21no—
66C2×C4×C179—21no—
67C2×C4×C179—21no—
68C2×C4×C179—81no—
69C2×C4×C179C2×D411yescharacteristic
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C22×C179—41no—
73C22×C179—41no—
74C22×C179—41no—
75C22×C179#12011yescharacteristic
76C4×C179—21no—
77C4×C179—21no—
78C4×C179—21no—
79C4×C179—41no—
80C4×C179—41no—
81C4×C179—41no—
82C4×C179—41no—
83C4×C179—41no—
84Dic179—81no—
85C2×C179—81no—
86C2×C179#45411yescharacteristic
87C2×C179#45511yescharacteristic
88C2×C179#45611yescharacteristic
89C179#166411yescharacteristic, complemented, Sylow
90#1664—1791nomaximal, Sylow
91#563D17911yescharacteristic
92#501—1791no—
93#491—1791no—
94#489—1791no—
95#330—1791no—
96#330—1791no—
97#329—1791no—
98C4⋊Q8—21no—
99C4⋊Q8—1791no—
100#126—21no—
101#126—21no—
102#125C2×D17911yescharacteristic
103#125C2×D17911yescharacteristic
104#124C2×D17911yescharacteristic
105#123—21no—
106C22⋊Q8—21no—
107C22⋊Q8—21no—
108#107—3581no—
109#106—3581no—
110#103—3581no—
111#103—3581no—
112#103—3581no—
113#102—3581no—
114#97—1791no—
115#97—1791no—
116#97—1791no—
117C2×Q8—21no—
118C2×Q8—3581no—
119C2×Q8C22⋊D17911yescharacteristic
120C2×D4C22⋊D17911yescharacteristic
121C22×C4—21no—
122C2×C8—3581no—
123C2×C8—3581no—
124C2×C8—3581no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—3581no—
132C4⋊C4—3581no—
133C4⋊C4C22⋊D17911yescharacteristic
134C4⋊C4C22⋊D17911yescharacteristic
135C4⋊C4C22⋊D17911yescharacteristic
136C4⋊C4C22⋊D17911yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D17911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—7162no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—7161no—
156C2×C4C2×C22⋊D17911yescharacteristic
157C2×C4C2×C22⋊D17911yescharacteristic
158C2×C4C2×C22⋊D17911yescharacteristic
159C8—3582no—
160C8—7161no—
161C8—7161no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1915308211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—14321no—
175C2—81no—
176C2#2603861211yescharacteristic
177C2#2603861711yescharacteristic
178C2#2603862211yescharacteristic
subgroupG/H
centerC22#19153082
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#563×C179C2
socleC22×C179#120
prime radicalC2×D4×C179D4
hypercenter#563D179
hypocenterC179#1664
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #26038849C2semidirect
2. #26038809C2semidirect
4. #26038181C2semidirect
5. #26038181C2semidirect
89. C179#1664semidirect

Maximal subgroups

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

subgroupindex
#260388492
#260388092
#260387982
#260381812
#260381792
#563×C1792
#1664179