Finite Group Databasebeta

← #37508041

Subgroups — #37508041

Order 22912.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#26039070C211yesmaximal, characteristic
2#26038774C212yesmaximal
3#26038175C212yesmaximal
4#26038165C211yesmaximal, characteristic
5#400×C179C211yesmaximal, characteristic
6#19153112—22no—
7#19153104—22no—
8#19153092—21no—
9#19153092C2212yes—
10#19153072—21no—
11#19153046—22no—
12#19153036—22no—
13C22⋊(C179⋊C8)C2212yes—
14C2×C4⋊C4×C179C2211yescharacteristic
15C2×C4⋊C4×C179C2211yescharacteristic
16#95×C179—21no—
17#95×C179—21no—
18#95×C179C2211yescharacteristic
19C2×Dic358—21no—
20C2×Dic358D412yes—
21C2×C179⋊C8—22no—
22C4⋊Dic179—21no—
23C4⋊Dic179—21no—
24C4⋊Dic179—21no—
25C4⋊Dic179D412yes—
26Dic179⋊C4—22no—
27Dic179⋊C4—22no—
28C22⋊Dic179—22no—
29C4×Dic179—22no—
30C22×C4×C179—21no—
31C22×C4×C179—21no—
32C22×C4×C179D411yescharacteristic
33C22×C4×C179D411yescharacteristic
34C22×C4×C179C2311yescharacteristic
35C4⋊C4×C179—22no—
36C4⋊C4×C179—22no—
37Dic358—42no—
38Dic358—81no—
39C2×Dic179—22no—
40C2×Dic179—22no—
41C179⋊C8—42no—
42C23×C179C2×D411yescharacteristic
43C2×C4×C179—21no—
44C2×C4×C179—21no—
45C2×C4×C179—21no—
46C2×C4×C179—41no—
47C2×C4×C179—41no—
48C2×C4×C179—41no—
49C2×C4×C179—41no—
50C2×C4×C179—42no—
51C2×C4×C179—41no—
52C2×C4×C179—41no—
53C2×C4×C179Q1612yes—
54C2×C4×C179C2×D412yes—
55C22×C179—21no—
56C22×C179—21no—
57C22×C179#12011yescharacteristic
58C22×C179C2×Q1611yescharacteristic
59C22×C179#13711yescharacteristic
60C4×C179—22no—
61C4×C179—22no—
62C4×C179—41no—
63C4×C179—81no—
64C4×C179—81no—
65Dic179—42no—
66Dic179—42no—
67C2×C179—21no—
68C2×C179—21no—
69C2×C179#45111yescharacteristic
70C2×C179#45411yescharacteristic
71C2×C179#45811yescharacteristic
72C179#161711yescharacteristic, complemented, Sylow
73#1617—1791nomaximal, Sylow
74#544—1791no—
75#484—1792no—
76#400D17911yescharacteristic
77#328—1792no—
78#324—1791no—
79C4⋊Q8—3582no—
80#125—3582no—
81C22⋊Q8—3581no—
82C22⋊Q8—1792no—
83#117—3581no—
84C2×C4⋊C4C2×D17911yescharacteristic
85C2×C4⋊C4C2×D17911yescharacteristic
86#107—3582no—
87#103—3582no—
88C22⋊C8—1792no—
89#95—21no—
90#95—21no—
91#95C2×D17911yescharacteristic
92C2×Q8—3581no—
93C2×Q8—1792no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D17911yescharacteristic
97C22×C4C22⋊D17911yescharacteristic
98C22×C4C22×D17911yescharacteristic
99C2×C8—3582no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—3582no—
103C4⋊C4—3581no—
104C4⋊C4—3581no—
105C4⋊C4—3581no—
106C4⋊C4—3582no—
107C4⋊C4—1792no—
108C22⋊C4—3582no—
109C42—3582no—
110C23C2×C22⋊D17911yescharacteristic
111Q8—14321no—
112Q8—7162no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—3582no—
124C2×C4—3582no—
125C2×C4#1566824912yes—
126C2×C4D4×D17912yes—
127C8—7162no—
128C22—21no—
129C22—21no—
130C22#1915308111yescharacteristic
131C22C2×#1566824911yescharacteristic
132C22#1915314311yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—7162no—
139C4—7162no—
140C2—21no—
141C2—21no—
142C2#2603859411yescharacteristic
143C2#2603861111yescharacteristic
144C2#2603862811yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#400×C179C2
socleC22×C179#120
prime radicalC23×C179C2×D4
hypercenter#400D179
hypocenterC179#1617
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
72. C179#1617semidirect

Maximal subgroups

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

subgroupindex
#260390702
#260387742
#260381752
#260381652
#400×C1792
#1617179