Finite Group Databasebeta

← #37508008

Subgroups — #37508008

Order 22912.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#26038767C212yesmaximal
2#26038369C211yesmaximal, characteristic
3#26038176C212yesmaximal
4#26038165C211yesmaximal, characteristic
5#544×C179C211yesmaximal, characteristic
6C2×C4⋊Dic179C2211yescharacteristic
7C2×Dic179⋊C4—21no—
8#19153044—22no—
9#19153037—22no—
10C22⋊(C179⋊C8)C2212yes—
11C179⋊#95—21no—
12C179⋊#95C2211yescharacteristic
13C4⋊Q8×C179—22no—
14#125×C179—22no—
15C22⋊Q8×C179—21no—
16C22⋊Q8×C179C2212yes—
17#117×C179—21no—
18C2×C4⋊C4×C179C2211yescharacteristic
19C22×Dic179—21no—
20C22×Dic179—21no—
21C2×C179⋊C8—22no—
22C4⋊Dic179—22no—
23Dic179⋊C4—42no—
24C2×Q8×C179—21no—
25C2×Q8×C179D412yes—
26C22×C4×C179D411yescharacteristic
27C22×C4×C179D411yescharacteristic
28C22×C4×C179C2311yescharacteristic
29C4⋊C4×C179—21no—
30C4⋊C4×C179—21no—
31C4⋊C4×C179—21no—
32C4⋊C4×C179—22no—
33C4⋊C4×C179—22no—
34C4⋊C4×C179—22no—
35C4⋊C4×C179D412yes—
36C22⋊C4×C179—22no—
37C42×C179—22no—
38C2×Dic179—22no—
39C2×Dic179—41no—
40C2×Dic179—41no—
41C2×Dic179—41no—
42C2×Dic179—41no—
43C2×Dic179—41no—
44C179⋊C8—42no—
45C23×C179C2×D411yescharacteristic
46Q8×C179—42no—
47Q8×C179—81no—
48C2×C4×C179—21no—
49C2×C4×C179—21no—
50C2×C4×C179—21no—
51C2×C4×C179—22no—
52C2×C4×C179—22no—
53C2×C4×C179—41no—
54C2×C4×C179—41no—
55C2×C4×C179SD1612yes—
56C2×C4×C179C2×D412yes—
57C22×C179—21no—
58C22×C179—21no—
59C22×C179#12011yescharacteristic
60C22×C179C2×SD1611yescharacteristic
61C22×C179#13711yescharacteristic
62C4×C179—22no—
63C4×C179—22no—
64C4×C179—42no—
65C4×C179—41no—
66C4×C179—42no—
67Dic179—42no—
68Dic179—81no—
69C2×C179—21no—
70C2×C179—21no—
71C2×C179#44811yescharacteristic
72C2×C179#45611yescharacteristic
73C2×C179#45811yescharacteristic
74C179#161111yescharacteristic, complemented, Sylow
75#1611—1791nomaximal, Sylow
76#544D17911yescharacteristic
77#483—1792no—
78#398—1791no—
79#328—1792no—
80#324—1791no—
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D17912yes—
85#117—21no—
86C2×C4⋊C4—3581no—
87C2×C4⋊C4—1791no—
88C2×C4⋊C4C2×D17911yescharacteristic
89#106—3582no—
90#103—3582no—
91C22⋊C8—1792no—
92#95—3581no—
93#95—1791no—
94C2×Q8—21no—
95C2×Q8C22⋊D17912yes—
96C22×C4—3581no—
97C22×C4—3581no—
98C22×C4C22⋊D17911yescharacteristic
99C22×C4C22⋊D17911yescharacteristic
100C22×C4C22×D17911yescharacteristic
101C2×C8—3582no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—3582no—
109C4⋊C4—7162no—
110C4⋊C4C22⋊D17912yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D17911yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—3582no—
124C2×C4—7161no—
125C2×C4—7161no—
126C2×C4—7161no—
127C2×C4—7161no—
128C2×C4—7161no—
129C2×C4#1566824612yes—
130C2×C4C2×C22⋊D17912yes—
131C8—7162no—
132C22—21no—
133C22—21no—
134C22#1915308211yescharacteristic
135C22C2×#1566824611yescharacteristic
136C22#1915314411yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—14321no—
143C4—7162no—
144C2—21no—
145C2—21no—
146C2#2603857811yescharacteristic
147C2#2603862211yescharacteristic
148C2#2603862911yescharacteristic
subgroupG/H
centerC22#19153082
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#544×C179C2
socleC22×C179#120
prime radicalC23×C179C2×D4
hypercenter#544D179
hypocenterC179#1611
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
74. C179#1611semidirect

Maximal subgroups

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

subgroupindex
#260387672
#260383692
#260381762
#260381652
#544×C1792
#1611179