Finite Group Databasebeta

← #37510692

Subgroups — #37510692

Order 22912.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#26038423C212yesmaximal, complemented
2#26038236C214yesmaximal, complemented
3#535×C179C211yesmaximal, characteristic
4C2×#15668243—22no—
5#19153032C2214yescomplemented
6#19153030—22no—
7C2×#41×C179C2211yescharacteristic
8C22×D4×C179C411yescharacteristic
9#127×C179C412yes—
10#124×C179C2212yes—
11#121×C179—22no—
12#120×C179—22no—
13#117×C179C411yescharacteristic
14#15668243—24no—
15#15668243—42no—
16C2×C179⋊C8—42no—
17C24×C179—21no—
18#41×C179—42no—
19C2×Q8×C179C2311yescharacteristic
20C2×D4×C179—24no—
21C2×D4×C179—21no—
22C2×D4×C179—42no—
23C2×D4×C179C2×C412yes—
24C2×D4×C179C2×C411yescharacteristic
25C2×D4×C179D412yes—
26C22×C4×C179C2×C411yescharacteristic
27C22×C4×C179D412yes—
28C4⋊C4×C179—21no—
29C22⋊C4×C179—21no—
30C22⋊C4×C179—24no—
31C42×C179C2×C412yes—
32C179⋊C8—44no—
33C23×C179—22no—
34C23×C179—42no—
35C23×C179—82no—
36C23×C179C22⋊C411yescharacteristic
37C23×C179C22⋊C412yes—
38Q8×C179—41no—
39D4×C179—41no—
40D4×C179—42no—
41D4×C179—42no—
42D4×C179—42no—
43D4×C179—84no—
44C2×C4×C179—22no—
45C2×C4×C179—22no—
46C2×C4×C179—22no—
47C2×C4×C179—22no—
48C2×C4×C179C22⋊C411yescharacteristic
49C2×C4×C179C22×C411yescharacteristic
50C2×C4×C179C2×D412yes—
51C22×C179—21no—
52C22×C179—22no—
53C22×C179—42no—
54C22×C179—41no—
55C22×C179—44no—
56C22×C179—42no—
57C22×C179—84no—
58C22×C179C2×C22⋊C411yescharacteristic
59C4×C179—21no—
60C4×C179—22no—
61C4×C179—42no—
62C4×C179#9912yes—
63C2×C179—21no—
64C2×C179—42no—
65C2×C179—41no—
66C2×C179—82no—
67C2×C179C2×#9911yescharacteristic
68C179#213411yescharacteristic, complemented, Sylow
69#2134—1791nomaximal, Sylow
70#535D17911yescharacteristic
71#413—1792no—
72#355—1794no—
73C2×#41C2×D17911yescharacteristic
74C22×D4Dic17911yescharacteristic
75C2×M16—3582no—
76#127Dic17912yes—
77#124C2×D17912yes—
78#121—22no—
79#120—22no—
80#117Dic17911yescharacteristic
81#101—1794no—
82#100—3582no—
83C24—21no—
84#41—42no—
85C2×Q8C22×D17911yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic17912yes—
90C2×D4C2×Dic17911yescharacteristic
91C2×D4C22⋊D17912yes—
92C22×C4C2×Dic17911yescharacteristic
93C22×C4C22⋊D17912yes—
94M16—3584no—
95M16—7162no—
96C2×C8—7162no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—24no—
100C42C2×Dic17912yes—
101C23—22no—
102C23—42no—
103C23—82no—
104C23C22⋊Dic17911yescharacteristic
105C23C22⋊Dic17912yes—
106Q8—41no—
107D4—41no—
108D4—42no—
109D4—42no—
110D4—42no—
111D4—84no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4C22⋊Dic17911yescharacteristic
117C2×C4C22×Dic17911yescharacteristic
118C2×C4C2×C22⋊D17912yes—
119C8—7164no—
120C22—21no—
121C22—22no—
122C22—42no—
123C22—41no—
124C22—44no—
125C22—42no—
126C22—84no—
127C22C2×C22⋊Dic17911yescharacteristic
128C4—22no—
129C4—21no—
130C4—42no—
131C4#1915302812yes—
132C2—21no—
133C2—41no—
134C2—42no—
135C2—82no—
136C2C2×#1915302811yescharacteristic
subgroupG/H
centerC2C2×#19153028
commutatorC2×C4×C179C22×C4
FrattiniC2×Q8C22×D179
Fitting, prime radical#535×C179C2
socleC2×C179C2×#99
cosocleC2×Q8×C179C23
hypercenter#535D179
hypocenterC179#2134
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #26038423C2semidirect
2. #26038236C2semidirect
5. #19153032C22semidirect
68. C179#2134semidirect

Maximal subgroups

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

subgroupindex
#260384232
#260382362
#535×C1792
#2134179