Finite Group Databasebeta

← #37510674

Subgroups — #37510674

Order 22912.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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#26039010C211yesmaximal, characteristic
2#26038413C211yesmaximal, characteristic
3#26038233C214yesmaximal, complemented
4#410×C179C211yesmaximal, characteristic
5C22×Dic358C411yescharacteristic, complemented
6#19153111C412yescomplemented
7#19153100C2212yes—
8#19153094—21no—
9#19153094—21no—
10#19153092—21no—
11#19153092—21no—
12#19153072—21no—
13#19153072C411yescharacteristic, complemented
14#19153028—21no—
15#19153028C2212yes—
16C2×#41×C179C2211yescharacteristic
17#117×C179—21no—
18#99×C179—21no—
19#99×C179C2212yes—
20C2×Dic358—21no—
21C2×Dic358—41no—
22C2×Dic358—41no—
23C2×Dic358C2×C412yes—
24C22×Dic179—21no—
25C4⋊Dic179—21no—
26C4⋊Dic179—41no—
27Dic179⋊C4—22no—
28Dic179⋊C4—22no—
29C22⋊Dic179—21no—
30C22⋊Dic179—22no—
31C22⋊Dic179—22no—
32C22⋊Dic179—22no—
33C4×Dic179—41no—
34C4×Dic179C2×C412yes—
35#41×C179—41no—
36#41×C179—41no—
37C2×Q8×C179C2×C411yescharacteristic
38C2×D4×C179D411yescharacteristic
39C2×D4×C179D411yescharacteristic
40C2×D4×C179C2311yescharacteristic
41C22×C4×C179C2×C411yescharacteristic
42C22×C4×C179D411yescharacteristic
43C22×C4×C179D411yescharacteristic
44C4⋊C4×C179—41no—
45C22⋊C4×C179—22no—
46C42×C179—41no—
47Dic358—41no—
48Dic358—41no—
49Dic358—42no—
50C2×Dic179—22no—
51C2×Dic179—22no—
52C2×Dic179—42no—
53C2×Dic179—42no—
54C23×C179C22⋊C411yescharacteristic
55C23×C179C2×D411yescharacteristic
56C23×C179C2×D411yescharacteristic
57Q8×C179—41no—
58D4×C179—41no—
59D4×C179—41no—
60D4×C179—41no—
61C2×C4×C179—21no—
62C2×C4×C179—21no—
63C2×C4×C179—21no—
64C2×C4×C179—21no—
65C2×C4×C179—21no—
66C2×C4×C179—21no—
67C2×C4×C179—42no—
68C2×C4×C179C22⋊C411yescharacteristic
69C2×C4×C179C22⋊C411yescharacteristic
70C2×C4×C179C22⋊C411yescharacteristic
71C2×C4×C179C22×C411yescharacteristic
72C22×C179—21no—
73C22×C179—21no—
74C22×C179—21no—
75C22×C179—41no—
76C22×C179—41no—
77C22×C179—41no—
78C22×C179C2×C22⋊C411yescharacteristic
79C4×C179—21no—
80C4×C179—21no—
81C4×C179—21no—
82C4×C179—82no—
83C4×C179#9911yescharacteristic
84C4×C179#9911yescharacteristic
85Dic179—42no—
86Dic179—42no—
87Dic179—82no—
88C2×C179—21no—
89C2×C179—41no—
90C2×C179—41no—
91C2×C179—41no—
92C2×C179C2×#9911yescharacteristic
93C179#212911yescharacteristic, complemented, Sylow
94#2129—1791nomaximal, Sylow
95#536—1791no—
96#410—1791no—
97#410D17911yescharacteristic
98#354—1794no—
99C2×#41C2×D17911yescharacteristic
100C22×Q8—1791no—
101C4⋊Q8—1792no—
102#124—1792no—
103#123—3581no—
104#123—3581no—
105C22⋊Q8—3581no—
106C22⋊Q8—3581no—
107#117—21no—
108#117—3581no—
109#117—1791no—
110#99—21no—
111#99—3581no—
112#99—1792no—
113#99C2×D17912yes—
114#41—41no—
115#41—41no—
116C2×Q8—3581no—
117C2×Q8—1792no—
118C2×Q8—7161no—
119C2×Q8—7161no—
120C2×Q8C4×D17911yescharacteristic
121C2×D4C22⋊D17911yescharacteristic
122C2×D4D71611yescharacteristic
123C2×D4C22×D17911yescharacteristic
124C22×C4—3581no—
125C22×C4C4×D17911yescharacteristic
126C22×C4C22⋊D17911yescharacteristic
127C22×C4D71611yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—3582no—
130C4⋊C4—3582no—
131C4⋊C4—3581no—
132C4⋊C4—7161no—
133C22⋊C4—22no—
134C22⋊C4—3581no—
135C22⋊C4—3582no—
136C22⋊C4—3582no—
137C22⋊C4—3582no—
138C42—41no—
139C42—1792no—
140C42—7161no—
141C23(C2×D179)⋊C411yescharacteristic
142C23C2×C22⋊D17911yescharacteristic
143C23C2×D71611yescharacteristic
144Q8—41no—
145Q8—7162no—
146Q8—7161no—
147Q8—7161no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—3582no—
159C2×C4—3582no—
160C2×C4—7162no—
161C2×C4—7162no—
162C2×C4(C2×D179)⋊C411yescharacteristic
163C2×C4(C2×D179)⋊C411yescharacteristic
164C2×C4(C2×D179)⋊C411yescharacteristic
165C2×C4C2×C4×D17911yescharacteristic
166C22—21no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C2×(C2×D179)⋊C411yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—14322no—
178C4—7162no—
179C4—7162no—
180C4#1915302711yescharacteristic
181C4#1915302711yescharacteristic
182C2—21no—
183C2—41no—
184C2—41no—
185C2—41no—
186C2C2×#1915302711yescharacteristic
subgroupG/H
centerC2C2×#19153027
commutatorC2×C4×C179C22×C4
FrattiniC2×D4C22×D179
Fitting#410×C179C2
socleC2×C179C2×#99
prime radicalC2×#41×C179C22
cosocleC2×D4×C179C23
hypercenter#410D179
hypocenterC179#2129
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #26038233C2semidirect
5. C22×Dic358C4semidirect
6. #19153111C4semidirect
13. #19153072C4semidirect
93. C179#2129semidirect

Maximal subgroups

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

subgroupindex
#260390102
#260384132
#260382332
#410×C1792
#2129179