Finite Group Databasebeta

← #37508136

Subgroups — #37508136

Order 22912.

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

normal subgroups only

This group has 214 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#26039146C211yesmaximal, characteristic
2#26038819C211yesmaximal, characteristic, complemented
3#26038735C211yesmaximal, characteristic, complemented
4#26038729C211yesmaximal, characteristic
5#26038187C211yesmaximal, characteristic, complemented
6#26038171C211yesmaximal, characteristic, complemented
7D4⋊C8×C179C211yesmaximal, characteristic
8C2×Dic716—22no—
9#19153113C2211yescharacteristic
10#19153113C2211yescharacteristic
11#19153104—21no—
12#19153092—21no—
13#19153090—22no—
14C4×Dic358C2211yescharacteristic
15D4×Dic179—21no—
16C2×C4⋊Dic179—21no—
17#19153047—21no—
18#19153044—21no—
19C4⋊(C179⋊C8)C2211yescharacteristic
20#19153038—21no—
21#19153034—21no—
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4×C8×C179C2211yescharacteristic
25C2×Dic358—21no—
26C2×Dic358D411yescharacteristic
27C2×Dic358D412yes—
28C22×Dic179—22no—
29Dic716—44no—
30C2×C179⋊C8—21no—
31C4⋊Dic179—22no—
32C4⋊Dic179—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179D411yescharacteristic
37Dic179⋊C4—22no—
38Dic179⋊C4—21no—
39C22⋊Dic179—22no—
40C4×Dic179—21no—
41C2×D4×C179D411yescharacteristic
42C22×C4×C179—21no—
43C2×C8×C179—21no—
44C2×C8×C179—21no—
45C4⋊C4×C179D411yescharacteristic
46C22⋊C4×C179—21no—
47C42×C179C2311yescharacteristic
48Dic358—21no—
49Dic358—21no—
50Dic358—42no—
51Dic358—42no—
52C2×Dic179—21no—
53C2×Dic179—21no—
54C2×Dic179—22no—
55C2×Dic179—41no—
56C2×Dic179—82no—
57C179⋊C8—41no—
58C23×C179—21no—
59D4×C179—21no—
60D4×C179Q1612yescomplemented
61C2×C4×C179—21no—
62C2×C4×C179—41no—
63C2×C4×C179—41no—
64C2×C4×C179C2×D411yescharacteristic
65C2×C4×C179C2×D411yescharacteristic
66C2×C4×C179C2×D411yescharacteristic
67C8×C179—22no—
68C8×C179—41no—
69C22×C179—22no—
70C22×C179—41no—
71C22×C179—41no—
72C22×C179#12011yescharacteristic
73C4×C179—21no—
74C4×C179—41no—
75C4×C179C2×Q1611yescharacteristic
76C4×C179#13511yescharacteristic
77C4×C179#13711yescharacteristic
78C4×C179#13711yescharacteristic
79Dic179—41no—
80Dic179—41no—
81Dic179—42no—
82Dic179—81no—
83C2×C179—42no—
84C2×C179#45111yescharacteristic
85C2×C179#45211yescharacteristic
86C2×C179#45311yescharacteristic
87C179#163211yescharacteristic, complemented, Sylow
88#1632—1791nomaximal, Sylow
89#554—1791no—
90#494—1791no—
91#477—1791no—
92#476—1791no—
93#333—1791no—
94Q8⋊C8—1791no—
95D4⋊C8D17911yescharacteristic
96C2×Q16—3582no—
97C4⋊Q8—1791no—
98C4⋊Q8—1791no—
99#125—3581no—
100C22⋊Q8—3582no—
101C22⋊Q8—3581no—
102C4×Q8—1791no—
103C4×D4—3581no—
104C4×D4C2×D17911yescharacteristic
105C2×C4⋊C4—3581no—
106#107—3581no—
107#106—3581no—
108C4⋊C8—1791no—
109C4⋊C8C2×D17911yescharacteristic
110#103—3581no—
111#102—3581no—
112C4×C8C2×D17911yescharacteristic
113C2×Q8—3581no—
114C2×Q8—1791no—
115C2×Q8—1792no—
116C2×D4D71611yescharacteristic
117C22×C4—21no—
118C22×C4—3582no—
119Q16—7164no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—3581no—
123C4⋊C4—3582no—
124C4⋊C4—3582no—
125C4⋊C4—3581no—
126C4⋊C4—3581no—
127C4⋊C4—3581no—
128C4⋊C4—3581no—
129C4⋊C4—3581no—
130C4⋊C4—1791no—
131C4⋊C4D71611yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—3582no—
134C42—3581no—
135C42C22×D17911yescharacteristic
136C23—21no—
137Q8—3581no—
138Q8—3581no—
139Q8—7162no—
140Q8—7162no—
141D4—21no—
142D4Dic71612yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—3581no—
147C2×C4—3581no—
148C2×C4—3582no—
149C2×C4—14322no—
150C2×C4—7161no—
151C2×C4D4×D17911yescharacteristic
152C2×C4D4×D17911yescharacteristic
153C2×C4C2×D71611yescharacteristic
154C8—22no—
155C8—41no—
156C8—7161no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1915308311yescharacteristic
161C4—21no—
162C4—41no—
163C4—14321no—
164C4—7161no—
165C4—7161no—
166C4—7162no—
167C4C2×Dic71611yescharacteristic
168C4#1915313211yescharacteristic
169C4#1915314211yescharacteristic
170C4#1915314611yescharacteristic
171C2—42no—
172C2#2603859711yescharacteristic
173C2#2603860211yescharacteristic
174C2#2603860811yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
FittingD4⋊C8×C179C2
socleC22×C179#120
prime radicalC2×D4×C179D4
hypercenterD4⋊C8D179
hypocenterC179#1632
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #26038819C2semidirect
3. #26038735C2semidirect
5. #26038187C2semidirect
6. #26038171C2semidirect
60. D4×C179Q16semidirect
87. C179#1632semidirect
142. D4Dic716semidirect

Maximal subgroups

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

subgroupindex
#260391462
#260388192
#260387352
#260387292
#260381872
#260381712
D4⋊C8×C1792
#1632179