Finite Group Databasebeta

← #37508168

Subgroups — #37508168

Order 22912.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic358C211yesmaximal, characteristic
2#26038790C211yesmaximal, characteristic, complemented
3#26038735C211yesmaximal, characteristic, complemented
4#26038729C211yesmaximal, characteristic
5#26038186C211yesmaximal, characteristic, complemented
6#26038171C211yesmaximal, characteristic, complemented
7D4⋊C8×C179C211yesmaximal, characteristic
8C22×Dic358—21no—
9#19153113C2211yescharacteristic
10#19153113C2211yescharacteristic
11#19153112—21no—
12#19153092—21no—
13#19153090—22no—
14C4×Dic358C2211yescharacteristic
15D4×Dic179—21no—
16#19153047—21no—
17#19153044—21no—
18C4⋊(C179⋊C8)C2211yescharacteristic
19#19153038—21no—
20#19153038—22no—
21#19153034—21no—
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4×C8×C179C2211yescharacteristic
25C2×Dic358—22no—
26C2×Dic358—21no—
27C2×Dic358—21no—
28C2×Dic358—42no—
29C2×Dic358—42no—
30C2×Dic358D411yescharacteristic
31C22×Dic179—22no—
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179D412yes—
37C4⋊Dic179D411yescharacteristic
38Dic179⋊C4—22no—
39Dic179⋊C4—21no—
40C22⋊Dic179—22no—
41C4×Dic179—21no—
42C2×D4×C179D411yescharacteristic
43C22×C4×C179—21no—
44C2×C8×C179—21no—
45C2×C8×C179—21no—
46C4⋊C4×C179D411yescharacteristic
47C22⋊C4×C179—21no—
48C42×C179C2311yescharacteristic
49Dic358—21no—
50Dic358—44no—
51Dic358—41no—
52Dic358—41no—
53Dic358—42no—
54Dic358SD1612yes—
55C2×Dic179—21no—
56C2×Dic179—21no—
57C2×Dic179—22no—
58C2×Dic179—44no—
59C2×Dic179—41no—
60C179⋊C8—41no—
61C23×C179—21no—
62D4×C179—21no—
63D4×C179Q1612yes—
64C2×C4×C179—21no—
65C2×C4×C179—41no—
66C2×C4×C179—41no—
67C2×C4×C179C2×D411yescharacteristic
68C2×C4×C179C2×D411yescharacteristic
69C2×C4×C179C2×D411yescharacteristic
70C8×C179—41no—
71C8×C179—41no—
72C22×C179—22no—
73C22×C179—41no—
74C22×C179—41no—
75C22×C179#12011yescharacteristic
76C4×C179—21no—
77C4×C179—41no—
78C4×C179C2×SD1611yescharacteristic
79C4×C179C2×Q1611yescharacteristic
80C4×C179AGL(1,ℤ/8)11yescharacteristic
81C4×C179#13711yescharacteristic
82Dic179—22no—
83Dic179—42no—
84Dic179—41no—
85Dic179—81no—
86C2×C179—42no—
87C2×C179#45011yescharacteristic
88C2×C179#45111yescharacteristic
89C2×C179#45411yescharacteristic
90C179#163711yescharacteristic, complemented, Sylow
91#1637—1791nomaximal, Sylow
92D4×Q8—1791no—
93#487—1791no—
94#477—1791no—
95#476—1791no—
96#332—1791no—
97Q8⋊C8—1791no—
98D4⋊C8D17911yescharacteristic
99C22×Q8—3581no—
100C4⋊Q8—3581no—
101C4⋊Q8—1791no—
102C4⋊Q8—1791no—
103C22⋊Q8—3582no—
104C22⋊Q8—3581no—
105C4×Q8—1791no—
106C4×D4—3581no—
107C4×D4C2×D17911yescharacteristic
108#107—3581no—
109#106—3581no—
110C4⋊C8—1791no—
111C4⋊C8C2×D17911yescharacteristic
112#103—3581no—
113#103—3582no—
114#102—3581no—
115C4×C8C2×D17911yescharacteristic
116C2×Q8—3582no—
117C2×Q8—3581no—
118C2×Q8—3581no—
119C2×Q8—1791no—
120C2×Q8—7162no—
121C2×Q8—7162no—
122C2×D4D71611yescharacteristic
123C22×C4—21no—
124C22×C4—3582no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—3581no—
128C4⋊C4—3582no—
129C4⋊C4—3581no—
130C4⋊C4—3581no—
131C4⋊C4—3581no—
132C4⋊C4—3581no—
133C4⋊C4—1792no—
134C4⋊C4—1791no—
135C4⋊C4D71611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—3582no—
138C42—3581no—
139C42C22×D17911yescharacteristic
140C23—21no—
141Q8—3581no—
142Q8—1792no—
143Q8—7162no—
144Q8—7164no—
145Q8—7161no—
146Q8—7161no—
147D4—21no—
148D4Dic71612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—3581no—
153C2×C4—3581no—
154C2×C4—3582no—
155C2×C4—7164no—
156C2×C4—7161no—
157C2×C4D4×D17911yescharacteristic
158C2×C4D4×D17911yescharacteristic
159C2×C4C2×D71611yescharacteristic
160C8—41no—
161C8—41no—
162C8—7161no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1915308311yescharacteristic
167C4—21no—
168C4—41no—
169C4—3582no—
170C4—14321no—
171C4—7162no—
172C4—7161no—
173C4SD16×D17911yescharacteristic
174C4C2×Dic71611yescharacteristic
175C4#1915313711yescharacteristic
176C4#1915314611yescharacteristic
177C2—42no—
178C2#2603859111yescharacteristic
179C2#2603859711yescharacteristic
180C2#2603861311yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
FittingD4⋊C8×C179C2
socleC22×C179#120
prime radicalC2×D4×C179D4
hypercenterD4⋊C8D179
hypocenterC179#1637
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. #26038790C2semidirect
3. #26038735C2semidirect
5. #26038186C2semidirect
6. #26038171C2semidirect
90. C179#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic3582
#260387902
#260387352
#260387292
#260381862
#260381712
D4⋊C8×C1792
#1637179