Finite Group Databasebeta

← #37508265

Subgroups — #37508265

Order 22912.

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

normal subgroups only

This group has 234 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#26038837C211yesmaximal, characteristic, complemented
3#26038725C211yesmaximal, characteristic, complemented
4#26038644C211yesmaximal, characteristic
5#26038186C211yesmaximal, characteristic, complemented
6#26038171C211yesmaximal, characteristic, complemented
7D4⋊C8×C179C211yesmaximal, characteristic
8C22×Dic358—21no—
9C2×#15668247—21no—
10#19153113C2211yescharacteristic
11#19153113C2211yescharacteristic
12#19153112—21no—
13#19153092—21no—
14#19153090—22no—
15C4×Dic358C2211yescharacteristic
16D4×Dic179—21no—
17#19153045—22no—
18#19153045—21no—
19C4⋊(C179⋊C8)C2211yescharacteristic
20#19153038—21no—
21#19153036—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—
32#15668247—42no—
33C2×C179⋊C8—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179—21no—
37C4⋊Dic179D411yescharacteristic
38C4⋊Dic179D412yes—
39Dic179⋊C4—22no—
40Dic179⋊C4—21no—
41C22⋊Dic179—22no—
42C4×Dic179—21no—
43C2×D4×C179D411yescharacteristic
44C22×C4×C179—21no—
45C2×C8×C179—21no—
46C2×C8×C179—21no—
47C4⋊C4×C179D411yescharacteristic
48C22⋊C4×C179—21no—
49C42×C179C2311yescharacteristic
50Dic358—21no—
51Dic358—44no—
52Dic358—41no—
53Dic358—41no—
54Dic358—41no—
55Dic358—41no—
56Dic358SD1612yescomplemented
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—22no—
60C2×Dic179—44no—
61C2×Dic179—41no—
62C179⋊C8—41no—
63C23×C179—21no—
64D4×C179—21no—
65D4×C179SD1612yes—
66C2×C4×C179—21no—
67C2×C4×C179—41no—
68C2×C4×C179—41no—
69C2×C4×C179C2×D411yescharacteristic
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C8×C179—22no—
73C8×C179—41no—
74C22×C179—22no—
75C22×C179—41no—
76C22×C179—41no—
77C22×C179#12011yescharacteristic
78C4×C179—21no—
79C4×C179—41no—
80C4×C179C2×SD1611yescharacteristic
81C4×C179C2×SD1611yescharacteristic
82C4×C179AGL(1,ℤ/8)11yescharacteristic
83C4×C179#13711yescharacteristic
84Dic179—22no—
85Dic179—42no—
86Dic179—41no—
87Dic179—81no—
88C2×C179—42no—
89C2×C179#44811yescharacteristic
90C2×C179#45011yescharacteristic
91C2×C179#45611yescharacteristic
92C179#165111yescharacteristic, complemented, Sylow
93#1651—1791nomaximal, Sylow
94D4×Q8—1791no—
95#498—1791no—
96#475—1791no—
97#461—1791no—
98#332—1791no—
99Q8⋊C8—1791no—
100D4⋊C8D17911yescharacteristic
101C22×Q8—3581no—
102C2×SD16—3581no—
103C4⋊Q8—3581no—
104C4⋊Q8—1791no—
105C4⋊Q8—1791no—
106C22⋊Q8—3582no—
107C22⋊Q8—3581no—
108C4×Q8—1791no—
109C4×D4—3581no—
110C4×D4C2×D17911yescharacteristic
111#106—3581no—
112#106—3582no—
113C4⋊C8—1791no—
114C4⋊C8C2×D17911yescharacteristic
115#103—3581no—
116#103—3581no—
117C4×C8C2×D17911yescharacteristic
118C2×Q8—3582no—
119C2×Q8—3581no—
120C2×Q8—3581no—
121C2×Q8—1791no—
122C2×Q8—7162no—
123C2×Q8—7162no—
124C2×D4D71611yescharacteristic
125C22×C4—21no—
126C22×C4—3582no—
127SD16—7162no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—3581no—
131C4⋊C4—3582no—
132C4⋊C4—3581no—
133C4⋊C4—3581no—
134C4⋊C4—3581no—
135C4⋊C4—3581no—
136C4⋊C4—1791no—
137C4⋊C4—1792no—
138C4⋊C4D71611yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—3582no—
141C42—3581no—
142C42C22×D17911yescharacteristic
143C23—21no—
144Q8—3581no—
145Q8—1792no—
146Q8—7164no—
147Q8—7161no—
148Q8—7161no—
149Q8—7161no—
150Q8—7161no—
151D4—21no—
152D4#1566824812yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—3581no—
157C2×C4—3581no—
158C2×C4—3582no—
159C2×C4—7164no—
160C2×C4—7161no—
161C2×C4D4×D17911yescharacteristic
162C2×C4D4×D17911yescharacteristic
163C2×C4C2×D71611yescharacteristic
164C8—22no—
165C8—41no—
166C8—7161no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1915308311yescharacteristic
171C4—21no—
172C4—41no—
173C4—3582no—
174C4—14321no—
175C4—7162no—
176C4—7161no—
177C4SD16×D17911yescharacteristic
178C4C2×#1566824811yescharacteristic
179C4#1915313711yescharacteristic
180C4#1915314611yescharacteristic
181C2—42no—
182C2#2603858011yescharacteristic
183C2#2603859111yescharacteristic
184C2#2603862311yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
FittingD4⋊C8×C179C2
socleC22×C179#120
prime radicalC2×D4×C179D4
hypercenterD4⋊C8D179
hypocenterC179#1651
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. #26038837C2semidirect
3. #26038725C2semidirect
5. #26038186C2semidirect
6. #26038171C2semidirect
56. Dic358SD16semidirect
92. C179#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic3582
#260388372
#260387252
#260386442
#260381862
#260381712
D4⋊C8×C1792
#1651179