Finite Group Databasebeta

← #37508261

Subgroups — #37508261

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#26038835C211yesmaximal, characteristic, complemented
3#26038721C211yesmaximal, characteristic, complemented
4#26038184C211yesmaximal, characteristic, complemented
5#26038169C211yesmaximal, characteristic, complemented
6D4⋊(C179⋊C8)C211yesmaximal, characteristic
7#461×C179C211yesmaximal, characteristic
8C22×Dic358—21no—
9#19153113C2211yescharacteristic
10#19153112—21no—
11#19153092—21no—
12#19153090—22no—
13C4×Dic358C2211yescharacteristic
14D4×Dic179—21no—
15#19153044—22no—
16#19153044—21no—
17C4⋊(C179⋊C8)C2211yescharacteristic
18#19153036—21no—
19C4×C179⋊C8C2211yescharacteristic
20C2×SD16×C179—21no—
21C4⋊Q8×C179C2211yescharacteristic
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24#103×C179—21no—
25C2×Dic358—22no—
26C2×Dic358—21no—
27C2×Dic358—42no—
28C2×Dic358—42no—
29C2×Dic358D411yescharacteristic
30C22×Dic179—22no—
31C2×C179⋊C8—21no—
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179D411yescharacteristic
35C4⋊Dic179D412yes—
36Dic179⋊C4—22no—
37Dic179⋊C4—21no—
38C22⋊Dic179—22no—
39C4×Dic179—21no—
40C2×Q8×C179—21no—
41C2×D4×C179D411yescharacteristic
42C22×C4×C179—21no—
43SD16×C179—42no—
44C2×C8×C179—21no—
45C4⋊C4×C179—21no—
46C4⋊C4×C179—21no—
47C4⋊C4×C179D411yescharacteristic
48C22⋊C4×C179—21no—
49C42×C179C2311yescharacteristic
50Dic358—21no—
51Dic358—44no—
52Dic358—41no—
53Dic358—41no—
54Dic358SD1612yescomplemented
55C2×Dic179—21no—
56C2×Dic179—21no—
57C2×Dic179—22no—
58C2×Dic179—44no—
59C179⋊C8—22no—
60C179⋊C8—41no—
61C23×C179—21no—
62Q8×C179—41no—
63Q8×C179—41no—
64D4×C179—21no—
65D4×C179SD1612yes—
66C2×C4×C179—21no—
67C2×C4×C179—41no—
68C2×C4×C179—41no—
69C2×C4×C179—41no—
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C2×C4×C179C2×D411yescharacteristic
73C8×C179—41no—
74C22×C179—22no—
75C22×C179—41no—
76C22×C179—41no—
77C22×C179#12011yescharacteristic
78C4×C179—21no—
79C4×C179—41no—
80C4×C179—81no—
81C4×C179C2×SD1611yescharacteristic
82C4×C179C2×SD1611yescharacteristic
83C4×C179AGL(1,ℤ/8)11yescharacteristic
84C4×C179#13711yescharacteristic
85Dic179—22no—
86Dic179—42no—
87Dic179—41no—
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#461D17911yescharacteristic
98#332—1791no—
99Q8⋊C8—1791no—
100D4⋊C8—1791no—
101C22×Q8—3581no—
102C2×SD16—21no—
103C4⋊Q8—3581no—
104C4⋊Q8—1791no—
105C4⋊Q8C2×D17911yescharacteristic
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—21no—
116#103—3581no—
117C4×C8—1791no—
118C2×Q8—21no—
119C2×Q8—3582no—
120C2×Q8—3581no—
121C2×Q8—1791no—
122C2×Q8—7162no—
123C2×Q8—7162no—
124C2×D4C22⋊D17911yescharacteristic
125C22×C4—21no—
126C22×C4—3582no—
127SD16—42no—
128C2×C8—21no—
129C2×C8—3581no—
130C2×C8—3581no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—3582no—
134C4⋊C4—3581no—
135C4⋊C4—3581no—
136C4⋊C4—1791no—
137C4⋊C4—1792no—
138C4⋊C4C22⋊D17911yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—3582no—
141C42—3581no—
142C42C22×D17911yescharacteristic
143C23—21no—
144Q8—41no—
145Q8—41no—
146Q8—3581no—
147Q8—1792no—
148Q8—7164no—
149Q8—7161no—
150Q8—7161no—
151D4—21no—
152D4#1566824712yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—3581no—
158C2×C4—3581no—
159C2×C4—3582no—
160C2×C4—7164no—
161C2×C4D4×D17911yescharacteristic
162C2×C4D4×D17911yescharacteristic
163C2×C4C2×C22⋊D17911yescharacteristic
164C8—41no—
165C8—3582no—
166C8—7161no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1915308111yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—3582no—
175C4—7162no—
176C4—7161no—
177C4SD16×D17911yescharacteristic
178C4C2×#1566824711yescharacteristic
179C4#1915314011yescharacteristic
180C4#1915314311yescharacteristic
181C2—42no—
182C2#2603857711yescharacteristic
183C2#2603858811yescharacteristic
184C2#2603862011yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#461×C179C2
socleC22×C179#120
prime radicalC2×D4×C179D4
hypercenter#461D179
hypocenterC179#1651
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #26038835C2semidirect
3. #26038721C2semidirect
4. #26038184C2semidirect
5. #26038169C2semidirect
54. 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
#260388352
#260387212
#260381842
#260381692
D4⋊(C179⋊C8)2
#461×C1792
#1651179