Finite Group Databasebeta

← #37508097

Subgroups — #37508097

Order 22912.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#26039164C211yesmaximal, characteristic, complemented
2#26038787C211yesmaximal, characteristic
3#26038640C211yesmaximal, characteristic
4#26038640C211yesmaximal, characteristic
5#26038169C211yesmaximal, characteristic, complemented
6#26038169C211yesmaximal, characteristic, complemented
7#332×C179C211yesmaximal, characteristic, complemented
8C2×#15668248—21no—
9C2×#15668248—21no—
10#19153111—21no—
11#19153110C2211yescharacteristic
12#19153104—21no—
13#19153103—22no—
14Q8×Dic179—21no—
15C4×Dic358C2211yescharacteristic
16C4×Dic358C2211yescharacteristic
17#19153078—21no—
18#19153035—21no—
19#19153035—21no—
20#19153033—22no—
21C4×C179⋊C8C2211yescharacteristic
22C4⋊Q8×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4⋊C8×C179C2211yescharacteristic
25C2×Dic358D411yescharacteristic
26C2×Dic358D411yescharacteristic
27C2×D716—21no—
28C2×D716—21no—
29C2×D716—21no—
30#15668248—42no—
31#15668248—42no—
32C2×C179⋊C8—21no—
33C4⋊Dic179—22no—
34C4⋊Dic179D411yescharacteristic
35C4⋊Dic179D411yescharacteristic
36Dic179⋊C4—22no—
37Dic179⋊C4—22no—
38Dic179⋊C4—21no—
39Dic179⋊C4—21no—
40C4×Dic179—22no—
41C4×Dic179—21no—
42C4×Dic179—21no—
43C2×Q8×C179—21no—
44C2×C8×C179—21no—
45C2×C8×C179—21no—
46C4⋊C4×C179—21no—
47C4⋊C4×C179D412yes—
48C42×C179C2311yescharacteristic
49C22×D179—41no—
50Dic358—21no—
51Dic358—21no—
52Dic358—21no—
53Dic358SD1612yescomplemented
54D716—42no—
55D716—41no—
56D716—41no—
57D716—41no—
58D716—41no—
59C2×Dic179—21no—
60C2×Dic179—21no—
61C2×Dic179—21no—
62C2×Dic179—21no—
63C179⋊C8—41no—
64Q8×C179—41no—
65Q8×C179—41no—
66C2×C4×C179—22no—
67C2×C4×C179C2×D411yescharacteristic
68C2×C4×C179C2×D411yescharacteristic
69C2×C4×C179C2×D411yescharacteristic
70C8×C179—41no—
71C8×C179—41no—
72C22×C179#12011yescharacteristic
73C2×D179—81no—
74C2×D179—81no—
75C2×D179—81no—
76C4×C179—21no—
77C4×C179—42no—
78C4×C179C2×SD1611yescharacteristic
79C4×C179#13511yescharacteristic
80C4×C179AGL(1,ℤ/8)11yescharacteristic
81C4×C179#13711yescharacteristic
82Dic179—22no—
83Dic179—41no—
84Dic179—41no—
85Dic179—41no—
86C2×C179#44811yescharacteristic
87C2×C179#44911yescharacteristic
88C2×C179#45411yescharacteristic
89D179—161no—
90C179#162611yescharacteristic, complemented, Sylow
91#1626—1791nomaximal, Sylow
92#557—1791no—
93#486—1791no—
94#460—1791no—
95#460—1791no—
96#332D17911yescharacteristic, complemented
97Q8⋊C8—1791no—
98Q8⋊C8—1791no—
99C2×SD16—3581no—
100C2×SD16—3581no—
101C4⋊Q8—3581no—
102C4⋊Q8C2×D17911yescharacteristic
103#127—1791no—
104#125—3581no—
105#125—3582no—
106C4×Q8—3581no—
107C4×Q8—3581no—
108C4×Q8—1791no—
109C4×Q8—1791no—
110C4⋊C8C2×D17911yescharacteristic
111C4⋊C8C2×D17911yescharacteristic
112#102—3581no—
113#102—3581no—
114#102—3582no—
115C4×C8—1791no—
116C2×Q8—21no—
117C2×Q8—1791no—
118C2×Q8—1791no—
119C2×D4—3581no—
120C2×D4—3581no—
121C2×D4—3581no—
122SD16—7162no—
123SD16—7162no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—3581no—
127C4⋊C4—21no—
128C4⋊C4—3582no—
129C4⋊C4—3582no—
130C4⋊C4—3582no—
131C4⋊C4—3581no—
132C4⋊C4—3581no—
133C4⋊C4—1791no—
134C4⋊C4—1791no—
135C4⋊C4D71612yes—
136C42—3582no—
137C42—3581no—
138C42—3581no—
139C42C22×D17911yescharacteristic
140C23—7161no—
141Q8—41no—
142Q8—41no—
143Q8—3581no—
144Q8—3581no—
145Q8—3581no—
146Q8—1792no—
147D4—7162no—
148D4—7161no—
149D4—7161no—
150D4—7161no—
151D4—7161no—
152C2×C4—22no—
153C2×C4—3581no—
154C2×C4—3581no—
155C2×C4—3581no—
156C2×C4—3581no—
157C2×C4D4×D17911yescharacteristic
158C2×C4D4×D17911yescharacteristic
159C2×C4C2×D71611yescharacteristic
160C8—41no—
161C8—41no—
162C8—7161no—
163C22—14321no—
164C22—14321no—
165C22—14321no—
166C22#1915308311yescharacteristic
167C4—21no—
168C4—42no—
169C4—3582no—
170C4—7161no—
171C4—7161no—
172C4—7161no—
173C4SD16×D17911yescharacteristic
174C4#1915313411yescharacteristic
175C4#1915313711yescharacteristic
176C4#1915314511yescharacteristic
177C2—28641no—
178C2#2603857911yescharacteristic
179C2#2603858511yescharacteristic
180C2#2603861411yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#332×C179C2
socleC22×C179#120
prime radical#19153110C22
hypercenter#332D179
hypocenterC179#1626
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #26039164C2semidirect
5. #26038169C2semidirect
6. #26038169C2semidirect
7. #332×C179C2semidirect
53. Dic358SD16semidirect
90. C179#1626semidirect
96. #332D179semidirect

Maximal subgroups

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

subgroupindex
#260391642
#260387872
#260386402
#260381692
#332×C1792
#1626179