Finite Group Databasebeta

← #37508160

Subgroups — #37508160

Order 22912.

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

normal subgroups only

This group has 188 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#26039167C211yesmaximal, characteristic
2#26038790C211yesmaximal, characteristic
3#26038735C211yesmaximal, characteristic
4#26038734C211yesmaximal, characteristic
5#26038184C211yesmaximal, characteristic
6#26038171C211yesmaximal, characteristic
7Q8⋊C8×C179C211yesmaximal, characteristic
8#19153113C2211yescharacteristic
9#19153113C2211yescharacteristic
10#19153111—21no—
11#19153105—21no—
12#19153103—22no—
13C4×Dic358—21no—
14C4×Dic358C2211yescharacteristic
15#19153078—21no—
16#19153047—21no—
17#19153046—21no—
18C4⋊(C179⋊C8)C2211yescharacteristic
19#19153038—21no—
20#19153038—22no—
21#19153037—21no—
22C4×Q8×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4×C8×C179C2211yescharacteristic
25C2×Dic358—21no—
26C2×Dic358—21no—
27C2×Dic358D411yescharacteristic
28C2×C179⋊C8—21no—
29C4⋊Dic179—21no—
30C4⋊Dic179—21no—
31C4⋊Dic179—21no—
32C4⋊Dic179D412yes—
33C4⋊Dic179D411yescharacteristic
34Dic179⋊C4—22no—
35Dic179⋊C4—22no—
36Dic179⋊C4—22no—
37Dic179⋊C4—21no—
38C4×Dic179—22no—
39C4×Dic179—21no—
40C2×Q8×C179D411yescharacteristic
41C2×C8×C179—21no—
42C2×C8×C179—21no—
43C4⋊C4×C179—21no—
44C4⋊C4×C179D411yescharacteristic
45C42×C179—21no—
46C42×C179C2311yescharacteristic
47Dic358—21no—
48Dic358—41no—
49Dic358—41no—
50Dic358—42no—
51Dic358Q1612yes—
52C2×Dic179—21no—
53C2×Dic179—21no—
54C2×Dic179—22no—
55C2×Dic179—41no—
56C179⋊C8—41no—
57Q8×C179—21no—
58Q8×C179—21no—
59C2×C4×C179—21no—
60C2×C4×C179—21no—
61C2×C4×C179C2×D411yescharacteristic
62C2×C4×C179C2×D411yescharacteristic
63C2×C4×C179C2×D411yescharacteristic
64C8×C179—41no—
65C8×C179—41no—
66C22×C179#12011yescharacteristic
67C4×C179—21no—
68C4×C179—41no—
69C4×C179—41no—
70C4×C179C2×Q1611yescharacteristic
71C4×C179#13511yescharacteristic
72C4×C179#13711yescharacteristic
73C4×C179#13711yescharacteristic
74Dic179—22no—
75Dic179—42no—
76Dic179—41no—
77Dic179—81no—
78C2×C179#45111yescharacteristic
79C2×C179#45211yescharacteristic
80C2×C179#45411yescharacteristic
81C179#163611yescharacteristic, complemented, Sylow
82#1636—1791nomaximal, Sylow
83#557—1791no—
84#487—1791no—
85#477—1791no—
86#477—1791no—
87#332—1791no—
88Q8⋊C8—1791no—
89Q8⋊C8D17911yescharacteristic
90C4⋊Q8—3581no—
91C4⋊Q8—1791no—
92C4⋊Q8—1791no—
93#125—3581no—
94#125—3582no—
95C4×Q8—3581no—
96C4×Q8—3581no—
97C4×Q8—1791no—
98C4×Q8C2×D17911yescharacteristic
99#107—3581no—
100#107—3581no—
101C4⋊C8—1791no—
102C4⋊C8C2×D17911yescharacteristic
103#103—3581no—
104#103—3581no—
105#103—3582no—
106C4×C8C2×D17911yescharacteristic
107C2×Q8—3581no—
108C2×Q8—3581no—
109C2×Q8—1791no—
110C2×Q8D71611yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—3581no—
114C4⋊C4—21no—
115C4⋊C4—3582no—
116C4⋊C4—3582no—
117C4⋊C4—3582no—
118C4⋊C4—3581no—
119C4⋊C4—3581no—
120C4⋊C4—3581no—
121C4⋊C4—3581no—
122C4⋊C4—1792no—
123C4⋊C4—1791no—
124C4⋊C4D71611yescharacteristic
125C42—21no—
126C42—3582no—
127C42—3581no—
128C42C22×D17911yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—3581no—
132Q8—1792no—
133Q8—7162no—
134Q8—7161no—
135Q8—7161no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—3581no—
139C2×C4—3581no—
140C2×C4—3582no—
141C2×C4—7161no—
142C2×C4D4×D17911yescharacteristic
143C2×C4D4×D17911yescharacteristic
144C2×C4C2×D71611yescharacteristic
145C8—41no—
146C8—41no—
147C8—7161no—
148C22#1915308311yescharacteristic
149C4—21no—
150C4—41no—
151C4—41no—
152C4—3582no—
153C4—14321no—
154C4—7162no—
155C4—7161no—
156C4Q16×D17911yescharacteristic
157C4#1915313511yescharacteristic
158C4#1915314211yescharacteristic
159C4#1915314611yescharacteristic
160C2#2603859611yescharacteristic
161C2#2603860311yescharacteristic
162C2#2603861311yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
FittingQ8⋊C8×C179C2
socle, prime radicalC22×C179#120
hypercenterQ8⋊C8D179
hypocenterC179#1636
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
81. C179#1636semidirect

Maximal subgroups

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

subgroupindex
#260391672
#260387902
#260387352
#260387342
#260381842
#260381712
Q8⋊C8×C1792
#1636179