Finite Group Databasebeta

← #37508330

Subgroups — #37508330

Order 22912.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C179⋊#564C211yesmaximal, characteristic
2#26038849C211yesmaximal, characteristic
3#26038848C211yesmaximal, characteristic
4#26038808C211yesmaximal, characteristic
5#26038180C211yesmaximal, characteristic
6#26038180C211yesmaximal, characteristic
7#330×C179C211yesmaximal, characteristic
8#19153113C2211yescharacteristic
9#19153105C2211yescharacteristic
10#19153105C2211yescharacteristic
11#19153104—21no—
12#19153104—21no—
13#19153103—21no—
14#19153103—21no—
15#19153103—21no—
16#19153103—21no—
17#19153047—21no—
18#19153046—21no—
19#19153045—21no—
20#19153044—21no—
21#19153038—21no—
22#19153038—21no—
23#19153024C2211yescharacteristic
24#125×C179C2211yescharacteristic
25#97×C179C2211yescharacteristic
26#97×C179C2211yescharacteristic
27C2×Dic358—21no—
28C2×C179⋊C8—21no—
29C4⋊Dic179—21no—
30C4⋊Dic179—21no—
31C4⋊Dic179—21no—
32C4⋊Dic179—21no—
33C4⋊Dic179D411yescharacteristic
34C4⋊Dic179D411yescharacteristic
35C4⋊Dic179D411yescharacteristic
36C4⋊Dic179D411yescharacteristic
37Dic179⋊C4—21no—
38Dic179⋊C4—21no—
39Dic179⋊C4—21no—
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42Dic179⋊C4—21no—
43Dic179⋊C4—21no—
44Dic179⋊C4—21no—
45C4×Dic179—21no—
46C4×Dic179—21no—
47C2×C8×C179—21no—
48C2×C8×C179—21no—
49C4⋊C4×C179—21no—
50C4⋊C4×C179—21no—
51C4⋊C4×C179D411yescharacteristic
52C4⋊C4×C179D411yescharacteristic
53C42×C179C2311yescharacteristic
54Dic358—42no—
55C2×Dic179—21no—
56C2×Dic179—21no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—41no—
60C179⋊C8—22no—
61C2×C4×C179—21no—
62C2×C4×C179—21no—
63C2×C4×C179C2×D411yescharacteristic
64C2×C4×C179C2×D411yescharacteristic
65C2×C4×C179C2×D411yescharacteristic
66C8×C179—22no—
67C8×C179—41no—
68C22×C179#12011yescharacteristic
69C4×C179—21no—
70C4×C179—21no—
71C4×C179—21no—
72C4×C179—41no—
73C4×C179—41no—
74Dic179—41no—
75Dic179—41no—
76Dic179—41no—
77Dic179—41no—
78Dic179—81no—
79C2×C179#45411yescharacteristic
80C2×C179#45611yescharacteristic
81C2×C179#45611yescharacteristic
82C179#166311yescharacteristic, complemented, Sylow
83#1663—1791nomaximal, Sylow
84#564—1791no—
85#501—1791no—
86#501—1791no—
87#491—1791no—
88#330—1791no—
89#330—1791no—
90#330D17911yescharacteristic
91C4⋊Q8—1791no—
92#125—3581no—
93#125—3581no—
94#125—3581no—
95#125—3581no—
96#125—3581no—
97#125—3581no—
98#125—1791no—
99#125—1791no—
100#125C2×D17911yescharacteristic
101#107—3581no—
102#107—3581no—
103#106—3581no—
104#106—3581no—
105#103—3581no—
106#103—3581no—
107#97—1791no—
108#97C2×D17911yescharacteristic
109#97C2×D17911yescharacteristic
110C2×Q8—3581no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—3581no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—3581no—
117C4⋊C4—3581no—
118C4⋊C4—3581no—
119C4⋊C4—3581no—
120C4⋊C4—3581no—
121C4⋊C4—3581no—
122C4⋊C4—3581no—
123C4⋊C4—3581no—
124C4⋊C4—3581no—
125C4⋊C4—3581no—
126C4⋊C4—3581no—
127C4⋊C4—3581no—
128C4⋊C4—1791no—
129C4⋊C4—1791no—
130C4⋊C4—1791no—
131C4⋊C4—1791no—
132C4⋊C4D71611yescharacteristic
133C4⋊C4D71611yescharacteristic
134C42—3581no—
135C42—3581no—
136C42C22×D17911yescharacteristic
137Q8—7162no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—3581no—
141C2×C4—3581no—
142C2×C4—3581no—
143C2×C4—3581no—
144C2×C4—7161no—
145C2×C4D4×D17911yescharacteristic
146C2×C4D4×D17911yescharacteristic
147C2×C4C2×D71611yescharacteristic
148C8—22no—
149C8—41no—
150C8—3582no—
151C22#1915308311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—14321no—
158C4—7161no—
159C4—7161no—
160C4—7161no—
161C4—7161no—
162C2#2603861311yescharacteristic
163C2#2603862311yescharacteristic
164C2#2603862411yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#330×C179C2
socle, prime radicalC22×C179#120
hypercenter#330D179
hypocenterC179#1663
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
82. C179#1663semidirect

Maximal subgroups

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

subgroupindex
C179⋊#5642
#260388492
#260388482
#260388082
#260381802
#330×C1792
#1663179