Finite Group Databasebeta

← #37508313

Subgroups — #37508313

Order 22912.

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

normal subgroups only

This group has 196 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
1#26039193C211yesmaximal, characteristic
2#26038849C211yesmaximal, characteristic, complemented
3#26038848C211yesmaximal, characteristic, complemented
4#26038833C211yesmaximal, characteristic
5#26038180C211yesmaximal, characteristic, complemented
6#26038178C211yesmaximal, characteristic
7#330×C179C211yesmaximal, characteristic, complemented
8C2×Dic716—21no—
9C2×#15668248—21no—
10#19153113C2211yescharacteristic
11#19153112—21no—
12#19153108—21no—
13#19153108—21no—
14#19153105C2211yescharacteristic
15#19153101C2211yescharacteristic
16#19153098—21no—
17#19153093—21no—
18#19153091—21no—
19#19153047—21no—
20#19153046—21no—
21#19153045—21no—
22#19153044—21no—
23#19153024C2211yescharacteristic
24#125×C179C2211yescharacteristic
25#97×C179C2211yescharacteristic
26#97×C179C2211yescharacteristic
27C2×Dic358—21no—
28C2×Dic358—21no—
29C2×Dic358D411yescharacteristic
30C2×D716D411yescharacteristic
31C2×C4×D179—21no—
32Dic716—42no—
33#15668248—42no—
34C2×C179⋊C8—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179—21no—
37C4⋊Dic179—21no—
38C4⋊Dic179D411yescharacteristic
39C4⋊Dic179D411yescharacteristic
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42Dic179⋊C4—21no—
43(C2×D179)⋊C4—21no—
44(C2×D179)⋊C4—21no—
45(C2×D179)⋊C4—21no—
46(C2×D179)⋊C4—21no—
47(C2×D179)⋊C4—21no—
48C4×Dic179—21no—
49C2×C8×C179—21no—
50C2×C8×C179—21no—
51C4⋊C4×C179—21no—
52C4⋊C4×C179—21no—
53C4⋊C4×C179D411yescharacteristic
54C4⋊C4×C179D411yescharacteristic
55C42×C179C2311yescharacteristic
56C22×D179—21no—
57Dic358—41no—
58Dic358—41no—
59Dic358—41no—
60Dic358—81no—
61D716—41no—
62C2×Dic179—21no—
63C2×Dic179—21no—
64C2×Dic179—21no—
65C2×Dic179—41no—
66C4×D179—81no—
67C179⋊C8—22no—
68C2×C4×C179—21no—
69C2×C4×C179—21no—
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C2×C4×C179C2×D411yescharacteristic
73C8×C179—22no—
74C8×C179—22no—
75C22×C179#12011yescharacteristic
76C2×D179—41no—
77C2×D179—41no—
78C2×D179—41no—
79C4×C179—21no—
80C4×C179—21no—
81C4×C179—21no—
82C4×C179—41no—
83C4×C179—41no—
84Dic179—41no—
85Dic179—41no—
86Dic179—41no—
87Dic179—81no—
88C2×C179#45311yescharacteristic
89C2×C179#45611yescharacteristic
90C2×C179#45611yescharacteristic
91D179—81no—
92C179#166011yescharacteristic, complemented, Sylow
93#1660—1791nomaximal, Sylow
94#563—1791no—
95#501—1791no—
96#501—1791no—
97#497—1791no—
98#330—1791no—
99#330D17911yescharacteristic, complemented
100#329—1791no—
101C2×Q16—3581no—
102C2×SD16—3581no—
103C4⋊Q8—3581no—
104C4⋊Q8—1791no—
105#126—3581no—
106#126—3581no—
107#125—1791no—
108#125C2×D17911yescharacteristic
109#124—1791no—
110#123—3581no—
111C22⋊Q8—3581no—
112C22⋊Q8—3581no—
113#107—3581no—
114#107—3581no—
115#106—3581no—
116#106—3581no—
117#97—1791no—
118#97C2×D17911yescharacteristic
119#97C2×D17911yescharacteristic
120C2×Q8—3581no—
121C2×Q8—3581no—
122C2×Q8—1791no—
123C2×D4—1791no—
124C22×C4—3581no—
125Q16—7162no—
126SD16—7162no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—3581no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—3581no—
133C4⋊C4—3581no—
134C4⋊C4—3581no—
135C4⋊C4—3581no—
136C4⋊C4—3581no—
137C4⋊C4—3581no—
138C4⋊C4—1791no—
139C4⋊C4—1791no—
140C4⋊C4D71611yescharacteristic
141C4⋊C4D71611yescharacteristic
142C22⋊C4—3581no—
143C22⋊C4—3581no—
144C22⋊C4—3581no—
145C22⋊C4—3581no—
146C22⋊C4—3581no—
147C42—3581no—
148C42C22×D17911yescharacteristic
149C23—3581no—
150Q8—14321no—
151Q8—7161no—
152Q8—7161no—
153Q8—7161no—
154D4—7161no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—3581no—
158C2×C4—3581no—
159C2×C4—3581no—
160C2×C4—14321no—
161C2×C4—7161no—
162C2×C4D4×D17911yescharacteristic
163C2×C4D4×D17911yescharacteristic
164C2×C4C2×D71611yescharacteristic
165C8—22no—
166C8—22no—
167C8—3582no—
168C22—7161no—
169C22—7161no—
170C22—7161no—
171C22#1915308311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—14321no—
178C4—7161no—
179C4—7161no—
180C4—7161no—
181C2—14321no—
182C2#2603860811yescharacteristic
183C2#2603862311yescharacteristic
184C2#2603862411yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#330×C179C2
socleC22×C179#120
prime radicalC2×D716D4
hypercenter#330D179
hypocenterC179#1660
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #26038849C2semidirect
3. #26038848C2semidirect
5. #26038180C2semidirect
7. #330×C179C2semidirect
92. C179#1660semidirect
99. #330D179semidirect

Maximal subgroups

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

subgroupindex
#260391932
#260388492
#260388482
#260388332
#260381802
#260381782
#330×C1792
#1660179