Finite Group Databasebeta

← #37508040

Subgroups — #37508040

Order 22912.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#26039068C211yesmaximal, characteristic
2#26038774C211yesmaximal, characteristic
3#26038377C211yesmaximal, characteristic
4#26038177C211yesmaximal, characteristic
5#26038176C211yesmaximal, characteristic
6#26038164C211yesmaximal, characteristic
7#484×C179C211yesmaximal, characteristic
8#19153112—21no—
9#19153111—21no—
10#19153103—21no—
11#19153103—21no—
12#19153092C2211yescharacteristic
13#19153090—21no—
14#19153069—21no—
15C2×Dic179⋊C4C2211yescharacteristic
16#19153046—21no—
17#19153036—21no—
18C22⋊(C179⋊C8)C2211yescharacteristic
19C179⋊#95—21no—
20C179⋊#95—21no—
21C179⋊#95C2211yescharacteristic
22C22⋊Q8×C179C2211yescharacteristic
23C2×C4⋊C4×C179C2211yescharacteristic
24#107×C179—21no—
25#103×C179—21no—
26C22⋊C8×C179C2211yescharacteristic
27C2×Dic358—21no—
28C2×Dic358D411yescharacteristic
29C22×Dic179—21no—
30C22×Dic179D411yescharacteristic
31C22×Dic179D411yescharacteristic
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179D411yescharacteristic
35Dic179⋊C4—21no—
36Dic179⋊C4—21no—
37Dic179⋊C4—21no—
38Dic179⋊C4—21no—
39Dic179⋊C4—21no—
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42C22⋊Dic179—21no—
43C4×Dic179—21no—
44C4×Dic179—21no—
45C2×Q8×C179D411yescharacteristic
46C22×C4×C179—21no—
47C22×C4×C179C2311yescharacteristic
48C2×C8×C179—21no—
49C4⋊C4×C179—21no—
50C4⋊C4×C179—21no—
51C4⋊C4×C179—21no—
52C4⋊C4×C179D411yescharacteristic
53C22⋊C4×C179—21no—
54Dic358—41no—
55Dic358—81no—
56C2×Dic179—21no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—21no—
60C2×Dic179—21no—
61C2×Dic179—41no—
62C2×Dic179—41no—
63C2×Dic179—41no—
64C2×Dic179—41no—
65C2×Dic179Q1612yes—
66C179⋊C8—41no—
67C23×C179C2×D411yescharacteristic
68Q8×C179—41no—
69C2×C4×C179—21no—
70C2×C4×C179—21no—
71C2×C4×C179—41no—
72C2×C4×C179—42no—
73C2×C4×C179—41no—
74C2×C4×C179C2×D411yescharacteristic
75C2×C4×C179C2×D411yescharacteristic
76C8×C179—41no—
77C22×C179—21no—
78C22×C179—21no—
79C22×C179#12011yescharacteristic
80C22×C179C2×Q1611yescharacteristic
81C22×C179#13711yescharacteristic
82C4×C179—21no—
83C4×C179—21no—
84C4×C179—41no—
85C4×C179—41no—
86C4×C179—81no—
87Dic179—22no—
88Dic179—41no—
89Dic179—41no—
90Dic179—41no—
91Dic179—81no—
92C2×C179—21no—
93C2×C179—21no—
94C2×C179#45111yescharacteristic
95C2×C179#45411yescharacteristic
96C2×C179#45811yescharacteristic
97C179#161711yescharacteristic, complemented, Sylow
98#1617—1791nomaximal, Sylow
99#544—1791no—
100#484—1791no—
101#484D17911yescharacteristic
102#400—1791no—
103#328—1791no—
104#328—1791no—
105#324—1791no—
106C4⋊Q8—3581no—
107C4⋊Q8—3581no—
108#125—3581no—
109#125—3581no—
110C22⋊Q8—3581no—
111C22⋊Q8—1791no—
112C22⋊Q8C2×D17911yescharacteristic
113#117—3581no—
114C2×C4⋊C4—1791no—
115C2×C4⋊C4C2×D17911yescharacteristic
116#107—21no—
117#107—3581no—
118#103—21no—
119#103—3581no—
120C22⋊C8—1791no—
121C22⋊C8C2×D17911yescharacteristic
122#95—3581no—
123#95—3581no—
124#95—1791no—
125C2×Q8—3581no—
126C2×Q8—1791no—
127C2×Q8C22⋊D17911yescharacteristic
128C22×C4—21no—
129C22×C4—3581no—
130C22×C4—1791no—
131C22×C4—1791no—
132C22×C4C22×D17911yescharacteristic
133C2×C8—21no—
134C2×C8—3581no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3581no—
139C4⋊C4—3581no—
140C4⋊C4—3581no—
141C4⋊C4—3581no—
142C4⋊C4—3581no—
143C4⋊C4—3581no—
144C4⋊C4—3581no—
145C4⋊C4—3581no—
146C4⋊C4—1791no—
147C4⋊C4C22⋊D17911yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3581no—
150C42—3581no—
151C42—3581no—
152C23D4×D17911yescharacteristic
153Q8—41no—
154Q8—14321no—
155Q8—7161no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—3581no—
162C2×C4—3581no—
163C2×C4—3581no—
164C2×C4—3581no—
165C2×C4—3581no—
166C2×C4—1792no—
167C2×C4—7161no—
168C2×C4—7161no—
169C2×C4—7161no—
170C2×C4—7161no—
171C2×C4D4×D17911yescharacteristic
172C2×C4C2×C22⋊D17911yescharacteristic
173C8—41no—
174C8—7161no—
175C22—21no—
176C22—21no—
177C22#1915308111yescharacteristic
178C22Q16×D17911yescharacteristic
179C22#1915314511yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3582no—
186C4—14321no—
187C4—7161no—
188C4—7161no—
189C4—7161no—
190C2—21no—
191C2—21no—
192C2#2603859311yescharacteristic
193C2#2603861011yescharacteristic
194C2#2603862811yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#484×C179C2
socleC22×C179#120
prime radicalC23×C179C2×D4
hypercenter#484D179
hypocenterC179#1617
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C179#1617semidirect

Maximal subgroups

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

subgroupindex
#260390682
#260387742
#260383772
#260381772
#260381762
#260381642
#484×C1792
#1617179