Finite Group Databasebeta

← #37508028

Subgroups — #37508028

Order 22912.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#26039034C211yesmaximal, characteristic
2#26038774C211yesmaximal, characteristic, complemented
3#26038377C211yesmaximal, characteristic, complemented
4#26038177C211yesmaximal, characteristic, complemented
5#26038173C211yesmaximal, characteristic
6#26038164C211yesmaximal, characteristic, complemented
7#481×C179C211yesmaximal, characteristic
8#19153106—21no—
9#19153103—21no—
10#19153094—21no—
11#19153094—21no—
12#19153092C2211yescharacteristic
13#19153090—21no—
14D4×Dic179—21no—
15C2×Dic179⋊C4C2211yescharacteristic
16#19153046—21no—
17#19153036—21no—
18C22⋊(C179⋊C8)C2211yescharacteristic
19C179⋊#95—21no—
20C179⋊#95—21no—
21C179⋊#95C2211yescharacteristic
22#121×C179C2211yescharacteristic
23C2×C4⋊C4×C179C2211yescharacteristic
24#106×C179—21no—
25#102×C179—21no—
26C22⋊C8×C179C2211yescharacteristic
27C2×Dic358D411yescharacteristic
28C22×Dic179—21no—
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—
40C22⋊Dic179—21no—
41C22⋊Dic179—21no—
42C22⋊Dic179—21no—
43C22⋊Dic179—21no—
44C4×Dic179—21no—
45C2×D4×C179—21no—
46C2×D4×C179D411yescharacteristic
47C22×C4×C179—21no—
48C22×C4×C179C2311yescharacteristic
49C2×C8×C179—21no—
50C4⋊C4×C179—21no—
51C4⋊C4×C179—21no—
52C4⋊C4×C179D411yescharacteristic
53C22⋊C4×C179—21no—
54Dic358—41no—
55C2×Dic179—21no—
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×Dic179—81no—
66C179⋊C8—41no—
67C23×C179—21no—
68C23×C179C2×D411yescharacteristic
69D4×C179—41no—
70D4×C179—41no—
71D4×C179—41no—
72C2×C4×C179—21no—
73C2×C4×C179—41no—
74C2×C4×C179—42no—
75C2×C4×C179—41no—
76C2×C4×C179C2×D411yescharacteristic
77C2×C4×C179C2×D411yescharacteristic
78C8×C179—41no—
79C22×C179—21no—
80C22×C179—21no—
81C22×C179—41no—
82C22×C179—41no—
83C22×C179—41no—
84C22×C179#12011yescharacteristic
85C22×C179#13511yescharacteristic
86C22×C179#13711yescharacteristic
87C4×C179—21no—
88C4×C179—21no—
89C4×C179—41no—
90C4×C179—81no—
91Dic179—41no—
92Dic179—41no—
93Dic179—41no—
94Dic179—41no—
95Dic179—81no—
96C2×C179—21no—
97C2×C179—21no—
98C2×C179—81no—
99C2×C179#45211yescharacteristic
100C2×C179#45411yescharacteristic
101C2×C179#45811yescharacteristic
102C179#161511yescharacteristic, complemented, Sylow
103#1615—1791nomaximal, Sylow
104#539—1791no—
105#484—1791no—
106#481D17911yescharacteristic
107#400—1791no—
108#328—1791no—
109#327—1791no—
110#324—1791no—
111#126—3581no—
112#125—3581no—
113#123—3581no—
114#123—3581no—
115C22⋊Q8—3581no—
116C22⋊Q8—1791no—
117#121C2×D17911yescharacteristic
118C4×D4—3581no—
119C2×C4⋊C4—1791no—
120C2×C4⋊C4C2×D17911yescharacteristic
121#107—3581no—
122#106—21no—
123#103—3581no—
124#102—21no—
125C22⋊C8—1791no—
126C22⋊C8C2×D17911yescharacteristic
127#95—3581no—
128#95—3581no—
129#95—1791no—
130C2×Q8—1791no—
131C2×D4—21no—
132C2×D4C22⋊D17911yescharacteristic
133C22×C4—21no—
134C22×C4—3581no—
135C22×C4—3581no—
136C22×C4—1791no—
137C22×C4—1791no—
138C22×C4C22×D17911yescharacteristic
139C2×C8—21no—
140C2×C8—3581no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3581no—
144C4⋊C4—3581no—
145C4⋊C4—3581no—
146C4⋊C4—3581no—
147C4⋊C4—3581no—
148C4⋊C4—3581no—
149C4⋊C4—1791no—
150C4⋊C4C22⋊D17911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3581no—
153C22⋊C4—3581no—
154C22⋊C4—3581no—
155C22⋊C4—3581no—
156C42—3581no—
157C23—21no—
158C23D4×D17911yescharacteristic
159Q8—7161no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—3581no—
168C2×C4—3581no—
169C2×C4—3581no—
170C2×C4—3581no—
171C2×C4—3581no—
172C2×C4—3581no—
173C2×C4—14321no—
174C2×C4—7161no—
175C2×C4—7161no—
176C2×C4—7161no—
177C2×C4—7161no—
178C2×C4D4×D17911yescharacteristic
179C2×C4C2×C22⋊D17911yescharacteristic
180C8—41no—
181C8—7161no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1915308111yescharacteristic
188C22#1915313411yescharacteristic
189C22#1915314211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—14321no—
195C4—7161no—
196C4—7161no—
197C4—7161no—
198C4—7161no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2603859811yescharacteristic
203C2#2603861011yescharacteristic
204C2#2603862811yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#481×C179C2
socleC22×C179#120
prime radical#121×C179C22
hypercenter#481D179
hypocenterC179#1615
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #26038774C2semidirect
3. #26038377C2semidirect
4. #26038177C2semidirect
6. #26038164C2semidirect
102. C179#1615semidirect

Maximal subgroups

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

subgroupindex
#260390342
#260387742
#260383772
#260381772
#260381732
#260381642
#481×C1792
#1615179