Finite Group Databasebeta

← #37510164

Subgroups — #37510164

Order 22912.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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#26039065C211yesmaximal, characteristic, complemented
2#26038295C212yesmaximal
3#26038206C211yesmaximal, characteristic, complemented
4#26038205C212yesmaximal, complemented
5#379×C179C211yesmaximal, characteristic
6#19153092—22no—
7#19153090—24no—
8C2×C22⋊Dic179—24no—
9C2×C22⋊Dic179C2212yes—
10C2×C22⋊Dic179C2212yes—
11C25×C179C2211yescharacteristic
12C2×C22⋊C4×C179—22no—
13C2×C22⋊C4×C179C2211yescharacteristic
14C2×C22⋊C4×C179C2211yescharacteristic
15C2×Dic358—22no—
16C22×Dic179—22no—
17C22×Dic179D414yes—
18C4⋊Dic179—22no—
19Dic179⋊C4—24no—
20C22⋊Dic179—22no—
21C22⋊Dic179—22no—
22C22⋊Dic179—22no—
23C22⋊Dic179—22no—
24C22⋊Dic179—48no—
25C24×C179—21no—
26C24×C179—22no—
27C24×C179—22no—
28C24×C179—21no—
29C24×C179—44no—
30C24×C179Q812yescomplemented
31C24×C179C2311yescharacteristic
32C22×C4×C179—21no—
33C22×C4×C179D412yes—
34C22⋊C4×C179—22no—
35C22⋊C4×C179—22no—
36C22⋊C4×C179—44no—
37Dic358—82no—
38C2×Dic179—24no—
39C2×Dic179—44no—
40C2×Dic179—44no—
41C2×Dic179—42no—
42C23×C179—28no—
43C23×C179—24no—
44C23×C179—24no—
45C23×C179—22no—
46C23×C179—44no—
47C23×C179—42no—
48C23×C179—42no—
49C23×C179—44no—
50C23×C179—48no—
51C23×C179—44no—
52C23×C179—41no—
53C23×C179—42no—
54C23×C179—41no—
55C23×C179C2×D412yes—
56C23×C179C2×D411yescharacteristic
57C23×C179C2×Q811yescharacteristic
58C23×C179#4112yes—
59C23×C179#4111yescharacteristic
60C2×C4×C179—22no—
61C2×C4×C179—42no—
62C2×C4×C179—42no—
63C2×C4×C179—41no—
64C22×C179—22no—
65C22×C179—24no—
66C22×C179—28no—
67C22×C179—24no—
68C22×C179—41no—
69C22×C179—42no—
70C22×C179—41no—
71C22×C179—48no—
72C22×C179—44no—
73C22×C179—44no—
74C22×C179—42no—
75C22×C179—42no—
76C22×C179—44no—
77C22×C179#12011yescharacteristic
78C22×C179C22⋊Q812yes—
79C22×C179C22⋊Q811yescharacteristic
80C22×C179#12412yes—
81C22×C179#12411yescharacteristic
82C4×C179—42no—
83C4×C179—81no—
84Dic179—44no—
85Dic179—82no—
86C2×C179—22no—
87C2×C179—21no—
88C2×C179—22no—
89C2×C179—21no—
90C2×C179—44no—
91C2×C179#39311yescharacteristic
92C2×C179B(4,𝔽2)12yes—
93C179#202911yescharacteristic, complemented, Sylow
94#2029—1791nomaximal, Sylow
95#543—1791no—
96#379—1792no—
97#379D17911yescharacteristic
98#342—1792no—
99#342—1791no—
100C25C2×D17911yescharacteristic
101C22⋊Q8—3584no—
102C22⋊Q8—3582no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—3584no—
105C2×C22⋊C4—1792no—
106C2×C22⋊C4—1792no—
107C2×C22⋊C4C2×D17911yescharacteristic
108C2×C22⋊C4C2×D17911yescharacteristic
109C24—22no—
110C24—21no—
111C24—22no—
112C24—21no—
113C24—44no—
114C24Dic35812yescomplemented
115C24C22×D17911yescharacteristic
116C2×Q8—3582no—
117C22×C4—21no—
118C22×C4—3582no—
119C22×C4—1794no—
120C22×C4C22⋊D17912yes—
121C4⋊C4—3584no—
122C4⋊C4—3582no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—3582no—
127C22⋊C4—3582no—
128C22⋊C4—3582no—
129C22⋊C4—3582no—
130C22⋊C4—7168no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—48no—
140C23—44no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23D4×D17912yes—
145C23C2×C22⋊D17911yescharacteristic
146C23C2×Dic35811yescharacteristic
147C23#1566825812yes—
148C23#1566825911yescharacteristic
149Q8—14322no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—3584no—
155C2×C4—7164no—
156C2×C4—7162no—
157C2×C4—7164no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—42no—
164C22—41no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#1915308111yescharacteristic
172C22#1915309012yes—
173C22#1915309211yescharacteristic
174C22#1915309912yes—
175C22#1915310011yescharacteristic
176C4—42no—
177C4—81no—
178C4—14322no—
179C4—7164no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#2603835111yescharacteristic
186C2#2603862512yes—
subgroupG/H
centerC22#19153081
commutator, cosocleC24×C179C23
FrattiniC24C22×D179
Fitting#379×C179C2
socleC22×C179#120
prime radicalC25×C179C22
hypercenter#379D179
hypocenterC179#2029
LCSG ▷ C24×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #26039065C2semidirect
3. #26038206C2semidirect
4. #26038205C2semidirect
30. C24×C179Q8semidirect
93. C179#2029semidirect
114. C24Dic358semidirect

Maximal subgroups

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

subgroupindex
#260390652
#260382952
#260382062
#260382052
#379×C1792
#2029179