Finite Group Databasebeta

← #37510132

Subgroups — #37510132

Order 22912.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#26039001C211yesmaximal, characteristic
2C2×#19153097C212yesmaximal, complemented
3C2×#19153027C212yesmaximal, complemented
4#26038300C211yesmaximal, characteristic, complemented
5#342×C179C211yesmaximal, characteristic, complemented
6C22×C22⋊D179C2212yes—
7C23×Dic179C2211yescharacteristic
8#19153097—24no—
9#19153097—22no—
10#19153097—24no—
11#19153087—22no—
12#19153083—22no—
13C2×C4⋊Dic179—22no—
14C2×C22⋊Dic179C2211yescharacteristic
15C2×(C2×D179)⋊C4—22no—
16#19153027—24no—
17C179⋊#95—22no—
18C2×C22⋊C4×C179C2212yes—
19C2×C22⋊C4×C179C2211yescharacteristic
20C23×D179D412yes—
21C2×D716—22no—
22C2×C22⋊D179—22no—
23C2×C22⋊D179—22no—
24C2×C22⋊D179—22no—
25C2×C22⋊D179—22no—
26C2×C22⋊D179—22no—
27C2×C22⋊D179—22no—
28C22×Dic179—21no—
29C22×Dic179—22no—
30C22×Dic179—22no—
31C22×Dic179—21no—
32C22×Dic179—21no—
33C22×Dic179D412yes—
34C22×Dic179D412yescomplemented
35C4⋊Dic179—28no—
36C4⋊Dic179—22no—
37C22⋊Dic179—22no—
38(C2×D179)⋊C4—28no—
39(C2×D179)⋊C4—24no—
40C24×C179C2311yescharacteristic
41C22×C4×C179—22no—
42C22×C4×C179D412yes—
43C22⋊C4×C179—22no—
44C22⋊C4×C179—22no—
45C22⋊C4×C179D414yescomplemented
46C22×D179—22no—
47C22×D179—22no—
48C22×D179—22no—
49C22×D179—44no—
50D716—82no—
51C22⋊D179—42no—
52C22⋊D179—42no—
53C22⋊D179—42no—
54C22⋊D179—42no—
55C2×Dic179—24no—
56C2×Dic179—22no—
57C2×Dic179—22no—
58C2×Dic179—22no—
59C2×Dic179—22no—
60C2×Dic179—41no—
61C2×Dic179—42no—
62C2×Dic179—41no—
63C2×Dic179—42no—
64C2×Dic179—41no—
65C23×C179—42no—
66C23×C179C2×D412yes—
67C23×C179C2×D411yescharacteristic
68C23×C179C2×D411yescharacteristic
69C23×C179C2×D412yes—
70C23×C179#4111yescharacteristic
71C2×C4×C179—24no—
72C2×C4×C179—22no—
73C2×C4×C179—44no—
74C2×C4×C179—42no—
75C22×C179—22no—
76C22×C179—24no—
77C22×C179—41no—
78C22×C179—42no—
79C22×C179—41no—
80C22×C179#12012yes—
81C22×C179#12011yescharacteristic
82C22×C179#12111yescharacteristic
83C22×C179#12112yes—
84C22×C179#12711yescharacteristic
85C2×D179—44no—
86C2×D179—42no—
87C2×D179—44no—
88C2×D179—82no—
89C4×C179—44no—
90C4×C179—42no—
91Dic179—42no—
92Dic179—42no—
93Dic179—81no—
94C2×C179—21no—
95C2×C179—22no—
96C2×C179—22no—
97C2×C179—21no—
98C2×C179#39211yescharacteristic
99C2×C179#45812yes—
100D179—82no—
101C179#202211yescharacteristic, complemented, Sylow
102#2022—1791nomaximal, Sylow
103#534—1791no—
104C2×#123—1792no—
105C2×#99—1792no—
106#381—1791no—
107#342D17911yescharacteristic, complemented
108C22×D4—1792no—
109C23×C4—1791no—
110#123—3584no—
111#123—3582no—
112#123—3584no—
113#121—3582no—
114#120—3582no—
115C2×C4⋊C4—3582no—
116C2×C22⋊C4—3582no—
117C2×C22⋊C4—1791no—
118C2×C22⋊C4C2×D17911yescharacteristic
119C2×C22⋊C4C2×D17912yes—
120#99—3584no—
121#95—3582no—
122C24—1792no—
123C24C22×D17911yescharacteristic
124C2×D4—3582no—
125C2×D4—3582no—
126C2×D4—3582no—
127C2×D4—3582no—
128C2×D4—3582no—
129C2×D4—3582no—
130C2×D4—3582no—
131C22×C4—22no—
132C22×C4—3582no—
133C22×C4—3581no—
134C22×C4—3582no—
135C22×C4—3581no—
136C22×C4—3581no—
137C22×C4—1792no—
138C22×C4—1792no—
139C22×C4D71612yes—
140C4⋊C4—3588no—
141C4⋊C4—3582no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—3588no—
145C22⋊C4—3584no—
146C22⋊C4—3582no—
147C22⋊C4D71614yescomplemented
148C23—42no—
149C23—3582no—
150C23—3582no—
151C23—3582no—
152C23—7164no—
153C23D4×D17912yes—
154C23D4×D17911yescharacteristic
155C23C2×D71611yescharacteristic
156C23C2×D71612yes—
157C23#1566826011yescharacteristic
158D4—14322no—
159D4—7162no—
160D4—7162no—
161D4—7162no—
162D4—7162no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—3584no—
168C2×C4—3582no—
169C2×C4—3582no—
170C2×C4—3582no—
171C2×C4—3582no—
172C2×C4—7162no—
173C2×C4—7161no—
174C2×C4—7161no—
175C2×C4—7162no—
176C2×C4—7161no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—14322no—
183C22—7164no—
184C22—7162no—
185C22—7164no—
186C22#1915308312yes—
187C22#1915308311yescharacteristic
188C22#1915308811yescharacteristic
189C22#1915308812yes—
190C22#1915311011yescharacteristic
191C4—44no—
192C4—42no—
193C4—14321no—
194C4—7162no—
195C4—7162no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—14322no—
201C2#2603834911yescharacteristic
202C2#2603863012yes—
subgroupG/H
centerC22#19153083
commutator, cosocleC24×C179C23
FrattiniC24C22×D179
Fitting#342×C179C2
socleC22×C179#120
prime radical#26039001C2
hypercenter#342D179
hypocenterC179#2022
LCSG ▷ C24×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#19153097C2semidirect
3. C2×#19153027C2semidirect
4. #26038300C2semidirect
5. #342×C179C2semidirect
34. C22×Dic179D4semidirect
45. C22⋊C4×C179D4semidirect
101. C179#2022semidirect
107. #342D179semidirect
147. C22⋊C4D716semidirect

Maximal subgroups

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

subgroupindex
#260390012
C2×#191530972
C2×#191530272
#260383002
#342×C1792
#2022179