Finite Group Databasebeta

← #44450149

Subgroups — #44450149

Order 29824.

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

normal subgroups only

This group has 300 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
1C2×#21418495C211yesmaximal, characteristic
2#28416489C212yesmaximal, complemented
3#28416159C211yesmaximal, characteristic, complemented
4#28416158C212yesmaximal, complemented
5#323×C233C211yesmaximal, characteristic, complemented
6C22×C22⋊D233C411yescharacteristic
7C23×Dic233C411yescharacteristic
8C22×C4×D233C411yescharacteristic
9#21418495—22no—
10#21418495—22no—
11C2×#16836573C411yescharacteristic
12C2×#16836571C2211yescharacteristic
13C2×C4×Dic233C2211yescharacteristic
14#21418464—22no—
15C22⋊#14272338C2212yes—
16#21418445—22no—
17C2×C22⋊C4×C233C2211yescharacteristic
18C22⋊C8×C233C2212yes—
19C23×D233C2×C411yescharacteristic
20C2×C22⋊D233—22no—
21C2×C22⋊D233—22no—
22C2×C22⋊D233—22no—
23C22×Dic233—21no—
24C22×Dic233—21no—
25C22×Dic233—42no—
26C22×Dic233C2×C411yescharacteristic
27C22×Dic233C2×C411yescharacteristic
28C22×Dic233C2×C411yescharacteristic
29C2×C4×D233—21no—
30C2×C4×D233—21no—
31C2×C4×D233—42no—
32C2×#14272338—22no—
33#16836573—22no—
34#16836571—22no—
35C4×Dic233D412yes—
36C4×Dic233D412yes—
37C24×C233C2×C411yescharacteristic
38C22×C4×C233C2×C411yescharacteristic
39C22×C4×C233C2311yescharacteristic
40C2×C8×C233—22no—
41C22⋊C4×C233—22no—
42C22×D233—21no—
43C22×D233—21no—
44C22×D233—41no—
45C22×D233—41no—
46C22×D233M1612yes—
47C22⋊D233—28no—
48C2×Dic233—21no—
49C2×Dic233—21no—
50C2×Dic233—22no—
51C2×Dic233—21no—
52C2×Dic233—42no—
53C2×Dic233—42no—
54C2×Dic233—41no—
55C2×Dic233C22⋊C412yes—
56C2×Dic233C22⋊C411yescharacteristic
57C2×Dic233C22⋊C411yescharacteristic
58C4×D233—42no—
59C4×D233—42no—
60#14272338—42no—
61C23×C233—21no—
62C23×C233—21no—
63C23×C233—41no—
64C23×C233—41no—
65C23×C233M1612yes—
66C23×C233C22×C411yescharacteristic
67C2×C4×C233—21no—
68C2×C4×C233—41no—
69C2×C4×C233—41no—
70C2×C4×C233C2×D412yes—
71C8×C233—42no—
72C22×C233—21no—
73C22×C233—21no—
74C22×C233—22no—
75C22×C233—42no—
76C22×C233—42no—
77C22×C233—41no—
78C22×C233—41no—
79C22×C233C2×C22⋊C411yescharacteristic
80C22×C233C2×M1611yescharacteristic
81C22×C233C2×M1611yescharacteristic
82C2×D233—22no—
83C2×D233—42no—
84C2×D233—41no—
85C2×D233—41no—
86C2×D233—42no—
87C4×C233—22no—
88C4×C233—41no—
89Dic233—22no—
90Dic233—21no—
91Dic233—41no—
92Dic233#10012yes—
93C2×C233—21no—
94C2×C233—21no—
95C2×C233—42no—
96C2×C233#40711yescharacteristic
97C2×C233#41011yescharacteristic
98C2×C233C2×#10011yescharacteristic
99D233—42no—
100C233#146611yescharacteristic, complemented, Sylow
101#1466—2331nomaximal, Sylow
102C2×C4×D4—2331no—
103#432—2332no—
104#323—2331no—
105#323—2332no—
106#323D23311yescharacteristic, complemented
107C22×D4—2331no—
108C23×C4—2331no—
109C23×C4—2331no—
110C4×D4—4662no—
111C4×D4—4662no—
112C2×C4⋊C4—2331no—
113C2×C22⋊C4—2331no—
114C2×C22⋊C4C2×D23311yescharacteristic
115C2×C42—2331no—
116C4⋊C8—4662no—
117C22⋊C8—2332no—
118C22⋊C8C2×D23312yes—
119#97—4662no—
120C24—2331no—
121C24C4×D23311yescharacteristic
122C2×D4—4662no—
123C2×D4—4662no—
124C2×D4—4662no—
125C22×C4—9322no—
126C22×C4—9322no—
127C22×C4—4661no—
128C22×C4—4661no—
129C22×C4—4661no—
130C22×C4—4661no—
131C22×C4—2331no—
132C22×C4—2331no—
133C22×C4—2331no—
134C22×C4C4×D23311yescharacteristic
135C22×C4C22×D23311yescharacteristic
136C2×C8—22no—
137C2×C8—4662no—
138C4⋊C4—4662no—
139C22⋊C4—22no—
140C22⋊C4—4662no—
141C42—2332no—
142C42—2332no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—9321no—
148C23—9321no—
149C23—4661no—
150C23—4661no—
151C23—2332no—
152C23#1683657712yes—
153C23C2×C4×D23311yescharacteristic
154D4—4668no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—9322no—
159C2×C4—9322no—
160C2×C4—9322no—
161C2×C4—9322no—
162C2×C4—9321no—
163C2×C4—4661no—
164C2×C4—4661no—
165C2×C4—4661no—
166C2×C4—4662no—
167C2×C4—2332no—
168C2×C4—2331no—
169C2×C4—2331no—
170C2×C4D4×D23312yes—
171C8—42no—
172C8—9322no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—9322no—
181C22—9322no—
182C22—9321no—
183C22—9321no—
184C22—4662no—
185C22C22⋊C4×D23311yescharacteristic
186C22M16×D23311yescharacteristic
187C22C2×#1683657711yescharacteristic
188C4—22no—
189C4—41no—
190C4—9321no—
191C4—4662no—
192C4—4661no—
193C4—2332no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—9322no—
198C2#2841639711yescharacteristic
199C2#2841640711yescharacteristic
200C2#100×D23311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D233
commutatorC23×C233C22×C4
FrattiniC22×C4C22×D233
Fitting#323×C233C2
socleC22×C233C2×C22⋊C4
prime radicalC22×C22⋊D233C4
cosocleC22×C4×C233C23
hypercenter#323D233
hypocenterC233#1466
LCSG ▷ C23×C233 ▷ C2×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #28416489C2semidirect
3. #28416159C2semidirect
4. #28416158C2semidirect
5. #323×C233C2semidirect
100. C233#1466semidirect
106. #323D233semidirect

Maximal subgroups

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

subgroupindex
C2×#214184952
#284164892
#284161592
#284161582
#323×C2332
#1466233