Finite Group Databasebeta

← #44450752

Subgroups — #44450752

Order 29824.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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#28417066C211yesmaximal, characteristic, complemented
2#28416588C212yesmaximal
3#28416352C211yesmaximal, characteristic
4#28416173C212yesmaximal, complemented
5#324×C233C211yesmaximal, characteristic, complemented
6C22×D932C2211yescharacteristic
7C2×#16836583—22no—
8#21418534—22no—
9#21418526—22no—
10#21418514—21no—
11#21418514C2212yes—
12#21418494—21no—
13C2×#16836571—21no—
14C2×#16836571—21no—
15#21418457—22no—
16#21418442C2211yescharacteristic
17C2×C4⋊C4×C233C2211yescharacteristic
18C22⋊C8×C233C2212yes—
19C23×D233—21no—
20C2×Dic466—21no—
21C2×Dic466D412yes—
22C2×D932—22no—
23C2×D932—42no—
24C22×Dic233—21no—
25#16836583—44no—
26C4⋊Dic233—21no—
27C4⋊Dic233—21no—
28C4⋊Dic233—21no—
29C4⋊Dic233D412yes—
30#16836573—22no—
31#16836573—22no—
32C22⋊Dic233—22no—
33#16836571—42no—
34#16836571—42no—
35C4×Dic233—22no—
36C22×C4×C233D411yescharacteristic
37C22×C4×C233D411yescharacteristic
38C22×C4×C233C2311yescharacteristic
39C2×C8×C233—22no—
40C4⋊C4×C233—22no—
41C22×D233—22no—
42C22×D233—41no—
43C22×D233—41no—
44C22×D233—41no—
45C22×D233—41no—
46C22×D233—41no—
47C22×D233—41no—
48Dic466—42no—
49Dic466—81no—
50D932—24no—
51D932—42no—
52C2×Dic233—22no—
53C2×Dic233—22no—
54C2×Dic233—41no—
55C2×Dic233—41no—
56C2×Dic233—41no—
57C23×C233C2×D411yescharacteristic
58C2×C4×C233—21no—
59C2×C4×C233—21no—
60C2×C4×C233—21no—
61C2×C4×C233—41no—
62C2×C4×C233—41no—
63C2×C4×C233SD1612yescomplemented
64C2×C4×C233C2×D412yes—
65C8×C233—42no—
66C22×C233—21no—
67C22×C233—21no—
68C22×C233#12011yescharacteristic
69C22×C233C2×SD1611yescharacteristic
70C22×C233#13711yescharacteristic
71C2×D233—42no—
72C2×D233—42no—
73C2×D233—42no—
74C2×D233—81no—
75C2×D233—81no—
76C2×D233—81no—
77C2×D233—81no—
78C4×C233—22no—
79C4×C233—22no—
80C4×C233—41no—
81Dic233—42no—
82Dic233—42no—
83Dic233—81no—
84C2×C233—21no—
85C2×C233—21no—
86C2×C233#44811yescharacteristic
87C2×C233#45411yescharacteristic
88C2×C233B(4,𝔽2)11yescharacteristic
89D233—82no—
90C233#159911yescharacteristic, complemented, Sylow
91#1599—2331nomaximal, Sylow
92#544—2331no—
93#450—2332no—
94#394—2331no—
95#328—2332no—
96#324D23311yescharacteristic, complemented
97C22×D4—2331no—
98C2×SD16—4662no—
99C4⋊Q8—4662no—
100#125—4662no—
101C22⋊Q8—4661no—
102C22⋊Q8—2332no—
103#117—4661no—
104C2×C4⋊C4C2×D23311yescharacteristic
105C2×C22⋊C4—4661no—
106C2×C22⋊C4—4661no—
107#102—4662no—
108C22⋊C8C2×D23312yes—
109#95—2331no—
110C24—4661no—
111C2×Q8—4661no—
112C2×Q8—2332no—
113C2×D4—9322no—
114C2×D4—4662no—
115C22×C4—4661no—
116C22×C4D93211yescharacteristic
117C22×C4D93211yescharacteristic
118C22×C4C22×D23311yescharacteristic
119SD16—9324no—
120C2×C8—22no—
121C4⋊C4—22no—
122C4⋊C4—4661no—
123C4⋊C4—4661no—
124C4⋊C4—4661no—
125C4⋊C4—4662no—
126C4⋊C4—4662no—
127C4⋊C4—2332no—
128C22⋊C4—9322no—
129C22⋊C4—9322no—
130C22⋊C4—4662no—
131C42—4662no—
132C23—9321no—
133C23—9321no—
134C23—9321no—
135C23—9321no—
136C23—9321no—
137C23—9321no—
138C23—4662no—
139C23C2×D93211yescharacteristic
140Q8—18641no—
141Q8—9322no—
142D4—9322no—
143D4—4664no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—9321no—
150C2×C4—9321no—
151C2×C4—9321no—
152C2×C4—4662no—
153C2×C4—4662no—
154C2×C4#1683658312yescomplemented
155C2×C4D4×D23312yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—18641no—
160C22—18641no—
161C22—18641no—
162C22—18641no—
163C22—9322no—
164C22—9322no—
165C22—9322no—
166C22#2141850511yescharacteristic
167C22C2×#1683658311yescharacteristic
168C22#2141856811yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—18641no—
173C4—9322no—
174C4—9322no—
175C2—21no—
176C2—21no—
177C2—18642no—
178C2#2841657611yescharacteristic
179C2#2841661011yescharacteristic
180C2#2841662311yescharacteristic
subgroupG/H
centerC22#21418505
commutator, cosocleC22×C4×C233C23
FrattiniC22×C4C22×D233
Fitting#324×C233C2
socleC22×C233#120
prime radicalC22×D932C22
hypercenter#324D233
hypocenterC233#1599
LCSG ▷ C22×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #28417066C2semidirect
4. #28416173C2semidirect
5. #324×C233C2semidirect
63. C2×C4×C233SD16semidirect
90. C233#1599semidirect
96. #324D233semidirect
154. C2×C4#16836583semidirect

Maximal subgroups

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

subgroupindex
#284170662
#284165882
#284163522
#284161732
#324×C2332
#1599233