Finite Group Databasebeta

← #49120201

Subgroups — #49120201

Order 36224.

266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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#31826615C212yesmaximal
2#31826382C211yesmaximal, characteristic
3#31826202C212yesmaximal, complemented
4#31826191C211yesmaximal, characteristic, complemented
5#544×C283C211yesmaximal, characteristic, complemented
6C22×D1132C2211yescharacteristic
7C2×#17985379—22no—
8C2×(C2×D283)⋊C4—21no—
9C2×(C2×D283)⋊C4—21no—
10#22583530—22no—
11C22⋊(C283⋊C8)C2212yes—
12C283⋊#95C2211yescharacteristic
13C4⋊Q8×C283—22no—
14#125×C283—22no—
15C22⋊Q8×C283—21no—
16C22⋊Q8×C283C2212yes—
17#117×C283—21no—
18C2×C4⋊C4×C283C2211yescharacteristic
19C23×D283—21no—
20C2×D1132—22no—
21C2×D1132—42no—
22C22×Dic283—21no—
23#17985379—44no—
24C2×C283⋊C8—22no—
25(C2×D283)⋊C4—42no—
26(C2×D283)⋊C4—42no—
27C2×Q8×C283—21no—
28C2×Q8×C283D412yes—
29C22×C4×C283D411yescharacteristic
30C22×C4×C283D411yescharacteristic
31C22×C4×C283C2311yescharacteristic
32C4⋊C4×C283—21no—
33C4⋊C4×C283—21no—
34C4⋊C4×C283—21no—
35C4⋊C4×C283—22no—
36C4⋊C4×C283—22no—
37C4⋊C4×C283—22no—
38C4⋊C4×C283D412yes—
39C22⋊C4×C283—22no—
40C42×C283—22no—
41C22×D283—22no—
42C22×D283—41no—
43C22×D283—41no—
44C22×D283—41no—
45C22×D283—41no—
46C22×D283—41no—
47C22×D283—41no—
48D1132—24no—
49D1132—42no—
50C2×Dic283—41no—
51C2×Dic283—41no—
52C2×Dic283—41no—
53C283⋊C8—42no—
54C23×C283C2×D411yescharacteristic
55Q8×C283—42no—
56Q8×C283—81no—
57C2×C4×C283—21no—
58C2×C4×C283—21no—
59C2×C4×C283—22no—
60C2×C4×C283—22no—
61C2×C4×C283—21no—
62C2×C4×C283—41no—
63C2×C4×C283—41no—
64C2×C4×C283SD1612yescomplemented
65C2×C4×C283C2×D412yes—
66C22×C283—21no—
67C22×C283—21no—
68C22×C283#12011yescharacteristic
69C22×C283C2×SD1611yescharacteristic
70C22×C283#13711yescharacteristic
71C2×D283—42no—
72C2×D283—42no—
73C2×D283—42no—
74C2×D283—81no—
75C2×D283—81no—
76C2×D283—81no—
77C2×D283—81no—
78C4×C283—22no—
79C4×C283—22no—
80C4×C283—42no—
81C4×C283—41no—
82C4×C283—42no—
83Dic283—81no—
84C2×C283—21no—
85C2×C283—21no—
86C2×C283#44811yescharacteristic
87C2×C283#45411yescharacteristic
88C2×C283B(4,𝔽2)11yescharacteristic
89D283—82no—
90C283#159911yescharacteristic, complemented, Sylow
91#1599—2831nomaximal, Sylow
92#544D28311yescharacteristic, complemented
93#450—2832no—
94#394—2831no—
95#328—2832no—
96#324—2831no—
97C22×D4—2831no—
98C2×SD16—5662no—
99C4⋊Q8—22no—
100#125—22no—
101C22⋊Q8—21no—
102C22⋊Q8C2×D28312yes—
103#117—21no—
104C2×C4⋊C4C2×D28311yescharacteristic
105C2×C22⋊C4—5661no—
106C2×C22⋊C4—5661no—
107#102—5662no—
108C22⋊C8—2832no—
109#95—2831no—
110C24—5661no—
111C2×Q8—21no—
112C2×Q8C22⋊D28312yes—
113C2×D4—5662no—
114C2×D4—11322no—
115C22×C4—5661no—
116C22×C4C22⋊D28311yescharacteristic
117C22×C4C22⋊D28311yescharacteristic
118C22×C4C22×D28311yescharacteristic
119SD16—11324no—
120C2×C8—5662no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D28312yes—
128C22⋊C4—22no—
129C22⋊C4—11322no—
130C22⋊C4—11322no—
131C42—22no—
132C23—5662no—
133C23—11321no—
134C23—11321no—
135C23—11321no—
136C23—11321no—
137C23—11321no—
138C23—11321no—
139C23C2×C22⋊D28311yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—5664no—
143D4—11322no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—11321no—
152C2×C4—11321no—
153C2×C4—11321no—
154C2×C4#1798537912yescomplemented
155C2×C4C2×C22⋊D28312yes—
156C8—11322no—
157C22—21no—
158C22—21no—
159C22—11322no—
160C22—11322no—
161C22—11322no—
162C22—22641no—
163C22—22641no—
164C22—22641no—
165C22—22641no—
166C22#2258357911yescharacteristic
167C22C2×#1798537911yescharacteristic
168C22#2258364111yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—22641no—
175C2—21no—
176C2—21no—
177C2—22642no—
178C2#3182660411yescharacteristic
179C2#3182663811yescharacteristic
180C2#3182665211yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#544×C283C2
socleC22×C283#120
prime radicalC22×D1132C22
hypercenter#544D283
hypocenterC283#1599
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #31826202C2semidirect
4. #31826191C2semidirect
5. #544×C283C2semidirect
64. C2×C4×C283SD16semidirect
90. C283#1599semidirect
92. #544D283semidirect
154. C2×C4#17985379semidirect

Maximal subgroups

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

subgroupindex
#318266152
#318263822
#318262022
#318261912
#544×C2832
#1599283