Finite Group Databasebeta

← #49121294

Subgroups — #49121294

Order 36224.

316 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22583544C211yesmaximal, characteristic, complemented
2C2×#22583542C211yesmaximal, characteristic, complemented
3#31826325C212yesmaximal
4#31826228C212yesmaximal, complemented
5C22×M16×C283C211yesmaximal, characteristic
6C2×C4⋊Dic283C2212yes—
7C2×C4⋊Dic283C2212yes—
8C2×C22⋊Dic283—22no—
9#22583544—22no—
10#22583542—22no—
11C283⋊#95—22no—
12C23×C4×C283C2211yescharacteristic
13C2×M16×C283—22no—
14C2×M16×C283—22no—
15C2×M16×C283C414yescomplemented
16C22×C8×C283C2211yescharacteristic
17C22×C8×C283C2211yescharacteristic
18C22×Dic283—22no—
19C22×Dic283—22no—
20C4⋊Dic283—22no—
21C4⋊Dic283—22no—
22C4⋊Dic283—22no—
23C4⋊Dic283—22no—
24C22⋊Dic283—44no—
25C24×C283D411yescharacteristic
26C22×C4×C283—21no—
27C22×C4×C283—21no—
28C22×C4×C283—21no—
29C22×C4×C283—21no—
30C22×C4×C283C2×C412yes—
31C22×C4×C283D411yescharacteristic
32C22×C4×C283Q812yes—
33C22×C4×C283C2311yescharacteristic
34M16×C283—28no—
35C2×C8×C283—21no—
36C2×C8×C283—21no—
37C2×C8×C283C2×C412yes—
38C2×C8×C283C2×C412yes—
39C2×C8×C283D412yes—
40C2×C8×C283D412yes—
41C2×Dic283—42no—
42C2×Dic283—42no—
43C2×Dic283—42no—
44C2×Dic283—42no—
45C2×Dic283—42no—
46C2×Dic283—42no—
47C23×C283—21no—
48C23×C283—21no—
49C23×C283—22no—
50C23×C283—22no—
51C23×C283C4⋊C412yes—
52C23×C283C2×D411yescharacteristic
53C2×C4×C283—21no—
54C2×C4×C283—21no—
55C2×C4×C283—22no—
56C2×C4×C283—22no—
57C2×C4×C283—22no—
58C2×C4×C283—22no—
59C2×C4×C283C4⋊C412yes—
60C2×C4×C283C22×C411yescharacteristic
61C2×C4×C283C2×D411yescharacteristic
62C2×C4×C283C2×D411yescharacteristic
63C2×C4×C283C2×Q811yescharacteristic
64C2×C4×C283#4111yescharacteristic
65C2×C4×C283#4111yescharacteristic
66C8×C283—22no—
67C8×C283C22⋊C414yescomplemented
68C22×C283—22no—
69C22×C283—24no—
70C22×C283—42no—
71C22×C283—41no—
72C22×C283—41no—
73C22×C283C2×C4⋊C411yescharacteristic
74C22×C283#12111yescharacteristic
75C22×C283#12111yescharacteristic
76C22×C283AGL(1,ℤ/8)12yes—
77C22×C283#13712yes—
78C4×C283—22no—
79C4×C283C2×C22⋊C411yescharacteristic
80C4×C283#11711yescharacteristic
81C4×C283C22⋊Q811yescharacteristic
82C4×C283C22⋊Q811yescharacteristic
83Dic283—82no—
84Dic283—82no—
85C2×C283—42no—
86C2×C283#38011yescharacteristic
87C2×C283#42812yes—
88C2×C283#46812yes—
89C2×C283#46911yescharacteristic
90C2×C283#47011yescharacteristic
91C283#180911yescharacteristic, complemented, Sylow
92#1809—2831nomaximal, Sylow
93C22×M16D28311yescharacteristic
94C2×#107—2831no—
95C2×#106—2831no—
96#380—2832no—
97#340—2832no—
98C23×C4C2×D28311yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16Dic28314yescomplemented
102C22×C8C2×D28311yescharacteristic
103C22×C8C2×D28311yescharacteristic
104C2×C4⋊C4—2832no—
105C2×C4⋊C4—2832no—
106C2×C22⋊C4—5662no—
107#107—5662no—
108#106—5662no—
109#95—5662no—
110C24D113211yescharacteristic
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—5662no—
116C22×C4—5662no—
117C22×C4C2×Dic28312yes—
118C22×C4D113211yescharacteristic
119C22×C4Dic56612yes—
120C22×C4C22×D28311yescharacteristic
121M16—28no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8C2×Dic28312yes—
125C2×C8C2×Dic28312yes—
126C2×C8C22⋊D28312yes—
127C2×C8C22⋊D28312yes—
128C4⋊C4—5662no—
129C4⋊C4—5662no—
130C4⋊C4—5662no—
131C4⋊C4—5662no—
132C22⋊C4—11324no—
133C23—21no—
134C23—21no—
135C23—22no—
136C23—22no—
137C23C4⋊Dic28312yes—
138C23C2×D113211yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—11322no—
146C2×C4—11322no—
147C2×C4—11322no—
148C2×C4—11322no—
149C2×C4—11322no—
150C2×C4—11322no—
151C2×C4C4⋊Dic28312yes—
152C2×C4C22×Dic28311yescharacteristic
153C2×C4C2×C22⋊D28311yescharacteristic
154C2×C4C2×C22⋊D28311yescharacteristic
155C2×C4C2×Dic56611yescharacteristic
156C2×C4#1798539211yescharacteristic
157C2×C4#1798539211yescharacteristic
158C8—22no—
159C8C22⋊Dic28314yescomplemented
160C22—24no—
161C22—22no—
162C22—42no—
163C22—41no—
164C22—41no—
165C22C2×C4⋊Dic28311yescharacteristic
166C22#2258358411yescharacteristic
167C22#2258358411yescharacteristic
168C22#2258363812yes—
169C22#2258364312yes—
170C4—22no—
171C4—22642no—
172C4—22642no—
173C4C2×C22⋊Dic28311yescharacteristic
174C4#2258356911yescharacteristic
175C4#2258358911yescharacteristic
176C4#2258358911yescharacteristic
177C2—42no—
178C2#3182632511yescharacteristic
179C2#3182650712yes—
180C2#3182671112yes—
181C2#3182671811yescharacteristic
182C2#3182672311yescharacteristic
subgroupG/H
centerC23C2×D1132
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC22×M16×C283C2
socleC23×C283C2×D4
prime radicalC24×C283D4
cosocleC22×C4×C283C23
hypercenterC22×M16D283
hypocenterC283#1809
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C2×#22583544C2semidirect
2. C2×#22583542C2semidirect
4. #31826228C2semidirect
15. C2×M16×C283C4semidirect
67. C8×C283C22⋊C4semidirect
91. C283#1809semidirect
101. C2×M16Dic283semidirect
159. C8C22⋊Dic283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835442
C2×#225835422
#318263252
#318262282
C22×M16×C2832
#1809283