Finite Group Databasebeta

← #49121291

Subgroups — #49121291

Order 36224.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×#17985375C211yesmaximal, characteristic
2C2×#22583544C211yesmaximal, characteristic, complemented
3#31826322C212yesmaximal
4#31826227C212yesmaximal, complemented
5C2×#106×C283C211yesmaximal, characteristic, complemented
6C22×C4×D283C2211yescharacteristic
7C2×#17985375—22no—
8C2×#17985375—22no—
9C2×#17985375C414yescomplemented
10C22×C283⋊C8C2211yescharacteristic
11C2×C4⋊Dic283C2212yes—
12C2×(C2×D283)⋊C4—22no—
13#22583544—22no—
14C283⋊#95—22no—
15C22×C8×C283C2211yescharacteristic
16C2×C4⋊C4×C283C2212yes—
17#106×C283—22no—
18C23×D283D411yescharacteristic
19C22×Dic283—22no—
20C22×Dic283D411yescharacteristic
21C2×C4×D283—21no—
22C2×C4×D283—21no—
23C2×C4×D283—21no—
24C2×C4×D283—21no—
25C2×C4×D283C2×C412yes—
26C2×C4×D283Q812yes—
27#17985375—28no—
28C2×C283⋊C8—21no—
29C2×C283⋊C8—21no—
30C2×C283⋊C8C2×C412yes—
31C4⋊Dic283—22no—
32C4⋊Dic283—22no—
33(C2×D283)⋊C4—44no—
34C22×C4×C283—22no—
35C22×C4×C283C2311yescharacteristic
36C2×C8×C283C2×C412yes—
37C2×C8×C283D412yes—
38C2×C8×C283D412yes—
39C4⋊C4×C283—22no—
40C4⋊C4×C283—22no—
41C22×D283—21no—
42C22×D283—21no—
43C22×D283—22no—
44C22×D283—22no—
45C22×D283C4⋊C412yes—
46C2×Dic283—21no—
47C2×Dic283—21no—
48C2×Dic283—42no—
49C2×Dic283—42no—
50C2×Dic283—42no—
51C2×Dic283C4⋊C412yes—
52C4×D283—22no—
53C4×D283—22no—
54C4×D283—22no—
55C4×D283—22no—
56C283⋊C8—22no—
57C23×C283C2×D411yescharacteristic
58C2×C4×C283—42no—
59C2×C4×C283—42no—
60C2×C4×C283—42no—
61C2×C4×C283C22×C411yescharacteristic
62C2×C4×C283C2×D411yescharacteristic
63C2×C4×C283C2×D411yescharacteristic
64C2×C4×C283C2×Q811yescharacteristic
65C2×C4×C283#4111yescharacteristic
66C2×C4×C283#4111yescharacteristic
67C8×C283C22⋊C414yescomplemented
68C22×C283C2×C4⋊C411yescharacteristic
69C22×C283#12111yescharacteristic
70C22×C283#12111yescharacteristic
71C22×C283AGL(1,ℤ/8)12yes—
72C22×C283#13712yes—
73C2×D283—22no—
74C2×D283—24no—
75C2×D283—42no—
76C2×D283—41no—
77C2×D283—41no—
78C4×C283—82no—
79C4×C283C2×C22⋊C411yescharacteristic
80C4×C283#11711yescharacteristic
81C4×C283C22⋊Q811yescharacteristic
82C4×C283C22⋊Q811yescharacteristic
83Dic283—22no—
84Dic283—82no—
85C2×C283#38011yescharacteristic
86C2×C283#42812yes—
87C2×C283#46812yes—
88C2×C283#46911yescharacteristic
89C2×C283#47011yescharacteristic
90D283—42no—
91C283#180911yescharacteristic, complemented, Sylow
92#1809—2831nomaximal, Sylow
93C22×M16—2831no—
94C2×#107—2831no—
95C2×#106D28311yescharacteristic, complemented
96#380—2832no—
97#340—2832no—
98C23×C4—2831no—
99C2×M16—2834no—
100C2×M16—5662no—
101C2×M16—5662no—
102C22×C8—2831no—
103C22×C8C2×D28311yescharacteristic
104C2×C4⋊C4—2832no—
105C2×C4⋊C4C2×D28312yes—
106C2×C22⋊C4—5662no—
107#107—5662no—
108#106—22no—
109#95—5662no—
110C24—2831no—
111C22×C4—22no—
112C22×C4—2831no—
113C22×C4—2832no—
114C22×C4—2832no—
115C22×C4—5661no—
116C22×C4—5661no—
117C22×C4—5661no—
118C22×C4—5661no—
119C22×C4—5662no—
120C22×C4C22×D28311yescharacteristic
121M16—5668no—
122C2×C8—2832no—
123C2×C8—5661no—
124C2×C8—5661no—
125C2×C8C4×D28312yes—
126C2×C8C22⋊D28312yes—
127C2×C8D113212yes—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—5662no—
131C4⋊C4—5662no—
132C22⋊C4—11324no—
133C23—2832no—
134C23—5661no—
135C23—5661no—
136C23—5662no—
137C23—5662no—
138C23D4×D28311yescharacteristic
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—2832no—
143C2×C4—5661no—
144C2×C4—5661no—
145C2×C4—5662no—
146C2×C4—5662no—
147C2×C4—5662no—
148C2×C4—5662no—
149C2×C4—11322no—
150C2×C4—11322no—
151C2×C4—11322no—
152C2×C4C2×C4×D28311yescharacteristic
153C2×C4C2×C22⋊D28311yescharacteristic
154C2×C4C2×D113211yescharacteristic
155C2×C4Q8×D28311yescharacteristic
156C2×C4#1798539111yescharacteristic
157C2×C4#1798539311yescharacteristic
158C8—5662no—
159C8(C2×D283)⋊C414yescomplemented
160C22—5664no—
161C22—5662no—
162C22—11322no—
163C22—11321no—
164C22—11321no—
165C22C4⋊C4×D28311yescharacteristic
166C22#2258358111yescharacteristic
167C22#2258358511yescharacteristic
168C22#2258363712yes—
169C22#2258363912yes—
170C4—82no—
171C4—5662no—
172C4—22642no—
173C4C2×(C2×D283)⋊C411yescharacteristic
174C4#2258356811yescharacteristic
175C4#2258358611yescharacteristic
176C4#2258359011yescharacteristic
177C2—11322no—
178C2#3182632211yescharacteristic
179C2#3182650412yes—
180C2#3182670812yes—
181C2#3182671911yescharacteristic
182C2#3182672411yescharacteristic
subgroupG/H
centerC23D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#106×C283C2
socleC23×C283C2×D4
prime radicalC23×D283D4
cosocleC22×C4×C283C23
hypercenterC2×#106D283
hypocenterC283#1809
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#22583544C2semidirect
4. #31826227C2semidirect
5. C2×#106×C283C2semidirect
9. C2×#17985375C4semidirect
67. C8×C283C22⋊C4semidirect
91. C283#1809semidirect
95. C2×#106D283semidirect
159. C8(C2×D283)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#179853752
C2×#225835442
#318263222
#318262272
C2×#106×C2832
#1809283