Finite Group Databasebeta

← #49124065

Subgroups — #49124065

Order 36224.

428 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22583602C211yesmaximal, characteristic
2#31826360C212yesmaximal
3#31826350C212yesmaximal
4#31826349C212yesmaximal
5#31826348C212yesmaximal
6#31826346C212yesmaximal
7#31826333C211yesmaximal, characteristic
8C4×Dic283⋊C4C212yesmaximal
9C4×C4⋊C4×C283C211yesmaximal, characteristic
10#22583602C418yescomplemented
11C2×C4⋊Dic283C2211yescharacteristic
12C2×C4⋊Dic283C2211yescharacteristic
13C2×Dic283⋊C4C2212yes—
14C2×Dic283⋊C4C2212yes—
15C2×Dic283⋊C4C2212yes—
16C2×Dic283⋊C4C2212yes—
17C2×C4×Dic283C2212yes—
18C2×C4×Dic283C2212yes—
19C283⋊#95C2212yes—
20C283⋊#95C2212yes—
21C283⋊#95C2211yescharacteristic
22C283⋊#95C2212yes—
23C283⋊#95C2211yescharacteristic
24C283⋊#95C2212yes—
25C283⋊#95C2212yes—
26C283⋊#95C2212yes—
27C2×C4⋊C4×C283C2212yes—
28C2×C42×C283C2211yescharacteristic
29C2×C42×C283C2211yescharacteristic
30C2×C42×C283C2211yescharacteristic
31#95×C283C2212yes—
32C22×Dic283C2312yes—
33C22×Dic283C2312yes—
34C22×Dic283C2312yes—
35C22×Dic283C2312yes—
36C4⋊Dic283C2×C414yes—
37C4⋊Dic283C2×C414yes—
38Dic283⋊C4—24no—
39Dic283⋊C4—42no—
40Dic283⋊C4C2×C418yes—
41Dic283⋊C4C2×C418yes—
42C4×Dic283—24no—
43C4×Dic283—42no—
44C22×C4×C283C2312yes—
45C22×C4×C283C2311yescharacteristic
46C22×C4×C283C2311yescharacteristic
47C22×C4×C283C2311yescharacteristic
48C22×C4×C283C2312yes—
49C4⋊C4×C283—24no—
50C42×C283—41no—
51C42×C283—41no—
52C42×C283C2×C414yes—
53C2×Dic283—22no—
54C2×Dic283—22no—
55C2×Dic283—22no—
56C2×Dic283—22no—
57C2×Dic283—22no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—22no—
62C2×Dic283—22no—
63C2×Dic283C22×C414yes—
64C2×Dic283C22×C414yes—
65C23×C283C2411yescharacteristic
66C2×C4×C283—22no—
67C2×C4×C283—21no—
68C2×C4×C283—22no—
69C2×C4×C283—22no—
70C2×C4×C283—22no—
71C2×C4×C283—21no—
72C2×C4×C283—22no—
73C2×C4×C283—22no—
74C2×C4×C283—22no—
75C2×C4×C283C22×C412yes—
76C2×C4×C283C22×C412yes—
77C2×C4×C283C22×C412yes—
78C2×C4×C283#4114yes—
79C22×C283C23×C411yescharacteristic
80C22×C283C2×#4112yes—
81C22×C283H(5,𝔽2)11yescharacteristic
82C22×C2832−1+412yes—
83C22×C2832−1+411yescharacteristic
84C4×C283—22no—
85C4×C283—22no—
86C4×C283—22no—
87C4×C283—24no—
88C4×C283—42no—
89Dic283—24no—
90Dic283—24no—
91Dic283—42no—
92Dic283—42no—
93C2×C283C4×#4111yescharacteristic
94C2×C283#51911yescharacteristic
95C2×C283#52011yescharacteristic
96C2×C283#53912yes—
97C2×C283#54112yes—
98C283#233611yescharacteristic, complemented, Sylow
99#2336—2831nomaximal, Sylow
100C2×#125—2831no—
101#389—2832no—
102#387—2832no—
103#387—2832no—
104#387—2832no—
105#387—2832no—
106#383—2831no—
107C4×C4⋊C4—2832no—
108C4×C4⋊C4D28311yescharacteristic
109#125—2838no—
110C2×C4⋊C4—2832no—
111C2×C4⋊C4—2832no—
112C2×C4⋊C4—2831no—
113C2×C4⋊C4—2831no—
114C2×C4⋊C4—2832no—
115C2×C4⋊C4—2832no—
116C2×C4⋊C4C2×D28312yes—
117C2×C42—2832no—
118C2×C42—2832no—
119C2×C42C2×D28311yescharacteristic
120C2×C42C2×D28311yescharacteristic
121C2×C42C2×D28311yescharacteristic
122#95—2832no—
123#95—2832no—
124#95—2831no—
125#95—2832no—
126#95—2831no—
127#95—2832no—
128#95—2832no—
129#95—2832no—
130#95C2×D28312yes—
131C22×C4—2832no—
132C22×C4—2832no—
133C22×C4—2832no—
134C22×C4—2832no—
135C22×C4C22×D28312yes—
136C22×C4C22×D28311yescharacteristic
137C22×C4C22×D28311yescharacteristic
138C22×C4C22×D28311yescharacteristic
139C22×C4C22×D28312yes—
140C4⋊C4—24no—
141C4⋊C4—2838no—
142C4⋊C4—2838no—
143C4⋊C4—2834no—
144C4⋊C4—2834no—
145C4⋊C4—5664no—
146C4⋊C4—11322no—
147C42—41no—
148C42—41no—
149C42—5664no—
150C42—11322no—
151C42C4×D28314yes—
152C23C23×D28311yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—2834no—
163C2×C4—2834no—
164C2×C4—5662no—
165C2×C4—5662no—
166C2×C4—5662no—
167C2×C4—5662no—
168C2×C4—5662no—
169C2×C4—5662no—
170C2×C4—5662no—
171C2×C4—5662no—
172C2×C4—5662no—
173C2×C4—5662no—
174C2×C4C2×C4×D28312yes—
175C2×C4C2×C4×D28312yes—
176C2×C4C2×C4×D28312yes—
177C2×C4#1798539214yes—
178C22C22×C4×D28311yescharacteristic
179C22C2×#1798539212yes—
180C22#2258365511yescharacteristic
181C22#2258365712yes—
182C22#2258365811yescharacteristic
183C4—22no—
184C4—24no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—5664no—
189C4—5664no—
190C4—11322no—
191C4—11322no—
192C2C4×#1798539211yescharacteristic
193C2#3182694211yescharacteristic
194C2#3182694611yescharacteristic
195C2#3182705712yes—
196C2#3182707312yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C4⋊C4×C283C2
socle, prime radical, cosocleC23×C283C24
hypercenterC4×C4⋊C4D283
hypocenterC283#2336
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #22583602C4semidirect
98. C283#2336semidirect

Maximal subgroups

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

subgroupindex
C2×#225836022
#318263602
#318263502
#318263492
#318263482
#318263462
#318263332
C4×Dic283⋊C42
C4×C4⋊C4×C2832
#2336283