Finite Group Databasebeta

← #49124440

Subgroups — #49124440

Order 36224.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22583608C211yesmaximal, characteristic
2#31826372C211yesmaximal, characteristic
3#31826369C212yesmaximal
4#31826352C212yesmaximal
5#31826349C212yesmaximal
6#31826347C212yesmaximal
7#31826346C212yesmaximal
8#31826332C212yesmaximal
9#391×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11#22583608C418yescomplemented
12C2×C4⋊Dic283C2211yescharacteristic
13C2×Dic283⋊C4C2212yes—
14C2×Dic283⋊C4C2212yes—
15C2×Dic283⋊C4C2212yes—
16C2×C4×Dic283C2212yes—
17C2×C4×Dic283C2211yescharacteristic
18C2×C4×Dic283C2211yescharacteristic
19C283⋊#95C2212yes—
20C283⋊#95C2212yes—
21C283⋊#95C2212yes—
22C283⋊#95C2212yes—
23C283⋊#95C2212yes—
24C283⋊#95C2212yes—
25C283⋊#95C2212yes—
26C283⋊#95C2212yes—
27C22×Q8×C283C2211yescharacteristic
28C2×C4⋊C4×C283C2211yescharacteristic
29C2×C42×C283C2211yescharacteristic
30#95×C283C2212yes—
31#95×C283C2212yes—
32C2×Dic566—41no—
33C2×Dic566—41no—
34C2×Dic566C2×C414yes—
35C22×Dic283C2312yes—
36C22×Dic283C2312yes—
37C22×Dic283C2312yes—
38C22×Dic283C2312yes—
39C4⋊Dic283—41no—
40Dic283⋊C4—42no—
41Dic283⋊C4C2×C418yes—
42Dic283⋊C4C2×C418yes—
43C4×Dic283—41no—
44C4×Dic283—42no—
45C4×Dic283C2×C414yes—
46C2×Q8×C283—41no—
47C2×Q8×C283—41no—
48C2×Q8×C283C2×C414yes—
49C22×C4×C283C2312yes—
50C22×C4×C283C2312yes—
51C22×C4×C283C2311yescharacteristic
52C22×C4×C283C2311yescharacteristic
53C22×C4×C283C2311yescharacteristic
54C4⋊C4×C283—41no—
55C42×C283—41no—
56Dic566—44no—
57C2×Dic283—22no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—22no—
62C2×Dic283—22no—
63C2×Dic283—22no—
64C2×Dic283—22no—
65C2×Dic283—24no—
66C2×Dic283C22×C414yes—
67C2×Dic283C22×C414yes—
68C23×C283C2411yescharacteristic
69Q8×C283—44no—
70C2×C4×C283—21no—
71C2×C4×C283—21no—
72C2×C4×C283—21no—
73C2×C4×C283—21no—
74C2×C4×C283—21no—
75C2×C4×C283—21no—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—24no—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283C22×C412yes—
82C2×C4×C283C22×C412yes—
83C2×C4×C283C22×C412yes—
84C22×C283C23×C411yescharacteristic
85C22×C283H(5,𝔽2)11yescharacteristic
86C22×C283H(5,𝔽2)11yescharacteristic
87C22×C2832−1+412yes—
88C22×C2832−1+412yes—
89C4×C283—22no—
90C4×C283—22no—
91C4×C283—22no—
92C4×C283—42no—
93C4×C283—42no—
94Dic283—24no—
95Dic283—24no—
96Dic283—42no—
97Dic283—42no—
98C2×C283#51811yescharacteristic
99C2×C283#51912yes—
100C2×C283#56311yescharacteristic
101C2×C283#56311yescharacteristic
102C2×C283#56312yes—
103C283#238111yescharacteristic, complemented, Sylow
104#2381—2831nomaximal, Sylow
105C2×C4⋊Q8—2831no—
106#391—2831no—
107#391—2832no—
108#391D28311yescharacteristic
109#387—2832no—
110#387—2832no—
111#387—2832no—
112#387—2832no—
113#383—2832no—
114C22×Q8—2831no—
115C22×Q8C2×D28311yescharacteristic
116C4⋊Q8—2838no—
117C2×C4⋊C4—2832no—
118C2×C4⋊C4—2832no—
119C2×C4⋊C4—2832no—
120C2×C4⋊C4—2831no—
121C2×C4⋊C4C2×D28311yescharacteristic
122C2×C42—2831no—
123C2×C42—2832no—
124C2×C42—2831no—
125C2×C42C2×D28311yescharacteristic
126#95—2832no—
127#95—2832no—
128#95—2832no—
129#95—2832no—
130#95—2832no—
131#95—2832no—
132#95—2832no—
133#95—2832no—
134#95C2×D28312yes—
135#95C2×D28312yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—2834no—
139C2×Q8—11321no—
140C2×Q8—11321no—
141C2×Q8C4×D28314yes—
142C22×C4—2832no—
143C22×C4—2832no—
144C22×C4—2832no—
145C22×C4—2832no—
146C22×C4C22×D28312yes—
147C22×C4C22×D28312yes—
148C22×C4C22×D28311yescharacteristic
149C22×C4C22×D28311yescharacteristic
150C22×C4C22×D28311yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—2838no—
153C4⋊C4—2838no—
154C4⋊C4—11322no—
155C4⋊C4—11321no—
156C42—41no—
157C42—2834no—
158C42—11321no—
159C42—11322no—
160C23C23×D28311yescharacteristic
161Q8—44no—
162Q8—11324no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—2834no—
175C2×C4—2834no—
176C2×C4—5662no—
177C2×C4—5662no—
178C2×C4—5662no—
179C2×C4—5662no—
180C2×C4—5662no—
181C2×C4—5662no—
182C2×C4—5662no—
183C2×C4—5664no—
184C2×C4—5662no—
185C2×C4C2×C4×D28312yes—
186C2×C4C2×C4×D28312yes—
187C2×C4C2×C4×D28312yes—
188C22C22×C4×D28311yescharacteristic
189C22#2258365511yescharacteristic
190C22#2258365511yescharacteristic
191C22#2258365712yes—
192C22#2258365812yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—5664no—
199C4—5664no—
200C4—11322no—
201C4—11322no—
202C2#3182693811yescharacteristic
203C2#3182694112yes—
204C2#3182721411yescharacteristic
205C2#3182721511yescharacteristic
206C2#3182721612yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#391×C283C2
socle, prime radical, cosocleC23×C283C24
hypercenter#391D283
hypocenterC283#2381
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #22583608C4semidirect
103. C283#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#225836082
#318263722
#318263692
#318263522
#318263492
#318263472
#318263462
#318263322
#391×C2832
#2381283