Finite Group Databasebeta

← #49124446

Subgroups — #49124446

Order 36224.

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

normal subgroups only

This group has 408 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×#22583602C211yesmaximal, characteristic
2#31826362C212yesmaximal
3#31826360C212yesmaximal
4#31826352C212yesmaximal
5#31826350C212yesmaximal
6#31826348C212yesmaximal
7#31826346C212yesmaximal
8#31826331C211yesmaximal, characteristic
9#382×C283C211yesmaximal, characteristic
10#22583602C418yescomplemented
11C2×C4⋊Dic283C2211yescharacteristic
12C2×C4⋊Dic283C2211yescharacteristic
13C2×C4⋊Dic283C2211yescharacteristic
14C2×C4⋊Dic283C2211yescharacteristic
15C2×Dic283⋊C4C2212yes—
16C2×Dic283⋊C4C2212yes—
17C2×Dic283⋊C4C2212yes—
18C2×Dic283⋊C4C2212yes—
19C2×C4×Dic283C2212yes—
20C2×C4×Dic283C2212yes—
21C283⋊#95C2212yes—
22C283⋊#95C2212yes—
23C283⋊#95C2212yes—
24C283⋊#95C2212yes—
25C283⋊#95C2212yes—
26C283⋊#95C2212yes—
27C2×C4⋊C4×C283C2211yescharacteristic
28C2×C4⋊C4×C283C2211yescharacteristic
29C2×C42×C283C2211yescharacteristic
30#95×C283C2212yes—
31#95×C283C2212yes—
32C22×Dic283C2312yes—
33C22×Dic283C2312yes—
34C22×Dic283C2312yes—
35C22×Dic283C2312yes—
36C4⋊Dic283—41no—
37C4⋊Dic283—41no—
38C4⋊Dic283C2×C414yes—
39C4⋊Dic283C2×C414yes—
40Dic283⋊C4—42no—
41Dic283⋊C4—42no—
42Dic283⋊C4C2×C418yes—
43Dic283⋊C4C2×C418yes—
44C4×Dic283—42no—
45C4×Dic283—42no—
46C22×C4×C283C2312yes—
47C22×C4×C283C2312yes—
48C22×C4×C283C2311yescharacteristic
49C22×C4×C283C2311yescharacteristic
50C22×C4×C283C2311yescharacteristic
51C4⋊C4×C283—41no—
52C4⋊C4×C283—41no—
53C42×C283C2×C414yes—
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×Dic283—22no—
64C2×Dic283C22×C414yes—
65C2×Dic283C22×C414yes—
66C23×C283C2411yescharacteristic
67C2×C4×C283—21no—
68C2×C4×C283—21no—
69C2×C4×C283—21no—
70C2×C4×C283—21no—
71C2×C4×C283—21no—
72C2×C4×C283—21no—
73C2×C4×C283—22no—
74C2×C4×C283—22no—
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283C22×C412yes—
80C2×C4×C283C22×C412yes—
81C2×C4×C283C22×C412yes—
82C22×C283C23×C411yescharacteristic
83C22×C283H(5,𝔽2)11yescharacteristic
84C22×C283H(5,𝔽2)11yescharacteristic
85C22×C2832−1+411yescharacteristic
86C22×C2832−1+411yescharacteristic
87C22×C2832−1+411yescharacteristic
88C22×C2832−1+411yescharacteristic
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#51911yescharacteristic
99C2×C283#52011yescharacteristic
100C2×C283#52011yescharacteristic
101C2×C283#56211yescharacteristic
102C2×C283#56311yescharacteristic
103C2×C283#56311yescharacteristic
104C2×C283#56411yescharacteristic
105C283#238211yescharacteristic, complemented, Sylow
106#2382—2831nomaximal, Sylow
107C2×#125—2831no—
108#389—2832no—
109#389—2832no—
110#387—2832no—
111#387—2832no—
112#387—2832no—
113#387—2832no—
114#382—2831no—
115#382D28311yescharacteristic
116#125—2838no—
117C2×C4⋊C4—2832no—
118C2×C4⋊C4—2832no—
119C2×C4⋊C4—2831no—
120C2×C4⋊C4—2831no—
121C2×C4⋊C4—2832no—
122C2×C4⋊C4—2832no—
123C2×C4⋊C4—2831no—
124C2×C4⋊C4—2831no—
125C2×C4⋊C4C2×D28311yescharacteristic
126C2×C4⋊C4C2×D28311yescharacteristic
127C2×C42—2832no—
128C2×C42—2832no—
129C2×C42C2×D28311yescharacteristic
130#95—2832no—
131#95—2832no—
132#95—2832no—
133#95—2832no—
134#95—2832no—
135#95—2832no—
136#95C2×D28312yes—
137#95C2×D28312yes—
138C22×C4—2832no—
139C22×C4—2832no—
140C22×C4—2832no—
141C22×C4—2832no—
142C22×C4C22×D28312yes—
143C22×C4C22×D28312yes—
144C22×C4C22×D28311yescharacteristic
145C22×C4C22×D28311yescharacteristic
146C22×C4C22×D28311yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—2838no—
150C4⋊C4—2838no—
151C4⋊C4—2834no—
152C4⋊C4—2834no—
153C4⋊C4—11322no—
154C4⋊C4—11322no—
155C4⋊C4—11321no—
156C4⋊C4—11321no—
157C42—11322no—
158C42—11322no—
159C42C4×D28314yes—
160C23C23×D28311yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2834no—
174C2×C4—2834no—
175C2×C4—5662no—
176C2×C4—5662no—
177C2×C4—5662no—
178C2×C4—5662no—
179C2×C4—5662no—
180C2×C4—5662no—
181C2×C4—5662no—
182C2×C4—5662no—
183C2×C4—5662no—
184C2×C4—5662no—
185C2×C4C2×C4×D28312yes—
186C2×C4C2×C4×D28312yes—
187C2×C4C2×C4×D28312yes—
188C22C22×C4×D28311yescharacteristic
189C22#2258365511yescharacteristic
190C22#2258365611yescharacteristic
191C22#2258365711yescharacteristic
192C22#2258365711yescharacteristic
193C22#2258365711yescharacteristic
194C22#2258365811yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—5664no—
201C4—5664no—
202C4—11322no—
203C4—11322no—
204C2#3182694211yescharacteristic
205C2#3182694511yescharacteristic
206C2#3182694611yescharacteristic
207C2#3182720911yescharacteristic
208C2#3182721511yescharacteristic
209C2#3182721911yescharacteristic
210C2C283⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#382×C283C2
socle, prime radical, cosocleC23×C283C24
hypercenter#382D283
hypocenterC283#2382
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #22583602C4semidirect
105. C283#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#225836022
#318263622
#318263602
#318263522
#318263502
#318263482
#318263462
#318263312
#382×C2832
#2382283