Finite Group Databasebeta

← #49131846

Subgroups — #49131846

Order 36224.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#31827020C211yesmaximal, characteristic
2#31827020C211yesmaximal, characteristic
3#31826868C211yesmaximal, characteristic, complemented
4#31826844C211yesmaximal, characteristic, complemented
5#31826816C211yesmaximal, characteristic, complemented
6#31826705C214yesmaximal
7#31826557C214yesmaximal, complemented
8C4×C8×D283C211yesmaximal, characteristic
9#487×C283C211yesmaximal, characteristic, complemented
10C2×#17985382C2214yes—
11C2×C8×D283C2212yes—
12#22583610C2211yescharacteristic
13#22583610C2211yescharacteristic
14#22583601—21no—
15#22583601—21no—
16#22583590—21no—
17#22583590C2212yes—
18#22583586—21no—
19#22583586C2212yes—
20Q8×Dic283—21no—
21Q8×Dic283C2212yes—
22#22583575—21no—
23#22583575C2212yes—
24#22583568—21no—
25#22583568—21no—
26C42×D283C2211yescharacteristic
27#22583543C2214yes—
28#22583535C2214yes—
29C4×C283⋊C8C2211yescharacteristic
30C8×Dic283C2212yes—
31C4⋊Q8×C283C2211yescharacteristic
32C4⋊Q8×C283C2211yescharacteristic
33#103×C283C2214yes—
34C4×C8×C283C2211yescharacteristic
35C2×Dic566—21no—
36C2×Dic566C2312yes—
37C2×C4×D283D411yescharacteristic
38C2×C4×D283D411yescharacteristic
39C2×C4×D283C2311yescharacteristic
40#17985382—28no—
41C2×C283⋊C8C2312yes—
42C8×D283—24no—
43C4⋊Dic283—22no—
44C4⋊Dic283—22no—
45C4⋊Dic283—21no—
46C4⋊Dic283—21no—
47C4⋊Dic283—21no—
48C4⋊Dic283C2312yes—
49Dic283⋊C4—22no—
50Dic283⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—22no—
54C4×Dic283—22no—
55C4×Dic283D411yescharacteristic
56C4×Dic283D411yescharacteristic
57C4×Dic283C2311yescharacteristic
58C2×Q8×C283—21no—
59C2×Q8×C283C2312yes—
60C2×C8×C283C2312yes—
61C4⋊C4×C283—21no—
62C4⋊C4×C283—21no—
63C4⋊C4×C283—21no—
64C4⋊C4×C283C2312yes—
65C42×C283C2311yescharacteristic
66C22×D283C2×D411yescharacteristic
67Dic566—24no—
68Dic566—42no—
69C2×Dic283—22no—
70C2×Dic283—22no—
71C2×Dic283C2×D411yescharacteristic
72C2×Dic283C2×D411yescharacteristic
73C2×Dic283C2×D411yescharacteristic
74C4×D283—22no—
75C4×D283—22no—
76C4×D283Q1614yescomplemented
77C283⋊C8#4114yes—
78Q8×C283—24no—
79Q8×C283—42no—
80C2×C4×C283—22no—
81C2×C4×C283—22no—
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2411yescharacteristic
85C8×C283—22no—
86C22×C283C22×D411yescharacteristic
87C2×D283—21no—
88C2×D283—21no—
89C2×D283C2×Q1612yes—
90C4×C283—42no—
91C4×C283—42no—
92C4×C283C2×Q1612yes—
93C4×C283#13512yes—
94C4×C283C2×#4112yes—
95Dic283—21no—
96Dic283—21no—
97Dic283—42no—
98Dic283—42no—
99Dic283C2×Q1612yes—
100C2×C283#53211yescharacteristic
101C2×C283C22×Q1611yescharacteristic
102C2×C283C2×#13511yescharacteristic
103D283—22no—
104C283#317011yescharacteristic, complemented, Sylow
105#3170—2831nomaximal, Sylow
106#533—2831no—
107#533—2831no—
108#500—2831no—
109#494—2831no—
110#487—2831no—
111#487D28311yescharacteristic, complemented
112#467—2834no—
113C4×Q16—2834no—
114C2×C4×C8—2831no—
115C2×Q16—2834no—
116C22×C8—2832no—
117C4⋊Q8—2831no—
118C4⋊Q8—2831no—
119C4⋊Q8C2×D28311yescharacteristic
120C4⋊Q8C2×D28311yescharacteristic
121#125—5661no—
122#125—5661no—
123C22⋊Q8—2832no—
124C22⋊Q8—2832no—
125C22⋊Q8—5661no—
126C22⋊Q8—5661no—
127C4×Q8—2832no—
128C4×Q8—2832no—
129C4×Q8—5661no—
130C4×Q8—5661no—
131#117—5661no—
132#117—5661no—
133C2×C42—2831no—
134#107—2834no—
135#103—2834no—
136#103C2×D28314yes—
137C4×C8—2832no—
138C4×C8—2831no—
139C4×C8C2×D28311yescharacteristic
140C2×Q8—21no—
141C2×Q8—2832no—
142C2×Q8—5661no—
143C2×Q8C22×D28312yes—
144C22×C4—2831no—
145C22×C4—2831no—
146C22×C4—2831no—
147Q16—5668no—
148C2×C8—2832no—
149C2×C8—5664no—
150C2×C8C22×D28312yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—2832no—
155C4⋊C4—5662no—
156C4⋊C4—5662no—
157C4⋊C4—5662no—
158C4⋊C4—5662no—
159C4⋊C4—5661no—
160C4⋊C4—5661no—
161C4⋊C4—5661no—
162C4⋊C4C22×D28312yes—
163C22⋊C4—5662no—
164C22⋊C4—5662no—
165C42—2831no—
166C42—2831no—
167C42—2831no—
168C42—5662no—
169C42—5662no—
170C42C22×D28311yescharacteristic
171C23—2831no—
172Q8—24no—
173Q8—42no—
174Q8—5664no—
175Q8—11322no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2831no—
179C2×C4—2834no—
180C2×C4—2831no—
181C2×C4—2831no—
182C2×C4—5662no—
183C2×C4—5662no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4D4×D28311yescharacteristic
187C2×C4D4×D28311yescharacteristic
188C2×C4C23×D28311yescharacteristic
189C8—22no—
190C8—2834no—
191C22—2832no—
192C22—5661no—
193C22—5661no—
194C22C2×D4×D28311yescharacteristic
195C4—42no—
196C4—42no—
197C4—2832no—
198C4—5661no—
199C4—5661no—
200C4—11322no—
201C4—11322no—
202C4Q16×D28312yes—
203C4#2258363112yes—
204C4#41×D28312yes—
205C2—5662no—
206C2#3182701411yescharacteristic
207C2C2×Q16×D28311yescharacteristic
208C2C2×#2258363111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#487×C283C2
socleC22×C283C22×D4
prime radicalC22×D283C2×D4
hypercenter#487D283
hypocenterC283#3170
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #31826868C2semidirect
4. #31826844C2semidirect
5. #31826816C2semidirect
7. #31826557C2semidirect
9. #487×C283C2semidirect
76. C4×D283Q16semidirect
104. C283#3170semidirect
111. #487D283semidirect

Maximal subgroups

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

subgroupindex
#318270202
#318268682
#318268442
#318268162
#318267052
#318265572
C4×C8×D2832
#487×C2832
#3170283