Finite Group Databasebeta

← #49119771

Subgroups — #49119771

Order 36224.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#31827017C211yesmaximal, characteristic
2#31826519C211yesmaximal, characteristic
3#31826310C211yesmaximal, characteristic
4#31826203C211yesmaximal, characteristic
5#31826202C211yesmaximal, characteristic
6#31826201C211yesmaximal, characteristic
7#328×C283C211yesmaximal, characteristic
8#22583609C411yescharacteristic, complemented
9#22583608C411yescharacteristic, complemented
10#22583600—21no—
11#22583589C2211yescharacteristic
12#22583587—21no—
13Q8×Dic283C411yescharacteristic, complemented
14#22583575—21no—
15#22583575C411yescharacteristic, complemented
16#22583566—21no—
17C2×C4×Dic283—21no—
18C2×C4×Dic283C2211yescharacteristic
19Dic283⋊C8—21no—
20C22⋊(C283⋊C8)C2211yescharacteristic
21#22583520—21no—
22C283⋊#95—21no—
23C283⋊#95C2211yescharacteristic
24C22⋊Q8×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C2×Dic566—21no—
28C2×Dic566C2×C411yescharacteristic
29C22×Dic283—21no—
30C22×Dic283D411yescharacteristic
31C22×Dic283D411yescharacteristic
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283C2×C411yescharacteristic
35Dic283⋊C4—21no—
36Dic283⋊C4—21no—
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40C22⋊Dic283—21no—
41C4×Dic283—24no—
42C4×Dic283—21no—
43C4×Dic283—21no—
44C4×Dic283C2×C411yescharacteristic
45C4×Dic283C2×C411yescharacteristic
46C4×Dic283D411yescharacteristic
47C4×Dic283D411yescharacteristic
48C2×Q8×C283C2×C411yescharacteristic
49C22×C4×C283—21no—
50C22×C4×C283C2311yescharacteristic
51C2×C8×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283C2×C411yescharacteristic
54C22⋊C4×C283—21no—
55Dic566—42no—
56Dic566—41no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C2×Dic283—41no—
64C2×Dic283—41no—
65C2×Dic283C22⋊C411yescharacteristic
66C2×Dic283C22⋊C411yescharacteristic
67C2×Dic283C22⋊C411yescharacteristic
68C2×Dic283C22⋊C411yescharacteristic
69C283⋊C8—41no—
70C23×C283C2×D411yescharacteristic
71Q8×C283—41no—
72C2×C4×C283—22no—
73C2×C4×C283—21no—
74C2×C4×C283—21no—
75C2×C4×C283—41no—
76C2×C4×C283—41no—
77C2×C4×C283—41no—
78C2×C4×C283C22×C411yescharacteristic
79C2×C4×C283C2×D411yescharacteristic
80C8×C283—41no—
81C22×C283—21no—
82C22×C283—21no—
83C22×C283C2×C22⋊C411yescharacteristic
84C22×C283#13711yescharacteristic
85C22×C283#13711yescharacteristic
86C4×C283—21no—
87C4×C283—21no—
88C4×C283—42no—
89C4×C283—41no—
90C4×C283—41no—
91Dic283—21no—
92Dic283—21no—
93Dic283—21no—
94Dic283—42no—
95Dic283—41no—
96Dic283—41no—
97Dic283#10412yes—
98C2×C283—21no—
99C2×C283—21no—
100C2×C283#41011yescharacteristic
101C2×C283#41911yescharacteristic
102C2×C283C2×#10411yescharacteristic
103C283#150611yescharacteristic, complemented, Sylow
104#1506—2831nomaximal, Sylow
105#533—2831no—
106#432—2831no—
107#376—2831no—
108#328—2831no—
109#328—2831no—
110#328—2831no—
111#328D28311yescharacteristic
112C4⋊Q8—2831no—
113C4⋊Q8—2831no—
114#125—5661no—
115C22⋊Q8—2831no—
116C22⋊Q8—5661no—
117C22⋊Q8C2×D28311yescharacteristic
118C4×Q8—2831no—
119C4×Q8—2831no—
120C4×Q8—5661no—
121#117—5661no—
122C2×C42—2831no—
123C2×C42—5661no—
124C4⋊C8—5661no—
125C22⋊C8—2831no—
126C22⋊C8C2×D28311yescharacteristic
127#97—5661no—
128#95—2831no—
129#95—5661no—
130#95C2×D28311yescharacteristic
131C2×Q8—2831no—
132C2×Q8—5661no—
133C2×Q8C4×D28311yescharacteristic
134C22×C4—21no—
135C22×C4—2831no—
136C22×C4—2831no—
137C22×C4—5661no—
138C22×C4C22×D28311yescharacteristic
139C2×C8—21no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—2831no—
143C4⋊C4—5661no—
144C4⋊C4—5661no—
145C4⋊C4—5661no—
146C4⋊C4—5661no—
147C4⋊C4—5661no—
148C4⋊C4—5661no—
149C4⋊C4C4×D28311yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—5661no—
152C42—2831no—
153C42—2831no—
154C42—2831no—
155C42—2831no—
156C42—5661no—
157C42—5661no—
158C42—5664no—
159C23D4×D28311yescharacteristic
160Q8—41no—
161Q8—11321no—
162Q8—11322no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2831no—
170C2×C4—2831no—
171C2×C4—2831no—
172C2×C4—2831no—
173C2×C4—5662no—
174C2×C4—5661no—
175C2×C4—5661no—
176C2×C4—5662no—
177C2×C4—5661no—
178C2×C4—5661no—
179C2×C4—11321no—
180C2×C4—11321no—
181C2×C4C2×C4×D28311yescharacteristic
182C2×C4D4×D28311yescharacteristic
183C8—41no—
184C8—11321no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D28311yescharacteristic
188C22#2258363911yescharacteristic
189C22#2258364211yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—2832no—
196C4—5661no—
197C4—5661no—
198C4—5661no—
199C4—11322no—
200C4—11321no—
201C4—11321no—
202C2—21no—
203C2—21no—
204C2#3182643711yescharacteristic
205C2#3182647211yescharacteristic
206C2#104×D28311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#328×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC23×C283C2×D4
cosocleC22×C4×C283C23
hypercenter#328D283
hypocenterC283#1506
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #22583609C4semidirect
9. #22583608C4semidirect
13. Q8×Dic283C4semidirect
15. #22583575C4semidirect
103. C283#1506semidirect

Maximal subgroups

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

subgroupindex
#318270172
#318265192
#318263102
#318262032
#318262022
#318262012
#328×C2832
#1506283