Finite Group Databasebeta

← #49119861

Subgroups — #49119861

Order 36224.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#125×D283C211yesmaximal, characteristic
2#31826520C211yesmaximal, characteristic
3#31826417C211yesmaximal, characteristic
4#31826207C211yesmaximal, characteristic, complemented
5#31826206C211yesmaximal, characteristic, complemented
6#31826206C211yesmaximal, characteristic, complemented
7#330×C283C211yesmaximal, characteristic, complemented
8C2×#17985375—21no—
9#22583602C2211yescharacteristic
10#22583601C411yescharacteristic
11#22583601C411yescharacteristic
12#22583600—21no—
13#22583600—21no—
14C4⋊C4×D283—21no—
15C4⋊C4×D283—21no—
16C4⋊C4×D283C411yescharacteristic
17C4⋊C4×D283C411yescharacteristic
18C42×D283C2211yescharacteristic
19Dic283⋊C8—21no—
20(C2×D283)⋊C8—21no—
21#22583521C2211yescharacteristic
22#22583521C2211yescharacteristic
23C8×Dic283—21no—
24#125×C283C2211yescharacteristic
25#97×C283C2211yescharacteristic
26#97×C283C2211yescharacteristic
27C2×C4×D283—21no—
28C2×C4×D283—21no—
29C2×C4×D283C2×C411yescharacteristic
30C2×C4×D283D411yescharacteristic
31C2×C4×D283D411yescharacteristic
32#17985375—24no—
33C2×C283⋊C8—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283C2×C411yescharacteristic
38C4⋊Dic283C2×C411yescharacteristic
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43Dic283⋊C4—21no—
44Dic283⋊C4—21no—
45C4×Dic283C2×C411yescharacteristic
46C4×Dic283D411yescharacteristic
47C4×Dic283D411yescharacteristic
48C2×C8×C283—21no—
49C2×C8×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283C2×C411yescharacteristic
53C4⋊C4×C283C2×C411yescharacteristic
54C42×C283C2311yescharacteristic
55C22×D283C22⋊C411yescharacteristic
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283C22⋊C411yescharacteristic
59C2×Dic283C22⋊C411yescharacteristic
60C2×Dic283C22⋊C411yescharacteristic
61C4×D283—22no—
62C4×D283—22no—
63C4×D283—41no—
64C4×D283—42no—
65C4×D283—42no—
66C283⋊C8—22no—
67C283⋊C8—41no—
68C2×C4×C283—21no—
69C2×C4×C283—21no—
70C2×C4×C283C22×C411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C8×C283—22no—
74C8×C283—41no—
75C22×C283C2×C22⋊C411yescharacteristic
76C2×D283—21no—
77C2×D283—21no—
78C2×D283#10412yes—
79C4×C283—21no—
80C4×C283—21no—
81C4×C283—21no—
82C4×C283—41no—
83C4×C283—41no—
84Dic283—21no—
85Dic283—21no—
86Dic283—41no—
87Dic283—41no—
88Dic283#10112yes—
89C2×C283C2×#10111yescharacteristic
90C2×C283C2×#10411yescharacteristic
91C2×C283#42111yescharacteristic
92D283—22no—
93C283#152811yescharacteristic, complemented, Sylow
94#1528—2831nomaximal, Sylow
95C2×#125—2831no—
96#432—2831no—
97C4×M16—2831no—
98#330—2831no—
99#330—2831no—
100#330—2831no—
101#330D28311yescharacteristic, complemented
102C2×M16—5661no—
103#125—2831no—
104#125—2831no—
105#125—2831no—
106#125—5661no—
107#125—5661no—
108#125C2×D28311yescharacteristic
109C2×C4⋊C4—2831no—
110C2×C4⋊C4—2831no—
111C2×C4⋊C4—5661no—
112C2×C4⋊C4—5661no—
113C2×C42—2831no—
114C4⋊C8—5661no—
115C22⋊C8—5661no—
116#97—2831no—
117#97—2831no—
118#97C2×D28311yescharacteristic
119#97C2×D28311yescharacteristic
120C4×C8—5661no—
121C22×C4—2831no—
122C22×C4—2831no—
123C22×C4—2831no—
124C22×C4—5661no—
125C22×C4—5661no—
126M16—5664no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5661no—
130C2×C8—5661no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—2831no—
134C4⋊C4—2831no—
135C4⋊C4—5661no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4—5661no—
139C4⋊C4—5661no—
140C4⋊C4—5661no—
141C4⋊C4—5661no—
142C4⋊C4—5661no—
143C4⋊C4C4×D28311yescharacteristic
144C4⋊C4C4×D28311yescharacteristic
145C42—2831no—
146C42—2831no—
147C42—2831no—
148C42C22×D28311yescharacteristic
149C23—2831no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2831no—
153C2×C4—2831no—
154C2×C4—2831no—
155C2×C4—5662no—
156C2×C4—5662no—
157C2×C4—5661no—
158C2×C4—5661no—
159C2×C4—11321no—
160C2×C4—11322no—
161C2×C4—11322no—
162C2×C4C2×C4×D28311yescharacteristic
163C2×C4D4×D28311yescharacteristic
164C2×C4D4×D28311yescharacteristic
165C8—22no—
166C8—41no—
167C8—5662no—
168C8—11321no—
169C22—2832no—
170C22—5661no—
171C22—5661no—
172C22C22⋊C4×D28311yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—2832no—
179C4—5661no—
180C4—5661no—
181C4—11321no—
182C4—11321no—
183C2—5662no—
184C2#101×D28311yescharacteristic
185C2#104×D28311yescharacteristic
186C2#3182648011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#330×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC22×D283C22⋊C4
cosocleC42×C283C23
hypercenter#330D283
hypocenterC283#1528
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #31826207C2semidirect
5. #31826206C2semidirect
6. #31826206C2semidirect
7. #330×C283C2semidirect
93. C283#1528semidirect
101. #330D283semidirect

Maximal subgroups

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

subgroupindex
#125×D2832
#318265202
#318264172
#318262072
#318262062
#330×C2832
#1528283