Finite Group Databasebeta

← #49119891

Subgroups — #49119891

Order 36224.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#31827000C211yesmaximal, characteristic
2#31826520C211yesmaximal, characteristic, complemented
3#31826520C211yesmaximal, characteristic, complemented
4#31826207C211yesmaximal, characteristic, complemented
5#31826204C211yesmaximal, characteristic, complemented
6#31826204C211yesmaximal, characteristic, complemented
7#330×C283C211yesmaximal, characteristic, complemented
8#22583605—21no—
9#22583598C2211yescharacteristic
10#22583595—21no—
11#22583590C411yescharacteristic
12#22583585C411yescharacteristic
13#22583575C411yescharacteristic
14#22583572—21no—
15#22583572C411yescharacteristic
16#22583568—21no—
17C42×D283C2211yescharacteristic
18Dic283⋊C8—21no—
19Dic283⋊C8—21no—
20(C2×D283)⋊C8—21no—
21(C2×D283)⋊C8—21no—
22#22583521C2211yescharacteristic
23#22583521C2211yescharacteristic
24#125×C283C2211yescharacteristic
25#97×C283C2211yescharacteristic
26#97×C283C2211yescharacteristic
27C2×Dic566C2×C411yescharacteristic
28C2×D1132—21no—
29C2×D1132C2×C411yescharacteristic
30C2×C4×D283—21no—
31C2×C4×D283C2×C411yescharacteristic
32C2×C4×D283D411yescharacteristic
33C2×C4×D283D411yescharacteristic
34C2×C283⋊C8—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283—21no—
37Dic283⋊C4—21no—
38(C2×D283)⋊C4—21no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43C4×Dic283—21no—
44C4×Dic283C2×C411yescharacteristic
45C4×Dic283D411yescharacteristic
46C4×Dic283D411yescharacteristic
47C2×C8×C283—21no—
48C2×C8×C283—21no—
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283C2×C411yescharacteristic
52C4⋊C4×C283C2×C411yescharacteristic
53C42×C283C2311yescharacteristic
54C22×D283—21no—
55C22×D283C22⋊C411yescharacteristic
56Dic566—41no—
57D1132—41no—
58D1132—42no—
59C2×Dic283—21no—
60C2×Dic283C22⋊C411yescharacteristic
61C2×Dic283C22⋊C411yescharacteristic
62C2×Dic283C22⋊C411yescharacteristic
63C4×D283—41no—
64C4×D283—41no—
65C4×D283—41no—
66C4×D283—42no—
67C283⋊C8—41no—
68C283⋊C8—41no—
69C2×C4×C283—21no—
70C2×C4×C283—21no—
71C2×C4×C283C22×C411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C2×C4×C283C2×D411yescharacteristic
74C8×C283—41no—
75C8×C283—41no—
76C22×C283C2×C22⋊C411yescharacteristic
77C2×D283—21no—
78C2×D283—21no—
79C2×D283—21no—
80C2×D283—41no—
81C2×D283—41no—
82C2×D283—41no—
83C4×C283—21no—
84C4×C283—21no—
85C4×C283—21no—
86C4×C283—41no—
87C4×C283—41no—
88Dic283—21no—
89Dic283—21no—
90Dic283—21no—
91Dic283—41no—
92C2×C283#41311yescharacteristic
93C2×C283#42111yescharacteristic
94C2×C283#42111yescharacteristic
95D283—41no—
96D283—81no—
97C283#153511yescharacteristic, complemented, Sylow
98#1535—2831nomaximal, Sylow
99#529—2831no—
100#432—2831no—
101#432—2831no—
102#330—2831no—
103#330D28311yescharacteristic, complemented
104#329—2831no—
105#329—2831no—
106#126—5661no—
107#125C2×D28311yescharacteristic
108#124—2831no—
109#123—5661no—
110C22⋊Q8—2831no—
111#121—2831no—
112C4×Q8—2831no—
113C4×D4—2831no—
114C4×D4—5661no—
115#117—5661no—
116C2×C42—2831no—
117C4⋊C8—5661no—
118C4⋊C8—5661no—
119C22⋊C8—5661no—
120C22⋊C8—5661no—
121#97—2831no—
122#97—2831no—
123#97C2×D28311yescharacteristic
124#97C2×D28311yescharacteristic
125C2×Q8—2831no—
126C2×D4—2831no—
127C2×D4—5661no—
128C22×C4—2831no—
129C22×C4—2831no—
130C22×C4—2831no—
131C22×C4—5661no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—5661no—
135C2×C8—5661no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—5661no—
139C4⋊C4—5661no—
140C4⋊C4C4×D28311yescharacteristic
141C4⋊C4C4×D28311yescharacteristic
142C22⋊C4—5661no—
143C22⋊C4—5661no—
144C22⋊C4—5661no—
145C22⋊C4—5661no—
146C22⋊C4—5661no—
147C42—2831no—
148C42—2831no—
149C42—2831no—
150C42—5661no—
151C42C22×D28311yescharacteristic
152C23—2831no—
153C23—5661no—
154Q8—11321no—
155D4—11321no—
156D4—11322no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—2831no—
160C2×C4—2831no—
161C2×C4—2831no—
162C2×C4—5661no—
163C2×C4—11321no—
164C2×C4—11321no—
165C2×C4—11321no—
166C2×C4—11322no—
167C2×C4C2×C4×D28311yescharacteristic
168C2×C4D4×D28311yescharacteristic
169C2×C4D4×D28311yescharacteristic
170C8—41no—
171C8—41no—
172C8—11321no—
173C8—11321no—
174C22—5661no—
175C22—5661no—
176C22—5661no—
177C22—11321no—
178C22—11321no—
179C22—11321no—
180C22C22⋊C4×D28311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—5661no—
187C4—5661no—
188C4—5661no—
189C4—11321no—
190C2—11321no—
191C2—22641no—
192C2#3182644811yescharacteristic
193C2#3182648011yescharacteristic
194C2#3182648011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#330×C283C2
socleC22×C283C2×C22⋊C4
prime radical#22583585C4
cosocleC42×C283C23
hypercenter#330D283
hypocenterC283#1535
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
2. #31826520C2semidirect
3. #31826520C2semidirect
4. #31826207C2semidirect
5. #31826204C2semidirect
6. #31826204C2semidirect
7. #330×C283C2semidirect
97. C283#1535semidirect
103. #330D283semidirect

Maximal subgroups

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

subgroupindex
#318270002
#318265202
#318262072
#318262042
#330×C2832
#1535283