Finite Group Databasebeta

← #49122931

Subgroups — #49122931

Order 36224.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827028C211yesmaximal, characteristic
2#31826437C212yesmaximal, complemented
3#31826258C211yesmaximal, characteristic, complemented
4#31826257C212yesmaximal, complemented
5#353×C283C211yesmaximal, characteristic, complemented
6C2×#17985391C2211yescharacteristic
7C2×D4×D283C411yescharacteristic, complemented
8#22583606C2211yescharacteristic
9#22583598C411yescharacteristic, complemented
10#22583597C411yescharacteristic, complemented
11#22583582—22no—
12#22583578—22no—
13#22583567C411yescharacteristic, complemented
14#22583566—22no—
15#22583525C2212yescomplemented
16#22583524—22no—
17#127×C283C2211yescharacteristic
18#99×C283C2212yescomplemented
19C23×D283—21no—
20#17985391—42no—
21C2×Dic566C2×C411yescharacteristic
22C2×D1132C2×C411yescharacteristic
23C2×C22⋊D283—21no—
24C2×C22⋊D283—22no—
25C2×C22⋊D283D412yes—
26D4×D283—42no—
27C22×Dic283D412yes—
28C2×C4×D283C2×C411yescharacteristic
29Dic283⋊C4—21no—
30Dic283⋊C4—42no—
31C22⋊Dic283—22no—
32C22⋊Dic283—22no—
33(C2×D283)⋊C4—21no—
34(C2×D283)⋊C4—22no—
35C4×Dic283—42no—
36C4×Dic283C2×C411yescharacteristic
37C2×D4×C283—22no—
38C2×D4×C283C2×C411yescharacteristic
39C2×D4×C283C2311yescharacteristic
40C22⋊C4×C283—22no—
41C42×C283C2×C411yescharacteristic
42C22×D283—21no—
43C22×D283—42no—
44C22×D283—82no—
45C22×D283C22⋊C411yescharacteristic
46Dic566—41no—
47D1132—41no—
48C22⋊D283—42no—
49C22⋊D283—42no—
50C22⋊D283—82no—
51C2×Dic283—22no—
52C2×Dic283—22no—
53C2×Dic283—21no—
54C2×Dic283—42no—
55C2×Dic283C22⋊C412yes—
56C2×Dic283C22⋊C411yescharacteristic
57C4×D283—22no—
58C23×C283—21no—
59C23×C283C2×D412yes—
60D4×C283—41no—
61D4×C283—41no—
62D4×C283—82no—
63C2×C4×C283—21no—
64C2×C4×C283—42no—
65C2×C4×C283C22×C411yescharacteristic
66C22×C283—22no—
67C22×C283—42no—
68C22×C283—42no—
69C22×C283—41no—
70C22×C283C2×C22⋊C411yescharacteristic
71C2×D283—21no—
72C2×D283—41no—
73C2×D283—42no—
74C2×D283—41no—
75C2×D283—84no—
76C4×C283—21no—
77C4×C283—41no—
78C4×C283—82no—
79Dic283—22no—
80Dic283—41no—
81Dic283—82no—
82Dic283#9912yes—
83C2×C283—21no—
84C2×C283—42no—
85C2×C283—81no—
86C2×C283C2×#9911yescharacteristic
87D283—41no—
88D283—81no—
89C283#212811yescharacteristic, complemented, Sylow
90#2128—2831nomaximal, Sylow
91#535—2831no—
92#410—2832no—
93#353—2831no—
94#353—2832no—
95#353D28311yescharacteristic, complemented
96C2×#41—2831no—
97C22×D4—2831no—
98#127—2831no—
99#127C2×D28311yescharacteristic
100#124—2831no—
101#124—2831no—
102#121—5662no—
103#120—5662no—
104#117—2831no—
105#117—5662no—
106#99—2832no—
107#99—5662no—
108#99C2×D28312yescomplemented
109C24—5661no—
110#41—11322no—
111C2×Q8—2831no—
112C2×D4—22no—
113C2×D4—2832no—
114C2×D4—2831no—
115C2×D4—5661no—
116C2×D4—5662no—
117C2×D4—11322no—
118C2×D4C4×D28311yescharacteristic
119C2×D4C22×D28311yescharacteristic
120C22×C4—2832no—
121C22×C4—2831no—
122C4⋊C4—5661no—
123C4⋊C4—11322no—
124C22⋊C4—22no—
125C22⋊C4—5662no—
126C22⋊C4—5661no—
127C22⋊C4—5662no—
128C22⋊C4—5662no—
129C42—2831no—
130C42—11322no—
131C42C4×D28311yescharacteristic
132C23—21no—
133C23—2831no—
134C23—5661no—
135C23—11322no—
136C23—22642no—
137C23D4×D28312yes—
138Q8—11321no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—11321no—
143D4—11322no—
144D4—11322no—
145D4—22642no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2831no—
149C2×C4—2832no—
150C2×C4—5662no—
151C2×C4—5662no—
152C2×C4—5662no—
153C2×C4—5661no—
154C2×C4—11322no—
155C2×C4C2×C4×D28311yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—5661no—
161C22—11321no—
162C22—11322no—
163C22—11321no—
164C22—22644no—
165C22C22⋊C4×D28311yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—2832no—
170C4—5662no—
171C4—11321no—
172C4—22642no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—11321no—
177C2—22641no—
178C2#99×D28311yescharacteristic
subgroupG/H
centerC2#99×D283
commutatorC2×C4×C283C22×C4
FrattiniC2×D4C22×D283
Fitting#353×C283C2
socleC2×C283C2×#99
prime radical#31827028C2
cosocleC2×D4×C283C23
hypercenter#353D283
hypocenterC283#2128
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #31826437C2semidirect
3. #31826258C2semidirect
4. #31826257C2semidirect
5. #353×C283C2semidirect
7. C2×D4×D283C4semidirect
9. #22583598C4semidirect
10. #22583597C4semidirect
13. #22583567C4semidirect
15. #22583525C22semidirect
18. #99×C283C22semidirect
89. C283#2128semidirect
95. #353D283semidirect
108. #99C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270282
#318264372
#318262582
#318262572
#353×C2832
#2128283