Finite Group Databasebeta

← #49122927

Subgroups — #49122927

Order 36224.

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

normal subgroups only

This group has 286 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#99×D283C212yesmaximal, complemented
3#31826259C212yesmaximal, complemented
4#31826258C211yesmaximal, characteristic, complemented
5#353×C283C211yesmaximal, characteristic, complemented
6C2×#17985391C411yescharacteristic, complemented
7C2×D4×D283C2211yescharacteristic
8#22583606C411yescharacteristic, complemented
9#22583598C411yescharacteristic, complemented
10#22583597C2211yescharacteristic
11#22583582—22no—
12#22583578—22no—
13#22583567C411yescharacteristic, complemented
14C22⋊C4×D283—22no—
15#22583525C2212yes—
16#22583524—22no—
17#127×C283C2211yescharacteristic
18#99×C283C2212yes—
19C23×D283D412yes—
20#17985391—42no—
21C2×Dic566C2×C411yescharacteristic, complemented
22C2×D1132C2×C411yescharacteristic
23C2×C22⋊D283—21no—
24C2×C22⋊D283—22no—
25C2×C22⋊D283D412yes—
26D4×D283—42no—
27C22×Dic283—21no—
28C2×C4×D283—42no—
29C2×C4×D283C2×C411yescharacteristic
30Dic283⋊C4—21no—
31C22⋊Dic283—22no—
32C22⋊Dic283—22no—
33(C2×D283)⋊C4—21no—
34(C2×D283)⋊C4—22no—
35(C2×D283)⋊C4—42no—
36C4×Dic283C2×C411yescharacteristic, complemented
37C2×D4×C283—22no—
38C2×D4×C283C2×C411yescharacteristic, complemented
39C2×D4×C283C2311yescharacteristic
40C22⋊C4×C283—22no—
41C42×C283C2×C411yescharacteristic, complemented
42C22×D283—22no—
43C22×D283—22no—
44C22×D283—82no—
45C22×D283C22⋊C412yes—
46C22×D283C22⋊C411yescharacteristic
47Dic566—41no—
48D1132—41no—
49C22⋊D283—42no—
50C22⋊D283—42no—
51C22⋊D283—82no—
52C2×Dic283—21no—
53C2×Dic283—21no—
54C2×Dic283—42no—
55C2×Dic283—42no—
56C2×Dic283C22⋊C411yescharacteristic
57C4×D283—22no—
58C4×D283—84no—
59C23×C283—21no—
60C23×C283C2×D412yes—
61D4×C283—41no—
62D4×C283—41no—
63D4×C283—82no—
64C2×C4×C283—21no—
65C2×C4×C283—42no—
66C2×C4×C283C22×C411yescharacteristic
67C22×C283—22no—
68C22×C283—42no—
69C22×C283—42no—
70C22×C283—41no—
71C22×C283C2×C22⋊C411yescharacteristic
72C2×D283—22no—
73C2×D283—41no—
74C2×D283—44no—
75C2×D283—42no—
76C2×D283—82no—
77C2×D283#9912yes—
78C4×C283—21no—
79C4×C283—41no—
80C4×C283—82no—
81Dic283—21no—
82Dic283—41no—
83Dic283—41no—
84Dic283—82no—
85C2×C283—21no—
86C2×C283—42no—
87C2×C283—81no—
88C2×C283C2×#9911yescharacteristic
89D283—22no—
90D283—42no—
91C283#212711yescharacteristic, complemented, Sylow
92#2127—2831nomaximal, Sylow
93#535—2831no—
94C2×#99—2832no—
95#354—2832no—
96#353—2831no—
97#353D28311yescharacteristic, complemented
98C2×#41—2831no—
99C22×D4—2831no—
100#127—2831no—
101#127C2×D28311yescharacteristic
102#124—2831no—
103#124—2831no—
104#121—5662no—
105#120—5662no—
106#117—2831no—
107C2×C22⋊C4—5662no—
108#99—2832no—
109#99—5662no—
110#99C2×D28312yes—
111C24—2832no—
112#41—11322no—
113C2×Q8—2831no—
114C2×D4—22no—
115C2×D4—2832no—
116C2×D4—2831no—
117C2×D4—5661no—
118C2×D4—5662no—
119C2×D4—11322no—
120C2×D4C4×D28311yescharacteristic, complemented
121C2×D4C22×D28311yescharacteristic
122C22×C4—2831no—
123C22×C4—5661no—
124C22×C4—11322no—
125C4⋊C4—5661no—
126C22⋊C4—22no—
127C22⋊C4—5661no—
128C22⋊C4—5662no—
129C22⋊C4—5662no—
130C22⋊C4—5662no—
131C22⋊C4—11322no—
132C42—2831no—
133C42C4×D28311yescharacteristic, complemented
134C23—21no—
135C23—2831no—
136C23—2832no—
137C23—5662no—
138C23—5662no—
139C23—22642no—
140C23D4×D28312yes—
141Q8—11321no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—11321no—
146D4—11322no—
147D4—11322no—
148D4—22642no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—2831no—
152C2×C4—5662no—
153C2×C4—5661no—
154C2×C4—5661no—
155C2×C4—11322no—
156C2×C4—11322no—
157C2×C4—22644no—
158C2×C4C2×C4×D28311yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—2832no—
164C22—5662no—
165C22—11321no—
166C22—11322no—
167C22—11324no—
168C22—22642no—
169C22C22⋊C4×D28311yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—5661no—
174C4—11321no—
175C4—11321no—
176C4—22642no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—5662no—
181C2—11322no—
182C2#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#2127
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. #99×D283C2semidirect
3. #31826259C2semidirect
4. #31826258C2semidirect
5. #353×C283C2semidirect
6. C2×#17985391C4semidirect
8. #22583606C4semidirect
9. #22583598C4semidirect
13. #22583567C4semidirect
21. C2×Dic566C2×C4semidirect
36. C4×Dic283C2×C4semidirect
38. C2×D4×C283C2×C4semidirect
41. C42×C283C2×C4semidirect
91. C283#2127semidirect
97. #353D283semidirect
120. C2×D4C4×D283semidirect
133. C42C4×D283semidirect

Maximal subgroups

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

subgroupindex
#318270282
#99×D2832
#318262592
#318262582
#353×C2832
#2127283