Finite Group Databasebeta

← #44543716

Subgroups — #44543716

Order 31936.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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#30630350C211yesmaximal, characteristic, complemented
2#30630346C211yesmaximal, characteristic, complemented
3#30630344C211yesmaximal, characteristic, complemented
4#30630338C211yesmaximal, characteristic, complemented
5#30630337C211yesmaximal, characteristic, complemented
6#30630337C211yesmaximal, characteristic, complemented
7#30630333C211yesmaximal, characteristic, complemented
8#30630330C211yesmaximal, characteristic, complemented
9#30630329C211yesmaximal, characteristic, complemented
10#30630328C211yesmaximal, characteristic, complemented
11#30630323C211yesmaximal, characteristic
12#30630316C211yesmaximal, characteristic, complemented
13C4×C22⋊D499C211yesmaximal, characteristic, complemented
14#30630307C211yesmaximal, characteristic, complemented
15#123×C499C211yesmaximal, characteristic, complemented
16C2×Dic998C2211yescharacteristic
17C2×Dic998C2211yescharacteristic
18C2×Dic998C2211yescharacteristic
19C2×C22⋊D499C2211yescharacteristic
20C2×C22⋊D499C2211yescharacteristic
21C22×Dic499C2211yescharacteristic
22C2×C4×D499C2211yescharacteristic
23C4⋊Dic499C2211yescharacteristic
24C4⋊Dic499C2211yescharacteristic
25Dic499⋊C4C2211yescharacteristic
26Dic499⋊C4C2211yescharacteristic
27Dic499⋊C4C2211yescharacteristic
28Dic499⋊C4C2211yescharacteristic
29Dic499⋊C4C2211yescharacteristic
30Dic499⋊C4C2211yescharacteristic
31C22⋊Dic499C2211yescharacteristic
32C22⋊Dic499C2211yescharacteristic
33C22⋊Dic499C2211yescharacteristic
34C22⋊Dic499C2211yescharacteristic
35C22⋊Dic499C2211yescharacteristic
36(C2×D499)⋊C4C2211yescharacteristic
37(C2×D499)⋊C4C2211yescharacteristic
38(C2×D499)⋊C4C2211yescharacteristic
39(C2×D499)⋊C4C2211yescharacteristic
40C4×Dic499C2211yescharacteristic
41C4×Dic499C2211yescharacteristic
42C4×Dic499C2211yescharacteristic
43C4×Dic499C2211yescharacteristic
44C2×D4×C499C2211yescharacteristic
45C22×C4×C499C2211yescharacteristic
46C4⋊C4×C499C2211yescharacteristic
47C4⋊C4×C499C2211yescharacteristic
48C22⋊C4×C499C2211yescharacteristic
49C22⋊C4×C499C2211yescharacteristic
50C22⋊C4×C499C2211yescharacteristic
51C22×D499C2311yescharacteristic
52Dic998—22no—
53Dic998—41no—
54Dic998—41no—
55C22⋊D499—22no—
56C22⋊D499—41no—
57C2×Dic499—22no—
58C2×Dic499C2311yescharacteristic
59C2×Dic499C2311yescharacteristic
60C2×Dic499C2311yescharacteristic
61C2×Dic499C2311yescharacteristic
62C2×Dic499C2311yescharacteristic
63C2×Dic499C2311yescharacteristic
64C2×Dic499C2311yescharacteristic
65C4×D499—41no—
66C23×C499C2311yescharacteristic
67C23×C499C2311yescharacteristic
68D4×C499—41no—
69C2×C4×C499—41no—
70C2×C4×C499C2311yescharacteristic
71C2×C4×C499C2311yescharacteristic
72C2×C4×C499C2311yescharacteristic
73C2×C4×C499C2311yescharacteristic
74C2×C4×C499C2311yescharacteristic
75C22×C499—21no—
76C22×C499—21no—
77C22×C499—21no—
78C22×C499—21no—
79C22×C499—21no—
80C22×C499—21no—
81C22×C499C2411yescharacteristic
82C2×D499—21no—
83C2×D499—21no—
84C2×D499—21no—
85C4×C499—21no—
86C4×C499—21no—
87C4×C499—21no—
88C4×C499—21no—
89C4×C499—21no—
90Dic499—21no—
91Dic499—21no—
92Dic499—21no—
93Dic499—21no—
94Dic499—21no—
95Dic499—21no—
96Dic499#4112yes—
97C2×C499—41no—
98C2×C499—41no—
99C2×C499C2×#4111yescharacteristic
100C2×C499H(5,𝔽2)11yescharacteristic
101C2×C4992−1+411yescharacteristic
102D499—41no—
103C499#54211yescharacteristic, complemented, Sylow
104#542—4991nomaximal, Sylow
105C4⋊Q8—4991no—
106#126—4991no—
107#126—4991no—
108#124—4991no—
109#124—4991no—
110#124—4991no—
111#123—4991no—
112#123D49911yescharacteristic, complemented
113C22⋊Q8—4991no—
114C22⋊Q8—4991no—
115C22⋊Q8—4991no—
116#121—4991no—
117C4×Q8—4991no—
118C4×D4—4991no—
119#117—4991no—
120C2×Q8—4991no—
121C2×Q8—4991no—
122C2×Q8—4991no—
123C2×D4—4991no—
124C2×D4—4991no—
125C2×D4C2×D49911yescharacteristic
126C22×C4—4991no—
127C22×C4—4991no—
128C22×C4C2×D49911yescharacteristic
129C4⋊C4—4991no—
130C4⋊C4—4991no—
131C4⋊C4—4991no—
132C4⋊C4—4991no—
133C4⋊C4—4991no—
134C4⋊C4—4991no—
135C4⋊C4—4991no—
136C4⋊C4—4991no—
137C4⋊C4C2×D49911yescharacteristic
138C4⋊C4C2×D49911yescharacteristic
139C22⋊C4—4991no—
140C22⋊C4—4991no—
141C22⋊C4—4991no—
142C22⋊C4—4991no—
143C22⋊C4—4991no—
144C22⋊C4—4991no—
145C22⋊C4—4991no—
146C22⋊C4—4991no—
147C22⋊C4—4991no—
148C22⋊C4C2×D49911yescharacteristic
149C22⋊C4C2×D49911yescharacteristic
150C22⋊C4C2×D49911yescharacteristic
151C42—4991no—
152C42—4991no—
153C42—4991no—
154C42—4991no—
155C23—4991no—
156C23C22×D49911yescharacteristic
157C23C22×D49911yescharacteristic
158Q8—19961no—
159Q8—19961no—
160Q8—9982no—
161D4—41no—
162D4—19961no—
163D4—9982no—
164C2×C4—41no—
165C2×C4—19961no—
166C2×C4—9982no—
167C2×C4—4991no—
168C2×C4—4991no—
169C2×C4—4991no—
170C2×C4—4991no—
171C2×C4—4991no—
172C2×C4—4991no—
173C2×C4—4991no—
174C2×C4C22×D49911yescharacteristic
175C2×C4C22×D49911yescharacteristic
176C2×C4C22×D49911yescharacteristic
177C2×C4C22×D49911yescharacteristic
178C2×C4C22×D49911yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—9981no—
186C22—9981no—
187C22—9981no—
188C22C23×D49911yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—9981no—
195C4—9981no—
196C4—9981no—
197C4—9981no—
198C4—9981no—
199C4—9981no—
200C4—4992no—
201C2—41no—
202C2—41no—
203C2—19961no—
204C2#41×D49911yescharacteristic
205C2#3063039611yescharacteristic
206C2#3063039811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#123×C499C2
prime radical#30630323C2
hypercenter#123D499
hypocenterC499#542
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #30630350C2semidirect
2. #30630346C2semidirect
3. #30630344C2semidirect
4. #30630338C2semidirect
5. #30630337C2semidirect
6. #30630337C2semidirect
7. #30630333C2semidirect
8. #30630330C2semidirect
9. #30630329C2semidirect
10. #30630328C2semidirect
12. #30630316C2semidirect
13. C4×C22⋊D499C2semidirect
14. #30630307C2semidirect
15. #123×C499C2semidirect
103. C499#542semidirect
112. #123D499semidirect

Maximal subgroups

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

subgroupindex
#306303502
#306303462
#306303442
#306303382
#306303372
#306303332
#306303302
#306303292
#306303282
#306303232
#306303162
C4×C22⋊D4992
#306303072
#123×C4992
#542499