Finite Group Databasebeta

← #49120392

Subgroups — #49120392

Order 36224.

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

normal subgroups only

This group has 214 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#31827176C211yesmaximal, characteristic
2#31826757C211yesmaximal, characteristic, complemented
3#31826752C211yesmaximal, characteristic
4#31826214C211yesmaximal, characteristic, complemented
5#31826197C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic
7#494×C283C211yesmaximal, characteristic, complemented
8#22583601—21no—
9#22583590—21no—
10#22583586—22no—
11C4×Dic566C2211yescharacteristic
12C4×D1132C2211yescharacteristic
13#22583572—21no—
14C4⋊C4×D283—21no—
15#22583543—21no—
16#22583541—21no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583533—21no—
20#22583530—21no—
21C2×Q16×C283—22no—
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊Q8×C283C2211yescharacteristic
24C4×C8×C283C2211yescharacteristic
25C2×Dic566D411yescharacteristic
26C2×D1132D411yescharacteristic
27C2×C4×D283—22no—
28C2×C4×D283—21no—
29C2×C283⋊C8—21no—
30C2×C283⋊C8—21no—
31C4⋊Dic283—22no—
32C4⋊Dic283D411yescharacteristic
33C4⋊Dic283D411yescharacteristic
34Dic283⋊C4—22no—
35Dic283⋊C4—21no—
36(C2×D283)⋊C4—22no—
37(C2×D283)⋊C4—21no—
38C4×Dic283—21no—
39C2×Q8×C283—21no—
40C2×Q8×C283D412yes—
41Q16×C283—44no—
42C2×C8×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—21no—
50Dic566—21no—
51D1132—21no—
52D1132Q1612yescomplemented
53C2×Dic283—21no—
54C2×Dic283—21no—
55C2×Dic283—21no—
56C4×D283—41no—
57C4×D283—41no—
58C4×D283—82no—
59C283⋊C8—41no—
60C283⋊C8—41no—
61Q8×C283—42no—
62Q8×C283—42no—
63C2×C4×C283—22no—
64C2×C4×C283—41no—
65C2×C4×C283C2×D411yescharacteristic
66C2×C4×C283C2×D411yescharacteristic
67C2×C4×C283C2×D411yescharacteristic
68C8×C283—22no—
69C22×C283#12011yescharacteristic
70C2×D283—22no—
71C2×D283—41no—
72C2×D283—41no—
73C4×C283—21no—
74C4×C283—42no—
75C4×C283—81no—
76C4×C283C2×Q1611yescharacteristic
77C4×C283#13511yescharacteristic
78C4×C283#13711yescharacteristic
79C4×C283#13711yescharacteristic
80Dic283—41no—
81Dic283—41no—
82Dic283—41no—
83C2×C283#45111yescharacteristic
84C2×C283#45211yescharacteristic
85C2×C283#45311yescharacteristic
86D283—42no—
87C283#163211yescharacteristic, complemented, Sylow
88#1632—2831nomaximal, Sylow
89#554—2831no—
90#494D28311yescharacteristic, complemented
91#477—2831no—
92#476—2831no—
93#333—2831no—
94Q8⋊C8—2831no—
95D4⋊C8—2831no—
96C2×Q16—22no—
97C4⋊Q8C2×D28311yescharacteristic
98C4⋊Q8C2×D28311yescharacteristic
99#125—5661no—
100C22⋊Q8—5661no—
101C22⋊Q8—5662no—
102C4×Q8—2831no—
103C4×D4—2831no—
104C4×D4—5661no—
105C2×C4⋊C4—5661no—
106#107—5661no—
107#106—5661no—
108C4⋊C8—2831no—
109C4⋊C8—2831no—
110#103—5661no—
111#102—5661no—
112C4×C8C2×D28311yescharacteristic
113C2×Q8—21no—
114C2×Q8—2831no—
115C2×Q8C22⋊D28312yes—
116C2×D4—2831no—
117C22×C4—5662no—
118C22×C4—5661no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—5661no—
122C2×C8—5661no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2831no—
128C4⋊C4—2831no—
129C4⋊C4—5662no—
130C4⋊C4—5662no—
131C4⋊C4—5661no—
132C22⋊C4—5662no—
133C22⋊C4—5661no—
134C42—5661no—
135C42C22×D28311yescharacteristic
136C23—5661no—
137Q8—42no—
138Q8—42no—
139Q8—5661no—
140Q8—5661no—
141D4—2832no—
142D4—5661no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—5661no—
146C2×C4—5661no—
147C2×C4—5661no—
148C2×C4—11321no—
149C2×C4—11321no—
150C2×C4—22642no—
151C2×C4D4×D28311yescharacteristic
152C2×C4D4×D28311yescharacteristic
153C2×C4C2×C22⋊D28311yescharacteristic
154C8—22no—
155C8—11321no—
156C8—11321no—
157C22—5662no—
158C22—11321no—
159C22—11321no—
160C22#2258357811yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—11321no—
165C4—11321no—
166C4—11321no—
167C4Q16×D28311yescharacteristic
168C4#2258363311yescharacteristic
169C4#2258364211yescharacteristic
170C4#2258364211yescharacteristic
171C2—11322no—
172C2#3182661911yescharacteristic
173C2#3182662611yescharacteristic
174C2#3182663211yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#494×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#494D283
hypocenterC283#1632
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #31826757C2semidirect
4. #31826214C2semidirect
5. #31826197C2semidirect
7. #494×C283C2semidirect
52. D1132Q16semidirect
87. C283#1632semidirect
90. #494D283semidirect

Maximal subgroups

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

subgroupindex
#318271762
#318267572
#318267522
#318262142
#318261972
#318261942
#494×C2832
#1632283