Finite Group Databasebeta

← #49120430

Subgroups — #49120430

Order 36224.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827189C211yesmaximal, characteristic
2#31826757C211yesmaximal, characteristic, complemented
3#31826752C211yesmaximal, characteristic
4#31826211C211yesmaximal, characteristic, complemented
5#31826197C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic
7#487×C283C211yesmaximal, characteristic, complemented
8#22583605—22no—
9#22583599—21no—
10#22583590—21no—
11Q8×Dic283—21no—
12C4×Dic566C2211yescharacteristic
13C4×D1132C2211yescharacteristic
14#22583568—21no—
15#22583543—21no—
16#22583541—21no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583533—21no—
20#22583530—21no—
21C4⋊Q8×C283C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23#103×C283—22no—
24C4×C8×C283C2211yescharacteristic
25C2×Dic566D411yescharacteristic
26C2×D1132D411yescharacteristic
27C2×C4×D283—21no—
28C2×C283⋊C8—21no—
29C2×C283⋊C8—21no—
30C4⋊Dic283—22no—
31C4⋊Dic283D411yescharacteristic
32C4⋊Dic283D411yescharacteristic
33Dic283⋊C4—21no—
34(C2×D283)⋊C4—22no—
35(C2×D283)⋊C4—22no—
36(C2×D283)⋊C4—21no—
37C4×Dic283—22no—
38C4×Dic283—21no—
39C2×Q8×C283—21no—
40C2×Q8×C283—21no—
41C2×C8×C283—21no—
42C4⋊C4×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D412yes—
46C42×C283C2311yescharacteristic
47C22×D283—21no—
48Dic566—21no—
49Dic566—21no—
50D1132—21no—
51D1132—21no—
52C2×Dic283—21no—
53C2×Dic283—21no—
54C2×Dic283—21no—
55C4×D283—41no—
56C4×D283—41no—
57C283⋊C8—41no—
58C283⋊C8—41no—
59Q8×C283—42no—
60Q8×C283—41no—
61Q8×C283—41no—
62C2×C4×C283—22no—
63C2×C4×C283—41no—
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C2×C4×C283C2×D411yescharacteristic
67C8×C283—41no—
68C22×C283#12011yescharacteristic
69C2×D283—41no—
70C2×D283—41no—
71C2×D283—41no—
72C4×C283—21no—
73C4×C283—42no—
74C4×C283—81no—
75C4×C283#13511yescharacteristic
76C4×C283#13511yescharacteristic
77C4×C283#13711yescharacteristic
78C4×C283#13711yescharacteristic
79Dic283—41no—
80Dic283—41no—
81Dic283—41no—
82C2×C283#45211yescharacteristic
83C2×C283#45211yescharacteristic
84C2×C283#45411yescharacteristic
85D283—81no—
86C283#163811yescharacteristic, complemented, Sylow
87#1638—2831nomaximal, Sylow
88#556—2831no—
89#487D28311yescharacteristic, complemented
90#477—2831no—
91#476—2831no—
92#332—2831no—
93Q8⋊C8—2831no—
94D4⋊C8—2831no—
95C4⋊Q8C2×D28311yescharacteristic
96C4⋊Q8C2×D28311yescharacteristic
97#126—5662no—
98#124—5661no—
99C22⋊Q8—5661no—
100C4×Q8—2831no—
101C4×Q8—5661no—
102C4×D4—2831no—
103#117—5661no—
104#107—5661no—
105#106—5661no—
106C4⋊C8—2831no—
107C4⋊C8—2831no—
108#103—22no—
109#103—5661no—
110#102—5661no—
111C4×C8C2×D28311yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—2831no—
115C2×D4—2831no—
116C22×C4—5661no—
117C2×C8—21no—
118C2×C8—5661no—
119C2×C8—5661no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—2831no—
124C4⋊C4—2831no—
125C4⋊C4—5662no—
126C4⋊C4—5661no—
127C4⋊C4C22⋊D28312yes—
128C22⋊C4—5662no—
129C22⋊C4—5662no—
130C22⋊C4—5661no—
131C42—5662no—
132C42—5661no—
133C42C22×D28311yescharacteristic
134C23—5661no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—5661no—
139Q8—5661no—
140D4—5661no—
141D4—5661no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—5661no—
145C2×C4—5661no—
146C2×C4—5661no—
147C2×C4—11321no—
148C2×C4—11321no—
149C2×C4D4×D28311yescharacteristic
150C2×C4D4×D28311yescharacteristic
151C2×C4C2×C22⋊D28311yescharacteristic
152C8—41no—
153C8—11321no—
154C8—11321no—
155C22—11321no—
156C22—11321no—
157C22—11321no—
158C22#2258357811yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—11321no—
163C4—11321no—
164C4—11321no—
165C4#2258363111yescharacteristic
166C4#2258363311yescharacteristic
167C4#2258363911yescharacteristic
168C4#2258364211yescharacteristic
169C2—22641no—
170C2#3182662411yescharacteristic
171C2#3182662611yescharacteristic
172C2#3182663711yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#487×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#487D283
hypocenterC283#1638
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31826757C2semidirect
4. #31826211C2semidirect
5. #31826197C2semidirect
7. #487×C283C2semidirect
86. C283#1638semidirect
89. #487D283semidirect

Maximal subgroups

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

subgroupindex
#318271892
#318267572
#318267522
#318262112
#318261972
#318261942
#487×C2832
#1638283