Finite Group Databasebeta

← #49120588

Subgroups — #49120588

Order 36224.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C283⋊#564C211yesmaximal, characteristic
2#31826871C211yesmaximal, characteristic
3#31826833C211yesmaximal, characteristic
4#31826207C211yesmaximal, characteristic
5#31826206C211yesmaximal, characteristic
6#31826206C211yesmaximal, characteristic
7#501×C283C211yesmaximal, characteristic
8#22583602C2211yescharacteristic
9#22583602C2211yescharacteristic
10#22583601—21no—
11#22583601—21no—
12#22583600—21no—
13#22583600—21no—
14#22583600—21no—
15#22583600—21no—
16#22583543—21no—
17#22583541—21no—
18#22583534—21no—
19#22583534—21no—
20#22583521C2211yescharacteristic
21#22583521C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23#125×C283C2211yescharacteristic
24#107×C283—21no—
25#106×C283—21no—
26#97×C283C2211yescharacteristic
27C2×C283⋊C8—21no—
28C2×C283⋊C8—21no—
29C4⋊Dic283—21no—
30C4⋊Dic283—21no—
31C4⋊Dic283D411yescharacteristic
32C4⋊Dic283D411yescharacteristic
33C4⋊Dic283D411yescharacteristic
34C4⋊Dic283D411yescharacteristic
35Dic283⋊C4—21no—
36Dic283⋊C4—21no—
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43C4×Dic283—21no—
44C4×Dic283—21no—
45C2×Q8×C283—21no—
46C2×C8×C283—21no—
47C4⋊C4×C283—21no—
48C4⋊C4×C283—21no—
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283D411yescharacteristic
52C4⋊C4×C283D411yescharacteristic
53C42×C283C2311yescharacteristic
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C283⋊C8—22no—
59C283⋊C8—41no—
60Q8×C283—42no—
61C2×C4×C283—21no—
62C2×C4×C283—21no—
63C2×C4×C283—41no—
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C2×C4×C283C2×D411yescharacteristic
67C8×C283—22no—
68C22×C283#12011yescharacteristic
69C4×C283—21no—
70C4×C283—21no—
71C4×C283—21no—
72C4×C283—41no—
73C4×C283—41no—
74C4×C283—81no—
75Dic283—41no—
76Dic283—41no—
77Dic283—41no—
78Dic283—41no—
79C2×C283#45411yescharacteristic
80C2×C283#45611yescharacteristic
81C2×C283#45611yescharacteristic
82C283#166311yescharacteristic, complemented, Sylow
83#1663—2831nomaximal, Sylow
84#564—2831no—
85#501—2831no—
86#501D28311yescharacteristic
87#491—2831no—
88#330—2831no—
89#330—2831no—
90#330—2831no—
91C4⋊Q8C2×D28311yescharacteristic
92#125—2831no—
93#125—2831no—
94#125—5661no—
95#125—5661no—
96#125—5661no—
97#125—5661no—
98#125—5661no—
99#125—5661no—
100#125C2×D28311yescharacteristic
101#107—21no—
102#107—5661no—
103#106—21no—
104#106—5661no—
105#103—5661no—
106#103—5661no—
107#97—2831no—
108#97—2831no—
109#97C2×D28311yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—5661no—
113C2×C8—5661no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—2831no—
119C4⋊C4—2831no—
120C4⋊C4—2831no—
121C4⋊C4—2831no—
122C4⋊C4—5661no—
123C4⋊C4—5661no—
124C4⋊C4—5661no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4—5661no—
128C4⋊C4—5661no—
129C4⋊C4—5661no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C4⋊C4C22⋊D28311yescharacteristic
133C4⋊C4C22⋊D28311yescharacteristic
134C42—5661no—
135C42—5661no—
136C42C22×D28311yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—5661no—
142C2×C4—5661no—
143C2×C4—5661no—
144C2×C4—5661no—
145C2×C4D4×D28311yescharacteristic
146C2×C4D4×D28311yescharacteristic
147C2×C4C2×C22⋊D28311yescharacteristic
148C8—22no—
149C8—5662no—
150C8—11321no—
151C22#2258357811yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—11321no—
159C4—11321no—
160C4—11321no—
161C4—11321no—
162C2#3182663611yescharacteristic
163C2#3182664611yescharacteristic
164C2#3182664711yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#501×C283C2
socle, prime radicalC22×C283#120
hypercenter#501D283
hypocenterC283#1663
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
82. C283#1663semidirect

Maximal subgroups

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

subgroupindex
C283⋊#5642
#318268712
#318268332
#318262072
#318262062
#501×C2832
#1663283