Finite Group Databasebeta

← #49120358

Subgroups — #49120358

Order 36224.

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

normal subgroups only

This group has 210 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#31827190C211yesmaximal, characteristic, complemented
2#31826813C211yesmaximal, characteristic
3#31826666C211yesmaximal, characteristic
4#31826666C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic, complemented
6#31826195C211yesmaximal, characteristic, complemented
7#332×C283C211yesmaximal, characteristic, complemented
8C2×#17985381—21no—
9C2×#17985381—21no—
10#22583608—21no—
11#22583607C2211yescharacteristic
12#22583601—21no—
13#22583600—22no—
14Q8×Dic283—21no—
15C4×Dic566C2211yescharacteristic
16C4×Dic566C2211yescharacteristic
17#22583575—21no—
18#22583532—21no—
19#22583532—21no—
20#22583530—22no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566D411yescharacteristic
26C2×Dic566D411yescharacteristic
27C2×D1132—21no—
28C2×D1132—21no—
29C2×D1132—21no—
30#17985381—42no—
31#17985381—42no—
32C2×C283⋊C8—21no—
33C4⋊Dic283—22no—
34C4⋊Dic283D411yescharacteristic
35C4⋊Dic283D411yescharacteristic
36Dic283⋊C4—22no—
37Dic283⋊C4—22no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40C4×Dic283—22no—
41C4×Dic283—21no—
42C4×Dic283—21no—
43C2×Q8×C283—21no—
44C2×C8×C283—21no—
45C2×C8×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D412yes—
48C42×C283C2311yescharacteristic
49C22×D283—41no—
50Dic566—21no—
51Dic566—21no—
52Dic566—21no—
53Dic566SD1612yescomplemented
54D1132—42no—
55D1132—41no—
56D1132—41no—
57D1132—41no—
58D1132—41no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C283⋊C8—41no—
64Q8×C283—41no—
65Q8×C283—41no—
66C2×C4×C283—22no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—41no—
71C8×C283—41no—
72C22×C283#12011yescharacteristic
73C2×D283—81no—
74C2×D283—81no—
75C2×D283—81no—
76C4×C283—21no—
77C4×C283—42no—
78C4×C283C2×SD1611yescharacteristic
79C4×C283#13511yescharacteristic
80C4×C283AGL(1,ℤ/8)11yescharacteristic
81C4×C283#13711yescharacteristic
82Dic283—22no—
83Dic283—41no—
84Dic283—41no—
85Dic283—41no—
86C2×C283#44811yescharacteristic
87C2×C283#44911yescharacteristic
88C2×C283#45411yescharacteristic
89D283—161no—
90C283#162611yescharacteristic, complemented, Sylow
91#1626—2831nomaximal, Sylow
92#557—2831no—
93#486—2831no—
94#460—2831no—
95#460—2831no—
96#332D28311yescharacteristic, complemented
97Q8⋊C8—2831no—
98Q8⋊C8—2831no—
99C2×SD16—5661no—
100C2×SD16—5661no—
101C4⋊Q8—5661no—
102C4⋊Q8C2×D28311yescharacteristic
103#127—2831no—
104#125—5661no—
105#125—5662no—
106C4×Q8—2831no—
107C4×Q8—2831no—
108C4×Q8—5661no—
109C4×Q8—5661no—
110C4⋊C8C2×D28311yescharacteristic
111C4⋊C8C2×D28311yescharacteristic
112#102—5661no—
113#102—5661no—
114#102—5662no—
115C4×C8—2831no—
116C2×Q8—21no—
117C2×Q8—2831no—
118C2×Q8—2831no—
119C2×D4—5661no—
120C2×D4—5661no—
121C2×D4—5661no—
122SD16—11322no—
123SD16—11322no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5661no—
127C4⋊C4—21no—
128C4⋊C4—2831no—
129C4⋊C4—2831no—
130C4⋊C4—5662no—
131C4⋊C4—5662no—
132C4⋊C4—5662no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4D113212yes—
136C42—5662no—
137C42—5661no—
138C42—5661no—
139C42C22×D28311yescharacteristic
140C23—11321no—
141Q8—41no—
142Q8—41no—
143Q8—2832no—
144Q8—5661no—
145Q8—5661no—
146Q8—5661no—
147D4—11322no—
148D4—11321no—
149D4—11321no—
150D4—11321no—
151D4—11321no—
152C2×C4—22no—
153C2×C4—5661no—
154C2×C4—5661no—
155C2×C4—5661no—
156C2×C4—5661no—
157C2×C4D4×D28311yescharacteristic
158C2×C4D4×D28311yescharacteristic
159C2×C4C2×D113211yescharacteristic
160C8—41no—
161C8—41no—
162C8—11321no—
163C22—22641no—
164C22—22641no—
165C22—22641no—
166C22#2258358011yescharacteristic
167C4—21no—
168C4—42no—
169C4—5662no—
170C4—11321no—
171C4—11321no—
172C4—11321no—
173C4SD16×D28311yescharacteristic
174C4#2258363111yescharacteristic
175C4#2258363411yescharacteristic
176C4#2258364211yescharacteristic
177C2—45281no—
178C2#3182660511yescharacteristic
179C2#3182661111yescharacteristic
180C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283#120
prime radical#22583607C22
hypercenter#332D283
hypocenterC283#1626
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #31827190C2semidirect
5. #31826195C2semidirect
6. #31826195C2semidirect
7. #332×C283C2semidirect
53. Dic566SD16semidirect
90. C283#1626semidirect
96. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318271902
#318268132
#318266662
#318261952
#332×C2832
#1626283