Finite Group Databasebeta

← #49120592

Subgroups — #49120592

Order 36224.

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

normal subgroups only

This group has 184 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
1#31827219C211yesmaximal, characteristic
2#31826871C211yesmaximal, characteristic, complemented
3#31826827C211yesmaximal, characteristic
4#31826207C211yesmaximal, characteristic, complemented
5#31826206C211yesmaximal, characteristic, complemented
6#31826204C211yesmaximal, characteristic
7#491×C283C211yesmaximal, characteristic, complemented
8#22583609—21no—
9#22583605—21no—
10#22583605—21no—
11#22583602C2211yescharacteristic
12#22583598C2211yescharacteristic
13#22583595—21no—
14#22583590—21no—
15#22583588—21no—
16#22583543—21no—
17#22583541—21no—
18#22583533—21no—
19#22583530—21no—
20#22583521C2211yescharacteristic
21#22583521C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23#125×C283C2211yescharacteristic
24#103×C283—21no—
25#103×C283—21no—
26#97×C283C2211yescharacteristic
27C2×Dic566—21no—
28C2×Dic566D411yescharacteristic
29C2×D1132D411yescharacteristic
30C2×C4×D283—21no—
31C2×C283⋊C8—21no—
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283D411yescharacteristic
35C4⋊Dic283D411yescharacteristic
36Dic283⋊C4—21no—
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—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
54C22×D283—21no—
55Dic566—41no—
56Dic566—81no—
57D1132—41no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C4×D283—81no—
62C283⋊C8—22no—
63C283⋊C8—41no—
64Q8×C283—42no—
65C2×C4×C283—21no—
66C2×C4×C283—21no—
67C2×C4×C283—41no—
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C8×C283—41no—
72C22×C283#12011yescharacteristic
73C2×D283—41no—
74C2×D283—41no—
75C2×D283—41no—
76C4×C283—21no—
77C4×C283—21no—
78C4×C283—21no—
79C4×C283—41no—
80C4×C283—41no—
81C4×C283—81no—
82Dic283—41no—
83Dic283—41no—
84Dic283—41no—
85C2×C283#45411yescharacteristic
86C2×C283#45511yescharacteristic
87C2×C283#45611yescharacteristic
88D283—81no—
89C283#166411yescharacteristic, complemented, Sylow
90#1664—2831nomaximal, Sylow
91#563—2831no—
92#501—2831no—
93#491D28311yescharacteristic, complemented
94#489—2831no—
95#330—2831no—
96#330—2831no—
97#329—2831no—
98C4⋊Q8—5661no—
99C4⋊Q8C2×D28311yescharacteristic
100#126—5661no—
101#126—5661no—
102#125—2831no—
103#125C2×D28311yescharacteristic
104#124—2831no—
105#123—5661no—
106C22⋊Q8—5661no—
107C22⋊Q8—5661no—
108#107—5661no—
109#106—5661no—
110#103—21no—
111#103—21no—
112#103—5661no—
113#102—5661no—
114#97—2831no—
115#97—2831no—
116#97C2×D28311yescharacteristic
117C2×Q8—21no—
118C2×Q8—2831no—
119C2×Q8—5661no—
120C2×D4—2831no—
121C22×C4—5661no—
122C2×C8—21no—
123C2×C8—5661no—
124C2×C8—5661no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2831no—
130C4⋊C4—2831no—
131C4⋊C4—5661no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4C22⋊D28311yescharacteristic
136C4⋊C4C22⋊D28311yescharacteristic
137C22⋊C4—5661no—
138C22⋊C4—5661no—
139C22⋊C4—5661no—
140C22⋊C4—5661no—
141C22⋊C4—5661no—
142C42—5661no—
143C42C22×D28311yescharacteristic
144C23—5661no—
145Q8—42no—
146Q8—11321no—
147Q8—22641no—
148D4—11321no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5661no—
153C2×C4—5661no—
154C2×C4—5661no—
155C2×C4—22641no—
156C2×C4D4×D28311yescharacteristic
157C2×C4D4×D28311yescharacteristic
158C2×C4C2×C22⋊D28311yescharacteristic
159C8—41no—
160C8—5662no—
161C8—11321no—
162C22—11321no—
163C22—11321no—
164C22—11321no—
165C22#2258357811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—11321no—
173C4—11321no—
174C4—11321no—
175C2—22641no—
176C2#3182663711yescharacteristic
177C2#3182664111yescharacteristic
178C2#3182664611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#491×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#491D283
hypocenterC283#1664
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #31826871C2semidirect
4. #31826207C2semidirect
5. #31826206C2semidirect
7. #491×C283C2semidirect
89. C283#1664semidirect
93. #491D283semidirect

Maximal subgroups

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

subgroupindex
#318272192
#318268712
#318268272
#318262072
#318262062
#318262042
#491×C2832
#1664283