Finite Group Databasebeta

← #49120446

Subgroups — #49120446

Order 36224.

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

normal subgroups only

This group has 212 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#31827200C211yesmaximal, characteristic
2#31826813C211yesmaximal, characteristic
3#31826672C211yesmaximal, characteristic, complemented
4#31826208C211yesmaximal, characteristic
5Q8⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826195C211yesmaximal, characteristic, complemented
7#475×C283C211yesmaximal, characteristic, complemented
8C2×#17985382—21no—
9#22583607C2211yescharacteristic
10#22583599—21no—
11#22583598—21no—
12#22583595—22no—
13C4×Dic566C2211yescharacteristic
14C4×D1132—21no—
15#22583572—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583534—21no—
18#22583530—22no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×Q8×C283C2211yescharacteristic
22#106×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#103×C283—21no—
25C2×Dic566D411yescharacteristic
26C2×D1132—21no—
27C2×D1132—21no—
28C2×D1132D412yes—
29C2×C4×D283—22no—
30#17985382—42no—
31C2×C283⋊C8—21no—
32C2×C283⋊C8—21no—
33C4⋊Dic283D411yescharacteristic
34Dic283⋊C4—21no—
35(C2×D283)⋊C4—22no—
36(C2×D283)⋊C4—22no—
37(C2×D283)⋊C4—22no—
38C4×Dic283—21no—
39C2×Q8×C283—21no—
40C2×Q8×C283D411yescharacteristic
41C2×C8×C283—21no—
42C4⋊C4×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C42×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—22no—
49Dic566—21no—
50Dic566—21no—
51D1132—42no—
52D1132—41no—
53D1132—41no—
54D1132—41no—
55D1132—41no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C4×D283—82no—
59C283⋊C8—41no—
60C283⋊C8—41no—
61Q8×C283—21no—
62Q8×C283—21no—
63Q8×C283—41no—
64Q8×C283—41no—
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—42no—
74C2×D283—42no—
75C2×D283—42no—
76C4×C283—21no—
77C4×C283—41no—
78C4×C283—41no—
79C4×C283—81no—
80C4×C283#13511yescharacteristic
81C4×C283#13511yescharacteristic
82C4×C283AGL(1,ℤ/8)11yescharacteristic
83C4×C283#13711yescharacteristic
84Dic283—41no—
85Dic283—41no—
86C2×C283#44911yescharacteristic
87C2×C283#45211yescharacteristic
88C2×C283#45511yescharacteristic
89D283—82no—
90C283#164011yescharacteristic, complemented, Sylow
91#1640—2831nomaximal, Sylow
92#559—2831no—
93#486—2831no—
94#475D28311yescharacteristic, complemented
95#462—2831no—
96#331—2831no—
97Q8⋊C8—2831no—
98Q8⋊C8—2831no—
99C2×Q16—5661no—
100C4⋊Q8C2×D28311yescharacteristic
101#127—2831no—
102#124—5661no—
103#124—5661no—
104#123—5662no—
105C4×Q8—2831no—
106C4×Q8C2×D28311yescharacteristic
107C4×D4—5661no—
108C4×D4—5661no—
109#106—21no—
110C4⋊C8—2831no—
111C4⋊C8C2×D28311yescharacteristic
112#103—21no—
113#103—5661no—
114#102—5662no—
115C4×C8—2831no—
116C2×Q8—21no—
117C2×Q8—2831no—
118C2×Q8C22⋊D28311yescharacteristic
119C2×D4—2832no—
120C2×D4—5661no—
121C2×D4—5661no—
122C22×C4—5662no—
123Q16—11322no—
124C2×C8—21no—
125C2×C8—5661no—
126C2×C8—5661no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2831no—
131C4⋊C4—5661no—
132C4⋊C4C22⋊D28311yescharacteristic
133C22⋊C4—5662no—
134C22⋊C4—5662no—
135C22⋊C4—5662no—
136C42—21no—
137C42—5661no—
138C42C22×D28311yescharacteristic
139C23—5662no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—5661no—
145Q8—5661no—
146D4—11322no—
147D4—11321no—
148D4—11321no—
149D4—11321no—
150D4—11321no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—5661no—
155C2×C4—5661no—
156C2×C4—22642no—
157C2×C4D4×D28311yescharacteristic
158C2×C4D4×D28311yescharacteristic
159C2×C4C2×C22⋊D28311yescharacteristic
160C8—41no—
161C8—11321no—
162C8—11321no—
163C22—11322no—
164C22—11322no—
165C22—11322no—
166C22#2258357811yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—11321no—
172C4—11321no—
173C4#2258363011yescharacteristic
174C4#2258363111yescharacteristic
175C4#2258363711yescharacteristic
176C4#2258364111yescharacteristic
177C2—22642no—
178C2#3182660911yescharacteristic
179C2#3182662511yescharacteristic
180C2#3182664111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#475×C283C2
socleC22×C283#120
prime radical#22583607C22
hypercenter#475D283
hypocenterC283#1640
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #31826672C2semidirect
5. Q8⋊(C283⋊C8)C2semidirect
6. #31826195C2semidirect
7. #475×C283C2semidirect
90. C283#1640semidirect
94. #475D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318268132
#318266722
#318262082
Q8⋊(C283⋊C8)2
#318261952
#475×C2832
#1640283