Finite Group Databasebeta

← #49122801

Subgroups — #49122801

Order 36224.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#22583541C211yesmaximal, characteristic
2C2×#22583535C211yesmaximal, characteristic
3C2×#22583533C211yesmaximal, characteristic
4#31826370C211yesmaximal, characteristic
5#31826334C211yesmaximal, characteristic
6#31826219C211yesmaximal, characteristic
7C2×#106×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C22×C283⋊C8C2211yescharacteristic
10C2×C4⋊Dic283C2211yescharacteristic
11C2×Dic283⋊C4—22no—
12C2×C4×Dic283C2211yescharacteristic
13#22583541—22no—
14#22583535—22no—
15#22583533—22no—
16C283⋊#95—22no—
17C22×C8×C283C2211yescharacteristic
18C2×C4⋊C4×C283C2211yescharacteristic
19C2×C4⋊C4×C283C2211yescharacteristic
20#106×C283—22no—
21C2×Dic566—21no—
22C2×Dic566—21no—
23C2×Dic566—21no—
24C2×Dic566—21no—
25C2×Dic566—21no—
26C2×Dic566Q812yes—
27C22×Dic283—21no—
28C22×Dic283—21no—
29C22×Dic283D412yes—
30C2×C283⋊C8—21no—
31C2×C283⋊C8—21no—
32C2×C283⋊C8D412yes—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35Dic283⋊C4—44no—
36C4×Dic283—21no—
37C4×Dic283—21no—
38C22×C4×C283—21no—
39C22×C4×C283—21no—
40C22×C4×C283C2311yescharacteristic
41C2×C8×C283—21no—
42C2×C8×C283—21no—
43C2×C8×C283D412yes—
44C4⋊C4×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283—21no—
48Dic566—22no—
49Dic566—22no—
50Dic566—41no—
51Dic566—41no—
52C2×Dic283—22no—
53C2×Dic283—22no—
54C2×Dic283—22no—
55C2×Dic283—41no—
56C2×Dic283—41no—
57C2×Dic283—41no—
58C2×Dic283—42no—
59C2×Dic283SD1614yes—
60C283⋊C8—22no—
61C23×C283C2×D411yescharacteristic
62C2×C4×C283—41no—
63C2×C4×C283—41no—
64C2×C4×C283—42no—
65C2×C4×C283—42no—
66C2×C4×C283C2×D411yescharacteristic
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×Q811yescharacteristic
69C2×C4×C283#4111yescharacteristic
70C2×C4×C283#4111yescharacteristic
71C2×C4×C283#4111yescharacteristic
72C8×C283—22no—
73C22×C283C22⋊Q811yescharacteristic
74C22×C283#12311yescharacteristic
75C22×C283#12711yescharacteristic
76C22×C283C2×SD1612yes—
77C22×C283#13712yes—
78C4×C283—81no—
79C4×C283—81no—
80C4×C283C22⋊Q811yescharacteristic
81C4×C283C22⋊Q811yescharacteristic
82C4×C283#12311yescharacteristic
83C4×C283#12311yescharacteristic
84Dic283—24no—
85Dic283—42no—
86Dic283—81no—
87C2×C283#39911yescharacteristic
88C2×C283#47512yes—
89C2×C283#48312yes—
90C2×C283#49211yescharacteristic
91C2×C283#49711yescharacteristic
92C283#209611yescharacteristic, complemented, Sylow
93#2096—2831nomaximal, Sylow
94C2×#106—2831no—
95C2×#106D28311yescharacteristic
96C2×#103—2831no—
97C2×#103—2831no—
98#391—2831no—
99#384—2831no—
100#336—2831no—
101C22×Q8—2831no—
102C22×C8—2831no—
103C22×C8C2×D28311yescharacteristic
104C2×C4⋊C4—2831no—
105C2×C4⋊C4—5662no—
106C2×C4⋊C4C2×D28311yescharacteristic
107C2×C4⋊C4C2×D28311yescharacteristic
108C2×C42—2831no—
109#106—22no—
110#106—5662no—
111#103—5662no—
112#103—5662no—
113#95—5662no—
114C2×Q8—2832no—
115C2×Q8—5661no—
116C2×Q8—5661no—
117C2×Q8—5661no—
118C2×Q8—5661no—
119C2×Q8—5661no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—2832no—
123C22×C4—5661no—
124C22×C4—5661no—
125C22×C4C22×D28311yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—2832no—
129C2×C8—5661no—
130C2×C8—5661no—
131C2×C8C22⋊D28312yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4—11324no—
139C42—5661no—
140C42—5661no—
141C23D4×D28311yescharacteristic
142Q8—5662no—
143Q8—5662no—
144Q8—11321no—
145Q8—11321no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—2834no—
151C2×C4—5662no—
152C2×C4—5662no—
153C2×C4—5662no—
154C2×C4—11321no—
155C2×C4—11321no—
156C2×C4—11321no—
157C2×C4—11322no—
158C2×C4D4×D28311yescharacteristic
159C2×C4C2×C22⋊D28311yescharacteristic
160C2×C4Q8×D28311yescharacteristic
161C2×C4#1798539211yescharacteristic
162C2×C4#1798539211yescharacteristic
163C2×C4#1798539311yescharacteristic
164C8—22no—
165C8—5662no—
166C22#2258358811yescharacteristic
167C22#2258359511yescharacteristic
168C22#2258360611yescharacteristic
169C22SD16×D28312yes—
170C22#2258363912yes—
171C4—81no—
172C4—81no—
173C4—5664no—
174C4—11322no—
175C4—22641no—
176C4#2258358611yescharacteristic
177C4#2258358811yescharacteristic
178C4#2258359311yescharacteristic
179C4#2258359511yescharacteristic
180C2#3182640011yescharacteristic
181C2#3182674912yes—
182C2#3182679712yes—
183C2#3182683611yescharacteristic
184C2#3182685611yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#106×C283C2
socle, prime radicalC23×C283C2×D4
hypercenterC2×#106D283
hypocenterC283#2096
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
92. C283#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#225835412
C2×#225835352
C2×#225835332
#318263702
#318263342
#318262192
C2×#106×C2832
#2096283