Finite Group Databasebeta

← #49122791

Subgroups — #49122791

Order 36224.

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

normal subgroups only

This group has 290 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, complemented
2C2×#22583532C211yesmaximal, characteristic
3C2×#22583530C211yesmaximal, characteristic
4#31826366C211yesmaximal, characteristic
5#31826334C211yesmaximal, characteristic, complemented
6#31826219C211yesmaximal, characteristic, complemented
7C2×#106×C283C211yesmaximal, characteristic, complemented
8C22×D1132C2211yescharacteristic
9C22×C283⋊C8C2211yescharacteristic
10C2×C4⋊Dic283C2211yescharacteristic
11C2×Dic283⋊C4—22no—
12C2×(C2×D283)⋊C4—22no—
13C2×C4×Dic283C2211yescharacteristic
14#22583541—22no—
15#22583532—22no—
16#22583530—22no—
17C22×C8×C283C2211yescharacteristic
18C2×C4⋊C4×C283C2211yescharacteristic
19C2×C4⋊C4×C283C2211yescharacteristic
20#106×C283—22no—
21C23×D283—21no—
22C2×D1132—21no—
23C2×D1132—21no—
24C2×D1132—21no—
25C2×D1132—21no—
26C2×D1132—21no—
27C2×D1132Q812yes—
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—
36(C2×D283)⋊C4—44no—
37C4×Dic283—21no—
38C4×Dic283—21no—
39C22×C4×C283—21no—
40C22×C4×C283—21no—
41C22×C4×C283C2311yescharacteristic
42C2×C8×C283—21no—
43C2×C8×C283—21no—
44C2×C8×C283D412yes—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283—21no—
48C4⋊C4×C283—21no—
49C22×D283—22no—
50C22×D283—41no—
51C22×D283—41no—
52C22×D283—42no—
53C22×D283—42no—
54D1132—22no—
55D1132—22no—
56D1132—41no—
57D1132—41no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283—41no—
61C2×Dic283—42no—
62C2×Dic283SD1614yes—
63C283⋊C8—22no—
64C23×C283C2×D411yescharacteristic
65C2×C4×C283—41no—
66C2×C4×C283—41no—
67C2×C4×C283—42no—
68C2×C4×C283—42no—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×Q811yescharacteristic
72C2×C4×C283#4111yescharacteristic
73C2×C4×C283#4111yescharacteristic
74C2×C4×C283#4111yescharacteristic
75C8×C283—22no—
76C22×C283C22⋊Q811yescharacteristic
77C22×C283#12311yescharacteristic
78C22×C283#12711yescharacteristic
79C22×C283C2×SD1612yes—
80C22×C283AGL(1,ℤ/8)12yes—
81C2×D283—42no—
82C2×D283—44no—
83C2×D283—82no—
84C2×D283—81no—
85C2×D283—81no—
86C4×C283—81no—
87C4×C283—81no—
88C4×C283C22⋊Q811yescharacteristic
89C4×C283C22⋊Q811yescharacteristic
90C4×C283#12311yescharacteristic
91C4×C283#12311yescharacteristic
92Dic283—24no—
93Dic283—81no—
94C2×C283#39911yescharacteristic
95C2×C283#47612yes—
96C2×C283#48112yes—
97C2×C283#49211yescharacteristic
98C2×C283#49611yescharacteristic
99D283—82no—
100C283#209411yescharacteristic, complemented, Sylow
101#2094—2831nomaximal, Sylow
102C2×#106—2831no—
103C2×#106D28311yescharacteristic, complemented
104C2×#102—2831no—
105C2×#102—2831no—
106#390—2831no—
107#384—2831no—
108#336—2831no—
109C22×D4—2831no—
110C22×C8—2831no—
111C22×C8C2×D28311yescharacteristic
112C2×C4⋊C4—2831no—
113C2×C4⋊C4—5662no—
114C2×C4⋊C4C2×D28311yescharacteristic
115C2×C4⋊C4C2×D28311yescharacteristic
116C2×C22⋊C4—5662no—
117C2×C42—2831no—
118#106—22no—
119#106—5662no—
120#102—5662no—
121#102—5662no—
122C24—5661no—
123C2×D4—2832no—
124C2×D4—5661no—
125C2×D4—5661no—
126C2×D4—5661no—
127C2×D4—5661no—
128C2×D4—5661no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—2832no—
132C22×C4—5661no—
133C22×C4C22×D28311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—2832no—
137C2×C8—5661no—
138C2×C8—5661no—
139C2×C8C22⋊D28312yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—5661no—
145C4⋊C4—5661no—
146C4⋊C4—11324no—
147C22⋊C4—11324no—
148C42—5661no—
149C42—5661no—
150C23—5662no—
151C23—11321no—
152C23—11321no—
153C23—11322no—
154C23—11322no—
155C23D4×D28311yescharacteristic
156D4—5662no—
157D4—5662no—
158D4—11321no—
159D4—11321no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2834no—
165C2×C4—5662no—
166C2×C4—5662no—
167C2×C4—11321no—
168C2×C4—11322no—
169C2×C4D4×D28311yescharacteristic
170C2×C4C2×C22⋊D28311yescharacteristic
171C2×C4Q8×D28311yescharacteristic
172C2×C4#1798539211yescharacteristic
173C2×C4#1798539211yescharacteristic
174C2×C4#1798539311yescharacteristic
175C8—22no—
176C8—5662no—
177C22—11324no—
178C22—11322no—
179C22—22642no—
180C22—22641no—
181C22—22641no—
182C22#2258358811yescharacteristic
183C22#2258359511yescharacteristic
184C22#2258360611yescharacteristic
185C22SD16×D28312yes—
186C22#2258363712yes—
187C4—81no—
188C4—81no—
189C4—5664no—
190C4—22641no—
191C4#2258358611yescharacteristic
192C4#2258358811yescharacteristic
193C4#2258359311yescharacteristic
194C4#2258359511yescharacteristic
195C2—22642no—
196C2#3182640011yescharacteristic
197C2#3182675412yes—
198C2#3182678512yes—
199C2#3182683611yescharacteristic
200C2#3182685111yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#106×C283C2
socleC23×C283C2×D4
prime radicalC22×D1132C22
hypercenterC2×#106D283
hypocenterC283#2094
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
1. C2×#22583541C2semidirect
5. #31826334C2semidirect
6. #31826219C2semidirect
7. C2×#106×C283C2semidirect
100. C283#2094semidirect
103. C2×#106D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835412
C2×#225835322
C2×#225835302
#318263662
#318263342
#318262192
C2×#106×C2832
#2094283