Finite Group Databasebeta

← #49120203

Subgroups — #49120203

Order 36224.

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

normal subgroups only

This group has 266 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#31827096C211yesmaximal, characteristic, complemented
2#31826618C212yesmaximal
3#31826382C211yesmaximal, characteristic
4#31826203C212yesmaximal, complemented
5#324×C283C211yesmaximal, characteristic, complemented
6C22×D1132C2211yescharacteristic
7C2×#17985381—22no—
8#22583609—22no—
9#22583601—22no—
10#22583589—21no—
11#22583589C2212yes—
12#22583569—21no—
13C2×(C2×D283)⋊C4—21no—
14C2×(C2×D283)⋊C4—21no—
15#22583532—22no—
16C283⋊#95C2211yescharacteristic
17C2×C4⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19C23×D283—21no—
20C2×Dic566—21no—
21C2×Dic566D412yes—
22C2×D1132—22no—
23C2×D1132—42no—
24C22×Dic283—21no—
25#17985381—44no—
26C4⋊Dic283—21no—
27C4⋊Dic283—21no—
28C4⋊Dic283—21no—
29C4⋊Dic283D412yes—
30Dic283⋊C4—22no—
31Dic283⋊C4—22no—
32C22⋊Dic283—22no—
33(C2×D283)⋊C4—42no—
34(C2×D283)⋊C4—42no—
35C4×Dic283—22no—
36C22×C4×C283D411yescharacteristic
37C22×C4×C283D411yescharacteristic
38C22×C4×C283C2311yescharacteristic
39C2×C8×C283—22no—
40C4⋊C4×C283—22no—
41C22×D283—22no—
42C22×D283—41no—
43C22×D283—41no—
44C22×D283—41no—
45C22×D283—41no—
46C22×D283—41no—
47C22×D283—41no—
48Dic566—42no—
49Dic566—81no—
50D1132—24no—
51D1132—42no—
52C2×Dic283—22no—
53C2×Dic283—22no—
54C2×Dic283—41no—
55C2×Dic283—41no—
56C2×Dic283—41no—
57C23×C283C2×D411yescharacteristic
58C2×C4×C283—21no—
59C2×C4×C283—21no—
60C2×C4×C283—21no—
61C2×C4×C283—41no—
62C2×C4×C283—41no—
63C2×C4×C283SD1612yescomplemented
64C2×C4×C283C2×D412yes—
65C8×C283—42no—
66C22×C283—21no—
67C22×C283—21no—
68C22×C283#12011yescharacteristic
69C22×C283C2×SD1611yescharacteristic
70C22×C283#13711yescharacteristic
71C2×D283—42no—
72C2×D283—42no—
73C2×D283—42no—
74C2×D283—81no—
75C2×D283—81no—
76C2×D283—81no—
77C2×D283—81no—
78C4×C283—22no—
79C4×C283—22no—
80C4×C283—41no—
81Dic283—42no—
82Dic283—42no—
83Dic283—81no—
84C2×C283—21no—
85C2×C283—21no—
86C2×C283#44811yescharacteristic
87C2×C283#45411yescharacteristic
88C2×C283B(4,𝔽2)11yescharacteristic
89D283—82no—
90C283#159911yescharacteristic, complemented, Sylow
91#1599—2831nomaximal, Sylow
92#544—2831no—
93#450—2832no—
94#394—2831no—
95#328—2832no—
96#324D28311yescharacteristic, complemented
97C22×D4—2831no—
98C2×SD16—5662no—
99C4⋊Q8—5662no—
100#125—5662no—
101C22⋊Q8—2832no—
102C22⋊Q8—5661no—
103#117—5661no—
104C2×C4⋊C4C2×D28311yescharacteristic
105C2×C22⋊C4—5661no—
106C2×C22⋊C4—5661no—
107#102—5662no—
108C22⋊C8C2×D28312yes—
109#95—2831no—
110C24—5661no—
111C2×Q8—2832no—
112C2×Q8—5661no—
113C2×D4—5662no—
114C2×D4—11322no—
115C22×C4—5661no—
116C22×C4D113211yescharacteristic
117C22×C4D113211yescharacteristic
118C22×C4C22×D28311yescharacteristic
119SD16—11324no—
120C2×C8—22no—
121C4⋊C4—22no—
122C4⋊C4—2832no—
123C4⋊C4—5662no—
124C4⋊C4—5661no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4—5662no—
128C22⋊C4—5662no—
129C22⋊C4—11322no—
130C22⋊C4—11322no—
131C42—5662no—
132C23—5662no—
133C23—11321no—
134C23—11321no—
135C23—11321no—
136C23—11321no—
137C23—11321no—
138C23—11321no—
139C23C2×D113211yescharacteristic
140Q8—11322no—
141Q8—22641no—
142D4—5664no—
143D4—11322no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—5662no—
150C2×C4—5662no—
151C2×C4—11321no—
152C2×C4—11321no—
153C2×C4—11321no—
154C2×C4#1798538112yescomplemented
155C2×C4D4×D28312yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—11322no—
160C22—11322no—
161C22—11322no—
162C22—22641no—
163C22—22641no—
164C22—22641no—
165C22—22641no—
166C22#2258358011yescharacteristic
167C22C2×#1798538111yescharacteristic
168C22#2258364311yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—11322no—
173C4—11322no—
174C4—22641no—
175C2—21no—
176C2—21no—
177C2—22642no—
178C2#3182660611yescharacteristic
179C2#3182664011yescharacteristic
180C2#3182665311yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#324×C283C2
socleC22×C283#120
prime radicalC22×D1132C22
hypercenter#324D283
hypocenterC283#1599
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #31827096C2semidirect
4. #31826203C2semidirect
5. #324×C283C2semidirect
63. C2×C4×C283SD16semidirect
90. C283#1599semidirect
96. #324D283semidirect
154. C2×C4#17985381semidirect

Maximal subgroups

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

subgroupindex
#318270962
#318266182
#318263822
#318262032
#324×C2832
#1599283