Finite Group Databasebeta

← #49120200

Subgroups — #49120200

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#31826616C212yesmaximal
3#31826201C212yesmaximal, complemented
4#31826191C211yesmaximal, characteristic, complemented
5#394×C283C211yesmaximal, characteristic
6C2×#17985380—22no—
7#22583609—22no—
8#22583601—22no—
9#22583589—21no—
10#22583589C2212yes—
11#22583569—21no—
12#22583531—22no—
13C22⋊(C283⋊C8)C2212yes—
14C22×D4×C283C2211yescharacteristic
15C2×C4⋊C4×C283C2211yescharacteristic
16C2×C22⋊C4×C283—21no—
17C2×C22⋊C4×C283—21no—
18#95×C283C2211yescharacteristic
19C2×Dic566—21no—
20C2×Dic566D412yes—
21#17985380—44no—
22C2×C283⋊C8—22no—
23C4⋊Dic283—21no—
24C4⋊Dic283—21no—
25C4⋊Dic283—21no—
26C4⋊Dic283D412yes—
27Dic283⋊C4—22no—
28Dic283⋊C4—22no—
29C22⋊Dic283—22no—
30C4×Dic283—22no—
31C24×C283—21no—
32C2×D4×C283—22no—
33C2×D4×C283—42no—
34C22×C4×C283—21no—
35C22×C4×C283D411yescharacteristic
36C22×C4×C283D411yescharacteristic
37C22×C4×C283C2311yescharacteristic
38C4⋊C4×C283—22no—
39C22⋊C4×C283—42no—
40C22⋊C4×C283—42no—
41Dic566—42no—
42Dic566—81no—
43C2×Dic283—22no—
44C2×Dic283—22no—
45C283⋊C8—42no—
46C23×C283—22no—
47C23×C283—41no—
48C23×C283—41no—
49C23×C283—41no—
50C23×C283—41no—
51C23×C283—41no—
52C23×C283—41no—
53C23×C283C2×D411yescharacteristic
54D4×C283—24no—
55D4×C283—42no—
56C2×C4×C283—21no—
57C2×C4×C283—21no—
58C2×C4×C283—21no—
59C2×C4×C283—41no—
60C2×C4×C283—41no—
61C2×C4×C283—41no—
62C2×C4×C283—41no—
63C2×C4×C283—41no—
64C2×C4×C283SD1612yescomplemented
65C2×C4×C283C2×D412yes—
66C22×C283—21no—
67C22×C283—21no—
68C22×C283—42no—
69C22×C283—42no—
70C22×C283—42no—
71C22×C283—81no—
72C22×C283—81no—
73C22×C283—81no—
74C22×C283—81no—
75C22×C283#12011yescharacteristic
76C22×C283C2×SD1611yescharacteristic
77C22×C283#13711yescharacteristic
78C4×C283—22no—
79C4×C283—22no—
80C4×C283—41no—
81C4×C283—81no—
82Dic283—42no—
83Dic283—42no—
84C2×C283—21no—
85C2×C283—21no—
86C2×C283—82no—
87C2×C283#44811yescharacteristic
88C2×C283#45411yescharacteristic
89C2×C283B(4,𝔽2)11yescharacteristic
90C283#159911yescharacteristic, complemented, Sylow
91#1599—2831nomaximal, Sylow
92#544—2831no—
93#450—2832no—
94#394D28311yescharacteristic
95#328—2832no—
96#324—2831no—
97C22×D4C2×D28311yescharacteristic
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—21no—
106C2×C22⋊C4—21no—
107#102—5662no—
108C22⋊C8—2832no—
109#95C2×D28311yescharacteristic
110C24—21no—
111C2×Q8—2832no—
112C2×Q8—5661no—
113C2×D4—22no—
114C2×D4—42no—
115C22×C4—21no—
116C22×C4C22⋊D28311yescharacteristic
117C22×C4C22⋊D28311yescharacteristic
118C22×C4C22×D28311yescharacteristic
119SD16—11324no—
120C2×C8—5662no—
121C4⋊C4—22no—
122C4⋊C4—2832no—
123C4⋊C4—5662no—
124C4⋊C4—5661no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4—5662no—
128C22⋊C4—42no—
129C22⋊C4—42no—
130C22⋊C4—5662no—
131C42—5662no—
132C23—22no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23C2×C22⋊D28311yescharacteristic
140Q8—11322no—
141Q8—22641no—
142D4—24no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5662no—
153C2×C4—5662no—
154C2×C4#1798538012yescomplemented
155C2×C4D4×D28312yes—
156C8—11322no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#2258357811yescharacteristic
167C22C2×#1798538011yescharacteristic
168C22#2258364011yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—81no—
173C4—11322no—
174C4—11322no—
175C2—21no—
176C2—21no—
177C2—82no—
178C2#3182660311yescharacteristic
179C2#3182663711yescharacteristic
180C2#3182665111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#394×C283C2
socleC22×C283#120
prime radicalC22×D4×C283C22
hypercenter#394D283
hypocenterC283#1599
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #31827096C2semidirect
3. #31826201C2semidirect
4. #31826191C2semidirect
64. C2×C4×C283SD16semidirect
90. C283#1599semidirect
154. C2×C4#17985380semidirect

Maximal subgroups

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

subgroupindex
#318270962
#318266162
#318262012
#318261912
#394×C2832
#1599283