Finite Group Databasebeta

← #49119990

Subgroups — #49119990

Order 36224.

202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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#31827020C211yesmaximal, characteristic
2#31826521C211yesmaximal, characteristic
3#31826487C211yesmaximal, characteristic
4#31826213C211yesmaximal, characteristic, complemented
5#31826213C211yesmaximal, characteristic, complemented
6#31826211C211yesmaximal, characteristic, complemented
7#332×C283C211yesmaximal, characteristic, complemented
8C2×#17985375—21no—
9#22583610C2211yescharacteristic
10#22583601—21no—
11#22583590C412yes—
12#22583586—21no—
13Q8×Dic283—21no—
14#22583575C412yes—
15#22583568—21no—
16C42×D283C2211yescharacteristic
17C4⋊(C283⋊C8)C2211yescharacteristic
18C4⋊(C283⋊C8)C2211yescharacteristic
19Dic283⋊C8—21no—
20(C2×D283)⋊C8—21no—
21#22583520—21no—
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566C2×C412yes—
26C2×C4×D283C2×C411yescharacteristic
27C2×C4×D283D411yescharacteristic
28C2×C4×D283D411yescharacteristic
29#17985375—42no—
30C2×C283⋊C8—21no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—22no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35Dic283⋊C4—22no—
36(C2×D283)⋊C4—22no—
37C4×Dic283—22no—
38C4×Dic283C2×C411yescharacteristic
39C4×Dic283D411yescharacteristic
40C4×Dic283D411yescharacteristic
41C2×Q8×C283—21no—
42C2×C8×C283—21no—
43C2×C8×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283C2×C412yes—
46C42×C283C2311yescharacteristic
47C22×D283C22⋊C411yescharacteristic
48Dic566—42no—
49C2×Dic283—22no—
50C2×Dic283C22⋊C411yescharacteristic
51C2×Dic283C22⋊C411yescharacteristic
52C2×Dic283C22⋊C411yescharacteristic
53C4×D283—21no—
54C4×D283—21no—
55C4×D283—21no—
56C4×D283—21no—
57C4×D283—41no—
58C283⋊C8—41no—
59C283⋊C8—41no—
60Q8×C283—41no—
61Q8×C283—41no—
62C2×C4×C283—22no—
63C2×C4×C283C22×C411yescharacteristic
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C8×C283—41no—
67C8×C283—41no—
68C22×C283C2×C22⋊C411yescharacteristic
69C2×D283—21no—
70C2×D283—21no—
71C2×D283—21no—
72C4×C283—21no—
73C4×C283—42no—
74C4×C283AGL(1,ℤ/8)11yescharacteristic
75C4×C283#13711yescharacteristic
76C4×C283#13711yescharacteristic
77C4×C283#13711yescharacteristic
78Dic283—21no—
79Dic283—21no—
80Dic283—21no—
81Dic283—42no—
82C2×C283#41311yescharacteristic
83C2×C283#41711yescharacteristic
84C2×C283#41911yescharacteristic
85D283—41no—
86C283#155911yescharacteristic, complemented, Sylow
87#1559—2831nomaximal, Sylow
88#533—2831no—
89#432—2831no—
90#423—2831no—
91#333—2831no—
92#333—2831no—
93#332—2831no—
94#332D28311yescharacteristic, complemented
95C2×M16—5661no—
96C4⋊Q8—2831no—
97C4⋊Q8C2×D28311yescharacteristic
98#125—5661no—
99C22⋊Q8—2832no—
100C22⋊Q8—5661no—
101C4×Q8—2832no—
102C4×Q8—5661no—
103#117—5661no—
104C2×C42—2831no—
105C4⋊C8—2831no—
106C4⋊C8—2831no—
107C4⋊C8—5661no—
108C4⋊C8C2×D28311yescharacteristic
109C4⋊C8C2×D28311yescharacteristic
110C22⋊C8—5661no—
111#97—5661no—
112C2×Q8—21no—
113C2×Q8—2832no—
114C22×C4—2831no—
115C22×C4—2831no—
116C22×C4—2831no—
117M16—11322no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—5661no—
121C2×C8—5661no—
122C4⋊C4—21no—
123C4⋊C4—5662no—
124C4⋊C4—5662no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4C4×D28312yes—
128C22⋊C4—5662no—
129C42—2831no—
130C42—2831no—
131C42—2831no—
132C42—5662no—
133C42C22×D28311yescharacteristic
134C23—2831no—
135Q8—41no—
136Q8—41no—
137Q8—11322no—
138C2×C4—22no—
139C2×C4—2831no—
140C2×C4—2831no—
141C2×C4—2831no—
142C2×C4—5661no—
143C2×C4—5661no—
144C2×C4—5661no—
145C2×C4—5661no—
146C2×C4—5662no—
147C2×C4—11321no—
148C2×C4C2×C4×D28311yescharacteristic
149C2×C4D4×D28311yescharacteristic
150C2×C4D4×D28311yescharacteristic
151C8—41no—
152C8—41no—
153C8—11321no—
154C8—11321no—
155C22—5661no—
156C22—5661no—
157C22—5661no—
158C22C22⋊C4×D28311yescharacteristic
159C4—21no—
160C4—42no—
161C4—5661no—
162C4—5661no—
163C4—5661no—
164C4—11322no—
165C4#2258363411yescharacteristic
166C4#2258363911yescharacteristic
167C4#2258363911yescharacteristic
168C4#2258364211yescharacteristic
169C2—11321no—
170C2#3182644811yescharacteristic
171C2#3182646311yescharacteristic
172C2#3182647211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC22×D283C22⋊C4
cosocleC42×C283C23
hypercenter#332D283
hypocenterC283#1559
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #31826213C2semidirect
5. #31826213C2semidirect
6. #31826211C2semidirect
7. #332×C283C2semidirect
86. C283#1559semidirect
94. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318270202
#318265212
#318264872
#318262132
#318262112
#332×C2832
#1559283