Finite Group Databasebeta

← #49119883

Subgroups — #49119883

Order 36224.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D283C211yesmaximal, characteristic
2#31826520C212yesmaximal, complemented
3#31826205C211yesmaximal, characteristic, complemented
4#31826204C212yesmaximal, complemented
5#329×C283C211yesmaximal, characteristic, complemented
6C2×Q8×D283C411yescharacteristic
7C2×D4×D283C411yescharacteristic
8#22583599C411yescharacteristic
9#22583598C2211yescharacteristic
10#22583597C411yescharacteristic
11#22583596—22no—
12C22⋊C4×D283—22no—
13C42×D283C2211yescharacteristic
14Dic283⋊C8—22no—
15(C2×D283)⋊C8—22no—
16#22583521C2212yescomplemented
17#124×C283C2211yescharacteristic
18#97×C283C2212yescomplemented
19C23×D283—21no—
20C2×Dic566—21no—
21C2×Dic566C2×C411yescharacteristic
22Q8×D283—42no—
23C2×D1132C2×C411yescharacteristic
24C2×C22⋊D283—21no—
25D4×D283—42no—
26C2×C4×D283—21no—
27C2×C4×D283C2×C411yescharacteristic
28C2×C4×D283D412yes—
29C2×C283⋊C8—22no—
30C22⋊Dic283—22no—
31(C2×D283)⋊C4—22no—
32(C2×D283)⋊C4—22no—
33C4×Dic283C2×C411yescharacteristic
34C4×Dic283D412yes—
35C2×Q8×C283C2×C411yescharacteristic
36C2×D4×C283C2×C411yescharacteristic
37C2×C8×C283—22no—
38C22⋊C4×C283—22no—
39C42×C283C2311yescharacteristic
40C22×D283—21no—
41C22×D283—44no—
42C22×D283—42no—
43C22×D283C22⋊C411yescharacteristic
44Dic566—42no—
45Dic566—41no—
46D1132—41no—
47C22⋊D283—42no—
48C2×Dic283—21no—
49C2×Dic283C22⋊C412yes—
50C2×Dic283C22⋊C411yescharacteristic
51C4×D283—22no—
52C4×D283—42no—
53C4×D283—42no—
54C283⋊C8—42no—
55C23×C283—21no—
56Q8×C283—41no—
57D4×C283—41no—
58C2×C4×C283—21no—
59C2×C4×C283C22×C411yescharacteristic
60C2×C4×C283C2×D412yes—
61C8×C283—42no—
62C22×C283—41no—
63C22×C283—42no—
64C22×C283C2×C22⋊C411yescharacteristic
65C2×D283—22no—
66C2×D283—41no—
67C2×D283—42no—
68C2×D283—84no—
69C2×D283#10012yes—
70C4×C283—21no—
71C4×C283—22no—
72C4×C283—41no—
73Dic283—21no—
74Dic283—22no—
75Dic283—41no—
76C2×C283—81no—
77C2×C283C2×#10011yescharacteristic
78C2×C283#42112yes—
79D283—22no—
80D283—81no—
81C283#153311yescharacteristic, complemented, Sylow
82#1533—2831nomaximal, Sylow
83C2×#124—2831no—
84#432—2832no—
85#329—2831no—
86#329—2832no—
87#329D28311yescharacteristic, complemented
88C22×Q8—2831no—
89C22×D4—2831no—
90#124—2831no—
91#124—2831no—
92#124—2831no—
93#124—5662no—
94#124C2×D28311yescharacteristic
95C2×C22⋊C4—5662no—
96C2×C42—2831no—
97C4⋊C8—5662no—
98C22⋊C8—5662no—
99#97—2832no—
100#97C2×D28312yescomplemented
101C24—5661no—
102C2×Q8—2831no—
103C2×Q8—5661no—
104C2×Q8—11322no—
105C2×Q8C4×D28311yescharacteristic
106C2×D4—2831no—
107C2×D4—5661no—
108C2×D4—11322no—
109C2×D4C4×D28311yescharacteristic
110C22×C4—2831no—
111C22×C4—2832no—
112C22×C4—5661no—
113C2×C8—22no—
114C2×C8—5662no—
115C22⋊C4—22no—
116C22⋊C4—5662no—
117C22⋊C4—5662no—
118C22⋊C4—5662no—
119C42—2831no—
120C42—2832no—
121C42C22×D28311yescharacteristic
122C23—21no—
123C23—2831no—
124C23—5661no—
125C23—11322no—
126C23—11324no—
127Q8—41no—
128Q8—11321no—
129Q8—11322no—
130D4—41no—
131D4—11321no—
132D4—11322no—
133C2×C4—21no—
134C2×C4—2832no—
135C2×C4—2831no—
136C2×C4—5662no—
137C2×C4—5661no—
138C2×C4—11322no—
139C2×C4—11322no—
140C2×C4C2×C4×D28311yescharacteristic
141C2×C4D4×D28312yes—
142C8—42no—
143C8—11322no—
144C22—41no—
145C22—42no—
146C22—2832no—
147C22—5662no—
148C22—11321no—
149C22—11322no—
150C22—22644no—
151C22C22⋊C4×D28311yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—5661no—
156C4—5662no—
157C4—11321no—
158C2—81no—
159C2—5662no—
160C2—22641no—
161C2#100×D28311yescharacteristic
162C2#3182648012yes—
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#329×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC2×D4×D283C4
cosocleC42×C283C23
hypercenter#329D283
hypocenterC283#1533
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31826520C2semidirect
3. #31826205C2semidirect
4. #31826204C2semidirect
5. #329×C283C2semidirect
16. #22583521C22semidirect
18. #97×C283C22semidirect
81. C283#1533semidirect
87. #329D283semidirect
100. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#124×D2832
#318265202
#318262052
#318262042
#329×C2832
#1533283