Finite Group Databasebeta

← #49120269

Subgroups — #49120269

Order 36224.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#31826793C212yesmaximal
2#31826395C211yesmaximal, characteristic
3#31826202C212yesmaximal
4#31826191C211yesmaximal, characteristic
5#544×C283C211yesmaximal, characteristic
6C2×C4⋊Dic283C2211yescharacteristic
7C2×Dic283⋊C4—21no—
8#22583541—22no—
9#22583534—22no—
10C22⋊(C283⋊C8)C2212yes—
11C283⋊#95—21no—
12C283⋊#95C2211yescharacteristic
13C4⋊Q8×C283—22no—
14#125×C283—22no—
15C22⋊Q8×C283—21no—
16C22⋊Q8×C283C2212yes—
17#117×C283—21no—
18C2×C4⋊C4×C283C2211yescharacteristic
19C22×Dic283—21no—
20C22×Dic283—21no—
21C2×C283⋊C8—22no—
22C4⋊Dic283—22no—
23Dic283⋊C4—42no—
24C2×Q8×C283—21no—
25C2×Q8×C283D412yes—
26C22×C4×C283D411yescharacteristic
27C22×C4×C283D411yescharacteristic
28C22×C4×C283C2311yescharacteristic
29C4⋊C4×C283—21no—
30C4⋊C4×C283—21no—
31C4⋊C4×C283—21no—
32C4⋊C4×C283—22no—
33C4⋊C4×C283—22no—
34C4⋊C4×C283—22no—
35C4⋊C4×C283D412yes—
36C22⋊C4×C283—22no—
37C42×C283—22no—
38C2×Dic283—22no—
39C2×Dic283—41no—
40C2×Dic283—41no—
41C2×Dic283—41no—
42C2×Dic283—41no—
43C2×Dic283—41no—
44C283⋊C8—42no—
45C23×C283C2×D411yescharacteristic
46Q8×C283—42no—
47Q8×C283—81no—
48C2×C4×C283—21no—
49C2×C4×C283—21no—
50C2×C4×C283—22no—
51C2×C4×C283—22no—
52C2×C4×C283—21no—
53C2×C4×C283—41no—
54C2×C4×C283—41no—
55C2×C4×C283SD1612yes—
56C2×C4×C283C2×D412yes—
57C22×C283—21no—
58C22×C283—21no—
59C22×C283#12011yescharacteristic
60C22×C283C2×SD1611yescharacteristic
61C22×C283#13711yescharacteristic
62C4×C283—22no—
63C4×C283—22no—
64C4×C283—42no—
65C4×C283—41no—
66C4×C283—42no—
67Dic283—42no—
68Dic283—81no—
69C2×C283—21no—
70C2×C283—21no—
71C2×C283#44811yescharacteristic
72C2×C283#45611yescharacteristic
73C2×C283#45811yescharacteristic
74C283#161111yescharacteristic, complemented, Sylow
75#1611—2831nomaximal, Sylow
76#544D28311yescharacteristic
77#483—2832no—
78#398—2831no—
79#328—2832no—
80#324—2831no—
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D28312yes—
85#117—21no—
86C2×C4⋊C4—2831no—
87C2×C4⋊C4—5661no—
88C2×C4⋊C4C2×D28311yescharacteristic
89#106—5662no—
90#103—5662no—
91C22⋊C8—2832no—
92#95—2831no—
93#95—5661no—
94C2×Q8—21no—
95C2×Q8C22⋊D28312yes—
96C22×C4—5661no—
97C22×C4—5661no—
98C22×C4C22⋊D28311yescharacteristic
99C22×C4C22⋊D28311yescharacteristic
100C22×C4C22×D28311yescharacteristic
101C2×C8—5662no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—5662no—
109C4⋊C4—11322no—
110C4⋊C4C22⋊D28312yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D28311yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—5662no—
124C2×C4—11321no—
125C2×C4—11321no—
126C2×C4—11321no—
127C2×C4—11321no—
128C2×C4—11321no—
129C2×C4#1798537912yes—
130C2×C4C2×C22⋊D28312yes—
131C8—11322no—
132C22—21no—
133C22—21no—
134C22#2258357911yescharacteristic
135C22C2×#1798537911yescharacteristic
136C22#2258364111yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—11322no—
143C4—22641no—
144C2—21no—
145C2—21no—
146C2#3182660411yescharacteristic
147C2#3182664811yescharacteristic
148C2#3182665511yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#544×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#544D283
hypocenterC283#1611
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
74. C283#1611semidirect

Maximal subgroups

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

subgroupindex
#318267932
#318263952
#318262022
#318261912
#544×C2832
#1611283