Finite Group Databasebeta

← #49120271

Subgroups — #49120271

Order 36224.

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

normal subgroups only

This group has 210 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
2#31826796C212yesmaximal
3#31826395C211yesmaximal, characteristic
4#31826203C212yesmaximal
5#324×C283C211yesmaximal, characteristic
6#22583609—22no—
7#22583601—22no—
8#22583589—21no—
9#22583589C2212yes—
10#22583569—21no—
11C2×C4⋊Dic283C2211yescharacteristic
12C2×Dic283⋊C4—21no—
13#22583542—22no—
14#22583535—22no—
15C283⋊#95—21no—
16C283⋊#95C2211yescharacteristic
17C2×C4⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19C2×Dic566—21no—
20C2×Dic566D412yes—
21C22×Dic283—21no—
22C22×Dic283—21no—
23C4⋊Dic283—21no—
24C4⋊Dic283—21no—
25C4⋊Dic283—21no—
26C4⋊Dic283—22no—
27C4⋊Dic283D412yes—
28Dic283⋊C4—22no—
29Dic283⋊C4—22no—
30Dic283⋊C4—42no—
31C22⋊Dic283—22no—
32C4×Dic283—22no—
33C22×C4×C283D411yescharacteristic
34C22×C4×C283D411yescharacteristic
35C22×C4×C283C2311yescharacteristic
36C2×C8×C283—22no—
37C4⋊C4×C283—22no—
38Dic566—42no—
39Dic566—81no—
40C2×Dic283—22no—
41C2×Dic283—22no—
42C2×Dic283—22no—
43C2×Dic283—41no—
44C2×Dic283—41no—
45C2×Dic283—41no—
46C2×Dic283—41no—
47C2×Dic283—41no—
48C23×C283C2×D411yescharacteristic
49C2×C4×C283—21no—
50C2×C4×C283—21no—
51C2×C4×C283—21no—
52C2×C4×C283—41no—
53C2×C4×C283—41no—
54C2×C4×C283SD1612yes—
55C2×C4×C283C2×D412yes—
56C8×C283—42no—
57C22×C283—21no—
58C22×C283—21no—
59C22×C283#12011yescharacteristic
60C22×C283C2×SD1611yescharacteristic
61C22×C283#13711yescharacteristic
62C4×C283—22no—
63C4×C283—22no—
64C4×C283—41no—
65Dic283—42no—
66Dic283—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#544—2831no—
77#483—2832no—
78#398—2831no—
79#328—2832no—
80#324D28311yescharacteristic
81C4⋊Q8—5662no—
82#125—5662no—
83C22⋊Q8—2832no—
84C22⋊Q8—5661no—
85#117—5661no—
86C2×C4⋊C4—2831no—
87C2×C4⋊C4—5661no—
88C2×C4⋊C4C2×D28311yescharacteristic
89#106—5662no—
90#103—5662no—
91C22⋊C8C2×D28312yes—
92#95—2831no—
93#95—5661no—
94C2×Q8—2832no—
95C2×Q8—5661no—
96C22×C4—5661no—
97C22×C4—5661no—
98C22×C4D113211yescharacteristic
99C22×C4D113211yescharacteristic
100C22×C4C22×D28311yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—2832no—
104C4⋊C4—5662no—
105C4⋊C4—5661no—
106C4⋊C4—5661no—
107C4⋊C4—5661no—
108C4⋊C4—5662no—
109C4⋊C4—5662no—
110C4⋊C4—11322no—
111C22⋊C4—5662no—
112C42—5662no—
113C23C2×D113211yescharacteristic
114Q8—11322no—
115Q8—22641no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—5662no—
122C2×C4—5662no—
123C2×C4—5662no—
124C2×C4—11321no—
125C2×C4—11321no—
126C2×C4—11321no—
127C2×C4—11321no—
128C2×C4—11321no—
129C2×C4#1798538112yes—
130C2×C4D4×D28312yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#2258358011yescharacteristic
135C22C2×#1798538111yescharacteristic
136C22#2258364311yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—11322no—
141C4—11322no—
142C4—11322no—
143C4—22641no—
144C2—21no—
145C2—21no—
146C2#3182660611yescharacteristic
147C2#3182665011yescharacteristic
148C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#324×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#324D283
hypocenterC283#1611
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
74. C283#1611semidirect

Maximal subgroups

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

subgroupindex
#318270962
#318267962
#318263952
#318262032
#324×C2832
#1611283