Finite Group Databasebeta

← #49122402

Subgroups — #49122402

Order 36224.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#22583610C211yesmaximal, characteristic
2C2×#22583534C212yesmaximal
3#31826227C212yesmaximal
4#31826220C211yesmaximal, characteristic
5#391×C283C211yesmaximal, characteristic
6C22×Dic566—21no—
7C22×C283⋊C8C2212yes—
8#22583610—24no—
9C2×C4⋊Dic283—21no—
10C2×C4⋊Dic283C2212yes—
11#22583534—24no—
12C22×Q8×C283C2211yescharacteristic
13C2×C4⋊C4×C283C2211yescharacteristic
14C2×C42×C283C2211yescharacteristic
15#95×C283—21no—
16#95×C283—21no—
17C2×Dic566—24no—
18C2×Dic566—42no—
19C2×Dic566—42no—
20C22×Dic283—22no—
21C2×C283⋊C8—22no—
22C2×C283⋊C8—22no—
23C2×C283⋊C8—22no—
24C4⋊Dic283—24no—
25C4⋊Dic283—22no—
26C4⋊Dic283D414yes—
27C2×Q8×C283—21no—
28C2×Q8×C283—22no—
29C2×Q8×C283—22no—
30C2×Q8×C283Q812yescomplemented
31C22×C4×C283—21no—
32C22×C4×C283—21no—
33C22×C4×C283D411yescharacteristic
34C22×C4×C283D411yescharacteristic
35C22×C4×C283C2311yescharacteristic
36C4⋊C4×C283—22no—
37C42×C283—22no—
38Dic566—48no—
39C2×Dic283—24no—
40C2×Dic283—42no—
41C2×Dic283—42no—
42C283⋊C8—42no—
43C23×C283C2×D411yescharacteristic
44Q8×C283—24no—
45Q8×C283—42no—
46C2×C4×C283—21no—
47C2×C4×C283—21no—
48C2×C4×C283—21no—
49C2×C4×C283—21no—
50C2×C4×C283—22no—
51C2×C4×C283—41no—
52C2×C4×C283—41no—
53C2×C4×C283—41no—
54C2×C4×C283—41no—
55C2×C4×C283—41no—
56C2×C4×C283SD1612yes—
57C2×C4×C283Q1612yes—
58C2×C4×C283C2×D412yes—
59C2×C4×C283C2×Q811yescharacteristic
60C2×C4×C283#4112yes—
61C2×C4×C283#4111yescharacteristic
62C22×C283#12011yescharacteristic
63C22×C283C22⋊Q811yescharacteristic
64C22×C283#12411yescharacteristic
65C22×C283C2×SD1611yescharacteristic
66C22×C283C2×Q1611yescharacteristic
67C22×C283AGL(1,ℤ/8)11yescharacteristic
68C22×C283#13711yescharacteristic
69C4×C283—22no—
70C4×C283—22no—
71C4×C283—42no—
72C4×C283—81no—
73C4×C283C22⋊Q812yes—
74C4×C283#12412yes—
75Dic283—44no—
76C2×C283#39311yescharacteristic
77C2×C283#45011yescharacteristic
78C2×C283#45111yescharacteristic
79C2×C283#47511yescharacteristic
80C2×C283#47711yescharacteristic
81C2×C283#48711yescharacteristic
82C2×C283#48911yescharacteristic
83C283#202411yescharacteristic, complemented, Sylow
84#2024—2831nomaximal, Sylow
85C2×C4⋊Q8—2831no—
86C2×#103—2832no—
87#391D28311yescharacteristic
88#340—2832no—
89#336—2831no—
90C22×Q8—5661no—
91C22×Q8C2×D28311yescharacteristic
92C22×C8—2832no—
93C4⋊Q8—5664no—
94C2×C4⋊C4—2832no—
95C2×C4⋊C4—5661no—
96C2×C4⋊C4C2×D28311yescharacteristic
97C2×C42C2×D28311yescharacteristic
98#103—5664no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—5664no—
105C2×Q8—11322no—
106C2×Q8—11322no—
107C2×Q8Dic56612yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—5662no—
111C22×C4C22⋊D28311yescharacteristic
112C22×C4C22⋊D28311yescharacteristic
113C22×C4C22×D28311yescharacteristic
114C2×C8—5662no—
115C2×C8—5662no—
116C2×C8—5662no—
117C4⋊C4—22no—
118C4⋊C4—2834no—
119C4⋊C4—5664no—
120C4⋊C4—5662no—
121C42—22no—
122C23C2×C22⋊D28311yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—11328no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—5664no—
137C2×C4—11322no—
138C2×C4—11322no—
139C2×C4#1798537912yes—
140C2×C4#1798538212yes—
141C2×C4D4×D28312yes—
142C2×C4C2×Dic56611yescharacteristic
143C2×C4#1798539112yes—
144C2×C4#1798539211yescharacteristic
145C8—11322no—
146C22#2258357811yescharacteristic
147C22#2258358911yescharacteristic
148C22#2258359711yescharacteristic
149C22C2×#1798537911yescharacteristic
150C22C2×#1798538211yescharacteristic
151C22#2258363511yescharacteristic
152C22#2258364011yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—11324no—
158C4#2258358712yes—
159C4#2258359612yes—
160C2#3182637711yescharacteristic
161C2#3182661511yescharacteristic
162C2#3182662011yescharacteristic
163C2#3182675011yescharacteristic
164C2#3182676011yescharacteristic
165C2#3182681511yescharacteristic
166C2#3182682411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#391×C283C2
socle, prime radicalC23×C283C2×D4
hypercenter#391D283
hypocenterC283#2024
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C283Q8semidirect
83. C283#2024semidirect
107. C2×Q8Dic566semidirect

Maximal subgroups

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

subgroupindex
C2×#225836102
C2×#225835342
#318262272
#318262202
#391×C2832
#2024283