Finite Group Databasebeta

← #49122418

Subgroups — #49122418

Order 36224.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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, complemented
2#31826471C212yesmaximal
3#31826366C211yesmaximal, characteristic
4#31826226C212yesmaximal, complemented
5#343×C283C211yesmaximal, characteristic, complemented
6C22×D1132C2211yescharacteristic
7#22583609—22no—
8#22583601—22no—
9#22583589—22no—
10#22583569C2212yes—
11C2×(C2×D283)⋊C4—22no—
12C2×C4×Dic283C2211yescharacteristic
13#22583532—22no—
14#22583532—22no—
15C2×M16×C283C2212yes—
16C2×C4⋊C4×C283C2211yescharacteristic
17C23×D283—21no—
18C2×Dic566—22no—
19C2×D1132—22no—
20C2×D1132—22no—
21C2×D1132—21no—
22C2×D1132Q812yescomplemented
23C22×Dic283—21no—
24C4⋊Dic283—22no—
25C4⋊Dic283D412yes—
26C4⋊Dic283D412yes—
27Dic283⋊C4—24no—
28C22⋊Dic283—22no—
29(C2×D283)⋊C4—44no—
30C4×Dic283—22no—
31C4×Dic283—22no—
32C22×C4×C283D412yes—
33C22×C4×C283C2311yescharacteristic
34M16×C283—22no—
35M16×C283—22no—
36C2×C8×C283—22no—
37C4⋊C4×C283—22no—
38C22×D283—22no—
39C22×D283—42no—
40C22×D283—42no—
41C22×D283—41no—
42C22×D283—41no—
43Dic566—82no—
44D1132—24no—
45D1132—42no—
46C2×Dic283—22no—
47C2×Dic283—22no—
48C2×Dic283—22no—
49C2×Dic283—41no—
50C2×Dic283—41no—
51C23×C283C2×D411yescharacteristic
52C2×C4×C283—22no—
53C2×C4×C283—42no—
54C2×C4×C283C2×D412yes—
55C2×C4×C283C2×Q811yescharacteristic
56C2×C4×C283#4111yescharacteristic
57C2×C4×C283#4112yes—
58C8×C283—42no—
59C22×C283—21no—
60C22×C283—21no—
61C22×C283#12011yescharacteristic
62C22×C283C22⋊Q811yescharacteristic
63C22×C283#12411yescharacteristic
64C2×D283—44no—
65C2×D283—42no—
66C2×D283—82no—
67C2×D283—81no—
68C2×D283—81no—
69C4×C283—42no—
70C4×C283C22⋊Q812yes—
71C4×C283#12412yes—
72Dic283—42no—
73Dic283—42no—
74Dic283—42no—
75C2×C283—21no—
76C2×C283—21no—
77C2×C283#39311yescharacteristic
78C2×C283#45311yescharacteristic
79C2×C283#45411yescharacteristic
80D283—82no—
81C283#202711yescharacteristic, complemented, Sylow
82#2027—2831nomaximal, Sylow
83#544—2831no—
84#418—2832no—
85#390—2831no—
86#343D28311yescharacteristic, complemented
87#339—2832no—
88C22×D4—2831no—
89C2×M16C2×D28312yes—
90C4⋊Q8—5662no—
91#125—5662no—
92C22⋊Q8—5662no—
93#117—2832no—
94C2×C4⋊C4C2×D28311yescharacteristic
95C2×C22⋊C4—5662no—
96C2×C42—2831no—
97#102—5662no—
98#102—5662no—
99C24—5661no—
100C2×Q8—5662no—
101C2×D4—2832no—
102C2×D4—5662no—
103C2×D4—5661no—
104C2×D4—5662no—
105C22×C4—5661no—
106C22×C4D113212yes—
107C22×C4C22×D28311yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—2832no—
113C4⋊C4—2832no—
114C4⋊C4—5664no—
115C4⋊C4—5662no—
116C22⋊C4—5662no—
117C22⋊C4—11324no—
118C42—5662no—
119C42—5662no—
120C23—5662no—
121C23—11322no—
122C23—11322no—
123C23—11321no—
124C23—11321no—
125C23C2×D113211yescharacteristic
126Q8—22642no—
127D4—5664no—
128D4—11322no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—5662no—
132C2×C4—5662no—
133C2×C4—5662no—
134C2×C4—11321no—
135C2×C4—11321no—
136C2×C4D4×D28312yes—
137C2×C4Q8×D28311yescharacteristic
138C2×C4#1798539111yescharacteristic
139C2×C4#1798539212yes—
140C8—42no—
141C22—21no—
142C22—21no—
143C22—11324no—
144C22—11322no—
145C22—22642no—
146C22—22641no—
147C22—22641no—
148C22#2258358011yescharacteristic
149C22#2258359011yescharacteristic
150C22#2258359811yescharacteristic
151C4—42no—
152C4—11322no—
153C4—11322no—
154C4—11322no—
155C4#2258358812yes—
156C4#2258359612yes—
157C2—21no—
158C2—21no—
159C2—22642no—
160C2#3182637811yescharacteristic
161C2#3182663511yescharacteristic
162C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#343×C283C2
socleC22×C283#120
prime radicalC22×D1132C22
hypercenter#343D283
hypocenterC283#2027
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #31827096C2semidirect
4. #31826226C2semidirect
5. #343×C283C2semidirect
22. C2×D1132Q8semidirect
81. C283#2027semidirect
86. #343D283semidirect

Maximal subgroups

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

subgroupindex
#318270962
#318264712
#318263662
#318262262
#343×C2832
#2027283