Finite Group Databasebeta

← #49122310

Subgroups — #49122310

Order 36224.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22583643C212yesmaximal, complemented
2#31827046C211yesmaximal, characteristic
3C2×#22583536C212yesmaximal, complemented
4#31826370C211yesmaximal, characteristic, complemented
5#343×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2212yes—
7C22×Dic566C2211yescharacteristic
8#22583643—24no—
9#22583643—24no—
10C2×Dic1132—22no—
11C2×#17985381—22no—
12#22583590—22no—
13#22583585—22no—
14#22583584—22no—
15C2×C4×Dic283C2211yescharacteristic
16#22583536—24no—
17C283⋊#95—22no—
18C2×M16×C283C2212yes—
19C2×C4⋊C4×C283C2211yescharacteristic
20#17985392—22no—
21#17985392—22no—
22#17985392—22no—
23#17985392—22no—
24C2×Dic566—22no—
25C2×Dic566—22no—
26C2×Dic566—21no—
27C2×Dic566D412yes—
28C2×Dic566D412yescomplemented
29C2×D1132—22no—
30C2×D1132D412yes—
31C2×C22⋊D283—22no—
32C22×Dic283—21no—
33C22×Dic283—21no—
34C2×C4×D283—22no—
35Dic1132—28no—
36#17985381—28no—
37C4⋊Dic283—22no—
38(C2×D283)⋊C4—24no—
39C4×Dic283—22no—
40C22×C4×C283D412yes—
41C22×C4×C283C2311yescharacteristic
42M16×C283—22no—
43M16×C283D414yescomplemented
44C2×C8×C283—22no—
45C4⋊C4×C283—22no—
46C22×D283—22no—
47Dic566—24no—
48Dic566—22no—
49Dic566—22no—
50Dic566—42no—
51D1132—22no—
52D1132—22no—
53D1132—82no—
54C22⋊D283—42no—
55C22⋊D283—42no—
56C2×Dic283—22no—
57C2×Dic283—22no—
58C2×Dic283—22no—
59C2×Dic283—41no—
60C2×Dic283—41no—
61C2×Dic283—41no—
62C2×Dic283—41no—
63C4×D283—42no—
64C4×D283—42no—
65C23×C283C2×D411yescharacteristic
66C2×C4×C283—22no—
67C2×C4×C283—42no—
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D412yes—
70C2×C4×C283C2×D412yes—
71C2×C4×C283#4111yescharacteristic
72C8×C283—24no—
73C22×C283—21no—
74C22×C283—21no—
75C22×C283#12011yescharacteristic
76C22×C283#12111yescharacteristic
77C22×C283#12711yescharacteristic
78C2×D283—42no—
79C2×D283—42no—
80C2×D283—42no—
81C4×C283—42no—
82C4×C283#12012yes—
83C4×C283#12112yes—
84Dic283—42no—
85Dic283—42no—
86Dic283—42no—
87C2×C283—21no—
88C2×C283—21no—
89C2×C283#39211yescharacteristic
90C2×C283#45511yescharacteristic
91C2×C283#45611yescharacteristic
92D283—82no—
93C283#200711yescharacteristic, complemented, Sylow
94#2007—2831nomaximal, Sylow
95C2×#137—2832no—
96#537—2831no—
97C2×#104—2832no—
98#391—2831no—
99#343D28311yescharacteristic, complemented
100C2×#41—2832no—
101C22×Q8—2831no—
102#137—5664no—
103#137—5664no—
104C2×Q16—5662no—
105C2×SD16—5662no—
106C2×M16C2×D28312yes—
107C22⋊Q8—5662no—
108#121—5662no—
109#121—5662no—
110C2×C4⋊C4C2×D28311yescharacteristic
111C2×C42—2831no—
112#104—5664no—
113#95—5662no—
114#41—5662no—
115#41—5662no—
116#41—5662no—
117#41—5662no—
118C2×Q8—2832no—
119C2×Q8—2832no—
120C2×Q8—5661no—
121C2×Q8—5662no—
122C2×Q8—5662no—
123C2×D4—2832no—
124C2×D4—5662no—
125C2×D4—5662no—
126C22×C4—5661no—
127C22×C4—5661no—
128C22×C4—5662no—
129C22×C4D113212yes—
130C22×C4C22×D28311yescharacteristic
131Q16—5668no—
132SD16—5668no—
133M16—22no—
134M16D113214yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—5662no—
138C22⋊C4—5664no—
139C42—5662no—
140C23—5662no—
141C23C2×D113211yescharacteristic
142Q8—5664no—
143Q8—5662no—
144Q8—5662no—
145Q8—11322no—
146D4—5662no—
147D4—5662no—
148D4—11322no—
149D4—11322no—
150D4—22642no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—5662no—
154C2×C4—5662no—
155C2×C4—5662no—
156C2×C4—11321no—
157C2×C4—11321no—
158C2×C4—11321no—
159C2×C4—11321no—
160C2×C4—11322no—
161C2×C4—11322no—
162C2×C4D4×D28311yescharacteristic
163C2×C4D4×D28312yes—
164C2×C4C2×D113212yes—
165C2×C4#1798539311yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—11322no—
170C22—11322no—
171C22—11322no—
172C22#2258358011yescharacteristic
173C22#2258358511yescharacteristic
174C22#2258360711yescharacteristic
175C4—42no—
176C4—11322no—
177C4—11322no—
178C4—11322no—
179C4#2258358012yes—
180C4#2258358512yes—
181C2—21no—
182C2—21no—
183C2—22642no—
184C2#3182637511yescharacteristic
185C2#3182664511yescharacteristic
186C2#3182665011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#343×C283C2
socleC22×C283#120
prime radical#31827046C2
hypercenter#343D283
hypocenterC283#2007
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. C2×#22583643C2semidirect
3. C2×#22583536C2semidirect
4. #31826370C2semidirect
5. #343×C283C2semidirect
28. C2×Dic566D4semidirect
43. M16×C283D4semidirect
93. C283#2007semidirect
99. #343D283semidirect
134. M16D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
#318270462
C2×#225835362
#318263702
#343×C2832
#2007283