Finite Group Databasebeta

← #49122305

Subgroups — #49122305

Order 36224.

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

normal subgroups only

This group has 406 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×#22583638C212yesmaximal, complemented
2#31827046C211yesmaximal, characteristic, complemented
3C2×#22583536C212yesmaximal, complemented
4#31826366C211yesmaximal, characteristic, complemented
5#343×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2212yes—
7C22×D1132C2211yescharacteristic
8#22583638—24no—
9#22583638—24no—
10C2×#17985381—22no—
11C2×D2264—22no—
12#22583590—22no—
13#22583585—22no—
14#22583584—22no—
15C2×(C2×D283)⋊C4—22no—
16C2×C4×Dic283C2211yescharacteristic
17#22583536—24no—
18C2×M16×C283C2212yes—
19C2×C4⋊C4×C283C2211yescharacteristic
20C23×D283—21no—
21#17985392—22no—
22#17985392—22no—
23#17985392—22no—
24#17985392—22no—
25C2×Dic566D412yes—
26C2×D1132—22no—
27C2×D1132—22no—
28C2×D1132—22no—
29C2×D1132—21no—
30C2×D1132D412yes—
31C2×D1132D412yescomplemented
32C2×C22⋊D283—22no—
33C22×Dic283—21no—
34C2×C4×D283—22no—
35#17985381—28no—
36D2264—28no—
37C4⋊Dic283—22no—
38(C2×D283)⋊C4—24no—
39(C2×D283)⋊C4—44no—
40C4×Dic283—22no—
41C22×C4×C283D412yes—
42C22×C4×C283C2311yescharacteristic
43M16×C283—22no—
44M16×C283D414yescomplemented
45C2×C8×C283—22no—
46C4⋊C4×C283—22no—
47C22×D283—22no—
48C22×D283—22no—
49C22×D283—42no—
50C22×D283—42no—
51C22×D283—41no—
52C22×D283—41no—
53Dic566—22no—
54Dic566—22no—
55D1132—22no—
56D1132—24no—
57D1132—22no—
58D1132—42no—
59D1132—82no—
60C22⋊D283—42no—
61C22⋊D283—42no—
62C2×Dic283—22no—
63C2×Dic283—22no—
64C2×Dic283—41no—
65C2×Dic283—41no—
66C4×D283—42no—
67C4×D283—42no—
68C23×C283C2×D411yescharacteristic
69C2×C4×C283—22no—
70C2×C4×C283—42no—
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D412yes—
73C2×C4×C283C2×D412yes—
74C2×C4×C283#4111yescharacteristic
75C8×C283—24no—
76C22×C283—21no—
77C22×C283—21no—
78C22×C283#12011yescharacteristic
79C22×C283#12111yescharacteristic
80C22×C283#12711yescharacteristic
81C2×D283—44no—
82C2×D283—42no—
83C2×D283—42no—
84C2×D283—42no—
85C2×D283—42no—
86C2×D283—82no—
87C2×D283—81no—
88C2×D283—81no—
89C4×C283—42no—
90C4×C283#12012yes—
91C4×C283#12112yes—
92Dic283—42no—
93Dic283—42no—
94C2×C283—21no—
95C2×C283—21no—
96C2×C283#39211yescharacteristic
97C2×C283#45311yescharacteristic
98C2×C283#45411yescharacteristic
99D283—82no—
100D283—82no—
101C283#200611yescharacteristic, complemented, Sylow
102#2006—2831nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2832no—
104#537—2831no—
105C2×#104—2832no—
106#390—2831no—
107#343D28311yescharacteristic, complemented
108C2×#41—2832no—
109C22×D4—2831no—
110AGL(1,ℤ/8)—5664no—
111AGL(1,ℤ/8)—5664no—
112C2×SD16—5662no—
113C2×D8—5662no—
114C2×M16C2×D28312yes—
115C22⋊Q8—5662no—
116#121—5662no—
117#121—5662no—
118C2×C4⋊C4C2×D28311yescharacteristic
119C2×C22⋊C4—5662no—
120C2×C42—2831no—
121#104—5664no—
122C24—5661no—
123#41—5662no—
124#41—5662no—
125#41—5662no—
126#41—5662no—
127C2×Q8—2832no—
128C2×D4—2832no—
129C2×D4—2832no—
130C2×D4—5662no—
131C2×D4—5662no—
132C2×D4—5662no—
133C2×D4—5662no—
134C2×D4—5661no—
135C22×C4—5661no—
136C22×C4—5662no—
137C22×C4D113212yes—
138C22×C4C22×D28311yescharacteristic
139SD16—5668no—
140D8—5668no—
141M16—22no—
142M16D113214yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—5662no—
146C22⋊C4—5664no—
147C22⋊C4—11324no—
148C42—5662no—
149C23—5662no—
150C23—5662no—
151C23—11322no—
152C23—11322no—
153C23—11321no—
154C23—11321no—
155C23C2×D113211yescharacteristic
156Q8—5662no—
157Q8—5662no—
158D4—5662no—
159D4—5664no—
160D4—5662no—
161D4—11322no—
162D4—11322no—
163D4—11322no—
164D4—22642no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—5662no—
168C2×C4—5662no—
169C2×C4—11321no—
170C2×C4—11321no—
171C2×C4—11322no—
172C2×C4—11322no—
173C2×C4D4×D28311yescharacteristic
174C2×C4D4×D28312yes—
175C2×C4C2×D113212yes—
176C2×C4#1798539311yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—11324no—
181C22—11322no—
182C22—11322no—
183C22—11322no—
184C22—11322no—
185C22—22642no—
186C22—22641no—
187C22—22641no—
188C22#2258358011yescharacteristic
189C22#2258358511yescharacteristic
190C22#2258360711yescharacteristic
191C4—42no—
192C4—11322no—
193C4—11322no—
194C4#2258358012yes—
195C4#2258358512yes—
196C2—21no—
197C2—21no—
198C2—22642no—
199C2—22642no—
200C2#3182637511yescharacteristic
201C2#3182663511yescharacteristic
202C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#343×C283C2
socleC22×C283#120
hypercenter#343D283
hypocenterC283#2006
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×#22583638C2semidirect
2. #31827046C2semidirect
3. C2×#22583536C2semidirect
4. #31826366C2semidirect
5. #343×C283C2semidirect
31. C2×D1132D4semidirect
44. M16×C283D4semidirect
101. C283#2006semidirect
107. #343D283semidirect
142. M16D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
#318270462
C2×#225835362
#318263662
#343×C2832
#2006283