Finite Group Databasebeta

← #49121707

Subgroups — #49121707

Order 36224.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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#31826976C211yesmaximal, characteristic
2C2×#22583569C211yesmaximal, characteristic, complemented
3C2×#22583536C212yesmaximal, complemented
4#31826226C212yesmaximal, complemented
5#407×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2211yescharacteristic
7#22583593—21no—
8#22583589C412yescomplemented
9#22583584C412yescomplemented
10#22583579—21no—
11C4×C22⋊D283—22no—
12#22583569—24no—
13#22583569C2211yescharacteristic
14C2×C4⋊Dic283—21no—
15C2×C22⋊Dic283—21no—
16C2×C4×Dic283C2212yes—
17#22583536—24no—
18C23×C4×C283C2211yescharacteristic
19C2×M16×C283C2212yes—
20C22⋊C8×C283—22no—
21#17985392—22no—
22#17985392—22no—
23C2×Dic566C2×C411yescharacteristic
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283—22no—
26C2×C22⋊D283—21no—
27C22×Dic283—22no—
28C2×C4×D283—21no—
29C4⋊Dic283—24no—
30C4⋊Dic283C2×C412yes—
31Dic283⋊C4—22no—
32C22⋊Dic283—24no—
33C22⋊Dic283—22no—
34C22⋊Dic283—21no—
35(C2×D283)⋊C4—22no—
36C4×Dic283—22no—
37C4×Dic283—21no—
38C4×Dic283D414yescomplemented
39C24×C283D411yescharacteristic
40C22×C4×C283—22no—
41C22×C4×C283—22no—
42C22×C4×C283C2×C412yes—
43C22×C4×C283D412yes—
44C22×C4×C283D411yescharacteristic
45C22×C4×C283C2311yescharacteristic
46M16×C283—22no—
47M16×C283—22no—
48C2×C8×C283—22no—
49C22×D283—21no—
50Dic566—22no—
51D1132—22no—
52C22⋊D283—44no—
53C22⋊D283—41no—
54C22⋊D283—41no—
55C2×Dic283—22no—
56C2×Dic283—21no—
57C2×Dic283—24no—
58C2×Dic283—44no—
59C4×D283—42no—
60C23×C283—21no—
61C23×C283—21no—
62C23×C283—42no—
63C23×C283C22⋊C412yes—
64C23×C283C2×D411yescharacteristic
65C2×C4×C283—21no—
66C2×C4×C283—21no—
67C2×C4×C283—24no—
68C2×C4×C283—24no—
69C2×C4×C283C22⋊C412yes—
70C2×C4×C283C22×C411yescharacteristic
71C2×C4×C283C2×D412yes—
72C2×C4×C283C2×D411yescharacteristic
73C2×C4×C283#4112yes—
74C8×C283—42no—
75C22×C283—22no—
76C22×C283—22no—
77C22×C283—22no—
78C22×C283—22no—
79C22×C283—42no—
80C22×C283—42no—
81C22×C283C2×C22⋊C411yescharacteristic
82C22×C283#12011yescharacteristic
83C22×C283#12311yescharacteristic
84C2×D283—41no—
85C2×D283—42no—
86C4×C283—22no—
87C4×C283C4×D412yes—
88C4×C283#12112yes—
89Dic283—44no—
90Dic283—41no—
91Dic283—42no—
92C2×C283—21no—
93C2×C283—21no—
94C2×C283—42no—
95C2×C283#38611yescharacteristic
96C2×C283#42112yes—
97D283—81no—
98C283#189711yescharacteristic, complemented, Sylow
99#1897—2831nomaximal, Sylow
100#525—2831no—
101C2×#117—2831no—
102C2×#104—2832no—
103#407D28311yescharacteristic, complemented
104#339—2832no—
105C2×#41—2831no—
106C23×C4C2×D28311yescharacteristic
107C2×M16C2×D28312yes—
108#123—5661no—
109C22⋊Q8—2832no—
110#121—2832no—
111#120—5661no—
112C4×D4—5662no—
113#117—2831no—
114#117—5664no—
115C2×C4⋊C4—5661no—
116C2×C22⋊C4—5661no—
117C2×C42—2832no—
118#104—5664no—
119C22⋊C8—22no—
120C24D113211yescharacteristic
121#41—5662no—
122#41—5662no—
123C2×Q8—2831no—
124C2×D4—2831no—
125C2×D4—5662no—
126C2×D4—5661no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—5662no—
130C22×C4—5661no—
131C22×C4C4×D28312yes—
132C22×C4C22⋊D28312yes—
133C22×C4D113211yescharacteristic
134C22×C4C22×D28311yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—2832no—
139C4⋊C4—5664no—
140C4⋊C4—5662no—
141C22⋊C4—5664no—
142C22⋊C4—5662no—
143C22⋊C4—5661no—
144C22⋊C4—5662no—
145C42—2834no—
146C42—5662no—
147C42—5661no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—5661no—
152C23(C2×D283)⋊C412yes—
153C23C2×D113211yescharacteristic
154Q8—5662no—
155D4—5662no—
156D4—11324no—
157D4—11321no—
158D4—11321no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—5662no—
164C2×C4—5661no—
165C2×C4—5664no—
166C2×C4—11324no—
167C2×C4—11322no—
168C2×C4(C2×D283)⋊C412yes—
169C2×C4C2×C4×D28311yescharacteristic
170C2×C4D4×D28312yes—
171C2×C4C2×C22⋊D28311yescharacteristic
172C2×C4#1798539112yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—11322no—
181C22—11321no—
182C22C2×(C2×D283)⋊C411yescharacteristic
183C22#2258358011yescharacteristic
184C22#2258359411yescharacteristic
185C4—22no—
186C4—11324no—
187C4—11322no—
188C4—11321no—
189C4(C22⋊D283)⋊C412yes—
190C4#2258358212yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—22641no—
195C2#3182634211yescharacteristic
196C2#3182648112yes—
subgroupG/H
centerC2×C4C2×C22⋊D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#407×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826976C2
cosocleC22×C4×C283C23
hypercenter#407D283
hypocenterC283#1897
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#22583569C2semidirect
3. C2×#22583536C2semidirect
4. #31826226C2semidirect
5. #407×C283C2semidirect
8. #22583589C4semidirect
9. #22583584C4semidirect
38. C4×Dic283D4semidirect
98. C283#1897semidirect
103. #407D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
C2×#225835692
C2×#225835362
#318262262
#407×C2832
#1897283