Finite Group Databasebeta

← #49121709

Subgroups — #49121709

Order 36224.

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

normal subgroups only

This group has 358 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
1#31826976C211yesmaximal, characteristic
2C2×#22583538C212yesmaximal, complemented
3#31826429C211yesmaximal, characteristic, complemented
4#31826225C212yesmaximal, complemented
5C2×#117×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2211yescharacteristic
7C2×#17985376C2212yes—
8#22583593—21no—
9#22583589C412yescomplemented
10#22583584C412yescomplemented
11#22583579—21no—
12C4×C22⋊D283—22no—
13#22583569C2211yescharacteristic
14#22583538—24no—
15C22⋊(C283⋊C8)—22no—
16C23×C4×C283C2211yescharacteristic
17#117×C283—24no—
18C2×C4⋊C4×C283—21no—
19C2×C22⋊C4×C283—21no—
20C2×C42×C283C2212yes—
21#17985392—22no—
22#17985392—22no—
23C2×Dic566C2×C411yescharacteristic
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283—22no—
26C2×C22⋊D283—21no—
27C2×C4×D283—21no—
28#17985376—22no—
29#17985376—22no—
30C2×C283⋊C8—22no—
31C4⋊Dic283C2×C412yes—
32Dic283⋊C4—22no—
33C22⋊Dic283—22no—
34C22⋊Dic283—21no—
35(C2×D283)⋊C4—22no—
36C4×Dic283—21no—
37C24×C283D411yescharacteristic
38C22×C4×C283—22no—
39C22×C4×C283—22no—
40C22×C4×C283—22no—
41C22×C4×C283C2×C412yes—
42C22×C4×C283D411yescharacteristic
43C22×C4×C283D412yes—
44C22×C4×C283C2311yescharacteristic
45C4⋊C4×C283—24no—
46C22⋊C4×C283—24no—
47C42×C283—22no—
48C42×C283D414yescomplemented
49C22×D283—21no—
50Dic566—22no—
51D1132—22no—
52C22⋊D283—44no—
53C22⋊D283—41no—
54C22⋊D283—41no—
55C2×Dic283—22no—
56C2×Dic283—21no—
57C4×D283—42no—
58C283⋊C8—42no—
59C23×C283—21no—
60C23×C283—21no—
61C23×C283—42no—
62C23×C283C22⋊C412yes—
63C23×C283C2×D411yescharacteristic
64C2×C4×C283—21no—
65C2×C4×C283—21no—
66C2×C4×C283—24no—
67C2×C4×C283—24no—
68C2×C4×C283—24no—
69C2×C4×C283—44no—
70C2×C4×C283C22⋊C412yes—
71C2×C4×C283C22×C411yescharacteristic
72C2×C4×C283C2×D412yes—
73C2×C4×C283C2×D411yescharacteristic
74C2×C4×C283#4112yes—
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×C283—44no—
88C4×C283C4×D412yes—
89C4×C283#12112yes—
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×#117D28311yescharacteristic, complemented
102C2×#104—2832no—
103#407—2831no—
104#339—2832no—
105C2×#41—2831no—
106C23×C4C2×D28311yescharacteristic
107C2×M16—2832no—
108#123—5661no—
109C22⋊Q8—2832no—
110#121—2832no—
111#120—5661no—
112C4×D4—5662no—
113#117—24no—
114#117—2831no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D28312yes—
118#104—5664no—
119C22⋊C8—5662no—
120C24C22⋊D28311yescharacteristic
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—22no—
130C22×C4—5661no—
131C22×C4C4×D28312yes—
132C22×C4C22⋊D28311yescharacteristic
133C22×C4D113212yes—
134C22×C4C22×D28311yescharacteristic
135M16—5662no—
136M16—5662no—
137C2×C8—5662no—
138C4⋊C4—24no—
139C4⋊C4—2832no—
140C4⋊C4—5662no—
141C22⋊C4—24no—
142C22⋊C4—5662no—
143C22⋊C4—5661no—
144C22⋊C4—5662no—
145C42—22no—
146C42—5661no—
147C42C22⋊D28314yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—5661no—
152C23(C2×D283)⋊C412yes—
153C23C2×C22⋊D28311yescharacteristic
154Q8—5662no—
155D4—5662no—
156D4—11324no—
157D4—11321no—
158D4—11321no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—5662no—
166C2×C4—5661no—
167C2×C4—11322no—
168C2×C4(C2×D283)⋊C412yes—
169C2×C4C2×C4×D28311yescharacteristic
170C2×C4C2×C22⋊D28312yes—
171C2×C4C2×D113211yescharacteristic
172C2×C4#1798539212yes—
173C8—11322no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—11322no—
181C22—11321no—
182C22C2×(C2×D283)⋊C411yescharacteristic
183C22#2258357911yescharacteristic
184C22#2258359311yescharacteristic
185C4—22no—
186C4—44no—
187C4—11322no—
188C4—11321no—
189C4C4×C22⋊D28312yes—
190C4#2258358412yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—22641no—
195C2#3182634411yescharacteristic
196C2#3182648312yes—
subgroupG/H
centerC2×C4C2×D1132
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#117×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826976C2
cosocleC22×C4×C283C23
hypercenterC2×#117D283
hypocenterC283#1897
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#22583538C2semidirect
3. #31826429C2semidirect
4. #31826225C2semidirect
5. C2×#117×C283C2semidirect
9. #22583589C4semidirect
10. #22583584C4semidirect
48. C42×C283D4semidirect
98. C283#1897semidirect
101. C2×#117D283semidirect
147. C42C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
C2×#225835382
#318264292
#318262252
C2×#117×C2832
#1897283