Finite Group Databasebeta

← #49097683

Subgroups — #49097683

Order 35968.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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
1C23×C4×D281C211yesmaximal, characteristic
2C2×#22582835C212yesmaximal, complemented
3#31823326C211yesmaximal, characteristic, complemented
4#31823322C214yesmaximal, complemented
5#31823318C212yesmaximal
6#31823310C214yesmaximal, complemented
7#381×C281C211yesmaximal, characteristic, complemented
8C24×D281C2211yescharacteristic
9C23×Dic281C2211yescharacteristic
10C22×C4×D281—28no—
11C22×C4×D281C418yescomplemented
12C22×C4×D281C2212yes—
13C22×C4×D281C2212yes—
14#22582835—28no—
15C2×#17985117C2214yescomplemented
16C2×C22⋊Dic281C2212yes—
17C2×#17985115C2218yes—
18C2×C4×Dic281C2214yescomplemented
19#22582786C2214yescomplemented
20C23×C4×C281C2211yescharacteristic
21C2×C22⋊C4×C281C2212yes—
22#95×C281C2214yescomplemented
23C23×D281—28no—
24C23×D281—24no—
25C23×D281C2×C414yes—
26C23×D281C2312yes—
27C22×Dic281C2×C414yes—
28C22×Dic281D418yes—
29C22×Dic281C2314yes—
30C22×Dic281C2311yescharacteristic
31C22×Dic281C2311yescharacteristic
32C2×C4×D281—232no—
33C2×C4×D281—28no—
34C2×C4×D281—28no—
35C2×C4×D281C2×C418yes—
36C2×C4×D281C2×C418yes—
37#17985117—28no—
38C22⋊Dic281—24no—
39#17985115—216no—
40C4×Dic281—28no—
41C24×C281C2311yescharacteristic
42C22×C4×C281—24no—
43C22×C4×C281C2×C414yes—
44C22×C4×C281C2314yes—
45C22×C4×C281C2312yes—
46C22⋊C4×C281—24no—
47C22×D281—232no—
48C22×D281—28no—
49C22×D281—24no—
50C22×D281—24no—
51C22×D281—216no—
52C22×D281C22×C414yes—
53C22×D281#4118yes—
54C2×Dic281—24no—
55C2×Dic281—28no—
56C2×Dic281C22⋊C4116yescomplemented
57C2×Dic281C22×C412yes—
58C2×Dic281C22×C412yes—
59C2×Dic281C2×D414yes—
60C2×Dic281C2×D414yes—
61C4×D281—216no—
62C4×D281—216no—
63C23×C281—24no—
64C23×C281C22×C412yes—
65C23×C281C2×D414yes—
66C23×C281C2411yescharacteristic
67C2×C4×C281—28no—
68C2×C4×C281—24no—
69C2×C4×C281—24no—
70C2×C4×C281—28no—
71C2×C4×C281C22×C414yes—
72C22×C281—24no—
73C22×C281—28no—
74C22×C281C2×C22⋊C414yes—
75C22×C281C23×C411yescharacteristic
76C22×C281C22×D412yes—
77C22×C281C2×#4114yes—
78C2×D281—232no—
79C2×D281—24no—
80C2×D281—24no—
81C2×D281—216no—
82C2×D281#11718yescomplemented
83C4×C281—24no—
84C4×C281—44no—
85Dic281—44no—
86Dic281C2×C22⋊C414yes—
87Dic281C2×C22⋊C414yes—
88C2×C281—24no—
89C2×C281C22×C22⋊C411yescharacteristic
90C2×C281C2×#11712yes—
91C2×C281#52514yes—
92D281—28no—
93C281#228011yescharacteristic, complemented, Sylow
94#2280—2811nomaximal, Sylow
95C24×C4—2811no—
96C2×#117—2812no—
97#381—2811no—
98#381D28111yescharacteristic, complemented
99#380—2814no—
100#379—2812no—
101C4×C22⋊C4—2814no—
102C25—2811no—
103C23×C4—2811no—
104C23×C4—2818no—
105C23×C4—2812no—
106C23×C4—2812no—
107C23×C4—5628no—
108C23×C4C2×D28111yescharacteristic
109#117—5628no—
110C2×C4⋊C4—2814no—
111C2×C22⋊C4—2812no—
112C2×C22⋊C4—2818no—
113C2×C22⋊C4C2×D28112yes—
114C2×C42—2814no—
115#95—2814no—
116#95C2×D28114yescomplemented
117C24—2812no—
118C24—2814no—
119C24—5628no—
120C24—5624no—
121C24C22×D28111yescharacteristic
122C22×C4—24no—
123C22×C4—2814no—
124C22×C4—2818no—
125C22×C4—2811no—
126C22×C4—2811no—
127C22×C4—2818no—
128C22×C4—2818no—
129C22×C4—2814no—
130C22×C4—56232no—
131C22×C4—5628no—
132C22×C4—5628no—
133C22×C4C4×D28114yes—
134C22×C4C22×D28114yes—
135C22×C4C22×D28112yes—
136C4⋊C4—5628no—
137C22⋊C4—24no—
138C22⋊C4—56216no—
139C22⋊C4—5624no—
140C42—5628no—
141C23—24no—
142C23—2814no—
143C23—2818no—
144C23—56216no—
145C23—56232no—
146C23—5628no—
147C23—5624no—
148C23—5624no—
149C23C2×C4×D28112yes—
150C23D4×D28114yes—
151C23C23×D28111yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—28116no—
157C2×C4—2812no—
158C2×C4—2812no—
159C2×C4—2814no—
160C2×C4—2814no—
161C2×C4—56216no—
162C2×C4—56216no—
163C2×C4—5624no—
164C2×C4—5628no—
165C2×C4C2×C4×D28114yes—
166C22—24no—
167C22—28no—
168C22—2818no—
169C22—56232no—
170C22—5624no—
171C22—5624no—
172C22—56216no—
173C22C22⋊C4×D28114yes—
174C22C22×C4×D28111yescharacteristic
175C22C2×D4×D28112yes—
176C22#41×D28114yes—
177C4—24no—
178C4—44no—
179C4—2814no—
180C4—2814no—
181C4—11244no—
182C2—24no—
183C2—5628no—
184C2C2×C22⋊C4×D28111yescharacteristic
185C2#117×D28112yes—
186C2#3182397114yes—
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#381×C281C2
socle, cosocleC23×C281C24
prime radicalC24×D281C22
hypercenter#381D281
hypocenterC281#2280
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22582835C2semidirect
3. #31823326C2semidirect
4. #31823322C2semidirect
6. #31823310C2semidirect
7. #381×C281C2semidirect
11. C22×C4×D281C4semidirect
15. C2×#17985117C22semidirect
18. C2×C4×Dic281C22semidirect
19. #22582786C22semidirect
22. #95×C281C22semidirect
56. C2×Dic281C22⋊C4semidirect
82. C2×D281#117semidirect
93. C281#2280semidirect
98. #381D281semidirect
116. #95C2×D281semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D2812
C2×#225828352
#318233262
#318233222
#318233182
#318233102
#381×C2812
#2280281