Finite Group Databasebeta

← #49098104

Subgroups — #49098104

Order 35968.

428 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 177 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×#22582871C211yesmaximal, characteristic
2#31823360C212yesmaximal
3#31823350C212yesmaximal
4#31823348C212yesmaximal
5#31823346C212yesmaximal
6#31823345C212yesmaximal
7C4×C4⋊Dic281C211yesmaximal, characteristic
8#31823314C212yesmaximal
9#383×C281C211yesmaximal, characteristic
10#22582871C418yescomplemented
11C2×C4⋊Dic281C2212yes—
12C2×C4⋊Dic281C2211yescharacteristic
13C2×C4⋊Dic281C2211yescharacteristic
14C2×#17985117C2212yes—
15C2×#17985117C2212yes—
16C2×#17985117C2212yes—
17C2×#17985117C2212yes—
18C2×C4×Dic281C2212yes—
19C2×C4×Dic281C2212yes—
20C2×C4×Dic281C2211yescharacteristic
21C2×C4×Dic281C2211yescharacteristic
22#22582786C2212yes—
23#22582786C2212yes—
24#22582786C2212yes—
25#22582786C2212yes—
26#22582786C2212yes—
27C2×C42×C281C2211yescharacteristic
28#95×C281C2211yescharacteristic
29#95×C281C2212yes—
30#95×C281C2212yes—
31#95×C281C2211yescharacteristic
32C22×Dic281C2312yes—
33C22×Dic281C2312yes—
34C22×Dic281C2312yes—
35C22×Dic281C2312yes—
36C4⋊Dic281—24no—
37C4⋊Dic281C2×C414yes—
38C4⋊Dic281C2×C414yes—
39#17985117—24no—
40#17985117—42no—
41#17985117C2×C418yes—
42#17985117C2×C418yes—
43C4×Dic281—24no—
44C4×Dic281—41no—
45C4×Dic281—41no—
46C4×Dic281—42no—
47C22×C4×C281C2312yes—
48C22×C4×C281C2312yes—
49C22×C4×C281C2311yescharacteristic
50C22×C4×C281C2311yescharacteristic
51C22×C4×C281C2311yescharacteristic
52C42×C281C2×C414yes—
53C2×Dic281—22no—
54C2×Dic281—22no—
55C2×Dic281—22no—
56C2×Dic281—22no—
57C2×Dic281—22no—
58C2×Dic281—22no—
59C2×Dic281—22no—
60C2×Dic281—22no—
61C2×Dic281—22no—
62C2×Dic281C22×C414yes—
63C2×Dic281C22×C414yes—
64C2×Dic281#4114yes—
65C23×C281C2411yescharacteristic
66C2×C4×C281—22no—
67C2×C4×C281—21no—
68C2×C4×C281—22no—
69C2×C4×C281—21no—
70C2×C4×C281—22no—
71C2×C4×C281—22no—
72C2×C4×C281—22no—
73C2×C4×C281—22no—
74C2×C4×C281—22no—
75C2×C4×C281—22no—
76C2×C4×C281C22×C412yes—
77C2×C4×C281C22×C412yes—
78C2×C4×C281C22×C412yes—
79C22×C281C23×C411yescharacteristic
80C22×C281C2×#4112yes—
81C22×C281H(5,𝔽2)11yescharacteristic
82C22×C2812−1+412yes—
83C22×C2812−1+411yescharacteristic
84C4×C281—22no—
85C4×C281—22no—
86C4×C281—22no—
87C4×C281—42no—
88C4×C281—42no—
89Dic281—24no—
90Dic281—24no—
91Dic281—24no—
92Dic281—42no—
93C2×C281C4×#4111yescharacteristic
94C2×C281#51911yescharacteristic
95C2×C281#52011yescharacteristic
96C2×C281#53912yes—
97C2×C281#54112yes—
98C281#233611yescharacteristic, complemented, Sylow
99#2336—2811nomaximal, Sylow
100C2×#125—2811no—
101#389—2812no—
102#387—2812no—
103#387—2812no—
104#387—2812no—
105#387—2812no—
106#383D28111yescharacteristic
107C4×C4⋊C4—2811no—
108C4×C4⋊C4—2812no—
109#125—2818no—
110C2×C4⋊C4—2812no—
111C2×C4⋊C4—2812no—
112C2×C4⋊C4—2811no—
113C2×C4⋊C4—2811no—
114C2×C4⋊C4—2812no—
115C2×C4⋊C4—2812no—
116C2×C4⋊C4—2812no—
117C2×C42—2812no—
118C2×C42—2811no—
119C2×C42—2811no—
120C2×C42—2812no—
121C2×C42C2×D28111yescharacteristic
122#95—2812no—
123#95—2812no—
124#95—2812no—
125#95—2812no—
126#95—2812no—
127#95C2×D28112yes—
128#95C2×D28111yescharacteristic
129#95C2×D28112yes—
130#95C2×D28111yescharacteristic
131C22×C4—2812no—
132C22×C4—2812no—
133C22×C4—2812no—
134C22×C4—2812no—
135C22×C4C22×D28112yes—
136C22×C4C22×D28112yes—
137C22×C4C22×D28111yescharacteristic
138C22×C4C22×D28111yescharacteristic
139C22×C4C22×D28111yescharacteristic
140C4⋊C4—2818no—
141C4⋊C4—2818no—
142C4⋊C4—2814no—
143C4⋊C4—2814no—
144C4⋊C4—5624no—
145C4⋊C4—5624no—
146C4⋊C4—11242no—
147C42—5624no—
148C42—11241no—
149C42—11241no—
150C42—11242no—
151C42C4×D28114yes—
152C23C23×D28111yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—2814no—
164C2×C4—2814no—
165C2×C4—2814no—
166C2×C4—5622no—
167C2×C4—5622no—
168C2×C4—5622no—
169C2×C4—5622no—
170C2×C4—5622no—
171C2×C4—5622no—
172C2×C4—5622no—
173C2×C4—5622no—
174C2×C4—5622no—
175C2×C4C2×C4×D28112yes—
176C2×C4C2×C4×D28112yes—
177C2×C4C2×C4×D28112yes—
178C22C22×C4×D28111yescharacteristic
179C22#41×D28112yes—
180C22#2258292511yescharacteristic
181C22#2258292612yes—
182C22#2258292611yescharacteristic
183C4—22no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—5624no—
189C4—5624no—
190C4—5624no—
191C4—11242no—
192C2#3182393111yescharacteristic
193C2#3182394011yescharacteristic
194C2#3182394311yescharacteristic
195C2#3182405412yes—
196C2#3182407012yes—
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#383×C281C2
socle, prime radical, cosocleC23×C281C24
hypercenter#383D281
hypocenterC281#2336
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #22582871C4semidirect
98. C281#2336semidirect

Maximal subgroups

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

subgroupindex
C2×#225828712
#318233602
#318233502
#318233482
#318233462
#318233452
C4×C4⋊Dic2812
#318233142
#383×C2812
#2336281