Finite Group Databasebeta

← #49097899

Subgroups — #49097899

Order 35968.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×C22⋊Dic281C211yesmaximal, characteristic
2#31823357C214yesmaximal, complemented
3#31823351C214yesmaximal, complemented
4#31823321C212yesmaximal, complemented
5#31823319C211yesmaximal, characteristic
6C22⋊C4×Dic281C212yesmaximal, complemented
7#379×C281C211yesmaximal, characteristic
8C23×Dic281C2211yescharacteristic
9C23×Dic281C2211yescharacteristic
10C2×#17985117C2214yescomplemented
11C2×C22⋊Dic281C418yescomplemented
12C2×C22⋊Dic281C2212yes—
13C2×C22⋊Dic281C2212yes—
14C2×C22⋊Dic281C2212yes—
15C2×C22⋊Dic281C2212yes—
16C2×C22⋊Dic281C2212yes—
17C2×C4×Dic281C2214yescomplemented
18#22582786C2214yescomplemented
19#22582786C2214yescomplemented
20C25×C281C2211yescharacteristic
21C2×C22⋊C4×C281C2212yes—
22C2×C22⋊C4×C281C2212yes—
23C2×C22⋊C4×C281C2212yes—
24C22×Dic281—42no—
25C22×Dic281—42no—
26C22×Dic281C2×C414yes—
27C22×Dic281C2×C414yes—
28C22×Dic281C2314yes—
29C22×Dic281C2312yes—
30C22×Dic281C2312yes—
31#17985117—44no—
32C22⋊Dic281—24no—
33C22⋊Dic281—42no—
34C22⋊Dic281—42no—
35C22⋊Dic281C2×C418yes—
36C22⋊Dic281C2×C418yes—
37C4×Dic281—44no—
38C24×C281—24no—
39C24×C281—42no—
40C24×C281—42no—
41C24×C281C2×C414yes—
42C24×C281C2311yescharacteristic
43C24×C281C2311yescharacteristic
44C24×C281C2311yescharacteristic
45C22×C4×C281C2314yes—
46C22⋊C4×C281—24no—
47C22⋊C4×C281—42no—
48C22⋊C4×C281—42no—
49C2×Dic281—24no—
50C2×Dic281—24no—
51C2×Dic281—24no—
52C2×Dic281—24no—
53C2×Dic281—24no—
54C2×Dic281—44no—
55C2×Dic281—44no—
56C2×Dic281C22×C414yes—
57C2×Dic281C22×C414yes—
58C23×C281—22no—
59C23×C281—22no—
60C23×C281—28no—
61C23×C281—22no—
62C23×C281—22no—
63C23×C281—22no—
64C23×C281—22no—
65C23×C281—22no—
66C23×C281—22no—
67C23×C281—44no—
68C23×C281—44no—
69C23×C281—416no—
70C23×C281C22×C412yes—
71C23×C281C22×C412yes—
72C23×C281C22×C412yes—
73C23×C281#4114yes—
74C23×C281C2411yescharacteristic
75C2×C4×C281—24no—
76C2×C4×C281—24no—
77C2×C4×C281—24no—
78C22×C281—22no—
79C22×C281—22no—
80C22×C281—28no—
81C22×C281—22no—
82C22×C281—22no—
83C22×C281—22no—
84C22×C281—22no—
85C22×C281—22no—
86C22×C281—22no—
87C22×C281—416no—
88C22×C281—44no—
89C22×C281—44no—
90C22×C281#11714yes—
91C22×C281C23×C411yescharacteristic
92C22×C281C2×#4112yes—
93C22×C281H(5,𝔽2)12yes—
94C22×C281H(5,𝔽2)12yes—
95C4×C281—44no—
96Dic281—24no—
97Dic281—24no—
98Dic281—44no—
99C2×C281—24no—
100C2×C281—42no—
101C2×C281—42no—
102C2×C281C2×#11711yescharacteristic
103C2×C281#51811yescharacteristic
104C2×C281#51811yescharacteristic
105C2×C281#53814yes—
106C281#231211yescharacteristic, complemented, Sylow
107#2312—2811nomaximal, Sylow
108C22×C22⋊C4—2811no—
109#388—2814no—
110#388—2814no—
111#380—2812no—
112#379—2811no—
113#379D28111yescharacteristic
114C4×C22⋊C4—2812no—
115C25C2×D28111yescharacteristic
116C23×C4—2811no—
117C23×C4—2811no—
118C2×C4⋊C4—2814no—
119C2×C22⋊C4—2818no—
120C2×C22⋊C4—2812no—
121C2×C22⋊C4—2812no—
122C2×C22⋊C4—2812no—
123C2×C22⋊C4—2812no—
124C2×C22⋊C4—2812no—
125C2×C22⋊C4C2×D28112yes—
126C2×C22⋊C4C2×D28112yes—
127C2×C22⋊C4C2×D28112yes—
128C2×C42—2814no—
129#95—2814no—
130#95—2814no—
131C24—24no—
132C24—42no—
133C24—42no—
134C24C4×D28114yes—
135C24C22×D28111yescharacteristic
136C24C22×D28111yescharacteristic
137C24C22×D28111yescharacteristic
138C22×C4—2812no—
139C22×C4—2812no—
140C22×C4—2814no—
141C22×C4—2814no—
142C22×C4—2814no—
143C22×C4—11242no—
144C22×C4—11242no—
145C22×C4C22×D28114yes—
146C4⋊C4—11244no—
147C22⋊C4—24no—
148C22⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4—2818no—
151C22⋊C4—2818no—
152C22⋊C4—5624no—
153C22⋊C4—11242no—
154C22⋊C4—11242no—
155C42—11244no—
156C23—22no—
157C23—22no—
158C23—28no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—44no—
166C23—44no—
167C23—416no—
168C23C2×C4×D28112yes—
169C23C2×C4×D28112yes—
170C23C2×C4×D28112yes—
171C23#1798513714yes—
172C23C23×D28111yescharacteristic
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—2814no—
177C2×C4—2814no—
178C2×C4—5624no—
179C2×C4—5624no—
180C2×C4—5624no—
181C2×C4—5624no—
182C2×C4—5624no—
183C2×C4—11244no—
184C2×C4—11244no—
185C22—22no—
186C22—22no—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—416no—
195C22—44no—
196C22—44no—
197C22#2258283514yes—
198C22C22×C4×D28111yescharacteristic
199C22C2×#1798513712yes—
200C22#2258292412yes—
201C22#2258292412yes—
202C4—44no—
203C4—5624no—
204C4—5624no—
205C4—11244no—
206C2—24no—
207C2—42no—
208C2—42no—
209C2C2×#2258283511yescharacteristic
210C2#3182393611yescharacteristic
211C2#3182393611yescharacteristic
212C2#3182404814yes—
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#379×C281C2
socle, cosocleC23×C281C24
prime radicalC25×C281C22
hypercenter#379D281
hypocenterC281#2312
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #31823357C2semidirect
3. #31823351C2semidirect
4. #31823321C2semidirect
6. C22⋊C4×Dic281C2semidirect
10. C2×#17985117C22semidirect
11. C2×C22⋊Dic281C4semidirect
17. C2×C4×Dic281C22semidirect
18. #22582786C22semidirect
19. #22582786C22semidirect
106. C281#2312semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Dic2812
#318233572
#318233512
#318233212
#318233192
C22⋊C4×Dic2812
#379×C2812
#2312281