Finite Group Databasebeta

← #49096370

Subgroups — #49096370

Order 35968.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#31824263C211yesmaximal, characteristic, complemented
2#31823974C212yesmaximal, complemented
3#31823479C212yesmaximal, complemented
4#31823220C211yesmaximal, characteristic, complemented
5#407×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7#22582912—22no—
8#22582907—22no—
9#22582901—22no—
10#22582862—22no—
11#22582858—22no—
12#22582853—22no—
13#22582848—22no—
14C4×C22⋊D281—24no—
15#22582838C2212yes—
16#22582805—24no—
17C23×C4×C281C2211yescharacteristic
18C2×M16×C281C2211yescharacteristic
19C2×M16×C281C2211yescharacteristic
20C22⋊C8×C281—22no—
21#17985138—22no—
22#17985138—22no—
23#17985138—22no—
24#17985138—22no—
25C2×Dic562D412yescomplemented
26C2×D1124D412yescomplemented
27C2×C22⋊D281—24no—
28C2×C22⋊D281—22no—
29C2×C4×D281—22no—
30Dic1124—22no—
31#17985127—24no—
32D2248—22no—
33C4⋊Dic281—22no—
34#17985117—24no—
35C22⋊Dic281—24no—
36C22⋊Dic281—22no—
37#17985115—24no—
38C4×Dic281D414yescomplemented
39C24×C281D411yescharacteristic
40C22×C4×C281—22no—
41C22×C4×C281—22no—
42C22×C4×C281—21no—
43C22×C4×C281—21no—
44C22×C4×C281D411yescharacteristic
45C22×C4×C281C2311yescharacteristic
46M16×C281—22no—
47M16×C281—22no—
48C2×C8×C281—21no—
49C2×C8×C281D412yescomplemented
50C22×D281—22no—
51Dic562—22no—
52Dic562—22no—
53D1124—22no—
54D1124—22no—
55C22⋊D281—48no—
56C22⋊D281—42no—
57C22⋊D281—42no—
58C2×Dic281—24no—
59C2×Dic281—22no—
60C4×D281—42no—
61C4×D281—42no—
62C23×C281—22no—
63C23×C281—21no—
64C23×C281—42no—
65C23×C281C2×D411yescharacteristic
66C2×C4×C281—22no—
67C2×C4×C281—21no—
68C2×C4×C281—41no—
69C2×C4×C281—42no—
70C2×C4×C281—41no—
71C2×C4×C281C2×D412yes—
72C2×C4×C281C2×D412yes—
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281#4111yescharacteristic
75C8×C281—22no—
76C8×C281—41no—
77C22×C281—22no—
78C22×C281—24no—
79C22×C281—41no—
80C22×C281—42no—
81C22×C281—41no—
82C22×C281—41no—
83C22×C281#12012yes—
84C22×C281#12111yescharacteristic
85C2×D281—44no—
86C2×D281—42no—
87C4×C281—41no—
88C4×C281#12011yescharacteristic
89C4×C281#12112yes—
90C4×C281#12711yescharacteristic
91Dic281—44no—
92Dic281—42no—
93C2×C281—22no—
94C2×C281—21no—
95C2×C281—42no—
96C2×C281#39211yescharacteristic
97D281—82no—
98C281#201011yescharacteristic, complemented, Sylow
99#2010—2811nomaximal, Sylow
100#575—2811no—
101#525—2812no—
102#421—2812no—
103#407D28111yescharacteristic, complemented
104H(3,ℤ/4)—2811no—
105C2×#41—2812no—
106C23×C4C2×D28111yescharacteristic
107#137—5622no—
108AGL(1,ℤ/8)—5622no—
109#135—5622no—
110C2×M16C2×D28111yescharacteristic
111C2×M16C2×D28111yescharacteristic
112#123—5622no—
113C22⋊Q8—5622no—
114#121—5622no—
115#120—5622no—
116C4×D4—5624no—
117#117—2812no—
118#104—5624no—
119C22⋊C8—22no—
120C24D112411yescharacteristic
121#41—5622no—
122#41—5622no—
123#41—5622no—
124#41—5622no—
125C2×Q8—2812no—
126C2×D4—2812no—
127C2×D4—5624no—
128C2×D4—5622no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—5622no—
134C22×C4D112411yescharacteristic
135C22×C4C22×D28111yescharacteristic
136Q16—5622no—
137SD16—5624no—
138D8—5622no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D28112yescomplemented
143C4⋊C4—5624no—
144C4⋊C4—5622no—
145C22⋊C4—5624no—
146C22⋊C4—5624no—
147C22⋊C4—5622no—
148C42—2814no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—5622no—
153C23C2×D112411yescharacteristic
154Q8—5622no—
155Q8—5622no—
156D4—5622no—
157D4—5622no—
158D4—11248no—
159D4—11242no—
160D4—11242no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—5624no—
167C2×C4—5622no—
168C2×C4—11242no—
169C2×C4—11242no—
170C2×C4D4×D28112yes—
171C2×C4D4×D28112yes—
172C2×C4C2×C22⋊D28111yescharacteristic
173C2×C4#1798513811yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—11244no—
183C22—11242no—
184C22#2258284912yes—
185C22#2258285311yescharacteristic
186C4—41no—
187C4—11244no—
188C4—11242no—
189C4#2258284711yescharacteristic
190C4#2258285212yes—
191C4#2258287511yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—22482no—
196C2#3182337211yescharacteristic
subgroupG/H
centerC4#22582875
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#407×C281C2
socleC2×C281#392
hypercenter#407D281
hypocenterC281#2010
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #31824263C2semidirect
2. #31823974C2semidirect
3. #31823479C2semidirect
4. #31823220C2semidirect
5. #407×C281C2semidirect
25. C2×Dic562D4semidirect
26. C2×D1124D4semidirect
38. C4×Dic281D4semidirect
49. C2×C8×C281D4semidirect
98. C281#2010semidirect
103. #407D281semidirect
142. C2×C8C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318242632
#318239742
#318234792
#318232202
#407×C2812
#2010281