Finite Group Databasebeta

← #49096371

Subgroups — #49096371

Order 35968.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#31823975C212yesmaximal, complemented
3#31823481C212yesmaximal, complemented
4#31823426C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7C22×C4×D281C2211yescharacteristic
8#22582912—22no—
9#22582907—22no—
10#22582901—22no—
11C2×#17985122C2211yescharacteristic
12#22582863—22no—
13#22582859—22no—
14#22582854—22no—
15#22582849—22no—
16C4×D1124—24no—
17#22582807—24no—
18#22582791—22no—
19C2×M16×C281C2211yescharacteristic
20#117×C281C2212yes—
21C23×D281D411yescharacteristic
22#17985138—22no—
23#17985138—22no—
24#17985138—22no—
25#17985138—22no—
26C2×Dic562D412yescomplemented
27C2×D1124—24no—
28C2×D1124D412yescomplemented
29C2×C22⋊D281—22no—
30C22×Dic281D411yescharacteristic
31C2×C4×D281—21no—
32C2×C4×D281—22no—
33C2×C4×D281—22no—
34C2×C4×D281—22no—
35C2×C4×D281—21no—
36Dic1124—22no—
37#17985127—24no—
38D2248—22no—
39#17985122—22no—
40C2×#14555886—21no—
41C4⋊Dic281—24no—
42#17985115—24no—
43#17985115—24no—
44C22×C4×C281C2311yescharacteristic
45M16×C281—22no—
46C2×C8×C281D412yescomplemented
47C4⋊C4×C281—22no—
48C22⋊C4×C281—22no—
49C42×C281D414yescomplemented
50C22×D281—22no—
51C22×D281—21no—
52C22×D281—22no—
53C22×D281—42no—
54Dic562—22no—
55Dic562—22no—
56D1124—22no—
57D1124—22no—
58D1124—48no—
59C22⋊D281—42no—
60C22⋊D281—42no—
61C2×Dic281—22no—
62C2×Dic281—22no—
63C2×Dic281—21no—
64C4×D281—41no—
65C4×D281—42no—
66C4×D281—42no—
67C4×D281—41no—
68C4×D281—42no—
69#14555886—41no—
70C23×C281C2×D411yescharacteristic
71C2×C4×C281—24no—
72C2×C4×C281C2×D412yes—
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281C2×D412yes—
75C2×C4×C281#4111yescharacteristic
76C8×C281—22no—
77C22×C281—41no—
78C22×C281#12012yes—
79C22×C281#12111yescharacteristic
80C2×D281—24no—
81C2×D281—22no—
82C2×D281—42no—
83C2×D281—41no—
84C2×D281—41no—
85C2×D281—44no—
86C2×D281—42no—
87C4×C281—44no—
88C4×C281#12011yescharacteristic
89C4×C281#12112yes—
90C4×C281#12711yescharacteristic
91Dic281—41no—
92Dic281—42no—
93C2×C281—22no—
94C2×C281—21no—
95C2×C281#39211yescharacteristic
96D281—42no—
97D281—82no—
98C281#201011yescharacteristic, complemented, Sylow
99#2010—2811nomaximal, Sylow
100#575—2811no—
101#525—2812no—
102#421—2812no—
103#407—2811no—
104H(3,ℤ/4)D28111yescharacteristic, complemented
105C2×#41—2812no—
106C23×C4—2811no—
107#137—5622no—
108AGL(1,ℤ/8)—5622no—
109#135—5622no—
110C2×M16—2811no—
111C2×M16C2×D28111yescharacteristic
112#123—5622no—
113C22⋊Q8—5622no—
114#121—5622no—
115#120—5622no—
116C4×D4—5624no—
117#117C2×D28112yes—
118#104—5624no—
119C22⋊C8—5622no—
120C24—2811no—
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—2811no—
130C22×C4—5622no—
131C22×C4—5621no—
132C22×C4—5622no—
133C22×C4—5622no—
134C22×C4—5621no—
135C22×C4C22×D28111yescharacteristic
136Q16—5622no—
137SD16—5624no—
138D8—5622no—
139M16—22no—
140M16—5622no—
141C2×C8—5621no—
142C2×C8D112412yescomplemented
143C4⋊C4—22no—
144C4⋊C4—5624no—
145C22⋊C4—22no—
146C22⋊C4—5624no—
147C22⋊C4—5624no—
148C42D112414yescomplemented
149C23—5622no—
150C23—5621no—
151C23—5622no—
152C23—11242no—
153C23D4×D28111yescharacteristic
154Q8—5622no—
155Q8—5622no—
156D4—5622no—
157D4—5622no—
158D4—11248no—
159D4—11242no—
160D4—11242no—
161C2×C4—24no—
162C2×C4—5622no—
163C2×C4—5622no—
164C2×C4—5621no—
165C2×C4—11241no—
166C2×C4—11242no—
167C2×C4—11242no—
168C2×C4—11241no—
169C2×C4—11242no—
170C2×C4D4×D28112yes—
171C2×C4C2×D112411yescharacteristic
172C2×C4C2×D112412yes—
173C2×C4#1798513911yescharacteristic
174C8—22no—
175C8—11241no—
176C22—41no—
177C22—5624no—
178C22—5622no—
179C22—11242no—
180C22—11241no—
181C22—11244no—
182C22—11241no—
183C22—11242no—
184C22#2258284912yes—
185C22#2258285411yescharacteristic
186C4—44no—
187C4—11241no—
188C4—11242no—
189C4#2258284911yescharacteristic
190C4#2258285412yes—
191C4#2258287611yescharacteristic
192C2—22no—
193C2—21no—
194C2—11242no—
195C2—22482no—
196C2#3182337311yescharacteristic
subgroupG/H
centerC4#22582876
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
FittingH(3,ℤ/4)×C281C2
socleC2×C281#392
hypercenterH(3,ℤ/4)D281
hypocenterC281#2010
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #31824263C2semidirect
2. #31823975C2semidirect
3. #31823481C2semidirect
4. #31823426C2semidirect
5. H(3,ℤ/4)×C281C2semidirect
26. C2×Dic562D4semidirect
28. C2×D1124D4semidirect
46. C2×C8×C281D4semidirect
49. C42×C281D4semidirect
98. C281#2010semidirect
104. H(3,ℤ/4)D281semidirect
142. C2×C8D1124semidirect
148. C42D1124semidirect

Maximal subgroups

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

subgroupindex
#318242632
#318239752
#318234812
#318234262
H(3,ℤ/4)×C2812
#2010281