Finite Group Databasebeta

← #49095744

Subgroups — #49095744

Order 35968.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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#31823974C211yesmaximal, characteristic
2C22×C4×Dic281C211yesmaximal, characteristic, complemented
3C2×#22582805C212yesmaximal, complemented
4#31823224C212yesmaximal, complemented
5#407×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2211yescharacteristic
7C23×Dic281—21no—
8#22582862—21no—
9#22582858C412yescomplemented
10#22582853C412yescomplemented
11#22582848—21no—
12C4×C22⋊D281—22no—
13#22582838C2211yescharacteristic
14C2×C4×Dic281—24no—
15C2×C4×Dic281—21no—
16C2×C4×Dic281C2212yes—
17#22582805—24no—
18C23×C4×C281C2211yescharacteristic
19C2×M16×C281C2212yes—
20C22⋊C8×C281—22no—
21#17985138—22no—
22#17985138—22no—
23C2×Dic562C2×C411yescharacteristic, complemented
24C2×D1124C2×C411yescharacteristic, complemented
25C2×C22⋊D281—22no—
26C2×C22⋊D281—21no—
27C22×Dic281—24no—
28C22×Dic281—28no—
29C22×Dic281—22no—
30C2×C4×D281—21no—
31C4⋊Dic281C2×C412yescomplemented
32#17985117—22no—
33C22⋊Dic281—22no—
34C22⋊Dic281—21no—
35#17985115—22no—
36C4×Dic281—24no—
37C4×Dic281—22no—
38C4×Dic281—21no—
39C4×Dic281D414yescomplemented
40C24×C281D411yescharacteristic
41C22×C4×C281—22no—
42C22×C4×C281—22no—
43C22×C4×C281C2×C412yes—
44C22×C4×C281D412yes—
45C22×C4×C281D411yescharacteristic
46C22×C4×C281C2311yescharacteristic
47M16×C281—22no—
48M16×C281—22no—
49C2×C8×C281—22no—
50C22×D281—21no—
51Dic562—22no—
52D1124—22no—
53C22⋊D281—44no—
54C22⋊D281—41no—
55C22⋊D281—41no—
56C2×Dic281—216no—
57C2×Dic281—28no—
58C2×Dic281—24no—
59C2×Dic281—22no—
60C2×Dic281—21no—
61C4×D281—42no—
62C23×C281—24no—
63C23×C281—21no—
64C23×C281—21no—
65C23×C281C22⋊C412yes—
66C23×C281C2×D411yescharacteristic
67C2×C4×C281—21no—
68C2×C4×C281—21no—
69C2×C4×C281—24no—
70C2×C4×C281—24no—
71C2×C4×C281C22⋊C412yes—
72C2×C4×C281C22×C411yescharacteristic
73C2×C4×C281C2×D412yes—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281#4112yes—
76C8×C281—42no—
77C22×C281—24no—
78C22×C281—24no—
79C22×C281—22no—
80C22×C281—22no—
81C22×C281—22no—
82C22×C281#10414yescomplemented
83C22×C281C2×C22⋊C411yescharacteristic
84C22×C281#12011yescharacteristic
85C22×C281#12311yescharacteristic
86C2×D281—41no—
87C2×D281—42no—
88C4×C281—22no—
89C4×C281C4×D412yes—
90C4×C281#12112yes—
91Dic281—28no—
92Dic281—41no—
93Dic281—42no—
94C2×C281—21no—
95C2×C281—24no—
96C2×C281—21no—
97C2×C281#38611yescharacteristic
98C2×C281C2×#10412yes—
99D281—81no—
100C281#189611yescharacteristic, complemented, Sylow
101#1896—2811nomaximal, Sylow
102#525—2811no—
103C22×C42—2811no—
104C2×#104—2812no—
105#407D28111yescharacteristic, complemented
106#339—2812no—
107C2×#41—2811no—
108C23×C4—5621no—
109C23×C4C2×D28111yescharacteristic
110C2×M16C2×D28112yes—
111#123—5621no—
112C22⋊Q8—2812no—
113#121—2812no—
114#120—5621no—
115C4×D4—5622no—
116#117—2811no—
117C2×C42—2812no—
118C2×C42—5624no—
119C2×C42—5621no—
120#104—5624no—
121C22⋊C8—22no—
122C24D112411yescharacteristic
123#41—5622no—
124#41—5622no—
125C2×Q8—2811no—
126C2×D4—2811no—
127C2×D4—5622no—
128C2×D4—5621no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—5624no—
132C22×C4—5628no—
133C22×C4—5622no—
134C22×C4—5621no—
135C22×C4C4×D28112yes—
136C22×C4C22⋊D28112yes—
137C22×C4D112411yescharacteristic
138C22×C4C22×D28111yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—2812no—
143C4⋊C4—5622no—
144C22⋊C4—5622no—
145C22⋊C4—5621no—
146C22⋊C4—5622no—
147C42—2814no—
148C42—5624no—
149C42—5622no—
150C42—5621no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—5621no—
155C23#1798511512yes—
156C23C2×D112411yescharacteristic
157Q8—5622no—
158D4—5622no—
159D4—11244no—
160D4—11241no—
161D4—11241no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—56216no—
167C2×C4—5628no—
168C2×C4—5624no—
169C2×C4—5622no—
170C2×C4—5621no—
171C2×C4—11242no—
172C2×C4#1798511512yes—
173C2×C4C2×C4×D28111yescharacteristic
174C2×C4D4×D28112yes—
175C2×C4C2×C22⋊D28111yescharacteristic
176C2×C4#1798513712yes—
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—11242no—
184C22—11241no—
185C22#2258280514yescomplemented
186C22C2×#1798511511yescharacteristic
187C22#2258284911yescharacteristic
188C22#2258286311yescharacteristic
189C4—22no—
190C4—5628no—
191C4—11242no—
192C4—11241no—
193C4#2258283912yes—
194C4#2258285112yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—22481no—
199C2#3182334011yescharacteristic
200C2C2×#2258280512yes—
subgroupG/H
centerC2×C4C2×C22⋊D281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#407×C281C2
socleC22×C281C2×C22⋊C4
prime radical#31823974C2
cosocleC22×C4×C281C23
hypercenter#407D281
hypocenterC281#1896
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic281C2semidirect
3. C2×#22582805C2semidirect
4. #31823224C2semidirect
5. #407×C281C2semidirect
9. #22582858C4semidirect
10. #22582853C4semidirect
23. C2×Dic562C2×C4semidirect
24. C2×D1124C2×C4semidirect
31. C4⋊Dic281C2×C4semidirect
39. C4×Dic281D4semidirect
82. C22×C281#104semidirect
100. C281#1896semidirect
105. #407D281semidirect
185. C22#22582805semidirect

Maximal subgroups

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

subgroupindex
#318239742
C22×C4×Dic2812
C2×#225828052
#318232242
#407×C2812
#1896281