Finite Group Databasebeta

← #49096973

Subgroups — #49096973

Order 35968.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824026C211yesmaximal, characteristic
2#31823435C212yesmaximal, complemented
3#31823256C211yesmaximal, characteristic, complemented
4#31823255C212yesmaximal, complemented
5#353×C281C211yesmaximal, characteristic, complemented
6C2×#17985137C2211yescharacteristic
7C2×D4×D281C411yescharacteristic, complemented
8#22582875C2211yescharacteristic
9#22582867C411yescharacteristic, complemented
10#22582866C411yescharacteristic, complemented
11#22582851—22no—
12#22582847—22no—
13#22582836C411yescharacteristic, complemented
14#22582835—22no—
15#22582794C2212yescomplemented
16#22582793—22no—
17#127×C281C2211yescharacteristic
18#99×C281C2212yescomplemented
19C23×D281—21no—
20#17985137—42no—
21C2×Dic562C2×C411yescharacteristic
22C2×D1124C2×C411yescharacteristic
23C2×C22⋊D281—21no—
24C2×C22⋊D281—22no—
25C2×C22⋊D281D412yes—
26D4×D281—42no—
27C22×Dic281D412yes—
28C2×C4×D281C2×C411yescharacteristic
29#17985117—21no—
30#17985117—42no—
31C22⋊Dic281—22no—
32C22⋊Dic281—22no—
33#17985115—21no—
34#17985115—22no—
35C4×Dic281—42no—
36C4×Dic281C2×C411yescharacteristic
37C2×D4×C281—22no—
38C2×D4×C281C2×C411yescharacteristic
39C2×D4×C281C2311yescharacteristic
40C22⋊C4×C281—22no—
41C42×C281C2×C411yescharacteristic
42C22×D281—21no—
43C22×D281—42no—
44C22×D281—82no—
45C22×D281C22⋊C411yescharacteristic
46Dic562—41no—
47D1124—41no—
48C22⋊D281—42no—
49C22⋊D281—42no—
50C22⋊D281—82no—
51C2×Dic281—22no—
52C2×Dic281—22no—
53C2×Dic281—21no—
54C2×Dic281—42no—
55C2×Dic281C22⋊C412yes—
56C2×Dic281C22⋊C411yescharacteristic
57C4×D281—22no—
58C23×C281—21no—
59C23×C281C2×D412yes—
60D4×C281—41no—
61D4×C281—41no—
62D4×C281—82no—
63C2×C4×C281—21no—
64C2×C4×C281—42no—
65C2×C4×C281C22×C411yescharacteristic
66C22×C281—22no—
67C22×C281—42no—
68C22×C281—42no—
69C22×C281—41no—
70C22×C281C2×C22⋊C411yescharacteristic
71C2×D281—21no—
72C2×D281—41no—
73C2×D281—42no—
74C2×D281—41no—
75C2×D281—84no—
76C4×C281—21no—
77C4×C281—41no—
78C4×C281—82no—
79Dic281—22no—
80Dic281—41no—
81Dic281—82no—
82Dic281#9912yes—
83C2×C281—21no—
84C2×C281—42no—
85C2×C281—81no—
86C2×C281C2×#9911yescharacteristic
87D281—41no—
88D281—81no—
89C281#212811yescharacteristic, complemented, Sylow
90#2128—2811nomaximal, Sylow
91#535—2811no—
92#410—2812no—
93#353—2811no—
94#353—2812no—
95#353D28111yescharacteristic, complemented
96C2×#41—2811no—
97C22×D4—2811no—
98#127—2811no—
99#127C2×D28111yescharacteristic
100#124—2811no—
101#124—2811no—
102#121—5622no—
103#120—5622no—
104#117—2811no—
105#117—5622no—
106#99—2812no—
107#99—5622no—
108#99C2×D28112yescomplemented
109C24—5621no—
110#41—11242no—
111C2×Q8—2811no—
112C2×D4—22no—
113C2×D4—2812no—
114C2×D4—2811no—
115C2×D4—5621no—
116C2×D4—5622no—
117C2×D4—11242no—
118C2×D4C4×D28111yescharacteristic
119C2×D4C22×D28111yescharacteristic
120C22×C4—2812no—
121C22×C4—2811no—
122C4⋊C4—5621no—
123C4⋊C4—11242no—
124C22⋊C4—22no—
125C22⋊C4—5622no—
126C22⋊C4—5621no—
127C22⋊C4—5622no—
128C22⋊C4—5622no—
129C42—2811no—
130C42—11242no—
131C42C4×D28111yescharacteristic
132C23—21no—
133C23—2811no—
134C23—5621no—
135C23—11242no—
136C23—22482no—
137C23D4×D28112yes—
138Q8—11241no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—11241no—
143D4—11242no—
144D4—11242no—
145D4—22482no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2811no—
149C2×C4—2812no—
150C2×C4—5622no—
151C2×C4—5622no—
152C2×C4—5622no—
153C2×C4—5621no—
154C2×C4—11242no—
155C2×C4C2×C4×D28111yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—5621no—
161C22—11241no—
162C22—11242no—
163C22—11241no—
164C22—22484no—
165C22C22⋊C4×D28111yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—2812no—
170C4—5622no—
171C4—11241no—
172C4—22482no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—11241no—
177C2—22481no—
178C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#353×C281C2
socleC2×C281C2×#99
prime radical#31824026C2
cosocleC2×D4×C281C23
hypercenter#353D281
hypocenterC281#2128
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #31823435C2semidirect
3. #31823256C2semidirect
4. #31823255C2semidirect
5. #353×C281C2semidirect
7. C2×D4×D281C4semidirect
9. #22582867C4semidirect
10. #22582866C4semidirect
13. #22582836C4semidirect
15. #22582794C22semidirect
18. #99×C281C22semidirect
89. C281#2128semidirect
95. #353D281semidirect
108. #99C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318240262
#318234352
#318232562
#318232552
#353×C2812
#2128281