Finite Group Databasebeta

← #49096971

Subgroups — #49096971

Order 35968.

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

normal subgroups only

This group has 286 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#31824031C211yesmaximal, characteristic
2#99×D281C212yesmaximal, complemented
3#31823258C211yesmaximal, characteristic, complemented
4#31823255C212yesmaximal, complemented
5#354×C281C211yesmaximal, characteristic, complemented
6C2×#17985139C411yescharacteristic, complemented
7C2×D4×D281C2211yescharacteristic
8#22582876C411yescharacteristic, complemented
9#22582875C2211yescharacteristic
10#22582868C411yescharacteristic, complemented
11#22582852—22no—
12#22582849—22no—
13#22582836C411yescharacteristic, complemented
14C22⋊C4×D281—22no—
15#22582794C2212yes—
16#22582793—22no—
17#124×C281C2211yescharacteristic
18#99×C281C2212yes—
19C23×D281D412yes—
20#17985139—42no—
21C2×D1124—21no—
22C2×D1124—22no—
23C2×D1124C2×C411yescharacteristic
24C2×D1124C2×C411yescharacteristic, complemented
25C2×C22⋊D281—22no—
26C2×C22⋊D281D412yes—
27D4×D281—42no—
28C2×C4×D281—21no—
29C2×C4×D281—42no—
30C2×C4×D281C2×C411yescharacteristic
31#17985117—21no—
32C22⋊Dic281—22no—
33#17985115—21no—
34#17985115—22no—
35#17985115—42no—
36C4×Dic281C2×C411yescharacteristic, complemented
37C2×Q8×C281C2×C411yescharacteristic, complemented
38C2×D4×C281C2311yescharacteristic
39C22⋊C4×C281—22no—
40C22⋊C4×C281—22no—
41C42×C281C2×C411yescharacteristic, complemented
42C22×D281—22no—
43C22×D281—22no—
44C22×D281—21no—
45C22×D281—82no—
46C22×D281C22⋊C412yes—
47C22×D281C22⋊C411yescharacteristic
48D1124—41no—
49D1124—41no—
50D1124—42no—
51D1124—82no—
52C22⋊D281—42no—
53C22⋊D281—82no—
54C2×Dic281—21no—
55C2×Dic281—42no—
56C2×Dic281C22⋊C411yescharacteristic
57C4×D281—22no—
58C4×D281—42no—
59C4×D281—84no—
60C23×C281C2×D412yes—
61Q8×C281—41no—
62D4×C281—41no—
63C2×C4×C281—21no—
64C2×C4×C281—21no—
65C2×C4×C281—42no—
66C2×C4×C281C22×C411yescharacteristic
67C22×C281—22no—
68C22×C281—42no—
69C22×C281C2×C22⋊C411yescharacteristic
70C2×D281—22no—
71C2×D281—41no—
72C2×D281—44no—
73C2×D281—42no—
74C2×D281—42no—
75C2×D281—41no—
76C2×D281—82no—
77C2×D281#9912yes—
78C4×C281—21no—
79C4×C281—41no—
80C4×C281—41no—
81C4×C281—82no—
82Dic281—21no—
83Dic281—41no—
84Dic281—82no—
85C2×C281—21no—
86C2×C281—42no—
87C2×C281C2×#9911yescharacteristic
88D281—22no—
89D281—42no—
90D281—81no—
91C281#212711yescharacteristic, complemented, Sylow
92#2127—2811nomaximal, Sylow
93#535—2811no—
94C2×#99—2812no—
95#354—2811no—
96#354D28111yescharacteristic, complemented
97#353—2812no—
98C2×#41—2811no—
99C22×D4—2811no—
100#127—2811no—
101#127—2811no—
102#124—2811no—
103#124C2×D28111yescharacteristic
104#121—5622no—
105#120—5622no—
106#117—2811no—
107C2×C22⋊C4—5622no—
108#99—2812no—
109#99—5622no—
110#99C2×D28112yes—
111C24—2812no—
112#41—11242no—
113C2×Q8C4×D28111yescharacteristic, complemented
114C2×D4—2812no—
115C2×D4—2811no—
116C2×D4—2811no—
117C2×D4—5621no—
118C2×D4—5622no—
119C2×D4—5622no—
120C2×D4—11242no—
121C2×D4C22×D28111yescharacteristic
122C22×C4—2811no—
123C22×C4—5621no—
124C22×C4—11242no—
125C4⋊C4—5621no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—5621no—
129C22⋊C4—5622no—
130C22⋊C4—5622no—
131C22⋊C4—11242no—
132C42—2811no—
133C42C4×D28111yescharacteristic, complemented
134C23—2811no—
135C23—2812no—
136C23—5622no—
137C23—5622no—
138C23—5621no—
139C23—22482no—
140C23D4×D28112yes—
141Q8—41no—
142D4—41no—
143D4—11241no—
144D4—11241no—
145D4—11242no—
146D4—11242no—
147D4—22482no—
148D4—22482no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—2811no—
153C2×C4—5622no—
154C2×C4—5621no—
155C2×C4—11242no—
156C2×C4—11242no—
157C2×C4—22484no—
158C2×C4C2×C4×D28111yescharacteristic
159C22—22no—
160C22—42no—
161C22—2812no—
162C22—5622no—
163C22—11241no—
164C22—11242no—
165C22—11242no—
166C22—11244no—
167C22—11241no—
168C22—22482no—
169C22C22⋊C4×D28111yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—5621no—
175C4—11241no—
176C4—22482no—
177C2—21no—
178C2—42no—
179C2—5622no—
180C2—11242no—
181C2—22481no—
182C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#354×C281C2
socleC2×C281C2×#99
prime radical#31824031C2
cosocleC2×D4×C281C23
hypercenter#354D281
hypocenterC281#2127
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D281C2semidirect
3. #31823258C2semidirect
4. #31823255C2semidirect
5. #354×C281C2semidirect
6. C2×#17985139C4semidirect
8. #22582876C4semidirect
10. #22582868C4semidirect
13. #22582836C4semidirect
24. C2×D1124C2×C4semidirect
36. C4×Dic281C2×C4semidirect
37. C2×Q8×C281C2×C4semidirect
41. C42×C281C2×C4semidirect
91. C281#2127semidirect
96. #354D281semidirect
113. C2×Q8C4×D281semidirect
133. C42C4×D281semidirect

Maximal subgroups

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

subgroupindex
#318240312
#99×D2812
#318232582
#318232552
#354×C2812
#2127281