Finite Group Databasebeta

← #353×D281 #49096959

Subgroups — #353×D281 #49096959

Order 35968.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#127×D281C211yesmaximal, characteristic
2#99×D281C212yesmaximal, complemented
3#31823256C211yesmaximal, characteristic, complemented
4#31823255C212yesmaximal, complemented
5#353×C281C211yesmaximal, characteristic, complemented
6C2×D4×D281—22no—
7C2×D4×D281C411yescharacteristic, complemented
8C2×D4×D281C2211yescharacteristic
9#22582876C411yescharacteristic, complemented
10#22582875—22no—
11#22582875C411yescharacteristic, complemented
12#22582875C2211yescharacteristic
13C22⋊C4×D281—22no—
14C42×D281C411yescharacteristic, complemented
15#22582794C2212yescomplemented
16#22582793—22no—
17#127×C281C2211yescharacteristic
18#99×C281C2212yescomplemented
19C23×D281—21no—
20C23×D281D412yes—
21C2×D1124—22no—
22C2×D1124C2×C411yescharacteristic
23C2×D1124C2×C411yescharacteristic, complemented
24C2×C22⋊D281—22no—
25C2×C22⋊D281—21no—
26C2×C22⋊D281—22no—
27C2×C22⋊D281D412yes—
28D4×D281—41no—
29D4×D281—41no—
30D4×D281—41no—
31D4×D281—41no—
32D4×D281—48no—
33C2×C4×D281—21no—
34C2×C4×D281—42no—
35C2×C4×D281C2×C411yescharacteristic
36C22⋊Dic281—22no—
37#17985115—42no—
38C4×Dic281—21no—
39C4×Dic281C2×C411yescharacteristic, complemented
40C2×D4×C281—22no—
41C2×D4×C281C2×C411yescharacteristic, complemented
42C2×D4×C281C2311yescharacteristic
43C22⋊C4×C281—22no—
44C42×C281C2×C411yescharacteristic, complemented
45C22×D281—22no—
46C22×D281—22no—
47C22×D281—21no—
48C22×D281—44no—
49C22×D281—44no—
50C22×D281—41no—
51C22×D281—41no—
52C22×D281C22⋊C411yescharacteristic
53C22×D281C22⋊C412yes—
54D1124—41no—
55D1124—41no—
56D1124—44no—
57C22⋊D281—42no—
58C22⋊D281—44no—
59C22⋊D281—44no—
60C22⋊D281—42no—
61C2×Dic281—21no—
62C2×Dic281—42no—
63C2×Dic281C22⋊C411yescharacteristic
64C4×D281—24no—
65C4×D281—21no—
66C4×D281—21no—
67C4×D281—84no—
68C23×C281—21no—
69C23×C281C2×D412yes—
70D4×C281—41no—
71D4×C281—41no—
72D4×C281—44no—
73C2×C4×C281—21no—
74C2×C4×C281—42no—
75C2×C4×C281C22×C411yescharacteristic
76C22×C281—22no—
77C22×C281—42no—
78C22×C281—42no—
79C22×C281—41no—
80C22×C281C2×C22⋊C411yescharacteristic
81C2×D281—22no—
82C2×D281—22no—
83C2×D281—44no—
84C2×D281—42no—
85C2×D281—42no—
86C2×D281—41no—
87C2×D281—82no—
88C2×D281—82no—
89C2×D281—82no—
90C2×D281#9911yescharacteristic
91C2×D281#9911yescharacteristic
92C4×C281—22no—
93C4×C281—21no—
94C4×C281—82no—
95Dic281—22no—
96Dic281—21no—
97Dic281—82no—
98C2×C281—21no—
99C2×C281—42no—
100C2×C281—81no—
101C2×C281C2×#9911yescharacteristic
102D281—21no—
103D281—42no—
104D281—81no—
105D281#35312yesdirect product factor
106C281C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—2811nomaximal, Sylow
108C2×#127—2811no—
109C2×#99—2812no—
110#353—2811no—
111#353—2812no—
112#353D28111yescharacteristic, direct product factor
113C22×D4—2811no—
114C22×D4—2811no—
115C22×D4—5622no—
116#127—2811no—
117#127—2811no—
118#127—2811no—
119#127—5622no—
120#127C2×D28111yescharacteristic
121C2×C22⋊C4—5622no—
122C2×C42—2811no—
123#99—2812no—
124#99—5622no—
125#99C2×D28112yescomplemented
126C24—2812no—
127C24—5621no—
128C2×D4—22no—
129C2×D4—2812no—
130C2×D4—2811no—
131C2×D4—2811no—
132C2×D4—5622no—
133C2×D4—5621no—
134C2×D4—5622no—
135C2×D4—5622no—
136C2×D4—11241no—
137C2×D4—11241no—
138C2×D4—11241no—
139C2×D4—11241no—
140C2×D4—11248no—
141C2×D4C4×D28111yescharacteristic, complemented
142C2×D4C22×D28111yescharacteristic
143C22×C4—2811no—
144C22×C4—5621no—
145C22×C4—11242no—
146C22⋊C4—22no—
147C22⋊C4—5622no—
148C22⋊C4—11242no—
149C42—2811no—
150C42—5621no—
151C42C4×D28111yescharacteristic, complemented
152C23—21no—
153C23—2811no—
154C23—2812no—
155C23—5622no—
156C23—5622no—
157C23—5621no—
158C23—11241no—
159C23—11241no—
160C23—11244no—
161C23—11244no—
162C23D4×D28112yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—11241no—
167D4—11241no—
168D4—11244no—
169D4—11242no—
170D4—11244no—
171D4—11244no—
172D4—11242no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—2811no—
176C2×C4—5621no—
177C2×C4—5621no—
178C2×C4—5624no—
179C2×C4—5621no—
180C2×C4—11242no—
181C2×C4—22484no—
182C2×C4C2×C4×D28111yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—2811no—
188C22—2811no—
189C22—5622no—
190C22—5622no—
191C22—11242no—
192C22—11242no—
193C22—11244no—
194C22—11241no—
195C22—22482no—
196C22—22482no—
197C22—22482no—
198C22C22⋊C4×D28111yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—5622no—
203C4—5621no—
204C4—22482no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—2812no—
209C2—5621no—
210C2—11242no—
211C2—22481no—
212C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#353×C281C2
socleC2×C281C2×#99
prime radical#127×D281C2
cosocleC2×D4×C281C23
hypercenter#353D281
hypocenterC281C2×#353
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. #99×D281C2semidirect
3. #31823256C2semidirect
4. #31823255C2semidirect
5. #353×C281C2semidirect
7. C2×D4×D281C4semidirect
9. #22582876C4semidirect
11. #22582875C4semidirect
14. C42×D281C4semidirect
15. #22582794C22semidirect
18. #99×C281C22semidirect
23. C2×D1124C2×C4semidirect
39. C4×Dic281C2×C4semidirect
41. C2×D4×C281C2×C4semidirect
44. C42×C281C2×C4semidirect
105. D281#353direct (N × H)
106. C281C2×#353semidirect
112. #353D281direct (N × H)
125. #99C2×D281semidirect
141. C2×D4C4×D281semidirect
151. C42C4×D281semidirect

Maximal subgroups

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

subgroupindex
#127×D2812
#99×D2812
#318232562
#318232552
#353×C2812
C2×#353281