Finite Group Databasebeta

← #49097307

Subgroups — #49097307

Order 35968.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824203C211yesmaximal, characteristic, complemented
2#31823650C211yesmaximal, characteristic, complemented
3#31823631C211yesmaximal, characteristic, complemented
4#31823255C211yesmaximal, characteristic, complemented
5#31823253C211yesmaximal, characteristic, complemented
6#31823249C211yesmaximal, characteristic, complemented
7#458×C281C211yesmaximal, characteristic, complemented
8#22582904—21no—
9#22582875C2211yescharacteristic
10#22582874—21no—
11#22582861—21no—
12#22582854—21no—
13#22582853—21no—
14#22582852—21no—
15#22582849—21no—
16#22582847—21no—
17#22582847C2211yescharacteristic
18#22582806—21no—
19#22582796C2211yescharacteristic
20#22582794—21no—
21#22582794C2211yescharacteristic
22H(5,𝔽2)×C281C2211yescharacteristic
23#123×C281—21no—
24#123×C281C2211yescharacteristic
25#99×C281—21no—
26#99×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C2×D1124—21no—
29C2×D1124—21no—
30C2×D1124D411yescharacteristic, complemented
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C2×C22⋊D281—41no—
35C2×C4×D281—21no—
36#17985125—41no—
37#17985123—41no—
38#17985122—21no—
39C4⋊Dic281—21no—
40#17985117—21no—
41C22⋊Dic281—21no—
42C22⋊Dic281D411yescharacteristic
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—41no—
48C4×Dic281D411yescharacteristic, complemented
49#41×C281—21no—
50#41×C281—41no—
51C2×D4×C281—21no—
52C2×D4×C281—21no—
53C2×D4×C281—41no—
54C2×D4×C281C2311yescharacteristic
55C22×C4×C281D411yescharacteristic, complemented
56C4⋊C4×C281—21no—
57C4⋊C4×C281—41no—
58C22⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—41no—
61C22⋊C4×C281D411yescharacteristic, complemented
62C22×D281—21no—
63C22×D281—21no—
64C22×D281—41no—
65C22×D281—81no—
66D1124—41no—
67D1124—81no—
68D1124—81no—
69C22⋊D281—81no—
70C22⋊D281—81no—
71C22⋊D281—81no—
72C22⋊D281—82no—
73C2×Dic281—21no—
74C2×Dic281—21no—
75C2×Dic281—41no—
76C4×D281—81no—
77#14555886—41no—
78C23×C281—21no—
79C23×C281—21no—
80C23×C281C2×D411yescharacteristic
81C23×C281C2×D411yescharacteristic
82Q8×C281—21no—
83D4×C281—21no—
84D4×C281—41no—
85D4×C281—41no—
86D4×C281—41no—
87D4×C281—41no—
88C2×C4×C281—21no—
89C2×C4×C281—21no—
90C2×C4×C281—21no—
91C2×C4×C281—21no—
92C2×C4×C281—41no—
93C2×C4×C281—41no—
94C2×C4×C281—41no—
95C2×C4×C281C2×D411yescharacteristic
96C22×C281—21no—
97C22×C281—21no—
98C22×C281—41no—
99C22×C281—41no—
100C22×C281—41no—
101C22×C281—81no—
102C22×C281—81no—
103C22×C281#12011yescharacteristic
104C2×D281—41no—
105C2×D281—41no—
106C2×D281—41no—
107C2×D281—41no—
108C2×D281—42no—
109C2×D281—41no—
110C2×D281—41no—
111C2×D281—81no—
112C4×C281—21no—
113C4×C281—41no—
114C4×C281—41no—
115C4×C281—41no—
116C4×C281—81no—
117Dic281—41no—
118Dic281—41no—
119Dic281—81no—
120C2×C281—21no—
121C2×C281—41no—
122C2×C281—41no—
123C2×C281—81no—
124C2×C281B(4,𝔽2)11yescharacteristic
125D281—81no—
126D281—81no—
127C281#220011yescharacteristic, complemented, Sylow
128#2200—2811nomaximal, Sylow
129#560—2811no—
130#458D28111yescharacteristic, complemented
131B(4,𝔽2)—2811no—
132#453—2811no—
133#353—2811no—
134#352—2811no—
135AΣL(1,𝔽16)—2811no—
136H(5,𝔽2)C2×D28111yescharacteristic
137AGL(1,ℤ/8)—5621no—
138#127—2811no—
139#126—5621no—
140#123—21no—
141#123—5621no—
142#123C2×D28111yescharacteristic
143#121—5621no—
144#121—5621no—
145#121—5621no—
146#120—2811no—
147#120—5621no—
148#120—5621no—
149#104—5621no—
150#100—2811no—
151#99—21no—
152#99—2811no—
153#99—5621no—
154#99C2×D28111yescharacteristic
155C24—2811no—
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—41no—
161C2×D4—2811no—
162C2×D4—5621no—
163C2×D4—5621no—
164C2×D4—5621no—
165C2×D4—5621no—
166C2×D4—5621no—
167C2×D4—11241no—
168C2×D4C22×D28111yescharacteristic
169C22×C4—5621no—
170C22×C4C22⋊D28111yescharacteristic, complemented
171SD16—11241no—
172D8—11241no—
173M16—5621no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—5621no—
177C4⋊C4—5621no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—41no—
181C22⋊C4—2811no—
182C22⋊C4—5621no—
183C22⋊C4—5621no—
184C22⋊C4—5621no—
185C22⋊C4—5621no—
186C22⋊C4—5621no—
187C22⋊C4—11241no—
188C22⋊C4C22⋊D28111yescharacteristic, complemented
189C42—2811no—
190C23—21no—
191C23—21no—
192C23—5621no—
193C23—5621no—
194C23—11241no—
195C23—22481no—
196C23D4×D28111yescharacteristic
197C23C2×C22⋊D28111yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—11241no—
205D4—22481no—
206D4—22481no—
207D4—22481no—
208D4—22481no—
209D4—22481no—
210D4—22482no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—5621no—
219C2×C4—5621no—
220C2×C4—11241no—
221C2×C4—22481no—
222C2×C4D4×D28111yescharacteristic
223C8—11241no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—81no—
230C22—81no—
231C22—11241no—
232C22—11241no—
233C22—11241no—
234C22—11241no—
235C22—11242no—
236C22—11241no—
237C22—11241no—
238C22—22481no—
239C22#2258284711yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—11241no—
246C4—11241no—
247C4—22481no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—22481no—
253C2—22481no—
254C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#458×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#458D281
hypocenterC281#2200
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #31824203C2semidirect
2. #31823650C2semidirect
3. #31823631C2semidirect
4. #31823255C2semidirect
5. #31823253C2semidirect
6. #31823249C2semidirect
7. #458×C281C2semidirect
30. C2×D1124D4semidirect
48. C4×Dic281D4semidirect
55. C22×C4×C281D4semidirect
61. C22⋊C4×C281D4semidirect
127. C281#2200semidirect
130. #458D281semidirect
170. C22×C4C22⋊D281semidirect
188. C22⋊C4C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318242032
#318236502
#318236312
#318232552
#318232532
#318232492
#458×C2812
#2200281