Finite Group Databasebeta

← #49097308

Subgroups — #49097308

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#31824202C211yesmaximal, characteristic, complemented
2#31823653C211yesmaximal, characteristic, complemented
3#31823631C211yesmaximal, characteristic, complemented
4#31823255C211yesmaximal, characteristic, complemented
5#31823252C211yesmaximal, characteristic, complemented
6#31823250C211yesmaximal, characteristic, complemented
7B(4,𝔽2)×C281C211yesmaximal, characteristic, complemented
8#22582904—21no—
9#22582875C2211yescharacteristic
10#22582872—21no—
11#22582861—21no—
12#22582860—21no—
13#22582860C2211yescharacteristic
14#22582852—21no—
15#22582851—21no—
16#22582850—21no—
17#22582848—21no—
18#22582806—21no—
19#22582796C2211yescharacteristic
20#22582794—21no—
21#22582794C2211yescharacteristic
22H(5,𝔽2)×C281C2211yescharacteristic
23#120×C281—21no—
24#120×C281C2211yescharacteristic
25#99×C281—21no—
26#99×C281C2211yescharacteristic
27C2×D1124D411yescharacteristic, complemented
28C2×C22⋊D281—21no—
29C2×C22⋊D281—21no—
30C2×C22⋊D281—21no—
31C2×C22⋊D281—21no—
32C22×Dic281D411yescharacteristic, complemented
33C2×C4×D281—21no—
34#17985125—41no—
35#17985123—41no—
36#17985122—21no—
37C4⋊Dic281—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—41no—
41C22⋊Dic281—21no—
42C22⋊Dic281—21no—
43C22⋊Dic281—21no—
44C22⋊Dic281—21no—
45C22⋊Dic281—41no—
46C22⋊Dic281D411yescharacteristic, complemented
47#17985115—21no—
48C4×Dic281D411yescharacteristic, complemented
49C24×C281D411yescharacteristic
50#41×C281—21no—
51#41×C281—41no—
52C2×D4×C281—21no—
53C2×D4×C281—21no—
54C2×D4×C281—21no—
55C2×D4×C281—41no—
56C2×D4×C281—41no—
57C2×D4×C281C2311yescharacteristic
58C22⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—41no—
61C22⋊C4×C281D411yescharacteristic
62C22×D281—21no—
63D1124—41no—
64C22⋊D281—81no—
65C22⋊D281—81no—
66C22⋊D281—81no—
67C22⋊D281—81no—
68C2×Dic281—21no—
69C2×Dic281—21no—
70C2×Dic281—21no—
71C2×Dic281—41no—
72C2×Dic281—41no—
73C4×D281—81no—
74#14555886—41no—
75C23×C281—21no—
76C23×C281—21no—
77C23×C281—21no—
78C23×C281—41no—
79C23×C281—81no—
80C23×C281C2×D411yescharacteristic
81C23×C281C2×D411yescharacteristic
82Q8×C281—21no—
83D4×C281—21no—
84D4×C281—41no—
85D4×C281—41no—
86D4×C281—41no—
87D4×C281—41no—
88D4×C281—81no—
89D4×C281—82no—
90C2×C4×C281—21no—
91C2×C4×C281—21no—
92C2×C4×C281—21no—
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—41no—
102C22×C281—42no—
103C22×C281—41no—
104C22×C281—41no—
105C22×C281—81no—
106C22×C281—81no—
107C22×C281—81no—
108C22×C281#12011yescharacteristic
109C2×D281—41no—
110C2×D281—41no—
111C2×D281—41no—
112C4×C281—21no—
113C4×C281—41no—
114C4×C281—41no—
115C4×C281—81no—
116Dic281—41no—
117Dic281—41no—
118Dic281—41no—
119Dic281—81no—
120C2×C281—21no—
121C2×C281—41no—
122C2×C281—41no—
123C2×C281—81no—
124C2×C281—81no—
125C2×C281B(4,𝔽2)11yescharacteristic
126D281—81no—
127C281#220011yescharacteristic, complemented, Sylow
128#2200—2811nomaximal, Sylow
129#560—2811no—
130#458—2811no—
131B(4,𝔽2)D28111yescharacteristic, complemented
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—2811no—
141#123—5621no—
142#123—5621no—
143#121—5621no—
144#121—5621no—
145#121—5621no—
146#120—21no—
147#120—5621no—
148#120C2×D28111yescharacteristic
149#104—5621no—
150#100—2811no—
151#99—21no—
152#99—2811no—
153#99—5621no—
154#99C2×D28111yescharacteristic
155C24C22⋊D28111yescharacteristic
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—2811no—
164C2×D4—5621no—
165C2×D4—5621no—
166C2×D4—5621no—
167C2×D4—5621no—
168C2×D4C22×D28111yescharacteristic
169C22×C4—2811no—
170C22×C4—5621no—
171SD16—11241no—
172D8—11241no—
173M16—5621no—
174C4⋊C4—5621no—
175C4⋊C4—5621no—
176C4⋊C4—5621no—
177C4⋊C4—11241no—
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
189C42—2811no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—5621no—
196C23D4×D28111yescharacteristic
197C23C2×C22⋊D28111yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—81no—
205D4—82no—
206D4—11241no—
207D4—22481no—
208D4—22481no—
209D4—22481no—
210D4—22481no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—5621no—
217C2×C4—5621no—
218C2×C4—5621no—
219C2×C4—11241no—
220C2×C4—11241no—
221C2×C4—22481no—
222C2×C4D4×D28111yescharacteristic
223C8—11241no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—81no—
234C22—81no—
235C22—81no—
236C22—11241no—
237C22—11241no—
238C22—11241no—
239C22#2258284711yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—81no—
244C4—11241no—
245C4—11241no—
246C4—11241no—
247C4—22481no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—22481no—
254C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
FittingB(4,𝔽2)×C281C2
socleC2×C281B(4,𝔽2)
hypercenterB(4,𝔽2)D281
hypocenterC281#2200
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #31824202C2semidirect
2. #31823653C2semidirect
3. #31823631C2semidirect
4. #31823255C2semidirect
5. #31823252C2semidirect
6. #31823250C2semidirect
7. B(4,𝔽2)×C281C2semidirect
27. C2×D1124D4semidirect
32. C22×Dic281D4semidirect
46. C22⋊Dic281D4semidirect
48. C4×Dic281D4semidirect
127. C281#2200semidirect
131. B(4,𝔽2)D281semidirect

Maximal subgroups

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

subgroupindex
#318242022
#318236532
#318236312
#318232552
#318232522
#318232502
B(4,𝔽2)×C2812
#2200281