Finite Group Databasebeta

← #49096951

Subgroups — #49096951

Order 35968.

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

normal subgroups only

This group has 266 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#31824028C211yesmaximal, characteristic
2#31823444C211yesmaximal, characteristic, complemented
3#31823435C211yesmaximal, characteristic, complemented
4#31823251C211yesmaximal, characteristic, complemented
5#31823250C211yesmaximal, characteristic, complemented
6#31823249C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C281C211yesmaximal, characteristic, complemented
8C2×#17985137C2211yescharacteristic
9C22×C22⋊D281C411yescharacteristic, complemented
10M16×D281—21no—
11#22582875—21no—
12#22582865—21no—
13#22582852—21no—
14#22582851—21no—
15#22582849C411yescharacteristic, complemented
16#22582848C411yescharacteristic, complemented
17#22582847C2211yescharacteristic
18#22582835—21no—
19#22582835C411yescharacteristic, complemented
20#22582797—21no—
21#22582796C2211yescharacteristic
22#22582794C2211yescharacteristic
23#22582793—21no—
24#120×C281C2211yescharacteristic
25#100×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27C23×D281C2×C411yescharacteristic
28#17985137—41no—
29#17985137—41no—
30C2×Dic562D411yescharacteristic
31C2×D1124—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C2×C22⋊D281—21no—
35C2×C22⋊D281—21no—
36C2×C22⋊D281—41no—
37C2×C22⋊D281—41no—
38C2×C22⋊D281C2×C411yescharacteristic
39C2×C22⋊D281D411yescharacteristic
40C22×Dic281C2×C411yescharacteristic
41C22×Dic281D411yescharacteristic
42C2×C4×D281D411yescharacteristic
43#17985122—21no—
44#17985121—41no—
45C8×D281—41no—
46#17985117—21no—
47#17985117—41no—
48C22⋊Dic281—21no—
49C22⋊Dic281—21no—
50C22⋊Dic281C2×C411yescharacteristic
51#17985115—21no—
52#17985115—21no—
53C4×Dic281—21no—
54C4×Dic281—41no—
55C24×C281C2×C411yescharacteristic
56C2×D4×C281—21no—
57C2×D4×C281C2311yescharacteristic
58M16×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C22⋊C4×C281C2×C411yescharacteristic
62C22×D281—21no—
63C22×D281—41no—
64C22×D281—81no—
65C22×D281C22⋊C411yescharacteristic
66Dic562—41no—
67D1124—81no—
68C22⋊D281—41no—
69C22⋊D281—41no—
70C22⋊D281—42no—
71C22⋊D281—41no—
72C22⋊D281—41no—
73C22⋊D281—81no—
74C22⋊D281—81no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—21no—
78C2×Dic281—21no—
79C2×Dic281—21no—
80C2×Dic281—41no—
81C2×Dic281C22⋊C411yescharacteristic
82C2×Dic281C22⋊C411yescharacteristic
83C2×Dic281C22⋊C411yescharacteristic
84C4×D281—21no—
85C4×D281—21no—
86#14555886—41no—
87C23×C281—21no—
88C23×C281—41no—
89C23×C281—81no—
90C23×C281C22×C411yescharacteristic
91C23×C281C2×D411yescharacteristic
92D4×C281—41no—
93D4×C281—81no—
94C2×C4×C281—21no—
95C2×C4×C281—41no—
96C2×C4×C281C2×D411yescharacteristic
97C8×C281—41no—
98C22×C281—21no—
99C22×C281—21no—
100C22×C281—41no—
101C22×C281—41no—
102C22×C281—41no—
103C22×C281—41no—
104C22×C281—41no—
105C22×C281—82no—
106C22×C281C2×C22⋊C411yescharacteristic
107C2×D281—21no—
108C2×D281—41no—
109C2×D281—41no—
110C2×D281—41no—
111C2×D281—41no—
112C2×D281—82no—
113C4×C281—21no—
114C4×C281—41no—
115C4×C281—81no—
116Dic281—21no—
117Dic281—21no—
118Dic281—41no—
119Dic281—81no—
120Dic281#9911yescharacteristic
121Dic281#9911yescharacteristic
122C2×C281—21no—
123C2×C281—41no—
124C2×C281—41no—
125C2×C281—81no—
126C2×C281C2×#9911yescharacteristic
127D281—41no—
128D281—81no—
129C281#212211yescharacteristic, complemented, Sylow
130#2122—2811nomaximal, Sylow
131#535—2811no—
132#413—2811no—
133#410—2811no—
134AΣL(1,𝔽16)—2811no—
135AΣL(1,𝔽16)—2811no—
136AΣL(1,𝔽16)—2811no—
137AΣL(1,𝔽16)D28111yescharacteristic, complemented
138C2×#41—2811no—
139C22×D4—2811no—
140C2×M16—5621no—
141#127—5621no—
142#124—5621no—
143#121—5621no—
144#121—5621no—
145#120—2811no—
146#120—2811no—
147#120—2811no—
148#120C2×D28111yescharacteristic
149#117—2811no—
150#117—5621no—
151#101—5621no—
152#100—2811no—
153#100C2×D28111yescharacteristic
154#99—2811no—
155#99—5621no—
156#99C2×D28111yescharacteristic
157C24—2811no—
158C24C4×D28111yescharacteristic
159#41—11241no—
160#41—11241no—
161C2×Q8—2811no—
162C2×D4—21no—
163C2×D4—2811no—
164C2×D4—2811no—
165C2×D4—5621no—
166C2×D4—5621no—
167C2×D4—5621no—
168C2×D4—5621no—
169C2×D4—5621no—
170C2×D4—11241no—
171C2×D4—11241no—
172C2×D4C22×D28111yescharacteristic
173C22×C4—2811no—
174C22×C4—2811no—
175C22×C4—2811no—
176M16—21no—
177M16—5621no—
178M16—11241no—
179C2×C8—11241no—
180C4⋊C4—5621no—
181C4⋊C4—11241no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—2811no—
185C22⋊C4—5621no—
186C22⋊C4—5621no—
187C22⋊C4—5621no—
188C22⋊C4—5621no—
189C22⋊C4C4×D28111yescharacteristic
190C42—5621no—
191C42—11241no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—2811no—
196C23—5621no—
197C23—11241no—
198C23—22481no—
199C23C2×C4×D28111yescharacteristic
200C23D4×D28111yescharacteristic
201Q8—11241no—
202D4—41no—
203D4—81no—
204D4—11241no—
205D4—11241no—
206D4—11241no—
207D4—11241no—
208D4—11242no—
209D4—22481no—
210D4—22481no—
211D4—22481no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—2811no—
215C2×C4—2811no—
216C2×C4—2811no—
217C2×C4—5621no—
218C2×C4—5621no—
219C2×C4—5621no—
220C2×C4—5621no—
221C2×C4—5621no—
222C2×C4—5621no—
223C2×C4—5621no—
224C2×C4—11241no—
225C2×C4D4×D28111yescharacteristic
226C8—41no—
227C8—11241no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—82no—
236C22—5621no—
237C22—11241no—
238C22—11241no—
239C22—11241no—
240C22—11241no—
241C22—22482no—
242C22C22⋊C4×D28111yescharacteristic
243C4—21no—
244C4—41no—
245C4—81no—
246C4—2811no—
247C4—2811no—
248C4—5621no—
249C4—5621no—
250C4—11241no—
251C4—22481no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—81no—
256C2—11241no—
257C2—22481no—
258C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
FittingAΣL(1,𝔽16)×C281C2
socleC2×C281C2×#99
prime radical#31824028C2
cosocleC2×D4×C281C23
hypercenterAΣL(1,𝔽16)D281
hypocenterC281#2122
LCSG ▷ C23×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #31823444C2semidirect
3. #31823435C2semidirect
4. #31823251C2semidirect
5. #31823250C2semidirect
6. #31823249C2semidirect
7. AΣL(1,𝔽16)×C281C2semidirect
9. C22×C22⋊D281C4semidirect
15. #22582849C4semidirect
16. #22582848C4semidirect
19. #22582835C4semidirect
129. C281#2122semidirect
137. AΣL(1,𝔽16)D281semidirect

Maximal subgroups

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

subgroupindex
#318240282
#318234442
#318234352
#318232512
#318232502
#318232492
AΣL(1,𝔽16)×C2812
#2122281