Finite Group Databasebeta

← #49096941

Subgroups — #49096941

Order 35968.

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

normal subgroups only

This group has 264 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#31823969C211yesmaximal, characteristic
2#31823444C211yesmaximal, characteristic, complemented
3#31823435C211yesmaximal, characteristic, complemented
4#31823254C211yesmaximal, characteristic, complemented
5#31823252C211yesmaximal, characteristic, complemented
6#31823250C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C281C211yesmaximal, characteristic, complemented
8C2×#17985137C2211yescharacteristic
9C23×Dic281C411yescharacteristic, complemented
10M16×D281—21no—
11#22582863C411yescharacteristic, complemented
12#22582860C2211yescharacteristic
13#22582856—21no—
14#22582851—21no—
15#22582848C411yescharacteristic, complemented
16D4×Dic281—21no—
17#22582839—21no—
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
27#17985137—41no—
28#17985137—41no—
29C2×Dic562D411yescharacteristic
30C2×C22⋊D281—21no—
31C2×C22⋊D281C2×C411yescharacteristic
32C2×C22⋊D281D411yescharacteristic
33C22×Dic281—21no—
34C22×Dic281—21no—
35C22×Dic281—41no—
36C22×Dic281—41no—
37C22×Dic281C2×C411yescharacteristic
38C22×Dic281C2×C411yescharacteristic
39C22×Dic281D411yescharacteristic
40C2×C4×D281D411yescharacteristic
41#17985122—21no—
42#17985121—41no—
43C8×D281—41no—
44C4⋊Dic281—21no—
45#17985117—21no—
46#17985117—21no—
47#17985117—41no—
48C22⋊Dic281—21no—
49C22⋊Dic281—21no—
50C22⋊Dic281—21no—
51C22⋊Dic281C2×C411yescharacteristic
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×D281C22⋊C411yescharacteristic
63Dic562—41no—
64C22⋊D281—41no—
65C22⋊D281—41no—
66C22⋊D281—42no—
67C2×Dic281—21no—
68C2×Dic281—21no—
69C2×Dic281—21no—
70C2×Dic281—21no—
71C2×Dic281—21no—
72C2×Dic281—21no—
73C2×Dic281—42no—
74C2×Dic281—41no—
75C2×Dic281—41no—
76C2×Dic281—41no—
77C2×Dic281—41no—
78C2×Dic281C22⋊C411yescharacteristic
79C2×Dic281C22⋊C411yescharacteristic
80C2×Dic281C22⋊C411yescharacteristic
81C4×D281—21no—
82C4×D281—21no—
83#14555886—41no—
84C23×C281—21no—
85C23×C281—42no—
86C23×C281—41no—
87C23×C281C22×C411yescharacteristic
88C23×C281C2×D411yescharacteristic
89D4×C281—41no—
90D4×C281—42no—
91C2×C4×C281—21no—
92C2×C4×C281—41no—
93C2×C4×C281C2×D411yescharacteristic
94C8×C281—41no—
95C22×C281—22no—
96C22×C281—21no—
97C22×C281—21no—
98C22×C281—41no—
99C22×C281—41no—
100C22×C281—41no—
101C22×C281—42no—
102C22×C281—42no—
103C22×C281—41no—
104C22×C281C2×C22⋊C411yescharacteristic
105C2×D281—21no—
106C2×D281—41no—
107C4×C281—21no—
108C4×C281—41no—
109C4×C281—81no—
110Dic281—21no—
111Dic281—21no—
112Dic281—41no—
113Dic281—41no—
114Dic281—81no—
115Dic281#9911yescharacteristic
116Dic281#9911yescharacteristic
117C2×C281—21no—
118C2×C281—41no—
119C2×C281—42no—
120C2×C281—41no—
121C2×C281C2×#9911yescharacteristic
122D281—41no—
123C281#212011yescharacteristic, complemented, Sylow
124#2120—2811nomaximal, Sylow
125#525—2811no—
126#413—2811no—
127#410—2811no—
128#352—2811no—
129#352—2811no—
130AΣL(1,𝔽16)—2811no—
131AΣL(1,𝔽16)D28111yescharacteristic, complemented
132C2×#41—2811no—
133C23×C4—2811no—
134C2×M16—5621no—
135#123—2811no—
136#123—2811no—
137C22⋊Q8—5621no—
138#121—5621no—
139#120—2811no—
140#120C2×D28111yescharacteristic
141C4×D4—5621no—
142C4×D4—5621no—
143#117—2811no—
144#117—5621no—
145#101—5621no—
146#100—2811no—
147#100C2×D28111yescharacteristic
148#99—2811no—
149#99—5621no—
150#99C2×D28111yescharacteristic
151C24C4×D28111yescharacteristic
152#41—11241no—
153#41—11241no—
154C2×Q8—2811no—
155C2×D4—21no—
156C2×D4—2811no—
157C2×D4—2811no—
158C2×D4—5621no—
159C2×D4C22×D28111yescharacteristic
160C22×C4—2811no—
161C22×C4—2811no—
162C22×C4—2811no—
163C22×C4—2811no—
164C22×C4—5621no—
165C22×C4—5621no—
166C22×C4—11241no—
167C22×C4—11241no—
168M16—21no—
169M16—5621no—
170M16—11241no—
171C2×C8—11241no—
172C4⋊C4—5621no—
173C4⋊C4—5621no—
174C4⋊C4—5621no—
175C4⋊C4—11241no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—2811no—
179C22⋊C4—5621no—
180C22⋊C4—5621no—
181C22⋊C4—5621no—
182C22⋊C4—5621no—
183C22⋊C4C4×D28111yescharacteristic
184C42—5621no—
185C42—11241no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23—2811no—
190C23C2×C4×D28111yescharacteristic
191C23D4×D28111yescharacteristic
192Q8—11241no—
193D4—41no—
194D4—42no—
195D4—11241no—
196D4—11241no—
197D4—11242no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—2811no—
201C2×C4—2811no—
202C2×C4—2811no—
203C2×C4—5621no—
204C2×C4—5621no—
205C2×C4—5621no—
206C2×C4—5621no—
207C2×C4—5621no—
208C2×C4—5621no—
209C2×C4—5621no—
210C2×C4—5621no—
211C2×C4—11241no—
212C2×C4—11241no—
213C2×C4—11242no—
214C2×C4—11241no—
215C2×C4—11241no—
216C2×C4D4×D28111yescharacteristic
217C8—41no—
218C8—11241no—
219C22—22no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—5621no—
229C22—11241no—
230C22C22⋊C4×D28111yescharacteristic
231C4—21no—
232C4—41no—
233C4—81no—
234C4—2811no—
235C4—2811no—
236C4—5621no—
237C4—5621no—
238C4—11241no—
239C4—11241no—
240C4—22481no—
241C2—21no—
242C2—41no—
243C2—42no—
244C2—41no—
245C2—11241no—
246C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
FittingAΣL(1,𝔽16)×C281C2
socleC2×C281C2×#99
prime radical#31823969C2
cosocleC2×D4×C281C23
hypercenterAΣL(1,𝔽16)D281
hypocenterC281#2120
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. #31823254C2semidirect
5. #31823252C2semidirect
6. #31823250C2semidirect
7. AΣL(1,𝔽16)×C281C2semidirect
9. C23×Dic281C4semidirect
11. #22582863C4semidirect
15. #22582848C4semidirect
19. #22582835C4semidirect
123. C281#2120semidirect
131. AΣL(1,𝔽16)D281semidirect

Maximal subgroups

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

subgroupindex
#318239692
#318234442
#318234352
#318232542
#318232522
#318232502
AΣL(1,𝔽16)×C2812
#2120281