Finite Group Databasebeta

← #49097295

Subgroups — #49097295

Order 35968.

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

normal subgroups only

This group has 258 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#31824144C211yesmaximal, characteristic, complemented
2#31823654C211yesmaximal, characteristic, complemented
3#31823649C211yesmaximal, characteristic
4#31823643C211yesmaximal, characteristic, complemented
5#31823257C211yesmaximal, characteristic, complemented
6#31823254C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C281C211yesmaximal, characteristic, complemented
8#22582924C2211yescharacteristic
9#22582912—21no—
10#22582872—21no—
11#22582866C2211yescharacteristic
12#22582863—21no—
13#22582860—21no—
14#22582860C2211yescharacteristic
15#22582856—21no—
16#22582848—21no—
17D4×Dic281—21no—
18#22582835—21no—
19C2×C22⋊Dic281—21no—
20#22582805—21no—
21#22582794C2211yescharacteristic
22#22582793—21no—
23#22582793—21no—
24#120×C281C2211yescharacteristic
25#100×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27#17985138—21no—
28#17985137—41no—
29C2×Dic562D411yescharacteristic, complemented
30C2×C22⋊D281—21no—
31C2×C22⋊D281—21no—
32C2×C22⋊D281—41no—
33D4×D281—41no—
34C22×Dic281—21no—
35C22×Dic281—21no—
36C22×Dic281D411yescharacteristic, complemented
37Dic1124—41no—
38#17985127—41no—
39C4⋊Dic281—21no—
40C4⋊Dic281—41no—
41#17985117—21no—
42#17985117—21no—
43#17985117—21no—
44C22⋊Dic281—21no—
45C22⋊Dic281—21no—
46C22⋊Dic281—21no—
47C22⋊Dic281—21no—
48C22⋊Dic281—21no—
49C22⋊Dic281—21no—
50C22⋊Dic281—41no—
51C22⋊Dic281D411yescharacteristic, complemented
52#17985115—41no—
53C4×Dic281—21no—
54C4×Dic281D411yescharacteristic, complemented
55C24×C281D411yescharacteristic
56C2×D4×C281—21no—
57C2×D4×C281C2311yescharacteristic
58M16×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C22⋊C4×C281D411yescharacteristic
62C22×D281—21no—
63C22×D281—21no—
64Dic562—21no—
65Dic562—41no—
66D1124—21no—
67C22⋊D281—41no—
68C22⋊D281—41no—
69C22⋊D281—41no—
70C22⋊D281—82no—
71C2×Dic281—21no—
72C2×Dic281—21no—
73C2×Dic281—21no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—42no—
78C2×Dic281—41no—
79C2×Dic281—41no—
80C2×Dic281—81no—
81C4×D281—41no—
82C23×C281—21no—
83C23×C281—42no—
84C23×C281—41no—
85C23×C281C2×D411yescharacteristic
86C23×C281C2×D411yescharacteristic
87D4×C281—41no—
88D4×C281—42no—
89C2×C4×C281—21no—
90C2×C4×C281—41no—
91C2×C4×C281C2×D411yescharacteristic
92C8×C281—41no—
93C22×C281—22no—
94C22×C281—21no—
95C22×C281—21no—
96C22×C281—41no—
97C22×C281—41no—
98C22×C281—41no—
99C22×C281—42no—
100C22×C281—41no—
101C22×C281—81no—
102C22×C281#12011yescharacteristic
103C2×D281—41no—
104C2×D281—81no—
105C2×D281—81no—
106C4×C281—21no—
107C4×C281—41no—
108C4×C281—81no—
109Dic281—41no—
110Dic281—41no—
111Dic281—41no—
112Dic281—41no—
113Dic281—41no—
114Dic281—81no—
115C2×C281—21no—
116C2×C281—41no—
117C2×C281—41no—
118C2×C281—42no—
119C2×C281B(4,𝔽2)11yescharacteristic
120D281—81no—
121C281#219711yescharacteristic, complemented, Sylow
122#2197—2811nomaximal, Sylow
123#551—2811no—
124#458—2811no—
125B(4,𝔽2)—2811no—
126#455—2811no—
127#354—2811no—
128#352—2811no—
129AΣL(1,𝔽16)D28111yescharacteristic, complemented
130H(5,𝔽2)—2811no—
131#137—5621no—
132#126—5621no—
133#124—2811no—
134#123—2811no—
135#123—5621no—
136#123—5621no—
137C22⋊Q8—5621no—
138#120—5621no—
139#120C2×D28111yescharacteristic
140C4×D4—5621no—
141#117—5621no—
142C2×C22⋊C4—5621no—
143#104—5621no—
144#100C2×D28111yescharacteristic
145#99—2811no—
146#99—5621no—
147#99—5621no—
148#99C2×D28111yescharacteristic
149C24D112411yescharacteristic
150#41—5621no—
151#41—11241no—
152C2×Q8—2811no—
153C2×D4—21no—
154C2×D4—5621no—
155C2×D4—5621no—
156C2×D4—11241no—
157C2×D4—11241no—
158C2×D4C22×D28111yescharacteristic
159C22×C4—2811no—
160C22×C4—5621no—
161C22×C4—5621no—
162Q16—11241no—
163SD16—11241no—
164M16—21no—
165C4⋊C4—5621no—
166C4⋊C4—5621no—
167C4⋊C4—5621no—
168C4⋊C4—5621no—
169C4⋊C4—11241no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—2811no—
173C22⋊C4—5621no—
174C22⋊C4—5621no—
175C22⋊C4—5621no—
176C22⋊C4—5621no—
177C22⋊C4—5621no—
178C22⋊C4—5621no—
179C22⋊C4—11241no—
180C22⋊C4—11241no—
181C22⋊C4D112411yescharacteristic
182C42—2811no—
183C42—5621no—
184C23—21no—
185C23—41no—
186C23—42no—
187C23—5621no—
188C23—5621no—
189C23D4×D28111yescharacteristic
190C23C2×D112411yescharacteristic
191Q8—5621no—
192Q8—11241no—
193D4—41no—
194D4—42no—
195D4—5621no—
196D4—11241no—
197D4—11241no—
198D4—11241no—
199D4—22482no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—5621no—
203C2×C4—5621no—
204C2×C4—5621no—
205C2×C4—5621no—
206C2×C4—5621no—
207C2×C4—5621no—
208C2×C4—11241no—
209C2×C4—11242no—
210C2×C4—11241no—
211C2×C4—11241no—
212C2×C4—22481no—
213C2×C4D4×D28111yescharacteristic
214C8—41no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22—11241no—
225C22—22481no—
226C22—22481no—
227C22#2258284911yescharacteristic
228C4—21no—
229C4—41no—
230C4—81no—
231C4—11241no—
232C4—11241no—
233C4—11241no—
234C4—11241no—
235C4—11241no—
236C4—22481no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—22481no—
242C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
FittingAΣL(1,𝔽16)×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823649C2
hypercenterAΣL(1,𝔽16)D281
hypocenterC281#2197
LCSG ▷ C2×D4×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
1. #31824144C2semidirect
2. #31823654C2semidirect
4. #31823643C2semidirect
5. #31823257C2semidirect
6. #31823254C2semidirect
7. AΣL(1,𝔽16)×C281C2semidirect
29. C2×Dic562D4semidirect
36. C22×Dic281D4semidirect
51. C22⋊Dic281D4semidirect
54. C4×Dic281D4semidirect
121. C281#2197semidirect
129. AΣL(1,𝔽16)D281semidirect

Maximal subgroups

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

subgroupindex
#318241442
#318236542
#318236492
#318236432
#318232572
#318232542
AΣL(1,𝔽16)×C2812
#2197281