Finite Group Databasebeta

← #49097285

Subgroups — #49097285

Order 35968.

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

normal subgroups only

This group has 354 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#31824095C211yesmaximal, characteristic, complemented
2#31823650C211yesmaximal, characteristic, complemented
3#31823631C211yesmaximal, characteristic, complemented
4#31823255C211yesmaximal, characteristic, complemented
5#31823250C211yesmaximal, characteristic, complemented
6#31823249C211yesmaximal, characteristic, complemented
7B(4,𝔽2)×C281C211yesmaximal, characteristic, complemented
8C22×C22⋊D281—21no—
9C2×D4×D281—21no—
10#22582904—21no—
11#22582875C2211yescharacteristic
12#22582852—21no—
13#22582851—21no—
14#22582849—21no—
15#22582847—21no—
16#22582847C2211yescharacteristic
17#22582839—21no—
18#22582806—21no—
19#22582796C2211yescharacteristic, complemented
20#22582794—21no—
21#22582794C2211yescharacteristic, complemented
22H(5,𝔽2)×C281C2211yescharacteristic, complemented
23#120×C281—21no—
24#120×C281C2211yescharacteristic
25#99×C281—21no—
26#99×C281C2211yescharacteristic, complemented
27C23×D281—21no—
28C23×D281D411yescharacteristic, complemented
29C2×D1124—21no—
30C2×D1124D411yescharacteristic, complemented
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C2×C22⋊D281—21no—
35C2×C22⋊D281—21no—
36C2×C22⋊D281—41no—
37C2×C22⋊D281—44no—
38D4×D281—44no—
39C22×Dic281—21no—
40C2×C4×D281—21no—
41#17985125—41no—
42#17985123—41no—
43#17985122—21no—
44#17985117—21no—
45C22⋊Dic281—21no—
46C22⋊Dic281D411yescharacteristic, complemented
47#17985115—21no—
48#17985115—21no—
49#17985115—41no—
50C4×Dic281D411yescharacteristic, complemented
51C24×C281D411yescharacteristic, complemented
52#41×C281—21no—
53#41×C281—41no—
54C2×D4×C281—21no—
55C2×D4×C281—21no—
56C2×D4×C281—21no—
57C2×D4×C281—41no—
58C2×D4×C281—41no—
59C2×D4×C281C2311yescharacteristic
60C22⋊C4×C281—21no—
61C22⋊C4×C281—21no—
62C22⋊C4×C281—41no—
63C22⋊C4×C281D411yescharacteristic, complemented
64C22×D281—21no—
65C22×D281—21no—
66C22×D281—42no—
67C22×D281—42no—
68C22×D281—41no—
69C22×D281—42no—
70C22×D281—81no—
71D1124—41no—
72D1124—42no—
73C22⋊D281—24no—
74C22⋊D281—42no—
75C22⋊D281—42no—
76C22⋊D281—42no—
77C22⋊D281—42no—
78C22⋊D281—82no—
79C2×Dic281—21no—
80C2×Dic281—21no—
81C2×Dic281—42no—
82C2×Dic281—41no—
83C4×D281—42no—
84#14555886—41no—
85C23×C281—21no—
86C23×C281—21no—
87C23×C281—21no—
88C23×C281—41no—
89C23×C281—42no—
90C23×C281C2×D411yescharacteristic
91C23×C281C2×D411yescharacteristic
92Q8×C281—21no—
93D4×C281—21no—
94D4×C281—41no—
95D4×C281—41no—
96D4×C281—41no—
97D4×C281—42no—
98D4×C281—41no—
99D4×C281—82no—
100C2×C4×C281—21no—
101C2×C4×C281—21no—
102C2×C4×C281—21no—
103C2×C4×C281—41no—
104C2×C4×C281—41no—
105C2×C4×C281C2×D411yescharacteristic
106C22×C281—22no—
107C22×C281—21no—
108C22×C281—21no—
109C22×C281—41no—
110C22×C281—41no—
111C22×C281—41no—
112C22×C281—42no—
113C22×C281—41no—
114C22×C281—41no—
115C22×C281—81no—
116C22×C281—81no—
117C22×C281—81no—
118C22×C281#12011yescharacteristic
119C2×D281—22no—
120C2×D281—41no—
121C2×D281—41no—
122C2×D281—42no—
123C2×D281—41no—
124C2×D281—41no—
125C2×D281—41no—
126C2×D281—81no—
127C2×D281—84no—
128C4×C281—21no—
129C4×C281—41no—
130C4×C281—41no—
131C4×C281—81no—
132Dic281—22no—
133Dic281—41no—
134Dic281—81no—
135C2×C281—21no—
136C2×C281—41no—
137C2×C281—41no—
138C2×C281—42no—
139C2×C281—81no—
140C2×C281B(4,𝔽2)11yescharacteristic
141D281—42no—
142D281—81no—
143C281#219611yescharacteristic, complemented, Sylow
144#2196—2811nomaximal, Sylow
145D42—2811no—
146B(4,𝔽2)—2811no—
147B(4,𝔽2)D28111yescharacteristic, complemented
148#453—2811no—
149#353—2811no—
150AΣL(1,𝔽16)—2811no—
151AΣL(1,𝔽16)—2811no—
152H(5,𝔽2)C2×D28111yescharacteristic, complemented
153C22×D4—5621no—
154C22×D4—5621no—
155AGL(1,ℤ/8)—5621no—
156#127—2811no—
157#121—5621no—
158#121—5621no—
159#120—21no—
160#120—2811no—
161#120—5621no—
162#120—5621no—
163#120C2×D28111yescharacteristic
164C4×D4—5621no—
165#104—5621no—
166#100—2811no—
167#99—21no—
168#99—2811no—
169#99—5621no—
170#99C2×D28111yescharacteristic, complemented
171C24—2811no—
172C24—5621no—
173C24C22⋊D28111yescharacteristic, complemented
174#41—21no—
175#41—41no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4—2811no—
182C2×D4—5621no—
183C2×D4—5621no—
184C2×D4—5621no—
185C2×D4—5621no—
186C2×D4—5621no—
187C2×D4—5621no—
188C2×D4—11244no—
189C2×D4—11244no—
190C2×D4—11241no—
191C2×D4C22×D28111yescharacteristic
192C22×C4—5621no—
193C22×C4—5621no—
194SD16—11241no—
195D8—11241no—
196M16—5621no—
197C4⋊C4—5621no—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—41no—
201C22⋊C4—2811no—
202C22⋊C4—5621no—
203C22⋊C4—5621no—
204C22⋊C4—5621no—
205C22⋊C4—11241no—
206C22⋊C4C22⋊D28111yescharacteristic, complemented
207C42—2811no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—41no—
212C23—42no—
213C23—5621no—
214C23—5621no—
215C23—11241no—
216C23—11242no—
217C23—11242no—
218C23—11242no—
219C23—22481no—
220C23D4×D28111yescharacteristic
221C23C2×C22⋊D28111yescharacteristic
222Q8—21no—
223D4—21no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—42no—
228D4—41no—
229D4—82no—
230D4—5624no—
231D4—11241no—
232D4—11242no—
233D4—11242no—
234D4—11242no—
235D4—11242no—
236D4—11242no—
237D4—22482no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—5621no—
244C2×C4—5621no—
245C2×C4—11242no—
246C2×C4—11242no—
247C2×C4—11241no—
248C2×C4D4×D28111yescharacteristic
249C8—11241no—
250C22—22no—
251C22—21no—
252C22—21no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—41no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—5622no—
263C22—11241no—
264C22—11241no—
265C22—11241no—
266C22—11242no—
267C22—11241no—
268C22—11241no—
269C22—22481no—
270C22—22484no—
271C22#2258284711yescharacteristic
272C4—21no—
273C4—41no—
274C4—41no—
275C4—81no—
276C4—5622no—
277C4—11241no—
278C4—22481no—
279C2—21no—
280C2—41no—
281C2—41no—
282C2—42no—
283C2—81no—
284C2—11242no—
285C2—22481no—
286C2#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#2196
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. #31824095C2semidirect
2. #31823650C2semidirect
3. #31823631C2semidirect
4. #31823255C2semidirect
5. #31823250C2semidirect
6. #31823249C2semidirect
7. B(4,𝔽2)×C281C2semidirect
19. #22582796C22semidirect
21. #22582794C22semidirect
22. H(5,𝔽2)×C281C22semidirect
26. #99×C281C22semidirect
28. C23×D281D4semidirect
30. C2×D1124D4semidirect
46. C22⋊Dic281D4semidirect
50. C4×Dic281D4semidirect
51. C24×C281D4semidirect
63. C22⋊C4×C281D4semidirect
143. C281#2196semidirect
147. B(4,𝔽2)D281semidirect
152. H(5,𝔽2)C2×D281semidirect
170. #99C2×D281semidirect
173. C24C22⋊D281semidirect
206. C22⋊C4C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318240952
#318236502
#318236312
#318232552
#318232502
#318232492
B(4,𝔽2)×C2812
#2196281