Finite Group Databasebeta

← #44401740

Subgroups — #44401740

Order 29056.

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#28409769C211yesmaximal, characteristic, complemented
2#28409222C211yesmaximal, characteristic, complemented
3#28409219C211yesmaximal, characteristic, complemented
4#28408825C211yesmaximal, characteristic, complemented
5#28408823C211yesmaximal, characteristic, complemented
6#28408820C211yesmaximal, characteristic, complemented
7#453×C227C211yesmaximal, characteristic, complemented
8#20300282—21no—
9#20300269—21no—
10#20300269—21no—
11#20300269C2211yescharacteristic
12#20300260—21no—
13#20300260—21no—
14#20300260—21no—
15#20300256—21no—
16#20300256—21no—
17#20300256C2211yescharacteristic
18#20300203—21no—
19#20300203—21no—
20#20300203C2211yescharacteristic
21#20300203C2211yescharacteristic
22H(5,𝔽2)×C227C2211yescharacteristic
23AGL(1,ℤ/8)×C227—21no—
24#127×C227C2211yescharacteristic
25#104×C227—21no—
26#100×C227C2211yescharacteristic
27C23×D227D411yescharacteristic
28C2×C22⋊D227—21no—
29C2×C22⋊D227—21no—
30C2×C22⋊D227—21no—
31C2×C22⋊D227—41no—
32C22×Dic227—21no—
33C22×Dic227D411yescharacteristic, complemented
34Dic227⋊C4—21no—
35Dic227⋊C4—21no—
36Dic227⋊C4—21no—
37Dic227⋊C4—41no—
38C22⋊Dic227—21no—
39C22⋊Dic227—21no—
40C22⋊Dic227—21no—
41C22⋊Dic227—21no—
42C22⋊Dic227—41no—
43C22⋊Dic227D411yescharacteristic
44C22⋊Dic227D411yescharacteristic, complemented
45(C2×D227)⋊C4—21no—
46(C2×D227)⋊C4—21no—
47(C2×D227)⋊C4—21no—
48(C2×D227)⋊C4—41no—
49#41×C227—21no—
50#41×C227—41no—
51C2×D4×C227—21no—
52C2×D4×C227—21no—
53C2×D4×C227—21no—
54C2×D4×C227—21no—
55C2×D4×C227—41no—
56C2×D4×C227D411yescharacteristic, complemented
57C2×D4×C227C2311yescharacteristic
58SD16×C227—41no—
59D8×C227—41no—
60M16×C227—21no—
61C42×C227D411yescharacteristic, complemented
62C22×D227—21no—
63C22×D227—41no—
64C22×D227—81no—
65C22⋊D227—81no—
66C22⋊D227—81no—
67C22⋊D227—81no—
68C22⋊D227—82no—
69C2×Dic227—21no—
70C2×Dic227—21no—
71C2×Dic227—21no—
72C2×Dic227—41no—
73C2×Dic227—41no—
74C2×Dic227—41no—
75C2×Dic227—81no—
76C23×C227—21no—
77C23×C227—21no—
78C23×C227—21no—
79C23×C227C2×D411yescharacteristic
80C23×C227C2×D411yescharacteristic
81Q8×C227—21no—
82D4×C227—21no—
83D4×C227—41no—
84D4×C227—41no—
85D4×C227—41no—
86D4×C227—41no—
87D4×C227—41no—
88D4×C227—81no—
89D4×C227—81no—
90C2×C4×C227—21no—
91C2×C4×C227—21no—
92C2×C4×C227—21no—
93C2×C4×C227—41no—
94C2×C4×C227C2×D411yescharacteristic
95C8×C227—41no—
96C22×C227—21no—
97C22×C227—21no—
98C22×C227—41no—
99C22×C227—41no—
100C22×C227—41no—
101C22×C227—41no—
102C22×C227—41no—
103C22×C227—41no—
104C22×C227—81no—
105C22×C227—81no—
106C22×C227#12011yescharacteristic
107C2×D227—41no—
108C2×D227—41no—
109C2×D227—42no—
110C2×D227—41no—
111C2×D227—81no—
112C4×C227—21no—
113C4×C227—41no—
114C4×C227—41no—
115Dic227—41no—
116Dic227—41no—
117Dic227—41no—
118Dic227—81no—
119Dic227—81no—
120C2×C227—21no—
121C2×C227—41no—
122C2×C227—41no—
123C2×C227—81no—
124C2×C227—81no—
125C2×C227B(4,𝔽2)11yescharacteristic
126D227—81no—
127C227#220011yescharacteristic, complemented, Sylow
128#2200—2271nomaximal, Sylow
129#560—2271no—
130#458—2271no—
131B(4,𝔽2)—2271no—
132#453D22711yescharacteristic, complemented
133#353—2271no—
134#352—2271no—
135AΣL(1,𝔽16)—2271no—
136H(5,𝔽2)C2×D22711yescharacteristic
137AGL(1,ℤ/8)—21no—
138#127C2×D22711yescharacteristic
139#126—4541no—
140#123—4541no—
141#123—4541no—
142#123—2271no—
143#121—4541no—
144#121—4541no—
145#121—4541no—
146#120—4541no—
147#120—4541no—
148#120—2271no—
149#104—21no—
150#100C2×D22711yescharacteristic
151#99—4541no—
152#99—4541no—
153#99—2271no—
154#99—2271no—
155C24—2271no—
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—9081no—
164C2×D4—4541no—
165C2×D4—4541no—
166C2×D4—4541no—
167C2×D4C22⋊D22711yescharacteristic, complemented
168C2×D4C22×D22711yescharacteristic
169C22×C4—4541no—
170C22×C4—2271no—
171SD16—41no—
172D8—41no—
173M16—21no—
174C4⋊C4—9081no—
175C4⋊C4—4541no—
176C4⋊C4—4541no—
177C4⋊C4—4541no—
178C22⋊C4—9081no—
179C22⋊C4—9081no—
180C22⋊C4—4541no—
181C22⋊C4—4541no—
182C22⋊C4—4541no—
183C22⋊C4—4541no—
184C22⋊C4—4541no—
185C22⋊C4—4541no—
186C22⋊C4—4541no—
187C22⋊C4—2271no—
188C22⋊C4—2271no—
189C42C22⋊D22711yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—21no—
193C23—18161no—
194C23—9081no—
195C23—4541no—
196C23D4×D22711yescharacteristic
197C23D4×D22711yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—41no—
205D4—81no—
206D4—81no—
207D4—18162no—
208D4—18161no—
209D4—18161no—
210D4—18161no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—18161no—
216C2×C4—9081no—
217C2×C4—9081no—
218C2×C4—9081no—
219C2×C4—4541no—
220C2×C4—4541no—
221C2×C4—4541no—
222C2×C4C2×C22⋊D22711yescharacteristic
223C8—41no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—18161no—
235C22—9081no—
236C22—9081no—
237C22—9082no—
238C22—9081no—
239C22#2030025611yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—18161no—
244C4—18161no—
245C4—9081no—
246C4—9081no—
247C4—9081no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—18161no—
254C2#2840921811yescharacteristic
subgroupG/H
centerC2#28409218
commutator, cosocleC2×D4×C227C23
FrattiniC2×D4C22×D227
Fitting#453×C227C2
socleC2×C227B(4,𝔽2)
hypercenter#453D227
hypocenterC227#2200
LCSG ▷ C2×D4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #28409769C2semidirect
2. #28409222C2semidirect
3. #28409219C2semidirect
4. #28408825C2semidirect
5. #28408823C2semidirect
6. #28408820C2semidirect
7. #453×C227C2semidirect
33. C22×Dic227D4semidirect
44. C22⋊Dic227D4semidirect
56. C2×D4×C227D4semidirect
61. C42×C227D4semidirect
127. C227#2200semidirect
132. #453D227semidirect
167. C2×D4C22⋊D227semidirect
189. C42C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
#284097692
#284092222
#284092192
#284088252
#284088232
#284088202
#453×C2272
#2200227