Finite Group Databasebeta

← #2865×D89 #36760466

Subgroups — #2865×D89 #36760466

Order 22784.

2186 conjugacy classes of subgroups; only the 591 normal subgroups are shown.

normal subgroups only

This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 591 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#26028642C217yesmaximal, complemented
2#26028641C211yesmaximal, characteristic, complemented
3#26028640C217yesmaximal, complemented
4#388×D89C217yesmaximal
5#387×D89C217yesmaximal, complemented
6C43×D89C211yesmaximal, characteristic, complemented
7C89×#2865C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D89C2217yes—
9C2×C22⋊C4×D89C2217yes—
10C2×C42×D89C2217yes—
11#19151492C2217yes—
12#19151491C2217yes—
13#19151490C2217yes—
14#19151489C2217yes—
15#19151488C2217yes—
16#19151487C2217yes—
17#19151486C2217yes—
18#19151485C2217yescomplemented
19#19151484C2217yescomplemented
20#19151483C2217yescomplemented
21#19151482C2217yescomplemented
22#19151481C2217yescomplemented
23#19151480C2217yescomplemented
24#19151479C2217yescomplemented
25#95×D89C2217yes—
26#95×D89C2217yes—
27C42×Dic89C2217yescomplemented
28#388×C89C2217yes—
29#387×C89C2217yescomplemented
30C43×C89C2211yescharacteristic, complemented
31C24×D89C2311yescharacteristic
32C22×C4×D89C2317yes—
33C22×C4×D89C2317yes—
34C2×C4⋊Dic89C2317yes—
35C2×#13083553C2317yes—
36C2×#13083553C2317yes—
37C4⋊C4×D89—228no—
38C2×C22⋊Dic89C2317yes—
39C2×#13083551C2317yes—
40C2×#13083551C2317yes—
41C22⋊C4×D89—228no—
42C2×C4×Dic89C2317yes—
43C2×C4×Dic89C2317yes—
44C2×C4×Dic89C2317yes—
45C42×D89—228no—
46#15667919C2317yes—
47#15667919C2317yes—
48#15667919C2317yes—
49#15667919C2317yes—
50#15667919C2317yes—
51#15667919C2317yes—
52C2×C4⋊C4×C89C2317yes—
53C2×C22⋊C4×C89C2317yes—
54C2×C42×C89C2317yes—
55#95×C89C2317yes—
56#95×C89C2317yes—
57C23×D89—214no—
58C23×D89C2411yescharacteristic
59C23×D89C2411yescharacteristic
60C22×Dic89C2417yes—
61C22×Dic89C2417yes—
62C2×C4×D89—214no—
63C2×C4×D89—214no—
64C2×C4×D89—214no—
65C2×C4×D89—214no—
66C2×C4×D89—214no—
67C2×C4×D89#41128yes—
68C4⋊Dic89—214no—
69#13083553—214no—
70#13083553—214no—
71C22⋊Dic89—214no—
72#13083551—214no—
73#13083551—214no—
74C4×Dic89—214no—
75C4×Dic89—214no—
76C4×Dic89—214no—
77C24×C89C2411yescharacteristic
78C22×C4×C89C2417yes—
79C22×C4×C89C2417yes—
80C4⋊C4×C89—214no—
81C22⋊C4×C89—214no—
82C42×C89—214no—
83C23×C89—27no—
84C23×C89C2511yescharacteristic
85C22×D89—27no—
86C22×D89—428no—
87C22×D89C2×#41114yes—
88C2×C4×C89—27no—
89C2×C4×C89—27no—
90C2×C4×C89—27no—
91C2×C4×C89—27no—
92C2×C4×C89—27no—
93C2×C4×C89C2×#41114yes—
94C2×Dic89—27no—
95C2×Dic89—27no—
96C2×Dic89—27no—
97C2×Dic89—27no—
98C2×Dic89—27no—
99C2×Dic89C2×#41114yes—
100C4×D89—256no—
101C4×D89—428no—
102C22×C89—47no—
103C22×C89C22×#4117yes—
104C2×D89—47no—
105C2×D89—88no—
106C2×D89#529128yes—
107C4×C89—214no—
108C4×C89—47no—
109Dic89—214no—
110Dic89—47no—
111C2×#2865—891nomaximal, Sylow
112C2×C89—81no—
113C2×C89C2×#52917yes—
114D89—81no—
115D89#286518yesdirect product factor
116#2865—897no—
117#2865—897no—
118#2865—891no—
119#2865D8911yescharacteristic, direct product factor
120C2×#388—897no—
121C2×#387—897no—
122C2×C43—891no—
123C89C2×#286511yescharacteristic, complemented, Sylow
124C22×C4⋊C4—897no—
125C22×C22⋊C4—897no—
126C22×C42—897no—
127#388—897no—
128#388—897no—
129#388—897no—
130#388—897no—
131#388—897no—
132#388—897no—
133#388—897no—
134#388C2×D8917yes—
135#387—897no—
136#387—897no—
137#387—897no—
138#387—897no—
139#387—897no—
140#387—897no—
141#387—897no—
142#387C2×D8917yescomplemented
143C2×#95—897no—
144C2×#95—897no—
145C43—897no—
146C43C2×D8911yescharacteristic, complemented
147C25—891no—
148C23×C4—897no—
149C23×C4—897no—
150C2×C4⋊C4—897no—
151C2×C4⋊C4—897no—
152C2×C4⋊C4—897no—
153C2×C4⋊C4—17828no—
154C2×C4⋊C4C22×D8917yes—
155C2×C22⋊C4—897no—
156C2×C22⋊C4—897no—
157C2×C22⋊C4—897no—
158C2×C22⋊C4—17828no—
159C2×C22⋊C4C22×D8917yes—
160C2×C42—897no—
161C2×C42—897no—
162C2×C42—897no—
163C2×C42—17828no—
164C2×C42C22×D8917yes—
165#95—897no—
166#95—897no—
167#95—897no—
168#95—897no—
169#95—897no—
170#95—897no—
171#95C22×D8917yes—
172#95C22×D8917yes—
173C24—891no—
174C24—891no—
175C24—17814no—
176C24C23×D8911yescharacteristic
177C22×C4—897no—
178C22×C4—8928no—
179C22×C4—897no—
180C22×C4—17814no—
181C22×C4—17814no—
182C22×C4—17814no—
183C22×C4—17814no—
184C22×C4—17814no—
185C22×C4C23×D8917yes—
186C22×C4C23×D8917yes—
187C4⋊C4—214no—
188C4⋊C4—17814no—
189C4⋊C4—17814no—
190C4⋊C4—17814no—
191C22⋊C4—214no—
192C22⋊C4—17814no—
193C22⋊C4—17814no—
194C22⋊C4—17814no—
195C42—214no—
196C42—17814no—
197C42—17814no—
198C42—17814no—
199C23—27no—
200C23—8914no—
201C23—35628no—
202C23—1787no—
203C23C24×D8911yescharacteristic
204C2×C4—27no—
205C2×C4—27no—
206C2×C4—27no—
207C2×C4—27no—
208C2×C4—27no—
209C2×C4—8914no—
210C2×C4—35628no—
211C2×C4—17856no—
212C2×C4—1787no—
213C2×C4—1787no—
214C2×C4—1787no—
215C2×C4—1787no—
216C2×C4—1787no—
217C2×C4#41×D89114yes—
218C22—47no—
219C22—8928no—
220C22—3567no—
221C22—7128no—
222C22C2×#41×D8917yes—
223C4—214no—
224C4—47no—
225C4—3567no—
226C4—17814no—
227C2—81no—
228C2—898no—
229C2—7121no—
230C2#529×D8917yes—
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2865C2
prime radicalC24×D89C23
hypercenter#2865D89
hypocenterC89C2×#2865
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2865

Complements

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

NH ≅ G/Ntype
1. #26028642C2semidirect
2. #26028641C2semidirect
3. #26028640C2semidirect
5. #387×D89C2semidirect
6. C43×D89C2semidirect
7. C89×#2865C2semidirect
18. #19151485C22semidirect
19. #19151484C22semidirect
20. #19151483C22semidirect
21. #19151482C22semidirect
22. #19151481C22semidirect
23. #19151480C22semidirect
24. #19151479C22semidirect
27. C42×Dic89C22semidirect
29. #387×C89C22semidirect
30. C43×C89C22semidirect
115. D89#2865direct (N × H)
119. #2865D89direct (N × H)
123. C89C2×#2865semidirect
142. #387C2×D89semidirect
146. C43C2×D89semidirect

Maximal subgroups

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

subgroupindex
#260286422
#260286412
#260286402
#388×D892
#387×D892
C43×D892
C89×#28652
C2×#286589