Finite Group Databasebeta

← D47×#2865 #26422316

Subgroups — D47×#2865 #26422316

Order 12032.

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#20251778C217yesmaximal, complemented
2#20251777C211yesmaximal, characteristic, complemented
3#20251776C217yesmaximal, complemented
4#388×D47C217yesmaximal
5#387×D47C217yesmaximal, complemented
6C43×D47C211yesmaximal, characteristic, complemented
7C47×#2865C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D47C2217yes—
9C2×C22⋊C4×D47C2217yes—
10C2×C42×D47C2217yes—
11#15689017C2217yes—
12#15689016C2217yes—
13#15689015C2217yes—
14#15689014C2217yes—
15#15689013C2217yes—
16#15689012C2217yes—
17#15689011C2217yes—
18#15689010C2217yescomplemented
19#15689009C2217yescomplemented
20#15689008C2217yescomplemented
21#15689007C2217yescomplemented
22#15689006C2217yescomplemented
23#15689005C2217yescomplemented
24#15689004C2217yescomplemented
25#95×D47C2217yes—
26#95×D47C2217yes—
27C42×Dic47C2217yescomplemented
28C47×#388C2217yes—
29C47×#387C2217yescomplemented
30C43×C47C2211yescharacteristic, complemented
31C24×D47C2311yescharacteristic
32C22×C4×D47C2317yes—
33C22×C4×D47C2317yes—
34C2×C4⋊Dic47C2317yes—
35C2×Dic47⋊C4C2317yes—
36C2×Dic47⋊C4C2317yes—
37C4⋊C4×D47—228no—
38C2×C22⋊Dic47C2317yes—
39C2×(C2×D47)⋊C4C2317yes—
40C2×(C2×D47)⋊C4C2317yes—
41C22⋊C4×D47—228no—
42C2×C4×Dic47C2317yes—
43C2×C4×Dic47C2317yes—
44C2×C4×Dic47C2317yes—
45C42×D47—228no—
46C47⋊#95C2317yes—
47C47⋊#95C2317yes—
48C47⋊#95C2317yes—
49C47⋊#95C2317yes—
50C47⋊#95C2317yes—
51C47⋊#95C2317yes—
52C2×C4⋊C4×C47C2317yes—
53C2×C22⋊C4×C47C2317yes—
54C2×C42×C47C2317yes—
55#95×C47C2317yes—
56#95×C47C2317yes—
57C24×C47C2411yescharacteristic
58C23×D47—214no—
59C23×D47C2411yescharacteristic
60C23×D47C2411yescharacteristic
61C22×C4×C47C2417yes—
62C22×C4×C47C2417yes—
63C22×Dic47C2417yes—
64C22×Dic47C2417yes—
65C2×C4×D47—214no—
66C2×C4×D47—214no—
67C2×C4×D47—214no—
68C2×C4×D47—214no—
69C2×C4×D47—214no—
70C2×C4×D47#41128yes—
71C4⋊C4×C47—214no—
72C22⋊C4×C47—214no—
73C42×C47—214no—
74C22⋊Dic47—214no—
75(C2×D47)⋊C4—214no—
76(C2×D47)⋊C4—214no—
77C4⋊Dic47—214no—
78Dic47⋊C4—214no—
79Dic47⋊C4—214no—
80C4×Dic47—214no—
81C4×Dic47—214no—
82C4×Dic47—214no—
83C23×C47—27no—
84C23×C47C2511yescharacteristic
85C22×D47—27no—
86C22×D47—428no—
87C22×D47C2×#41114yes—
88C2×C4×C47—27no—
89C2×C4×C47—27no—
90C2×C4×C47—27no—
91C2×C4×C47—27no—
92C2×C4×C47—27no—
93C2×C4×C47C2×#41114yes—
94C2×Dic47—27no—
95C2×Dic47—27no—
96C2×Dic47—27no—
97C2×Dic47—27no—
98C2×Dic47—27no—
99C2×Dic47C2×#41114yes—
100C4×D47—256no—
101C4×D47—428no—
102C2×#2865—471nomaximal, Sylow
103C22×C47—47no—
104C22×C47C22×#4117yes—
105C2×D47—47no—
106C2×D47—88no—
107C2×D47#529128yes—
108C4×C47—214no—
109C4×C47—47no—
110Dic47—214no—
111Dic47—47no—
112#2865—477no—
113#2865—477no—
114#2865—471no—
115#2865D4711yescharacteristic, direct product factor
116C2×#388—477no—
117C2×#387—477no—
118C2×C43—471no—
119C2×C47—81no—
120C2×C47C2×#52917yes—
121D47—81no—
122D47#286518yesdirect product factor
123C22×C4⋊C4—477no—
124C22×C22⋊C4—477no—
125C22×C42—477no—
126#388—477no—
127#388—477no—
128#388—477no—
129#388—477no—
130#388—477no—
131#388—477no—
132#388—477no—
133#388C2×D4717yes—
134#387—477no—
135#387—477no—
136#387—477no—
137#387—477no—
138#387—477no—
139#387—477no—
140#387—477no—
141#387C2×D4717yescomplemented
142C2×#95—477no—
143C2×#95—477no—
144C43—477no—
145C43C2×D4711yescharacteristic, complemented
146C47C2×#286511yescharacteristic, complemented, Sylow
147C25—471no—
148C23×C4—477no—
149C23×C4—477no—
150C2×C4⋊C4—477no—
151C2×C4⋊C4—477no—
152C2×C4⋊C4—477no—
153C2×C4⋊C4—9428no—
154C2×C4⋊C4C22×D4717yes—
155C2×C22⋊C4—477no—
156C2×C22⋊C4—477no—
157C2×C22⋊C4—477no—
158C2×C22⋊C4—9428no—
159C2×C22⋊C4C22×D4717yes—
160C2×C42—477no—
161C2×C42—477no—
162C2×C42—477no—
163C2×C42—9428no—
164C2×C42C22×D4717yes—
165#95—477no—
166#95—477no—
167#95—477no—
168#95—477no—
169#95—477no—
170#95—477no—
171#95C22×D4717yes—
172#95C22×D4717yes—
173C24—471no—
174C24—471no—
175C24—9414no—
176C24C23×D4711yescharacteristic
177C22×C4—477no—
178C22×C4—4728no—
179C22×C4—477no—
180C22×C4—9414no—
181C22×C4—9414no—
182C22×C4—9414no—
183C22×C4—9414no—
184C22×C4—9414no—
185C22×C4C23×D4717yes—
186C22×C4C23×D4717yes—
187C4⋊C4—214no—
188C4⋊C4—9414no—
189C4⋊C4—9414no—
190C4⋊C4—9414no—
191C22⋊C4—214no—
192C22⋊C4—9414no—
193C22⋊C4—9414no—
194C22⋊C4—9414no—
195C42—214no—
196C42—9414no—
197C42—9414no—
198C42—9414no—
199C23—27no—
200C23—4714no—
201C23—947no—
202C23—18828no—
203C23C24×D4711yescharacteristic
204C2×C4—27no—
205C2×C4—27no—
206C2×C4—27no—
207C2×C4—27no—
208C2×C4—27no—
209C2×C4—4714no—
210C2×C4—9456no—
211C2×C4—947no—
212C2×C4—947no—
213C2×C4—947no—
214C2×C4—947no—
215C2×C4—947no—
216C2×C4—18828no—
217C2×C4#41×D47114yes—
218C22—47no—
219C22—4728no—
220C22—3768no—
221C22—1887no—
222C22C2×#41×D4717yes—
223C4—214no—
224C4—47no—
225C4—9414no—
226C4—1887no—
227C2—81no—
228C2—478no—
229C2—3761no—
230C2#529×D4717yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2865C2
prime radicalC24×D47C23
hypercenter#2865D47
hypocenterC47C2×#2865
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2865

Complements

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

NH ≅ G/Ntype
1. #20251778C2semidirect
2. #20251777C2semidirect
3. #20251776C2semidirect
5. #387×D47C2semidirect
6. C43×D47C2semidirect
7. C47×#2865C2semidirect
18. #15689010C22semidirect
19. #15689009C22semidirect
20. #15689008C22semidirect
21. #15689007C22semidirect
22. #15689006C22semidirect
23. #15689005C22semidirect
24. #15689004C22semidirect
27. C42×Dic47C22semidirect
29. C47×#387C22semidirect
30. C43×C47C22semidirect
115. #2865D47direct (N × H)
122. D47#2865direct (N × H)
141. #387C2×D47semidirect
145. C43C2×D47semidirect
146. C47C2×#2865semidirect

Maximal subgroups

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

subgroupindex
#202517782
#202517772
#202517762
#388×D472
#387×D472
C43×D472
C47×#28652
C2×#286547