Finite Group Databasebeta

← #2865×D83 #35610442

Subgroups — #2865×D83 #35610442

Order 21248.

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#24915853C217yesmaximal, complemented
2#24915852C211yesmaximal, characteristic, complemented
3#24915851C217yesmaximal, complemented
4#388×D83C217yesmaximal
5#387×D83C217yesmaximal, complemented
6C43×D83C211yesmaximal, characteristic, complemented
7C83×#2865C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D83C2217yes—
9C2×C22⋊C4×D83C2217yes—
10C2×C42×D83C2217yes—
11#19127595C2217yes—
12#19127594C2217yes—
13#19127593C2217yes—
14#19127592C2217yes—
15#19127591C2217yes—
16#19127590C2217yes—
17#19127589C2217yes—
18#19127588C2217yescomplemented
19#19127587C2217yescomplemented
20#19127586C2217yescomplemented
21#19127585C2217yescomplemented
22#19127584C2217yescomplemented
23#19127583C2217yescomplemented
24#19127582C2217yescomplemented
25#95×D83C2217yes—
26#95×D83C2217yes—
27C42×Dic83C2217yescomplemented
28#388×C83C2217yes—
29#387×C83C2217yescomplemented
30C43×C83C2211yescharacteristic, complemented
31C24×D83C2311yescharacteristic
32C22×C4×D83C2317yes—
33C22×C4×D83C2317yes—
34C2×C4⋊Dic83C2317yes—
35C2×Dic83⋊C4C2317yes—
36C2×Dic83⋊C4C2317yes—
37C4⋊C4×D83—228no—
38C2×C22⋊Dic83C2317yes—
39C2×(C2×D83)⋊C4C2317yes—
40C2×(C2×D83)⋊C4C2317yes—
41C22⋊C4×D83—228no—
42C2×C4×Dic83C2317yes—
43C2×C4×Dic83C2317yes—
44C2×C4×Dic83C2317yes—
45C42×D83—228no—
46C83⋊#95C2317yes—
47C83⋊#95C2317yes—
48C83⋊#95C2317yes—
49C83⋊#95C2317yes—
50C83⋊#95C2317yes—
51C83⋊#95C2317yes—
52C2×C4⋊C4×C83C2317yes—
53C2×C22⋊C4×C83C2317yes—
54C2×C42×C83C2317yes—
55#95×C83C2317yes—
56#95×C83C2317yes—
57C23×D83—214no—
58C23×D83C2411yescharacteristic
59C23×D83C2411yescharacteristic
60C22×Dic83C2417yes—
61C22×Dic83C2417yes—
62C2×C4×D83—214no—
63C2×C4×D83—214no—
64C2×C4×D83—214no—
65C2×C4×D83—214no—
66C2×C4×D83—214no—
67C2×C4×D83#41128yes—
68C4⋊Dic83—214no—
69Dic83⋊C4—214no—
70Dic83⋊C4—214no—
71C22⋊Dic83—214no—
72(C2×D83)⋊C4—214no—
73(C2×D83)⋊C4—214no—
74C4×Dic83—214no—
75C4×Dic83—214no—
76C4×Dic83—214no—
77C24×C83C2411yescharacteristic
78C22×C4×C83C2417yes—
79C22×C4×C83C2417yes—
80C4⋊C4×C83—214no—
81C22⋊C4×C83—214no—
82C42×C83—214no—
83C23×C83—27no—
84C23×C83C2511yescharacteristic
85C22×D83—27no—
86C22×D83—428no—
87C22×D83C2×#41114yes—
88C2×C4×C83—27no—
89C2×C4×C83—27no—
90C2×C4×C83—27no—
91C2×C4×C83—27no—
92C2×C4×C83—27no—
93C2×C4×C83C2×#41114yes—
94C2×Dic83—27no—
95C2×Dic83—27no—
96C2×Dic83—27no—
97C2×Dic83—27no—
98C2×Dic83—27no—
99C2×Dic83C2×#41114yes—
100C4×D83—256no—
101C4×D83—428no—
102C22×C83—47no—
103C22×C83C22×#4117yes—
104C2×D83—47no—
105C2×D83—88no—
106C2×D83#529128yes—
107C4×C83—214no—
108C4×C83—47no—
109Dic83—214no—
110Dic83—47no—
111C2×#2865—831nomaximal, Sylow
112C2×C83—81no—
113C2×C83C2×#52917yes—
114D83—81no—
115D83#286518yesdirect product factor
116#2865—837no—
117#2865—837no—
118#2865—831no—
119#2865D8311yescharacteristic, direct product factor
120C2×#388—837no—
121C2×#387—837no—
122C2×C43—831no—
123C83C2×#286511yescharacteristic, complemented, Sylow
124C22×C4⋊C4—837no—
125C22×C22⋊C4—837no—
126C22×C42—837no—
127#388—837no—
128#388—837no—
129#388—837no—
130#388—837no—
131#388—837no—
132#388—837no—
133#388—837no—
134#388C2×D8317yes—
135#387—837no—
136#387—837no—
137#387—837no—
138#387—837no—
139#387—837no—
140#387—837no—
141#387—837no—
142#387C2×D8317yescomplemented
143C2×#95—837no—
144C2×#95—837no—
145C43—837no—
146C43C2×D8311yescharacteristic, complemented
147C25—831no—
148C23×C4—837no—
149C23×C4—837no—
150C2×C4⋊C4—837no—
151C2×C4⋊C4—837no—
152C2×C4⋊C4—837no—
153C2×C4⋊C4—16628no—
154C2×C4⋊C4C22×D8317yes—
155C2×C22⋊C4—837no—
156C2×C22⋊C4—837no—
157C2×C22⋊C4—837no—
158C2×C22⋊C4—16628no—
159C2×C22⋊C4C22×D8317yes—
160C2×C42—837no—
161C2×C42—837no—
162C2×C42—837no—
163C2×C42—16628no—
164C2×C42C22×D8317yes—
165#95—837no—
166#95—837no—
167#95—837no—
168#95—837no—
169#95—837no—
170#95—837no—
171#95C22×D8317yes—
172#95C22×D8317yes—
173C24—831no—
174C24—831no—
175C24—16614no—
176C24C23×D8311yescharacteristic
177C22×C4—837no—
178C22×C4—8328no—
179C22×C4—837no—
180C22×C4—16614no—
181C22×C4—16614no—
182C22×C4—16614no—
183C22×C4—16614no—
184C22×C4—16614no—
185C22×C4C23×D8317yes—
186C22×C4C23×D8317yes—
187C4⋊C4—214no—
188C4⋊C4—16614no—
189C4⋊C4—16614no—
190C4⋊C4—16614no—
191C22⋊C4—214no—
192C22⋊C4—16614no—
193C22⋊C4—16614no—
194C22⋊C4—16614no—
195C42—214no—
196C42—16614no—
197C42—16614no—
198C42—16614no—
199C23—27no—
200C23—33228no—
201C23—8314no—
202C23—1667no—
203C23C24×D8311yescharacteristic
204C2×C4—27no—
205C2×C4—27no—
206C2×C4—27no—
207C2×C4—27no—
208C2×C4—27no—
209C2×C4—33228no—
210C2×C4—8314no—
211C2×C4—16656no—
212C2×C4—1667no—
213C2×C4—1667no—
214C2×C4—1667no—
215C2×C4—1667no—
216C2×C4—1667no—
217C2×C4#41×D83114yes—
218C22—47no—
219C22—3327no—
220C22—8328no—
221C22—6648no—
222C22C2×#41×D8317yes—
223C4—214no—
224C4—47no—
225C4—3327no—
226C4—16614no—
227C2—81no—
228C2—838no—
229C2—6641no—
230C2#529×D8317yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2865C2
prime radicalC24×D83C23
hypercenter#2865D83
hypocenterC83C2×#2865
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2865

Complements

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

NH ≅ G/Ntype
1. #24915853C2semidirect
2. #24915852C2semidirect
3. #24915851C2semidirect
5. #387×D83C2semidirect
6. C43×D83C2semidirect
7. C83×#2865C2semidirect
18. #19127588C22semidirect
19. #19127587C22semidirect
20. #19127586C22semidirect
21. #19127585C22semidirect
22. #19127584C22semidirect
23. #19127583C22semidirect
24. #19127582C22semidirect
27. C42×Dic83C22semidirect
29. #387×C83C22semidirect
30. C43×C83C22semidirect
115. D83#2865direct (N × H)
119. #2865D83direct (N × H)
123. C83C2×#2865semidirect
142. #387C2×D83semidirect
146. C43C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249158532
#249158522
#249158512
#388×D832
#387×D832
C43×D832
C83×#28652
C2×#286583