Finite Group Databasebeta

← #24906452

Subgroups — #24906452

Order 10624.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#19128326C211yesmaximal, characteristic
2#19128031C211yesmaximal, characteristic, complemented
3#19127627C211yesmaximal, characteristic
4#19127439C211yesmaximal, characteristic, complemented
5#19127438C211yesmaximal, characteristic, complemented
6#19127424C211yesmaximal, characteristic
7#483×C83C211yesmaximal, characteristic, complemented
8#14581772—21no—
9#14581771C2211yescharacteristic
10#14581770—21no—
11#14581770—21no—
12#14581769—21no—
13#14581768—21no—
14C2×(C2×D83)⋊C4—21no—
15C2×(C2×D83)⋊C4C2211yescharacteristic
16C22⋊C4×D83—21no—
17#14581723—21no—
18#14581715—21no—
19C22⋊(C83⋊C8)C2211yescharacteristic
20C83⋊#95—21no—
21C83⋊#95C2211yescharacteristic
22C22⋊Q8×C83C2211yescharacteristic
23C2×C4⋊C4×C83C2211yescharacteristic
24#106×C83—21no—
25#103×C83—21no—
26C22⋊C8×C83C2211yescharacteristic
27C23×D83D411yescharacteristic
28C2×Dic166—21no—
29C2×Dic166D411yescharacteristic
30C22×Dic83—21no—
31C22×Dic83D411yescharacteristic
32C2×C4×D83—21no—
33C2×C4×D83—21no—
34C2×C83⋊C8—21no—
35C4⋊Dic83—21no—
36C4⋊Dic83D411yescharacteristic
37Dic83⋊C4—21no—
38Dic83⋊C4—21no—
39Dic83⋊C4—21no—
40C22⋊Dic83—21no—
41(C2×D83)⋊C4—21no—
42(C2×D83)⋊C4—21no—
43(C2×D83)⋊C4—21no—
44(C2×D83)⋊C4—21no—
45(C2×D83)⋊C4—42no—
46C2×Q8×C83D411yescharacteristic
47C22×C4×C83—21no—
48C22×C4×C83C2311yescharacteristic
49C2×C8×C83—21no—
50C4⋊C4×C83—21no—
51C4⋊C4×C83—21no—
52C4⋊C4×C83—21no—
53C4⋊C4×C83D411yescharacteristic
54C22⋊C4×C83—21no—
55C23×C83C2×D411yescharacteristic
56C22×D83—21no—
57C22×D83—21no—
58C22×D83—41no—
59C22×D83—41no—
60C22×D83SD1612yes—
61Q8×C83—41no—
62C2×C4×C83—21no—
63C2×C4×C83—21no—
64C2×C4×C83—41no—
65C2×C4×C83—41no—
66C2×C4×C83—41no—
67C2×C4×C83—41no—
68C2×C4×C83C2×D411yescharacteristic
69C2×C4×C83C2×D411yescharacteristic
70C2×Dic83—21no—
71C2×Dic83—21no—
72C2×Dic83—21no—
73C2×Dic83—41no—
74C2×Dic83—41no—
75C2×Dic83—41no—
76C2×Dic83—41no—
77C4×D83—81no—
78C4×D83—81no—
79Dic166—41no—
80Dic166—81no—
81C8×C83—41no—
82C83⋊C8—41no—
83C22×C83—21no—
84C22×C83—21no—
85C22×C83#12011yescharacteristic
86C22×C83C2×SD1611yescharacteristic
87C22×C83#13711yescharacteristic
88C2×D83—22no—
89C2×D83—41no—
90C2×D83—41no—
91C2×D83—42no—
92C2×D83—81no—
93C4×C83—21no—
94C4×C83—21no—
95C4×C83—41no—
96C4×C83—41no—
97C4×C83—81no—
98Dic83—41no—
99Dic83—41no—
100Dic83—41no—
101Dic83—81no—
102C2×C83—21no—
103C2×C83—21no—
104C2×C83#44811yescharacteristic
105C2×C83#45511yescharacteristic
106C2×C83#45811yescharacteristic
107D83—42no—
108#1608—831nomaximal, Sylow
109C83#160811yescharacteristic, complemented, Sylow
110#543—831no—
111#483—831no—
112#483D8311yescharacteristic, complemented
113#397—831no—
114#328—831no—
115#328—831no—
116#323—831no—
117C22⋊Q8—831no—
118C22⋊Q8—1661no—
119C22⋊Q8—1661no—
120C22⋊Q8—1661no—
121C22⋊Q8—1661no—
122C22⋊Q8—1661no—
123C22⋊Q8C2×D8311yescharacteristic
124C2×C4⋊C4C2×D8311yescharacteristic
125C2×C22⋊C4—831no—
126C2×C22⋊C4—1661no—
127C2×C22⋊C4—1661no—
128#106—21no—
129#106—1661no—
130#103—21no—
131#103—1661no—
132C22⋊C8—831no—
133C22⋊C8C2×D8311yescharacteristic
134#95—831no—
135#95—1661no—
136C24—831no—
137C2×Q8—831no—
138C2×Q8—1661no—
139C2×Q8C22⋊D8311yescharacteristic
140C22×C4—21no—
141C22×C4—831no—
142C22×C4—1661no—
143C22×C4—1661no—
144C22×C4—1661no—
145C22×C4C22×D8311yescharacteristic
146C2×C8—21no—
147C2×C8—1661no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—831no—
152C4⋊C4—1661no—
153C4⋊C4—1661no—
154C4⋊C4—1661no—
155C4⋊C4—1661no—
156C4⋊C4C22⋊D8311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—3322no—
159C22⋊C4—1661no—
160C22⋊C4—1661no—
161C22⋊C4—1661no—
162C22⋊C4—1661no—
163C22⋊C4—1661no—
164C23—3321no—
165C23—3321no—
166C23—832no—
167C23—1661no—
168C23—1661no—
169C23D4×D8311yescharacteristic
170Q8—41no—
171Q8—3321no—
172Q8—6641no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—3321no—
180C2×C4—3321no—
181C2×C4—3321no—
182C2×C4—3321no—
183C2×C4—6641no—
184C2×C4—6641no—
185C2×C4—1661no—
186C2×C4—1661no—
187C2×C4—1661no—
188C2×C4D4×D8311yescharacteristic
189C2×C4C2×C22⋊D8311yescharacteristic
190C8—41no—
191C8—3321no—
192C22—21no—
193C22—21no—
194C22—3322no—
195C22—3321no—
196C22—3321no—
197C22—6641no—
198C22—1662no—
199C22#1458176011yescharacteristic
200C22SD16×D8311yescharacteristic
201C22#1458182111yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—3321no—
208C4—3321no—
209C4—3321no—
210C4—6641no—
211C2—21no—
212C2—21no—
213C2—3322no—
214C2#1912783811yescharacteristic
215C2#1912787711yescharacteristic
216C2#1912789011yescharacteristic
subgroupG/H
centerC22#14581760
commutator, cosocleC22×C4×C83C23
FrattiniC22×C4C22×D83
Fitting#483×C83C2
socleC22×C83#120
prime radicalC23×D83D4
hypercenter#483D83
hypocenterC83#1608
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #19128031C2semidirect
4. #19127439C2semidirect
5. #19127438C2semidirect
7. #483×C83C2semidirect
109. C83#1608semidirect
112. #483D83semidirect

Maximal subgroups

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

subgroupindex
#191283262
#191280312
#191276272
#191274392
#191274382
#191274242
#483×C832
#160883