Finite Group Databasebeta

← #24911915

Subgroups — #24911915

Order 10624.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#14581768C211yesmaximal, characteristic
2C2×#14581750C211yesmaximal, characteristic
3#19127630C214yesmaximal
4#19127608C211yesmaximal, characteristic, complemented
5#19127583C214yesmaximal, complemented
6#19127570C211yesmaximal, characteristic, complemented
7#19127567C211yesmaximal, characteristic, complemented
8C4×(C2×D83)⋊C4C211yesmaximal, characteristic
9#391×C83C211yesmaximal, characteristic, complemented
10C22×C4×D83C2211yescharacteristic
11#14581768—24no—
12#14581750—24no—
13C2×C4⋊Dic83C2211yescharacteristic
14C2×C4⋊Dic83C2211yescharacteristic
15C2×Dic83⋊C4C2214yes—
16C2×Dic83⋊C4C2212yes—
17C2×(C2×D83)⋊C4C2212yes—
18C2×(C2×D83)⋊C4C2212yes—
19C2×(C2×D83)⋊C4C2212yes—
20C2×C4×Dic83C2211yescharacteristic
21C2×C4×Dic83C2212yes—
22C83⋊#95C2214yes—
23C83⋊#95C2212yes—
24C83⋊#95C2214yes—
25C22×Q8×C83C2211yescharacteristic
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C42×C83C2211yescharacteristic
28#95×C83C2214yes—
29C23×D83C2311yescharacteristic
30C22×Dic83C2312yes—
31C22×Dic83C2312yes—
32C22×Dic83C2311yescharacteristic
33C22×Dic83C2312yes—
34C2×C4×D83—22no—
35C2×C4×D83—22no—
36C2×C4×D83D414yes—
37C4⋊Dic83—22no—
38C4⋊Dic83—22no—
39Dic83⋊C4—24no—
40Dic83⋊C4—28no—
41(C2×D83)⋊C4—24no—
42(C2×D83)⋊C4—24no—
43(C2×D83)⋊C4—24no—
44C4×Dic83—22no—
45C4×Dic83—24no—
46C2×Q8×C83—22no—
47C2×Q8×C83—22no—
48C2×Q8×C83—22no—
49C22×C4×C83C2312yes—
50C22×C4×C83C2312yes—
51C22×C4×C83C2312yes—
52C22×C4×C83C2311yescharacteristic
53C4⋊C4×C83—22no—
54C42×C83—22no—
55C23×C83C2411yescharacteristic
56C22×D83—22no—
57C22×D83—21no—
58C22×D83—21no—
59C22×D83—22no—
60C22×D83C2×D412yes—
61Q8×C83—44no—
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83—22no—
68C2×C4×C83—24no—
69C2×C4×C83—22no—
70C2×C4×C83C2×D412yes—
71C2×C4×C83#4112yes—
72C2×C4×C83#4112yes—
73C2×Dic83—22no—
74C2×Dic83—21no—
75C2×Dic83—21no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83—24no—
80C2×Dic83—24no—
81C2×Dic83C2×D412yes—
82C2×Dic83#4114yes—
83C4×D83—28no—
84C22×C83C22×D411yescharacteristic
85C22×C83C2×#4112yes—
86C22×C83C2×#4111yescharacteristic
87C22×C83C2×#4111yescharacteristic
88C22×C832−1+412yes—
89C2×D83—22no—
90C2×D83—22no—
91C2×D83—22no—
92C2×D83—42no—
93C2×D83—42no—
94C4×C83—42no—
95C4×C83—42no—
96C4×C83—42no—
97C4×C83#12314yes—
98Dic83—22no—
99Dic83—24no—
100Dic83—42no—
101Dic83—42no—
102C2×C83C2×#12311yescharacteristic
103C2×C83#53211yescharacteristic
104C2×C83#53611yescharacteristic
105C2×C83#55212yes—
106C2×C83#55612yes—
107D83—42no—
108#2499—831nomaximal, Sylow
109C83#249911yescharacteristic, complemented, Sylow
110C2×C22⋊Q8—831no—
111C2×#117—831no—
112#397—834no—
113#391—831no—
114#391D8311yescharacteristic, complemented
115#387—834no—
116#384—831no—
117#382—831no—
118C4×C22⋊C4—831no—
119C22×Q8C2×D8311yescharacteristic
120C23×C4—831no—
121C22⋊Q8—1664no—
122#117—1664no—
123C2×C4⋊C4—831no—
124C2×C4⋊C4—831no—
125C2×C4⋊C4—832no—
126C2×C4⋊C4—834no—
127C2×C4⋊C4C2×D8311yescharacteristic
128C2×C22⋊C4—832no—
129C2×C22⋊C4—832no—
130C2×C22⋊C4—832no—
131C2×C42—832no—
132C2×C42—831no—
133C2×C42C2×D8311yescharacteristic
134#95—832no—
135#95—834no—
136#95—834no—
137#95C2×D8314yes—
138C24—831no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C22×C4—832no—
143C22×C4—831no—
144C22×C4—834no—
145C22×C4—832no—
146C22×C4—832no—
147C22×C4—1662no—
148C22×C4—1662no—
149C22×C4C22×D8312yes—
150C22×C4C22×D8312yes—
151C22×C4C22×D8312yes—
152C22×C4C22×D8311yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—1664no—
155C4⋊C4—1668no—
156C4⋊C4—1662no—
157C4⋊C4—1662no—
158C22⋊C4—1664no—
159C22⋊C4—1664no—
160C22⋊C4—1664no—
161C42—22no—
162C42—1664no—
163C42—1662no—
164C23—832no—
165C23—1662no—
166C23—1661no—
167C23—1661no—
168C23—1662no—
169C23C23×D8311yescharacteristic
170Q8—44no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—832no—
180C2×C4—834no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4—1664no—
184C2×C4—1664no—
185C2×C4—1661no—
186C2×C4—1662no—
187C2×C4—1661no—
188C2×C4—1662no—
189C2×C4—1668no—
190C2×C4D4×D8312yes—
191C2×C4#1305058912yes—
192C2×C4#1305059012yes—
193C22—3322no—
194C22—3322no—
195C22—1662no—
196C22—1662no—
197C22—1662no—
198C22C2×D4×D8311yescharacteristic
199C22#41×D8312yes—
200C22C2×#1305058911yescharacteristic
201C22C2×#1305059011yescharacteristic
202C22#1458184012yes—
203C4—42no—
204C4—42no—
205C4—42no—
206C4—3322no—
207C4—3322no—
208C4—1664no—
209C4—1662no—
210C4#1458177414yes—
211C2—3322no—
212C2C2×#1458177411yescharacteristic
213C2#1912825011yescharacteristic
214C2#1912827611yescharacteristic
215C2#1912839212yes—
216C2#1912842212yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#391×C83C2
prime radicalC23×D83C23
hypercenter#391D83
hypocenterC83#2499
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
4. #19127608C2semidirect
5. #19127583C2semidirect
6. #19127570C2semidirect
7. #19127567C2semidirect
9. #391×C83C2semidirect
109. C83#2499semidirect
114. #391D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817682
C2×#145817502
#191276302
#191276082
#191275832
#191275702
#191275672
C4×(C2×D83)⋊C42
#391×C832
#249983