Finite Group Databasebeta

← #24905948

Subgroups — #24905948

Order 10624.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#19128237C211yesmaximal, characteristic
2#19127751C211yesmaximal, characteristic, complemented
3#19127546C211yesmaximal, characteristic, complemented
4#19127438C211yesmaximal, characteristic, complemented
5#19127436C211yesmaximal, characteristic
6#19127434C211yesmaximal, characteristic
7#328×C83C211yesmaximal, characteristic, complemented
8#14581787—21no—
9#14581783C411yescharacteristic, complemented
10#14581781C411yescharacteristic, complemented
11#14581776—21no—
12#14581766C2211yescharacteristic
13Q8×Dic83C411yescharacteristic, complemented
14#14581754C411yescharacteristic, complemented
15(C22⋊D83)⋊C4—21no—
16#14581750—21no—
17C2×C4×Dic83—21no—
18C2×C4×Dic83C2211yescharacteristic
19Dic83⋊C8—21no—
20C22⋊(C83⋊C8)C2211yescharacteristic
21C8×Dic83—21no—
22C83⋊#95—21no—
23C83⋊#95C2211yescharacteristic
24C22⋊Q8×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26#95×C83C2211yescharacteristic
27C2×D332C2×C411yescharacteristic
28C2×C22⋊D83—21no—
29C22×Dic83—21no—
30C22×Dic83D411yescharacteristic
31C22×Dic83D411yescharacteristic
32C2×C4×D83—21no—
33C2×C83⋊C8—21no—
34C4⋊Dic83—21no—
35C4⋊Dic83—21no—
36C4⋊Dic83C2×C411yescharacteristic
37Dic83⋊C4—21no—
38(C2×D83)⋊C4—21no—
39(C2×D83)⋊C4—21no—
40(C2×D83)⋊C4—21no—
41(C2×D83)⋊C4—21no—
42C4×Dic83—24no—
43C4×Dic83—21no—
44C4×Dic83C2×C411yescharacteristic
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83D411yescharacteristic
47C4×Dic83D411yescharacteristic
48C2×Q8×C83C2×C411yescharacteristic
49C22×C4×C83—21no—
50C22×C4×C83C2311yescharacteristic
51C2×C8×C83—21no—
52C4⋊C4×C83—21no—
53C4⋊C4×C83C2×C411yescharacteristic
54C22⋊C4×C83—21no—
55C23×C83C2×D411yescharacteristic
56C22×D83—21no—
57Q8×C83—41no—
58C2×C4×C83—22no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—41no—
62C2×C4×C83—41no—
63C2×C4×C83—41no—
64C2×C4×C83C22×C411yescharacteristic
65C2×C4×C83C2×D411yescharacteristic
66C22⋊D83—41no—
67C22⋊D83—41no—
68C2×Dic83—21no—
69C2×Dic83—21no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—21no—
73C2×Dic83—41no—
74C2×Dic83—41no—
75C2×Dic83C22⋊C411yescharacteristic
76C2×Dic83C22⋊C411yescharacteristic
77C2×Dic83C22⋊C411yescharacteristic
78C2×Dic83C22⋊C411yescharacteristic
79D332—41no—
80C4×D83—42no—
81C8×C83—41no—
82C83⋊C8—41no—
83C22×C83—21no—
84C22×C83—21no—
85C22×C83C2×C22⋊C411yescharacteristic
86C22×C83#13511yescharacteristic
87C22×C83#13511yescharacteristic
88C2×D83—41no—
89C2×D83—41no—
90C2×D83—41no—
91C4×C83—21no—
92C4×C83—21no—
93C4×C83—42no—
94C4×C83—41no—
95C4×C83—41no—
96Dic83—21no—
97Dic83—21no—
98Dic83—21no—
99Dic83—42no—
100Dic83—41no—
101Dic83#10412yes—
102C2×C83—21no—
103C2×C83—21no—
104C2×C83#41011yescharacteristic
105C2×C83#41611yescharacteristic
106C2×C83C2×#10411yescharacteristic
107D83—81no—
108#1500—831nomaximal, Sylow
109C83#150011yescharacteristic, complemented, Sylow
110#529—831no—
111#431—831no—
112#376—831no—
113#328—831no—
114#328D8311yescharacteristic, complemented
115#327—831no—
116#327—831no—
117#126—1661no—
118#125—831no—
119#124—831no—
120#123—1661no—
121C22⋊Q8C2×D8311yescharacteristic
122#121—831no—
123C4×Q8—831no—
124C4×D4—831no—
125C4×D4—1661no—
126#117—1661no—
127C2×C42—831no—
128C2×C42—1661no—
129C4⋊C8—1661no—
130C22⋊C8—831no—
131C22⋊C8C2×D8311yescharacteristic
132C4×C8—1661no—
133#95—831no—
134#95—1661no—
135#95C2×D8311yescharacteristic
136C2×Q8C4×D8311yescharacteristic
137C2×D4—831no—
138C2×D4—1661no—
139C22×C4—21no—
140C22×C4—831no—
141C22×C4—831no—
142C22×C4—1661no—
143C22×C4—1661no—
144C22×C4C22×D8311yescharacteristic
145C2×C8—21no—
146C2×C8—1661no—
147C4⋊C4—21no—
148C4⋊C4—831no—
149C4⋊C4—1661no—
150C4⋊C4—1661no—
151C4⋊C4—1661no—
152C4⋊C4C4×D8311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1661no—
155C22⋊C4—1661no—
156C22⋊C4—1661no—
157C22⋊C4—1661no—
158C42—831no—
159C42—831no—
160C42—831no—
161C42—831no—
162C42—1661no—
163C42—1664no—
164C23—1661no—
165C23D4×D8311yescharacteristic
166Q8—41no—
167D4—3321no—
168D4—3321no—
169D4—3321no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—3322no—
177C2×C4—3321no—
178C2×C4—3321no—
179C2×C4—831no—
180C2×C4—831no—
181C2×C4—831no—
182C2×C4—831no—
183C2×C4—1662no—
184C2×C4—1661no—
185C2×C4—1662no—
186C2×C4—1661no—
187C2×C4—1661no—
188C2×C4C2×C4×D8311yescharacteristic
189C2×C4D4×D8311yescharacteristic
190C8—41no—
191C8—3321no—
192C22—21no—
193C22—21no—
194C22—3321no—
195C22—3321no—
196C22—3321no—
197C22C22⋊C4×D8311yescharacteristic
198C22#1458181311yescharacteristic
199C22#1458181511yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—3322no—
206C4—3321no—
207C4—832no—
208C4—1661no—
209C4—1661no—
210C4—1661no—
211C2—21no—
212C2—21no—
213C2—6641no—
214C2#1912767311yescharacteristic
215C2#1912769611yescharacteristic
216C2#104×D8311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#328×C83C2
socleC22×C83C2×C22⋊C4
prime radical#14581766C22
cosocleC22×C4×C83C23
hypercenter#328D83
hypocenterC83#1500
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #19127751C2semidirect
3. #19127546C2semidirect
4. #19127438C2semidirect
7. #328×C83C2semidirect
9. #14581783C4semidirect
10. #14581781C4semidirect
13. Q8×Dic83C4semidirect
14. #14581754C4semidirect
109. C83#1500semidirect
114. #328D83semidirect