Finite Group Databasebeta

← #24918548

Subgroups — #24918548

Order 10624.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#19128313C211yesmaximal, characteristic, complemented
2#19128277C211yesmaximal, characteristic
3#19128095C211yesmaximal, characteristic, complemented
4#19128081C211yesmaximal, characteristic, complemented
5#19128070C211yesmaximal, characteristic, complemented
6#19128056C211yesmaximal, characteristic, complemented
7#19127924C212yesmaximal, complemented
8#19127912C212yesmaximal, complemented
9#19127865C212yesmaximal
10#19127859C212yesmaximal, complemented
11#433×C83C211yesmaximal, characteristic, complemented
12C2×#13050590C2211yescharacteristic
13C22×Dic166C2211yescharacteristic
14C2×Dic332C2212yes—
15C2×Dic332C2212yes—
16C2×Dic332C2212yes—
17C2×#13050579C2212yes—
18#14581792C2211yescharacteristic
19#14581792C2211yescharacteristic
20#14581792C2211yescharacteristic
21#14581785—22no—
22#14581784C2211yescharacteristic
23#14581782—22no—
24#14581780C2211yescharacteristic
25#14581780C2211yescharacteristic
26#14581776—22no—
27#14581772—22no—
28#14581771C2212yes—
29C4×Dic166C2212yes—
30#14581717C2212yes—
31#14581717C2212yes—
32#14581717C2212yes—
33#14581714C2212yes—
34#117×C83C2211yescharacteristic
35C4⋊C8×C83C2212yes—
36C22⋊C8×C83C2212yes—
37#97×C83C2211yescharacteristic
38C4×C8×C83C2211yescharacteristic
39#13050590—42no—
40C2×Dic166—21no—
41C2×Dic166—42no—
42C2×Dic166C2312yes—
43C2×Dic166C2311yescharacteristic
44C2×Dic166C2311yescharacteristic
45C2×Dic166C2311yescharacteristic
46C2×D332C2311yescharacteristic
47C2×C22⋊D83—21no—
48C22×Dic83—21no—
49C2×C4×D83—21no—
50Dic332—42no—
51Dic332—42no—
52Dic332—42no—
53#13050579—42no—
54C4⋊Dic83—22no—
55C4⋊Dic83—22no—
56C4⋊Dic83—22no—
57C4⋊Dic83C2312yes—
58Dic83⋊C4—22no—
59Dic83⋊C4—22no—
60Dic83⋊C4—22no—
61C22⋊Dic83—22no—
62(C2×D83)⋊C4—22no—
63(C2×D83)⋊C4—22no—
64C4×Dic83—22no—
65C22×C4×C83C2311yescharacteristic
66C2×C8×C83C2312yes—
67C2×C8×C83C2312yes—
68C4⋊C4×C83D412yes—
69C22⋊C4×C83D412yes—
70C42×C83C2311yescharacteristic
71C42×C83C2311yescharacteristic
72C23×C83C2×D411yescharacteristic
73C22×D83—21no—
74C2×C4×C83—22no—
75C2×C4×C83C2×D412yes—
76C2×C4×C83C2×D412yes—
77C2×C4×C83C2×D411yescharacteristic
78C2×C4×C83C2411yescharacteristic
79C22⋊D83—42no—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83—21no—
83C2×Dic83—21no—
84C2×Dic83—21no—
85C2×Dic83—42no—
86D332—22no—
87C4×D83—42no—
88Dic166—22no—
89Dic166—22no—
90Dic166—22no—
91Dic166—22no—
92Dic166—22no—
93Dic166—42no—
94C8×C83—22no—
95C8×C83—22no—
96C22×C83—21no—
97C22×C83—22no—
98C22×C83C22×D411yescharacteristic
99C2×D83—41no—
100C2×D83—42no—
101C4×C83—21no—
102C4×C83—22no—
103C4×C83—22no—
104C4×C83H(5,𝔽2)12yes—
105Dic83—41no—
106Dic83—41no—
107Dic83—41no—
108Dic83—42no—
109Dic83—42no—
110C2×C83—41no—
111C2×C83#53511yescharacteristic
112C2×C83#57812yes—
113D83—81no—
114#3223—831nomaximal, Sylow
115C83#322311yescharacteristic, complemented, Sylow
116#541—831no—
117#536—831no—
118#497—831no—
119#494—831no—
120#491—831no—
121#488—831no—
122#464—832no—
123#462—832no—
124#452—832no—
125#451—832no—
126#433D8311yescharacteristic, complemented
127C2×#41—831no—
128C22×Q8—831no—
129C2×Q16—832no—
130C2×Q16—832no—
131C2×Q16—832no—
132C2×SD16—832no—
133C4⋊Q8—831no—
134C4⋊Q8—831no—
135C4⋊Q8—831no—
136#126—1662no—
137#125—831no—
138#125—1662no—
139#124—831no—
140#124—831no—
141#123—1662no—
142C22⋊Q8—832no—
143C22⋊Q8—1662no—
144C4×Q8—832no—
145#117C2×D8311yescharacteristic
146C4⋊C8C2×D8312yes—
147#103—832no—
148#103—832no—
149#103—832no—
150#102—832no—
151C22⋊C8C2×D8312yes—
152#97C2×D8311yescharacteristic
153C4×C8C2×D8311yescharacteristic
154#41—3322no—
155C2×Q8—3322no—
156C2×Q8—831no—
157C2×Q8—831no—
158C2×Q8—831no—
159C2×Q8—832no—
160C2×Q8—1661no—
161C2×D4—831no—
162C2×D4—1661no—
163C22×C4—1661no—
164C22×C4—1661no—
165C22×C4C22×D8311yescharacteristic
166Q16—3322no—
167Q16—3322no—
168Q16—3322no—
169SD16—3322no—
170C2×C8C22×D8312yes—
171C2×C8C22×D8312yes—
172C4⋊C4—832no—
173C4⋊C4—1662no—
174C4⋊C4—1662no—
175C4⋊C4—1662no—
176C4⋊C4—1662no—
177C4⋊C4—1662no—
178C4⋊C4—1662no—
179C4⋊C4D33212yes—
180C22⋊C4—1662no—
181C22⋊C4—1662no—
182C22⋊C4—1662no—
183C22⋊C4D33212yes—
184C42—1662no—
185C42C22×D8311yescharacteristic
186C42C22×D8311yescharacteristic
187C23—1661no—
188C23C2×D33211yescharacteristic
189Q8—3322no—
190Q8—1662no—
191Q8—1662no—
192Q8—1662no—
193Q8—1662no—
194Q8—1662no—
195D4—3322no—
196D4—1662no—
197C2×C4—22no—
198C2×C4—3322no—
199C2×C4—3322no—
200C2×C4—1662no—
201C2×C4—1662no—
202C2×C4—1661no—
203C2×C4—1661no—
204C2×C4—1661no—
205C2×C4C2×D33212yes—
206C2×C4C2×D33212yes—
207C2×C4C2×D33211yescharacteristic
208C2×C4C23×D8311yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—3322no—
214C22—3321no—
215C22C22×D33211yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—3322no—
220C4—3321no—
221C4—3321no—
222C4—3321no—
223C4—3322no—
224C4#1458183812yes—
225C2—41no—
226C2—6641no—
227C2#1912827011yescharacteristic
228C2#1912851812yes—
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#433×C83C2
socleC22×C83C22×D4
prime radicalC2×#13050590C22
hypercenter#433D83
hypocenterC83#3223
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19128313C2semidirect
3. #19128095C2semidirect
4. #19128081C2semidirect
5. #19128070C2semidirect
6. #19128056C2semidirect
7. #19127924C2semidirect
8. #19127912C2semidirect
10. #19127859C2semidirect
11. #433×C83C2semidirect
115. C83#3223semidirect
126. #433D83semidirect

Maximal subgroups

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

subgroupindex
#191283132
#191282772
#191280952
#191280812
#191280702
#191280562
#191279242
#191279122
#191278652
#191278592
#433×C832
#322383