Finite Group Databasebeta

← #24919769

Subgroups — #24919769

Order 10624.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#19128356C211yesmaximal, characteristic, complemented
2#19128355C211yesmaximal, characteristic, complemented
3#19128052C211yesmaximal, characteristic, complemented
4#19128037C212yesmaximal, complemented
5#19127982C211yesmaximal, characteristic, complemented
6#19127947C212yesmaximal, complemented
7#19127907C211yesmaximal, characteristic, complemented
8#19127848C212yesmaximal, complemented
9C4×D664C211yesmaximal, characteristic, complemented
10#19127703C212yesmaximal, complemented
11#436×C83C211yesmaximal, characteristic, complemented
12C2×#13050590C2212yes—
13C2×#13050589—21no—
14C2×#13050579C2212yes—
15C2×D664C2211yescharacteristic
16#14581792C2211yescharacteristic
17#14581792C2211yescharacteristic
18#14581776—22no—
19#14581774—22no—
20#14581772—21no—
21#14581771C2212yes—
22#14581766C2212yes—
23#14581763—21no—
24C4×D332C2211yescharacteristic
25C4×D332C2211yescharacteristic
26C2×C4⋊Dic83C2212yes—
27C4⋊C4×D83—21no—
28#14581726C2212yes—
29#14581726C2211yescharacteristic
30#14581717C2212yes—
31#14581717C2212yes—
32#14581717C2212yes—
33#14581714C2212yes—
34#14581714C2211yescharacteristic
35#14581714C2211yescharacteristic
36C2×M16×C83C2212yes—
37C4×D4×C83C2211yescharacteristic
38C4⋊C8×C83C2211yescharacteristic
39C22⋊C8×C83C2212yes—
40C4×C8×C83C2211yescharacteristic
41#13050590—24no—
42#13050590—42no—
43#13050589—44no—
44C2×Dic166—21no—
45C2×Dic166C2312yes—
46C2×D332C2311yescharacteristic
47C2×D332C2311yescharacteristic
48C2×C22⋊D83—22no—
49C2×C22⋊D83—22no—
50C22×Dic83—22no—
51C2×C4×D83—21no—
52C2×C4×D83—21no—
53C2×C4×D83—22no—
54#13050579—42no—
55D664—22no—
56C4⋊Dic83—21no—
57C4⋊Dic83—22no—
58C4⋊Dic83—21no—
59C4⋊Dic83—21no—
60C4⋊Dic83C2312yes—
61C4⋊Dic83C2311yescharacteristic
62C4⋊Dic83C2311yescharacteristic
63Dic83⋊C4—22no—
64C22⋊Dic83—22no—
65(C2×D83)⋊C4—22no—
66(C2×D83)⋊C4—21no—
67(C2×D83)⋊C4—21no—
68C2×D4×C83D411yescharacteristic
69C22×C4×C83C2312yes—
70M16×C83—42no—
71C2×C8×C83C2311yescharacteristic
72C2×C8×C83C2312yes—
73C2×C8×C83C2311yescharacteristic
74C4⋊C4×C83D411yescharacteristic
75C22⋊C4×C83D412yes—
76C42×C83C2311yescharacteristic
77C23×C83C2×D412yes—
78C22×D83—21no—
79C22×D83—21no—
80D4×C83—22no—
81C2×C4×C83—22no—
82C2×C4×C83—22no—
83C2×C4×C83C2×D411yescharacteristic
84C2×C4×C83C2×D412yes—
85C2×C4×C83C2×D411yescharacteristic
86C2×C4×C83C2411yescharacteristic
87C22⋊D83—44no—
88C22⋊D83—44no—
89C2×Dic83—21no—
90C2×Dic83—21no—
91C2×Dic83—22no—
92C2×Dic83—22no—
93C2×Dic83—44no—
94D332—21no—
95D332—21no—
96D332—21no—
97D332#4112yescomplemented
98C4×D83—44no—
99C4×D83—42no—
100C4×D83—42no—
101Dic166—22no—
102Dic166—22no—
103Dic166—42no—
104C8×C83—21no—
105C8×C83—21no—
106C8×C83—22no—
107C22×C83—22no—
108C22×C83—22no—
109C22×C83—22no—
110C22×C83C22×D411yescharacteristic
111C2×D83—22no—
112C2×D83—41no—
113C2×D83—41no—
114C2×D83—41no—
115C2×D83—41no—
116C2×D83—41no—
117C4×C83—22no—
118C4×C83—21no—
119C4×C83AGL(1,ℤ/8)12yes—
120C4×C83C2×#4111yescharacteristic
121C4×C83H(5,𝔽2)11yescharacteristic
122Dic83—42no—
123Dic83—42no—
124Dic83—41no—
125Dic83—41no—
126C2×C83—42no—
127C2×C83#54611yescharacteristic
128C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C83#57811yescharacteristic
130D83—42no—
131D83—81no—
132#3330—831nomaximal, Sylow
133C83#333011yescharacteristic, complemented, Sylow
134#547—831no—
135#547—831no—
136#487—831no—
137#484—832no—
138#474—831no—
139#468—832no—
140#461—831no—
141#449—832no—
142C4×D8—831no—
143#436D8311yescharacteristic, complemented
144#417—832no—
145C2×#41—832no—
146C2×#41—1661no—
147C2×SD16—832no—
148C2×D8—831no—
149C2×M16C2×D8312yes—
150C4⋊Q8—831no—
151C4⋊Q8—831no—
152#123—1662no—
153#123—1662no—
154C22⋊Q8—832no—
155C22⋊Q8—1661no—
156#121—832no—
157#121—1661no—
158C4×D4—831no—
159C4×D4—831no—
160C4×D4C2×D8311yescharacteristic
161C2×C4⋊C4—832no—
162C2×C4⋊C4—1661no—
163#107—831no—
164#107—832no—
165C4⋊C8C2×D8311yescharacteristic
166#103—832no—
167#103—832no—
168#103—832no—
169#102—831no—
170#102—832no—
171#102—831no—
172C22⋊C8C2×D8312yes—
173C4×C8C2×D8311yescharacteristic
174#41—3322no—
175#41—3324no—
176#41—1664no—
177C2×Q8—832no—
178C2×Q8—1661no—
179C2×D4—831no—
180C2×D4—831no—
181C2×D4—1662no—
182C2×D4—1662no—
183C2×D4D33211yescharacteristic
184C22×C4—1662no—
185C22×C4—1661no—
186C22×C4—1662no—
187C22×C4—1661no—
188C22×C4C22×D8312yes—
189SD16—3322no—
190D8—1662no—
191M16—42no—
192C2×C8C22×D8311yescharacteristic
193C2×C8C22×D8311yescharacteristic
194C2×C8C22×D8312yes—
195C4⋊C4—831no—
196C4⋊C4—832no—
197C4⋊C4—831no—
198C4⋊C4—1662no—
199C4⋊C4—1661no—
200C4⋊C4—1662no—
201C4⋊C4—1661no—
202C4⋊C4—1661no—
203C4⋊C4D33211yescharacteristic
204C22⋊C4—1662no—
205C22⋊C4—1661no—
206C22⋊C4—1661no—
207C22⋊C4—1662no—
208C22⋊C4D33212yes—
209C42C22×D8311yescharacteristic
210C23—1661no—
211C23—1661no—
212C23C2×D33212yes—
213Q8—3322no—
214Q8—1662no—
215Q8—1662no—
216D4—22no—
217D4—3324no—
218D4—3324no—
219D4—832no—
220D4—1661no—
221D4—1661no—
222D4—1661no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—3324no—
226C2×C4—3324no—
227C2×C4—3322no—
228C2×C4—3322no—
229C2×C4—1661no—
230C2×C4—1661no—
231C2×C4—1662no—
232C2×C4—1662no—
233C2×C4C2×D33211yescharacteristic
234C2×C4C2×D33212yes—
235C2×C4C2×D33211yescharacteristic
236C2×C4C23×D8311yescharacteristic
237C8—21no—
238C8—21no—
239C8—22no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—3321no—
244C22—3321no—
245C22—3321no—
246C22—3321no—
247C22—3321no—
248C22—1662no—
249C22C22×D33211yescharacteristic
250C4—22no—
251C4—21no—
252C4—3322no—
253C4—3321no—
254C4—3322no—
255C4—3321no—
256C4#1458182012yes—
257C4#41×D8311yescharacteristic
258C4#1458183711yescharacteristic
259C2—42no—
260C2—3322no—
261C2—6641no—
262C2#1912834611yescharacteristic
263C2C2×#1458182011yescharacteristic
264C2#1912851811yescharacteristic
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#436×C83C2
socleC22×C83C22×D4
hypercenter#436D83
hypocenterC83#3330
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #19128356C2semidirect
2. #19128355C2semidirect
3. #19128052C2semidirect
4. #19128037C2semidirect
5. #19127982C2semidirect
6. #19127947C2semidirect
7. #19127907C2semidirect
8. #19127848C2semidirect
9. C4×D664C2semidirect
10. #19127703C2semidirect
11. #436×C83C2semidirect
97. D332#41semidirect
133. C83#3330semidirect
143. #436D83semidirect

Maximal subgroups

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

subgroupindex
#191283562
#191283552
#191280522
#191280372
#191279822
#191279472
#191279072
#191278482
C4×D6642
#191277032
#436×C832
#333083