Finite Group Databasebeta

← #24916524

Subgroups — #24916524

Order 10624.

402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 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#19128213C211yesmaximal, characteristic
2#19127780C212yesmaximal, complemented
3#19127778C212yesmaximal, complemented
4#19127774C212yesmaximal, complemented
5#19127771C212yesmaximal, complemented
6#19127762C211yesmaximal, characteristic, complemented
7#19127666C212yesmaximal, complemented
8#19127663C212yesmaximal, complemented
9#433×C83C211yesmaximal, characteristic, complemented
10C2×#13050590C2211yescharacteristic
11C22×C4×D83C2211yescharacteristic
12C2×#13050573C2212yes—
13C2×#13050573C2212yes—
14C2×#13050573C2212yescomplemented
15C2×C8×D83C2212yescomplemented
16#14581776C412yes—
17#14581772C412yes—
18#14581767C412yes—
19#14581762C412yes—
20C4×D332C2212yes—
21C4×D332C2212yes—
22C4⋊(C83⋊C8)C2212yescomplemented
23C22⋊(C83⋊C8)C2212yes—
24(C2×D83)⋊C8C2212yes—
25(C2×D83)⋊C8C2212yes—
26(C2×D83)⋊C8C2212yescomplemented
27(C2×D83)⋊C8C2212yescomplemented
28#14581703C2211yescharacteristic, complemented
29C4×C83⋊C8C2211yescharacteristic, complemented
30#117×C83C2211yescharacteristic
31C4⋊C8×C83C2212yescomplemented
32C22⋊C8×C83C2212yes—
33#97×C83C2211yescharacteristic, complemented
34C4×C8×C83C2211yescharacteristic, complemented
35C23×D83C2×C411yescharacteristic
36#13050590—42no—
37C2×Dic166C2×C411yescharacteristic
38C2×D332C2×C412yes—
39C2×D332C2×C412yes—
40C2×D332C2×C411yescharacteristic
41C2×C22⋊D83C2×C412yes—
42C22×Dic83C2×C411yescharacteristic
43C2×C4×D83—42no—
44C2×C4×D83C2×C412yes—
45C2×C4×D83C2312yes—
46C2×C4×D83C2312yes—
47#13050573—42no—
48#13050573—42no—
49#13050573—42no—
50C2×C83⋊C8C2312yes—
51C2×C83⋊C8C2312yes—
52C8×D83—42no—
53C4⋊Dic83C2×C412yes—
54C4⋊Dic83C2×C412yes—
55(C2×D83)⋊C4C2×C412yes—
56(C2×D83)⋊C4C2×C412yes—
57(C2×D83)⋊C4C2×C412yes—
58(C2×D83)⋊C4C2×C412yes—
59C22×C4×C83C2311yescharacteristic
60C2×C8×C83C2312yes—
61C2×C8×C83C2312yes—
62C4⋊C4×C83C2×C412yes—
63C22⋊C4×C83C2×C412yes—
64C42×C83C2311yescharacteristic
65C42×C83C2311yescharacteristic
66C23×C83C22×C411yescharacteristic
67C22×D83—41no—
68C22×D83—42no—
69C22×D83C22×C412yes—
70C22×D83C22×C412yes—
71C2×C4×C83—22no—
72C2×C4×C83C22×C412yes—
73C2×C4×C83C22×C412yes—
74C2×C4×C83C22×C411yescharacteristic
75C2×C4×C83C2411yescharacteristic
76C22⋊D83—42no—
77C2×Dic83—41no—
78C2×Dic83C22×C412yes—
79C2×Dic83C22×C412yes—
80D332—42no—
81D332—42no—
82D332—41no—
83C4×D83—22no—
84C4×D83—22no—
85C4×D83—22no—
86C4×D83—22no—
87C4×D83—42no—
88Dic166—41no—
89C8×C83—22no—
90C8×C83—22no—
91C83⋊C8—22no—
92C83⋊C8—22no—
93C22×C83—21no—
94C22×C83—22no—
95C22×C83C23×C411yescharacteristic
96C2×D83—22no—
97C2×D83—22no—
98C2×D83—22no—
99C2×D83—22no—
100C2×D83—22no—
101C2×D83—22no—
102C2×D83—44no—
103C4×C83—21no—
104C4×C83—22no—
105C4×C83—22no—
106C4×C83H(5,𝔽2)12yes—
107Dic83—22no—
108Dic83—22no—
109C2×C83—41no—
110C2×C83#51811yescharacteristic
111C2×C83#56812yes—
112D83—42no—
113D83—42no—
114#2978—831nomaximal, Sylow
115C83#297811yescharacteristic, complemented, Sylow
116#525—831no—
117#436—832no—
118#436—832no—
119#435—832no—
120#435—832no—
121#433—831no—
122#433D8311yescharacteristic, complemented
123#408—832no—
124#407—832no—
125C2×#41—831no—
126C23×C4—831no—
127C2×M16—832no—
128C2×M16—832no—
129C2×M16—832no—
130C22×C8—832no—
131#123—832no—
132C22⋊Q8—832no—
133#121—832no—
134#120—832no—
135C4×D4—832no—
136C4×D4—832no—
137#117C2×D8311yescharacteristic
138C4⋊C8—832no—
139C4⋊C8C2×D8312yescomplemented
140C22⋊C8—832no—
141C22⋊C8—832no—
142C22⋊C8—832no—
143C22⋊C8—832no—
144C22⋊C8—832no—
145C22⋊C8C2×D8312yes—
146#97—831no—
147#97C2×D8311yescharacteristic, complemented
148C4×C8—831no—
149C4×C8C2×D8311yescharacteristic, complemented
150C24—831no—
151#41—3322no—
152C2×Q8—831no—
153C2×D4—832no—
154C2×D4—832no—
155C2×D4—832no—
156C2×D4—831no—
157C22×C4—3322no—
158C22×C4—831no—
159C22×C4—832no—
160C22×C4—832no—
161C22×C4—832no—
162C22×C4C22×D8311yescharacteristic
163M16—3322no—
164M16—3322no—
165M16—3322no—
166C2×C8—3322no—
167C2×C8—832no—
168C2×C8—832no—
169C2×C8C22×D8312yes—
170C2×C8C22×D8312yes—
171C4⋊C4—832no—
172C4⋊C4—832no—
173C4⋊C4C4×D8312yes—
174C22⋊C4—832no—
175C22⋊C4—832no—
176C22⋊C4—832no—
177C22⋊C4—832no—
178C22⋊C4C4×D8312yes—
179C42C22×D8311yescharacteristic
180C42C22×D8311yescharacteristic
181C23—3321no—
182C23—3322no—
183C23—832no—
184C23—832no—
185C23C2×C4×D8311yescharacteristic
186Q8—3321no—
187D4—3321no—
188D4—3322no—
189D4—3322no—
190D4—3322no—
191C2×C4—22no—
192C2×C4—3322no—
193C2×C4—3321no—
194C2×C4—832no—
195C2×C4—832no—
196C2×C4—1662no—
197C2×C4—1662no—
198C2×C4—1662no—
199C2×C4—1662no—
200C2×C4C2×C4×D8312yes—
201C2×C4C2×C4×D8312yes—
202C2×C4C2×C4×D8311yescharacteristic
203C2×C4C23×D8311yescharacteristic
204C8—22no—
205C8—22no—
206C8—1662no—
207C8—1662no—
208C22—21no—
209C22—22no—
210C22—3324no—
211C22—1662no—
212C22—1662no—
213C22—1662no—
214C22—1662no—
215C22—1662no—
216C22—1662no—
217C22C22×C4×D8311yescharacteristic
218C4—21no—
219C4—22no—
220C4—22no—
221C4—1662no—
222C4—1662no—
223C4#1458183812yes—
224C2—41no—
225C2—3322no—
226C2—3322no—
227C2#1912817511yescharacteristic
228C2#1912846612yes—
subgroupG/H
center, FrattiniC2×C4C23×D83
commutator, socleC22×C83C23×C4
Fitting#433×C83C2
prime radical#19128213C2
cosocleC2×C4×C83C24
hypercenter#433D83
hypocenterC83#2978
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #19127780C2semidirect
3. #19127778C2semidirect
4. #19127774C2semidirect
5. #19127771C2semidirect
6. #19127762C2semidirect
7. #19127666C2semidirect
8. #19127663C2semidirect
9. #433×C83C2semidirect
14. C2×#13050573C22semidirect
15. C2×C8×D83C22semidirect
22. C4⋊(C83⋊C8)C22semidirect
26. (C2×D83)⋊C8C22semidirect
27. (C2×D83)⋊C8C22semidirect
28. #14581703C22semidirect
29. C4×C83⋊C8C22semidirect
31. C4⋊C8×C83C22semidirect
33. #97×C83C22semidirect
34. C4×C8×C83C22semidirect
115. C83#2978semidirect
122. #433D83semidirect
139. C4⋊C8C2×D83semidirect
147. #97C2×D83semidirect
149. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191282132
#191277802
#191277782
#191277742
#191277712
#191277622
#191276662
#191276632
#433×C832
#297883