Finite Group Databasebeta

← #21430470

Subgroups — #21430470

Order 7552.

592 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273705C212yesmaximal, complemented
2C2×#14273703C212yesmaximal, complemented
3#16837326C212yesmaximal, complemented
4#16837324C212yesmaximal, complemented
5#16837322C211yesmaximal, characteristic, complemented
6#16837303C211yesmaximal, characteristic
7#16837299C212yesmaximal, complemented
8#16837280C212yesmaximal
9C59×#395C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12C22×C4×D59C2212yes—
13#14273705—28no—
14#14273703—28no—
15C2×C4⋊Dic59C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×C4×Dic59C2211yescharacteristic
26C59⋊#95C2212yes—
27C59⋊#95C2211yescharacteristic
28C22×Q8×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2212yes—
30C2×C4⋊C4×C59C2211yescharacteristic
31#95×C59C2212yes—
32#95×C59C2211yescharacteristic
33C23×D59C2312yes—
34C2×Q8×C59—24no—
35C2×Q8×C59—41no—
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C2×D236—41no—
45C2×D236—41no—
46C2×D236Q814yescomplemented
47C2×C4×D59—24no—
48C2×C4×D59—24no—
49C2×C4×D59—42no—
50C2×Dic118—24no—
51C2×Dic118—41no—
52C4⋊C4×C59—24no—
53C4⋊C4×C59—41no—
54(C2×D59)⋊C4—24no—
55(C2×D59)⋊C4—24no—
56(C2×D59)⋊C4—24no—
57(C2×D59)⋊C4—24no—
58(C2×D59)⋊C4—42no—
59C4⋊Dic59—24no—
60Dic59⋊C4—24no—
61Dic59⋊C4—24no—
62Dic59⋊C4—42no—
63Dic59⋊C4D418yescomplemented
64C4×Dic59—41no—
65C23×C59C2411yescharacteristic
66C22×D59—22no—
67C22×D59—22no—
68C22×D59—22no—
69C22×D59—22no—
70C22×D59—22no—
71C22×D59—22no—
72C22×D59C2×Q814yes—
73Q8×C59—44no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59C2×D414yes—
86C2×C4×C59C2×Q812yes—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59C2×D414yes—
95C2×Dic59C2×D414yes—
96D236—44no—
97C4×D59—48no—
98Dic118—44no—
99C22×C59C22×D412yes—
100C22×C59C22×Q811yescharacteristic
101C22×C59H(5,𝔽2)11yescharacteristic
102C22×C59H(5,𝔽2)11yescharacteristic
103C22×C592−1+412yes—
104C2×D59—24no—
105C2×D59—24no—
106C2×D59—24no—
107C2×D59—42no—
108C2×D59—42no—
109C2×D59—42no—
110C2×D59—42no—
111C4×C59—22no—
112C4×C59—24no—
113C4×C59—42no—
114C4×C59—41no—
115C4×C59—41no—
116Dic59—24no—
117Dic59—24no—
118Dic59—42no—
119#2683—591nomaximal, Sylow
120C2×C59#53712yes—
121C2×C59#54311yescharacteristic
122C2×C59D4211yescharacteristic
123C2×C59D4×Q812yes—
124C2×C59#56311yescharacteristic
125D59—44no—
126C2×C22⋊Q8—592no—
127C2×C22⋊Q8—592no—
128#396—592no—
129#396—592no—
130#395—591no—
131#395D5911yescharacteristic, complemented
132#390—591no—
133#389—592no—
134#386—592no—
135C59#268311yescharacteristic, complemented, Sylow
136C22×Q8—591no—
137C22×Q8C2×D5911yescharacteristic
138C22×D4—591no—
139C23×C4—592no—
140C22⋊Q8—1188no—
141C22⋊Q8—1188no—
142C2×C4⋊C4—592no—
143C2×C4⋊C4—592no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4C2×D5912yes—
148C2×C4⋊C4C2×D5911yescharacteristic
149C2×C22⋊C4—592no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4—592no—
152C2×C22⋊C4—592no—
153C2×C22⋊C4—592no—
154C2×C42—591no—
155#95—592no—
156#95—591no—
157#95C2×D5912yes—
158#95C2×D5911yescharacteristic
159C24—592no—
160C2×Q8—24no—
161C2×Q8—41no—
162C2×Q8—1184no—
163C2×Q8—2361no—
164C2×D4—594no—
165C2×D4—2361no—
166C2×D4—2361no—
167C22×C4—592no—
168C22×C4—592no—
169C22×C4—592no—
170C22×C4—1184no—
171C22×C4—1184no—
172C22×C4—2362no—
173C22×C4C22×D5911yescharacteristic
174C22×C4C22×D5912yes—
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5912yes—
177C22×C4C22×D5911yescharacteristic
178C4⋊C4—24no—
179C4⋊C4—41no—
180C4⋊C4—598no—
181C4⋊C4—1184no—
182C4⋊C4—1184no—
183C4⋊C4—1184no—
184C4⋊C4—2362no—
185C22⋊C4—1184no—
186C22⋊C4—1184no—
187C22⋊C4—1184no—
188C22⋊C4—1184no—
189C22⋊C4—2362no—
190C42—2361no—
191C23—594no—
192C23—1182no—
193C23—1182no—
194C23—1182no—
195C23—1182no—
196C23—1182no—
197C23—1182no—
198C23C23×D5911yescharacteristic
199Q8—44no—
200Q8—2364no—
201D4—2364no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—594no—
214C2×C4—594no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—2368no—
223C2×C4D4×D5914yes—
224C2×C4Q8×D5912yes—
225C22—1184no—
226C22—1184no—
227C22—1184no—
228C22—2362no—
229C22—2362no—
230C22—2362no—
231C22—2362no—
232C22C2×D4×D5912yes—
233C22C2×Q8×D5911yescharacteristic
234C22#1427377211yescharacteristic
235C22#1427377311yescharacteristic
236C22#1427377512yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—1184no—
243C4—1184no—
244C4—2362no—
245C2—2364no—
246C2#1683798212yes—
247C2#1683802711yescharacteristic
248C2#1683803411yescharacteristic
249C2#1683806712yes—
250C2#1683815111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2683
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14273705C2semidirect
2. C2×#14273703C2semidirect
3. #16837326C2semidirect
4. #16837324C2semidirect
5. #16837322C2semidirect
7. #16837299C2semidirect
9. C59×#395C2semidirect
46. C2×D236Q8semidirect
63. Dic59⋊C4D4semidirect
131. #395D59semidirect
135. C59#2683semidirect