Finite Group Databasebeta

← #21429897

Subgroups — #21429897

Order 7552.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273705C211yesmaximal, characteristic
2C2×#14273685C211yesmaximal, characteristic
3#16837340C211yesmaximal, characteristic, complemented
4#16837334C211yesmaximal, characteristic, complemented
5#16837332C211yesmaximal, characteristic, complemented
6#16837331C212yesmaximal
7#16837329C212yesmaximal
8#16837306C212yesmaximal, complemented
9#16837299C212yesmaximal, complemented
10#16837261C211yesmaximal, characteristic
11C59×#400C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×C4×D59C2211yescharacteristic
14#14273705—24no—
15#14273685—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2212yes—
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2212yes—
26C2×C4×Dic59C2212yes—
27C59⋊#95C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2211yescharacteristic
35#95×C59C2212yes—
36#95×C59C2212yes—
37C23×D59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×Dic59C2312yes—
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×C4×D59—24no—
49C2×C4×D59D414yes—
50C2×Dic118—22no—
51C2×Dic118—24no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—22no—
54(C2×D59)⋊C4—24no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—42no—
58C4⋊Dic59—22no—
59C4⋊Dic59—42no—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62Dic59⋊C4—24no—
63Dic59⋊C4—42no—
64C4×Dic59—24no—
65C23×C59C2411yescharacteristic
66C22×D59—22no—
67C22×D59—21no—
68C22×D59—22no—
69C22×D59—21no—
70C22×D59C2×D412yes—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—24no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59C2×D412yes—
83C2×Dic59—22no—
84C2×Dic59—21no—
85C2×Dic59—21no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—21no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—21no—
94C2×Dic59C2×D412yes—
95C2×Dic59#4114yes—
96C4×D59—28no—
97Dic118—44no—
98C22×C59C22×D411yescharacteristic
99C22×C59C2×#4112yes—
100C22×C59H(5,𝔽2)11yescharacteristic
101C22×C592−1+412yes—
102C22×C592−1+411yescharacteristic
103C2×D59—22no—
104C2×D59—22no—
105C2×D59—22no—
106C2×D59—42no—
107C2×D59—42no—
108C4×C59—22no—
109C4×C59—41no—
110C4×C59—42no—
111C4×C59—41no—
112C4×C59—42no—
113Dic59—41no—
114Dic59—42no—
115Dic59—41no—
116Dic59—42no—
117Dic59#12314yes—
118#2625—591nomaximal, Sylow
119C2×C59C2×#12311yescharacteristic
120C2×C59#53611yescharacteristic
121C2×C59#53711yescharacteristic
122C2×C59#54112yes—
123C2×C59#54212yes—
124D59—42no—
125C2×C22⋊Q8—591no—
126C2×#117—591no—
127#400—591no—
128#400D5911yescharacteristic, complemented
129#398—591no—
130#398—591no—
131#397—592no—
132#397—592no—
133#391—592no—
134#389—592no—
135#380—591no—
136C59#262511yescharacteristic, complemented, Sylow
137C22×Q8—591no—
138C23×C4—591no—
139C22⋊Q8—1184no—
140#117—1184no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4C2×D5911yescharacteristic
148C2×C4⋊C4C2×D5911yescharacteristic
149C2×C22⋊C4—592no—
150C2×C22⋊C4—591no—
151C2×C22⋊C4—591no—
152C2×C22⋊C4—592no—
153C2×C42—592no—
154#95—591no—
155#95—592no—
156#95—592no—
157#95—592no—
158#95—592no—
159#95C2×D5911yescharacteristic
160#95C2×D5912yes—
161#95C2×D5912yes—
162C24—591no—
163C2×Q8—1182no—
164C2×Q8—1184no—
165C22×C4—591no—
166C22×C4—594no—
167C22×C4—592no—
168C22×C4—591no—
169C22×C4—592no—
170C22×C4—591no—
171C22×C4—1184no—
172C22×C4C22×D5912yes—
173C22×C4C22×D5911yescharacteristic
174C22×C4C22×D5912yes—
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—1182no—
180C4⋊C4—1184no—
181C4⋊C4—1182no—
182C4⋊C4—1182no—
183C4⋊C4—2362no—
184C4⋊C4—2362no—
185C22⋊C4—1184no—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C22⋊C4—2362no—
189C42—1184no—
190C23—592no—
191C23—1182no—
192C23—1181no—
193C23—1182no—
194C23—1181no—
195C23C23×D5911yescharacteristic
196Q8—2364no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—592no—
209C2×C4—594no—
210C2×C4—1188no—
211C2×C4—1182no—
212C2×C4—1181no—
213C2×C4—1181no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1181no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4—1181no—
222C2×C4D4×D5912yes—
223C22—1182no—
224C22—1182no—
225C22—1182no—
226C22—2362no—
227C22—2362no—
228C22C2×D4×D5911yescharacteristic
229C22#41×D5912yes—
230C22#1427377311yescharacteristic
231C22#1427377412yes—
232C22#1427377511yescharacteristic
233C4—22no—
234C4—41no—
235C4—42no—
236C4—41no—
237C4—42no—
238C4—594no—
239C4—2361no—
240C4—2362no—
241C4—2361no—
242C4—2362no—
243C2—2362no—
244C2#123×D5911yescharacteristic
245C2#1683797211yescharacteristic
246C2#1683798211yescharacteristic
247C2#1683801112yes—
248C2#1683801812yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2625
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #16837340C2semidirect
4. #16837334C2semidirect
5. #16837332C2semidirect
8. #16837306C2semidirect
9. #16837299C2semidirect
11. C59×#400C2semidirect
128. #400D59semidirect
136. C59#2625semidirect