Finite Group Databasebeta

← #21429924

Subgroups — #21429924

Order 7552.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14273726C211yesmaximal, characteristic, complemented
2C2×#14273685C211yesmaximal, characteristic
3#16837341C211yesmaximal, characteristic, complemented
4#16837339C211yesmaximal, characteristic
5#16837337C211yesmaximal, characteristic
6#16837323C212yesmaximal, complemented
7#16837315C212yesmaximal
8#16837299C212yesmaximal, complemented
9#16837266C211yesmaximal, characteristic, complemented
10#16837261C212yesmaximal
11C59×#400C211yesmaximal, characteristic, complemented
12C22×Dic118C2212yes—
13C22×C4×D59C2211yescharacteristic
14#14273726—24no—
15#14273685—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2212yes—
26C2×C4×Dic59C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2211yescharacteristic
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C23×D59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×Dic59C2312yes—
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×C4×D59—22no—
49C2×C4×D59—22no—
50C2×C4×D59Q814yescomplemented
51C2×Dic118—24no—
52C2×Dic118—42no—
53C2×Dic118—42no—
54C4⋊C4×C59—22no—
55C4⋊C4×C59—22no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—42no—
59(C2×D59)⋊C4—42no—
60C4⋊Dic59—22no—
61C4⋊Dic59—22no—
62C4⋊Dic59—42no—
63Dic59⋊C4—24no—
64Dic59⋊C4—24no—
65Dic59⋊C4—42no—
66C4×Dic59—22no—
67C4×Dic59D414yes—
68C23×C59C2411yescharacteristic
69C22×D59—21no—
70C22×D59—21no—
71C22×D59—22no—
72C22×D59—22no—
73C22×D59C2×Q812yes—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59C2×D412yes—
86C2×C4×C59C2×Q812yes—
87C2×Dic59—22no—
88C2×Dic59—21no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59C2×D412yes—
97C2×Dic59C2×D412yes—
98C2×Dic59C2×Q812yes—
99C2×Dic59#4112yes—
100C4×D59—28no—
101Dic118—48no—
102C22×C59C22×D411yescharacteristic
103C22×C59C22×Q811yescharacteristic
104C22×C59C2×#4111yescharacteristic
105C22×C59H(5,𝔽2)12yes—
106C22×C592−1+412yes—
107C2×D59—22no—
108C2×D59—24no—
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—42no—
112C4×C59—22no—
113C4×C59—22no—
114C4×C59—42no—
115C4×C59—41no—
116C4×C59—42no—
117Dic59—22no—
118Dic59—42no—
119Dic59—41no—
120Dic59—42no—
121Dic59C22⋊Q814yes—
122#2628—591nomaximal, Sylow
123C2×C59C2×C22⋊Q811yescharacteristic
124C2×C59#53511yescharacteristic
125C2×C59#53611yescharacteristic
126C2×C59#54212yes—
127C2×C59#54412yes—
128D59—42no—
129C2×C4⋊Q8—591no—
130C2×#117—591no—
131#400—591no—
132#400D5911yescharacteristic, complemented
133#399—591no—
134#399—591no—
135#395—592no—
136#393—592no—
137#389—592no—
138#382—591no—
139#380—592no—
140C59#262811yescharacteristic, complemented, Sylow
141C22×Q8—592no—
142C23×C4—591no—
143C4⋊Q8—1184no—
144#117—1184no—
145C2×C4⋊C4—591no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4—591no—
148C2×C4⋊C4—592no—
149C2×C4⋊C4—592no—
150C2×C4⋊C4—592no—
151C2×C4⋊C4C2×D5911yescharacteristic
152C2×C4⋊C4C2×D5911yescharacteristic
153C2×C22⋊C4—591no—
154C2×C22⋊C4—591no—
155C2×C22⋊C4—592no—
156C2×C22⋊C4—592no—
157C2×C42—591no—
158C2×C42—591no—
159#95—592no—
160#95—592no—
161#95—591no—
162#95—592no—
163#95C2×D5912yes—
164#95C2×D5911yescharacteristic
165#95C2×D5912yes—
166C24—591no—
167C2×Q8—1184no—
168C2×Q8—2362no—
169C2×Q8—2362no—
170C22×C4—591no—
171C22×C4—591no—
172C22×C4—594no—
173C22×C4—592no—
174C22×C4—592no—
175C22×C4—591no—
176C22×C4—1182no—
177C22×C4—1182no—
178C22×C4C22×D5911yescharacteristic
179C22×C4C22×D5912yes—
180C22×C4C22×D5912yes—
181C22×C4C22×D5911yescharacteristic
182C22×C4C22×D5911yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—1182no—
186C4⋊C4—1184no—
187C4⋊C4—1184no—
188C4⋊C4—1182no—
189C4⋊C4—2362no—
190C4⋊C4—2362no—
191C22⋊C4—1182no—
192C22⋊C4—1182no—
193C22⋊C4—2362no—
194C22⋊C4—2362no—
195C42—594no—
196C42—1182no—
197C23—592no—
198C23—1181no—
199C23—1181no—
200C23—1182no—
201C23—1182no—
202C23C23×D5911yescharacteristic
203Q8—2368no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—592no—
216C2×C4—592no—
217C2×C4—592no—
218C2×C4—592no—
219C2×C4—1188no—
220C2×C4—1182no—
221C2×C4—1181no—
222C2×C4—1182no—
223C2×C4—1182no—
224C2×C4—1182no—
225C2×C4—1182no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1182no—
229C2×C4D4×D5912yes—
230C2×C4Q8×D5912yes—
231C22—1182no—
232C22—1184no—
233C22—2361no—
234C22—2361no—
235C22—2362no—
236C22C2×D4×D5911yescharacteristic
237C22C2×Q8×D5911yescharacteristic
238C22#41×D5911yescharacteristic
239C22#1427377312yes—
240C22#1427377412yes—
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—594no—
247C4—1182no—
248C4—2362no—
249C4—2361no—
250C4—2362no—
251C2—2362no—
252C2C22⋊Q8×D5911yescharacteristic
253C2#1683797011yescharacteristic
254C2#1683797411yescharacteristic
255C2#1683801812yes—
256C2#1683803212yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2628
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14273726C2semidirect
3. #16837341C2semidirect
6. #16837323C2semidirect
8. #16837299C2semidirect
9. #16837266C2semidirect
11. C59×#400C2semidirect
50. C2×C4×D59Q8semidirect
132. #400D59semidirect
140. C59#2628semidirect