Finite Group Databasebeta

← #21429794

Subgroups — #21429794

Order 7552.

476 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14273719C211yesmaximal, characteristic, complemented
2#16837341C211yesmaximal, characteristic, complemented
3#16837338C211yesmaximal, characteristic
4#16837332C211yesmaximal, characteristic, complemented
5#16837327C211yesmaximal, characteristic
6#16837297C212yesmaximal, complemented
7#16837296C212yesmaximal
8#16837286C212yesmaximal, complemented
9#16837275C212yesmaximal
10#16837248C211yesmaximal, characteristic, complemented
11C2×#117×C59C211yesmaximal, characteristic
12#14273719—24no—
13C2×C4⋊Dic59C2211yescharacteristic
14C2×C4⋊Dic59C2211yescharacteristic
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×C22⋊Dic59C2212yes—
20C2×C22⋊Dic59C2212yes—
21C2×C4×Dic59C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2211yescharacteristic
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C23×C4×C59C2211yescharacteristic
30#117×C59—24no—
31C2×C4⋊C4×C59C2211yescharacteristic
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C22⋊C4×C59C2211yescharacteristic
34C2×C22⋊C4×C59C2211yescharacteristic
35C2×C42×C59C2211yescharacteristic
36C2×C42×C59C2211yescharacteristic
37C24×C59C2311yescharacteristic
38C22×C4×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×C4×C59C2311yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C22×C4×C59C2311yescharacteristic
47C22×Dic59C2312yes—
48C22×Dic59C2312yes—
49C22×Dic59C2312yes—
50C22×Dic59C2312yes—
51C4⋊C4×C59—22no—
52C4⋊C4×C59—22no—
53C22⋊C4×C59—22no—
54C22⋊C4×C59—22no—
55C42×C59—22no—
56C42×C59D414yes—
57C22⋊Dic59—24no—
58C22⋊Dic59—24no—
59C4⋊Dic59—22no—
60C4⋊Dic59—22no—
61Dic59⋊C4—24no—
62Dic59⋊C4—24no—
63Dic59⋊C4—24no—
64Dic59⋊C4—24no—
65C4×Dic59—24no—
66C23×C59—21no—
67C23×C59—22no—
68C23×C59—21no—
69C23×C59—22no—
70C23×C59#4112yes—
71C23×C59C2411yescharacteristic
72C2×C4×C59—28no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—21no—
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59C2×D412yes—
84C2×C4×C59C2×D412yes—
85C2×C4×C59C2×D412yes—
86C2×C4×C59#4112yes—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59#4114yes—
99C22×C59—22no—
100C22×C59—24no—
101C22×C59—41no—
102C22×C59—41no—
103C22×C59—42no—
104C22×C59C22×D411yescharacteristic
105C22×C59C2×#4112yes—
106C22×C59C2×#4111yescharacteristic
107C22×C59C2×#4111yescharacteristic
108C22×C592−1+412yes—
109C4×C59—22no—
110C4×C59—22no—
111C4×C59—22no—
112C4×C59—22no—
113C4×C59—41no—
114C4×C59—41no—
115Dic59—24no—
116Dic59—42no—
117Dic59—42no—
118Dic59—42no—
119#2611—591nomaximal, Sylow
120C2×C59—42no—
121C2×C59#52511yescharacteristic
122C2×C59#53211yescharacteristic
123C2×C59#53611yescharacteristic
124C2×C59#55212yes—
125C2×C59#55212yes—
126C2×#125—591no—
127C2×#117D5911yescharacteristic
128#400—591no—
129#399—591no—
130#398—591no—
131#397—591no—
132#389—592no—
133#388—592no—
134#387—592no—
135#385—592no—
136#376—591no—
137C59#261111yescharacteristic, complemented, Sylow
138C23×C4C2×D5911yescharacteristic
139#125—1184no—
140#117—24no—
141C2×C4⋊C4—592no—
142C2×C4⋊C4—592no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—591no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4C2×D5911yescharacteristic
148C2×C4⋊C4C2×D5911yescharacteristic
149C2×C22⋊C4—592no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4C2×D5911yescharacteristic
152C2×C22⋊C4C2×D5911yescharacteristic
153C2×C42—592no—
154C2×C42C2×D5911yescharacteristic
155C2×C42C2×D5911yescharacteristic
156#95—592no—
157#95—591no—
158#95—591no—
159#95—592no—
160#95—592no—
161#95—592no—
162#95—592no—
163C24C22×D5911yescharacteristic
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—592no—
168C22×C4—592no—
169C22×C4—592no—
170C22×C4—592no—
171C22×C4C22×D5911yescharacteristic
172C22×C4C22×D5911yescharacteristic
173C22×C4C22×D5911yescharacteristic
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—1184no—
180C4⋊C4—1184no—
181C4⋊C4—1184no—
182C4⋊C4—1184no—
183C4⋊C4—1182no—
184C4⋊C4—1182no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—1184no—
188C22⋊C4—1184no—
189C42—22no—
190C42—1184no—
191C42C22⋊D5914yes—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#1174568512yes—
197C23C23×D5911yescharacteristic
198C2×C4—28no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—594no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4#1174568512yes—
222C2×C4C2×C22⋊D5912yes—
223C2×C4C2×C22⋊D5912yes—
224C2×C4C2×C22⋊D5912yes—
225C22—22no—
226C22—24no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22C22×C22⋊D5911yescharacteristic
231C22#41×D5912yes—
232C22C2×#1174568511yescharacteristic
233C22C2×#1174568511yescharacteristic
234C22#1427377412yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—22no—
239C4—41no—
240C4—41no—
241C4—1184no—
242C4—2362no—
243C4—2362no—
244C4—2362no—
245C2—42no—
246C2#1683791311yescharacteristic
247C2#1683794811yescharacteristic
248C2#1683797311yescharacteristic
249C2#1683808512yes—
250C2#1683809112yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×#117×C59C2
hypercenterC2×#117D59
hypocenterC59#2611
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#14273719C2semidirect
2. #16837341C2semidirect
4. #16837332C2semidirect
6. #16837297C2semidirect
8. #16837286C2semidirect
10. #16837248C2semidirect
137. C59#2611semidirect