Finite Group Databasebeta

← #21429774

Subgroups — #21429774

Order 7552.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14273685C212yesmaximal, complemented
2#16837324C212yesmaximal, complemented
3#16837319C211yesmaximal, characteristic
4#16837292C212yesmaximal, complemented
5#16837289C212yesmaximal, complemented
6#16837280C212yesmaximal
7#16837276C212yesmaximal, complemented
8#16837267C211yesmaximal, characteristic, complemented
9C59×#398C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C4×D59C2212yes—
12#14273685—28no—
13C2×C4⋊Dic59C2212yes—
14C2×C4⋊Dic59C2211yescharacteristic
15C2×Dic59⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×C4×Dic59C2212yes—
22C2×C4×Dic59C2211yescharacteristic
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C59⋊#95C2212yes—
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2211yescharacteristic
30#95×C59C2211yescharacteristic
31#95×C59C2212yes—
32C23×D59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2311yescharacteristic
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2312yes—
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C2×D236—24no—
42C2×D236—41no—
43C2×C4×D59—24no—
44C2×C4×D59—24no—
45C2×C4×D59—24no—
46C4⋊C4×C59—24no—
47C4⋊C4×C59—41no—
48C4⋊C4×C59—41no—
49(C2×D59)⋊C4—24no—
50(C2×D59)⋊C4—24no—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—24no—
53(C2×D59)⋊C4—42no—
54C4⋊Dic59—24no—
55C4⋊Dic59—41no—
56Dic59⋊C4—24no—
57C4×Dic59—24no—
58C4×Dic59D414yescomplemented
59C23×C59C2411yescharacteristic
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59#4114yes—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59C2×D412yes—
79C2×C4×C59#4114yes—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59C2×D414yes—
89D236—44no—
90C4×D59—216no—
91C22×C59C22×D411yescharacteristic
92C22×C59C2×#4112yes—
93C22×C59C2×#4112yes—
94C22×C59H(5,𝔽2)11yescharacteristic
95C22×C592−1+411yescharacteristic
96C2×D59—24no—
97C2×D59—24no—
98C2×D59—24no—
99C2×D59—42no—
100C2×D59—42no—
101C2×D59—42no—
102C2×D59—42no—
103C4×C59—24no—
104C4×C59—22no—
105C4×C59—42no—
106C4×C59—41no—
107C4×C59—41no—
108Dic59—24no—
109Dic59—42no—
110Dic59—42no—
111#2609—591nomaximal, Sylow
112C2×C59#52512yes—
113C2×C59#53711yescharacteristic
114C2×C59#55111yescharacteristic
115C2×C59#55212yes—
116C2×C59#55511yescharacteristic
117D59—44no—
118C2×#117—592no—
119#398D5911yescharacteristic, complemented
120#396—592no—
121#394—591no—
122#388—592no—
123#387—592no—
124#386—592no—
125#385—592no—
126#382—591no—
127C59#260911yescharacteristic, complemented, Sylow
128C22×D4—591no—
129C23×C4—592no—
130#117—1188no—
131C2×C4⋊C4—592no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4C2×D5912yes—
135C2×C4⋊C4C2×D5911yescharacteristic
136C2×C4⋊C4C2×D5911yescharacteristic
137C2×C22⋊C4—592no—
138C2×C22⋊C4—592no—
139C2×C22⋊C4—592no—
140C2×C22⋊C4—592no—
141C2×C22⋊C4—592no—
142C2×C42—591no—
143C2×C42—592no—
144#95—592no—
145#95—592no—
146#95—591no—
147#95—592no—
148#95C2×D5911yescharacteristic
149#95C2×D5912yes—
150C24—592no—
151C2×D4—1184no—
152C2×D4—2361no—
153C22×C4—592no—
154C22×C4—592no—
155C22×C4—592no—
156C22×C4—1184no—
157C22×C4—1184no—
158C22×C4—1184no—
159C22×C4C22×D5911yescharacteristic
160C22×C4C22×D5911yescharacteristic
161C22×C4C22×D5912yes—
162C22×C4C22×D5911yescharacteristic
163C22×C4C22×D5912yes—
164C4⋊C4—24no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—1184no—
168C4⋊C4—1184no—
169C4⋊C4—2361no—
170C22⋊C4—1184no—
171C22⋊C4—1184no—
172C22⋊C4—1184no—
173C22⋊C4—1184no—
174C22⋊C4—2362no—
175C42—594no—
176C42—1184no—
177C23—594no—
178C23—1182no—
179C23—1182no—
180C23—1182no—
181C23—1182no—
182C23—1182no—
183C23—1182no—
184C23C23×D5911yescharacteristic
185D4—2364no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—594no—
198C2×C4—11816no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4D4×D5912yes—
208C2×C4#1174568914yes—
209C22—1184no—
210C22—1184no—
211C22—1184no—
212C22—2362no—
213C22—2362no—
214C22—2362no—
215C22—2362no—
216C22C2×D4×D5911yescharacteristic
217C22#41×D5912yes—
218C22C2×#1174568912yes—
219C22#1427377211yescharacteristic
220C22#1427377411yescharacteristic
221C4—24no—
222C4—22no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—1184no—
227C4—2362no—
228C4—2362no—
229C2—2364no—
230C2#1683791512yes—
231C2#1683797911yescharacteristic
232C2#1683808011yescharacteristic
233C2#1683809012yes—
234C2#1683811811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2609
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14273685C2semidirect
2. #16837324C2semidirect
4. #16837292C2semidirect
5. #16837289C2semidirect
7. #16837276C2semidirect
8. #16837267C2semidirect
9. C59×#398C2semidirect
58. C4×Dic59D4semidirect
119. #398D59semidirect
127. C59#2609semidirect