Finite Group Databasebeta

← #21431799

Subgroups — #21431799

Order 7552.

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

normal subgroups only

This group has 472 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
1#16837341C211yesmaximal, characteristic, complemented
2#16837324C212yesmaximal, complemented
3#16837313C212yesmaximal, complemented
4#16837303C211yesmaximal, characteristic
5#16837289C212yesmaximal, complemented
6#16837280C212yesmaximal
7#16837276C212yesmaximal, complemented
8#16837259C212yesmaximal, complemented
9C59×#395C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C4×D59C2212yes—
12C2×C4⋊Dic59C2212yes—
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×C4×Dic59C2211yescharacteristic
21C59⋊#95C2211yescharacteristic
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C22×Q8×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2211yescharacteristic
29#95×C59C2211yescharacteristic
30#95×C59C2212yes—
31C23×D59C2312yes—
32C2×Q8×C59—42no—
33C2×Q8×C59—41no—
34C22×C4×C59C2311yescharacteristic
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C2×D236—41no—
43C2×D236—41no—
44C2×D236Q814yescomplemented
45C2×C4×D59—24no—
46C2×C4×D59—42no—
47C2×C4×D59—42no—
48C4⋊C4×C59—42no—
49C4⋊C4×C59—41no—
50(C2×D59)⋊C4—24no—
51(C2×D59)⋊C4—42no—
52(C2×D59)⋊C4—42no—
53(C2×D59)⋊C4—42no—
54(C2×D59)⋊C4—42no—
55C4⋊Dic59—42no—
56C4⋊Dic59—41no—
57Dic59⋊C4—24no—
58C4×Dic59—41no—
59C23×C59C2411yescharacteristic
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59C2×Q814yes—
67Q8×C59—44no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—21no—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59C2×Q812yes—
80C2×C4×C59#4114yes—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90D236—44no—
91C4×D59—48no—
92C22×C59C22×Q811yescharacteristic
93C22×C59C2×#4112yes—
94C22×C59H(5,𝔽2)12yes—
95C22×C59H(5,𝔽2)11yescharacteristic
96C22×C59H(5,𝔽2)11yescharacteristic
97C2×D59—24no—
98C2×D59—24no—
99C2×D59—24no—
100C2×D59—42no—
101C2×D59—42no—
102C2×D59—42no—
103C2×D59—42no—
104C4×C59—24no—
105C4×C59—22no—
106C4×C59—41no—
107C4×C59—41no—
108C4×C59—42no—
109Dic59—42no—
110Dic59—42no—
111Dic59—42no—
112#2784—591nomaximal, Sylow
113C2×C59#53812yes—
114C2×C59#54311yescharacteristic
115C2×C59#55412yes—
116C2×C59#55511yescharacteristic
117C2×C59#56011yescharacteristic
118D59—44no—
119#400—591no—
120#396—592no—
121#395D5911yescharacteristic, complemented
122#393—592no—
123#390—591no—
124#387—592no—
125#386—592no—
126#385—592no—
127#380—592no—
128C59#278411yescharacteristic, complemented, Sylow
129C22×Q8C2×D5911yescharacteristic
130C22×D4—591no—
131C23×C4—592no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—592no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4C2×D5912yes—
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—
143#95—591no—
144#95—592no—
145#95—592no—
146#95—592no—
147#95—592no—
148#95C2×D5911yescharacteristic
149#95C2×D5912yes—
150C24—592no—
151C2×Q8—42no—
152C2×Q8—41no—
153C2×D4—594no—
154C2×D4—2361no—
155C2×D4—2361no—
156C22×C4—592no—
157C22×C4—592no—
158C22×C4—592no—
159C22×C4—1184no—
160C22×C4—2362no—
161C22×C4—2362no—
162C22×C4C22×D5912yes—
163C22×C4C22×D5911yescharacteristic
164C22×C4C22×D5911yescharacteristic
165C22×C4C22×D5911yescharacteristic
166C22×C4C22×D5912yes—
167C4⋊C4—42no—
168C4⋊C4—41no—
169C4⋊C4—1184no—
170C4⋊C4—2362no—
171C4⋊C4—2361no—
172C22⋊C4—1184no—
173C22⋊C4—2362no—
174C22⋊C4—2362no—
175C22⋊C4—2362no—
176C22⋊C4—2362no—
177C42—2361no—
178C23—594no—
179C23—1182no—
180C23—1182no—
181C23—1182no—
182C23—1182no—
183C23—1182no—
184C23—1182no—
185C23C23×D5911yescharacteristic
186Q8—44no—
187D4—2364no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—21no—
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×C4—1182no—
208C2×C4—2368no—
209C2×C4Q8×D5912yes—
210C2×C4#1174568914yes—
211C22—1184no—
212C22—1184no—
213C22—1184no—
214C22—2362no—
215C22—2362no—
216C22—2362no—
217C22—2362no—
218C22C2×Q8×D5911yescharacteristic
219C22C2×#1174568912yes—
220C22#1427377212yes—
221C22#1427377211yescharacteristic
222C22#1427377311yescharacteristic
223C4—24no—
224C4—22no—
225C4—41no—
226C4—42no—
227C4—41no—
228C4—2362no—
229C4—2362no—
230C4—2362no—
231C2—2364no—
232C2#1683799212yes—
233C2#1683802711yescharacteristic
234C2#1683811312yes—
235C2#1683811811yescharacteristic
236C2#1683814111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2784
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #16837341C2semidirect
2. #16837324C2semidirect
3. #16837313C2semidirect
5. #16837289C2semidirect
7. #16837276C2semidirect
8. #16837259C2semidirect
9. C59×#395C2semidirect
44. C2×D236Q8semidirect
121. #395D59semidirect
128. C59#2784semidirect