Finite Group Databasebeta

← #21429586

Subgroups — #21429586

Order 7552.

440 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 129 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#16837319C212yesmaximal
3#16837303C211yesmaximal, characteristic
4#16837294C212yesmaximal, complemented
5#16837294C212yesmaximal, complemented
6#16837294C212yesmaximal, complemented
7#16837292C212yesmaximal, complemented
8C4⋊C4×Dic59C212yesmaximal, complemented
9C59×#398C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C2×C4⋊Dic59C2212yes—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×(C2×D59)⋊C4C2212yes—
14C2×(C2×D59)⋊C4C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×C4×Dic59C2212yes—
20C2×C4×Dic59C2211yescharacteristic
21C2×C4×Dic59C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C2×C4⋊C4×C59C2212yes—
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2211yescharacteristic
29#95×C59C2212yes—
30#95×C59C2211yescharacteristic
31C23×D59C2312yes—
32C22×C4×C59C2311yescharacteristic
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2312yes—
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×Dic59C2312yes—
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C2×D236—22no—
41C2×D236—41no—
42C2×D236—41no—
43C4⋊C4×C59—24no—
44C4⋊C4×C59—41no—
45C4⋊C4×C59—41no—
46(C2×D59)⋊C4—24no—
47(C2×D59)⋊C4—24no—
48(C2×D59)⋊C4—24no—
49(C2×D59)⋊C4—24no—
50(C2×D59)⋊C4—42no—
51(C2×D59)⋊C4—42no—
52C4⋊Dic59—24no—
53C4⋊Dic59—41no—
54C4×Dic59—24no—
55C4×Dic59—41no—
56C4×Dic59—42no—
57C23×C59C2411yescharacteristic
58C22×D59—22no—
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59#4112yes—
77C2×C4×C59#4114yes—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59#4114yes—
87D236—44no—
88C22×C59C2×#4112yes—
89C22×C59C2×#4111yescharacteristic
90C22×C59C2×#4112yes—
91C22×C59H(5,𝔽2)11yescharacteristic
92C22×C59H(5,𝔽2)11yescharacteristic
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—42no—
98C2×D59—42no—
99C2×D59—42no—
100C4×C59—24no—
101C4×C59—22no—
102C4×C59—42no—
103C4×C59—41no—
104C4×C59—41no—
105Dic59—24no—
106Dic59—42no—
107Dic59—42no—
108#2593—591nomaximal, Sylow
109C2×C59#52912yes—
110C2×C59#53811yescharacteristic
111C2×C59#55312yes—
112C2×C59#55511yescharacteristic
113C2×C59#55911yescharacteristic
114D59—82no—
115#400—591no—
116#398D5911yescharacteristic, complemented
117#394—592no—
118#390—591no—
119#388—592no—
120#388—592no—
121#388—592no—
122#388—592no—
123C4×C4⋊C4—592no—
124C59#259311yescharacteristic, complemented, Sylow
125C22×D4—591no—
126C2×C4⋊C4—592no—
127C2×C4⋊C4—591no—
128C2×C4⋊C4C2×D5912yes—
129C2×C4⋊C4C2×D5911yescharacteristic
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C22⋊C4—592no—
132C2×C22⋊C4—592no—
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C42—592no—
138C2×C42—591no—
139C2×C42—592no—
140#95—592no—
141#95—592no—
142#95—592no—
143#95—591no—
144#95C2×D5911yescharacteristic
145#95C2×D5912yes—
146C24—592no—
147C2×D4—1182no—
148C2×D4—2361no—
149C2×D4—2361no—
150C22×C4—592no—
151C22×C4—592no—
152C22×C4—592no—
153C22×C4C22×D5911yescharacteristic
154C22×C4C22×D5911yescharacteristic
155C22×C4C22×D5912yes—
156C22×C4C22×D5911yescharacteristic
157C22×C4C22×D5912yes—
158C4⋊C4—24no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—1184no—
162C4⋊C4—2361no—
163C22⋊C4—1184no—
164C22⋊C4—1184no—
165C22⋊C4—1184no—
166C22⋊C4—1184no—
167C22⋊C4—2362no—
168C22⋊C4—2362no—
169C42—1184no—
170C42—2361no—
171C42—2362no—
172C23—1182no—
173C23—1182no—
174C23—1182no—
175C23—1182no—
176C23—1182no—
177C23—1182no—
178C23—1182no—
179C23C23×D5911yescharacteristic
180D4—2364no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—594no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4#1174568712yes—
202C2×C4#1174568914yes—
203C22—2362no—
204C22—2362no—
205C22—2362no—
206C22—2362no—
207C22—2362no—
208C22—2362no—
209C22—2362no—
210C22#41×D5912yes—
211C22C2×#1174568711yescharacteristic
212C22C2×#1174568912yes—
213C22#1427377211yescharacteristic
214C22#1427377311yescharacteristic
215C4—24no—
216C4—22no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—1184no—
221C4—2362no—
222C4—2362no—
223C2—4722no—
224C2#1683793812yes—
225C2#1683798911yescharacteristic
226C2#1683810512yes—
227C2#1683811811yescharacteristic
228C2#1683813611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2593
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #16837341C2semidirect
4. #16837294C2semidirect
5. #16837294C2semidirect
6. #16837294C2semidirect
7. #16837292C2semidirect
8. C4⋊C4×Dic59C2semidirect
9. C59×#398C2semidirect
116. #398D59semidirect
124. C59#2593semidirect