Finite Group Databasebeta

← #21429345

Subgroups — #21429345

Order 7552.

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

normal subgroups only

This group has 476 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#16837319C211yesmaximal, characteristic
3#16837313C212yesmaximal, complemented
4#16837294C212yesmaximal, complemented
5#16837280C212yesmaximal
6#16837269C212yesmaximal, complemented
7#16837264C212yesmaximal, complemented
8C4×(C2×D59)⋊C4C212yesmaximal, complemented
9C59×#391C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C4×D59C2212yes—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×(C2×D59)⋊C4C2212yes—
14C2×(C2×D59)⋊C4C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×C4×Dic59C2212yes—
19C59⋊#95C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2211yescharacteristic
22C59⋊#95C2212yes—
23C59⋊#95C2211yescharacteristic
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C22×Q8×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C42×C59C2211yescharacteristic
29#95×C59C2212yes—
30#95×C59C2212yes—
31C23×D59C2312yes—
32C2×Q8×C59—22no—
33C2×Q8×C59—41no—
34C2×Q8×C59—41no—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2312yes—
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C2×D236—24no—
44C2×D236—41no—
45C2×C4×D59—24no—
46C2×C4×D59—24no—
47C2×C4×D59—42no—
48C4⋊C4×C59—41no—
49C42×C59—41no—
50(C2×D59)⋊C4—24no—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—24no—
53(C2×D59)⋊C4—42no—
54(C2×D59)⋊C4—42no—
55C4⋊Dic59—41no—
56C4×Dic59—24no—
57C23×C59C2411yescharacteristic
58C22×D59—22no—
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59#4114yes—
65Q8×C59—44no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—21no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59#4112yes—
78C2×C4×C59#4114yes—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88D236—44no—
89C4×D59—48no—
90C22×C59C2×#4112yes—
91C22×C59C2×#4111yescharacteristic
92C22×C59C2×#4112yes—
93C22×C59H(5,𝔽2)11yescharacteristic
94C22×C59H(5,𝔽2)11yescharacteristic
95C2×D59—24no—
96C2×D59—24no—
97C2×D59—24no—
98C2×D59—42no—
99C2×D59—42no—
100C2×D59—42no—
101C2×D59—42no—
102C4×C59—22no—
103C4×C59—24no—
104C4×C59—42no—
105C4×C59—41no—
106C4×C59—41no—
107Dic59—42no—
108Dic59—42no—
109Dic59—42no—
110#2572—591nomaximal, Sylow
111C2×C59#52912yes—
112C2×C59#53811yescharacteristic
113C2×C59#55112yes—
114C2×C59#55111yescharacteristic
115C2×C59#55511yescharacteristic
116D59—44no—
117#400—591no—
118#394—591no—
119#393—592no—
120#391D5911yescharacteristic, complemented
121#388—592no—
122#386—592no—
123#383—592no—
124#381—592no—
125C4×C22⋊C4—592no—
126C59#257211yescharacteristic, complemented, Sylow
127C22×Q8C2×D5911yescharacteristic
128C22×D4—591no—
129C23×C4—592no—
130C2×C4⋊C4—591no—
131C2×C4⋊C4C2×D5911yescharacteristic
132C2×C22⋊C4—592no—
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C42—592no—
138C2×C42C2×D5911yescharacteristic
139#95—592no—
140#95—592no—
141#95—591no—
142#95—592no—
143#95—591no—
144#95—592no—
145#95—592no—
146#95C2×D5912yes—
147#95C2×D5912yes—
148C24—592no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×D4—1184no—
153C2×D4—2361no—
154C22×C4—592no—
155C22×C4—592no—
156C22×C4—592no—
157C22×C4—1184no—
158C22×C4—1184no—
159C22×C4—2362no—
160C22×C4C22×D5911yescharacteristic
161C22×C4C22×D5912yes—
162C22×C4C22×D5911yescharacteristic
163C22×C4C22×D5911yescharacteristic
164C22×C4C22×D5912yes—
165C4⋊C4—41no—
166C4⋊C4—2361no—
167C22⋊C4—1184no—
168C22⋊C4—1184no—
169C22⋊C4—1184no—
170C22⋊C4—2362no—
171C22⋊C4—2362no—
172C42—41no—
173C42—1184no—
174C23—594no—
175C23—1182no—
176C23—1182no—
177C23—1182no—
178C23—1182no—
179C23—1182no—
180C23—1182no—
181C23C23×D5911yescharacteristic
182Q8—44no—
183D4—2364no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—2368no—
205C2×C4#1174568512yes—
206C2×C4#1174568914yes—
207C22—1184no—
208C22—1184no—
209C22—1184no—
210C22—2362no—
211C22—2362no—
212C22—2362no—
213C22—2362no—
214C22#41×D5912yes—
215C22C2×#1174568511yescharacteristic
216C22C2×#1174568912yes—
217C22#1427377211yescharacteristic
218C22#1427377211yescharacteristic
219C4—22no—
220C4—24no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—2362no—
225C4—2362no—
226C4—2362no—
227C2—2364no—
228C2#1683793912yes—
229C2#1683799011yescharacteristic
230C2#1683807912yes—
231C2#1683808211yescharacteristic
232C2#1683811811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#391C2
hypercenter#391D59
hypocenterC59#2572
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #16837341C2semidirect
3. #16837313C2semidirect
4. #16837294C2semidirect
6. #16837269C2semidirect
7. #16837264C2semidirect
8. C4×(C2×D59)⋊C4C2semidirect
9. C59×#391C2semidirect
120. #391D59semidirect
126. C59#2572semidirect