Finite Group Databasebeta

← #21435403

Subgroups — #21435403

Order 7552.

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

normal subgroups only

This group has 436 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
1#16837952C211yesmaximal, characteristic, complemented
2#16837682C212yesmaximal, complemented
3#16837679C212yesmaximal, complemented
4#16837636C214yesmaximal, complemented
5#16837597C212yesmaximal, complemented
6#16837594C212yesmaximal, complemented
7C2×C4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
8C59×#532C211yesmaximal, characteristic, complemented
9C2×#11745685—21no—
10C2×#11745669C2214yes—
11C22×C59⋊C8C2212yes—
12#14273727C2211yescharacteristic
13#14273724C2211yescharacteristic
14#14273715—21no—
15#14273701—21no—
16#14273701C2212yes—
17C4×D236—21no—
18C4×D236C2212yes—
19#14273660C2214yes—
20C4⋊(C59⋊C8)C2212yes—
21C4⋊(C59⋊C8)C2212yes—
22#14273648C2214yes—
23#14273647C2214yes—
24C2×#41×C59—21no—
25C4⋊Q8×C59C2211yescharacteristic
26#127×C59C2211yescharacteristic
27#124×C59—21no—
28#121×C59—21no—
29#121×C59C2212yes—
30C4×D4×C59—21no—
31C4×D4×C59C2212yes—
32C2×C42×C59C2211yescharacteristic
33#41×C59—44no—
34C2×Q8×C59—21no—
35C2×D4×C59—22no—
36C2×D4×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59C2312yes—
39C22×C4×C59—22no—
40C22×C4×C59D411yescharacteristic
41C22×C4×C59D411yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C2×C22⋊D59—22no—
44#11745685—44no—
45C2×D236—21no—
46C2×D236—21no—
47C2×D236C2312yes—
48C2×C4×D59—22no—
49C2×Dic118—21no—
50C4⋊C4×C59—21no—
51C4⋊C4×C59C2312yes—
52C22⋊C4×C59—22no—
53C22⋊C4×C59—22no—
54C42×C59D411yescharacteristic
55C42×C59D411yescharacteristic
56C42×C59C2311yescharacteristic
57C42×C59C2311yescharacteristic
58#11745669—44no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61C4⋊Dic59—21no—
62C4⋊Dic59C2312yes—
63C2×C59⋊C8—42no—
64C2×C59⋊C8C2314yes—
65C23×C59—22no—
66C23×C59C2×D411yescharacteristic
67C22×D59—22no—
68Q8×C59—42no—
69D4×C59—22no—
70D4×C59—22no—
71D4×C59—42no—
72D4×C59—44no—
73D4×C59—42no—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—41no—
78C2×C4×C59—44no—
79C2×C4×C59D814yescomplemented
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C22⋊D59—44no—
87C2×Dic59—22no—
88D236—22no—
89D236—22no—
90D236—42no—
91D236—42no—
92C4×D59—44no—
93Dic118—42no—
94C59⋊C8—24no—
95C22×C59—21no—
96C22×C59—21no—
97C22×C59—42no—
98C22×C59—42no—
99C22×C59—42no—
100C22×C59C2×D812yes—
101C22×C59C22×D411yescharacteristic
102C2×D59—42no—
103C2×D59—42no—
104C2×D59—42no—
105C4×C59—21no—
106C4×C59—21no—
107C4×C59—21no—
108C4×C59—42no—
109C4×C59C2×D812yes—
110C4×C59C2×D812yes—
111C4×C59H(5,𝔽2)11yescharacteristic
112C4×C592−1+411yescharacteristic
113Dic59—42no—
114#3245—591nomaximal, Sylow
115C2×C59—22no—
116C2×C59—82no—
117C2×C59#53711yescharacteristic
118C2×C59C22×D811yescharacteristic
119C2×C59#57511yescharacteristic
120D59—82no—
121#532—591no—
122#532D5911yescharacteristic, complemented
123#474—592no—
124#474—592no—
125#466—594no—
126#459—592no—
127#459—592no—
128C2×C4⋊C8—591no—
129C59#324511yescharacteristic, complemented, Sylow
130C2×#41—21no—
131C2×#41—1181no—
132C2×D8—594no—
133C22×C8—592no—
134C4⋊Q8—591no—
135C4⋊Q8C2×D5911yescharacteristic
136#127—591no—
137#127C2×D5911yescharacteristic
138#124—21no—
139#124—1181no—
140#121—21no—
141#121—592no—
142#121—1181no—
143#121C2×D5912yes—
144C4×D4—21no—
145C4×D4—592no—
146C4×D4—1181no—
147C4×D4C2×D5912yes—
148C2×C42C2×D5911yescharacteristic
149#107—594no—
150C4⋊C8—592no—
151C4⋊C8—592no—
152#102—594no—
153#102—594no—
154#41—44no—
155#41—2364no—
156C2×Q8—21no—
157C2×Q8—1181no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—592no—
162C2×D4—1182no—
163C2×D4—1181no—
164C2×D4—1181no—
165C2×D4C22×D5912yes—
166C22×C4—22no—
167C22×C4—1182no—
168C22×C4C22⋊D5911yescharacteristic
169C22×C4C22⋊D5911yescharacteristic
170C22×C4C22×D5911yescharacteristic
171D8—2364no—
172C2×C8—594no—
173C2×C8—2362no—
174C4⋊C4—21no—
175C4⋊C4—592no—
176C4⋊C4—1181no—
177C4⋊C4C22×D5912yes—
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—1182no—
181C22⋊C4—1182no—
182C42C22⋊D5911yescharacteristic
183C42C22⋊D5911yescharacteristic
184C42C22×D5911yescharacteristic
185C42C22×D5911yescharacteristic
186C23—22no—
187C23—1182no—
188C23C2×C22⋊D5911yescharacteristic
189Q8—42no—
190Q8—2362no—
191D4—22no—
192D4—22no—
193D4—42no—
194D4—44no—
195D4—42no—
196D4—1182no—
197D4—1182no—
198D4—2362no—
199D4—2364no—
200D4—2362no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—44no—
206C2×C4—1182no—
207C2×C4—2364no—
208C2×C4#1174566914yescomplemented
209C2×C4C2×C22⋊D5911yescharacteristic
210C2×C4C2×C22⋊D5911yescharacteristic
211C2×C4C2×C22⋊D5911yescharacteristic
212C2×C4C2×C22⋊D5911yescharacteristic
213C2×C4C2×C22⋊D5911yescharacteristic
214C2×C4C23×D5911yescharacteristic
215C8—1184no—
216C22—21no—
217C22—21no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—2362no—
222C22—2362no—
223C22—2362no—
224C22C2×#1174566912yes—
225C22C22×C22⋊D5911yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—42no—
230C4—2362no—
231C4C2×#1174566912yes—
232C4C2×#1174566912yes—
233C4#1427377311yescharacteristic
234C4#1427377411yescharacteristic
235C2—22no—
236C2—82no—
237C2—4722no—
238C2#1683798011yescharacteristic
239C2C22×#1174566911yescharacteristic
240C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#532C2
socleC22×C59C22×D4
hypercenter#532D59
hypocenterC59#3245
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #16837952C2semidirect
2. #16837682C2semidirect
3. #16837679C2semidirect
4. #16837636C2semidirect
5. #16837597C2semidirect
6. #16837594C2semidirect
7. C2×C4⋊(C59⋊C8)C2semidirect
8. C59×#532C2semidirect
79. C2×C4×C59D8semidirect
122. #532D59semidirect
129. C59#3245semidirect
208. C2×C4#11745669semidirect