Finite Group Databasebeta

← #21435275

Subgroups — #21435275

Order 7552.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837936C211yesmaximal, characteristic
2#16837801C212yesmaximal, complemented
3#16837759C212yesmaximal, complemented
4#16837743C212yesmaximal, complemented
5#16837726C212yesmaximal
6#16837694C211yesmaximal, characteristic, complemented
7#16837689C211yesmaximal, characteristic, complemented
8#16837684C211yesmaximal, characteristic, complemented
9#16837679C211yesmaximal, characteristic, complemented
10#16837455C211yesmaximal, characteristic, complemented
11C59×#533C211yesmaximal, characteristic, complemented
12#14273721—21no—
13#14273719C2211yescharacteristic
14#14273715C2211yescharacteristic
15#14273710—21no—
16#14273706C2211yescharacteristic
17#14273701C2211yescharacteristic
18C4×Dic118C2211yescharacteristic
19C4×D236C2211yescharacteristic
20C4×C22⋊D59—21no—
21#14273684—21no—
22#14273660C2212yes—
23#14273660C2212yes—
24#14273658C2212yes—
25#14273658C2212yes—
26C4⋊(C59⋊C8)C2211yescharacteristic
27C4⋊(C59⋊C8)C2211yescharacteristic
28#14273650C2212yes—
29#14273650C2212yes—
30#14273647C2212yes—
31#14273647C2212yes—
32C22⋊(C59⋊C8)C2212yes—
33C4×C59⋊C8C2212yes—
34C4⋊Q8×C59C2211yescharacteristic
35C4⋊Q8×C59C2211yescharacteristic
36#125×C59C2212yes—
37C22⋊Q8×C59—21no—
38C22⋊Q8×C59—21no—
39C4×Q8×C59—21no—
40C4×Q8×C59—21no—
41#117×C59C2212yes—
42C2×C42×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44C2×Q8×C59—21no—
45C22×C4×C59D411yescharacteristic
46C22×C4×C59D411yescharacteristic
47C22×C4×C59C2311yescharacteristic
48C2×C22⋊D59—21no—
49C2×D236C2311yescharacteristic
50C2×C4×D59—21no—
51C2×Dic118C2311yescharacteristic
52C4⋊C4×C59—22no—
53C4⋊C4×C59—22no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2312yes—
57C4⋊C4×C59C2312yes—
58C22⋊C4×C59—22no—
59C42×C59—22no—
60C42×C59D411yescharacteristic
61C42×C59D411yescharacteristic
62C42×C59C2311yescharacteristic
63C42×C59C2311yescharacteristic
64C22⋊Dic59—21no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—21no—
69C4⋊Dic59C2311yescharacteristic
70C4⋊Dic59C2311yescharacteristic
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—21no—
74Dic59⋊C4—21no—
75C4×Dic59—21no—
76C2×C59⋊C8C2312yes—
77C2×C59⋊C8C2312yes—
78C23×C59C2×D411yescharacteristic
79C22×D59—21no—
80Q8×C59—42no—
81Q8×C59—42no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—41no—
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2411yescharacteristic
94C22⋊D59—42no—
95C2×Dic59—21no—
96C2×Dic59—21no—
97C2×Dic59—21no—
98D236—21no—
99D236—21no—
100C4×D59—42no—
101Dic118—21no—
102Dic118—21no—
103C59⋊C8—22no—
104C59⋊C8—22no—
105C22×C59—21no—
106C22×C59—21no—
107C22×C59—21no—
108C22×C59C22×D411yescharacteristic
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—41no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—21no—
115C4×C59—21no—
116C4×C59—42no—
117C4×C59—42no—
118C4×C59#13512yes—
119C4×C592−1+411yescharacteristic
120C4×C592−1+411yescharacteristic
121Dic59—41no—
122Dic59—41no—
123Dic59—41no—
124#3233—591nomaximal, Sylow
125C2×C59—41no—
126C2×C59#53611yescharacteristic
127C2×C59C2×#13511yescharacteristic
128C2×C59#57511yescharacteristic
129D59—81no—
130#533D5911yescharacteristic, complemented
131#529—591no—
132#499—592no—
133#488—592no—
134#485—592no—
135#482—592no—
136#477—591no—
137#476—591no—
138#475—591no—
139#474—591no—
140#431—591no—
141C59#323311yescharacteristic, complemented, Sylow
142C4⋊Q8C2×D5911yescharacteristic
143C4⋊Q8C2×D5911yescharacteristic
144#126—1181no—
145#125—591no—
146#125C2×D5912yes—
147#124—591no—
148#123—1181no—
149C22⋊Q8—21no—
150C22⋊Q8—21no—
151C22⋊Q8—591no—
152#121—591no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—591no—
156C4×D4—591no—
157C4×D4—1181no—
158#117—1181no—
159#117C2×D5912yes—
160C2×C42C2×D5911yescharacteristic
161#107—592no—
162#107—592no—
163#106—592no—
164#106—592no—
165C4⋊C8—591no—
166C4⋊C8—591no—
167#103—592no—
168#103—592no—
169#102—592no—
170#102—592no—
171C22⋊C8—592no—
172C4×C8—592no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—591no—
176C2×D4—591no—
177C2×D4—1181no—
178C22×C4—1181no—
179C22×C4C22⋊D5911yescharacteristic
180C22×C4C22⋊D5911yescharacteristic
181C22×C4C22×D5911yescharacteristic
182C2×C8—592no—
183C2×C8—592no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—591no—
189C4⋊C4—591no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C4⋊C4C22×D5912yes—
195C4⋊C4C22×D5912yes—
196C22⋊C4—22no—
197C22⋊C4—1181no—
198C22⋊C4—1181no—
199C22⋊C4—1181no—
200C22⋊C4—1181no—
201C22⋊C4—1181no—
202C42—22no—
203C42—1181no—
204C42C22⋊D5911yescharacteristic
205C42C22⋊D5911yescharacteristic
206C42C22×D5911yescharacteristic
207C42C22×D5911yescharacteristic
208C23—1181no—
209C23C2×C22⋊D5911yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—1181no—
213Q8—1181no—
214D4—1181no—
215D4—1181no—
216D4—2362no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—1181no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—2362no—
227C2×C4C2×C22⋊D5911yescharacteristic
228C2×C4C2×C22⋊D5911yescharacteristic
229C2×C4C2×C22⋊D5911yescharacteristic
230C2×C4C2×C22⋊D5911yescharacteristic
231C2×C4C2×C22⋊D5911yescharacteristic
232C2×C4C23×D5911yescharacteristic
233C8—1182no—
234C8—1182no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—2361no—
239C22—2361no—
240C22—2361no—
241C22C22×C22⋊D5911yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—2361no—
249C4—2361no—
250C4—2361no—
251C4#1427374712yes—
252C4#1427377511yescharacteristic
253C4#1427377511yescharacteristic
254C2—41no—
255C2—4721no—
256C2#1683797611yescharacteristic
257C2C2×#1427374711yescharacteristic
258C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#533C2
socleC22×C59C22×D4
hypercenter#533D59
hypocenterC59#3233
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16837801C2semidirect
3. #16837759C2semidirect
4. #16837743C2semidirect
6. #16837694C2semidirect
7. #16837689C2semidirect
8. #16837684C2semidirect
9. #16837679C2semidirect
10. #16837455C2semidirect
11. C59×#533C2semidirect
130. #533D59semidirect
141. C59#3233semidirect