Finite Group Databasebeta

← #21430027

Subgroups — #21430027

Order 7552.

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

normal subgroups only

This group has 576 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
1C2×#14273705C211yesmaximal, characteristic, complemented
2C2×#14273698C211yesmaximal, characteristic
3#16837342C211yesmaximal, characteristic, complemented
4#16837341C211yesmaximal, characteristic, complemented
5#16837330C212yesmaximal, complemented
6#16837316C211yesmaximal, characteristic, complemented
7#16837314C212yesmaximal, complemented
8#16837278C212yesmaximal, complemented
9#16837278C212yesmaximal, complemented
10#95×D59C211yesmaximal, characteristic, complemented
11C59×#394C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×C22⋊D59C2212yes—
14C22×C4×D59C2212yes—
15C22×C4×D59C2211yescharacteristic
16#14273705—24no—
17#14273698—24no—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×C22⋊Dic59C2212yes—
22C2×C22⋊Dic59C2212yes—
23C2×C22⋊Dic59C2212yes—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C59⋊#95C2212yes—
27C59⋊#95C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C22×D4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C22⋊C4×C59C2212yes—
35C2×C22⋊C4×C59C2212yes—
36#95×C59C2211yescharacteristic
37C24×C59C2312yes—
38C23×D59C2311yescharacteristic
39C2×D4×C59—22no—
40C2×D4×C59—42no—
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×C4×C59C2311yescharacteristic
45C2×C22⋊D59—24no—
46C2×C22⋊D59—24no—
47C2×C22⋊D59—24no—
48C22×Dic59C2312yes—
49C22×Dic59C2312yes—
50C22×Dic59C2311yescharacteristic
51C22×Dic59C2311yescharacteristic
52C22×Dic59C2311yescharacteristic
53C2×C4×D59—24no—
54C2×C4×D59—42no—
55C2×C4×D59—42no—
56C2×C4×D59—42no—
57C2×C4×D59D414yes—
58C2×Dic118—22no—
59C2×Dic118—42no—
60C4⋊C4×C59—22no—
61C22⋊C4×C59—42no—
62C22⋊C4×C59—42no—
63C22⋊Dic59—24no—
64C22⋊Dic59—42no—
65C22⋊Dic59—42no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—22no—
68C4⋊Dic59—22no—
69Dic59⋊C4—22no—
70Dic59⋊C4—22no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—22no—
75C23×C59—22no—
76C23×C59—22no—
77C23×C59—22no—
78C23×C59C2411yescharacteristic
79C22×D59—22no—
80C22×D59—21no—
81C22×D59—21no—
82C22×D59C2×D412yes—
83C22×D59#4114yes—
84D4×C59—44no—
85C2×C4×C59—22no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—22no—
89C2×C4×C59—21no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59C2×D412yes—
95C22⋊D59—48no—
96C2×Dic59—22no—
97C2×Dic59—21no—
98C2×Dic59—21no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—22no—
103C2×Dic59—21no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59—22no—
107C2×Dic59—21no—
108C2×Dic59C2×D412yes—
109C4×D59—44no—
110C4×D59—48no—
111Dic118—44no—
112C22×C59—42no—
113C22×C59—42no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59—42no—
117C22×C59—42no—
118C22×C59—42no—
119C22×C59C22×D411yescharacteristic
120C22×C59C2×#4112yes—
121C22×C59H(5,𝔽2)12yes—
122C22×C59H(5,𝔽2)11yescharacteristic
123C22×C592−1+411yescharacteristic
124C2×D59—22no—
125C2×D59—22no—
126C2×D59—24no—
127C2×D59—24no—
128C2×D59#12414yes—
129C4×C59—22no—
130C4×C59—41no—
131C4×C59—41no—
132C4×C59—42no—
133Dic59—22no—
134Dic59—42no—
135Dic59—41no—
136Dic59—41no—
137Dic59—42no—
138#2639—591nomaximal, Sylow
139C2×C59—82no—
140C2×C59C2×#12411yescharacteristic
141C2×C59#53411yescharacteristic
142C2×C59#53711yescharacteristic
143C2×C59#53812yes—
144C2×C59#53912yes—
145D59—24no—
146C2×C22⋊Q8—591no—
147C2×#121—591no—
148#400—591no—
149#400—591no—
150#397—592no—
151#394—591no—
152#394D5911yescharacteristic, complemented
153#393—592no—
154#386—592no—
155#386—592no—
156C2×#95—591no—
157C59#263911yescharacteristic, complemented, Sylow
158C22×Q8—591no—
159C22×D4—592no—
160C22×D4C2×D5911yescharacteristic
161C23×C4—591no—
162C23×C4—592no—
163C22⋊Q8—1184no—
164#121—1184no—
165C2×C4⋊C4—591no—
166C2×C4⋊C4—591no—
167C2×C4⋊C4—591no—
168C2×C4⋊C4C2×D5911yescharacteristic
169C2×C22⋊C4—592no—
170C2×C22⋊C4—591no—
171C2×C22⋊C4—591no—
172C2×C22⋊C4—592no—
173C2×C22⋊C4—592no—
174C2×C22⋊C4C2×D5912yes—
175C2×C22⋊C4C2×D5912yes—
176#95—592no—
177#95—591no—
178#95—592no—
179#95—592no—
180#95—592no—
181#95—592no—
182#95C2×D5911yescharacteristic
183C24—591no—
184C24C22×D5912yes—
185C2×Q8—1182no—
186C2×Q8—2362no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—1184no—
190C2×D4—1184no—
191C2×D4—1184no—
192C22×C4—591no—
193C22×C4—594no—
194C22×C4—592no—
195C22×C4—592no—
196C22×C4—591no—
197C22×C4—591no—
198C22×C4—1184no—
199C22×C4—2362no—
200C22×C4—2362no—
201C22×C4—2362no—
202C22×C4C22×D5912yes—
203C22×C4C22×D5911yescharacteristic
204C22×C4C22×D5911yescharacteristic
205C22×C4C22×D5911yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—1182no—
208C4⋊C4—1182no—
209C4⋊C4—1182no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—1182no—
213C22⋊C4—1182no—
214C22⋊C4—1184no—
215C22⋊C4—2362no—
216C22⋊C4—2362no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—592no—
225C23—594no—
226C23—1182no—
227C23—1181no—
228C23—1181no—
229C23C23×D5911yescharacteristic
230Q8—2364no—
231D4—44no—
232D4—2368no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—592no—
243C2×C4—1182no—
244C2×C4—1181no—
245C2×C4—1182no—
246C2×C4—1181no—
247C2×C4—1182no—
248C2×C4—1182no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—1182no—
252C2×C4—1182no—
253C2×C4—1182no—
254C2×C4—1181no—
255C2×C4—2364no—
256C2×C4—2368no—
257C2×C4D4×D5912yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—594no—
266C22—1182no—
267C22—1182no—
268C22—1184no—
269C22—1184no—
270C22C2×D4×D5911yescharacteristic
271C22#41×D5912yes—
272C22#1427377212yes—
273C22#1427377211yescharacteristic
274C22#1427377411yescharacteristic
275C4—22no—
276C4—41no—
277C4—41no—
278C4—42no—
279C4—1182no—
280C4—2362no—
281C4—2361no—
282C4—2361no—
283C4—2362no—
284C2—82no—
285C2—1184no—
286C2#124×D5911yescharacteristic
287C2#1683796211yescharacteristic
288C2#1683798111yescharacteristic
289C2#1683798412yes—
290C2#1683799512yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2639
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14273705C2semidirect
3. #16837342C2semidirect
4. #16837341C2semidirect
5. #16837330C2semidirect
6. #16837316C2semidirect
7. #16837314C2semidirect
8. #16837278C2semidirect
9. #16837278C2semidirect
10. #95×D59C2semidirect
11. C59×#394C2semidirect
152. #394D59semidirect
157. C59#2639semidirect