Finite Group Databasebeta

← #21429829

Subgroups — #21429829

Order 7552.

824 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14273698C211yesmaximal, characteristic, complemented
2C2×#14273695C212yesmaximal, complemented
3C2×C22⋊C4×D59C211yesmaximal, characteristic, complemented
4#16837329C211yesmaximal, characteristic, complemented
5#16837327C211yesmaximal, characteristic, complemented
6#16837317C212yesmaximal, complemented
7#16837316C212yesmaximal, complemented
8#16837310C211yesmaximal, characteristic, complemented
9#16837278C212yesmaximal, complemented
10#16837261C211yesmaximal, characteristic, complemented
11C59×#392C211yesmaximal, characteristic, complemented
12C24×D59C2211yescharacteristic
13C22×C22⋊D59C2212yes—
14C22×C22⋊D59C2212yes—
15C22×C4×D59C2211yescharacteristic
16C22×C4×D59C2211yescharacteristic
17#14273698—24no—
18#14273695—28no—
19C2×C4⋊Dic59C2211yescharacteristic, complemented
20C2×Dic59⋊C4C2212yescomplemented
21C2×C22⋊Dic59C2211yescharacteristic
22C2×C22⋊Dic59C2212yes—
23C2×C22⋊Dic59C2212yescomplemented
24C2×C22⋊Dic59C2212yescomplemented
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2211yescharacteristic
27C2×(C2×D59)⋊C4C2211yescharacteristic
28C2×(C2×D59)⋊C4C2212yes—
29C22⋊C4×D59—24no—
30C59⋊#95C2211yescharacteristic, complemented
31C59⋊#95C2212yescomplemented
32C59⋊#95C2212yescomplemented
33C22×D4×C59C2212yes—
34C22×D4×C59C2211yescharacteristic, complemented
35C2×C22⋊C4×C59C2211yescharacteristic
36C2×C22⋊C4×C59C2212yescomplemented
37#95×C59C2211yescharacteristic, complemented
38C24×C59C2312yes—
39C24×C59C2311yescharacteristic
40C23×D59—22no—
41C23×D59—22no—
42C23×D59—42no—
43C23×D59—42no—
44C23×D59D414yescomplemented
45C23×D59C2311yescharacteristic
46C23×D59C2311yescharacteristic
47C2×D4×C59—24no—
48C2×D4×C59—22no—
49C2×D4×C59—42no—
50C2×D4×C59—42no—
51C2×D4×C59—42no—
52C22×C4×C59C2312yes—
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C2×C22⋊D59—24no—
56C2×C22⋊D59—24no—
57C2×C22⋊D59—24no—
58C2×C22⋊D59—24no—
59C2×C22⋊D59—42no—
60C2×C22⋊D59—42no—
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2312yes—
63C22×Dic59C2312yes—
64C22×Dic59C2311yescharacteristic
65C2×C4×D59—22no—
66C2×C4×D59—42no—
67C2×C4×D59—42no—
68C2×C4×D59D414yescomplemented
69C22⋊C4×C59—22no—
70C22⋊C4×C59—42no—
71C22⋊Dic59—24no—
72C22⋊Dic59—22no—
73C22⋊Dic59—24no—
74C22⋊Dic59—42no—
75(C2×D59)⋊C4—24no—
76(C2×D59)⋊C4—24no—
77(C2×D59)⋊C4—22no—
78(C2×D59)⋊C4—22no—
79C4⋊Dic59—22no—
80Dic59⋊C4—42no—
81C23×C59—21no—
82C23×C59—21no—
83C23×C59—22no—
84C23×C59—22no—
85C23×C59—22no—
86C23×C59—22no—
87C23×C59—22no—
88C23×C59—22no—
89C23×C59—22no—
90C23×C59—22no—
91C23×C59—22no—
92C23×C59C2×D412yes—
93C23×C59C2411yescharacteristic
94C22×D59—22no—
95C22×D59—22no—
96C22×D59—21no—
97C22×D59—21no—
98C22×D59—22no—
99C22×D59—22no—
100C22×D59—28no—
101C22×D59—48no—
102C22×D59—44no—
103C22×D59—44no—
104C22×D59—48no—
105C22×D59C2×D412yes—
106C22×D59C2×D412yes—
107C22×D59C2×D412yes—
108C22×D59#4112yes—
109D4×C59—44no—
110D4×C59—48no—
111C2×C4×C59—22no—
112C2×C4×C59—22no—
113C2×C4×C59—21no—
114C2×C4×C59—22no—
115C2×C4×C59—22no—
116C2×C4×C59—22no—
117C2×C4×C59C2×D412yes—
118C22⋊D59—48no—
119C22⋊D59—48no—
120C2×Dic59—22no—
121C2×Dic59—22no—
122C2×Dic59—21no—
123C2×Dic59—22no—
124C2×Dic59—22no—
125C2×Dic59—22no—
126C2×Dic59—22no—
127C2×Dic59—22no—
128C2×Dic59—22no—
129C2×Dic59C2×D412yes—
130C4×D59—44no—
131C4×D59—44no—
132C22×C59—22no—
133C22×C59—24no—
134C22×C59—41no—
135C22×C59—41no—
136C22×C59—42no—
137C22×C59—42no—
138C22×C59—42no—
139C22×C59—42no—
140C22×C59—42no—
141C22×C59—42no—
142C22×C59—42no—
143C22×C59—42no—
144C22×C59C22×D411yescharacteristic
145C22×C59C22×D411yescharacteristic
146C22×C59C2×#4111yescharacteristic
147C22×C59H(5,𝔽2)12yes—
148C22×C59H(5,𝔽2)12yes—
149C2×D59—22no—
150C2×D59—24no—
151C2×D59—22no—
152C2×D59—24no—
153C2×D59—22no—
154C2×D59—24no—
155C2×D59—416no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—42no—
159C2×D59#12114yes—
160C4×C59—22no—
161C4×C59—42no—
162C4×C59—41no—
163Dic59—22no—
164Dic59—42no—
165Dic59—42no—
166Dic59—41no—
167#2617—591nomaximal, Sylow
168C2×C59—42no—
169C2×C59—82no—
170C2×C59C2×#12111yescharacteristic
171C2×C59#53411yescharacteristic
172C2×C59#53412yes—
173C2×C59#53511yescharacteristic
174C2×C59#53812yes—
175D59—24no—
176D59—42no—
177C2×#121—591no—
178C2×#120—592no—
179C22×C22⋊C4—591no—
180#397—591no—
181#397—591no—
182#394—592no—
183#394—592no—
184#392—591no—
185#392D5911yescharacteristic, complemented
186#386—592no—
187#380—591no—
188C59#261711yescharacteristic, complemented, Sylow
189C25—591no—
190C22×D4—592no—
191C22×D4—592no—
192C22×D4C2×D5912yes—
193C22×D4C2×D5911yescharacteristic, complemented
194C23×C4—591no—
195C23×C4—591no—
196#121—1184no—
197#120—1188no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—592no—
200C2×C22⋊C4—591no—
201C2×C22⋊C4—592no—
202C2×C22⋊C4—592no—
203C2×C22⋊C4—591no—
204C2×C22⋊C4—591no—
205C2×C22⋊C4—592no—
206C2×C22⋊C4—592no—
207C2×C22⋊C4—592no—
208C2×C22⋊C4—1184no—
209C2×C22⋊C4C2×D5911yescharacteristic
210C2×C22⋊C4C2×D5912yescomplemented
211#95—591no—
212#95—592no—
213#95—592no—
214#95C2×D5911yescharacteristic, complemented
215C24—591no—
216C24—591no—
217C24—594no—
218C24—1182no—
219C24—1182no—
220C24—2362no—
221C24—2362no—
222C24C22×D5912yes—
223C24C22×D5911yescharacteristic
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—1184no—
230C2×D4—1184no—
231C2×D4—1184no—
232C2×D4—1184no—
233C2×D4—2362no—
234C2×D4—2362no—
235C22×C4—591no—
236C22×C4—594no—
237C22×C4—591no—
238C22×C4—592no—
239C22×C4—592no—
240C22×C4—1182no—
241C22×C4—2362no—
242C22×C4—2362no—
243C22×C4C22×D5911yescharacteristic
244C22×C4C22×D5912yes—
245C22×C4C22×D5911yescharacteristic
246C4⋊C4—1182no—
247C4⋊C4—2362no—
248C22⋊C4—22no—
249C22⋊C4—42no—
250C22⋊C4—1182no—
251C22⋊C4—1184no—
252C22⋊C4—1184no—
253C22⋊C4—1182no—
254C22⋊C4—1184no—
255C22⋊C4—1184no—
256C22⋊C4—1182no—
257C22⋊C4—2362no—
258C23—21no—
259C23—21no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—592no—
270C23—592no—
271C23—592no—
272C23—592no—
273C23—1188no—
274C23—1182no—
275C23—1182no—
276C23—1181no—
277C23—1181no—
278C23—1182no—
279C23—1182no—
280C23—2368no—
281C23—2364no—
282C23—2364no—
283C23—2368no—
284C23D4×D5912yes—
285C23C23×D5911yescharacteristic
286D4—44no—
287D4—48no—
288D4—2368no—
289D4—2368no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—592no—
297C2×C4—1182no—
298C2×C4—1181no—
299C2×C4—1182no—
300C2×C4—1182no—
301C2×C4—1182no—
302C2×C4—1182no—
303C2×C4—1182no—
304C2×C4—1182no—
305C2×C4—1182no—
306C2×C4—2364no—
307C2×C4—2364no—
308C2×C4D4×D5912yes—
309C22—22no—
310C22—24no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—594no—
322C22—1182no—
323C22—1184no—
324C22—1182no—
325C22—1184no—
326C22—1182no—
327C22—1184no—
328C22—23616no—
329C22—2361no—
330C22—2361no—
331C22—2362no—
332C22C2×D4×D5911yescharacteristic
333C22C2×D4×D5911yescharacteristic
334C22#41×D5911yescharacteristic
335C22#1427377212yes—
336C22#1427377212yes—
337C4—22no—
338C4—42no—
339C4—41no—
340C4—1182no—
341C4—2362no—
342C4—2362no—
343C4—2361no—
344C2—42no—
345C2—82no—
346C2—1184no—
347C2—2362no—
348C2#121×D5911yescharacteristic
349C2#1683796211yescharacteristic
350C2#1683796212yes—
351C2#1683796511yescharacteristic
352C2#1683798412yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#392C2
hypercenter#392D59
hypocenterC59#2617
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14273698C2semidirect
2. C2×#14273695C2semidirect
3. C2×C22⋊C4×D59C2semidirect
4. #16837329C2semidirect
5. #16837327C2semidirect
6. #16837317C2semidirect
7. #16837316C2semidirect
8. #16837310C2semidirect
9. #16837278C2semidirect
10. #16837261C2semidirect
11. C59×#392C2semidirect
19. C2×C4⋊Dic59C22semidirect
20. C2×Dic59⋊C4C22semidirect
23. C2×C22⋊Dic59C22semidirect
24. C2×C22⋊Dic59C22semidirect
30. C59⋊#95C22semidirect
31. C59⋊#95C22semidirect
32. C59⋊#95C22semidirect
34. C22×D4×C59C22semidirect
36. C2×C22⋊C4×C59C22semidirect
37. #95×C59C22semidirect
44. C23×D59D4semidirect
68. C2×C4×D59D4semidirect
185. #392D59semidirect
188. C59#2617semidirect
193. C22×D4C2×D59semidirect
210. C2×C22⋊C4C2×D59semidirect
214. #95C2×D59semidirect