Finite Group Databasebeta

← #21431791

Subgroups — #21431791

Order 7552.

472 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837343C211yesmaximal, characteristic, complemented
2#16837326C211yesmaximal, characteristic, complemented
3#16837325C211yesmaximal, characteristic, complemented
4#16837321C211yesmaximal, characteristic, complemented
5#16837313C211yesmaximal, characteristic, complemented
6#16837302C211yesmaximal, characteristic
7#16837287C211yesmaximal, characteristic, complemented
8#16837284C211yesmaximal, characteristic, complemented
9#16837279C211yesmaximal, characteristic
10#16837278C211yesmaximal, characteristic
11#16837276C211yesmaximal, characteristic, complemented
12#16837274C211yesmaximal, characteristic, complemented
13#16837261C211yesmaximal, characteristic, complemented
14#16837260C211yesmaximal, characteristic, complemented
15C59×#393C211yesmaximal, characteristic, complemented
16C22×C22⋊D59C2211yescharacteristic
17C23×Dic59C2211yescharacteristic
18C22×C4×D59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×Dic59⋊C4C2211yescharacteristic
24C2×Dic59⋊C4C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×C4×Dic59C2211yescharacteristic
35C59⋊#95C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C22×Q8×C59C2211yescharacteristic
45C2×C22⋊C4×C59C2211yescharacteristic
46C2×C22⋊C4×C59C2211yescharacteristic
47C2×C22⋊C4×C59C2211yescharacteristic
48#95×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51C24×C59C2311yescharacteristic
52C23×D59C2311yescharacteristic
53C2×Q8×C59—41no—
54C2×Q8×C59—41no—
55C2×Q8×C59—41no—
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—41no—
63C2×C22⋊D59—41no—
64C2×C22⋊D59Q814yescomplemented
65C22×Dic59—22no—
66C22×Dic59—41no—
67C22×Dic59—41no—
68C22×Dic59C2311yescharacteristic
69C22×Dic59C2311yescharacteristic
70C22×Dic59C2311yescharacteristic
71C22×Dic59C2311yescharacteristic
72C22×Dic59C2311yescharacteristic
73C22×Dic59C2311yescharacteristic
74C22×Dic59C2311yescharacteristic
75C2×C4×D59—22no—
76C2×C4×D59—41no—
77C2×C4×D59—41no—
78C22⋊C4×C59—41no—
79C22⋊C4×C59—41no—
80C22⋊C4×C59—41no—
81C22⋊Dic59—22no—
82C22⋊Dic59—41no—
83(C2×D59)⋊C4—22no—
84(C2×D59)⋊C4—41no—
85(C2×D59)⋊C4—41no—
86(C2×D59)⋊C4—41no—
87(C2×D59)⋊C4—41no—
88C4⋊Dic59—22no—
89Dic59⋊C4—22no—
90Dic59⋊C4—41no—
91Dic59⋊C4—41no—
92Dic59⋊C4—41no—
93Dic59⋊C4—41no—
94Dic59⋊C4—41no—
95Dic59⋊C4—41no—
96C4×Dic59—41no—
97C23×C59—21no—
98C23×C59—21no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59C2×Q812yes—
104C23×C59C2411yescharacteristic
105C22×D59—21no—
106C22×D59—21no—
107C22×D59—21no—
108C22×D59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59C2×Q812yes—
112Q8×C59—44no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C22⋊D59—44no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—44no—
151C2×Dic59C2×Q812yes—
152C2×Dic59#4112yes—
153C2×Dic59#4112yes—
154C4×D59—44no—
155C22×C59—22no—
156C22×C59—22no—
157C22×C59—22no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59C22×Q811yescharacteristic
163C22×C59C2×#4111yescharacteristic
164C22×C59C2×#4111yescharacteristic
165C22×C59H(5,𝔽2)11yescharacteristic
166C22×C59H(5,𝔽2)11yescharacteristic
167C22×C59H(5,𝔽2)11yescharacteristic
168C22×C59H(5,𝔽2)11yescharacteristic
169C2×D59—22no—
170C2×D59—22no—
171C2×D59—22no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C4×C59—41no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—41no—
182Dic59—22no—
183Dic59—22no—
184Dic59—22no—
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188Dic59—41no—
189#2784—591nomaximal, Sylow
190C2×C59—42no—
191C2×C59#53811yescharacteristic
192C2×C59#53811yescharacteristic
193C2×C59#54311yescharacteristic
194C2×C59#55411yescharacteristic
195C2×C59#55411yescharacteristic
196C2×C59#55511yescharacteristic
197C2×C59#56011yescharacteristic
198D59—42no—
199#400—591no—
200#396—591no—
201#396—591no—
202#395—591no—
203#393—591no—
204#393D5911yescharacteristic, complemented
205#390—591no—
206#387—591no—
207#387—591no—
208#386—591no—
209#386—591no—
210#385—591no—
211#385—591no—
212#380—591no—
213#380—591no—
214C59#278411yescharacteristic, complemented, Sylow
215C22×Q8C2×D5911yescharacteristic
216C22×D4—591no—
217C23×C4—591no—
218C23×C4—591no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4—591no—
221C2×C4⋊C4—591no—
222C2×C4⋊C4—591no—
223C2×C4⋊C4—591no—
224C2×C4⋊C4—591no—
225C2×C4⋊C4—591no—
226C2×C4⋊C4—591no—
227C2×C22⋊C4—591no—
228C2×C22⋊C4—591no—
229C2×C22⋊C4—591no—
230C2×C22⋊C4—591no—
231C2×C22⋊C4—591no—
232C2×C22⋊C4—591no—
233C2×C22⋊C4—591no—
234C2×C22⋊C4C2×D5911yescharacteristic
235C2×C22⋊C4C2×D5911yescharacteristic
236C2×C22⋊C4C2×D5911yescharacteristic
237C2×C42—591no—
238#95—591no—
239#95—591no—
240#95—591no—
241#95—591no—
242#95—591no—
243#95—591no—
244#95—591no—
245#95—591no—
246#95—591no—
247#95C2×D5911yescharacteristic
248#95C2×D5911yescharacteristic
249#95C2×D5911yescharacteristic
250C24—591no—
251C24C22×D5911yescharacteristic
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×D4—594no—
256C2×D4—2361no—
257C2×D4—2361no—
258C22×C4—591no—
259C22×C4—591no—
260C22×C4—591no—
261C22×C4—591no—
262C22×C4—591no—
263C22×C4—591no—
264C22×C4—591no—
265C22×C4—1182no—
266C22×C4—1182no—
267C22×C4—2361no—
268C22×C4—2361no—
269C22×C4—2361no—
270C22×C4—2361no—
271C22×C4C22×D5911yescharacteristic
272C22×C4C22×D5911yescharacteristic
273C22×C4C22×D5911yescharacteristic
274C22×C4C22×D5911yescharacteristic
275C22×C4C22×D5911yescharacteristic
276C22×C4C22×D5911yescharacteristic
277C4⋊C4—1182no—
278C4⋊C4—1182no—
279C4⋊C4—2361no—
280C4⋊C4—2361no—
281C4⋊C4—2361no—
282C4⋊C4—2361no—
283C4⋊C4—2361no—
284C4⋊C4—2361no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—1182no—
289C22⋊C4—1182no—
290C22⋊C4—2361no—
291C22⋊C4—2361no—
292C22⋊C4—2361no—
293C22⋊C4—2361no—
294C22⋊C4—2361no—
295C42—2361no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—592no—
303C23—1181no—
304C23—1181no—
305C23—1181no—
306C23—1181no—
307C23—1181no—
308C23—1181no—
309C23Q8×D5912yes—
310C23C23×D5911yescharacteristic
311Q8—44no—
312D4—2364no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—592no—
332C2×C4—592no—
333C2×C4—592no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—2364no—
353C2×C4—2364no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—1182no—
362C22—1182no—
363C22—1182no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22C2×Q8×D5911yescharacteristic
369C22#41×D5911yescharacteristic
370C22#41×D5911yescharacteristic
371C22#1427377211yescharacteristic
372C22#1427377211yescharacteristic
373C22#1427377211yescharacteristic
374C22#1427377311yescharacteristic
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—1182no—
382C4—1182no—
383C4—1182no—
384C4—2361no—
385C4—2361no—
386C4—2361no—
387C4—2361no—
388C2—42no—
389C2—2362no—
390C2#1683798611yescharacteristic
391C2#1683798611yescharacteristic
392C2#1683802711yescharacteristic
393C2#1683810611yescharacteristic
394C2#1683810611yescharacteristic
395C2#1683811411yescharacteristic
396C2#1683814111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#393C2
hypercenter#393D59
hypocenterC59#2784
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #16837343C2semidirect
2. #16837326C2semidirect
3. #16837325C2semidirect
4. #16837321C2semidirect
5. #16837313C2semidirect
7. #16837287C2semidirect
8. #16837284C2semidirect
11. #16837276C2semidirect
12. #16837274C2semidirect
13. #16837261C2semidirect
14. #16837260C2semidirect
15. C59×#393C2semidirect
64. C2×C22⋊D59Q8semidirect
204. #393D59semidirect
214. C59#2784semidirect