Finite Group Databasebeta

← #21436429

Subgroups — #21436429

Order 7552.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838110C211yesmaximal, characteristic, complemented
2#16838070C211yesmaximal, characteristic
3#16837747C211yesmaximal, characteristic, complemented
4#16837717C211yesmaximal, characteristic, complemented
5#16837713C211yesmaximal, characteristic, complemented
6#16837696C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837600C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837494C211yesmaximal, characteristic, complemented
12#16837478C211yesmaximal, characteristic, complemented
13#16837404C211yesmaximal, characteristic, complemented
14#16837400C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273723—21no—
23#14273723C2211yescharacteristic
24#14273717—21no—
25#14273707—21no—
26#14273704—21no—
27#14273703C2211yescharacteristic
28#14273702C2211yescharacteristic
29#14273700—21no—
30#14273699—21no—
31Q8×Dic59C2211yescharacteristic
32#14273692C2211yescharacteristic
33C4×C22⋊D59C2211yescharacteristic
34(C22⋊D59)⋊C4—21no—
35(C22⋊D59)⋊C4—21no—
36C2×C4⋊Dic59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273660C2211yescharacteristic
39#14273660C2211yescharacteristic
40Dic59⋊C8C2211yescharacteristic
41#14273652C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#107×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70#11745687—22no—
71#11745687—41no—
72#11745685—22no—
73#11745685—41no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79C2×Dic118—21no—
80C2×Dic118C2311yescharacteristic
81SD16×C59—41no—
82M16×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊Dic59D411yescharacteristic
91#11745672—22no—
92#11745671—41no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4D411yescharacteristic
105C4×Dic59—21no—
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59—21no—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—81no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2411yescharacteristic
127C22⋊D59—22no—
128C22⋊D59—42no—
129C22⋊D59—42no—
130C22⋊D59—42no—
131C22⋊D59—81no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—42no—
136C2×Dic59—81no—
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140D236—21no—
141D236—21no—
142D236—81no—
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—42no—
146C4×D59—81no—
147Dic118—21no—
148Dic118—81no—
149Dic118#4112yes—
150C8×C59—21no—
151C8×C59—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59C22×D411yescharacteristic
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C4×C59—21no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59C2×#4111yescharacteristic
172C4×C59H(5,𝔽2)11yescharacteristic
173Dic59—22no—
174Dic59—21no—
175Dic59—21no—
176Dic59—41no—
177Dic59—41no—
178Dic59#13712yes—
179#3333—591nomaximal, Sylow
180C2×C59—41no—
181C2×C59—81no—
182C2×C59#54611yescharacteristic
183C2×C59C2×#13711yescharacteristic
184C2×C59#57611yescharacteristic
185D59—41no—
186D59—81no—
187#554—591no—
188#550—591no—
189#486—591no—
190#480—591no—
191#480—591no—
192#477—591no—
193#468—591no—
194#468D5911yescharacteristic, complemented
195#460—591no—
196#452—591no—
197#452—591no—
198C4×Q16—591no—
199#436—591no—
200#417—591no—
201#417—591no—
202C59#333311yescharacteristic, complemented, Sylow
203C2×#41—591no—
204C2×#41—591no—
205C2×Q16—591no—
206C2×SD16—591no—
207C2×SD16C2×D5911yescharacteristic
208C2×M16—591no—
209C2×M16C2×D5911yescharacteristic
210C4⋊Q8—591no—
211#127—591no—
212#127—1181no—
213#125—1181no—
214C22⋊Q8—591no—
215C22⋊Q8—1181no—
216C22⋊Q8—1181no—
217C22⋊Q8C2×D5911yescharacteristic
218#121—591no—
219#121—1181no—
220#121—1181no—
221#121C2×D5911yescharacteristic
222C4×Q8—591no—
223C4×Q8—591no—
224C4×D4—591no—
225C4×D4—1181no—
226C4×D4—1181no—
227C2×C4⋊C4—591no—
228C2×C4⋊C4—591no—
229#107—591no—
230#107—591no—
231#107C2×D5911yescharacteristic
232C4⋊C8—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103C2×D5911yescharacteristic
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241#102—591no—
242#102C2×D5911yescharacteristic
243C22⋊C8—591no—
244C22⋊C8—591no—
245C4×C8—591no—
246#41—1182no—
247#41—1182no—
248#41—2361no—
249#41—2361no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—21no—
254C2×D4—591no—
255C2×D4—591no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4C22×D5911yescharacteristic
262C22×C4—591no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4C22×D5911yescharacteristic
268Q16—1182no—
269SD16—41no—
270SD16—2361no—
271M16—41no—
272M16—2361no—
273C2×C8—591no—
274C2×C8—591no—
275C2×C8C22×D5911yescharacteristic
276C2×C8C22×D5911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—591no—
279C4⋊C4—591no—
280C4⋊C4—591no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—591no—
292C22⋊C4—591no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C42—591no—
296C42—1181no—
297C42—1181no—
298C23—21no—
299C23—591no—
300C23—1181no—
301C23D4×D5911yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—592no—
305Q8—1181no—
306Q8—4721no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—1182no—
311D4—1181no—
312D4—1181no—
313D4—4721no—
314D4—4721no—
315D4—2362no—
316D4—2362no—
317D4—2362no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—591no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—4721no—
332C2×C4—4721no—
333C2×C4—2362no—
334C2×C4—2362no—
335C2×C4D4×D5911yescharacteristic
336C2×C4C23×D5911yescharacteristic
337C8—21no—
338C8—21no—
339C8—1181no—
340C8—1181no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—1181no—
348C22—1181no—
349C22—1181no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22C2×D4×D5911yescharacteristic
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—592no—
359C4—1181no—
360C4—1181no—
361C4—1182no—
362C4—2361no—
363C4—2361no—
364C4#41×D5911yescharacteristic
365C4#1427377211yescharacteristic
366C2—41no—
367C2—81no—
368C2—4721no—
369C2—2361no—
370C2#1683804111yescharacteristic
371C2#137×D5911yescharacteristic
372C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3333
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16838110C2semidirect
3. #16837747C2semidirect
4. #16837717C2semidirect
5. #16837713C2semidirect
6. #16837696C2semidirect
7. #16837651C2semidirect
8. #16837600C2semidirect
9. #16837562C2semidirect
10. #16837561C2semidirect
11. #16837494C2semidirect
12. #16837478C2semidirect
13. #16837404C2semidirect
14. #16837400C2semidirect
15. C59×#468C2semidirect
194. #468D59semidirect
202. C59#3333semidirect