Finite Group Databasebeta

← #21437146

Subgroups — #21437146

Order 7552.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838134C211yesmaximal, characteristic
2#16838127C211yesmaximal, characteristic, complemented
3#16837795C211yesmaximal, characteristic, complemented
4#16837773C211yesmaximal, characteristic
5#16837626C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837610C211yesmaximal, characteristic, complemented
8#16837605C211yesmaximal, characteristic, complemented
9#16837604C211yesmaximal, characteristic, complemented
10#16837600C211yesmaximal, characteristic
11#16837530C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13#16837503C211yesmaximal, characteristic, complemented
14Q16×Dic59C211yesmaximal, characteristic, complemented
15C59×#497C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21#14273725C2211yescharacteristic
22#14273725C2211yescharacteristic
23#14273723C2211yescharacteristic
24#14273718—21no—
25#14273717—21no—
26#14273717—21no—
27#14273716C2211yescharacteristic
28#14273713—21no—
29#14273711—21no—
30#14273709—21no—
31Q8×Dic59C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34C4×Dic118C2211yescharacteristic
35C4×Dic118C2211yescharacteristic
36#14273692—21no—
37C4×D236C2211yescharacteristic
38D4×Dic59C2211yescharacteristic
39(C22⋊D59)⋊C4—21no—
40#14273661C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43Dic59⋊C8C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273648C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×Q16×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55C2×SD16×C59C2211yescharacteristic
56C4⋊Q8×C59C2211yescharacteristic
57#124×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C22×Dic59—21no—
66C2×D236C2311yescharacteristic
67C2×C4×D59—21no—
68C2×Dic118D411yescharacteristic
69C2×Dic118C2311yescharacteristic
70Q16×C59—22no—
71Q16×C59—41no—
72SD16×C59—22no—
73SD16×C59—41no—
74C2×C8×C59C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C22⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C42×C59C2311yescharacteristic
81C22⋊Dic59—21no—
82#11745672—41no—
83#11745671—41no—
84#11745671—41no—
85#11745670—41no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89C4⋊Dic59—21no—
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59D411yescharacteristic
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95Dic59⋊C4—21no—
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4D411yescharacteristic
101Dic59⋊C4D411yescharacteristic
102C4×Dic59—21no—
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745660—22no—
111C23×C59—21no—
112C22×D59—21no—
113Q8×C59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2411yescharacteristic
127C22⋊D59—42no—
128C22⋊D59—81no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—81no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137D236—21no—
138D236—21no—
139C4×D59—81no—
140Dic118—22no—
141Dic118—21no—
142Dic118—21no—
143C8×C59—21no—
144C8×C59#4112yes—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59C22×D411yescharacteristic
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—41no—
157C4×C59—41no—
158C4×C59—41no—
159C4×C59C2×#4111yescharacteristic
160C4×C59H(5,𝔽2)11yescharacteristic
161Dic59—21no—
162Dic59—21no—
163Dic59—21no—
164Dic59—41no—
165Dic59—41no—
166Dic59—41no—
167Dic59#13712yes—
168#3400—591nomaximal, Sylow
169C2×C59—81no—
170C2×C59#55011yescharacteristic
171C2×C59C2×#13711yescharacteristic
172C2×C59#57711yescharacteristic
173D59—81no—
174#559—591no—
175#557—591no—
176#497—591no—
177#497D5911yescharacteristic, complemented
178#492—591no—
179#464—591no—
180#464—591no—
181#462—591no—
182#461—591no—
183#461—591no—
184#460—591no—
185#446—591no—
186#440—591no—
187#440—591no—
188C4×Q16—591no—
189C59#340011yescharacteristic, complemented, Sylow
190C2×Q16—591no—
191C2×Q16C2×D5911yescharacteristic
192C2×Q16C2×D5911yescharacteristic
193C2×SD16—591no—
194C2×SD16—591no—
195C2×SD16—591no—
196C2×SD16—591no—
197C2×SD16C2×D5911yescharacteristic
198C2×SD16C2×D5911yescharacteristic
199C4⋊Q8—591no—
200C4⋊Q8—591no—
201C4⋊Q8C2×D5911yescharacteristic
202#127—591no—
203#125—1181no—
204#125—1181no—
205#125—1181no—
206#124—591no—
207#124—1181no—
208#124C2×D5911yescharacteristic
209#123—1181no—
210#123—1181no—
211C4×Q8—591no—
212C4×Q8—591no—
213C4×Q8—591no—
214C4×Q8—591no—
215C4×Q8—591no—
216C4×Q8—1181no—
217C4×D4—591no—
218C4×D4—591no—
219C4×D4—1181no—
220#107—591no—
221C4⋊C8—591no—
222C4⋊C8—591no—
223C4⋊C8—591no—
224#103—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#102—591no—
229#102—591no—
230#97—591no—
231#97C2×D5911yescharacteristic
232C4×C8—591no—
233C2×Q8—591no—
234C2×Q8—591no—
235C2×Q8C22×D5911yescharacteristic
236C2×Q8C22×D5911yescharacteristic
237C2×Q8C22×D5911yescharacteristic
238C2×D4—591no—
239C2×D4—1181no—
240C2×D4—1181no—
241C2×D4C22×D5911yescharacteristic
242C22×C4—1181no—
243C22×C4—1181no—
244Q16—22no—
245Q16—41no—
246Q16—2361no—
247SD16—22no—
248SD16—41no—
249SD16—1182no—
250SD16—2361no—
251SD16—2361no—
252SD16—2361no—
253C2×C8—591no—
254C2×C8—591no—
255C2×C8C22×D5911yescharacteristic
256C2×C8C22×D5911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—591no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—591no—
263C4⋊C4—591no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C42—591no—
279C42—591no—
280C42—1181no—
281C42—1181no—
282C42—1181no—
283C42—1181no—
284C42C22×D5911yescharacteristic
285C23—21no—
286C23—1181no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—1182no—
294Q8—1181no—
295Q8—1181no—
296D4—21no—
297D4—21no—
298D4—1181no—
299D4—1181no—
300D4—4721no—
301D4—2362no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—591no—
306C2×C4—591no—
307C2×C4—591no—
308C2×C4—591no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—4721no—
313C2×C4—4721no—
314C2×C4D4×D5911yescharacteristic
315C2×C4D4×D5911yescharacteristic
316C2×C4C23×D5911yescharacteristic
317C8—21no—
318C8—1181no—
319C8—1181no—
320C8#1174568712yes—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—2361no—
325C22—2361no—
326C22—2361no—
327C22C2×D4×D5911yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—592no—
334C4—1181no—
335C4—1181no—
336C4—1181no—
337C4—2361no—
338C4—2361no—
339C4—2361no—
340C4C2×#1174568711yescharacteristic
341C4#1427377211yescharacteristic
342C2—81no—
343C2—4721no—
344C2#1683807211yescharacteristic
345C2#137×D5911yescharacteristic
346C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#497C2
socleC22×C59C22×D4
hypercenter#497D59
hypocenterC59#3400
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #16838127C2semidirect
3. #16837795C2semidirect
5. #16837626C2semidirect
6. #16837621C2semidirect
7. #16837610C2semidirect
8. #16837605C2semidirect
9. #16837604C2semidirect
11. #16837530C2semidirect
12. #16837504C2semidirect
13. #16837503C2semidirect
14. Q16×Dic59C2semidirect
15. C59×#497C2semidirect
177. #497D59semidirect
189. C59#3400semidirect