Finite Group Databasebeta

← #21434776

Subgroups — #21434776

Order 7552.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838021C211yesmaximal, characteristic, complemented
2#16838006C211yesmaximal, characteristic, complemented
3#16837811C211yesmaximal, characteristic, complemented
4#16837756C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837652C211yesmaximal, characteristic, complemented
7#16837645C211yesmaximal, characteristic, complemented
8#16837635C211yesmaximal, characteristic, complemented
9#16837628C211yesmaximal, characteristic, complemented
10#16837514C211yesmaximal, characteristic, complemented
11#16837503C211yesmaximal, characteristic, complemented
12SD16×Dic59C211yesmaximal, characteristic, complemented
13D8×Dic59C211yesmaximal, characteristic, complemented
14#16837359C211yesmaximal, characteristic, complemented
15C59×#496C211yesmaximal, characteristic, complemented
16C2×#11745659C2211yescharacteristic
17C2×C8×D59C2211yescharacteristic
18#14273727C2211yescharacteristic
19#14273720—21no—
20#14273719C2211yescharacteristic
21#14273713—21no—
22#14273711—21no—
23#14273708—21no—
24#14273708—21no—
25#14273704—21no—
26#14273703C2211yescharacteristic
27#14273699—21no—
28#14273699—21no—
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic
31#14273698C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33D4×Dic59C2211yescharacteristic
34D4×Dic59C2211yescharacteristic
35D4×Dic59C2211yescharacteristic
36#14273684C2211yescharacteristic
37#14273661C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273659C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273637C2211yescharacteristic
50C4×C59⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55C2×D8×C59C2211yescharacteristic
56#127×C59C2211yescharacteristic
57#124×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C2×C4×D59C2311yescharacteristic
72C2×Dic118—21no—
73SD16×C59—22no—
74SD16×C59—22no—
75D8×C59—22no—
76D8×C59—22no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C42×C59C2311yescharacteristic
82C22⋊Dic59—21no—
83C22⋊Dic59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4D411yescharacteristic
90(C2×D59)⋊C4D411yescharacteristic
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4D411yescharacteristic
101Dic59⋊C4D411yescharacteristic
102C4×Dic59—21no—
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106#11745659—22no—
107C8×D59—22no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C22×D59C2×D411yescharacteristic
112Q8×C59—21no—
113Q8×C59—21no—
114D4×C59—21no—
115D4×C59—21no—
116D4×C59—21no—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—81no—
121D4×C59—81no—
122C2×C4×C59—21no—
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2411yescharacteristic
126C22⋊D59—81no—
127C22⋊D59—81no—
128C22⋊D59—81no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135C2×Dic59—81no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139C4×D59—21no—
140C4×D59—21no—
141Dic118—81no—
142C8×C59#4112yes—
143C8×C59#4112yes—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59C22×D411yescharacteristic
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59C2×#4111yescharacteristic
163C4×C59C2×#4111yescharacteristic
164Dic59—21no—
165Dic59—21no—
166Dic59—21no—
167Dic59—41no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171#3179—591nomaximal, Sylow
172C2×C59—81no—
173C2×C59—81no—
174C2×C59—81no—
175C2×C59#53211yescharacteristic
176C2×C59#57611yescharacteristic
177C2×C59#57711yescharacteristic
178D59—41no—
179#542—591no—
180#540—591no—
181#501—591no—
182#496D5911yescharacteristic, complemented
183#488—591no—
184#486—591no—
185#469—591no—
186#468—591no—
187#466—591no—
188#465—591no—
189#442—591no—
190#440—591no—
191C4×SD16—591no—
192C4×D8—591no—
193#405—591no—
194C59#317911yescharacteristic, complemented, Sylow
195C2×SD16C2×D5911yescharacteristic
196C2×SD16C2×D5911yescharacteristic
197C2×D8C2×D5911yescharacteristic
198C2×D8C2×D5911yescharacteristic
199C2×M16—591no—
200C22×C8—591no—
201C4⋊Q8—591no—
202#127C2×D5911yescharacteristic
203#126—1181no—
204#125—591no—
205#124—1181no—
206#124C2×D5911yescharacteristic
207#123—1181no—
208#123—1181no—
209#123—1181no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—591no—
214#121—591no—
215#121—1181no—
216#121—1181no—
217C4×Q8—591no—
218C4×D4—591no—
219C4×D4—591no—
220C4×D4—591no—
221#117—591no—
222#107—591no—
223#107—591no—
224#106—591no—
225#106—591no—
226#103—591no—
227#103—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#97—591no—
235#97C2×D5911yescharacteristic
236C4×C8—591no—
237C4×C8—591no—
238C2×Q8—1181no—
239C2×Q8C22×D5911yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—1181no—
243C2×D4—1181no—
244C2×D4—1181no—
245C2×D4C22×D5911yescharacteristic
246C2×D4C22×D5911yescharacteristic
247C2×D4C22×D5911yescharacteristic
248C22×C4—591no—
249C22×C4—1181no—
250C22×C4—1181no—
251C22×C4—1181no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—1182no—
257C2×C8—591no—
258C2×C8—591no—
259C2×C8—1182no—
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C4⋊C4—591no—
263C4⋊C4—591no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—591no—
276C22⋊C4—591no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C42—591no—
285C42—1181no—
286C42C22×D5911yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—591no—
291Q8—21no—
292Q8—21no—
293Q8—4721no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—4721no—
303D4—4721no—
304D4—4721no—
305C2×C4—21no—
306C2×C4—591no—
307C2×C4—591no—
308C2×C4—591no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4D4×D5911yescharacteristic
319C2×C4D4×D5911yescharacteristic
320C2×C4C23×D5911yescharacteristic
321C8—1181no—
322C8—1181no—
323C8#1174568712yes—
324C8#1174568712yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1181no—
335C22—1181no—
336C22—1181no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—1181no—
342C4—1181no—
343C4—1181no—
344C4—2361no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4C2×#1174568711yescharacteristic
349C4C2×#1174568711yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—2361no—
354C2#1683795011yescharacteristic
355C2#1683820611yescharacteristic
356C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16838021C2semidirect
2. #16838006C2semidirect
3. #16837811C2semidirect
4. #16837756C2semidirect
5. #16837748C2semidirect
6. #16837652C2semidirect
7. #16837645C2semidirect
8. #16837635C2semidirect
9. #16837628C2semidirect
10. #16837514C2semidirect
11. #16837503C2semidirect
12. SD16×Dic59C2semidirect
13. D8×Dic59C2semidirect
14. #16837359C2semidirect
15. C59×#496C2semidirect
182. #496D59semidirect
194. C59#3179semidirect