Finite Group Databasebeta

← #21434783

Subgroups — #21434783

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#16838017C211yesmaximal, characteristic, complemented
2#16838003C211yesmaximal, characteristic, complemented
3#16837810C211yesmaximal, characteristic, complemented
4#16837790C211yesmaximal, characteristic, complemented
5#16837755C211yesmaximal, characteristic, complemented
6#16837747C211yesmaximal, characteristic, complemented
7#16837652C211yesmaximal, characteristic, complemented
8#16837649C211yesmaximal, characteristic, complemented
9#16837637C211yesmaximal, characteristic, complemented
10#16837630C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837502C211yesmaximal, characteristic, complemented
13C4×#11745660C211yesmaximal, characteristic, complemented
14#16837356C211yesmaximal, characteristic, complemented
15C4×D8×C59C211yesmaximal, characteristic, complemented
16C2×#11745660C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×#11745659C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273723C2211yescharacteristic
23#14273720—21no—
24#14273718C2211yescharacteristic
25#14273714C2211yescharacteristic
26#14273713—21no—
27#14273710—21no—
28#14273710—21no—
29#14273709—21no—
30#14273707C2211yescharacteristic
31#14273706—21no—
32#14273702C2211yescharacteristic
33#14273701—21no—
34#14273700—21no—
35#14273698C2211yescharacteristic
36#14273698C2211yescharacteristic
37C4×Dic118C2211yescharacteristic
38C4×D236C2211yescharacteristic
39#14273684C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273658C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273650C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273638C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×D8×C59C2211yescharacteristic
53C4×D4×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C4×C8×C59C2211yescharacteristic
59C2×D4×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×D236—21no—
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59C2311yescharacteristic
71C2×Dic118—21no—
72C2×Dic118C2311yescharacteristic
73D8×C59—22no—
74C2×C8×C59C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C4⋊C4×C59C2311yescharacteristic
77C4⋊C4×C59C2311yescharacteristic
78C22⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C42×C59C2311yescharacteristic
81C22⋊Dic59—21no—
82C22⋊Dic59—21no—
83C22⋊Dic59—21no—
84C22⋊Dic59—21no—
85#11745670—22no—
86#11745669—22no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4D411yescharacteristic
91(C2×D59)⋊C4D411yescharacteristic
92C4⋊Dic59—21no—
93C4⋊Dic59—21no—
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4D411yescharacteristic
100Dic59⋊C4D411yescharacteristic
101C4×Dic59—21no—
102C4×Dic59C2311yescharacteristic
103C2×C59⋊C8C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105#11745660—22no—
106#11745659—22no—
107C8×D59—22no—
108C23×C59—21no—
109C23×C59—21no—
110C22×D59—21no—
111C22×D59C2×D411yescharacteristic
112D4×C59—21no—
113D4×C59—21no—
114D4×C59—21no—
115D4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—81no—
119C2×C4×C59—81no—
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2411yescharacteristic
123C22⋊D59—81no—
124C22⋊D59—81no—
125C22⋊D59—81no—
126C22⋊D59—81no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59C2×D411yescharacteristic
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133D236—21no—
134D236—21no—
135D236—81no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—81no—
139Dic118—21no—
140Dic118—21no—
141Dic118—81no—
142C8×C59—21no—
143C8×C59#4112yes—
144C59⋊C8—21no—
145C59⋊C8#4112yes—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59C22×D411yescharacteristic
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59C2×#4111yescharacteristic
164C4×C59C2×#4111yescharacteristic
165Dic59—21no—
166Dic59—21no—
167Dic59—21no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171#3179—591nomaximal, Sylow
172C2×C59—81no—
173C2×C59—81no—
174C2×C59#53211yescharacteristic
175C2×C59#57611yescharacteristic
176C2×C59#57711yescharacteristic
177D59—41no—
178D59—81no—
179#542—591no—
180#540—591no—
181#501—591no—
182#496—591no—
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×D8D5911yescharacteristic, complemented
193#405—591no—
194C59#317911yescharacteristic, complemented, Sylow
195C2×SD16—591no—
196C2×SD16—591no—
197C2×D8—591no—
198C2×D8C2×D5911yescharacteristic
199C2×M16—591no—
200C22×C8—591no—
201C4⋊Q8—591no—
202#127—591no—
203#126—1181no—
204#125—591no—
205#124—591no—
206#124—1181no—
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×D4C2×D5911yescharacteristic
220C4×D4C2×D5911yescharacteristic
221#117—591no—
222#107—591no—
223#107C2×D5911yescharacteristic
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#102C2×D5911yescharacteristic
233#102C2×D5911yescharacteristic
234#97—591no—
235#97—591no—
236C4×C8—591no—
237C4×C8C2×D5911yescharacteristic
238C2×Q8—591no—
239C2×Q8—1181no—
240C2×D4—591no—
241C2×D4—1181no—
242C2×D4—1181no—
243C2×D4—1181no—
244C2×D4—1181no—
245C2×D4—1181no—
246C2×D4C22×D5911yescharacteristic
247C2×D4C22×D5911yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—591no—
251C22×C4—1181no—
252SD16—1182no—
253SD16—1182no—
254D8—22no—
255D8—1182no—
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—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4C22×D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
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—591no—
290C23—1181no—
291Q8—1181no—
292Q8—1181no—
293Q8—4721no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—1181no—
299D4—1181no—
300D4—4721no—
301D4—4721no—
302D4—4721no—
303D4—4721no—
304D4—4721no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—591no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—4721no—
318C2×C4D4×D5911yescharacteristic
319C2×C4D4×D5911yescharacteristic
320C2×C4C23×D5911yescharacteristic
321C8—21no—
322C8—592no—
323C8—1181no—
324C8#1174568512yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1181no—
332C22—1181no—
333C22—1181no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—1181no—
343C4—1181no—
344C4—1181no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4#41×D5911yescharacteristic
349C4C2×#1174568511yescharacteristic
350C2—81no—
351C2—81no—
352C2—4721no—
353C2—2361no—
354C2#1683794911yescharacteristic
355C2#1683820311yescharacteristic
356C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC4×D8×C59C2
socleC22×C59C22×D4
hypercenterC4×D8D59
hypocenterC59#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #16838017C2semidirect
2. #16838003C2semidirect
3. #16837810C2semidirect
4. #16837790C2semidirect
5. #16837755C2semidirect
6. #16837747C2semidirect
7. #16837652C2semidirect
8. #16837649C2semidirect
9. #16837637C2semidirect
10. #16837630C2semidirect
11. #16837512C2semidirect
12. #16837502C2semidirect
13. C4×#11745660C2semidirect
14. #16837356C2semidirect
15. C4×D8×C59C2semidirect
192. C4×D8D59semidirect
194. C59#3179semidirect