Finite Group Databasebeta

← #21436360

Subgroups — #21436360

Order 7552.

380 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#16838091C211yesmaximal, characteristic, complemented
2#16838063C211yesmaximal, characteristic
3#16837758C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837726C211yesmaximal, characteristic, complemented
6#16837711C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837627C211yesmaximal, characteristic, complemented
10#16837567C211yesmaximal, characteristic, complemented
11#16837558C211yesmaximal, characteristic, complemented
12#16837494C211yesmaximal, characteristic, complemented
13#16837478C211yesmaximal, characteristic, complemented
14#16837402C211yesmaximal, characteristic, complemented
15C59×#419C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21#14273720—21no—
22#14273719—21no—
23#14273718C2211yescharacteristic
24#14273716—21no—
25#14273716C2211yescharacteristic
26#14273709—21no—
27#14273707C2211yescharacteristic
28#14273706C2211yescharacteristic
29#14273703—21no—
30#14273703C2211yescharacteristic
31#14273701—21no—
32#14273701C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34#14273692C2211yescharacteristic
35C4×C22⋊D59—21no—
36C4×C22⋊D59C2211yescharacteristic
37#14273684—21no—
38C4⋊C4×D59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273658C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54#117×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#103×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59D411yescharacteristic
68#11745689—22no—
69#11745689—41no—
70C2×D236—21no—
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76M16×C59—41no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C22⋊C4×C59—21no—
82C42×C59—21no—
83C22⋊Dic59—21no—
84C22⋊Dic59D411yescharacteristic
85#11745672—22no—
86#11745672—41no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745660—41no—
110#11745659—41no—
111C23×C59C2×D411yescharacteristic
112C22×D59—21no—
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—42no—
118Q8×C59#4112yes—
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—42no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—41no—
129C22⋊D59—42no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135C2×Dic59C2×D411yescharacteristic
136D236—21no—
137D236—21no—
138D236—42no—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—42no—
142C4×D59—42no—
143Dic118—21no—
144Dic118—21no—
145C8×C59—21no—
146C8×C59—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59C22×D411yescharacteristic
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—22no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59C2×#4111yescharacteristic
165C4×C59H(5,𝔽2)11yescharacteristic
166Dic59—21no—
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3327—591nomaximal, Sylow
173C2×C59—41no—
174C2×C59#54611yescharacteristic
175C2×C59#57511yescharacteristic
176C2×C59#57811yescharacteristic
177D59—41no—
178D59—81no—
179#552—591no—
180#548—591no—
181#488—591no—
182#484—591no—
183#482—591no—
184#479—591no—
185#470—591no—
186#468—591no—
187#464—591no—
188#452—591no—
189#451—591no—
190C4×Q16—591no—
191#436—591no—
192#419D5911yescharacteristic, complemented
193#417—591no—
194C59#332711yescharacteristic, complemented, Sylow
195C2×#41—591no—
196C22×Q8C2×D5911yescharacteristic
197C2×Q16—591no—
198C2×Q16—591no—
199C2×SD16—591no—
200C2×M16—591no—
201C2×M16C2×D5911yescharacteristic
202#126—1181no—
203#125—591no—
204#125—1181no—
205#124—591no—
206#124—1181no—
207#123—1181no—
208C22⋊Q8—591no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—1181no—
214C4×Q8—591no—
215C4×Q8—591no—
216C4×D4—591no—
217C4×D4—1181no—
218#117—1181no—
219#117C2×D5911yescharacteristic
220C2×C4⋊C4—591no—
221#107—591no—
222#107—591no—
223#106—591no—
224C4⋊C8—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103C2×D5911yescharacteristic
229#103C2×D5911yescharacteristic
230#103C2×D5911yescharacteristic
231#103C2×D5911yescharacteristic
232#102—591no—
233#102—591no—
234#102—591no—
235C22⋊C8—591no—
236C22⋊C8—591no—
237C4×C8—591no—
238#41—1182no—
239#41—2361no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—591no—
244C2×Q8C22×D5911yescharacteristic
245C2×Q8C22×D5911yescharacteristic
246C2×D4—591no—
247C2×D4—591no—
248C2×D4—1181no—
249C2×D4—1181no—
250C22×C4—21no—
251C22×C4—591no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4C22×D5911yescharacteristic
255Q16—1182no—
256Q16—2361no—
257SD16—2361no—
258M16—41no—
259M16—2361no—
260C2×C8—591no—
261C2×C8—591no—
262C2×C8C22×D5911yescharacteristic
263C2×C8C22×D5911yescharacteristic
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4C22×D5911yescharacteristic
276C4⋊C4C22×D5911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—591no—
279C22⋊C4—591no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C42—21no—
287C42—591no—
288C42—1181no—
289C42—1181no—
290C23—591no—
291C23—1181no—
292C23D4×D5911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—1181no—
298Q8—1181no—
299Q8#1174568512yes—
300D4—1181no—
301D4—1181no—
302D4—2362no—
303D4—2361no—
304D4—2362no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—591no—
313C2×C4—591no—
314C2×C4—591no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—2362no—
321C2×C4—2362no—
322C2×C4D4×D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—21no—
325C8—21no—
326C8—1181no—
327C8—1181no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—1181no—
332C22—1181no—
333C22—1181no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1181no—
344C4—1181no—
345C4—1181no—
346C4—2361no—
347C4—2361no—
348C4—2361no—
349C4C2×#1174568511yescharacteristic
350C4#1427377211yescharacteristic
351C2—41no—
352C2—4721no—
353C2—2361no—
354C2#1683804211yescharacteristic
355C2#1683820111yescharacteristic
356C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#419C2
socleC22×C59C22×D4
hypercenter#419D59
hypocenterC59#3327
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #16838091C2semidirect
3. #16837758C2semidirect
4. #16837736C2semidirect
5. #16837726C2semidirect
6. #16837711C2semidirect
7. #16837659C2semidirect
8. #16837648C2semidirect
9. #16837627C2semidirect
10. #16837567C2semidirect
11. #16837558C2semidirect
12. #16837494C2semidirect
13. #16837478C2semidirect
14. #16837402C2semidirect
15. C59×#419C2semidirect
192. #419D59semidirect
194. C59#3327semidirect