Finite Group Databasebeta

← #21436364

Subgroups — #21436364

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#16838092C211yesmaximal, characteristic, complemented
2#16837756C211yesmaximal, characteristic, complemented
3#16837735C211yesmaximal, characteristic, complemented
4#16837723C211yesmaximal, characteristic, complemented
5#16837709C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837646C211yesmaximal, characteristic, complemented
8#16837621C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837558C211yesmaximal, characteristic, complemented
11C4×#11745672C211yesmaximal, characteristic, complemented
12#16837480C211yesmaximal, characteristic, complemented
13#16837411C211yesmaximal, characteristic, complemented
14#16837403C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic
16C2×#11745672C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C2×#11745664C2211yescharacteristic
21#14273720—21no—
22#14273719C2211yescharacteristic
23#14273717—21no—
24#14273708—21no—
25#14273706C2211yescharacteristic
26#14273706C2211yescharacteristic
27C4×Dic118C2211yescharacteristic
28#14273686C2211yescharacteristic
29#14273683—21no—
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273651C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C22×Q8×C59C2211yescharacteristic
50#124×C59—21no—
51#124×C59C2211yescharacteristic
52C22⋊Q8×C59—21no—
53C22⋊Q8×C59C2211yescharacteristic
54#121×C59—21no—
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59—21no—
62C2×Q8×C59—22no—
63C2×Q8×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59C2311yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C22×Dic59—21no—
75C2×Dic118C2311yescharacteristic
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59D411yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59D411yescharacteristic
85C22⋊C4×C59D411yescharacteristic
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91#11745672—22no—
92#11745672—41no—
93#11745670—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
104C4×Dic59—21no—
105#11745664—41no—
106#11745664—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—42no—
118Q8×C59#4112yes—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—41no—
122D4×C59—42no—
123D4×C59—42no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—42no—
132C2×C4×C59—42no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—42no—
143Dic118—21no—
144Dic118—21no—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—22no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59C2×#4111yescharacteristic
167C4×C59H(5,𝔽2)11yescharacteristic
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3327—591nomaximal, Sylow
173C2×C59—41no—
174C2×C59—41no—
175C2×C59—81no—
176C2×C59#54611yescharacteristic
177C2×C59#57511yescharacteristic
178C2×C59#57811yescharacteristic
179#552—591no—
180#548D5911yescharacteristic
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#419—591no—
193#417—591no—
194C59#332711yescharacteristic, complemented, Sylow
195C2×#41C2×D5911yescharacteristic
196C22×Q8C2×D5911yescharacteristic
197C2×Q16—591no—
198C2×Q16—591no—
199C2×SD16—591no—
200C2×M16—591no—
201C2×M16—591no—
202#126—1181no—
203#125—591no—
204#125—1181no—
205#124—21no—
206#124C2×D5911yescharacteristic
207#123—1181no—
208C22⋊Q8—21no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8C2×D5911yescharacteristic
212#121—21no—
213#121C2×D5911yescharacteristic
214C4×Q8—591no—
215C4×Q8C2×D5911yescharacteristic
216C4×D4—21no—
217C4×D4C2×D5911yescharacteristic
218#117—591no—
219#117—1181no—
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#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235C22⋊C8—591no—
236C22⋊C8—591no—
237C4×C8—591no—
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—591no—
244C2×Q8C22×D5911yescharacteristic
245C2×Q8C22×D5911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22⋊D5911yescharacteristic
249C2×D4C22×D5911yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—1181no—
253C22×C4C22×D5911yescharacteristic
254C22×C4C22×D5911yescharacteristic
255Q16—1182no—
256Q16—2361no—
257SD16—2361no—
258M16—2361no—
259M16—2361no—
260C2×C8—591no—
261C2×C8—591no—
262C2×C8—591no—
263C2×C8—591no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
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—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4C22⋊D5911yescharacteristic
285C22⋊C4C22⋊D5911yescharacteristic
286C42—21no—
287C42—1181no—
288C42—1181no—
289C42C22×D5911yescharacteristic
290C23—21no—
291C23C2×C22⋊D5911yescharacteristic
292C23C2×C22⋊D5911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—1181no—
298Q8—1181no—
299Q8#1174568712yes—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—2362no—
319C2×C4C2×C22⋊D5911yescharacteristic
320C2×C4C2×C22⋊D5911yescharacteristic
321C2×C4C2×C22⋊D5911yescharacteristic
322C2×C4C2×C22⋊D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—1181no—
325C8—1181no—
326C8—1181no—
327C8—1181no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4—2361no—
349C4C2×#1174568711yescharacteristic
350C4#1427377211yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2#1683804611yescharacteristic
355C2#1683820011yescharacteristic
356C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3327
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
2. #16837756C2semidirect
3. #16837735C2semidirect
4. #16837723C2semidirect
5. #16837709C2semidirect
6. #16837658C2semidirect
7. #16837646C2semidirect
8. #16837621C2semidirect
9. #16837564C2semidirect
10. #16837558C2semidirect
11. C4×#11745672C2semidirect
12. #16837480C2semidirect
13. #16837411C2semidirect
14. #16837403C2semidirect
194. C59#3327semidirect