Finite Group Databasebeta

← #21436206

Subgroups — #21436206

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838113C211yesmaximal, characteristic, complemented
2#16838060C211yesmaximal, characteristic
3#16837731C211yesmaximal, characteristic, complemented
4#16837719C211yesmaximal, characteristic, complemented
5#16837684C211yesmaximal, characteristic, complemented
6#16837659C211yesmaximal, characteristic, complemented
7#16837630C211yesmaximal, characteristic, complemented
8#16837621C211yesmaximal, characteristic, complemented
9#16837565C211yesmaximal, characteristic, complemented
10#16837559C211yesmaximal, characteristic, complemented
11#16837510C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837400C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#489C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×Dic236C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22C2×C8×D59C2211yescharacteristic
23#14273718—21no—
24#14273713—21no—
25#14273707C2211yescharacteristic
26#14273707C2211yescharacteristic
27#14273704—21no—
28#14273703—21no—
29#14273703—21no—
30#14273703C2211yescharacteristic
31#14273700—21no—
32#14273698C2211yescharacteristic
33C4×Dic118C2211yescharacteristic
34C4×Dic118C2211yescharacteristic
35C4×D236C2211yescharacteristic
36#14273689—21no—
37(C22⋊D59)⋊C4—21no—
38C4⋊C4×D59C2211yescharacteristic
39C4⋊C4×D59C2211yescharacteristic
40#14273659C2211yescharacteristic
41#14273658C2211yescharacteristic
42#14273658C2211yescharacteristic
43C4⋊(C59⋊C8)C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273650C2211yescharacteristic
48#14273650C2211yescharacteristic
49#14273648C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C4⋊Q8×C59C2211yescharacteristic
53#124×C59C2211yescharacteristic
54#103×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65Q8×D59—22no—
66Q8×D59—41no—
67#11745687—22no—
68#11745687—41no—
69C2×D236D411yescharacteristic
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59C2311yescharacteristic
74C2×C4×D59C2311yescharacteristic
75C2×Dic118—21no—
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C42×C59C2311yescharacteristic
86C22⋊Dic59—21no—
87#11745672—41no—
88#11745670—41no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93(C2×D59)⋊C4D411yescharacteristic
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59D411yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108Dic236—22no—
109#11745659—41no—
110C8×D59—41no—
111C23×C59—21no—
112C22×D59C2×D411yescharacteristic
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—81no—
117D4×C59—21no—
118D4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—42no—
126C22⋊D59—42no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—42no—
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134D236—22no—
135C4×D59—21no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—42no—
140C4×D59—81no—
141C4×D59—81no—
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145Dic118—42no—
146Dic118#4112yes—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59C22×D411yescharacteristic
155C2×D59—21no—
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C2×D59—21no—
160C2×D59#13712yes—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59C2×#4111yescharacteristic
167C4×C59H(5,𝔽2)11yescharacteristic
168Dic59—22no—
169Dic59—21no—
170Dic59—21no—
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3316—591nomaximal, Sylow
175C2×C59—81no—
176C2×C59#54611yescharacteristic
177C2×C59C2×#13711yescharacteristic
178C2×C59#57711yescharacteristic
179D59—22no—
180D59—41no—
181#554—591no—
182#548—591no—
183#489D5911yescharacteristic, complemented
184#483—591no—
185#481—591no—
186#475—591no—
187#470—591no—
188#465—591no—
189#464—591no—
190#452—591no—
191#451—591no—
192#441—591no—
193#435—591no—
194#417—591no—
195C2×#103—591no—
196C59#331611yescharacteristic, complemented, Sylow
197C2×#41—591no—
198C22×Q8—591no—
199C2×Q16—591no—
200C2×Q16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8C2×D5911yescharacteristic
205#125—1181no—
206#124—1181no—
207#124C2×D5911yescharacteristic
208C22⋊Q8—591no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213C22⋊Q8—1181no—
214#121—591no—
215#121—1181no—
216C4×Q8—591no—
217C4×Q8—591no—
218C4×D4—591no—
219C4×D4—1181no—
220C4×D4—1181no—
221C2×C4⋊C4—591no—
222C2×C4⋊C4—591no—
223#106—591no—
224#106—591no—
225#106—591no—
226C4⋊C8—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103C2×D5911yescharacteristic
233#103C2×D5911yescharacteristic
234#102—591no—
235#102C2×D5911yescharacteristic
236#102C2×D5911yescharacteristic
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97C2×D5911yescharacteristic
240#41—1182no—
241#41—2361no—
242C2×Q8—21no—
243C2×Q8—591no—
244C2×Q8—591no—
245C2×Q8—1181no—
246C2×Q8—1182no—
247C2×Q8—2361no—
248C2×Q8C22×D5911yescharacteristic
249C2×D4—591no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4C22×D5911yescharacteristic
253C22×C4—591no—
254C22×C4—591no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259Q16—1182no—
260Q16—2361no—
261SD16—2361no—
262M16—2361no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—2361no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—591no—
270C4⋊C4—591no—
271C4⋊C4—591no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4C22×D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—591no—
284C22⋊C4—591no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C42—1181no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—21no—
293C23—591no—
294C23—591no—
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—592no—
299Q8—1181no—
300Q8—1181no—
301Q8—1181no—
302Q8—2362no—
303D4—21no—
304D4—21no—
305D4—1182no—
306D4—2362no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—591no—
312C2×C4—591no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4—2362no—
324C2×C4—2362no—
325C2×C4D4×D5911yescharacteristic
326C2×C4D4×D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1181no—
331C8—1181no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—592no—
336C22—1181no—
337C22—1181no—
338C22—1181no—
339C22—1181no—
340C22—1181no—
341C22C2×D4×D5911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1181no—
348C4—1181no—
349C4—1182no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4#41×D5911yescharacteristic
354C4#1427377311yescharacteristic
355C2—81no—
356C2—1182no—
357C2—2361no—
358C2#1683804511yescharacteristic
359C2#137×D5911yescharacteristic
360C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#489C2
socleC22×C59C22×D4
hypercenter#489D59
hypocenterC59#3316
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16838113C2semidirect
3. #16837731C2semidirect
4. #16837719C2semidirect
5. #16837684C2semidirect
6. #16837659C2semidirect
7. #16837630C2semidirect
8. #16837621C2semidirect
9. #16837565C2semidirect
10. #16837559C2semidirect
11. #16837510C2semidirect
12. #16837475C2semidirect
13. #16837400C2semidirect
14. #103×D59C2semidirect
15. C59×#489C2semidirect
183. #489D59semidirect
196. C59#3316semidirect