Finite Group Databasebeta

← #21436197

Subgroups — #21436197

Order 7552.

382 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#16838093C211yesmaximal, characteristic, complemented
2#16838056C211yesmaximal, characteristic
3#16837771C211yesmaximal, characteristic, complemented
4#16837745C211yesmaximal, characteristic, complemented
5#16837739C211yesmaximal, characteristic, complemented
6#16837702C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837642C211yesmaximal, characteristic, complemented
9#16837612C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837561C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837400C211yesmaximal, characteristic, complemented
14#16837395C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273721—21no—
24#14273719C2211yescharacteristic
25#14273717—21no—
26#14273712—21no—
27#14273711—21no—
28#14273711—21no—
29#14273707C2211yescharacteristic
30#14273707C2211yescharacteristic
31#14273703C2211yescharacteristic
32#14273703C2211yescharacteristic
33#14273701—21no—
34C4×D236C2211yescharacteristic
35#14273685C2211yescharacteristic
36#14273684—21no—
37C2×C4⋊Dic59—21no—
38C4⋊C4×D59C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273658C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273650C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66#11745687—22no—
67#11745687—22no—
68#11745687—41no—
69#11745687—41no—
70C2×D236D411yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59C2311yescharacteristic
73C2×C4×D59C2311yescharacteristic
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76SD16×C59—22no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C42×C59—21no—
84C42×C59C2311yescharacteristic
85#11745672—41no—
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
93(C2×D59)⋊C4D411yescharacteristic
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745659—41no—
110C8×D59—41no—
111C23×C59—21no—
112C22×D59C2×D411yescharacteristic
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116D4×C59—21no—
117D4×C59#4112yes—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—42no—
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×Dic59—42no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135D236—41no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—21no—
140C4×D59—42no—
141Dic118—21no—
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145C8×C59—21no—
146C8×C59—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59—22no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59C22×D411yescharacteristic
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C4×C59—21no—
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—41no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3315—591nomaximal, Sylow
173C2×C59—42no—
174C2×C59#54611yescharacteristic
175C2×C59#57511yescharacteristic
176C2×C59#57811yescharacteristic
177D59—41no—
178D59—41no—
179#552—591no—
180#547—591no—
181#491—591no—
182#485—591no—
183#484—591no—
184#478—591no—
185#470—591no—
186#467—591no—
187#462—591no—
188#452—591no—
189#452—591no—
190#440D5911yescharacteristic, complemented
191#435—591no—
192#417—591no—
193#416—591no—
194C59#331511yescharacteristic, complemented, Sylow
195C2×#41—591no—
196C2×#41—591no—
197C2×Q16—591no—
198C2×Q16—591no—
199C2×SD16C2×D5911yescharacteristic
200C2×M16—591no—
201C22×C8—591no—
202C4⋊Q8—591no—
203#126—1181no—
204#125—591no—
205#125—1181no—
206#123—1181no—
207#123—1181no—
208#123—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—591no—
212C22⋊Q8—591no—
213#121—1181no—
214C4×Q8C2×D5911yescharacteristic
215C4×D4—591no—
216C4×D4C2×D5911yescharacteristic
217#117—591no—
218#117—1181no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4—1181no—
221#107—591no—
222#107C2×D5911yescharacteristic
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#103C2×D5911yescharacteristic
232#102—591no—
233#102—591no—
234#102C2×D5911yescharacteristic
235C22⋊C8—591no—
236C22⋊C8—591no—
237#97C2×D5911yescharacteristic
238#41—1182no—
239#41—1182no—
240#41—2361no—
241#41—2361no—
242C2×Q8—591no—
243C2×Q8—591no—
244C2×Q8C22×D5911yescharacteristic
245C2×D4—591no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4C22×D5911yescharacteristic
249C22×C4—21no—
250C22×C4—591no—
251C22×C4—591no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255Q16—2361no—
256Q16—2361no—
257SD16—22no—
258M16—2361no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—2361no—
262C2×C8C22×D5911yescharacteristic
263C2×C8C22×D5911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4C22×D5911yescharacteristic
278C4⋊C4C22×D5911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—591no—
281C22⋊C4—591no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C42—21no—
288C42—1181no—
289C42C22×D5911yescharacteristic
290C23—21no—
291C23—591no—
292C23—591no—
293Q8—21no—
294Q8—21no—
295Q8—1181no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299D4—21no—
300D4—2361no—
301D4—2362no—
302D4—2362no—
303D4#1174568512yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—591no—
309C2×C4—591no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—2362no—
319C2×C4—2362no—
320C2×C4—2362no—
321C2×C4D4×D5911yescharacteristic
322C2×C4D4×D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—21no—
325C8—21no—
326C8—1181no—
327C8—1181no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—1181no—
332C22—1181no—
333C22—1181no—
334C22—1181no—
335C22—1181no—
336C22—1181no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1181no—
344C4—1181no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4—2361no—
349C4C2×#1174568511yescharacteristic
350C4#1427377311yescharacteristic
351C2—42no—
352C2—2361no—
353C2—2361no—
354C2#1683804811yescharacteristic
355C2#1683819811yescharacteristic
356C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3315
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16838093C2semidirect
3. #16837771C2semidirect
4. #16837745C2semidirect
5. #16837739C2semidirect
6. #16837702C2semidirect
7. #16837659C2semidirect
8. #16837642C2semidirect
9. #16837612C2semidirect
10. #16837561C2semidirect
11. #16837561C2semidirect
12. #16837475C2semidirect
13. #16837400C2semidirect
14. #16837395C2semidirect
15. C59×#440C2semidirect
190. #440D59semidirect
194. C59#3315semidirect