Finite Group Databasebeta

← #21436103

Subgroups — #21436103

Order 7552.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838100C211yesmaximal, characteristic, complemented
2#16838071C211yesmaximal, characteristic, complemented
3#16837765C211yesmaximal, characteristic, complemented
4#16837725C211yesmaximal, characteristic, complemented
5#16837715C211yesmaximal, characteristic, complemented
6#16837707C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837637C211yesmaximal, characteristic, complemented
9#16837596C211yesmaximal, characteristic, complemented
10#16837550C211yesmaximal, characteristic, complemented
11#16837547C211yesmaximal, characteristic, complemented
12#16837505C211yesmaximal, characteristic, complemented
13#16837471C211yesmaximal, characteristic, complemented
14#16837397C211yesmaximal, characteristic, complemented
15C59×#417C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×D472C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273723—21no—
22#14273723C2211yescharacteristic
23#14273722—21no—
24#14273718C2211yescharacteristic
25#14273712—21no—
26#14273702C2211yescharacteristic
27#14273701—21no—
28#14273701—21no—
29#14273701C2211yescharacteristic
30#14273701C2211yescharacteristic
31#14273698—21no—
32#14273698C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34#14273689C2211yescharacteristic
35C4×C22⋊D59—21no—
36C4×C22⋊D59—21no—
37C4×C22⋊D59C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273659C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic
54C2×C4⋊C4×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59D411yescharacteristic
73#11745689—22no—
74#11745689—41no—
75C2×D236—21no—
76C2×D236—21no—
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59C2311yescharacteristic
82M16×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59D411yescharacteristic
90#11745671—22no—
91#11745669—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109D472—41no—
110C8×D59—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59C2×D411yescharacteristic
116Q8×C59—21no—
117Q8×C59#4112yes—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—42no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—42no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—41no—
131C22⋊D59—42no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C22⋊D59—81no—
135C22⋊D59—81no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141D236—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—42no—
146D236—81no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—42no—
150C4×D59—81no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59C22×D411yescharacteristic
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C4×C59—22no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59C2×#4111yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—21no—
178Dic59—21no—
179Dic59—21no—
180Dic59—41no—
181Dic59—41no—
182#3309—591nomaximal, Sylow
183C2×C59—41no—
184C2×C59—81no—
185C2×C59#54611yescharacteristic
186C2×C59#57511yescharacteristic
187C2×C59#57611yescharacteristic
188D59—41no—
189D59—81no—
190D59—81no—
191#553—591no—
192#550—591no—
193#490—591no—
194#482—591no—
195#480—591no—
196#479—591no—
197#469—591no—
198#466—591no—
199#459—591no—
200#449—591no—
201#449—591no—
202#440—591no—
203#435—591no—
204#417D5911yescharacteristic, complemented
205#416—591no—
206C59#330911yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C2×#41C2×D5911yescharacteristic
209C2×SD16—591no—
210C2×D8—591no—
211C2×D8—591no—
212C2×M16C2×D5911yescharacteristic
213C22×C8—591no—
214#127—591no—
215#127—1181no—
216#126—1181no—
217#125—591no—
218#123—1181no—
219#121—591no—
220#121—591no—
221#121—591no—
222#121—591no—
223#121—1181no—
224#121—1181no—
225#121—1181no—
226C4×Q8—591no—
227C4×D4—591no—
228C4×D4—591no—
229C4×D4—1181no—
230C4×D4—1181no—
231#117—591no—
232C2×C4⋊C4C2×D5911yescharacteristic
233#107—591no—
234#107—591no—
235#106—591no—
236C4⋊C8—591no—
237#103—591no—
238#103C2×D5911yescharacteristic
239#103C2×D5911yescharacteristic
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102C2×D5911yescharacteristic
246#102C2×D5911yescharacteristic
247C22⋊C8—591no—
248C22⋊C8—591no—
249#97—591no—
250#41—22no—
251#41—41no—
252#41—1182no—
253#41—2361no—
254C2×Q8C22×D5911yescharacteristic
255C2×D4—21no—
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4C22×D5911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—591no—
270C22×C4—1181no—
271C22×C4—1181no—
272C22×C4C22×D5911yescharacteristic
273SD16—1182no—
274D8—2361no—
275D8—2361no—
276M16—41no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8—2361no—
280C2×C8C22×D5911yescharacteristic
281C2×C8C22×D5911yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—591no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4C22×D5911yescharacteristic
290C4⋊C4C22×D5911yescharacteristic
291C22⋊C4—591no—
292C22⋊C4—591no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C42—591no—
300C42—1181no—
301C42—1181no—
302C23—21no—
303C23—591no—
304C23—1181no—
305C23—1181no—
306C23D4×D5911yescharacteristic
307Q8—21no—
308Q8#1174568512yes—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—1181no—
313D4—1181no—
314D4—1181no—
315D4—1181no—
316D4—4721no—
317D4—4721no—
318D4—4721no—
319D4—4721no—
320D4—2362no—
321D4—2361no—
322D4—2362no—
323D4—2362no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—591no—
332C2×C4—591no—
333C2×C4—591no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—4721no—
339C2×C4—2362no—
340C2×C4D4×D5911yescharacteristic
341C2×C4C23×D5911yescharacteristic
342C8—21no—
343C8—21no—
344C8—1181no—
345C8—1181no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—1181no—
353C22—1181no—
354C22—1181no—
355C22—2361no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C2×D4×D5911yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—1181no—
367C4—1181no—
368C4—1181no—
369C4—2361no—
370C4—2361no—
371C4C2×#1174568511yescharacteristic
372C4#1427377211yescharacteristic
373C2—41no—
374C2—81no—
375C2—4721no—
376C2—4721no—
377C2—2361no—
378C2#1683804211yescharacteristic
379C2#1683820111yescharacteristic
380C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#417C2
socleC22×C59C22×D4
hypercenter#417D59
hypocenterC59#3309
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #16838100C2semidirect
2. #16838071C2semidirect
3. #16837765C2semidirect
4. #16837725C2semidirect
5. #16837715C2semidirect
6. #16837707C2semidirect
7. #16837655C2semidirect
8. #16837637C2semidirect
9. #16837596C2semidirect
10. #16837550C2semidirect
11. #16837547C2semidirect
12. #16837505C2semidirect
13. #16837471C2semidirect
14. #16837397C2semidirect
15. C59×#417C2semidirect
204. #417D59semidirect
206. C59#3309semidirect