Finite Group Databasebeta

← #21436102

Subgroups — #21436102

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#16838098C211yesmaximal, characteristic, complemented
2#16837766C211yesmaximal, characteristic, complemented
3#16837723C211yesmaximal, characteristic, complemented
4#16837713C211yesmaximal, characteristic, complemented
5#16837709C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837594C211yesmaximal, characteristic, complemented
9#16837547C211yesmaximal, characteristic, complemented
10#16837547C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14#16837398C211yesmaximal, characteristic, complemented
15C59×#550C211yesmaximal, characteristic, complemented
16C2×#11745671C2211yescharacteristic
17C2×#11745669C2211yescharacteristic
18C2×#11745669C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273722—21no—
22#14273719C2211yescharacteristic
23#14273709—21no—
24#14273701C2211yescharacteristic
25#14273701C2211yescharacteristic
26#14273699—21no—
27C4×D236C2211yescharacteristic
28(C22⋊D59)⋊C4—21no—
29#14273686C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273648C2211yescharacteristic
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C2×#41×C59C2211yescharacteristic
50#127×C59—21no—
51#127×C59C2211yescharacteristic
52#121×C59—21no—
53#121×C59—21no—
54#121×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—22no—
61#41×C59—41no—
62#41×C59—41no—
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79C22×Dic59—21no—
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59D411yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59D411yescharacteristic
88C22⋊C4×C59D411yescharacteristic
89C42×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92#11745671—22no—
93#11745669—41no—
94#11745669—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116Q8×C59—21no—
117Q8×C59#4112yes—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—41no—
123D4×C59—42no—
124D4×C59—42no—
125D4×C59—42no—
126D4×C59—81no—
127D4×C59—81no—
128D4×C59—81no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—42no—
136C2×C4×C59—42no—
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2411yescharacteristic
142C22⋊D59—42no—
143C22⋊D59—81no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—81no—
148D236—21no—
149D236—21no—
150C4×D59—81no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59C22×D411yescharacteristic
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—22no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—41no—
177C4×C59C2×#4111yescharacteristic
178C4×C59H(5,𝔽2)11yescharacteristic
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182#3309—591nomaximal, Sylow
183C2×C59—41no—
184C2×C59—41no—
185C2×C59—81no—
186C2×C59—81no—
187C2×C59#54611yescharacteristic
188C2×C59#57511yescharacteristic
189C2×C59#57611yescharacteristic
190D59—81no—
191#553—591no—
192#550D5911yescharacteristic, complemented
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#417—591no—
205#416—591no—
206C59#330911yescharacteristic, complemented, Sylow
207C2×#41C2×D5911yescharacteristic
208C2×#41C2×D5911yescharacteristic
209C2×SD16—591no—
210C2×D8—591no—
211C2×D8—591no—
212C2×M16—591no—
213C22×C8—591no—
214#127—21no—
215#127C2×D5911yescharacteristic
216#126—1181no—
217#125—591no—
218#123—1181no—
219#121—21no—
220#121—21no—
221#121—591no—
222#121—591no—
223#121—1181no—
224#121C2×D5911yescharacteristic
225#121C2×D5911yescharacteristic
226C4×Q8C2×D5911yescharacteristic
227C4×D4—21no—
228C4×D4—591no—
229C4×D4—1181no—
230C4×D4C2×D5911yescharacteristic
231#117—591no—
232C2×C4⋊C4—591no—
233#107—591no—
234#107—591no—
235#106—591no—
236C4⋊C8—591no—
237#103—591no—
238#103—591no—
239#103—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247C22⋊C8—591no—
248C22⋊C8—591no—
249#97—591no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D5911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—591no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4C22⋊D5911yescharacteristic
265C2×D4C22×D5911yescharacteristic
266C2×D4C22×D5911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4C22×D5911yescharacteristic
272C22×C4C22×D5911yescharacteristic
273SD16—1182no—
274D8—2361no—
275D8—2361no—
276M16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8—591no—
280C2×C8—591no—
281C2×C8—2361no—
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—21no—
292C22⋊C4—21no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4C22⋊D5911yescharacteristic
298C22⋊C4C22⋊D5911yescharacteristic
299C42—21no—
300C42—1181no—
301C42C22×D5911yescharacteristic
302C23—21no—
303C23—21no—
304C23—1181no—
305C23C2×C22⋊D5911yescharacteristic
306C23C2×C22⋊D5911yescharacteristic
307Q8—21no—
308Q8#1174568712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—1181no—
321D4—1181no—
322D4—4721no—
323D4—2362no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—4721no—
336C2×C4—4721no—
337C2×C4C2×C22⋊D5911yescharacteristic
338C2×C4C2×C22⋊D5911yescharacteristic
339C2×C4C2×C22⋊D5911yescharacteristic
340C2×C4C2×C22⋊D5911yescharacteristic
341C2×C4C23×D5911yescharacteristic
342C8—1181no—
343C8—1181no—
344C8—1181no—
345C8—1181no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C22×C22⋊D5911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4C2×#1174568711yescharacteristic
372C4#1427377211yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—4721no—
378C2#1683804611yescharacteristic
379C2#1683820011yescharacteristic
380C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#550C2
socleC22×C59C22×D4
hypercenter#550D59
hypocenterC59#3309
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #16838098C2semidirect
2. #16837766C2semidirect
3. #16837723C2semidirect
4. #16837713C2semidirect
5. #16837709C2semidirect
6. #16837653C2semidirect
7. #16837636C2semidirect
8. #16837594C2semidirect
9. #16837547C2semidirect
10. #16837547C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837403C2semidirect
14. #16837398C2semidirect
15. C59×#550C2semidirect
192. #550D59semidirect
206. C59#3309semidirect