Finite Group Databasebeta

← #21436226

Subgroups — #21436226

Order 7552.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838086C211yesmaximal, characteristic, complemented
2#16838071C211yesmaximal, characteristic
3#16837765C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837711C211yesmaximal, characteristic, complemented
7#16837645C211yesmaximal, characteristic, complemented
8#16837633C211yesmaximal, characteristic, complemented
9#16837600C211yesmaximal, characteristic, complemented
10#16837563C211yesmaximal, characteristic, complemented
11#16837509C211yesmaximal, characteristic, complemented
12#16837470C211yesmaximal, characteristic, complemented
13#16837402C211yesmaximal, characteristic, complemented
14#16837398C211yesmaximal, characteristic, complemented
15C59×#452C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745659C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic
20#14273723—21no—
21#14273723C2211yescharacteristic
22#14273720—21no—
23#14273718C2211yescharacteristic
24#14273717—21no—
25#14273709—21no—
26#14273703C2211yescharacteristic
27#14273701—21no—
28#14273701C2211yescharacteristic
29#14273698—21no—
30#14273698C2211yescharacteristic
31Q8×Dic59C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33C4×C22⋊D59—21no—
34C4×C22⋊D59C2211yescharacteristic
35#14273686C2211yescharacteristic
36#14273685—21no—
37C4⋊C4×D59C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273658C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55C22⋊Q8×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59C2311yescharacteristic
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
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⋊D59D411yescharacteristic
72#11745689—22no—
73#11745689—41no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79Q16×C59—22no—
80SD16×C59—41no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59—21no—
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59D411yescharacteristic
89#11745671—41no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59#4112yes—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—42no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—42no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—41no—
131C22⋊D59—42no—
132C22⋊D59—81no—
133C22⋊D59—81no—
134C22⋊D59—81no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141D236—21no—
142D236—21no—
143D236—42no—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—42no—
147C4×D59—42no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—22no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—21no—
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3317—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59#57511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—41no—
184D59—81no—
185#552—591no—
186#550—591no—
187#490—591no—
188#482—591no—
189#481—591no—
190#479—591no—
191#468—591no—
192#465—591no—
193#460—591no—
194#452—591no—
195#452D5911yescharacteristic, complemented
196#441—591no—
197#435—591no—
198#417—591no—
199#416—591no—
200C59#331711yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C2×#41C2×D5911yescharacteristic
203C2×Q16C2×D5911yescharacteristic
204C2×SD16—591no—
205C2×SD16C2×D5911yescharacteristic
206C2×M16—591no—
207C22×C8—591no—
208#127—591no—
209#127—1181no—
210#126—1181no—
211#125—591no—
212#125—1181no—
213#123—1181no—
214C22⋊Q8—591no—
215C22⋊Q8C2×D5911yescharacteristic
216#121—591no—
217#121—591no—
218#121—1181no—
219#121—1181no—
220C4×Q8—591no—
221C4×Q8—591no—
222C4×D4—591no—
223C4×D4—1181no—
224#117—591no—
225#117—1181no—
226C2×C4⋊C4—591no—
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103C2×D5911yescharacteristic
235#102—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102C2×D5911yescharacteristic
241C22⋊C8—591no—
242C22⋊C8C2×D5911yescharacteristic
243#97—591no—
244#41—22no—
245#41—41no—
246#41—1182no—
247#41—2361no—
248C2×Q8C22×D5911yescharacteristic
249C2×Q8C22×D5911yescharacteristic
250C2×D4—21no—
251C2×D4—591no—
252C2×D4—591no—
253C2×D4—1181no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4C22×D5911yescharacteristic
259C22×C4—21no—
260C22×C4—591no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4C22×D5911yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—2361no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—2361no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—591no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4C22×D5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—591no—
287C22⋊C4—591no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C42—591no—
293C42—1181no—
294C42—1181no—
295C42—1181no—
296C23—21no—
297C23—591no—
298C23—1181no—
299C23D4×D5911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8#1174568712yes—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—1181no—
308D4—1181no—
309D4—4721no—
310D4—4721no—
311D4—4721no—
312D4—2362no—
313D4—2361no—
314D4—2362no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—591no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—2362no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—2361no—
347C22—2361no—
348C22—2361no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—1181no—
355C4—1181no—
356C4—1181no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568711yescharacteristic
361C4#1427377211yescharacteristic
362C2—41no—
363C2—81no—
364C2—4721no—
365C2—2361no—
366C2#1683803911yescharacteristic
367C2#1683819911yescharacteristic
368C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#452C2
socleC22×C59C22×D4
hypercenter#452D59
hypocenterC59#3317
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16838086C2semidirect
3. #16837765C2semidirect
4. #16837727C2semidirect
5. #16837719C2semidirect
6. #16837711C2semidirect
7. #16837645C2semidirect
8. #16837633C2semidirect
9. #16837600C2semidirect
10. #16837563C2semidirect
11. #16837509C2semidirect
12. #16837470C2semidirect
13. #16837402C2semidirect
14. #16837398C2semidirect
15. C59×#452C2semidirect
195. #452D59semidirect
200. C59#3317semidirect