Finite Group Databasebeta

← #21436002

Subgroups — #21436002

Order 7552.

398 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#16838104C211yesmaximal, characteristic, complemented
2#16838063C211yesmaximal, characteristic, complemented
3#16837758C211yesmaximal, characteristic, complemented
4#16837741C211yesmaximal, characteristic, complemented
5#16837721C211yesmaximal, characteristic, complemented
6#16837707C211yesmaximal, characteristic, complemented
7#16837636C211yesmaximal, characteristic, complemented
8#16837628C211yesmaximal, characteristic, complemented
9#16837619C211yesmaximal, characteristic, complemented
10#16837546C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13#16837397C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15C59×#448C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745669C2211yescharacteristic
18C22×C59⋊C8C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20#14273720—21no—
21#14273718C2211yescharacteristic
22#14273716—21no—
23#14273716C2211yescharacteristic
24#14273711—21no—
25#14273703—21no—
26#14273703C2211yescharacteristic
27#14273701—21no—
28#14273701C2211yescharacteristic
29#14273699—21no—
30#14273698C2211yescharacteristic
31Q8×Dic59C2211yescharacteristic
32D4×Dic59—21no—
33D4×Dic59C2211yescharacteristic
34C4×C22⋊D59—21no—
35C4×C22⋊D59C2211yescharacteristic
36#14273685C2211yescharacteristic
37C2×C4⋊Dic59C2211yescharacteristic
38#14273660C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273659C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59D411yescharacteristic
71C22×Dic59—21no—
72C22×Dic59—21no—
73#11745689—22no—
74#11745689—41no—
75C2×D236—21no—
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79SD16×C59—22no—
80SD16×C59—41no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59D411yescharacteristic
88#11745669—41no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C8×D59—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—42no—
119Q8×C59#4112yes—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—42no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—22no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—81no—
138C2×Dic59—81no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142D236—21no—
143D236—21no—
144D236—42no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—42no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59#13512yes—
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#3301—591nomaximal, Sylow
178C2×C59—22no—
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59C2×#13511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—41no—
184D59—81no—
185#553—591no—
186#548—591no—
187#488—591no—
188#485—591no—
189#481—591no—
190#479—591no—
191#466—591no—
192#465—591no—
193#463—591no—
194#449—591no—
195#448D5911yescharacteristic, complemented
196C4×SD16—591no—
197C8×D4—591no—
198#416—591no—
199C2×#103—591no—
200C59#330111yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C22×Q8C2×D5911yescharacteristic
203C2×SD16C2×D5911yescharacteristic
204C2×SD16C2×D5911yescharacteristic
205C2×D8—591no—
206C22×C8—591no—
207C22×C8—591no—
208#126—1181no—
209#125—591no—
210#124—591no—
211#124—1181no—
212#123—1181no—
213C22⋊Q8—591no—
214C22⋊Q8—1181no—
215#121—591no—
216#121—591no—
217#121—1181no—
218#121—1181no—
219#121C2×D5911yescharacteristic
220C4×Q8—591no—
221C4×D4—591no—
222C4×D4—591no—
223C4×D4—1181no—
224C4×D4—1181no—
225#117—591no—
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#103—591no—
235#103C2×D5911yescharacteristic
236#103C2×D5911yescharacteristic
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241C22⋊C8—591no—
242C22⋊C8C2×D5911yescharacteristic
243C4×C8—591no—
244#41—1182no—
245#41—2361no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D5911yescharacteristic
250C2×Q8C22×D5911yescharacteristic
251C2×D4—21no—
252C2×D4—591no—
253C2×D4—591no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4C22×D5911yescharacteristic
258C22×C4—21no—
259C22×C4—591no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4C22×D5911yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—2361no—
267C2×C8—591no—
268C2×C8—591no—
269C2×C8—2361no—
270C2×C8—2361no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4C22×D5911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—591no—
285C22⋊C4—591no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—591no—
294C42—1181no—
295C42—1181no—
296C23—21no—
297C23—591no—
298C23—1181no—
299C23D4×D5911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1174568712yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—1182no—
309D4—1181no—
310D4—1181no—
311D4—4721no—
312D4—2362no—
313D4—2362no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—591no—
321C2×C4—591no—
322C2×C4—591no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—4721no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—1181no—
343C22—1181no—
344C22—1181no—
345C22—2361no—
346C22—2361no—
347C22—2361no—
348C22#1427374812yes—
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—22no—
363C2—81no—
364C2—4721no—
365C2—2361no—
366C2#1683803911yescharacteristic
367C2C2×#1427374811yescharacteristic
368C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#448C2
socleC22×C59C22×D4
hypercenter#448D59
hypocenterC59#3301
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #16838104C2semidirect
2. #16838063C2semidirect
3. #16837758C2semidirect
4. #16837741C2semidirect
5. #16837721C2semidirect
6. #16837707C2semidirect
7. #16837636C2semidirect
8. #16837628C2semidirect
9. #16837619C2semidirect
10. #16837546C2semidirect
11. SD16×Dic59C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. #16837397C2semidirect
14. C2×#14273651C2semidirect
15. C59×#448C2semidirect
195. #448D59semidirect
200. C59#3301semidirect