Finite Group Databasebeta

← #21436091

Subgroups — #21436091

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838063C211yesmaximal, characteristic, complemented
2#16838052C211yesmaximal, characteristic, complemented
3#16837763C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837716C211yesmaximal, characteristic, complemented
6#16837695C211yesmaximal, characteristic, complemented
7#16837645C211yesmaximal, characteristic, complemented
8#16837636C211yesmaximal, characteristic, complemented
9#16837619C211yesmaximal, characteristic, complemented
10#16837546C211yesmaximal, characteristic, complemented
11#16837503C211yesmaximal, characteristic, complemented
12#16837470C211yesmaximal, characteristic, complemented
13#16837402C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15C59×#448C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687—21no—
18C2×#11745669C2211yescharacteristic
19C2×#11745659C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273716—21no—
23#14273716C2211yescharacteristic
24#14273709—21no—
25#14273708—21no—
26#14273704—21no—
27#14273703—21no—
28#14273703C2211yescharacteristic
29#14273701—21no—
30#14273701C2211yescharacteristic
31#14273698C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33D4×Dic59C2211yescharacteristic
34C4×C22⋊D59—21no—
35C4×C22⋊D59C2211yescharacteristic
36C2×C4⋊Dic59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273660C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic
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—
75#11745687—44no—
76C2×D236—21no—
77C2×D236C2311yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82SD16×C59—22no—
83SD16×C59—41no—
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59D411yescharacteristic
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)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8—41no—
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111#11745659—41no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59C2×D411yescharacteristic
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—42no—
120Q8×C59#4112yescomplemented
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—42no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—22no—
133C22⋊D59—42no—
134C22⋊D59—42no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—42no—
139C2×Dic59—42no—
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143D236—21no—
144D236—21no—
145D236—42no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—42no—
149C4×D59—42no—
150Dic118—42no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59AGL(1,ℤ/8)12yes—
161C22×C59C22×D411yescharacteristic
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—22no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59C2×#4111yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—21no—
175Dic59—21no—
176Dic59—21no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3308—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59—81no—
183C2×C59#54611yescharacteristic
184C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C59#57811yescharacteristic
186D59—41no—
187D59—81no—
188#548—591no—
189#547—591no—
190#489—591no—
191#484—591no—
192#480—591no—
193#477—591no—
194#468—591no—
195#466—591no—
196#463—591no—
197#449—591no—
198#448D5911yescharacteristic, complemented
199#440—591no—
200#435—591no—
201#417—591no—
202C2×#103—591no—
203C59#330811yescharacteristic, complemented, Sylow
204C2×#41—591no—
205C2×#41—1181no—
206C22×Q8C2×D5911yescharacteristic
207C2×SD16C2×D5911yescharacteristic
208C2×SD16C2×D5911yescharacteristic
209C2×D8—591no—
210C2×M16—591no—
211C22×C8—591no—
212C4⋊Q8—591no—
213#124—591no—
214#124—1181no—
215#123—1181no—
216#123—1181no—
217C22⋊Q8—591no—
218C22⋊Q8—1181no—
219C22⋊Q8—1181no—
220#121—591no—
221#121—591no—
222#121—1181no—
223#121C2×D5911yescharacteristic
224C4×Q8—591no—
225C4×D4—591no—
226C4×D4—591no—
227C4×D4—1181no—
228C2×C4⋊C4—591no—
229C2×C4⋊C4—591no—
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103—591no—
238#103C2×D5911yescharacteristic
239#103C2×D5911yescharacteristic
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8—591no—
245C22⋊C8C2×D5911yescharacteristic
246#97—591no—
247#41—1182no—
248#41—2361no—
249#41—2364no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—1181no—
254C2×Q8C22×D5911yescharacteristic
255C2×Q8C22×D5911yescharacteristic
256C2×D4—21no—
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4C22×D5911yescharacteristic
263C22×C4—21no—
264C22×C4—591no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4C22×D5911yescharacteristic
270SD16—22no—
271SD16—41no—
272D8—2361no—
273M16—2361no—
274C2×C8—591no—
275C2×C8—591no—
276C2×C8—2361no—
277C2×C8C22×D5911yescharacteristic
278C2×C8C22×D5911yescharacteristic
279C4⋊C4—591no—
280C4⋊C4—591no—
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—591no—
291C22⋊C4—591no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C42—591no—
299C42—1181no—
300C23—21no—
301C23—591no—
302C23—1181no—
303C23D4×D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—2362no—
309Q8#1174568712yescomplemented
310D4—21no—
311D4—21no—
312D4—42no—
313D4—1182no—
314D4—1181no—
315D4—1181no—
316D4—2362no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—591no—
326C2×C4—591no—
327C2×C4—591no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—2362no—
334C2×C4—2362no—
335C2×C4—2362no—
336C2×C4—2362no—
337C2×C4D4×D5911yescharacteristic
338C2×C4C23×D5911yescharacteristic
339C8—21no—
340C8—21no—
341C8—1181no—
342C8—1181no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—1181no—
349C22—1181no—
350C22—1181no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375412yes—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—1181no—
361C4—1181no—
362C4—1181no—
363C4—2361no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568711yescharacteristic
367C4#1427377211yescharacteristic
368C2—22no—
369C2—81no—
370C2—4721no—
371C2—2361no—
372C2#1683803911yescharacteristic
373C2C2×#1427375411yescharacteristic
374C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#448C2
socleC22×C59C22×D4
hypercenter#448D59
hypocenterC59#3308
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. #16838063C2semidirect
2. #16838052C2semidirect
3. #16837763C2semidirect
4. #16837736C2semidirect
5. #16837716C2semidirect
6. #16837695C2semidirect
7. #16837645C2semidirect
8. #16837636C2semidirect
9. #16837619C2semidirect
10. #16837546C2semidirect
11. #16837503C2semidirect
12. #16837470C2semidirect
13. #16837402C2semidirect
14. C2×#14273651C2semidirect
15. C59×#448C2semidirect
120. Q8×C59#41semidirect
198. #448D59semidirect
203. C59#3308semidirect
309. Q8#11745687semidirect