Finite Group Databasebeta

← #21436083

Subgroups — #21436083

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#16838053C211yesmaximal, characteristic, complemented
3#16837763C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837715C211yesmaximal, characteristic, complemented
6#16837695C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837638C211yesmaximal, characteristic, complemented
9#16837620C211yesmaximal, characteristic, complemented
10#16837550C211yesmaximal, characteristic, complemented
11#16837541C211yesmaximal, characteristic, complemented
12#16837505C211yesmaximal, characteristic, complemented
13#16837473C211yesmaximal, characteristic, complemented
14#16837402C211yesmaximal, characteristic, complemented
15C2×#103×C59C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745685—21no—
18C2×#11745671C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×D472C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22#14273726C2211yescharacteristic
23#14273716—21no—
24#14273716C2211yescharacteristic
25#14273712—21no—
26#14273710—21no—
27#14273705—21no—
28#14273703—21no—
29#14273703C2211yescharacteristic
30#14273702C2211yescharacteristic
31#14273701—21no—
32#14273701C2211yescharacteristic
33#14273701C2211yescharacteristic
34Q8×Dic59C2211yescharacteristic
35#14273689C2211yescharacteristic
36C4×C22⋊D59—21no—
37C4×C22⋊D59C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273660C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C2×C4⋊C4×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#103×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70#11745689—22no—
71#11745689—41no—
72#11745685—44no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82C2×C8×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊Dic59D411yescharacteristic
89#11745671—22no—
90#11745671—41no—
91(C2×D59)⋊C4—21no—
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)⋊C4—21no—
98(C2×D59)⋊C4D411yescharacteristic
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110D472—41no—
111#11745659—41no—
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59C2×D411yescharacteristic
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—42no—
120Q8×C59#4112yescomplemented
121C2×C4×C59—21no—
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×C59—42no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—22no—
132C22⋊D59—42no—
133C22⋊D59—42no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139D236—21no—
140D236—21no—
141D236—21no—
142D236—21no—
143D236—42no—
144D236—42no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—42no—
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×C59AGL(1,ℤ/8)12yes—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—22no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59C2×#4111yescharacteristic
174C4×C59H(5,𝔽2)11yescharacteristic
175Dic59—21no—
176Dic59—21no—
177Dic59—21no—
178Dic59—41no—
179Dic59—41no—
180#3308—591nomaximal, Sylow
181C2×C59—22no—
182C2×C59#54611yescharacteristic
183C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C59#57811yescharacteristic
185D59—41no—
186D59—81no—
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#448—591no—
199#440—591no—
200#435—591no—
201#417—591no—
202C2×#103D5911yescharacteristic, complemented
203C59#330811yescharacteristic, complemented, Sylow
204C2×#41—591no—
205C2×#41—1181no—
206C22×Q8C2×D5911yescharacteristic
207C2×SD16—591no—
208C2×SD16—591no—
209C2×D8—591no—
210C2×M16—591no—
211C22×C8C2×D5911yescharacteristic
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—591no—
223#121—1181no—
224C4×Q8—591no—
225C4×D4—591no—
226C4×D4—591no—
227C4×D4—1181no—
228C2×C4⋊C4—591no—
229C2×C4⋊C4C2×D5911yescharacteristic
230#107—591no—
231#107—591no—
232#107—591no—
233C4⋊C8—591no—
234#103—591no—
235#103—591no—
236#103C2×D5911yescharacteristic
237#103C2×D5911yescharacteristic
238#103C2×D5911yescharacteristic
239#103C2×D5911yescharacteristic
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244C22⋊C8—591no—
245C22⋊C8—591no—
246#97—591no—
247#41—1182no—
248#41—2364no—
249#41—2361no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—1181no—
254C2×Q8C22×D5911yescharacteristic
255C2×Q8C22×D5911yescharacteristic
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—591no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4C22×D5911yescharacteristic
270SD16—1182no—
271SD16—2361no—
272D8—2361no—
273M16—2361no—
274C2×C8—41no—
275C2×C8—591no—
276C2×C8—591no—
277C2×C8C22×D5911yescharacteristic
278C2×C8C22×D5911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—591no—
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4C22×D5911yescharacteristic
288C4⋊C4C22×D5911yescharacteristic
289C22⋊C4—591no—
290C22⋊C4—591no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C42—591no—
299C42—1181no—
300C23—591no—
301C23—1181no—
302C23—1181no—
303C23D4×D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—2362no—
309Q8#1174568512yescomplemented
310D4—1182no—
311D4—1181no—
312D4—1181no—
313D4—1181no—
314D4—1181no—
315D4—2362no—
316D4—2362no—
317D4—2362no—
318D4—2362no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—591no—
328C2×C4—591no—
329C2×C4—591no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
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—1181no—
346C22—1181no—
347C22—1181no—
348C22—2361no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1427375412yes—
355C22C2×D4×D5911yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1181no—
362C4—1181no—
363C4—1181no—
364C4—2361no—
365C4—2361no—
366C4C2×#1174568511yescharacteristic
367C4#1427377211yescharacteristic
368C2—22no—
369C2—4721no—
370C2—4721no—
371C2—2361no—
372C2#1683804211yescharacteristic
373C2C2×#1427375411yescharacteristic
374C2#1683821511yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#103×C59C2
socleC22×C59C22×D4
hypercenterC2×#103D59
hypocenterC59#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #16838063C2semidirect
2. #16838053C2semidirect
3. #16837763C2semidirect
4. #16837736C2semidirect
5. #16837715C2semidirect
6. #16837695C2semidirect
7. #16837651C2semidirect
8. #16837638C2semidirect
9. #16837620C2semidirect
10. #16837550C2semidirect
11. #16837541C2semidirect
12. #16837505C2semidirect
13. #16837473C2semidirect
14. #16837402C2semidirect
15. C2×#103×C59C2semidirect
120. Q8×C59#41semidirect
202. C2×#103D59semidirect
203. C59#3308semidirect
309. Q8#11745685semidirect