Finite Group Databasebeta

← #21435642

Subgroups — #21435642

Order 7552.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273751C211yesmaximal, characteristic, complemented
2C2×#14273746C211yesmaximal, characteristic, complemented
3#16838072C211yesmaximal, characteristic, complemented
4#16838047C211yesmaximal, characteristic, complemented
5#16837789C211yesmaximal, characteristic, complemented
6#16837647C211yesmaximal, characteristic, complemented
7#16837637C211yesmaximal, characteristic, complemented
8#16837625C211yesmaximal, characteristic, complemented
9#16837565C211yesmaximal, characteristic, complemented
10#16837548C211yesmaximal, characteristic, complemented
11#16837544C211yesmaximal, characteristic, complemented
12#16837534C211yesmaximal, characteristic, complemented
13#16837502C211yesmaximal, characteristic, complemented
14#16837472C211yesmaximal, characteristic, complemented
15C59×#459C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×#11745687C2211yescharacteristic, complemented
19C2×D4×D59C2211yescharacteristic
20#14273751—24no—
21#14273746—24no—
22C2×Dic236C2211yescharacteristic, complemented
23C2×#11745660C2211yescharacteristic
24C2×#11745670C2211yescharacteristic
25C2×#11745670C2211yescharacteristic, complemented
26C2×#11745670C2211yescharacteristic, complemented
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745659C2211yescharacteristic
30C2×C8×D59C2211yescharacteristic, complemented
31#14273723—21no—
32#14273715C2211yescharacteristic
33#14273711—21no—
34#14273707C2211yescharacteristic
35#14273702C2211yescharacteristic
36#14273701—21no—
37#14273699—21no—
38#14273699—21no—
39#14273698C2211yescharacteristic
40#14273698C2211yescharacteristic, complemented
41#14273697—21no—
42C4×Dic118C2211yescharacteristic, complemented
43C4×D236C2211yescharacteristic
44D4×Dic59—21no—
45C2×(C2×D59)⋊C4—21no—
46#14273660C2211yescharacteristic, complemented
47#14273652C2211yescharacteristic, complemented
48#14273650C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273648C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53#14273638C2211yescharacteristic, complemented
54C2×D8×C59C2211yescharacteristic
55C2×D8×C59C2211yescharacteristic
56#127×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic
58C4⋊C8×C59C2211yescharacteristic, complemented
59#102×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×D4×C59—21no—
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77#11745687—22no—
78#11745687—22no—
79#11745687—22no—
80#11745687—41no—
81#11745687—41no—
82#11745687—41no—
83D4×D59—22no—
84D4×D59—41no—
85C2×D236—21no—
86C2×D236D411yescharacteristic
87C2×D236C2311yescharacteristic
88C2×C4×D59C2311yescharacteristic
89C2×C4×D59C2311yescharacteristic
90C2×Dic118C2311yescharacteristic
91C2×Dic118C2311yescharacteristic
92D8×C59—22no—
93D8×C59—22no—
94C2×C8×C59C2311yescharacteristic
95C2×C8×C59C2311yescharacteristic
96C4⋊C4×C59C2311yescharacteristic
97C22⋊C4×C59—21no—
98C42×C59C2311yescharacteristic
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101#11745670—22no—
102#11745670—41no—
103#11745670D414yescomplemented
104#11745669—22no—
105#11745669—41no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4D411yescharacteristic
111(C2×D59)⋊C4D411yescharacteristic
112C4⋊Dic59—21no—
113C4⋊Dic59D411yescharacteristic
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116C4×Dic59—21no—
117C2×C59⋊C8C2311yescharacteristic
118C2×C59⋊C8C2311yescharacteristic
119Dic236—22no—
120#11745660—22no—
121#11745659—22no—
122C8×D59—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C22×D59—21no—
127C22×D59—42no—
128C22×D59—42no—
129C22×D59—81no—
130C22×D59C2×D411yescharacteristic
131C22×D59C2×D411yescharacteristic
132D4×C59—21no—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—42no—
138D4×C59—81no—
139D4×C59C2×D412yes—
140C2×C4×C59—21no—
141C2×C4×C59—81no—
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2×D411yescharacteristic
144C2×C4×C59C2411yescharacteristic
145C22⋊D59—42no—
146C22⋊D59—42no—
147C22⋊D59—42no—
148C22⋊D59—42no—
149C22⋊D59—81no—
150C22⋊D59—81no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—42no—
155C2×Dic59—42no—
156C2×Dic59—42no—
157C2×Dic59C2×D411yescharacteristic
158C2×Dic59C2×D411yescharacteristic
159D236—21no—
160D236—21no—
161D236—41no—
162D236—81no—
163C4×D59—21no—
164C4×D59—21no—
165C4×D59—21no—
166C4×D59—21no—
167Dic118—21no—
168Dic118—21no—
169Dic118—21no—
170Dic118C2×D412yes—
171C8×C59—21no—
172C8×C59—21no—
173C59⋊C8—21no—
174C59⋊C8C2×D412yes—
175C22×C59—22no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59C22×D411yescharacteristic
185C2×D59—21no—
186C2×D59—21no—
187C2×D59—21no—
188C2×D59—21no—
189C2×D59—21no—
190C2×D59—21no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—84no—
195C4×C59—21no—
196C4×C59—21no—
197C4×C59—41no—
198C4×C59C22×D411yescharacteristic
199C4×C59H(5,𝔽2)11yescharacteristic
200Dic59—22no—
201Dic59—21no—
202Dic59—21no—
203Dic59—41no—
204Dic59—41no—
205#3268—591nomaximal, Sylow
206C2×C59—42no—
207C2×C59—81no—
208C2×C59—81no—
209C2×C59D4211yescharacteristic
210C2×C59#57511yescharacteristic
211C2×C59#57611yescharacteristic
212D59—41no—
213D59—41no—
214D59—81no—
215C2×AGL(1,ℤ/8)—591no—
216C2×#135—591no—
217#550—591no—
218#546—591no—
219#496—591no—
220#468—591no—
221#466—591no—
222#464—591no—
223#459D5911yescharacteristic, complemented
224#452—591no—
225#449—591no—
226#449—591no—
227#447—591no—
228#440—591no—
229#435—591no—
230C59#326811yescharacteristic, complemented, Sylow
231C2×#41—591no—
232C2×#41—591no—
233C2×#41—591no—
234C22×D4—591no—
235AGL(1,ℤ/8)—1184no—
236#135—1184no—
237C2×Q16—591no—
238C2×SD16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16—591no—
242C2×D8—591no—
243C2×D8—591no—
244C2×D8C2×D5911yescharacteristic
245C2×D8C2×D5911yescharacteristic
246C2×M16—591no—
247C22×C8—591no—
248#127—1181no—
249#127C2×D5911yescharacteristic, complemented
250#124—591no—
251#123—1181no—
252C22⋊Q8—591no—
253#121—591no—
254#121—591no—
255#121—591no—
256#121—1181no—
257#121—1181no—
258#121—1181no—
259#120—1181no—
260C4×Q8—591no—
261C4×D4—591no—
262C4×D4—1181no—
263C4×D4C2×D5911yescharacteristic
264C2×C22⋊C4—1181no—
265#107—591no—
266C4⋊C8C2×D5911yescharacteristic, complemented
267#103—591no—
268#103—591no—
269#102—591no—
270#102—591no—
271#102C2×D5911yescharacteristic, complemented
272#102C2×D5911yescharacteristic, complemented
273C22⋊C8—591no—
274C22⋊C8—591no—
275#97—591no—
276C24—1181no—
277#41—1182no—
278#41—1182no—
279#41—1182no—
280#41—2361no—
281#41—2361no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8—591no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—591no—
288C2×D4—591no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—1182no—
292C2×D4—1181no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—1181no—
297C2×D4—2361no—
298C2×D4C22×D5911yescharacteristic
299C2×D4C22×D5911yescharacteristic
300C2×D4C22×D5911yescharacteristic
301C22×C4—21no—
302C22×C4—591no—
303C22×C4—591no—
304C22×C4—1181no—
305C22×C4—1181no—
306C22×C4—1181no—
307Q16—1182no—
308SD16—594no—
309SD16—1182no—
310SD16—1182no—
311SD16—2361no—
312D8—22no—
313D8—22no—
314D8—1182no—
315D8—2361no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—1182no—
320C2×C8C22×D5911yescharacteristic
321C2×C8C22×D5911yescharacteristic
322C4⋊C4—591no—
323C4⋊C4—591no—
324C4⋊C4—1181no—
325C4⋊C4—1181no—
326C4⋊C4C22×D5911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—591no—
329C22⋊C4—591no—
330C22⋊C4—1181no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4—1181no—
335C22⋊C4—1181no—
336C42—1181no—
337C42C22×D5911yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—591no—
342C23—591no—
343C23—1181no—
344C23—4721no—
345C23—2362no—
346C23—2362no—
347Q8—592no—
348Q8—1181no—
349Q8—1181no—
350Q8—1181no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—1181no—
359D4—1181no—
360D4—4721no—
361D4—4721no—
362D4—4721no—
363D4—2361no—
364D4—2362no—
365D4—2362no—
366D4—2362no—
367D4—2362no—
368D4D4×D5912yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—591no—
372C2×C4—591no—
373C2×C4—1181no—
374C2×C4—1181no—
375C2×C4—1181no—
376C2×C4—1181no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—2362no—
381C2×C4—2362no—
382C2×C4—2362no—
383C2×C4D4×D5911yescharacteristic
384C2×C4D4×D5911yescharacteristic
385C2×C4C23×D5911yescharacteristic
386C8—21no—
387C8—21no—
388C8—592no—
389C8—1181no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—1181no—
400C22—1181no—
401C22—1181no—
402C22—1181no—
403C22—1181no—
404C22—1181no—
405C22—4724no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22C2×D4×D5911yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—1181no—
414C4—1181no—
415C4—1182no—
416C4—2361no—
417C4—2361no—
418C4C2×D4×D5911yescharacteristic
419C4#1427377311yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—4721no—
424C2—2361no—
425C2—2361no—
426C2#1683803611yescharacteristic
427C2#1683819811yescharacteristic
428C2#1683820311yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3268
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14273751C2semidirect
2. C2×#14273746C2semidirect
3. #16838072C2semidirect
4. #16838047C2semidirect
5. #16837789C2semidirect
6. #16837647C2semidirect
7. #16837637C2semidirect
8. #16837625C2semidirect
9. #16837565C2semidirect
10. #16837548C2semidirect
11. #16837544C2semidirect
12. #16837534C2semidirect
13. #16837502C2semidirect
14. #16837472C2semidirect
15. C59×#459C2semidirect
18. C2×#11745687C22semidirect
22. C2×Dic236C22semidirect
25. C2×#11745670C22semidirect
26. C2×#11745670C22semidirect
30. C2×C8×D59C22semidirect
40. #14273698C22semidirect
42. C4×Dic118C22semidirect
46. #14273660C22semidirect
47. #14273652C22semidirect
48. #14273650C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. #14273638C22semidirect
56. #127×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #102×C59C22semidirect
60. #102×C59C22semidirect
103. #11745670D4semidirect
223. #459D59semidirect
230. C59#3268semidirect
249. #127C2×D59semidirect
266. C4⋊C8C2×D59semidirect
271. #102C2×D59semidirect
272. #102C2×D59semidirect