Finite Group Databasebeta

← #21435638

Subgroups — #21435638

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×#14273754C211yesmaximal, characteristic, complemented
2C2×#14273748C211yesmaximal, characteristic, complemented
3#16838074C211yesmaximal, characteristic, complemented
4#16838047C211yesmaximal, characteristic, complemented
5#16837791C211yesmaximal, characteristic, complemented
6#16837649C211yesmaximal, characteristic, complemented
7#16837639C211yesmaximal, characteristic, complemented
8#16837624C211yesmaximal, characteristic, complemented
9#16837597C211yesmaximal, characteristic, complemented
10#16837567C211yesmaximal, characteristic, complemented
11#16837550C211yesmaximal, characteristic, complemented
12#16837548C211yesmaximal, characteristic, complemented
13#16837537C211yesmaximal, characteristic, complemented
14#16837475C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745689C2211yescharacteristic, complemented
18C2×#11745687C2211yescharacteristic
19C2×D4×D59C2211yescharacteristic
20#14273754—24no—
21#14273748—24no—
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745660C2211yescharacteristic, complemented
24C2×#11745660C2211yescharacteristic, complemented
25C2×#11745671C2211yescharacteristic
26C2×D472C2211yescharacteristic
27C2×D472C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745669C2211yescharacteristic
30C2×#11745659C2211yescharacteristic
31C2×C8×D59C2211yescharacteristic, complemented
32#14273724—21no—
33#14273724C2211yescharacteristic, complemented
34#14273715C2211yescharacteristic
35#14273711—21no—
36#14273707C2211yescharacteristic
37#14273702—21no—
38#14273702—21no—
39#14273702C2211yescharacteristic
40#14273702C2211yescharacteristic
41#14273702C2211yescharacteristic, complemented
42#14273701—21no—
43#14273697—21no—
44C4×D236—21no—
45C4×D236C2211yescharacteristic
46C2×(C2×D59)⋊C4—21no—
47C4⋊(C59⋊C8)C2211yescharacteristic, complemented
48#14273650C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic
50#14273647C2211yescharacteristic, complemented
51#14273647C2211yescharacteristic, complemented
52(C2×D59)⋊C8C2211yescharacteristic
53(C2×D59)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic
55C4×Q8×C59C2211yescharacteristic, complemented
56C4×D4×C59C2211yescharacteristic
57#107×C59C2211yescharacteristic, complemented
58#103×C59C2211yescharacteristic, complemented
59#102×C59C2211yescharacteristic
60#97×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68#11745689—22no—
69#11745689—22no—
70#11745689—41no—
71#11745689—41no—
72#11745687—22no—
73#11745687—41no—
74D4×D59—22no—
75D4×D59—41no—
76C2×D236—21no—
77C2×D236—21no—
78C2×D236—21no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236—21no—
82C2×D236—21no—
83C2×D236D411yescharacteristic
84C2×D236C2311yescharacteristic
85C2×D236C2311yescharacteristic
86C2×D236C2311yescharacteristic
87C2×C4×D59—21no—
88C2×C4×D59—21no—
89C2×C4×D59C2311yescharacteristic
90C2×C4×D59C2311yescharacteristic
91C2×Dic118C2311yescharacteristic
92SD16×C59D414yescomplemented
93C2×C8×C59C2311yescharacteristic
94C2×C8×C59C2311yescharacteristic
95C4⋊C4×C59—21no—
96C4⋊C4×C59C2311yescharacteristic
97C4⋊C4×C59C2311yescharacteristic
98C22⋊C4×C59—21no—
99C42×C59—21no—
100C42×C59C2311yescharacteristic
101#11745672—22no—
102#11745671—22no—
103#11745669—22no—
104#11745669—22no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4—21no—
109(C2×D59)⋊C4—21no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4D411yescharacteristic
112(C2×D59)⋊C4D411yescharacteristic
113C4⋊Dic59—21no—
114C4⋊Dic59D411yescharacteristic
115C2×C59⋊C8C2311yescharacteristic
116C2×C59⋊C8C2311yescharacteristic
117D472—22no—
118D472—41no—
119#11745660—22no—
120#11745660—41no—
121#11745659—22no—
122C8×D59—22no—
123C23×C59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—42no—
128C22×D59—42no—
129C22×D59—81no—
130C22×D59C2×D411yescharacteristic
131C22×D59C2×D411yescharacteristic
132Q8×C59—21no—
133Q8×C59C2×D412yes—
134D4×C59—21no—
135D4×C59C2×D412yes—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—81no—
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2411yescharacteristic
143C22⋊D59—42no—
144C22⋊D59—42no—
145C2×Dic59—21no—
146C2×Dic59—42no—
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149D236—21no—
150D236—21no—
151D236—21no—
152D236—21no—
153D236—21no—
154D236—21no—
155D236—41no—
156D236—42no—
157D236—42no—
158D236—42no—
159D236—81no—
160D236—81no—
161D236—81no—
162D236—81no—
163C4×D59—21no—
164C4×D59—21no—
165C4×D59—21no—
166C4×D59—21no—
167C4×D59—42no—
168C4×D59—42no—
169Dic118—21no—
170Dic118—21no—
171C8×C59—21no—
172C8×C59C2×D412yes—
173C59⋊C8—21no—
174C59⋊C8—21no—
175C22×C59—22no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59C22×D411yescharacteristic
179C2×D59—21no—
180C2×D59—21no—
181C2×D59—21no—
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—21no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—41no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—84no—
195C4×C59—22no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—41no—
199C4×C59—41no—
200C4×C59C22×D411yescharacteristic
201C4×C59H(5,𝔽2)11yescharacteristic
202Dic59—21no—
203Dic59—21no—
204Dic59—41no—
205#3268—591nomaximal, Sylow
206C2×C59—42no—
207C2×C59D4211yescharacteristic
208C2×C59#57511yescharacteristic
209C2×C59#57611yescharacteristic
210D59—41no—
211D59—41no—
212D59—81no—
213D59—81no—
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#459—591no—
224#452—591no—
225#449—591no—
226#449—591no—
227#447—591no—
228#440D5911yescharacteristic, complemented
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×SD16C2×D5911yescharacteristic
242C2×D8—591no—
243C2×D8—591no—
244C2×D8—591no—
245C2×D8—591no—
246C2×M16—591no—
247C22×C8—591no—
248#127—591no—
249#127—1181no—
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×Q8C2×D5911yescharacteristic, complemented
261C4×D4—591no—
262C4×D4—1181no—
263C4×D4C2×D5911yescharacteristic
264C2×C22⋊C4—1181no—
265#107C2×D5911yescharacteristic, complemented
266C4⋊C8—591no—
267#103—591no—
268#103C2×D5911yescharacteristic, complemented
269#102—591no—
270#102—591no—
271#102—591no—
272#102C2×D5911yescharacteristic
273C22⋊C8—591no—
274C22⋊C8—591no—
275#97C2×D5911yescharacteristic, complemented
276C24—1181no—
277#41—1182no—
278#41—1182no—
279#41—1182no—
280#41—2361no—
281#41—2361no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—591no—
286C2×D4—591no—
287C2×D4—591no—
288C2×D4—591no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—1181no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1182no—
296C2×D4—1181no—
297C2×D4—1181no—
298C2×D4—1181no—
299C2×D4—2361no—
300C2×D4C22×D5911yescharacteristic
301C22×C4—21no—
302C22×C4—591no—
303C22×C4—591no—
304C22×C4—1181no—
305C22×C4—1181no—
306C22×C4—1181no—
307Q16—1182no—
308SD16—1182no—
309SD16—1182no—
310SD16—2361no—
311SD16D23614yescomplemented
312D8—1182no—
313D8—1182no—
314D8—1182no—
315D8—2361no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—1182no—
320C2×C8C22×D5911yescharacteristic
321C2×C8C22×D5911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—591no—
324C4⋊C4—1181no—
325C4⋊C4C22×D5911yescharacteristic
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—21no—
337C42C22×D5911yescharacteristic
338C23—21no—
339C23—591no—
340C23—591no—
341C23—1181no—
342C23—1181no—
343C23—1181no—
344C23—4721no—
345C23—2362no—
346C23—2362no—
347Q8—21no—
348Q8—1181no—
349Q8—1181no—
350Q8C2×D23612yes—
351D4—21no—
352D4—1181no—
353D4—1181no—
354D4—1181no—
355D4—1181no—
356D4—1181no—
357D4—1181no—
358D4—4721no—
359D4—4721no—
360D4—4721no—
361D4—4721no—
362D4—2361no—
363D4—2362no—
364D4—2362no—
365D4—2362no—
366D4—2362no—
367D4—2362no—
368D4C2×D23612yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—591no—
374C2×C4—591no—
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—1181no—
388C8—1181no—
389C8C2×D23612yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—1181no—
394C22—1181no—
395C22—1181no—
396C22—1181no—
397C22—1181no—
398C22—1181no—
399C22—4724no—
400C22—2361no—
401C22—2361no—
402C22—2361no—
403C22—2361no—
404C22—2361no—
405C22—2361no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22C2×D4×D5911yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—1181no—
416C4—1181no—
417C4—2361no—
418C4C22×D23611yescharacteristic
419C4#1427377311yescharacteristic
420C2—42no—
421C2—4721no—
422C2—4721no—
423C2—4721no—
424C2—2361no—
425C2—2361no—
426C2D4×D23611yescharacteristic
427C2#1683820111yescharacteristic
428C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3268
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#14273754C2semidirect
2. C2×#14273748C2semidirect
3. #16838074C2semidirect
4. #16838047C2semidirect
5. #16837791C2semidirect
6. #16837649C2semidirect
7. #16837639C2semidirect
8. #16837624C2semidirect
9. #16837597C2semidirect
10. #16837567C2semidirect
11. #16837550C2semidirect
12. #16837548C2semidirect
13. #16837537C2semidirect
14. #16837475C2semidirect
15. C59×#440C2semidirect
17. C2×#11745689C22semidirect
22. C2×#11745672C22semidirect
23. C2×#11745660C22semidirect
24. C2×#11745660C22semidirect
31. C2×C8×D59C22semidirect
33. #14273724C22semidirect
41. #14273702C22semidirect
47. C4⋊(C59⋊C8)C22semidirect
48. #14273650C22semidirect
50. #14273647C22semidirect
51. #14273647C22semidirect
53. (C2×D59)⋊C8C22semidirect
55. C4×Q8×C59C22semidirect
57. #107×C59C22semidirect
58. #103×C59C22semidirect
60. #97×C59C22semidirect
92. SD16×C59D4semidirect
228. #440D59semidirect
230. C59#3268semidirect
260. C4×Q8C2×D59semidirect
265. #107C2×D59semidirect
268. #103C2×D59semidirect
275. #97C2×D59semidirect
311. SD16D236semidirect