Finite Group Databasebeta

← #21433451

Subgroups — #21433451

Order 7552.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273773C211yesmaximal, characteristic, complemented
2#16838200C211yesmaximal, characteristic, complemented
3#16837966C211yesmaximal, characteristic, complemented
4#16837578C214yesmaximal, complemented
5#16837568C214yesmaximal, complemented
6#16837419C211yesmaximal, characteristic, complemented
7#16837418C211yesmaximal, characteristic, complemented
8C2×#14273643C211yesmaximal, characteristic, complemented
9C59×#575C211yesmaximal, characteristic, complemented
10#14273773—22no—
11#14273773—22no—
12#14273773—22no—
13#14273773C2214yes—
14C2×#11745689—21no—
15C2×#11745685—21no—
16C2×#11745685C2211yescharacteristic
17C22×D236—21no—
18C22×D236C2211yescharacteristic
19C2×D4×D59—22no—
20C2×D4×D59—21no—
21#14273758C2212yescomplemented
22#14273757—21no—
23#14273753C2212yescomplemented
24#14273752—21no—
25#14273747—22no—
26C2×#11745664C2211yescharacteristic, complemented
27#14273723C2212yescomplemented
28#14273716C2212yescomplemented
29#14273701—22no—
30#14273695—22no—
31#14273686C2211yescharacteristic, complemented
32#14273654C2214yescomplemented
33#14273653C2214yescomplemented
34#14273643C2214yescomplemented
35C2×#41×C59C2211yescharacteristic
36C2×#41×C59C2211yescharacteristic, complemented
37#137×C59—21no—
38#137×C59C2212yescomplemented
39AGL(1,ℤ/8)×C59—21no—
40AGL(1,ℤ/8)×C59C2212yescomplemented
41#135×C59—22no—
42C2×M16×C59C2211yescharacteristic, complemented
43C23×D59—22no—
44C23×D59D412yes—
45#41×C59—21no—
46#41×C59—21no—
47#41×C59—21no—
48#41×C59—21no—
49#41×C59—21no—
50#41×C59—21no—
51#41×C59D412yescomplemented
52#41×C59C2312yes—
53C2×Q8×C59D411yescharacteristic, complemented
54C2×Q8×C59C2311yescharacteristic, complemented
55C2×D4×C59—21no—
56C2×D4×C59—21no—
57C2×D4×C59D411yescharacteristic, complemented
58C2×D4×C59C2311yescharacteristic, complemented
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—22no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—24no—
65#11745689—24no—
66#11745689—24no—
67D4×D59—28no—
68D4×D59—24no—
69D4×D59—28no—
70D4×D59—24no—
71#11745685—24no—
72#11745685—21no—
73#11745685—21no—
74#11745685—24no—
75#11745685D412yescomplemented
76#11745685C2312yes—
77C2×D236—22no—
78C2×D236—24no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236—21no—
82C2×D236—21no—
83C2×D236—24no—
84C2×D236D412yes—
85C2×D236D411yescharacteristic, complemented
86C2×D236C2312yes—
87C2×C4×D59—22no—
88C2×C4×D59—21no—
89C2×Dic118D411yescharacteristic, complemented
90Q16×C59—22no—
91SD16×C59—22no—
92SD16×C59—22no—
93D8×C59—22no—
94M16×C59—21no—
95M16×C59C2312yescomplemented
96C2×C8×C59—21no—
97C22⋊Dic59—21no—
98#11745672—22no—
99#11745671—22no—
100#11745670—22no—
101#11745669—22no—
102(C2×D59)⋊C4—24no—
103C4⋊Dic59—21no—
104C4×Dic59C2312yescomplemented
105#11745664—21no—
106#11745664C2312yescomplemented
107C2×C59⋊C8—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59C2×D411yescharacteristic
111C22×D59—22no—
112C22×D59—21no—
113C22×D59—28no—
114C22×D59—22no—
115C22×D59—82no—
116C22×D59—84no—
117C22×D59C2×D414yes—
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59C2×D412yes—
122D4×C59—22no—
123D4×C59—22no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—41no—
128D4×C59—41no—
129D4×C59C2×D412yes—
130C2×C4×C59—21no—
131C2×C4×C59—22no—
132C2×C4×C59—22no—
133C2×C4×C59—21no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2411yescharacteristic
142C22⋊D59—28no—
143C22⋊D59—22no—
144C22⋊D59—22no—
145C22⋊D59—84no—
146C2×Dic59—21no—
147C2×Dic59—22no—
148D236—28no—
149D236—22no—
150D236—21no—
151D236—22no—
152D236—22no—
153D236—22no—
154D236C2×D412yes—
155C4×D59—28no—
156C4×D59—22no—
157C4×D59—22no—
158Dic118—21no—
159Dic118C2×D412yes—
160C8×C59—22no—
161C59⋊C8—22no—
162C22×C59—22no—
163C22×C59—41no—
164C22×C59—42no—
165C22×C59—42no—
166C22×C59—41no—
167C22×C59#12011yescharacteristic
168C22×C59#12011yescharacteristic
169C22×C59C22×D411yescharacteristic
170C2×D59—24no—
171C2×D59—22no—
172C2×D59—44no—
173C2×D59—42no—
174C2×D59—44no—
175C2×D59—82no—
176C2×D59—88no—
177C4×C59—22no—
178C4×C59—41no—
179C4×C59#12011yescharacteristic
180C4×C59#12011yescharacteristic
181C4×C59C22×D411yescharacteristic
182C4×C59C22×D411yescharacteristic
183Dic59—22no—
184Dic59—42no—
185#3019—591nomaximal, Sylow
186C2×C59—21no—
187C2×C59—21no—
188C2×C59—21no—
189C2×C59—42no—
190C2×C59—81no—
191C2×C59C2×#12011yescharacteristic
192D59—44no—
193D59—42no—
194C2×H(5,𝔽2)—591no—
195#575—591no—
196#575D5911yescharacteristic, complemented
197#535—591no—
198#455—594no—
199#453—594no—
200#421—591no—
201#421—591no—
202C2×#100—591no—
203C59#301911yescharacteristic, complemented, Sylow
204H(5,𝔽2)—594no—
205H(5,𝔽2)—1182no—
206H(5,𝔽2)—1182no—
207H(5,𝔽2)—1182no—
208C2×#41—591no—
209C2×#41—1181no—
210C2×#41—1181no—
211C2×#41C2×D5911yescharacteristic
212C2×#41C2×D5911yescharacteristic, complemented
213C22×D4—591no—
214C22×D4—1181no—
215C22×D4—1182no—
216C22×D4—1181no—
217#137—21no—
218#137—592no—
219#137—1181no—
220#137C2×D5912yescomplemented
221AGL(1,ℤ/8)—21no—
222AGL(1,ℤ/8)—592no—
223AGL(1,ℤ/8)—1181no—
224AGL(1,ℤ/8)C2×D5912yescomplemented
225#135—22no—
226#135—1182no—
227C2×M16—591no—
228C2×M16C2×D5911yescharacteristic, complemented
229#127—592no—
230#124—592no—
231#121—1182no—
232#120—1182no—
233#117—591no—
234#104—594no—
235#104—594no—
236#100—594no—
237C24—592no—
238C24—1182no—
239#41—21no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—592no—
246#41—592no—
247#41—1184no—
248#41—1184no—
249#41—1184no—
250#41—1184no—
251#41—1181no—
252#41—1181no—
253#41C22⋊D5912yescomplemented
254#41C22×D5912yes—
255C2×Q8—591no—
256C2×Q8C22⋊D5911yescharacteristic, complemented
257C2×Q8C22×D5911yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—591no—
261C2×D4—592no—
262C2×D4—592no—
263C2×D4—1184no—
264C2×D4—1182no—
265C2×D4—1184no—
266C2×D4—1188no—
267C2×D4—1188no—
268C2×D4—1184no—
269C2×D4—1182no—
270C2×D4—1181no—
271C2×D4—1184no—
272C2×D4—1184no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4C22⋊D5911yescharacteristic, complemented
278C2×D4C22×D5911yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—1182no—
282C22×C4—1181no—
283C22×C4C22×D5911yescharacteristic
284Q16—22no—
285Q16—1182no—
286SD16—22no—
287SD16—22no—
288SD16—1182no—
289SD16—1182no—
290D8—22no—
291D8—1182no—
292M16—21no—
293M16—592no—
294M16—1181no—
295M16C22×D5912yescomplemented
296C2×C8—21no—
297C2×C8—1181no—
298C4⋊C4—1181no—
299C22⋊C4—1184no—
300C22⋊C4—1181no—
301C42—592no—
302C23—21no—
303C23—21no—
304C23—594no—
305C23—1188no—
306C23—1182no—
307C23—1181no—
308C23—1182no—
309C23—4724no—
310C23—4722no—
311C23D4×D5911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—592no—
316Q8—1181no—
317Q8C2×C22⋊D5912yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—592no—
326D4—1188no—
327D4—1188no—
328D4—1182no—
329D4—1182no—
330D4—1181no—
331D4—1182no—
332D4—1182no—
333D4—1182no—
334D4—1182no—
335D4—4724no—
336D4C2×C22⋊D5912yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—1188no—
344C2×C4—1181no—
345C2×C4—1182no—
346C2×C4—1182no—
347C2×C4—1182no—
348C2×C4D4×D5911yescharacteristic
349C2×C4D4×D5911yescharacteristic
350C2×C4D4×D5911yescharacteristic
351C2×C4C2×C22⋊D5911yescharacteristic
352C2×C4C2×C22⋊D5911yescharacteristic
353C2×C4C23×D5911yescharacteristic
354C8—22no—
355C8—1182no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—1182no—
362C22—1184no—
363C22—4722no—
364C22—4728no—
365C22—2364no—
366C22—2362no—
367C22—2364no—
368C22#1427369511yescharacteristic
369C22#1427369511yescharacteristic
370C22C2×D4×D5911yescharacteristic
371C4—22no—
372C4—41no—
373C4—1182no—
374C4—2362no—
375C4#1427369511yescharacteristic
376C4#1427369511yescharacteristic
377C4C2×D4×D5911yescharacteristic
378C4C22×C22⋊D5911yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—81no—
384C2—2362no—
385C2—2364no—
386C2C2×#1427369511yescharacteristic
subgroupG/H
centerC2C2×#14273695
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#575C2
socleC2×C59C2×#120
hypercenter#575D59
hypocenterC59#3019
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#14273773C2semidirect
2. #16838200C2semidirect
3. #16837966C2semidirect
4. #16837578C2semidirect
5. #16837568C2semidirect
6. #16837419C2semidirect
7. #16837418C2semidirect
8. C2×#14273643C2semidirect
9. C59×#575C2semidirect
21. #14273758C22semidirect
23. #14273753C22semidirect
26. C2×#11745664C22semidirect
27. #14273723C22semidirect
28. #14273716C22semidirect
31. #14273686C22semidirect
32. #14273654C22semidirect
33. #14273653C22semidirect
34. #14273643C22semidirect
36. C2×#41×C59C22semidirect
38. #137×C59C22semidirect
40. AGL(1,ℤ/8)×C59C22semidirect
42. C2×M16×C59C22semidirect
51. #41×C59D4semidirect
53. C2×Q8×C59D4semidirect
54. C2×Q8×C59C23semidirect
57. C2×D4×C59D4semidirect
58. C2×D4×C59C23semidirect
75. #11745685D4semidirect
85. C2×D236D4semidirect
89. C2×Dic118D4semidirect
95. M16×C59C23semidirect
104. C4×Dic59C23semidirect
106. #11745664C23semidirect
196. #575D59semidirect
203. C59#3019semidirect
212. C2×#41C2×D59semidirect
220. #137C2×D59semidirect
224. AGL(1,ℤ/8)C2×D59semidirect
228. C2×M16C2×D59semidirect
253. #41C22⋊D59semidirect
256. C2×Q8C22⋊D59semidirect
257. C2×Q8C22×D59semidirect
277. C2×D4C22⋊D59semidirect
278. C2×D4C22×D59semidirect
295. M16C22×D59semidirect