Finite Group Databasebeta

← #21436438

Subgroups — #21436438

Order 7552.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838053C211yesmaximal, characteristic, complemented
2#16838052C211yesmaximal, characteristic, complemented
3#16837806C211yesmaximal, characteristic, complemented
4#16837717C211yesmaximal, characteristic, complemented
5#16837716C211yesmaximal, characteristic, complemented
6#16837714C211yesmaximal, characteristic, complemented
7#16837681C211yesmaximal, characteristic, complemented
8#16837680C211yesmaximal, characteristic, complemented
9#16837637C211yesmaximal, characteristic, complemented
10#16837636C211yesmaximal, characteristic, complemented
11#16837482C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14273660C211yesmaximal, characteristic, complemented
14#107×D59C211yesmaximal, characteristic, complemented
15C59×#480C211yesmaximal, characteristic, complemented
16C2×#11745685—21no—
17C2×#11745687—21no—
18C2×#11745669C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273726C2211yescharacteristic
22#14273726C2211yescharacteristic
23#14273712—21no—
24#14273710—21no—
25#14273709—21no—
26#14273708—21no—
27#14273705—21no—
28#14273704—21no—
29#14273702C2211yescharacteristic
30#14273701C2211yescharacteristic
31#14273698C2211yescharacteristic
32D4×Dic59C2211yescharacteristic
33#14273689C2211yescharacteristic
34C4×C22⋊D59C2211yescharacteristic
35C2×C4⋊Dic59C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273660C2211yescharacteristic
42#14273660C2211yescharacteristic
43#14273660C2211yescharacteristic
44#14273660C2211yescharacteristic
45Dic59⋊C8C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52#121×C59C2211yescharacteristic
53C2×C4⋊C4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59D411yescharacteristic
66C22×Dic59—21no—
67C22×Dic59—21no—
68#11745687—44no—
69#11745685—44no—
70C2×D236—21no—
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×Dic118—21no—
77C2×Dic118—21no—
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59D411yescharacteristic
88#11745669—22no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4D411yescharacteristic
102C4×Dic59C2311yescharacteristic
103C2×C59⋊C8—22no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C8×D59—22no—
107C23×C59—21no—
108C23×C59C2×D411yescharacteristic
109C22×D59—21no—
110C22×D59C2×D411yescharacteristic
111D4×C59—21no—
112D4×C59—21no—
113D4×C59—42no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—42no—
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2411yescharacteristic
122C22⋊D59—42no—
123C22⋊D59—42no—
124C22⋊D59D814yescomplemented
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—42no—
129C2×Dic59—42no—
130C2×Dic59C2×D411yescharacteristic
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133D236—21no—
134D236—21no—
135D236—42no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—42no—
139C4×D59—42no—
140C4×D59—42no—
141Dic118—42no—
142Dic118—42no—
143C8×C59—21no—
144C8×C59—21no—
145C59⋊C8—21no—
146C59⋊C8#4112yescomplemented
147C22×C59—21no—
148C22×C59—21no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59C2×D812yes—
153C22×C59C22×D411yescharacteristic
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59C2×D812yes—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59C2×#4111yescharacteristic
165C4×C592−1+411yescharacteristic
166Dic59—21no—
167Dic59—21no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171Dic59C2×D812yes—
172#3334—591nomaximal, Sylow
173C2×C59—22no—
174C2×C59—81no—
175C2×C59#54711yescharacteristic
176C2×C59C22×D811yescharacteristic
177C2×C59#57811yescharacteristic
178D59—22no—
179D59—81no—
180#547—591no—
181#547—591no—
182#500—591no—
183#480—591no—
184#480—591no—
185#480—591no—
186#480D5911yescharacteristic, complemented
187#474—591no—
188#474—591no—
189#466—591no—
190#466—591no—
191C4×D8—591no—
192C8×D4—591no—
193C2×#107—591no—
194C2×#107—591no—
195C59#333411yescharacteristic, complemented, Sylow
196C2×#41—1181no—
197C2×#41—1181no—
198C2×D8—591no—
199C22×C8—591no—
200C22×C8—591no—
201C4⋊Q8—591no—
202C4⋊Q8—591no—
203#123—1181no—
204#123—1181no—
205#123—1181no—
206#123—1181no—
207C22⋊Q8—1181no—
208C22⋊Q8—1181no—
209#121—591no—
210#121—591no—
211#121—591no—
212#121C2×D5911yescharacteristic
213C4×D4—591no—
214C4×D4—591no—
215C4×D4—591no—
216C2×C4⋊C4—591no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4C2×D5911yescharacteristic
220#107—591no—
221#107—591no—
222#107—591no—
223#107—591no—
224#107—591no—
225#107—591no—
226#107—591no—
227#107C2×D5911yescharacteristic
228#107C2×D5911yescharacteristic
229C4⋊C8—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#102C2×D5911yescharacteristic
235#102C2×D5911yescharacteristic
236C22⋊C8—591no—
237C22⋊C8C2×D5911yescharacteristic
238C4×C8—591no—
239#41—2364no—
240#41—2364no—
241C2×Q8—1181no—
242C2×Q8—1181no—
243C2×D4—21no—
244C2×D4—591no—
245C2×D4—591no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4—1181no—
249C2×D4C22×D5911yescharacteristic
250C22×C4—21no—
251C22×C4—591no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4C22×D5911yescharacteristic
258D8—1182no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—1182no—
262C2×C8—1182no—
263C2×C8C22×D5911yescharacteristic
264C2×C8C22×D5911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
269C4⋊C4—591no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4C22×D5911yescharacteristic
276C4⋊C4C22×D5911yescharacteristic
277C4⋊C4C22×D5911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—591no—
280C22⋊C4—591no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C42—591no—
287C23—21no—
288C23—591no—
289C23—1181no—
290C23D4×D5911yescharacteristic
291Q8—2362no—
292Q8—2362no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—594no—
297D4—1181no—
298D4—1181no—
299D4—2362no—
300D4—2362no—
301D4—2362no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—591no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—2362no—
317C2×C4—2362no—
318C2×C4—2362no—
319C2×C4—2362no—
320C2×C4—2362no—
321C2×C4D4×D5911yescharacteristic
322C2×C4C23×D5911yescharacteristic
323C8—21no—
324C8—21no—
325C8—592no—
326C8—1181no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—592no—
333C22—1181no—
334C22—1181no—
335C22—2361no—
336C22—2361no—
337C22—2361no—
338C22D8×D5912yes—
339C22C2×D4×D5911yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—592no—
345C4—1181no—
346C4—1181no—
347C4—2361no—
348C4—2361no—
349C4—2361no—
350C4#41×D5911yescharacteristic
351C4#1427377411yescharacteristic
352C2—22no—
353C2—81no—
354C2—1182no—
355C2—4721no—
356C2#1683805011yescharacteristic
357C2C2×D8×D5911yescharacteristic
358C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#480C2
socleC22×C59C22×D4
hypercenter#480D59
hypocenterC59#3334
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #16838053C2semidirect
2. #16838052C2semidirect
3. #16837806C2semidirect
4. #16837717C2semidirect
5. #16837716C2semidirect
6. #16837714C2semidirect
7. #16837681C2semidirect
8. #16837680C2semidirect
9. #16837637C2semidirect
10. #16837636C2semidirect
11. #16837482C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. C2×#14273660C2semidirect
14. #107×D59C2semidirect
15. C59×#480C2semidirect
124. C22⋊D59D8semidirect
146. C59⋊C8#41semidirect
186. #480D59semidirect
195. C59#3334semidirect