Finite Group Databasebeta

← #21436201

Subgroups — #21436201

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838061C211yesmaximal, characteristic
2#16837764C211yesmaximal, characteristic, complemented
3#16837732C211yesmaximal, characteristic, complemented
4#16837720C211yesmaximal, characteristic, complemented
5#16837684C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837624C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837557C211yesmaximal, characteristic, complemented
11#16837507C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14C2×#14273650C211yesmaximal, characteristic, complemented
15C59×#554C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273713—21no—
25#14273706C2211yescharacteristic
26#14273705—21no—
27#14273701C2211yescharacteristic
28#14273699—21no—
29C4×Dic118C2211yescharacteristic
30(C22⋊D59)⋊C4—21no—
31#14273658C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C4⋊Q8×C59C2211yescharacteristic
49#125×C59—21no—
50C22⋊Q8×C59—21no—
51C22⋊Q8×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53C22⋊Q8×C59C2211yescharacteristic
54C4×Q8×C59C2211yescharacteristic
55C4×D4×C59—21no—
56C4×D4×C59C2211yescharacteristic
57C2×C4⋊C4×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59D411yescharacteristic
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59—21no—
69#11745685—22no—
70#11745685—41no—
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×Dic118—22no—
74C2×Dic118—21no—
75C2×Dic118—41no—
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59D411yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59D411yescharacteristic
91C22⋊C4×C59D411yescharacteristic
92C42×C59—21no—
93C42×C59C2311yescharacteristic
94C22⋊Dic59—21no—
95#11745672—22no—
96#11745672—41no—
97#11745671—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—81no—
117D4×C59—22no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—81no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—42no—
134C22⋊D59—42no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—42no—
139D236—21no—
140D236—21no—
141C4×D59—42no—
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145Dic118—42no—
146Dic118#4112yes—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59#13712yes—
157C22×C59C22×D411yescharacteristic
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—22no—
172Dic59—41no—
173Dic59—41no—
174#3316—591nomaximal, Sylow
175C2×C59—22no—
176C2×C59—41no—
177C2×C59#54611yescharacteristic
178C2×C59C2×#13711yescharacteristic
179C2×C59#57711yescharacteristic
180D59—81no—
181#554D5911yescharacteristic, complemented
182#548—591no—
183#489—591no—
184#483—591no—
185#481—591no—
186#475—591no—
187#470—591no—
188#465—591no—
189#464—591no—
190#452—591no—
191#451—591no—
192#441—591no—
193#435—591no—
194#417—591no—
195C2×#103—591no—
196C59#331611yescharacteristic, complemented, Sylow
197C2×#41—591no—
198C22×Q8—591no—
199C2×Q16—591no—
200C2×Q16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8C2×D5911yescharacteristic
205#125—21no—
206#124—591no—
207#124—1181no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8C2×D5911yescharacteristic
213C22⋊Q8C2×D5911yescharacteristic
214#121—591no—
215#121—1181no—
216C4×Q8—591no—
217C4×Q8C2×D5911yescharacteristic
218C4×D4—21no—
219C4×D4—1181no—
220C4×D4C2×D5911yescharacteristic
221C2×C4⋊C4C2×D5911yescharacteristic
222C2×C4⋊C4C2×D5911yescharacteristic
223#106—591no—
224#106—591no—
225#106—591no—
226C4⋊C8—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#102—591no—
235#102—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240#41—1182no—
241#41—2361no—
242C2×Q8—21no—
243C2×Q8—591no—
244C2×Q8—591no—
245C2×Q8—1182no—
246C2×Q8—1181no—
247C2×Q8—2361no—
248C2×Q8C22×D5911yescharacteristic
249C2×D4—591no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4C22⋊D5911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4C22×D5911yescharacteristic
258C22×C4C22×D5911yescharacteristic
259Q16—1182no—
260Q16—2361no—
261SD16—2361no—
262M16—2361no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—591no—
266C2×C8—591no—
267C2×C8—2361no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—591no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4C22⋊D5911yescharacteristic
278C4⋊C4C22×D5911yescharacteristic
279C4⋊C4C22×D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4C22⋊D5911yescharacteristic
288C22⋊C4C22⋊D5911yescharacteristic
289C42—21no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—1181no—
293C23C2×C22⋊D5911yescharacteristic
294C23C2×C22⋊D5911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—592no—
299Q8—1181no—
300Q8—1181no—
301Q8—1181no—
302Q8—2362no—
303D4—22no—
304D4—1181no—
305D4—1181no—
306D4—2362no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—2362no—
322C2×C4—2362no—
323C2×C4C2×C22⋊D5911yescharacteristic
324C2×C4C2×C22⋊D5911yescharacteristic
325C2×C4C2×C22⋊D5911yescharacteristic
326C2×C4C2×C22⋊D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—1181no—
329C8—1181no—
330C8—1181no—
331C8—1181no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—2361no—
338C22—2361no—
339C22—2361no—
340C22#1427375812yes—
341C22C22×C22⋊D5911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—1182no—
351C4—2361no—
352C4—2361no—
353C4#41×D5911yescharacteristic
354C4#1427377311yescharacteristic
355C2—22no—
356C2—41no—
357C2—4721no—
358C2#1683804011yescharacteristic
359C2C2×#1427375811yescharacteristic
360C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#554C2
socleC22×C59C22×D4
hypercenter#554D59
hypocenterC59#3316
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #16837764C2semidirect
3. #16837732C2semidirect
4. #16837720C2semidirect
5. #16837684C2semidirect
6. #16837658C2semidirect
7. #16837633C2semidirect
8. #16837624C2semidirect
9. #16837562C2semidirect
10. #16837557C2semidirect
11. #16837507C2semidirect
12. #16837474C2semidirect
13. #16837401C2semidirect
14. C2×#14273650C2semidirect
15. C59×#554C2semidirect
181. #554D59semidirect
196. C59#3316semidirect