Finite Group Databasebeta

← #21436186

Subgroups — #21436186

Order 7552.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838057C211yesmaximal, characteristic
2#16837772C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837737C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837612C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837562C211yesmaximal, characteristic, complemented
11#16837500C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14#16837396C211yesmaximal, characteristic, complemented
15C59×#552C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273727C2211yescharacteristic
24#14273709—21no—
25#14273709—21no—
26#14273706C2211yescharacteristic
27#14273706C2211yescharacteristic
28#14273698—21no—
29C4×D236C2211yescharacteristic
30C4⋊C4×D59—21no—
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
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
48#126×C59—21no—
49#125×C59—21no—
50#125×C59C2211yescharacteristic
51#123×C59—21no—
52C22⋊Q8×C59C2211yescharacteristic
53C22⋊Q8×C59C2211yescharacteristic
54C4×Q8×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56#117×C59—21no—
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59D411yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66#11745685—22no—
67#11745685—22no—
68#11745685—41no—
69#11745685—41no—
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59D411yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C42×C59—21no—
92C42×C59—21no—
93C42×C59C2311yescharacteristic
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96#11745672—41no—
97#11745672—41no—
98#11745671—22no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—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—
116D4×C59—41no—
117C2×C4×C59—21no—
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—42no—
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C22⋊D59—42no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136D236—21no—
137D236#4112yes—
138C4×D59—42no—
139C4×D59—42no—
140C4×D59—42no—
141Dic118—21no—
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59C22×D411yescharacteristic
156C2×D59—22no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59H(5,𝔽2)11yescharacteristic
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3315—591nomaximal, Sylow
173C2×C59—41no—
174C2×C59—41no—
175C2×C59#54611yescharacteristic
176C2×C59#57511yescharacteristic
177C2×C59#57811yescharacteristic
178D59—42no—
179#552D5911yescharacteristic, complemented
180#547—591no—
181#491—591no—
182#485—591no—
183#484—591no—
184#478—591no—
185#470—591no—
186#467—591no—
187#462—591no—
188#452—591no—
189#452—591no—
190#440—591no—
191#435—591no—
192#417—591no—
193#416—591no—
194C59#331511yescharacteristic, complemented, Sylow
195C2×#41—591no—
196C2×#41—591no—
197C2×Q16—591no—
198C2×Q16—591no—
199C2×SD16—591no—
200C2×M16—591no—
201C22×C8—591no—
202C4⋊Q8—591no—
203#126—21no—
204#125—21no—
205#125C2×D5911yescharacteristic
206#123—21no—
207#123—1181no—
208#123—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8C2×D5911yescharacteristic
212C22⋊Q8C2×D5911yescharacteristic
213#121—1181no—
214C4×Q8C2×D5911yescharacteristic
215C4×D4—591no—
216C4×D4C2×D5911yescharacteristic
217#117—21no—
218#117C2×D5911yescharacteristic
219C2×C4⋊C4—1181no—
220C2×C4⋊C4C2×D5911yescharacteristic
221#107—591no—
222#107—591no—
223#106—591no—
224C4⋊C8—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235C22⋊C8—591no—
236C22⋊C8—591no—
237#97—591no—
238#41—1182no—
239#41—1182no—
240#41—2361no—
241#41—2361no—
242C2×Q8—591no—
243C2×Q8—591no—
244C2×Q8C22×D5911yescharacteristic
245C2×D4—591no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4C22⋊D5911yescharacteristic
249C22×C4—21no—
250C22×C4—1181no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4C22×D5911yescharacteristic
254C22×C4C22×D5911yescharacteristic
255Q16—2361no—
256Q16—2361no—
257SD16—1182no—
258M16—2361no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—591no—
262C2×C8—591no—
263C2×C8—2361no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—591no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4C22⋊D5911yescharacteristic
276C4⋊C4C22×D5911yescharacteristic
277C4⋊C4C22×D5911yescharacteristic
278C4⋊C4C22×D5911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4C22⋊D5911yescharacteristic
286C22⋊C4C22⋊D5911yescharacteristic
287C42—21no—
288C42—21no—
289C42C22×D5911yescharacteristic
290C23—1181no—
291C23C2×C22⋊D5911yescharacteristic
292C23C2×C22⋊D5911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1181no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299D4—41no—
300D4—592no—
301D4—1181no—
302D4—2362no—
303D4—2362no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—2362no—
317C2×C4—2362no—
318C2×C4—2362no—
319C2×C4C2×C22⋊D5911yescharacteristic
320C2×C4C2×C22⋊D5911yescharacteristic
321C2×C4C2×C22⋊D5911yescharacteristic
322C2×C4C2×C22⋊D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—1181no—
325C8—1181no—
326C8—1181no—
327C8—1181no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—1182no—
335C22—2361no—
336C22—2361no—
337C22C22×C22⋊D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2361no—
347C4—2361no—
348C4—2361no—
349C4#41×D5911yescharacteristic
350C4#1427377311yescharacteristic
351C2—41no—
352C2—41no—
353C2—2362no—
354C2#1683804011yescharacteristic
355C2#1683820011yescharacteristic
356C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#552C2
socleC22×C59C22×D4
hypercenter#552D59
hypocenterC59#3315
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16837772C2semidirect
3. #16837743C2semidirect
4. #16837737C2semidirect
5. #16837699C2semidirect
6. #16837658C2semidirect
7. #16837641C2semidirect
8. #16837612C2semidirect
9. #16837562C2semidirect
10. #16837562C2semidirect
11. #16837500C2semidirect
12. #16837474C2semidirect
13. #16837401C2semidirect
14. #16837396C2semidirect
15. C59×#552C2semidirect
179. #552D59semidirect
194. C59#3315semidirect