Finite Group Databasebeta

← #21434989

Subgroups — #21434989

Order 7552.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837976C211yesmaximal, characteristic
2#16837975C211yesmaximal, characteristic
3#16837744C211yesmaximal, characteristic, complemented
4#16837742C211yesmaximal, characteristic, complemented
5#16837741C211yesmaximal, characteristic, complemented
6#16837740C211yesmaximal, characteristic, complemented
7#16837659C211yesmaximal, characteristic, complemented
8#16837657C211yesmaximal, characteristic, complemented
9#16837642C211yesmaximal, characteristic, complemented
10#16837640C211yesmaximal, characteristic, complemented
11#16837558C211yesmaximal, characteristic, complemented
12#16837556C211yesmaximal, characteristic, complemented
13#16837556C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic
15C59×#451C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273726—21no—
23#14273725—21no—
24#14273716—21no—
25#14273713—21no—
26#14273712—21no—
27#14273710—21no—
28#14273710—21no—
29#14273709—21no—
30#14273707C2211yescharacteristic
31#14273706C2211yescharacteristic
32#14273703C2211yescharacteristic
33#14273703C2211yescharacteristic
34#14273703C2211yescharacteristic
35#14273703C2211yescharacteristic
36#14273703C2211yescharacteristic
37#14273686C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273658C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273651C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic
54C2×Q16×C59C2211yescharacteristic
55C22⋊Q8×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—41no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×Q8×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59D411yescharacteristic
68C2×C22⋊D59D411yescharacteristic
69Q8×D59—41no—
70Q8×D59—41no—
71#11745685—41no—
72#11745685—41no—
73C2×D236D411yescharacteristic
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118D411yescharacteristic
79C2×Dic118C2311yescharacteristic
80Q16×C59—41no—
81Q16×C59—41no—
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C4⋊C4×C59—21no—
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89#11745672—41no—
90#11745672—41no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108C4×Dic59—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113C8×D59—41no—
114C23×C59C2×D411yescharacteristic
115C22×D59C2×D411yescharacteristic
116C22×D59C2×D411yescharacteristic
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—42no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C22⋊D59—41no—
134C22⋊D59—41no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59C2×D411yescharacteristic
140C2×Dic59C2×D411yescharacteristic
141D236—41no—
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—42no—
147Dic118—21no—
148Dic118—21no—
149Dic118—41no—
150Dic118—42no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59C22×D411yescharacteristic
159C2×D59—21no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C4×C59—21no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59H(5,𝔽2)11yescharacteristic
171C4×C59H(5,𝔽2)11yescharacteristic
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177Dic59—41no—
178#3202—591nomaximal, Sylow
179C2×C59—41no—
180C2×C59#53411yescharacteristic
181C2×C59#57811yescharacteristic
182C2×C59#57811yescharacteristic
183D59—41no—
184D59—41no—
185#536—591no—
186#536—591no—
187#485—591no—
188#485—591no—
189#485—591no—
190#485—591no—
191#470—591no—
192#470—591no—
193#467—591no—
194#467—591no—
195#451—591no—
196#451—591no—
197#451—591no—
198#451D5911yescharacteristic, complemented
199#408—591no—
200C59#320211yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C22×Q8—591no—
203C22×Q8C2×D5911yescharacteristic
204C2×Q16—591no—
205C2×Q16—591no—
206C2×Q16C2×D5911yescharacteristic
207C2×Q16C2×D5911yescharacteristic
208C2×M16—591no—
209C22×C8—591no—
210C4⋊Q8—1181no—
211C4⋊Q8—1181no—
212#124—1181no—
213#124—1181no—
214#123—1181no—
215#123—1181no—
216#123—1181no—
217#123—1181no—
218C22⋊Q8—591no—
219C22⋊Q8—591no—
220C22⋊Q8—591no—
221C22⋊Q8—591no—
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8C2×D5911yescharacteristic
226#117—591no—
227#117—591no—
228#107—591no—
229#107—591no—
230#106—591no—
231#106—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#103—591no—
238#103C2×D5911yescharacteristic
239#103C2×D5911yescharacteristic
240C22⋊C8—591no—
241C22⋊C8—591no—
242C22⋊C8—591no—
243C22⋊C8C2×D5911yescharacteristic
244#41—2361no—
245#41—2361no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—591no—
250C2×Q8—591no—
251C2×Q8—1181no—
252C2×Q8—2361no—
253C2×Q8—2361no—
254C2×Q8C22×D5911yescharacteristic
255C2×Q8C22×D5911yescharacteristic
256C2×Q8C22×D5911yescharacteristic
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—591no—
260C22×C4—21no—
261C22×C4—591no—
262C22×C4—591no—
263C22×C4—1181no—
264C22×C4C22×D5911yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—2361no—
268Q16—2361no—
269M16—2361no—
270C2×C8—591no—
271C2×C8—591no—
272C2×C8—2361no—
273C2×C8C22×D5911yescharacteristic
274C2×C8C22×D5911yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—591no—
277C4⋊C4—591no—
278C4⋊C4—591no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4C22×D5911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C42—1181no—
298C42—1181no—
299C23—591no—
300C23—591no—
301C23D4×D5911yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—1181no—
310Q8—1181no—
311Q8—2361no—
312Q8—2362no—
313D4—2361no—
314D4—2361no—
315D4—2361no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—2362no—
334C2×C4D4×D5911yescharacteristic
335C2×C4C23×D5911yescharacteristic
336C8—21no—
337C8—21no—
338C8—1181no—
339C8—1181no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—1181no—
347C22—1181no—
348C22—1181no—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1181no—
356C4—1181no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4—2361no—
361C4#1427377211yescharacteristic
362C4#1427377211yescharacteristic
363C2—41no—
364C2—2361no—
365C2—2361no—
366C2#1683796211yescharacteristic
367C2#1683821511yescharacteristic
368C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#451C2
socleC22×C59C22×D4
hypercenter#451D59
hypocenterC59#3202
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #16837744C2semidirect
4. #16837742C2semidirect
5. #16837741C2semidirect
6. #16837740C2semidirect
7. #16837659C2semidirect
8. #16837657C2semidirect
9. #16837642C2semidirect
10. #16837640C2semidirect
11. #16837558C2semidirect
12. #16837556C2semidirect
13. #16837556C2semidirect
15. C59×#451C2semidirect
198. #451D59semidirect
200. C59#3202semidirect