Finite Group Databasebeta

← #21435199

Subgroups — #21435199

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837978C211yesmaximal, characteristic, complemented
2#16837797C211yesmaximal, characteristic, complemented
3#16837784C211yesmaximal, characteristic, complemented
4#16837764C211yesmaximal, characteristic, complemented
5#16837754C211yesmaximal, characteristic, complemented
6#16837624C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837612C211yesmaximal, characteristic, complemented
9#16837607C211yesmaximal, characteristic, complemented
10#16837562C211yesmaximal, characteristic, complemented
11#16837557C211yesmaximal, characteristic, complemented
12#16837545C211yesmaximal, characteristic
13#16837540C211yesmaximal, characteristic, complemented
14#16837463C211yesmaximal, characteristic, complemented
15C59×#542C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745672C2211yescharacteristic
21C2×#11745670C2211yescharacteristic
22C2×#11745670C2211yescharacteristic
23C2×#11745670C2211yescharacteristic
24C2×#11745671C2211yescharacteristic
25C2×#11745669C2211yescharacteristic
26#14273727C2211yescharacteristic
27#14273727C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273715C2211yescharacteristic
30#14273711—21no—
31#14273711—21no—
32#14273707—21no—
33#14273707—21no—
34C4⋊(C59⋊C8)C2211yescharacteristic
35C4⋊(C59⋊C8)C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273647C2211yescharacteristic
43#14273647C2211yescharacteristic
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46#14273638C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48C4⋊Q8×C59C2211yescharacteristic
49#126×C59—21no—
50#124×C59—21no—
51#124×C59C2211yescharacteristic
52#123×C59—21no—
53C22⋊Q8×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58#117×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C22×Dic59—21no—
67#11745685—41no—
68#11745685—41no—
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×Dic118—21no—
72C2×Dic118—41no—
73C2×Dic118—41no—
74C2×Dic118C2311yescharacteristic
75C2×Dic118C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59D411yescharacteristic
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C42×C59—21no—
92C42×C59C2311yescharacteristic
93C42×C59C2311yescharacteristic
94#11745672—41no—
95#11745672—41no—
96#11745672—41no—
97#11745671—41no—
98#11745670—41no—
99#11745670—41no—
100#11745670—41no—
101#11745669—41no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106C4⋊Dic59—21no—
107C4⋊Dic59—21no—
108C4⋊Dic59—21no—
109C4⋊Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C22×D59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—81no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—81no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—81no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—42no—
140D236—21no—
141D236—21no—
142C4×D59—42no—
143Dic118—21no—
144Dic118—21no—
145Dic118—21no—
146Dic118—21no—
147Dic118—21no—
148Dic118—21no—
149Dic118—42no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C59⋊C8—21no—
153C59⋊C8—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59C22×D411yescharacteristic
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59H(5,𝔽2)11yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3225—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—81no—
180C2×C59#53511yescharacteristic
181C2×C59#57711yescharacteristic
182C2×C59#57811yescharacteristic
183D59—81no—
184#542D5911yescharacteristic, complemented
185#536—591no—
186#497—591no—
187#495—591no—
188#489—591no—
189#487—591no—
190#464—591no—
191#463—591no—
192#462—591no—
193#461—591no—
194#452—591no—
195#451—591no—
196#449—591no—
197#448—591no—
198#433—591no—
199C59#322511yescharacteristic, complemented, Sylow
200C2×#41—591no—
201C22×Q8—591no—
202C2×Q16—591no—
203C2×Q16—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C2×SD16—591no—
208C2×SD16—591no—
209C2×D8—591no—
210C4⋊Q8—591no—
211C4⋊Q8—591no—
212C4⋊Q8C2×D5911yescharacteristic
213#126—21no—
214#124—21no—
215#124—591no—
216#124—591no—
217#124C2×D5911yescharacteristic
218#123—21no—
219#123—1181no—
220#123—1181no—
221C22⋊Q8—21no—
222C22⋊Q8—1181no—
223C22⋊Q8—1181no—
224C22⋊Q8C2×D5911yescharacteristic
225#121C2×D5911yescharacteristic
226C4×Q8C2×D5911yescharacteristic
227C4×D4C2×D5911yescharacteristic
228#117C2×D5911yescharacteristic
229C4⋊C8—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#103—591no—
237#102—591no—
238#102—591no—
239C22⋊C8—591no—
240C22⋊C8—591no—
241#97—591no—
242C4×C8—591no—
243#41—2361no—
244#41—2361no—
245C2×Q8—21no—
246C2×Q8—591no—
247C2×Q8—591no—
248C2×Q8—591no—
249C2×Q8—1181no—
250C2×Q8—2361no—
251C2×Q8—2361no—
252C2×Q8C22×D5911yescharacteristic
253C2×D4—21no—
254C2×D4—591no—
255C2×D4—1181no—
256C2×D4C22×D5911yescharacteristic
257C22×C4—21no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4C22×D5911yescharacteristic
261Q16—2361no—
262Q16—2361no—
263Q16—2361no—
264SD16—2361no—
265SD16—2361no—
266SD16—2361no—
267SD16—2361no—
268D8—2361no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8—591no—
272C2×C8—591no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4C22⋊D5911yescharacteristic
281C4⋊C4C22⋊D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4C22⋊D5911yescharacteristic
294C22⋊C4C22⋊D5911yescharacteristic
295C42—21no—
296C42C22×D5911yescharacteristic
297C42C22×D5911yescharacteristic
298C23—21no—
299C23—1181no—
300C23C2×C22⋊D5911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—81no—
304Q8—1181no—
305Q8—1181no—
306Q8—1181no—
307Q8—1181no—
308Q8—1181no—
309Q8—1181no—
310Q8—2362no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—1181no—
315D4—1181no—
316D4—2362no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—2362no—
327C2×C4—2362no—
328C2×C4C2×C22⋊D5911yescharacteristic
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C2×C22⋊D5911yescharacteristic
331C2×C4C2×C22⋊D5911yescharacteristic
332C2×C4C2×C22⋊D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—1181no—
335C8—1181no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22C22×C22⋊D5911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2361no—
357C4—2361no—
358C4—2361no—
359C4#1427377311yescharacteristic
360C4#1427377311yescharacteristic
361C2—41no—
362C2—81no—
363C2—4721no—
364C2#1683796611yescharacteristic
365C2#1683821311yescharacteristic
366C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#542C2
socleC22×C59C22×D4
hypercenter#542D59
hypocenterC59#3225
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16837978C2semidirect
2. #16837797C2semidirect
3. #16837784C2semidirect
4. #16837764C2semidirect
5. #16837754C2semidirect
6. #16837624C2semidirect
7. #16837617C2semidirect
8. #16837612C2semidirect
9. #16837607C2semidirect
10. #16837562C2semidirect
11. #16837557C2semidirect
13. #16837540C2semidirect
14. #16837463C2semidirect
15. C59×#542C2semidirect
184. #542D59semidirect
199. C59#3225semidirect