Finite Group Databasebeta

← #21435175

Subgroups — #21435175

Order 7552.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838012C211yesmaximal, characteristic, complemented
2#16837976C211yesmaximal, characteristic
3#16837795C211yesmaximal, characteristic, complemented
4#16837780C211yesmaximal, characteristic, complemented
5#16837769C211yesmaximal, characteristic, complemented
6#16837758C211yesmaximal, characteristic, complemented
7#16837627C211yesmaximal, characteristic, complemented
8#16837626C211yesmaximal, characteristic, complemented
9#16837611C211yesmaximal, characteristic, complemented
10#16837610C211yesmaximal, characteristic, complemented
11#16837566C211yesmaximal, characteristic
12#16837562C211yesmaximal, characteristic
13#16837558C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#451C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Dic236C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745672C2211yescharacteristic
21C2×#11745660C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23#14273725C2211yescharacteristic
24#14273725C2211yescharacteristic
25#14273725C2211yescharacteristic
26#14273720—21no—
27#14273720—21no—
28#14273718—21no—
29#14273718C2211yescharacteristic
30#14273717—21no—
31#14273716C2211yescharacteristic
32#14273716C2211yescharacteristic
33#14273710—21no—
34#14273710—21no—
35#14273706C2211yescharacteristic
36#14273703—21no—
37#14273703—21no—
38Q8×Dic59C2211yescharacteristic
39#14273692C2211yescharacteristic
40#14273686C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
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⋊D59—21no—
68#11745685—41no—
69#11745685—41no—
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×Dic118C2311yescharacteristic
73C2×Dic118C2311yescharacteristic
74Q16×C59—41no—
75Q16×C59—41no—
76C2×C8×C59C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C4⋊C4×C59—21no—
79C4⋊C4×C59C2311yescharacteristic
80C22⋊C4×C59—21no—
81C22⋊Dic59—21no—
82C22⋊Dic59D411yescharacteristic
83C22⋊Dic59D411yescharacteristic
84#11745672—41no—
85#11745672—41no—
86#11745672—41no—
87#11745671—41no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59—21no—
94C4⋊Dic59D411yescharacteristic
95C4⋊Dic59D411yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112Dic236—41no—
113#11745660—41no—
114C23×C59C2×D411yescharacteristic
115C22×D59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—21no—
121Q8×C59—21no—
122Q8×C59—42no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—42no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140D236—21no—
141D236—21no—
142C4×D59—42no—
143Dic118—21no—
144Dic118—21no—
145Dic118—21no—
146Dic118—21no—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59C22×D411yescharacteristic
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C4×C59—21no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59H(5,𝔽2)11yescharacteristic
164C4×C59H(5,𝔽2)11yescharacteristic
165Dic59—21no—
166Dic59—21no—
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3223—591nomaximal, Sylow
173C2×C59—41no—
174C2×C59#53511yescharacteristic
175C2×C59#57811yescharacteristic
176C2×C59#57811yescharacteristic
177D59—81no—
178#541—591no—
179#536—591no—
180#497—591no—
181#494—591no—
182#491—591no—
183#488—591no—
184#464—591no—
185#464—591no—
186#462—591no—
187#462—591no—
188#452—591no—
189#452—591no—
190#451—591no—
191#451D5911yescharacteristic, complemented
192#433—591no—
193C59#322311yescharacteristic, complemented, Sylow
194C2×#41—591no—
195C22×Q8C2×D5911yescharacteristic
196C2×Q16—591no—
197C2×Q16—591no—
198C2×Q16—591no—
199C2×Q16—591no—
200C2×Q16C2×D5911yescharacteristic
201C2×Q16C2×D5911yescharacteristic
202C2×SD16—591no—
203C2×SD16—591no—
204C4⋊Q8—591no—
205C4⋊Q8—591no—
206C4⋊Q8—591no—
207#126—1181no—
208#126—1181no—
209#125—591no—
210#125—1181no—
211#125—1181no—
212#124—591no—
213#124—591no—
214#123—1181no—
215#123—1181no—
216C22⋊Q8—591no—
217C22⋊Q8—1181no—
218C22⋊Q8—1181no—
219C22⋊Q8C2×D5911yescharacteristic
220C4×Q8—591no—
221C4×Q8—591no—
222#117—591no—
223C4⋊C8—591no—
224C4⋊C8—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103C2×D5911yescharacteristic
230#103C2×D5911yescharacteristic
231#102—591no—
232#102—591no—
233C22⋊C8—591no—
234C22⋊C8C2×D5911yescharacteristic
235#97—591no—
236C4×C8—591no—
237#41—2361no—
238#41—2361no—
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—591no—
243C2×Q8—591no—
244C2×Q8C22×D5911yescharacteristic
245C2×Q8C22×D5911yescharacteristic
246C2×Q8C22×D5911yescharacteristic
247C2×D4—591no—
248C2×D4—1181no—
249C22×C4—21no—
250C22×C4—1181no—
251C22×C4C22×D5911yescharacteristic
252Q16—41no—
253Q16—41no—
254Q16—2361no—
255Q16—2361no—
256Q16—2361no—
257Q16—2361no—
258SD16—2361no—
259SD16—2361no—
260C2×C8—591no—
261C2×C8—591no—
262C2×C8C22×D5911yescharacteristic
263C2×C8C22×D5911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4C22×D5911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—591no—
282C22⋊C4—591no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C42—591no—
289C42—591no—
290C42—1181no—
291C42—1181no—
292C23—1181no—
293C23D4×D5911yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—1181no—
302Q8—1181no—
303Q8—1181no—
304Q8—1181no—
305D4—1181no—
306D4—1181no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—591no—
316C2×C4—591no—
317C2×C4—591no—
318C2×C4—591no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—2362no—
323C2×C4D4×D5911yescharacteristic
324C2×C4C23×D5911yescharacteristic
325C8—21no—
326C8—21no—
327C8—1181no—
328C8—1181no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—2361no—
333C22—2361no—
334C22—2361no—
335C22C2×D4×D5911yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1181no—
342C4—1181no—
343C4—1181no—
344C4—1181no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4#1427377211yescharacteristic
349C4#1427377211yescharacteristic
350C2—41no—
351C2—4721no—
352C2#1683796711yescharacteristic
353C2#1683821511yescharacteristic
354C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#451C2
socleC22×C59C22×D4
hypercenter#451D59
hypocenterC59#3223
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
1. #16838012C2semidirect
3. #16837795C2semidirect
4. #16837780C2semidirect
5. #16837769C2semidirect
6. #16837758C2semidirect
7. #16837627C2semidirect
8. #16837626C2semidirect
9. #16837611C2semidirect
10. #16837610C2semidirect
13. #16837558C2semidirect
14. #16837460C2semidirect
15. C59×#451C2semidirect
191. #451D59semidirect
193. C59#3223semidirect