Finite Group Databasebeta

← #21431895

Subgroups — #21431895

Order 7552.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837336C211yesmaximal, characteristic
2#16837335C211yesmaximal, characteristic
3#16837334C211yesmaximal, characteristic
4#16837323C211yesmaximal, characteristic
5#16837323C211yesmaximal, characteristic
6#16837323C211yesmaximal, characteristic
7#16837301C211yesmaximal, characteristic
8#16837301C211yesmaximal, characteristic
9#16837299C211yesmaximal, characteristic
10#16837299C211yesmaximal, characteristic
11#16837289C211yesmaximal, characteristic
12#16837288C211yesmaximal, characteristic
13#16837286C211yesmaximal, characteristic
14#16837272C211yesmaximal, characteristic
15C59×#387C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×C4⋊Dic59C2211yescharacteristic
21C2×C4⋊Dic59C2211yescharacteristic
22C2×C4⋊Dic59C2211yescharacteristic
23C2×C4⋊Dic59C2211yescharacteristic
24C2×C4⋊Dic59C2211yescharacteristic
25C2×C4⋊Dic59C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×Dic59⋊C4C2211yescharacteristic
28C2×Dic59⋊C4C2211yescharacteristic
29C2×Dic59⋊C4C2211yescharacteristic
30C2×Dic59⋊C4C2211yescharacteristic
31C2×Dic59⋊C4C2211yescharacteristic
32C2×C4×Dic59C2211yescharacteristic
33C2×C4×Dic59C2211yescharacteristic
34C59⋊#95C2211yescharacteristic
35C59⋊#95C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C2×C4⋊C4×C59C2211yescharacteristic
45C2×C4⋊C4×C59C2211yescharacteristic
46C2×C42×C59C2211yescharacteristic
47#95×C59C2211yescharacteristic
48#95×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51C22×C4×C59C2311yescharacteristic
52C22×C4×C59C2311yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×Dic59C2311yescharacteristic
59C22×Dic59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C2×Dic118—41no—
67C2×Dic118—41no—
68C2×Dic118—41no—
69C4⋊C4×C59—22no—
70C4⋊C4×C59Q814yescomplemented
71C42×C59—22no—
72C4⋊Dic59—41no—
73C4⋊Dic59—41no—
74C4⋊Dic59—41no—
75C4⋊Dic59—41no—
76C4⋊Dic59—41no—
77C4⋊Dic59—41no—
78C4⋊Dic59—41no—
79C4⋊Dic59—41no—
80C4⋊Dic59—41no—
81Dic59⋊C4—22no—
82Dic59⋊C4—41no—
83Dic59⋊C4—41no—
84Dic59⋊C4—41no—
85Dic59⋊C4—41no—
86Dic59⋊C4Q814yescomplemented
87C4×Dic59—41no—
88C4×Dic59—41no—
89C23×C59C2411yescharacteristic
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59C2×Q812yes—
107C2×C4×C59C2×Q812yes—
108C2×C4×C59C2×Q812yes—
109C2×C4×C59C2×Q812yes—
110C2×C4×C59#4112yes—
111C2×Dic59—21no—
112C2×Dic59—21no—
113C2×Dic59—21no—
114C2×Dic59—21no—
115C2×Dic59—21no—
116C2×Dic59—21no—
117C2×Dic59—21no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59C2×Q812yes—
134C2×Dic59C2×Q812yes—
135Dic118—44no—
136C22×C59C22×Q811yescharacteristic
137C22×C59C22×Q811yescharacteristic
138C22×C59C2×#4111yescharacteristic
139C22×C59H(5,𝔽2)11yescharacteristic
140C22×C59H(5,𝔽2)11yescharacteristic
141C22×C59H(5,𝔽2)11yescharacteristic
142C22×C592−1+411yescharacteristic
143C4×C59—22no—
144C4×C59—22no—
145C4×C59—22no—
146C4×C59—22no—
147C4×C59—22no—
148C4×C59—41no—
149C4×C59—41no—
150Dic59—22no—
151Dic59—22no—
152Dic59—41no—
153Dic59—41no—
154Dic59—41no—
155Dic59—41no—
156Dic59—41no—
157Dic59—41no—
158#2792—591nomaximal, Sylow
159C2×C59#53911yescharacteristic
160C2×C59#54411yescharacteristic
161C2×C59#54411yescharacteristic
162C2×C59#55411yescharacteristic
163C2×C59#55411yescharacteristic
164C2×C59Q8211yescharacteristic
165C2×C59#56011yescharacteristic
166#398—591no—
167#398—591no—
168#398—591no—
169#395—591no—
170#395—591no—
171#395—591no—
172#389—591no—
173#389—591no—
174#389—591no—
175#389—591no—
176#387—591no—
177#387—591no—
178#387—591no—
179#387D5911yescharacteristic
180#384—591no—
181C59#279211yescharacteristic, complemented, Sylow
182C22×Q8—591no—
183C2×C4⋊C4—591no—
184C2×C4⋊C4—591no—
185C2×C4⋊C4—591no—
186C2×C4⋊C4—591no—
187C2×C4⋊C4—591no—
188C2×C4⋊C4—591no—
189C2×C4⋊C4—591no—
190C2×C4⋊C4—591no—
191C2×C4⋊C4—591no—
192C2×C4⋊C4—591no—
193C2×C4⋊C4—591no—
194C2×C4⋊C4—591no—
195C2×C4⋊C4—591no—
196C2×C4⋊C4—591no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4C2×D5911yescharacteristic
199C2×C4⋊C4C2×D5911yescharacteristic
200C2×C42—591no—
201C2×C42—591no—
202C2×C42C2×D5911yescharacteristic
203#95—591no—
204#95—591no—
205#95—591no—
206#95—591no—
207#95—591no—
208#95—591no—
209#95—591no—
210#95—591no—
211#95—591no—
212#95—591no—
213#95C2×D5911yescharacteristic
214#95C2×D5911yescharacteristic
215#95C2×D5911yescharacteristic
216#95C2×D5911yescharacteristic
217C2×Q8—2361no—
218C2×Q8—2361no—
219C2×Q8—2361no—
220C22×C4—591no—
221C22×C4—591no—
222C22×C4—591no—
223C22×C4—591no—
224C22×C4—591no—
225C22×C4—591no—
226C22×C4—591no—
227C22×C4—591no—
228C22×C4C22×D5911yescharacteristic
229C22×C4C22×D5911yescharacteristic
230C22×C4C22×D5911yescharacteristic
231C22×C4C22×D5911yescharacteristic
232C22×C4C22×D5911yescharacteristic
233C22×C4C22×D5911yescharacteristic
234C22×C4C22×D5911yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—594no—
237C4⋊C4—1182no—
238C4⋊C4—2361no—
239C4⋊C4—2361no—
240C4⋊C4—2361no—
241C4⋊C4—2361no—
242C4⋊C4—2361no—
243C4⋊C4—2361no—
244C4⋊C4—2361no—
245C4⋊C4—2361no—
246C4⋊C4—2361no—
247C4⋊C4—2361no—
248C4⋊C4—2361no—
249C4⋊C4—2361no—
250C4⋊C4—2361no—
251C4⋊C4Dic11814yescomplemented
252C42—22no—
253C42—2361no—
254C42—2361no—
255C23C23×D5911yescharacteristic
256Q8—2364no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—592no—
274C2×C4—592no—
275C2×C4—1181no—
276C2×C4—1181no—
277C2×C4—1181no—
278C2×C4—1181no—
279C2×C4—1181no—
280C2×C4—1181no—
281C2×C4—1181no—
282C2×C4—1181no—
283C2×C4—1181no—
284C2×C4—1181no—
285C2×C4—1181no—
286C2×C4—1181no—
287C2×C4—1181no—
288C2×C4—1181no—
289C2×C4—1181no—
290C2×C4—1181no—
291C2×C4—1181no—
292C2×C4—1181no—
293C2×C4—1181no—
294C2×C4—1181no—
295C2×C4—1181no—
296C2×C4—1181no—
297C2×C4C2×Dic11812yes—
298C2×C4C2×Dic11812yes—
299C2×C4C2×Dic11812yes—
300C2×C4#1174568712yes—
301C2×C4Q8×D5912yes—
302C22C2×Q8×D5911yescharacteristic
303C22C22×Dic11811yescharacteristic
304C22C2×#1174568711yescharacteristic
305C22#1427377311yescharacteristic
306C22#1427377311yescharacteristic
307C22#1427377311yescharacteristic
308C22#1427377411yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—1182no—
317C4—1182no—
318C4—2361no—
319C4—2361no—
320C4—2361no—
321C4—2361no—
322C4—2361no—
323C4—2361no—
324C2#1683799611yescharacteristic
325C2#1683803011yescharacteristic
326C2#1683803211yescharacteristic
327C2#1683810911yescharacteristic
328C2#1683811011yescharacteristic
329C2Q8×Dic11811yescharacteristic
330C2#1683814311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#387C2
hypercenter#387D59
hypocenterC59#2792
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
70. C4⋊C4×C59Q8semidirect
86. Dic59⋊C4Q8semidirect
181. C59#2792semidirect
251. C4⋊C4Dic118semidirect