Finite Group Databasebeta

← #21426839

Subgroups — #21426839

Order 7552.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273725C211yesmaximal, characteristic
2#16837309C211yesmaximal, characteristic
3#16837306C211yesmaximal, characteristic
4#16837306C211yesmaximal, characteristic
5#16837299C211yesmaximal, characteristic
6#16837297C211yesmaximal, characteristic
7#16837289C211yesmaximal, characteristic
8#16837286C211yesmaximal, characteristic
9#16837284C211yesmaximal, characteristic
10#16837283C211yesmaximal, characteristic
11#16837266C211yesmaximal, characteristic
12C4×Dic59⋊C4C211yesmaximal, characteristic
13#16837253C211yesmaximal, characteristic
14#16837247C211yesmaximal, characteristic
15C59×#391C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17#14273725C418yescomplemented
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×Dic59⋊C4C2211yescharacteristic
24C2×Dic59⋊C4C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2211yescharacteristic
29C2×C4×Dic59C2211yescharacteristic
30C2×C4×Dic59C2211yescharacteristic
31C2×C4×Dic59C2211yescharacteristic
32C2×C4×Dic59C2211yescharacteristic
33C59⋊#95C2211yescharacteristic
34C59⋊#95C2211yescharacteristic
35C59⋊#95C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C22×Q8×C59C2211yescharacteristic
46C2×C4⋊C4×C59C2211yescharacteristic
47C2×C42×C59C2211yescharacteristic
48#95×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52C2×Q8×C59—41no—
53C2×Q8×C59—41no—
54C2×Q8×C59C2×C414yes—
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C22×Dic59C2311yescharacteristic
67C22×Dic59C2311yescharacteristic
68C22×Dic59C2311yescharacteristic
69C22×Dic59C2311yescharacteristic
70C2×Dic118—41no—
71C2×Dic118—41no—
72C2×Dic118C2×C414yes—
73C4⋊C4×C59—41no—
74C42×C59—41no—
75C4⋊Dic59—41no—
76Dic59⋊C4—22no—
77Dic59⋊C4—22no—
78Dic59⋊C4—41no—
79Dic59⋊C4—41no—
80Dic59⋊C4C2×C414yes—
81Dic59⋊C4C2×C414yes—
82Dic59⋊C4C2×C414yes—
83Dic59⋊C4C2×C414yes—
84C4×Dic59—22no—
85C4×Dic59—41no—
86C4×Dic59—41no—
87C4×Dic59—41no—
88C4×Dic59C2×C414yes—
89C4×Dic59Q814yescomplemented
90C23×C59C2411yescharacteristic
91Q8×C59—44no—
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×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59C22×C412yes—
110C2×C4×C59C22×C412yes—
111C2×C4×C59C22×C412yes—
112C2×C4×C59C2×Q812yes—
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×Dic59C22×C412yes—
131C2×Dic59C22×C412yes—
132C2×Dic59C22×C412yes—
133C2×Dic59C22×C412yes—
134C2×Dic59C2×Q812yes—
135C2×Dic59C2×Q812yes—
136C2×Dic59#4112yes—
137Dic118—44no—
138C22×C59C23×C411yescharacteristic
139C22×C59C22×Q811yescharacteristic
140C22×C59C2×#4111yescharacteristic
141C22×C59H(5,𝔽2)11yescharacteristic
142C22×C59H(5,𝔽2)11yescharacteristic
143C22×C592−1+411yescharacteristic
144C22×C592−1+411yescharacteristic
145C4×C59—22no—
146C4×C59—22no—
147C4×C59—22no—
148C4×C59—22no—
149C4×C59—41no—
150C4×C59—41no—
151C4×C59—41no—
152Dic59—22no—
153Dic59—22no—
154Dic59—22no—
155Dic59—22no—
156Dic59—41no—
157Dic59—41no—
158Dic59—41no—
159Dic59C4×Q814yes—
160#2331—591nomaximal, Sylow
161C2×C59C2×C4×Q811yescharacteristic
162C2×C59#51811yescharacteristic
163C2×C59#51911yescharacteristic
164C2×C59#54211yescharacteristic
165C2×C59#54211yescharacteristic
166C2×C59#54411yescharacteristic
167C2×C59#54411yescharacteristic
168C2×C4⋊Q8—591no—
169#391—591no—
170#391—591no—
171#391—591no—
172#391D5911yescharacteristic
173#389—591no—
174#389—591no—
175#387—591no—
176#387—591no—
177#387—591no—
178#387—591no—
179#382—591no—
180C4×C4⋊C4—591no—
181C4×C4⋊C4—591no—
182#376—591no—
183C59#233111yescharacteristic, complemented, Sylow
184C22×Q8—591no—
185C22×Q8C2×D5911yescharacteristic
186C4⋊Q8—598no—
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⋊C4C2×D5911yescharacteristic
197C2×C42—591no—
198C2×C42—591no—
199C2×C42—591no—
200C2×C42—591no—
201C2×C42—591no—
202C2×C42—591no—
203C2×C42C2×D5911yescharacteristic
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#95—591no—
214#95—591no—
215#95—591no—
216#95C2×D5911yescharacteristic
217#95C2×D5911yescharacteristic
218#95C2×D5911yescharacteristic
219#95C2×D5911yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—594no—
223C2×Q8—2361no—
224C2×Q8—2361no—
225C2×Q8C4×D5914yes—
226C22×C4—591no—
227C22×C4—591no—
228C22×C4—591no—
229C22×C4—591no—
230C22×C4—591no—
231C22×C4—591no—
232C22×C4—591no—
233C22×C4—591no—
234C22×C4C22×D5911yescharacteristic
235C22×C4C22×D5911yescharacteristic
236C22×C4C22×D5911yescharacteristic
237C22×C4C22×D5911yescharacteristic
238C22×C4C22×D5911yescharacteristic
239C22×C4C22×D5911yescharacteristic
240C22×C4C22×D5911yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—594no—
243C4⋊C4—594no—
244C4⋊C4—594no—
245C4⋊C4—594no—
246C4⋊C4—1182no—
247C4⋊C4—1182no—
248C4⋊C4—2361no—
249C4⋊C4—2361no—
250C4⋊C4—2361no—
251C42—41no—
252C42—594no—
253C42—594no—
254C42—1182no—
255C42—2361no—
256C42—2361no—
257C42—2361no—
258C23C23×D5911yescharacteristic
259Q8—44no—
260Q8—2364no—
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—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—592no—
279C2×C4—592no—
280C2×C4—592no—
281C2×C4—592no—
282C2×C4—592no—
283C2×C4—592no—
284C2×C4—592no—
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×C4—1181no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4C2×C4×D5912yes—
303C2×C4C2×C4×D5912yes—
304C2×C4C2×C4×D5912yes—
305C2×C4Q8×D5912yes—
306C22C22×C4×D5911yescharacteristic
307C22C2×Q8×D5911yescharacteristic
308C22#41×D5911yescharacteristic
309C22#1427377211yescharacteristic
310C22#1427377211yescharacteristic
311C22#1427377411yescharacteristic
312C22#1427377511yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—594no—
321C4—1182no—
322C4—1182no—
323C4—1182no—
324C4—1182no—
325C4—2361no—
326C4—2361no—
327C4—2361no—
328C2C4×Q8×D5911yescharacteristic
329C2#1683787511yescharacteristic
330C2#1683787811yescharacteristic
331C2#1683801611yescharacteristic
332C2#1683802211yescharacteristic
333C2#1683802911yescharacteristic
334C2#1683803111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutatorC22×C59C23×C4
FittingC59×#391C2
socleC23×C59C24
hypercenter#391D59
hypocenterC59#2331
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #14273725C4semidirect
89. C4×Dic59Q8semidirect
183. C59#2331semidirect