Finite Group Databasebeta

← #21426653

Subgroups — #21426653

Order 7552.

484 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
1C2×#14273717C211yesmaximal, characteristic
2#16837299C211yesmaximal, characteristic
3#16837297C211yesmaximal, characteristic
4#16837289C211yesmaximal, characteristic
5#16837286C211yesmaximal, characteristic
6#16837285C211yesmaximal, characteristic
7#16837266C211yesmaximal, characteristic
8C4⋊C4×Dic59C211yesmaximal, characteristic
9C4⋊C4×Dic59C211yesmaximal, characteristic
10#16837253C211yesmaximal, characteristic
11#16837253C211yesmaximal, characteristic
12#16837253C211yesmaximal, characteristic
13#16837253C211yesmaximal, characteristic
14C42×Dic59C211yesmaximal, characteristic
15C59×#387C211yesmaximal, characteristic
16#14273717C418yescomplemented
17C2×C4⋊Dic59C2211yescharacteristic
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
33C2×C4×Dic59C2211yescharacteristic
34C2×C4×Dic59C2211yescharacteristic
35C2×C4×Dic59C2211yescharacteristic
36C2×C4×Dic59C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C2×C4⋊C4×C59C2211yescharacteristic
46C2×C4⋊C4×C59C2211yescharacteristic
47C2×C42×C59C2211yescharacteristic
48#95×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52C22×C4×C59C2311yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×Dic59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C22×Dic59C2311yescharacteristic
67C4⋊C4×C59—22no—
68C4⋊C4×C59C2×C414yes—
69C42×C59—22no—
70C4⋊Dic59—22no—
71C4⋊Dic59C2×C414yes—
72Dic59⋊C4—22no—
73Dic59⋊C4—22no—
74Dic59⋊C4—22no—
75Dic59⋊C4—22no—
76Dic59⋊C4C2×C414yes—
77Dic59⋊C4C2×C414yes—
78Dic59⋊C4C2×C414yes—
79Dic59⋊C4C2×C414yes—
80C4×Dic59—22no—
81C4×Dic59—22no—
82C4×Dic59—22no—
83C4×Dic59—22no—
84C4×Dic59—22no—
85C4×Dic59—22no—
86C4×Dic59—22no—
87C4×Dic59—22no—
88C4×Dic59C2×C414yes—
89C4×Dic59Q814yes—
90C23×C59C2411yescharacteristic
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×C59—21no—
107C2×C4×C59C22×C412yes—
108C2×C4×C59C22×C412yes—
109C2×C4×C59C22×C412yes—
110C2×C4×C59C2×Q812yes—
111C2×C4×C59#4112yes—
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×Dic59C22×C412yes—
127C2×Dic59C22×C412yes—
128C2×Dic59C22×C412yes—
129C2×Dic59C22×C412yes—
130C2×Dic59C2×Q812yes—
131C2×Dic59C2×Q812yes—
132C2×Dic59#4112yes—
133C2×Dic59#4112yes—
134C2×Dic59#4112yes—
135C2×Dic59#4112yes—
136C22×C59C23×C411yescharacteristic
137C22×C59C22×Q811yescharacteristic
138C22×C59C2×#4111yescharacteristic
139C22×C59C2×#4111yescharacteristic
140C22×C59C2×#4111yescharacteristic
141C22×C59C2×#4111yescharacteristic
142C22×C59C2×#4111yescharacteristic
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—22no—
153Dic59—22no—
154Dic59—41no—
155Dic59—41no—
156Dic59C4×Q814yes—
157Dic59#12514yescomplemented
158C4×#125—591nomaximal, Sylow
159C2×C59C2×C4×Q811yescharacteristic
160C2×C59C4×#4111yescharacteristic
161C2×C59C4×#4111yescharacteristic
162C2×C59C2×#12511yescharacteristic
163C2×C59#52911yescharacteristic
164C2×C59#52911yescharacteristic
165C2×C59#53311yescharacteristic
166C2×#125—591no—
167#389—591no—
168#389—591no—
169#387—591no—
170#387—591no—
171#387—591no—
172#387D5911yescharacteristic
173#382—591no—
174C4×C4⋊C4—591no—
175C4×C4⋊C4—591no—
176C4×C4⋊C4—591no—
177C4×C4⋊C4—591no—
178C4×C4⋊C4—591no—
179C4×C4⋊C4—591no—
180C43—591no—
181C59C4×#12511yescharacteristic, complemented, Sylow
182#125—598no—
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⋊C4C2×D5911yescharacteristic
194C2×C4⋊C4C2×D5911yescharacteristic
195C2×C42—591no—
196C2×C42—591no—
197C2×C42—591no—
198C2×C42—591no—
199C2×C42—591no—
200C2×C42—591no—
201C2×C42—591no—
202C2×C42—591no—
203C2×C42—591no—
204C2×C42—591no—
205C2×C42C2×D5911yescharacteristic
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#95C2×D5911yescharacteristic
215#95C2×D5911yescharacteristic
216#95C2×D5911yescharacteristic
217#95C2×D5911yescharacteristic
218C22×C4—591no—
219C22×C4—591no—
220C22×C4—591no—
221C22×C4—591no—
222C22×C4—591no—
223C22×C4—591no—
224C22×C4—591no—
225C22×C4—591no—
226C22×C4C22×D5911yescharacteristic
227C22×C4C22×D5911yescharacteristic
228C22×C4C22×D5911yescharacteristic
229C22×C4C22×D5911yescharacteristic
230C22×C4C22×D5911yescharacteristic
231C22×C4C22×D5911yescharacteristic
232C22×C4C22×D5911yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—594no—
235C4⋊C4—594no—
236C4⋊C4—594no—
237C4⋊C4—594no—
238C4⋊C4—594no—
239C4⋊C4—1182no—
240C4⋊C4—1182no—
241C4⋊C4—1182no—
242C4⋊C4—1182no—
243C4⋊C4—1182no—
244C4⋊C4C4×D5914yes—
245C42—22no—
246C42—594no—
247C42—594no—
248C42—1182no—
249C42—1182no—
250C42—1182no—
251C42—1182no—
252C42—1182no—
253C42—1182no—
254C42—1182no—
255C42—1182no—
256C23C23×D5911yescharacteristic
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—592no—
276C2×C4—592no—
277C2×C4—592no—
278C2×C4—592no—
279C2×C4—592no—
280C2×C4—592no—
281C2×C4—592no—
282C2×C4—592no—
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×C4×D5912yes—
298C2×C4C2×C4×D5912yes—
299C2×C4C2×C4×D5912yes—
300C2×C4#1174568712yes—
301C2×C4Q8×D5912yes—
302C22C22×C4×D5911yescharacteristic
303C22C2×Q8×D5911yescharacteristic
304C22#41×D5911yescharacteristic
305C22#41×D5911yescharacteristic
306C22#41×D5911yescharacteristic
307C22#41×D5911yescharacteristic
308C22C2×#1174568711yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—594no—
317C4—594no—
318C4—1182no—
319C4—1182no—
320C4—1182no—
321C4—1182no—
322C4—2361no—
323C4—2361no—
324C2C4×Q8×D5911yescharacteristic
325C2C4×#1174568711yescharacteristic
326C2#1683787011yescharacteristic
327C2#125×D5911yescharacteristic
328C2#1683792911yescharacteristic
329C2#1683793511yescharacteristic
330C2#1683795411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutatorC22×C59C23×C4
FittingC59×#387C2
socleC23×C59C24
hypercenter#387D59
hypocenterC59C4×#125
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #14273717C4semidirect
157. Dic59#125semidirect
181. C59C4×#125semidirect