Finite Group Databasebeta

← #21428085

Subgroups — #21428085

Order 7552.

452 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×#14273718C211yesmaximal, characteristic
2C2×C4×Dic118C211yesmaximal, characteristic
3#16837335C211yesmaximal, characteristic
4#16837334C211yesmaximal, characteristic
5#16837323C211yesmaximal, characteristic
6#16837323C211yesmaximal, characteristic
7#16837300C211yesmaximal, characteristic
8#16837299C211yesmaximal, characteristic
9#16837289C211yesmaximal, characteristic
10#16837289C211yesmaximal, characteristic
11#16837289C211yesmaximal, characteristic
12#16837288C211yesmaximal, characteristic
13#16837285C211yesmaximal, characteristic
14C4⋊C4×Dic59C211yesmaximal, characteristic
15C59×#387C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17#14273718—24no—
18C4×Dic118—24no—
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
34C2×C4×Dic59C2211yescharacteristic
35C2×C4×Dic59C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C59⋊#95C2211yescharacteristic
46C2×C4⋊C4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic
48C2×C42×C59C2211yescharacteristic
49#95×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52#95×C59C2211yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C22×Dic59C2311yescharacteristic
67C22×Dic59C2311yescharacteristic
68C2×Dic118—22no—
69C2×Dic118—22no—
70C2×Dic118—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59Q814yescomplemented
73C42×C59—22no—
74C4⋊Dic59—22no—
75C4⋊Dic59—22no—
76C4⋊Dic59—22no—
77C4⋊Dic59—22no—
78C4⋊Dic59—22no—
79C4⋊Dic59—22no—
80C4⋊Dic59—22no—
81Dic59⋊C4—22no—
82Dic59⋊C4—22no—
83Dic59⋊C4—22no—
84Dic59⋊C4—22no—
85Dic59⋊C4—22no—
86Dic59⋊C4D414yes—
87C4×Dic59—22no—
88C4×Dic59—22no—
89C4×Dic59—22no—
90C4×Dic59—22no—
91C23×C59C2411yescharacteristic
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×C59C2×D412yes—
109C2×C4×C59C2×Q812yes—
110C2×C4×C59C2×Q812yes—
111C2×C4×C59C2×Q812yes—
112C2×C4×C59#4112yes—
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×D412yes—
134C2×Dic59C2×D412yes—
135C2×Dic59#4112yes—
136C2×Dic59#4112yes—
137Dic118—28no—
138C22×C59C22×D411yescharacteristic
139C22×C59C22×Q811yescharacteristic
140C22×C59C2×#4111yescharacteristic
141C22×C59C2×#4111yescharacteristic
142C22×C59C2×#4111yescharacteristic
143C22×C592−1+411yescharacteristic
144C22×C592−1+411yescharacteristic
145C4×C59—22no—
146C4×C59—22no—
147C4×C59—22no—
148C4×C59—22no—
149C4×C59—22no—
150C4×C59—41no—
151C4×C59—41no—
152Dic59—22no—
153Dic59—22no—
154Dic59—22no—
155Dic59—22no—
156Dic59—41no—
157Dic59—41no—
158Dic59—41no—
159Dic59—41no—
160#2462—591nomaximal, Sylow
161C2×C59#52511yescharacteristic
162C2×C59#53311yescharacteristic
163C2×C59#54111yescharacteristic
164C2×C59#54711yescharacteristic
165C2×C59D4×Q811yescharacteristic
166C2×C59#55211yescharacteristic
167C2×C59#55711yescharacteristic
168C2×#125—591no—
169C2×C4×Q8—591no—
170#398—591no—
171#398—591no—
172#395—591no—
173#395—591no—
174#389—591no—
175#389—591no—
176#387—591no—
177#387—591no—
178#387—591no—
179#387—591no—
180#387—591no—
181#387D5911yescharacteristic
182C4×C4⋊C4—591no—
183C59#246211yescharacteristic, complemented, Sylow
184C22×Q8—591no—
185#125—1184no—
186C4×Q8—1184no—
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⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4C2×D5911yescharacteristic
201C2×C4⋊C4C2×D5911yescharacteristic
202C2×C42—591no—
203C2×C42—591no—
204C2×C42—591no—
205C2×C42—591no—
206C2×C42C2×D5911yescharacteristic
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#95—591no—
217#95C2×D5911yescharacteristic
218#95C2×D5911yescharacteristic
219#95C2×D5911yescharacteristic
220#95C2×D5911yescharacteristic
221C2×Q8—1182no—
222C2×Q8—1182no—
223C2×Q8—1182no—
224C22×C4—591no—
225C22×C4—591no—
226C22×C4—591no—
227C22×C4—591no—
228C22×C4—591no—
229C22×C4—591no—
230C22×C4—591no—
231C22×C4—591no—
232C22×C4C22×D5911yescharacteristic
233C22×C4C22×D5911yescharacteristic
234C22×C4C22×D5911yescharacteristic
235C22×C4C22×D5911yescharacteristic
236C22×C4C22×D5911yescharacteristic
237C22×C4C22×D5911yescharacteristic
238C22×C4C22×D5911yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—594no—
241C4⋊C4—1182no—
242C4⋊C4—1182no—
243C4⋊C4—1182no—
244C4⋊C4—1182no—
245C4⋊C4—1182no—
246C4⋊C4—1182no—
247C4⋊C4—1182no—
248C4⋊C4—1182no—
249C4⋊C4—1182no—
250C4⋊C4—1182no—
251C4⋊C4—1182no—
252C4⋊C4—1182no—
253C4⋊C4Dic11814yescomplemented
254C42—22no—
255C42—1182no—
256C42—1182no—
257C42—1182no—
258C42—1182no—
259C23C23×D5911yescharacteristic
260Q8—1188no—
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—592no—
278C2×C4—592no—
279C2×C4—592no—
280C2×C4—592no—
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×C4—1181no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4C2×Dic11812yes—
302C2×C4C2×Dic11812yes—
303C2×C4C2×Dic11812yes—
304C2×C4D4×D5912yes—
305C2×C4#1174568912yes—
306C22C2×D4×D5911yescharacteristic
307C22C22×Dic11811yescharacteristic
308C22#41×D5911yescharacteristic
309C22#41×D5911yescharacteristic
310C22C2×#1174568911yescharacteristic
311C22#1427377411yescharacteristic
312C22#1427377411yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—1182no—
321C4—1182no—
322C4—1182no—
323C4—1182no—
324C4—2361no—
325C4—2361no—
326C4—2361no—
327C4—2361no—
328C2#1683791511yescharacteristic
329C2#1683795511yescharacteristic
330C2#1683800911yescharacteristic
331C2#1683805011yescharacteristic
332C2D4×Dic11811yescharacteristic
333C2#1683809011yescharacteristic
334C2#1683813111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#387C2
hypercenter#387D59
hypocenterC59#2462
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
72. C4⋊C4×C59Q8semidirect
183. C59#2462semidirect
253. C4⋊C4Dic118semidirect