Finite Group Databasebeta

← #20248418

Subgroups — #20248418

Order 6016.

452 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094014C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic
4#15689056C211yesmaximal, characteristic
5#15689055C211yesmaximal, characteristic
6#15689020C211yesmaximal, characteristic
7#15689020C211yesmaximal, characteristic
8#15689018C211yesmaximal, characteristic
9#15689018C211yesmaximal, characteristic
10#15688992C211yesmaximal, characteristic
11#15688992C211yesmaximal, characteristic
12#15688992C211yesmaximal, characteristic
13#15688974C211yesmaximal, characteristic
14#15688974C211yesmaximal, characteristic
15C47×#398C211yesmaximal, characteristic
16#13094014—24no—
17#13094014—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×Dic47⋊C4C2211yescharacteristic
35C2×Dic47⋊C4C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C4⋊C4×C47—22no—
69C4⋊C4×C47—22no—
70C4⋊C4×C47—41no—
71C4⋊C4×C47—41no—
72C4⋊Dic47—22no—
73C4⋊Dic47—22no—
74C4⋊Dic47—41no—
75C4⋊Dic47—41no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—22no—
79Dic47⋊C4—22no—
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—41no—
87Dic47⋊C4—41no—
88Dic47⋊C4D414yes—
89Dic47⋊C4Q814yes—
90C4×Dic47—22no—
91C4×Dic47—22no—
92C4×Dic47—22no—
93C4×Dic47—22no—
94C4×Dic47Q814yes—
95C23×C47C2411yescharacteristic
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D412yes—
115C2×C4×C47C2×Q812yes—
116C2×C4×C47C2×Q812yes—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47C2×D412yes—
134C2×Dic47C2×D412yes—
135C2×Dic47C2×Q812yes—
136C2×Dic47C2×Q812yes—
137C2×Dic47C2×Q812yes—
138C2×Dic47C2×Q812yes—
139C2×Dic47#4112yes—
140C2×Dic47#4112yes—
141C22×C47C22×D411yescharacteristic
142C22×C47C22×Q811yescharacteristic
143C22×C47C22×Q811yescharacteristic
144C22×C47C2×#4111yescharacteristic
145C22×C47C2×#4111yescharacteristic
146C22×C47H(5,𝔽2)11yescharacteristic
147C22×C472−1+411yescharacteristic
148C4×C47—22no—
149C4×C47—22no—
150C4×C47—22no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155Dic47—22no—
156Dic47—22no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47#12514yescomplemented
162Dic47C4⋊Q814yes—
163#2552—471nomaximal, Sylow
164C2×C47C2×#12511yescharacteristic
165C2×C47C2×C4⋊Q811yescharacteristic
166C2×C47#54411yescharacteristic
167C2×C47#54711yescharacteristic
168C2×C47#55011yescharacteristic
169C2×C47#55411yescharacteristic
170C2×C47#55711yescharacteristic
171C2×#125—471no—
172C2×#125—471no—
173#398—471no—
174#398—471no—
175#398—471no—
176#398D4711yescharacteristic
177#389—471no—
178#389—471no—
179#389—471no—
180#389—471no—
181#384—471no—
182#384—471no—
183#384—471no—
184C4×C4⋊C4—471no—
185C4×C4⋊C4—471no—
186C47#255211yescharacteristic, complemented, Sylow
187#125—944no—
188#125—944no—
189C2×C4⋊C4—471no—
190C2×C4⋊C4—471no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4—471no—
195C2×C4⋊C4—471no—
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4C2×D4711yescharacteristic
208C2×C4⋊C4C2×D4711yescharacteristic
209C2×C4⋊C4C2×D4711yescharacteristic
210C2×C4⋊C4C2×D4711yescharacteristic
211C2×C42—471no—
212C2×C42—471no—
213C2×C42—471no—
214C2×C42—471no—
215C2×C42—471no—
216#95—471no—
217#95—471no—
218#95—471no—
219#95—471no—
220#95—471no—
221#95C2×D4711yescharacteristic
222#95C2×D4711yescharacteristic
223#95C2×D4711yescharacteristic
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4C22×D4711yescharacteristic
233C22×C4C22×D4711yescharacteristic
234C22×C4C22×D4711yescharacteristic
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237C22×C4C22×D4711yescharacteristic
238C22×C4C22×D4711yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—474no—
244C4⋊C4—474no—
245C4⋊C4—942no—
246C4⋊C4—942no—
247C4⋊C4—942no—
248C4⋊C4—942no—
249C4⋊C4—942no—
250C4⋊C4—942no—
251C4⋊C4—942no—
252C4⋊C4—942no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—942no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C42—474no—
262C42—942no—
263C42—942no—
264C42—942no—
265C42—942no—
266C23C23×D4711yescharacteristic
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—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—472no—
286C2×C4—472no—
287C2×C4—472no—
288C2×C4—472no—
289C2×C4—472no—
290C2×C4—472no—
291C2×C4—472no—
292C2×C4—472no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4D4×D4712yes—
310C2×C4Q8×D4712yes—
311C2×C4Q8×D4712yes—
312C22C2×D4×D4711yescharacteristic
313C22C2×Q8×D4711yescharacteristic
314C22C2×Q8×D4711yescharacteristic
315C22#41×D4711yescharacteristic
316C22#41×D4711yescharacteristic
317C22#1309406911yescharacteristic
318C22#1309407111yescharacteristic
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—474no—
327C4—474no—
328C4—942no—
329C4—942no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4—1881no—
334C2#125×D4711yescharacteristic
335C2C4⋊Q8×D4711yescharacteristic
336C2#1568975211yescharacteristic
337C2#1568977111yescharacteristic
338C2#1568979111yescharacteristic
339C2#1568982711yescharacteristic
340C2#1568985011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2552
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
161. Dic47#125semidirect
186. C47#2552semidirect