Finite Group Databasebeta

← #20249217

Subgroups — #20249217

Order 6016.

472 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094014C211yesmaximal, characteristic, complemented
2C2×#13093980C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic, complemented
4#15689056C211yesmaximal, characteristic, complemented
5#15689054C211yesmaximal, characteristic, complemented
6#15689053C211yesmaximal, characteristic, complemented
7#15689046C211yesmaximal, characteristic
8#15689046C211yesmaximal, characteristic
9#15689046C211yesmaximal, characteristic
10#15689020C211yesmaximal, characteristic, complemented
11#15689018C211yesmaximal, characteristic, complemented
12#15688992C211yesmaximal, characteristic, complemented
13#15688981C211yesmaximal, characteristic
14#15688981C211yesmaximal, characteristic
15C47×#396C211yesmaximal, characteristic
16C23×Dic47C2211yescharacteristic
17#13094014—24no—
18#13093980—24no—
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×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47—22no—
61C22×Dic47—22no—
62C22×Dic47Q814yes—
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C4⋊C4×C47—22no—
72C4⋊C4×C47—41no—
73C4⋊C4×C47—41no—
74C22⋊C4×C47—22no—
75C22⋊C4×C47—41no—
76C22⋊C4×C47—41no—
77C22⋊Dic47—22no—
78C22⋊Dic47—41no—
79C22⋊Dic47—41no—
80C4⋊Dic47—22no—
81C4⋊Dic47—41no—
82C4⋊Dic47—41no—
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—41no—
92Dic47⋊C4—41no—
93Dic47⋊C4—41no—
94Dic47⋊C4—41no—
95C4×Dic47—22no—
96C4×Dic47D414yes—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47C2×Q812yes—
104C23×C47C2411yescharacteristic
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×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D412yes—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—28no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47C2×D412yes—
144C2×Dic47C2×D412yes—
145C2×Dic47C2×Q812yes—
146C2×Dic47C2×Q812yes—
147C2×Dic47#4112yes—
148C22×C47—22no—
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C22×C47C22×Q811yescharacteristic
157C22×C47C2×#4111yescharacteristic
158C22×C47H(5,𝔽2)11yescharacteristic
159C22×C47H(5,𝔽2)11yescharacteristic
160C22×C472−1+411yescharacteristic
161C22×C472−1+411yescharacteristic
162C4×C47—22no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—41no—
168Dic47—22no—
169Dic47—22no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174Dic47—41no—
175Dic47C22⋊Q814yes—
176#2629—471nomaximal, Sylow
177C2×C47—42no—
178C2×C47C2×C22⋊Q811yescharacteristic
179C2×C47#53711yescharacteristic
180C2×C47#53711yescharacteristic
181C2×C47#54011yescharacteristic
182C2×C47#54111yescharacteristic
183C2×C47#54411yescharacteristic
184C2×C47#54411yescharacteristic
185C2×#125—471no—
186C2×#117—471no—
187#398—471no—
188#398—471no—
189#398—471no—
190#398—471no—
191#396—471no—
192#396—471no—
193#396—471no—
194#396D4711yescharacteristic
195#389—471no—
196#389—471no—
197#384—471no—
198#380—471no—
199#380—471no—
200C47#262911yescharacteristic, complemented, Sylow
201C23×C4—471no—
202#125—944no—
203#117—944no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4C2×D4711yescharacteristic
220C2×C4⋊C4C2×D4711yescharacteristic
221C2×C4⋊C4C2×D4711yescharacteristic
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C22⋊C4C2×D4711yescharacteristic
226C2×C22⋊C4C2×D4711yescharacteristic
227C2×C22⋊C4C2×D4711yescharacteristic
228C2×C42—471no—
229C2×C42—471no—
230#95—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95C2×D4711yescharacteristic
238C24C22×D4711yescharacteristic
239C22×C4—471no—
240C22×C4—474no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—942no—
249C22×C4—942no—
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252C22×C4C22×D4711yescharacteristic
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—942no—
262C4⋊C4—942no—
263C4⋊C4—942no—
264C4⋊C4—942no—
265C4⋊C4—942no—
266C4⋊C4—942no—
267C4⋊C4—942no—
268C4⋊C4—1881no—
269C4⋊C4—1881no—
270C4⋊C4—1881no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C4⋊C4—1881no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—942no—
278C22⋊C4—1881no—
279C22⋊C4—1881no—
280C42—474no—
281C42—942no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23Q8×D4712yes—
289C23C23×D4711yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—472no—
308C2×C4—472no—
309C2×C4—472no—
310C2×C4—472no—
311C2×C4—472no—
312C2×C4—948no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4D4×D4712yes—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22C2×D4×D4711yescharacteristic
341C22C2×Q8×D4711yescharacteristic
342C22#41×D4711yescharacteristic
343C22#1309406911yescharacteristic
344C22#1309406911yescharacteristic
345C22#1309407111yescharacteristic
346C22#1309407111yescharacteristic
347C4—22no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—474no—
354C4—942no—
355C4—942no—
356C4—1881no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4—1881no—
361C2—42no—
362C2C22⋊Q8×D4711yescharacteristic
363C2#1568970011yescharacteristic
364C2#1568970211yescharacteristic
365C2#1568972311yescharacteristic
366C2#1568973011yescharacteristic
367C2#1568975211yescharacteristic
368C2#1568975211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2629
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13094014C2semidirect
3. #15689057C2semidirect
4. #15689056C2semidirect
5. #15689054C2semidirect
6. #15689053C2semidirect
10. #15689020C2semidirect
11. #15689018C2semidirect
12. #15688992C2semidirect
200. C47#2629semidirect