Finite Group Databasebeta

← #20250041

Subgroups — #20250041

Order 6016.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094014C211yesmaximal, characteristic, complemented
2C2×#13094004C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic, complemented
4#15689056C211yesmaximal, characteristic, complemented
5#15689056C211yesmaximal, characteristic, complemented
6#15689047C211yesmaximal, characteristic
7#15689045C211yesmaximal, characteristic
8#15689043C211yesmaximal, characteristic, complemented
9#15689027C211yesmaximal, characteristic, complemented
10#15689021C211yesmaximal, characteristic, complemented
11#15689014C211yesmaximal, characteristic
12#15689013C211yesmaximal, characteristic
13#15688994C211yesmaximal, characteristic
14#15688982C211yesmaximal, characteristic
15C47×#389C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13094014—24no—
19#13094004—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
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×C4⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—41no—
71C2×Dic94—22no—
72C2×Dic94—22no—
73C2×Dic94—41no—
74C4⋊C4×C47—22no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—22no—
77C4⋊C4×C47—41no—
78C42×C47—41no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—22no—
81(C2×D47)⋊C4—41no—
82(C2×D47)⋊C4—41no—
83(C2×D47)⋊C4—41no—
84(C2×D47)⋊C4Q814yescomplemented
85C4⋊Dic47—22no—
86C4⋊Dic47—41no—
87C4⋊Dic47D414yes—
88Dic47⋊C4—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—41no—
93Dic47⋊C4—41no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96C4×Dic47—22no—
97C23×C47C2411yescharacteristic
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47C2×Q812yes—
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×C47—21no—
123C2×C4×C47C2×D412yes—
124C2×C4×C47C2×Q812yes—
125C2×C4×C47#4112yes—
126C2×Dic47—21no—
127C2×Dic47—21no—
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×Dic47—21no—
144C2×Dic47C2×D412yes—
145C2×Dic47C2×D412yes—
146C2×Dic47C2×Q812yes—
147C4×D47—44no—
148Dic94—44no—
149C22×C47C22×D411yescharacteristic
150C22×C47C22×Q811yescharacteristic
151C22×C47C2×#4111yescharacteristic
152C22×C47H(5,𝔽2)11yescharacteristic
153C22×C47H(5,𝔽2)11yescharacteristic
154C22×C472−1+411yescharacteristic
155C22×C472−1+411yescharacteristic
156C2×D47—22no—
157C2×D47—22no—
158C2×D47—22no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C4×C47—22no—
164C4×C47—22no—
165C4×C47—22no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170Dic47—22no—
171Dic47—22no—
172Dic47—22no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177#2704—471nomaximal, Sylow
178C2×C47#53711yescharacteristic
179C2×C47#54111yescharacteristic
180C2×C47#54411yescharacteristic
181C2×C47#54611yescharacteristic
182C2×C47D4×Q811yescharacteristic
183C2×C47#55411yescharacteristic
184C2×C47#56211yescharacteristic
185D47—42no—
186C2×#125—471no—
187C2×C22⋊Q8—471no—
188#398—471no—
189#398—471no—
190#398—471no—
191#396—471no—
192#396—471no—
193#395—471no—
194#391—471no—
195#389—471no—
196#389D4711yescharacteristic, complemented
197#388—471no—
198#388—471no—
199#385—471no—
200#380—471no—
201C47#270411yescharacteristic, complemented, Sylow
202C22×Q8—471no—
203C23×C4—471no—
204#125—944no—
205C22⋊Q8—944no—
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⋊C4C2×D4711yescharacteristic
218C2×C4⋊C4C2×D4711yescharacteristic
219C2×C4⋊C4C2×D4711yescharacteristic
220C2×C4⋊C4C2×D4711yescharacteristic
221C2×C22⋊C4—471no—
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C22⋊C4—471no—
226C2×C22⋊C4—471no—
227C2×C42—471no—
228C2×C42C2×D4711yescharacteristic
229#95—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
238#95C2×D4711yescharacteristic
239C24—471no—
240C2×Q8—942no—
241C2×Q8—942no—
242C2×Q8—1881no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—942no—
251C22×C4—942no—
252C22×C4—1881no—
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C22×C4C22×D4711yescharacteristic
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—474no—
265C4⋊C4—942no—
266C4⋊C4—942no—
267C4⋊C4—942no—
268C4⋊C4—942no—
269C4⋊C4—942no—
270C4⋊C4—1881no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C4⋊C4—1881no—
274C4⋊C4—1881no—
275C22⋊C4—474no—
276C22⋊C4—942no—
277C22⋊C4—942no—
278C22⋊C4—1881no—
279C22⋊C4—1881no—
280C22⋊C4—1881no—
281C42—41no—
282C42—942no—
283C23—472no—
284C23—941no—
285C23—941no—
286C23—941no—
287C23—941no—
288C23—941no—
289C23—941no—
290C23C23×D4711yescharacteristic
291Q8—1884no—
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—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—472no—
311C2×C4—472no—
312C2×C4—472no—
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—1884no—
332C2×C4#1062535012yes—
333C2×C4D4×D4712yes—
334C2×C4Q8×D4712yes—
335C22—942no—
336C22—942no—
337C22—942no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22C2×D4×D4711yescharacteristic
343C22C2×Q8×D4711yescharacteristic
344C22C2×#1062535011yescharacteristic
345C22#1309406911yescharacteristic
346C22#1309407011yescharacteristic
347C22#1309407111yescharacteristic
348C22#1309407211yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—942no—
357C4—942no—
358C4—942no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4—1881no—
363C2—1882no—
364C2#1568970011yescharacteristic
365C2#1568973111yescharacteristic
366C2#1568975311yescharacteristic
367C2#1568976911yescharacteristic
368C2#1568978811yescharacteristic
369C2#1568982811yescharacteristic
370C2#1568986911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2704
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#13094014C2semidirect
3. #15689057C2semidirect
4. #15689056C2semidirect
5. #15689056C2semidirect
8. #15689043C2semidirect
9. #15689027C2semidirect
10. #15689021C2semidirect
15. C47×#389C2semidirect
84. (C2×D47)⋊C4Q8semidirect
196. #389D47semidirect
201. C47#2704semidirect