Finite Group Databasebeta

← #20246117

Subgroups — #20246117

Order 6016.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094004C211yesmaximal, characteristic
2#15689027C211yesmaximal, characteristic, complemented
3#15689027C211yesmaximal, characteristic, complemented
4#15689021C211yesmaximal, characteristic, complemented
5#15689019C211yesmaximal, characteristic, complemented
6#15689009C211yesmaximal, characteristic, complemented
7#15689008C211yesmaximal, characteristic, complemented
8#15689006C211yesmaximal, characteristic, complemented
9#15688997C211yesmaximal, characteristic
10#15688994C211yesmaximal, characteristic
11#15688982C211yesmaximal, characteristic
12C4×(C2×D47)⋊C4C211yesmaximal, characteristic
13#15688970C211yesmaximal, characteristic
14#95×D47C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094004C418yescomplemented
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C2×C4×Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C42×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52C23×D47C2311yescharacteristic
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
67C2×C4×D47—22no—
68C2×C4×D47—41no—
69C2×C4×D47—41no—
70C2×C4×D47—41no—
71C2×C4×D47—41no—
72C2×C4×D47—41no—
73C2×C4×D47—41no—
74C2×C4×D47C2×C414yes—
75C2×C4×D47Q814yescomplemented
76C2×Dic94—41no—
77C2×Dic94—41no—
78C2×Dic94C2×C414yescomplemented
79C4⋊C4×C47—41no—
80C4⋊C4×C47C2×C414yescomplemented
81C42×C47—41no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4C2×C414yes—
85(C2×D47)⋊C4C2×C414yes—
86C4⋊Dic47—41no—
87C4⋊Dic47C2×C414yescomplemented
88C4⋊Dic47C2×C414yescomplemented
89Dic47⋊C4—41no—
90Dic47⋊C4—41no—
91Dic47⋊C4—41no—
92Dic47⋊C4—41no—
93C4×Dic47—41no—
94C4×Dic47—41no—
95C4×Dic47—41no—
96C23×C47C2411yescharacteristic
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47C22×C412yes—
102C22×D47C2×Q812yes—
103C22×D47#4112yes—
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×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×C47C22×C412yes—
122C2×C4×C47C22×C412yes—
123C2×C4×C47C22×C412yes—
124C2×C4×C47C2×Q812yes—
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×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×Dic47C22×C412yes—
143C2×Dic47C22×C412yes—
144C2×Dic47C22×C412yes—
145C2×Dic47C2×Q812yes—
146C4×D47—44no—
147C4×D47—44no—
148C4×D47—44no—
149Dic94—44no—
150C22×C47C23×C411yescharacteristic
151C22×C47C22×Q811yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47H(5,𝔽2)11yescharacteristic
154C22×C47H(5,𝔽2)11yescharacteristic
155C22×C47H(5,𝔽2)11yescharacteristic
156C22×C472−1+411yescharacteristic
157C2×D47—22no—
158C2×D47—22no—
159C2×D47—22no—
160C2×D47—22no—
161C2×D47—22no—
162C2×D47—22no—
163C2×D47C4×Q814yes—
164C4×C47—22no—
165C4×C47—22no—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171Dic47—22no—
172Dic47—22no—
173Dic47—22no—
174Dic47—22no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#2329—471nomaximal, Sylow
179C2×C47C2×C4×Q811yescharacteristic
180C2×C47#51811yescharacteristic
181C2×C47#52011yescharacteristic
182C2×C47#53811yescharacteristic
183C2×C47#53911yescharacteristic
184C2×C47#54311yescharacteristic
185C2×C47#54411yescharacteristic
186D47—24no—
187C2×C22⋊Q8—471no—
188#391—471no—
189#391—471no—
190#389—471no—
191#389—471no—
192#387—471no—
193#387—471no—
194#387—471no—
195#387D4711yescharacteristic, complemented
196#385—471no—
197#385—471no—
198#380—471no—
199C4×C22⋊C4—471no—
200C4×C22⋊C4—471no—
201C2×#95—471no—
202C47#232911yescharacteristic, complemented, Sylow
203C22×Q8—471no—
204C23×C4—471no—
205C23×C4—471no—
206C23×C4—471no—
207C22⋊Q8—478no—
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⋊C4C2×D4711yescharacteristic
216C2×C4⋊C4C2×D4711yescharacteristic
217C2×C22⋊C4—471no—
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C22⋊C4—471no—
221C2×C42—471no—
222C2×C42—471no—
223C2×C42—471no—
224C2×C42C2×D4711yescharacteristic
225#95—471no—
226#95—471no—
227#95—471no—
228#95—471no—
229#95—471no—
230#95—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95C2×D4711yescharacteristic
236#95C2×D4711yescharacteristic
237#95C2×D4711yescharacteristic
238#95C2×D4711yescharacteristic
239C24—471no—
240C2×Q8—474no—
241C2×Q8—1881no—
242C2×Q8—1881no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—474no—
248C22×C4—474no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—942no—
253C22×C4—1881no—
254C22×C4—1881no—
255C22×C4—1881no—
256C22×C4—1881no—
257C22×C4—1881no—
258C22×C4—1881no—
259C22×C4C22×D4711yescharacteristic
260C22×C4C22×D4711yescharacteristic
261C22×C4C22×D4711yescharacteristic
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264C22×C4C22×D4711yescharacteristic
265C22×C4C22×D4711yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—474no—
268C4⋊C4—474no—
269C4⋊C4—1881no—
270C4⋊C4—1881no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C4⋊C4—1881no—
274C4⋊C4C4×D4714yescomplemented
275C22⋊C4—474no—
276C22⋊C4—474no—
277C22⋊C4—942no—
278C22⋊C4—942no—
279C42—41no—
280C42—1881no—
281C42—1881no—
282C42—1881no—
283C23—472no—
284C23—472no—
285C23—472no—
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—472no—
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—1884no—
331C2×C4—1884no—
332C2×C4—1884no—
333C2×C4C2×C4×D4712yes—
334C2×C4C2×C4×D4712yes—
335C2×C4C2×C4×D4712yes—
336C2×C4Q8×D4712yes—
337C22—474no—
338C22—942no—
339C22—942no—
340C22—942no—
341C22—942no—
342C22—942no—
343C22—942no—
344C22C22×C4×D4711yescharacteristic
345C22C2×Q8×D4711yescharacteristic
346C22#41×D4711yescharacteristic
347C22#1309406911yescharacteristic
348C22#1309407011yescharacteristic
349C22#1309407011yescharacteristic
350C22#1309407111yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—942no—
359C4—942no—
360C4—942no—
361C4—942no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C2—944no—
366C2C4×Q8×D4711yescharacteristic
367C2#1568959711yescharacteristic
368C2#1568960211yescharacteristic
369C2#1568970911yescharacteristic
370C2#1568971411yescharacteristic
371C2#1568974811yescharacteristic
372C2#1568975311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#387C2
socleC23×C47C24
hypercenter#387D47
hypocenterC47#2329
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #15689027C2semidirect
3. #15689027C2semidirect
4. #15689021C2semidirect
5. #15689019C2semidirect
6. #15689009C2semidirect
7. #15689008C2semidirect
8. #15689006C2semidirect
15. C47×#387C2semidirect
20. #13094004C4semidirect
75. C2×C4×D47Q8semidirect
78. C2×Dic94C2×C4semidirect
80. C4⋊C4×C47C2×C4semidirect
87. C4⋊Dic47C2×C4semidirect
88. C4⋊Dic47C2×C4semidirect
195. #387D47semidirect
202. C47#2329semidirect
274. C4⋊C4C4×D47semidirect