Finite Group Databasebeta

← #20250408

Subgroups — #20250408

Order 6016.

528 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094003C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3#15689059C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689057C211yesmaximal, characteristic, complemented
6#15689055C211yesmaximal, characteristic, complemented
7#15689046C211yesmaximal, characteristic, complemented
8#15689046C211yesmaximal, characteristic, complemented
9#15689027C211yesmaximal, characteristic, complemented
10#15689026C211yesmaximal, characteristic
11#15689020C211yesmaximal, characteristic, complemented
12#15689003C211yesmaximal, characteristic
13#15688996C211yesmaximal, characteristic, complemented
14#15688995C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18#13094003—24no—
19#13094001—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
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×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C23×C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C2×D4×C47—41no—
56C2×D4×C47—41no—
57C2×D4×C47Q814yescomplemented
58C22×C4×C47—22no—
59C22×C4×C47—41no—
60C22×C4×C47—41no—
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×Dic47—22no—
67C22×Dic47—41no—
68C22×Dic47—41no—
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C2×Dic94—41no—
78C2×Dic94—41no—
79C2×Dic94D414yescomplemented
80C22⋊C4×C47—22no—
81C22⋊C4×C47—41no—
82C22⋊C4×C47—41no—
83C22⋊Dic47—22no—
84C22⋊Dic47—22no—
85C22⋊Dic47—22no—
86C22⋊Dic47—22no—
87C22⋊Dic47—22no—
88C22⋊Dic47—41no—
89C22⋊Dic47—41no—
90C4⋊Dic47—22no—
91C4⋊Dic47—22no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94Dic47⋊C4—22no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—41no—
100Dic47⋊C4—41no—
101Dic47⋊C4—41no—
102C4×Dic47—41no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47C2×Q812yes—
116C23×C47C2×Q812yes—
117C23×C47C2411yescharacteristic
118D4×C47—44no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—44no—
133C2×C4×C47C2×D412yes—
134C2×C4×C47C2×Q812yes—
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×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—44no—
157C2×Dic47C2×D412yes—
158C2×Dic47C2×D412yes—
159C2×Dic47#4112yes—
160Dic94—44no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47C22×D411yescharacteristic
176C22×C47C22×Q811yescharacteristic
177C22×C47C2×#4111yescharacteristic
178C22×C47H(5,𝔽2)11yescharacteristic
179C22×C47H(5,𝔽2)11yescharacteristic
180C22×C47H(5,𝔽2)11yescharacteristic
181C22×C472−1+411yescharacteristic
182C4×C47—22no—
183C4×C47—22no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47—41no—
187Dic47—22no—
188Dic47—22no—
189Dic47—22no—
190Dic47—41no—
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194Dic47—41no—
195#2732—471nomaximal, Sylow
196C2×C47—42no—
197C2×C47—42no—
198C2×C47#53411yescharacteristic
199C2×C47#53911yescharacteristic
200C2×C47#54311yescharacteristic
201C2×C47D4×Q811yescharacteristic
202C2×C47#55011yescharacteristic
203C2×C47#55411yescharacteristic
204C2×C47#56211yescharacteristic
205C2×C22⋊Q8—471no—
206C2×C22⋊Q8—471no—
207#399—471no—
208#399—471no—
209#398—471no—
210#398—471no—
211#396—471no—
212#396—471no—
213#391—471no—
214#390—471no—
215#389—471no—
216#386—471no—
217#386D4711yescharacteristic
218#385—471no—
219#385—471no—
220C47#273211yescharacteristic, complemented, Sylow
221C22×Q8—471no—
222C22×D4C2×D4711yescharacteristic
223C23×C4—471no—
224C23×C4C2×D4711yescharacteristic
225C22⋊Q8—944no—
226C22⋊Q8—944no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4—471no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C4⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4C2×D4711yescharacteristic
247C2×C22⋊C4C2×D4711yescharacteristic
248C2×C22⋊C4C2×D4711yescharacteristic
249C2×C42—471no—
250#95—471no—
251#95—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95C2×D4711yescharacteristic
257#95C2×D4711yescharacteristic
258C24C22×D4711yescharacteristic
259C24C22×D4711yescharacteristic
260C2×Q8—474no—
261C2×Q8—1881no—
262C2×Q8—1881no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4Dic9414yescomplemented
266C22×C4—22no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—942no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4C22×D4711yescharacteristic
281C22×C4C22×D4711yescharacteristic
282C22×C4C22×D4711yescharacteristic
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285C4⋊C4—942no—
286C4⋊C4—942no—
287C4⋊C4—942no—
288C4⋊C4—942no—
289C4⋊C4—942no—
290C4⋊C4—942no—
291C4⋊C4—942no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C4⋊C4—1881no—
295C4⋊C4—1881no—
296C4⋊C4—1881no—
297C22⋊C4—22no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—942no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C22⋊C4—942no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C42—1881no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×Dic9412yes—
321C23C2×Dic9412yes—
322C23C23×D4711yescharacteristic
323Q8—1884no—
324D4—44no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—472no—
340C2×C4—472no—
341C2×C4—472no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—1884no—
364C2×C4C2×Dic9412yes—
365C2×C4D4×D4712yes—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22C2×D4×D4711yescharacteristic
381C22C22×Dic9411yescharacteristic
382C22#41×D4711yescharacteristic
383C22#1309406911yescharacteristic
384C22#1309406911yescharacteristic
385C22#1309406911yescharacteristic
386C22#1309407111yescharacteristic
387C4—22no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—942no—
393C4—942no—
394C4—942no—
395C4—1881no—
396C4—1881no—
397C4—1881no—
398C4—1881no—
399C4—1881no—
400C2—42no—
401C2—42no—
402C2#1568968311yescharacteristic
403C2#1568971611yescharacteristic
404C2#1568974911yescharacteristic
405C2D4×Dic9411yescharacteristic
406C2#1568979111yescharacteristic
407C2#1568983211yescharacteristic
408C2#1568986811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2732
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13094003C2semidirect
2. C2×#13094001C2semidirect
3. #15689059C2semidirect
4. #15689059C2semidirect
5. #15689057C2semidirect
6. #15689055C2semidirect
7. #15689046C2semidirect
8. #15689046C2semidirect
9. #15689027C2semidirect
11. #15689020C2semidirect
13. #15688996C2semidirect
14. #15688995C2semidirect
57. C2×D4×C47Q8semidirect
79. C2×Dic94D4semidirect
220. C47#2732semidirect
265. C2×D4Dic94semidirect