Finite Group Databasebeta

← #20249881

Subgroups — #20249881

Order 6016.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094001C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3#15689059C211yesmaximal, characteristic, complemented
4#15689056C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689043C211yesmaximal, characteristic, complemented
7#15689035C211yesmaximal, characteristic, complemented
8#15689035C211yesmaximal, characteristic, complemented
9#15689029C211yesmaximal, characteristic, complemented
10#15689007C211yesmaximal, characteristic, complemented
11#15689003C211yesmaximal, characteristic
12#15689003C211yesmaximal, characteristic
13#15688995C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C47×#390C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20#13094001—24no—
21#13094001—24no—
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×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C2×D4×C47—41no—
56C2×D4×C47—41no—
57C2×D4×C47Q814yescomplemented
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47—22no—
64C22×Dic47—22no—
65C22×Dic47—22no—
66C22×Dic47—41no—
67C22×Dic47—41no—
68C22×Dic47—41no—
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C2×Dic94—22no—
78C2×Dic94—22no—
79C2×Dic94—22no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83C4⋊C4×C47—41no—
84C22⋊C4×C47—22no—
85C22⋊C4×C47—22no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C42×C47—41no—
89C22⋊Dic47—22no—
90C22⋊Dic47—22no—
91C22⋊Dic47—22no—
92C22⋊Dic47—41no—
93C22⋊Dic47—41no—
94C22⋊Dic47—41no—
95C4⋊Dic47—22no—
96C4⋊Dic47—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—41no—
100Dic47⋊C4—41no—
101Dic47⋊C4—41no—
102Dic47⋊C4D414yescomplemented
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×C47C2×D412yes—
133C2×C4×C47C2×Q812yes—
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×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—44no—
156C2×Dic47—44no—
157C2×Dic47C2×D412yes—
158C2×Dic47C2×D412yes—
159C2×Dic47#4112yes—
160Dic94—44no—
161Dic94—44no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C22×D411yescharacteristic
177C22×C47C22×Q811yescharacteristic
178C22×C47C2×#4111yescharacteristic
179C22×C47H(5,𝔽2)11yescharacteristic
180C22×C47H(5,𝔽2)11yescharacteristic
181C22×C47H(5,𝔽2)11yescharacteristic
182C22×C472−1+411yescharacteristic
183C4×C47—22no—
184C4×C47—22no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—41no—
188Dic47—22no—
189Dic47—22no—
190Dic47—22no—
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194Dic47—41no—
195Dic47—41no—
196#2692—471nomaximal, Sylow
197C2×C47—42no—
198C2×C47—42no—
199C2×C47#53511yescharacteristic
200C2×C47#54211yescharacteristic
201C2×C47#54311yescharacteristic
202C2×C47#54611yescharacteristic
203C2×C47D4×Q811yescharacteristic
204C2×C47#55411yescharacteristic
205C2×C47#56211yescharacteristic
206C2×C22⋊Q8—471no—
207C2×C22⋊Q8—471no—
208#399—471no—
209#398—471no—
210#396—471no—
211#395—471no—
212#393—471no—
213#393—471no—
214#391—471no—
215#390D4711yescharacteristic
216#387—471no—
217#386—471no—
218#386—471no—
219#385—471no—
220#380—471no—
221C47#269211yescharacteristic, complemented, Sylow
222C22×Q8—471no—
223C22×Q8—471no—
224C22×D4C2×D4711yescharacteristic
225C23×C4—471no—
226C23×C4—471no—
227C22⋊Q8—944no—
228C22⋊Q8—944no—
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⋊C4C2×D4711yescharacteristic
238C2×C22⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4C2×D4711yescharacteristic
245C2×C22⋊C4C2×D4711yescharacteristic
246C2×C22⋊C4C2×D4711yescharacteristic
247C2×C22⋊C4C2×D4711yescharacteristic
248C2×C42C2×D4711yescharacteristic
249#95—471no—
250#95—471no—
251#95—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95—471no—
258#95—471no—
259C24C22×D4711yescharacteristic
260C24C22×D4711yescharacteristic
261C2×Q8—942no—
262C2×Q8—942no—
263C2×Q8—942no—
264C2×Q8—1881no—
265C2×Q8—1881no—
266C2×Q8—1881no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4Dic9414yescomplemented
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—942no—
279C22×C4—942no—
280C22×C4—942no—
281C22×C4—1881no—
282C22×C4—1881no—
283C22×C4—1881no—
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—474no—
291C4⋊C4—942no—
292C4⋊C4—942no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4—1881no—
296C4⋊C4—1881no—
297C4⋊C4—1881no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C22⋊C4—942no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C42—41no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×Dic9412yes—
322C23C2×Dic9412yes—
323C23C23×D4711yescharacteristic
324Q8—1884no—
325Q8—1884no—
326D4—44no—
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—21no—
339C2×C4—21no—
340C2×C4—472no—
341C2×C4—472no—
342C2×C4—472no—
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—941no—
364C2×C4—1884no—
365C2×C4—1884no—
366C2×C4C2×Dic9412yes—
367C2×C4D4×D4712yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22C2×D4×D4711yescharacteristic
383C22C22×Dic9411yescharacteristic
384C22#41×D4711yescharacteristic
385C22#1309406911yescharacteristic
386C22#1309406911yescharacteristic
387C22#1309406911yescharacteristic
388C22#1309407111yescharacteristic
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—942no—
395C4—942no—
396C4—942no—
397C4—1881no—
398C4—1881no—
399C4—1881no—
400C4—1881no—
401C4—1881no—
402C2—42no—
403C2—42no—
404C2#1568968611yescharacteristic
405C2#1568973711yescharacteristic
406C2#1568974911yescharacteristic
407C2#1568976211yescharacteristic
408C2D4×Dic9411yescharacteristic
409C2#1568983211yescharacteristic
410C2#1568986811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2692
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094001C2semidirect
2. C2×#13094001C2semidirect
3. #15689059C2semidirect
4. #15689056C2semidirect
5. #15689046C2semidirect
6. #15689043C2semidirect
7. #15689035C2semidirect
8. #15689035C2semidirect
9. #15689029C2semidirect
10. #15689007C2semidirect
13. #15688995C2semidirect
14. #15688981C2semidirect
57. C2×D4×C47Q8semidirect
102. Dic47⋊C4D4semidirect
221. C47#2692semidirect
269. C2×D4Dic94semidirect