Finite Group Databasebeta

← #26107267

Subgroups — #26107267

Order 12032.

534 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252083C211yesmaximal, characteristic
2#20243162C211yesmaximal, characteristic, complemented
3C22⋊C4×C47⋊C8C211yesmaximal, characteristic, complemented
4#20241879C211yesmaximal, characteristic
5#20241276C211yesmaximal, characteristic, complemented
6#20241274C211yesmaximal, characteristic, complemented
7C47×#1501C211yesmaximal, characteristic
8C2×#13094031C411yescharacteristic, complemented
9C23×C47⋊C8C2211yescharacteristic
10#15689195—21no—
11#15689195—21no—
12D4×C47⋊C8—21no—
13D4×C47⋊C8—21no—
14#15689150C411yescharacteristic, complemented
15#15689090C411yescharacteristic, complemented
16#15689087C2211yescharacteristic
17C2×C22⋊(C47⋊C8)C2211yescharacteristic
18#15689079C411yescharacteristic, complemented
19C2×C4×C47⋊C8—21no—
20C2×C8×Dic47—21no—
21C4×C22⋊Dic47C2211yescharacteristic
22#15688878—21no—
23#15688877—21no—
24#15688860C412yescomplemented
25#15688857C412yescomplemented
26C47×#525C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C4×C22⋊C4×C47C2211yescharacteristic
29C47×#328C412yescomplemented
30C47×#327C412yescomplemented
31#13094031—42no—
32C2×#10625329—21no—
33C2×#10625329C2×C411yescharacteristic
34C2×#10625329C2×C411yescharacteristic
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C22×C47⋊C8—42no—
38C22×C47⋊C8C2×C411yescharacteristic
39C22×C47⋊C8C2×C411yescharacteristic
40C22×C47⋊C8D411yescharacteristic
41C22×C47⋊C8D411yescharacteristic
42C22×C47⋊C8D411yescharacteristic
43C22×C47⋊C8D411yescharacteristic
44C2×C22⋊Dic47—21no—
45C2×C4×Dic47—21no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)—21no—
51C22⋊(C47⋊C8)—21no—
52C22⋊(C47⋊C8)—21no—
53C22⋊(C47⋊C8)C2×C412yes—
54#13093935—21no—
55C4×C47⋊C8—21no—
56C4×C47⋊C8—42no—
57C8×Dic47—42no—
58C47⋊#95C2×C412yes—
59C2×#41×C47C2×C411yescharacteristic
60C23×C4×C47C2311yescharacteristic
61C22×C8×C47—21no—
62#123×C47—21no—
63C22⋊Q8×C47C2×C411yescharacteristic
64C22⋊Q8×C47C2×C411yescharacteristic
65#121×C47C2×C411yescharacteristic
66#121×C47C2×C411yescharacteristic
67#120×C47—21no—
68C4×D4×C47—21no—
69C4×D4×C47—21no—
70#117×C47C2×C411yescharacteristic
71C2×C22⋊C4×C47—21no—
72C2×C42×C47—21no—
73C22⋊C8×C47—21no—
74C22⋊C8×C47C2×C412yes—
75#95×C47C2×C412yes—
76C24×C47#4111yescharacteristic
77#41×C47—41no—
78#41×C47—41no—
79C2×Q8×C47C4211yescharacteristic
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47C4211yescharacteristic
84C22×C4×C47—22no—
85C22×C4×C47—21no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47C22×C411yescharacteristic
89C22×C4×C47C22×C411yescharacteristic
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47#4111yescharacteristic
94C22×Dic47—22no—
95C2×C8×C47—22no—
96C2×C8×C47—41no—
97C2×C8×C47—41no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47C4211yescharacteristic
101C4⋊C4×C47C4211yescharacteristic
102C22⋊C4×C47—24no—
103C22⋊C4×C47—21no—
104C22⋊C4×C47—21no—
105C22⋊C4×C47—21no—
106C22⋊C4×C47—21no—
107C22⋊C4×C47—21no—
108C42×C47—21no—
109C42×C47—41no—
110C42×C47—41no—
111C22⋊Dic47—24no—
112C4×Dic47—41no—
113C4×Dic47—41no—
114#10625329—42no—
115#10625329—41no—
116#10625329—41no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—21no—
121C2×C47⋊C8—21no—
122C2×C47⋊C8—22no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8—41no—
125C2×C47⋊C8—41no—
126C2×C47⋊C8—41no—
127C2×C47⋊C8—41no—
128C2×C47⋊C8—42no—
129C2×C47⋊C8C22⋊C411yescharacteristic
130C2×C47⋊C8C22⋊C411yescharacteristic
131C2×C47⋊C8C22⋊C411yescharacteristic
132C2×C47⋊C8C22⋊C411yescharacteristic
133C23×C47—22no—
134C23×C47—22no—
135C23×C47—21no—
136C23×C47—41no—
137C23×C47#11711yescharacteristic
138C23×C47C4×D411yescharacteristic
139C23×C47C4×D411yescharacteristic
140Q8×C47—41no—
141D4×C47—41no—
142D4×C47—42no—
143D4×C47—42no—
144D4×C47—42no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—24no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—42no—
159C2×C4×C47—42no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47C2×C4211yescharacteristic
163C2×C4×C47C2×C22⋊C411yescharacteristic
164C2×C4×C47C4×D411yescharacteristic
165C2×C4×C47C4×D411yescharacteristic
166C2×Dic47—24no—
167C2×Dic47—42no—
168C2×Dic47—42no—
169C8×C47—42no—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C47⋊C8—21no—
173C47⋊C8—42no—
174C47⋊C8—41no—
175C47⋊C8—41no—
176C47⋊C8#9912yes—
177#8238—471nomaximal, Sylow
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—44no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47C4×C22⋊C411yescharacteristic
190C22×C47#44312yes—
191C22×C47#44312yes—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—44no—
196C4×C47—41no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47C2×#9911yescharacteristic
200C4×C47#41011yescharacteristic
201Dic47—44no—
202#2929—471no—
203C8×C22⋊C4—471no—
204C8×C22⋊C4—471no—
205#1501—471no—
206#1501D4711yescharacteristic
207#1298—471no—
208#1297—471no—
209C2×C47—22no—
210C2×C47—22no—
211C2×C47—41no—
212C2×C47—81no—
213C2×C47C4×#9911yescharacteristic
214C2×C47#176411yescharacteristic
215C2×C47#176411yescharacteristic
216C2×#131—471no—
217C23×C8—471no—
218#525C2×D4711yescharacteristic
219#435—941no—
220#435—941no—
221C8×D4—941no—
222C8×D4—941no—
223#424—471no—
224#408—471no—
225#407—471no—
226C2×C22⋊C8—471no—
227C2×C22⋊C8C2×D4711yescharacteristic
228#405—471no—
229C2×C4×C8—941no—
230C2×C4×C8—941no—
231C4×C22⋊C4—471no—
232C4×C22⋊C4C2×D4711yescharacteristic
233#336—941no—
234#336—941no—
235#328—472no—
236#328Dic4712yescomplemented
237#327—472no—
238#327Dic4712yescomplemented
239C47#823811yescharacteristic, complemented, Sylow
240C2×#41C4×D4711yescharacteristic
241C23×C4C22×D4711yescharacteristic
242#131—1882no—
243C2×M16—471no—
244C2×M16—471no—
245C2×M16—941no—
246C22×C8—21no—
247C22×C8—471no—
248C22×C8—471no—
249C22×C8—471no—
250C22×C8—471no—
251C22×C8—471no—
252C22×C8—471no—
253C22×C8—941no—
254C22×C8—941no—
255C22×C8—1882no—
256#123—21no—
257C22⋊Q8C4×D4711yescharacteristic
258C22⋊Q8C2×Dic4711yescharacteristic
259#121C4×D4711yescharacteristic
260#121C2×Dic4711yescharacteristic
261#120—21no—
262C4×D4—21no—
263C4×D4—21no—
264#117C4×D4711yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—941no—
267C2×C42—21no—
268C2×C42—941no—
269C4⋊C8—941no—
270C4⋊C8—941no—
271C22⋊C8—21no—
272C22⋊C8—472no—
273C22⋊C8—941no—
274C22⋊C8—941no—
275C22⋊C8—941no—
276C22⋊C8—941no—
277C22⋊C8—941no—
278C22⋊C8C2×Dic4712yes—
279#97—941no—
280C4×C8—941no—
281C4×C8—1882no—
282C4×C8—1882no—
283#95—472no—
284#95C2×Dic4712yes—
285C24#1062535211yescharacteristic
286#41—41no—
287#41—41no—
288C2×Q8C4×Dic4711yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C4×Dic4711yescharacteristic
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—942no—
298C22×C4C2×C4×D4711yescharacteristic
299C22×C4C2×C4×D4711yescharacteristic
300C22×C4D4×D4711yescharacteristic
301C22×C4D4×D4711yescharacteristic
302C22×C4#1062535211yescharacteristic
303C22×C4C22×Dic4711yescharacteristic
304M16—1882no—
305M16—1881no—
306M16—1881no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—471no—
311C2×C8—471no—
312C2×C8—471no—
313C2×C8—471no—
314C2×C8—942no—
315C2×C8—942no—
316C2×C8—942no—
317C2×C8—941no—
318C2×C8—941no—
319C2×C8—942no—
320C2×C8—1882no—
321C2×C8—1881no—
322C2×C8—1881no—
323C2×C8—1881no—
324C2×C8—1881no—
325C2×C8—1881no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4C4×Dic4711yescharacteristic
329C4⋊C4C4×Dic4711yescharacteristic
330C22⋊C4—24no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—944no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—1881no—
341C42—1881no—
342C23—22no—
343C23—22no—
344C23—21no—
345C23—41no—
346C23#1309398011yescharacteristic
347C23(C22⋊D47)⋊C411yescharacteristic
348C23D4×Dic4711yescharacteristic
349Q8—41no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—42no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—944no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4C2×C4×Dic4711yescharacteristic
375C2×C4C22⋊C4×D4711yescharacteristic
376C2×C4(C22⋊D47)⋊C411yescharacteristic
377C2×C4D4×Dic4711yescharacteristic
378C8—42no—
379C8—472no—
380C8—941no—
381C8—941no—
382C8—941no—
383C8—1882no—
384C8—1881no—
385C8—1881no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22C22⋊C4×Dic4711yescharacteristic
398C22#1568923712yes—
399C22#1568924012yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—1884no—
408C4#99×D4711yescharacteristic
409C4#1568909511yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—81no—
414C2#99×Dic4711yescharacteristic
415C2#2024322611yescharacteristic
416C2#2024322811yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1501C2
socleC22×C47C4×C22⋊C4
prime radicalC47×#525C22
cosocleC23×C4×C47C23
hypercenter#1501D47
hypocenterC47#8238
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #20243162C2semidirect
3. C22⋊C4×C47⋊C8C2semidirect
5. #20241276C2semidirect
6. #20241274C2semidirect
8. C2×#13094031C4semidirect
14. #15689150C4semidirect
15. #15689090C4semidirect
18. #15689079C4semidirect
24. #15688860C4semidirect
25. #15688857C4semidirect
29. C47×#328C4semidirect
30. C47×#327C4semidirect
236. #328Dic47semidirect
238. #327Dic47semidirect
239. C47#8238semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202520832
#202431622
C22⋊C4×C47⋊C82
#202418792
#202412762
#202412742
C47×#15012
#823847