Finite Group Databasebeta

← #26107271

Subgroups — #26107271

Order 12032.

510 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#20252082C211yesmaximal, characteristic
2#20243164C211yesmaximal, characteristic, complemented
3#20241880C211yesmaximal, characteristic
4#20241877C211yesmaximal, characteristic
5#20241276C211yesmaximal, characteristic, complemented
6#20241274C211yesmaximal, characteristic, complemented
7C47×#1752C211yesmaximal, characteristic, complemented
8C2×#13094030C411yescharacteristic, complemented
9#15689634C2211yescharacteristic
10#15689194—21no—
11#15689194—21no—
12C8×C22⋊D47—21no—
13C8×C22⋊D47—21no—
14#15689149C411yescharacteristic, complemented
15#15689089C411yescharacteristic, complemented
16#15689087C2211yescharacteristic
17C2×C22⋊(C47⋊C8)C2211yescharacteristic
18#15689078C411yescharacteristic, complemented
19C2×#13093934—21no—
20C4×C22⋊Dic47C2211yescharacteristic
21#15688877—21no—
22#15688861C412yescomplemented
23#15688859C412yescomplemented
24#15688858C412yescomplemented
25#15688856C412yescomplemented
26C23×C8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C2×#97×C47—21no—
29C4×C22⋊C4×C47C2211yescharacteristic
30C47×#336—21no—
31C2×#10625350C2×C411yescharacteristic
32#13094030—42no—
33C2×#10625329C2×C411yescharacteristic
34C2×#10625329C2×C411yescharacteristic
35C2×#10625324—21no—
36C22×C47⋊C8—21no—
37C2×C8×D47—21no—
38#13094007—21no—
39#13094003C2×C411yescharacteristic
40#13094003C2×C411yescharacteristic
41#13093998C2×C411yescharacteristic
42#13093998C2×C411yescharacteristic
43#13093993—21no—
44C4×C22⋊D47—21no—
45C4×C22⋊D47—21no—
46#13093983C2×C411yescharacteristic
47C2×C22⋊Dic47—21no—
48C2×C4×Dic47—21no—
49Dic47⋊C8—21no—
50Dic47⋊C8—21no—
51C22⋊(C47⋊C8)—21no—
52C22⋊(C47⋊C8)—21no—
53C22⋊(C47⋊C8)—21no—
54C22⋊(C47⋊C8)C2×C412yes—
55(C2×D47)⋊C8—21no—
56(C2×D47)⋊C8—21no—
57#13093934—21no—
58#13093934—42no—
59C8×Dic47—21no—
60C47⋊#95C2×C412yes—
61C23×C4×C47C2311yescharacteristic
62C22×C8×C47—21no—
63C22×C8×C47—42no—
64C22×C8×C47C2×C411yescharacteristic
65C22×C8×C47C2×C411yescharacteristic
66C22×C8×C47D411yescharacteristic
67C22×C8×C47D411yescharacteristic
68C22×C8×C47D411yescharacteristic
69C22×C8×C47D411yescharacteristic
70C2×C22⋊C4×C47—21no—
71C2×C42×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47C2×C412yes—
74#97×C47—42no—
75#95×C47C2×C412yes—
76C24×C47#4111yescharacteristic
77C22×C4×C47—22no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47C22×C411yescharacteristic
81C22×C4×C47C22×C411yescharacteristic
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47#4111yescharacteristic
86C2×C22⋊D47—21no—
87C2×C22⋊D47—21no—
88C2×C22⋊D47—21no—
89C22×Dic47—22no—
90#10625350—41no—
91#10625350—41no—
92C2×D188C4211yescharacteristic
93C2×C4×D47—21no—
94C2×Dic94C4211yescharacteristic
95C2×C8×C47—22no—
96C2×C8×C47—22no—
97C2×C8×C47—22no—
98C2×C8×C47—22no—
99C2×C8×C47—41no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C2×C8×C47—41no—
103C2×C8×C47—41no—
104C2×C8×C47C22⋊C411yescharacteristic
105C2×C8×C47C22⋊C411yescharacteristic
106C2×C8×C47C22⋊C411yescharacteristic
107C2×C8×C47C22⋊C411yescharacteristic
108C22⋊C4×C47—42no—
109C42×C47—41no—
110C42×C47—41no—
111C22⋊Dic47—21no—
112C22⋊Dic47—21no—
113C22⋊Dic47—21no—
114C22⋊Dic47—42no—
115(C2×D47)⋊C4—21no—
116(C2×D47)⋊C4—21no—
117C4⋊Dic47C4211yescharacteristic
118C4⋊Dic47C4211yescharacteristic
119Dic47⋊C4—21no—
120Dic47⋊C4—21no—
121C4×Dic47—21no—
122C4×Dic47—41no—
123C4×Dic47—41no—
124#10625329—41no—
125#10625329—41no—
126C2×C47⋊C8—21no—
127C2×C47⋊C8—21no—
128C2×C47⋊C8—22no—
129C2×C47⋊C8—41no—
130C2×C47⋊C8—41no—
131#10625324—42no—
132C8×D47—42no—
133C23×C47—22no—
134C23×C47—22no—
135C23×C47—41no—
136C23×C47#11711yescharacteristic
137C23×C47C4×D411yescharacteristic
138C23×C47C4×D411yescharacteristic
139C22×D47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—42no—
150C2×C4×C47—42no—
151C2×C4×C47—42no—
152C2×C4×C47C2×C4211yescharacteristic
153C2×C4×C47C2×C22⋊C411yescharacteristic
154C2×C4×C47C4×D411yescharacteristic
155C2×C4×C47C4×D411yescharacteristic
156C22⋊D47—42no—
157C22⋊D47—42no—
158C22⋊D47—42no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—42no—
163C2×Dic47—42no—
164C2×Dic47—42no—
165D188—41no—
166C4×D47—41no—
167C4×D47—41no—
168Dic94—41no—
169C8×C47—21no—
170C8×C47—21no—
171C8×C47—21no—
172C8×C47—42no—
173C8×C47#9912yes—
174C47⋊C8—42no—
175C47⋊C8—41no—
176C47⋊C8—41no—
177#8239—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×C47C4×C22⋊C411yescharacteristic
187C22×C47#44412yes—
188C22×C47#44412yes—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—82no—
196C4×C47C2×#9911yescharacteristic
197C4×C47#41011yescharacteristic
198Dic47—41no—
199Dic47—41no—
200Dic47—41no—
201Dic47—82no—
202#2929—471no—
203#1752—471no—
204#1752D4711yescharacteristic, complemented
205#1501—471no—
206#1501—471no—
207#1298—471no—
208#1297—471no—
209C2×C47—22no—
210C2×C47—22no—
211C2×C47—41no—
212C2×C47C4×#9911yescharacteristic
213C2×C47#176511yescharacteristic
214C2×C47#176511yescharacteristic
215D47—81no—
216C2×#131—471no—
217C23×C8C2×D4711yescharacteristic
218#525—471no—
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×#97—21no—
230C2×#97—941no—
231C4×C22⋊C4—471no—
232C4×C22⋊C4C2×D4711yescharacteristic
233#336—21no—
234#336—941no—
235#328—472no—
236#328—472no—
237#327—472no—
238#327—472no—
239C47#823911yescharacteristic, complemented, Sylow
240C2×#41—471no—
241C23×C4C22×D4711yescharacteristic
242#131—1882no—
243C2×M16—471no—
244C2×M16—471no—
245C2×M16—941no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—941no—
249C22×C8—941no—
250C22×C8C4×D4711yescharacteristic
251C22×C8C4×D4711yescharacteristic
252C22×C8D18811yescharacteristic
253C22×C8D18811yescharacteristic
254C22×C8C22⋊D4711yescharacteristic
255C22×C8C22⋊D4711yescharacteristic
256#123—941no—
257C22⋊Q8—471no—
258C22⋊Q8—471no—
259#121—471no—
260#121—471no—
261#120—941no—
262C4×D4—941no—
263C4×D4—941no—
264#117—471no—
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⋊C8C4×D4712yes—
279#97—42no—
280#97—941no—
281#97—1882no—
282C4×C8—941no—
283#95—472no—
284#95C4×D4712yes—
285C24#1062535011yescharacteristic
286#41—1881no—
287#41—1881no—
288C2×Q8—471no—
289C2×D4—471no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—941no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—941no—
297C22×C4—942no—
298C22×C4C2×C4×D4711yescharacteristic
299C22×C4C2×C4×D4711yescharacteristic
300C22×C4C2×C4×D4711yescharacteristic
301C22×C4C2×D18811yescharacteristic
302C22×C4#1062535011yescharacteristic
303C22×C4C2×C22⋊D4711yescharacteristic
304M16—1882no—
305M16—1881no—
306M16—1881no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—941no—
317C2×C8—941no—
318C2×C8—942no—
319C2×C8—1881no—
320C2×C8—1881no—
321C2×C8—1882no—
322C2×C8(C2×D47)⋊C411yescharacteristic
323C2×C8(C2×D47)⋊C411yescharacteristic
324C2×C8(C2×D47)⋊C411yescharacteristic
325C2×C8(C2×D47)⋊C411yescharacteristic
326C4⋊C4—471no—
327C4⋊C4—471no—
328C4⋊C4—941no—
329C4⋊C4—941no—
330C22⋊C4—42no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—1882no—
337C42—41no—
338C42—41no—
339C42—941no—
340C42—1881no—
341C42—1881no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—941no—
346C23#1309398111yescharacteristic
347C23C4×C22⋊D4711yescharacteristic
348C23C4×D18811yescharacteristic
349Q8—1881no—
350D4—1881no—
351D4—1882no—
352D4—1882no—
353D4—1882no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—1882no—
370C2×C4—1882no—
371C2×C4—1882no—
372C2×C4—1881no—
373C2×C4—1881no—
374C2×C4C42×D4711yescharacteristic
375C2×C4C2×(C2×D47)⋊C411yescharacteristic
376C2×C4C4×C22⋊D4711yescharacteristic
377C2×C4C4×D18811yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—1882no—
383C8—1881no—
384C8—1881no—
385C8#1309393812yes—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C4×(C2×D47)⋊C411yescharacteristic
398C22#1568924312yes—
399C22#1568924612yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—82no—
404C4—3762no—
405C4—1881no—
406C4—1881no—
407C4—1881no—
408C4C2×#1309393811yescharacteristic
409C4#1568909611yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—3761no—
414C2C4×#1309393811yescharacteristic
415C2#2024323211yescharacteristic
416C2#2024323411yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1752C2
socleC22×C47C4×C22⋊C4
prime radical#15689634C22
cosocleC23×C4×C47C23
hypercenter#1752D47
hypocenterC47#8239
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. #20243164C2semidirect
5. #20241276C2semidirect
6. #20241274C2semidirect
7. C47×#1752C2semidirect
8. C2×#13094030C4semidirect
14. #15689149C4semidirect
15. #15689089C4semidirect
18. #15689078C4semidirect
22. #15688861C4semidirect
23. #15688859C4semidirect
24. #15688858C4semidirect
25. #15688856C4semidirect
204. #1752D47semidirect
239. C47#8239semidirect

Maximal subgroups

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

subgroupindex
#202520822
#202431642
#202418802
#202418772
#202412762
#202412742
C47×#17522
#823947