Finite Group Databasebeta

← #26186818

Subgroups — #26186818

Order 12032.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253961C211yesmaximal, characteristic
2#20252362C212yesmaximal, complemented
3#20242278C212yesmaximal, complemented
4#20242274C211yesmaximal, characteristic, complemented
5Q16×C47⋊C8C211yesmaximal, characteristic, complemented
6#20242185C212yesmaximal, complemented
7#20242182C211yesmaximal, characteristic, complemented
8#20242150C211yesmaximal, characteristic, complemented
9#20241847C212yesmaximal, complemented
10C82×D47C211yesmaximal, characteristic, complemented
11C47×#1591C211yesmaximal, characteristic, complemented
12#15689660C2212yes—
13#15689524C411yescharacteristic
14#15689508C411yescharacteristic
15#15689479C412yes—
16#15689361C411yescharacteristic
17#15689360C411yescharacteristic
18#15689355C412yes—
19Q8×C47⋊C8C2212yes—
20C4×#10625336C2212yes—
21C4×D376C2211yescharacteristic
22#15689202C2212yes—
23#15689196—22no—
24#15689188—22no—
25#15689188C2212yes—
26#15689183—22no—
27#15689179C2212yes—
28#15689080—22no—
29C4×C8×D47C2211yescharacteristic
30C4×C8×D47C2211yescharacteristic
31C4×C8×D47C2211yescharacteristic
32#15688876C2211yescharacteristic
33#15688873C2212yes—
34Q8⋊(C47⋊C8)C2212yes—
35#15688852C2212yes—
36#15688850C2212yes—
37C8×C47⋊C8C2211yescharacteristic
38C8×C47⋊C8C2211yescharacteristic
39C8×C47⋊C8C2211yescharacteristic
40C47×#446C2212yes—
41C4×Q16×C47C2211yescharacteristic
42C47×#335C2211yescharacteristic
43C47×Q8⋊C8C2212yes—
44C82×C47C2211yescharacteristic
45C2×#10625336C2×C412yes—
46C2×D376C2×C411yescharacteristic
47C2×#10625324—22no—
48C2×C8×D47—21no—
49C2×C8×D47—22no—
50C2×C8×D47C2×C411yescharacteristic
51C2×C8×D47C2×C411yescharacteristic
52C2×C8×D47D411yescharacteristic
53C2×C8×D47D411yescharacteristic
54#13094019—22no—
55#13094015C2×C412yes—
56#13094013C2×C412yes—
57#13094009—22no—
58#13094000C2×C412yes—
59#13093999C2×C412yes—
60C4×D188—22no—
61C4×D188C2312yes—
62#13093981—22no—
63C42×D47C2311yescharacteristic
64#13093958C2×C411yescharacteristic
65#13093955C2×C412yes—
66C4⋊(C47⋊C8)—22no—
67C4⋊(C47⋊C8)C2312yes—
68#13093948C2×C412yes—
69#13093946C2×C412yes—
70#13093944C2×C412yes—
71(C2×D47)⋊C8—22no—
72(C2×D47)⋊C8—22no—
73(C2×D47)⋊C8—22no—
74#13093934—22no—
75C4×C47⋊C8—22no—
76C4×C47⋊C8C2311yescharacteristic
77C4×C47⋊C8C2311yescharacteristic
78C4×C47⋊C8C2311yescharacteristic
79C8×Dic47—21no—
80C8×Dic47C2×C411yescharacteristic
81C8×Dic47C2×C411yescharacteristic
82C8×Dic47D411yescharacteristic
83C8×Dic47D411yescharacteristic
84C2×Q16×C47C2×C411yescharacteristic
85C4×Q8×C47C2312yes—
86#107×C47C2×C411yescharacteristic
87C4⋊C8×C47—22no—
88C4⋊C8×C47C2312yes—
89#103×C47C2×C412yes—
90#97×C47—22no—
91C4×C8×C47C2311yescharacteristic
92C4×C8×C47C2311yescharacteristic
93C4×C8×C47C2311yescharacteristic
94C2×Q8×C47C22×C412yes—
95C2×D188—22no—
96C2×D188C22×C412yes—
97C2×C4×D47—22no—
98C2×C4×D47C22×C411yescharacteristic
99C2×C4×D47C2×D411yescharacteristic
100C2×C4×D47#4111yescharacteristic
101Q16×C47—22no—
102C2×C8×C47—21no—
103C2×C8×C47—22no—
104C2×C8×C47C22×C411yescharacteristic
105C2×C8×C47C22×C411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47C2×D411yescharacteristic
108C4⋊C4×C47—22no—
109C4⋊C4×C47C22×C412yes—
110C42×C47—22no—
111C42×C47C2411yescharacteristic
112#10625336—24no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115(C2×D47)⋊C4—22no—
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—22no—
118C4⋊Dic47—22no—
119C4⋊Dic47C22×C412yes—
120Dic47⋊C4—22no—
121Dic47⋊C4—22no—
122C4×Dic47C22×C411yescharacteristic
123C4×Dic47C2×D411yescharacteristic
124C4×Dic47#4111yescharacteristic
125C2×C47⋊C8—21no—
126C2×C47⋊C8—22no—
127C2×C47⋊C8C22×C411yescharacteristic
128C2×C47⋊C8C22×C411yescharacteristic
129C2×C47⋊C8C2×D411yescharacteristic
130C2×C47⋊C8C2×D411yescharacteristic
131D376—22no—
132#10625324—44no—
133C8×D47—24no—
134C8×D47—22no—
135C8×D47—22no—
136C8×D47—22no—
137C8×D47—22no—
138C8×D47—44no—
139C22×D47—22no—
140C22×D47C4×D411yescharacteristic
141Q8×C47—22no—
142Q8×C47—22no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47C23×C411yescharacteristic
146C2×C4×C47C22×D411yescharacteristic
147C2×C4×C47C2×#4111yescharacteristic
148C2×Dic47—22no—
149C2×Dic47C4×D411yescharacteristic
150C2×Dic47C4×D411yescharacteristic
151C2×Dic47C4×D411yescharacteristic
152D188—22no—
153D188—22no—
154D188—44no—
155C4×D47—22no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—42no—
161C4×D47—42no—
162C8×C47—22no—
163C8×C47—21no—
164C8×C47—21no—
165C8×C47—42no—
166C8×C47#13112yes—
167C8×C47#13512yes—
168C47⋊C8—22no—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C47⋊C8—42no—
172C47⋊C8#13112yes—
173C47⋊C8#13512yes—
174#17959—471nomaximal, Sylow
175C22×C47C2×C4×D411yescharacteristic
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—42no—
179C2×D47—42no—
180C2×D47—42no—
181C2×D47#44312yes—
182C4×C47—21no—
183C4×C47—42no—
184C4×C47—42no—
185C4×C47C2×#13111yescharacteristic
186C4×C47C2×#13111yescharacteristic
187C4×C47C2×#13511yescharacteristic
188C4×C47C2×#13511yescharacteristic
189Dic47—21no—
190Dic47—21no—
191Dic47—21no—
192Dic47—42no—
193#3168—471no—
194#2966—472no—
195#1591D4711yescharacteristic, complemented
196#1590—472no—
197#1589—471no—
198C8×Q16—471no—
199C8×SD16—472no—
200C8×D8—471no—
201#1568—471no—
202#1494—472no—
203C2×C82—471no—
204C2×C47#293111yescharacteristic
205C2×C47C4×#13511yescharacteristic
206C2×C47C2×#44311yescharacteristic
207D47—22no—
208D47—82no—
209#529—472no—
210#499—471no—
211#495—471no—
212#488—472no—
213#467—471no—
214#466—471no—
215#465—472no—
216#446C2×D4712yes—
217C8×Q8—472no—
218C4×Q16C2×D4711yescharacteristic
219C4×SD16—472no—
220C4×D8—471no—
221#436—472no—
222#435—942no—
223C8×D4—472no—
224C8×D4—942no—
225#433—942no—
226#432—472no—
227#405—942no—
228C2×C4×C8—471no—
229C2×C4×C8—471no—
230C2×C4×C8—471no—
231#335—471no—
232#335C2×D4711yescharacteristic
233#334—472no—
234Q8⋊C8—472no—
235Q8⋊C8C2×D4712yes—
236D4⋊C8—472no—
237D4⋊C8—472no—
238C82—471no—
239C82—471no—
240C82—471no—
241C82C2×D4711yescharacteristic
242C47#1795911yescharacteristic, complemented, Sylow
243C2×Q16C4×D4711yescharacteristic
244C2×SD16—472no—
245C2×D8—471no—
246C2×M16—942no—
247C22×C8—471no—
248C22×C8—471no—
249C22×C8—471no—
250C22×C8—471no—
251C22×C8—942no—
252C22×C8—941no—
253#126—942no—
254#125—472no—
255#124—472no—
256#123—942no—
257C22⋊Q8—472no—
258#121—472no—
259C4×Q8C22×D4712yes—
260C4×D4—472no—
261C4×D4—942no—
262#117—942no—
263C2×C42—471no—
264#107—471no—
265#107C4×D4711yescharacteristic
266#106—472no—
267C4⋊C8—22no—
268C4⋊C8—472no—
269C4⋊C8—942no—
270C4⋊C8C22×D4712yes—
271#103—472no—
272#103C4×D4712yes—
273#102—472no—
274#102—472no—
275C22⋊C8—942no—
276C22⋊C8—942no—
277C22⋊C8—942no—
278#97—22no—
279#97—942no—
280C4×C8—471no—
281C4×C8—471no—
282C4×C8—471no—
283C4×C8—471no—
284C4×C8—471no—
285C4×C8—471no—
286C4×C8—471no—
287C4×C8—942no—
288C4×C8—941no—
289C4×C8C22×D4711yescharacteristic
290C4×C8C22×D4711yescharacteristic
291C4×C8C22×D4711yescharacteristic
292C2×Q8C2×C4×D4712yes—
293C2×D4—472no—
294C2×D4—942no—
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—942no—
299Q16—22no—
300SD16—944no—
301D8—942no—
302M16—1884no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—471no—
306C2×C8—471no—
307C2×C8—471no—
308C2×C8—471no—
309C2×C8—942no—
310C2×C8—942no—
311C2×C8—944no—
312C2×C8—941no—
313C2×C8—942no—
314C2×C8—942no—
315C2×C8—942no—
316C2×C8—1884no—
317C2×C8C2×C4×D4711yescharacteristic
318C2×C8C2×C4×D4711yescharacteristic
319C2×C8D4×D4711yescharacteristic
320C2×C8D4×D4711yescharacteristic
321C4⋊C4—22no—
322C4⋊C4—472no—
323C4⋊C4—942no—
324C4⋊C4—942no—
325C4⋊C4—942no—
326C4⋊C4C2×C4×D4712yes—
327C22⋊C4—942no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—942no—
331C22⋊C4—942no—
332C42—22no—
333C42—471no—
334C42—471no—
335C42—471no—
336C42C23×D4711yescharacteristic
337C23—471no—
338C23—942no—
339Q8—22no—
340Q8—22no—
341D4—942no—
342D4—942no—
343D4—1884no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—471no—
347C2×C4—471no—
348C2×C4—471no—
349C2×C4—942no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—942no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4C22×C4×D4711yescharacteristic
358C2×C4C2×D4×D4711yescharacteristic
359C2×C4#41×D4711yescharacteristic
360C8—22no—
361C8—21no—
362C8—21no—
363C8—42no—
364C8—472no—
365C8—472no—
366C8—942no—
367C8—941no—
368C8—941no—
369C8—1882no—
370C8#1309403212yes—
371C8#1309404712yes—
372C22—472no—
373C22—941no—
374C22—941no—
375C22—1882no—
376C22—1882no—
377C22—1882no—
378C22C4×D4×D4711yescharacteristic
379C4—21no—
380C4—42no—
381C4—42no—
382C4—941no—
383C4—941no—
384C4—941no—
385C4—1882no—
386C4#131×D4711yescharacteristic
387C4C2×#1309403211yescharacteristic
388C4#135×D4711yescharacteristic
389C4C2×#1309404711yescharacteristic
390C2—942no—
391C2—3762no—
392C2#2025209711yescharacteristic
393C2C4×#1309404711yescharacteristic
394C2#443×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1591C2
socleC22×C47C2×C4×D4
prime radical#15689360C4
cosocleC42×C47C24
hypercenter#1591D47
hypocenterC47#17959
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1591

Complements

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

NH ≅ G/Ntype
2. #20252362C2semidirect
3. #20242278C2semidirect
4. #20242274C2semidirect
5. Q16×C47⋊C8C2semidirect
6. #20242185C2semidirect
7. #20242182C2semidirect
8. #20242150C2semidirect
9. #20241847C2semidirect
10. C82×D47C2semidirect
11. C47×#1591C2semidirect
195. #1591D47semidirect
242. C47#17959semidirect

Maximal subgroups

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

subgroupindex
#202539612
#202523622
#202422782
#202422742
Q16×C47⋊C82
#202421852
#202421822
#202421502
#202418472
C82×D472
C47×#15912
#1795947