Finite Group Databasebeta

← #26185493

Subgroups — #26185493

Order 12032.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252505C211yesmaximal, characteristic
2#20252032C211yesmaximal, characteristic
3#20242179C211yesmaximal, characteristic, complemented
4#20242176C211yesmaximal, characteristic, complemented
5#20242174C211yesmaximal, characteristic, complemented
6#20242171C211yesmaximal, characteristic, complemented
7#20242169C211yesmaximal, characteristic, complemented
8#20242166C211yesmaximal, characteristic, complemented
9#20242164C211yesmaximal, characteristic, complemented
10#20242162C211yesmaximal, characteristic, complemented
11#20242156C211yesmaximal, characteristic, complemented
12#20242153C211yesmaximal, characteristic, complemented
13#20242149C211yesmaximal, characteristic, complemented
14#20242146C211yesmaximal, characteristic, complemented
15C47×#2989C211yesmaximal, characteristic
16#15689254—21no—
17#15689201—21no—
18#15689195—21no—
19#15689195—21no—
20#15689184C412yes—
21#15689184C412yes—
22#15689180C2211yescharacteristic
23#15689180C2211yescharacteristic
24#15689176C2211yescharacteristic
25#15689176C2211yescharacteristic
26#15689176C2211yescharacteristic
27#15689176C2211yescharacteristic
28#15689176C2211yescharacteristic
29#15689150C412yes—
30#15689147C2211yescharacteristic
31#15689147C2211yescharacteristic
32C2×C4⋊(C47⋊C8)C2211yescharacteristic
33#15689090C412yes—
34C4×#10625329C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36#15688875C2211yescharacteristic
37#15688875C2211yescharacteristic
38#15688875C2211yescharacteristic
39#15688875C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688875C2211yescharacteristic
43#15688875C2211yescharacteristic
44#15688875C2211yescharacteristic
45#15688875C2211yescharacteristic
46#15688873C2211yescharacteristic
47#15688873C2211yescharacteristic
48#15688873C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52C4×#41×C47C2211yescharacteristic
53C47×#446—21no—
54C47×#436—21no—
55C47×#435—21no—
56C47×#435—21no—
57C47×#432C2211yescharacteristic
58C47×#432C2211yescharacteristic
59C47×#431C2211yescharacteristic
60C47×#423C2211yescharacteristic
61C47×#423C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329C2×C412yes—
66C22×C47⋊C8—21no—
67C22×C47⋊C8C2×C412yes—
68C4⋊(C47⋊C8)—21no—
69C4⋊(C47⋊C8)—21no—
70C4⋊(C47⋊C8)—21no—
71C4⋊(C47⋊C8)C2×C412yes—
72C4⋊(C47⋊C8)C2×C412yes—
73C4⋊(C47⋊C8)C2×C412yes—
74C4⋊(C47⋊C8)C2×C412yes—
75C4⋊(C47⋊C8)C2311yescharacteristic
76C4⋊(C47⋊C8)C2311yescharacteristic
77C4⋊(C47⋊C8)C2311yescharacteristic
78C4⋊(C47⋊C8)C2311yescharacteristic
79C22⋊(C47⋊C8)—21no—
80C22⋊(C47⋊C8)—21no—
81C22⋊(C47⋊C8)—21no—
82C22⋊(C47⋊C8)C2×C412yes—
83C22⋊(C47⋊C8)C2×C412yes—
84C22⋊(C47⋊C8)C2×C412yes—
85C22⋊(C47⋊C8)C2×C412yes—
86#13093935—21no—
87#13093935—21no—
88#13093935C2×C412yes—
89C4×C47⋊C8—21no—
90C4×C47⋊C8C2×C412yes—
91C4×C47⋊C8C2311yescharacteristic
92C4×C47⋊C8C2311yescharacteristic
93C4×C47⋊C8C2311yescharacteristic
94C4×C47⋊C8C2311yescharacteristic
95C2×#41×C47C2×C411yescharacteristic
96C2×M16×C47—21no—
97C2×M16×C47—21no—
98C22×C8×C47—21no—
99C4×Q8×C47D411yescharacteristic
100C4×Q8×C47Q811yescharacteristic
101C4×D4×C47D411yescharacteristic
102C4×D4×C47D411yescharacteristic
103C4×D4×C47D411yescharacteristic
104C4×D4×C47Q811yescharacteristic
105C4×D4×C47Q811yescharacteristic
106C4×D4×C47Q811yescharacteristic
107#117×C47C2×C411yescharacteristic
108#117×C47C2×C411yescharacteristic
109#117×C47C2×C411yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C4⋊C8×C47—21no—
114C4⋊C8×C47—21no—
115C4⋊C8×C47—21no—
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120C22⋊C8×C47—21no—
121C22⋊C8×C47—21no—
122C22⋊C8×C47—21no—
123#97×C47—21no—
124#97×C47—21no—
125C4×C8×C47—21no—
126#41×C47—42no—
127C2×Q8×C47C4⋊C411yescharacteristic
128C2×D4×C47C4⋊C411yescharacteristic
129C2×D4×C47C4⋊C411yescharacteristic
130C2×D4×C47C4⋊C411yescharacteristic
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×Q811yescharacteristic
138C22×C4×C47C2×Q811yescharacteristic
139C22×C4×C47C2×Q811yescharacteristic
140M16×C47—81no—
141M16×C47—81no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—81no—
147C4⋊C4×C47C4⋊C411yescharacteristic
148C4⋊C4×C47C4⋊C411yescharacteristic
149C4⋊C4×C47C4⋊C411yescharacteristic
150C4⋊C4×C47C4⋊C411yescharacteristic
151C4⋊C4×C47C4⋊C411yescharacteristic
152C4⋊C4×C47C4⋊C411yescharacteristic
153C22⋊C4×C47C4⋊C411yescharacteristic
154C22⋊C4×C47C4⋊C411yescharacteristic
155C22⋊C4×C47C4⋊C411yescharacteristic
156C22⋊C4×C47C4⋊C411yescharacteristic
157C22⋊C4×C47C4⋊C411yescharacteristic
158C22⋊C4×C47C4⋊C411yescharacteristic
159C42×C47C22×C411yescharacteristic
160C42×C47C22×C411yescharacteristic
161C42×C47C22×C411yescharacteristic
162C42×C47C2×D411yescharacteristic
163C42×C47C2×D411yescharacteristic
164C42×C47C2×D411yescharacteristic
165C42×C47C2×Q811yescharacteristic
166C42×C47C2×Q811yescharacteristic
167C42×C47C2×Q811yescharacteristic
168C42×C47C2411yescharacteristic
169#10625329—42no—
170#10625329—81no—
171#10625329—81no—
172C2×C47⋊C8—21no—
173C2×C47⋊C8—21no—
174C2×C47⋊C8—21no—
175C2×C47⋊C8—21no—
176C2×C47⋊C8—42no—
177C2×C47⋊C8—81no—
178C2×C47⋊C8C22×C412yes—
179C2×C47⋊C8C22×C412yes—
180C2×C47⋊C8C22×C412yes—
181C2×C47⋊C8C22×C412yes—
182C23×C47C2×C4⋊C411yescharacteristic
183C23×C47C2×C4⋊C411yescharacteristic
184C23×C47C2×C4⋊C411yescharacteristic
185Q8×C47—41no—
186D4×C47—41no—
187D4×C47—41no—
188D4×C47—41no—
189C2×C4×C47—22no—
190C2×C4×C47—22no—
191C2×C4×C47—22no—
192C2×C4×C47—21no—
193C2×C4×C47—21no—
194C2×C4×C47—21no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47C2×C4⋊C411yescharacteristic
202C2×C4×C47C2×C4⋊C411yescharacteristic
203C2×C4×C47C2×C4⋊C411yescharacteristic
204C2×C4×C47C2×C4⋊C411yescharacteristic
205C2×C4×C47C2×C4⋊C411yescharacteristic
206C2×C4×C47C2×C4⋊C411yescharacteristic
207C2×C4×C47C2×C4⋊C411yescharacteristic
208C2×C4×C47C2×C4⋊C411yescharacteristic
209C2×C4×C47C2×C4⋊C411yescharacteristic
210C2×C4×C47C23×C411yescharacteristic
211C2×C4×C47C22×D411yescharacteristic
212C2×C4×C47C22×Q811yescharacteristic
213C8×C47—41no—
214C8×C47—41no—
215C8×C47—41no—
216C8×C47—41no—
217C47⋊C8—22no—
218C47⋊C8—22no—
219C47⋊C8—22no—
220C47⋊C8—22no—
221C47⋊C8—41no—
222C47⋊C8—41no—
223C47⋊C8—41no—
224C47⋊C8—41no—
225#17825—471nomaximal, Sylow
226C22×C47—21no—
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—21no—
230C22×C47—21no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47C22×C4⋊C411yescharacteristic
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—21no—
241C4×C47—21no—
242C4×C47—21no—
243C4×C47—21no—
244C4×C47—21no—
245C4×C47—21no—
246C4×C47#56812yes—
247C4×C47#57611yescharacteristic
248C4×C47#57811yescharacteristic
249#2989—471no—
250#2989D4711yescharacteristic
251#2922—471no—
252#1574—471no—
253#1574—471no—
254#1573—471no—
255#1573—471no—
256#1572—471no—
257#1572—471no—
258#1571—471no—
259#1571—471no—
260#1569—471no—
261#1569—471no—
262#1568—471no—
263#1567—471no—
264C2×C47—41no—
265C2×C47—41no—
266C2×C47—41no—
267C2×C47#290511yescharacteristic
268C2×C47#291311yescharacteristic
269C2×C47#291611yescharacteristic
270C4×#41C2×D4711yescharacteristic
271#446—21no—
272#446—941no—
273#436—21no—
274#436—941no—
275#435—21no—
276#435—21no—
277#435—941no—
278#435—941no—
279#433—472no—
280#433—472no—
281#432—471no—
282#432—471no—
283#432C2×D4711yescharacteristic
284#432C2×D4711yescharacteristic
285#431—471no—
286#431—471no—
287#431—471no—
288#431—471no—
289#431—471no—
290#431C2×D4711yescharacteristic
291#424—472no—
292#423—471no—
293#423—471no—
294#423C2×D4711yescharacteristic
295#423C2×D4711yescharacteristic
296C2×C4⋊C8—471no—
297C2×C4⋊C8C2×D4711yescharacteristic
298#408—472no—
299C4×M16—471no—
300C2×C4×C8—471no—
301#335—471no—
302#335—471no—
303#335—471no—
304#335—471no—
305#335—471no—
306#335—471no—
307#335—471no—
308#335—471no—
309#335—471no—
310#335—471no—
311#334—471no—
312#334—471no—
313#334—471no—
314#334—471no—
315#334—471no—
316#334—471no—
317C47#1782511yescharacteristic, complemented, Sylow
318C2×#41C4×D4711yescharacteristic
319C2×M16—21no—
320C2×M16—21no—
321C2×M16—472no—
322C2×M16—941no—
323C2×M16—941no—
324C22×C8—21no—
325C22×C8—472no—
326C22×C8—941no—
327C4×Q8Dic9411yescharacteristic
328C4×Q8C22⋊D4711yescharacteristic
329C4×D4Dic9411yescharacteristic
330C4×D4Dic9411yescharacteristic
331C4×D4Dic9411yescharacteristic
332C4×D4C22⋊D4711yescharacteristic
333C4×D4C22⋊D4711yescharacteristic
334C4×D4C22⋊D4711yescharacteristic
335#117C4×D4711yescharacteristic
336#117C4×D4711yescharacteristic
337#117C4×D4711yescharacteristic
338C2×C42C22×D4711yescharacteristic
339C2×C42C22×D4711yescharacteristic
340C2×C42C22×D4711yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—472no—
345C4⋊C8—472no—
346C4⋊C8—472no—
347C4⋊C8—472no—
348C4⋊C8—471no—
349C4⋊C8—471no—
350C4⋊C8—471no—
351C4⋊C8—471no—
352C4⋊C8—941no—
353C4⋊C8—941no—
354C4⋊C8—941no—
355C4⋊C8C22×D4711yescharacteristic
356C4⋊C8C22×D4711yescharacteristic
357C4⋊C8C22×D4711yescharacteristic
358C4⋊C8C22×D4711yescharacteristic
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—472no—
363C22⋊C8—472no—
364C22⋊C8—472no—
365C22⋊C8—472no—
366C22⋊C8—941no—
367C22⋊C8—941no—
368C22⋊C8—941no—
369#97—21no—
370#97—21no—
371#97—472no—
372#97—941no—
373#97—941no—
374C4×C8—21no—
375C4×C8—472no—
376C4×C8—471no—
377C4×C8—471no—
378C4×C8—471no—
379C4×C8—471no—
380C4×C8—941no—
381#41—42no—
382C2×Q8Dic47⋊C411yescharacteristic
383C2×D4Dic47⋊C411yescharacteristic
384C2×D4Dic47⋊C411yescharacteristic
385C2×D4Dic47⋊C411yescharacteristic
386C22×C4C2×Dic9411yescharacteristic
387C22×C4C2×Dic9411yescharacteristic
388C22×C4C2×Dic9411yescharacteristic
389C22×C4C2×C4×D4711yescharacteristic
390C22×C4C2×C4×D4711yescharacteristic
391C22×C4C2×C4×D4711yescharacteristic
392C22×C4C2×C22⋊D4711yescharacteristic
393C22×C4C2×C22⋊D4711yescharacteristic
394C22×C4C2×C22⋊D4711yescharacteristic
395M16—81no—
396M16—81no—
397M16—3761no—
398M16—3761no—
399M16—1882no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—81no—
405C2×C8—472no—
406C2×C8—472no—
407C2×C8—472no—
408C2×C8—472no—
409C2×C8—941no—
410C2×C8—941no—
411C2×C8—941no—
412C2×C8—941no—
413C2×C8—3761no—
414C2×C8—1882no—
415C4⋊C4Dic47⋊C411yescharacteristic
416C4⋊C4Dic47⋊C411yescharacteristic
417C4⋊C4Dic47⋊C411yescharacteristic
418C4⋊C4Dic47⋊C411yescharacteristic
419C4⋊C4Dic47⋊C411yescharacteristic
420C4⋊C4Dic47⋊C411yescharacteristic
421C22⋊C4Dic47⋊C411yescharacteristic
422C22⋊C4Dic47⋊C411yescharacteristic
423C22⋊C4Dic47⋊C411yescharacteristic
424C22⋊C4Dic47⋊C411yescharacteristic
425C22⋊C4Dic47⋊C411yescharacteristic
426C22⋊C4Dic47⋊C411yescharacteristic
427C42C2×Dic9411yescharacteristic
428C42C2×Dic9411yescharacteristic
429C42C2×Dic9411yescharacteristic
430C42C2×C4×D4711yescharacteristic
431C42C2×C4×D4711yescharacteristic
432C42C2×C4×D4711yescharacteristic
433C42C2×C22⋊D4711yescharacteristic
434C42C2×C22⋊D4711yescharacteristic
435C42C2×C22⋊D4711yescharacteristic
436C42C23×D4711yescharacteristic
437C23C2×Dic47⋊C411yescharacteristic
438C23C2×Dic47⋊C411yescharacteristic
439C23C2×Dic47⋊C411yescharacteristic
440Q8—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4C2×Dic47⋊C411yescharacteristic
457C2×C4C2×Dic47⋊C411yescharacteristic
458C2×C4C2×Dic47⋊C411yescharacteristic
459C2×C4C2×Dic47⋊C411yescharacteristic
460C2×C4C2×Dic47⋊C411yescharacteristic
461C2×C4C2×Dic47⋊C411yescharacteristic
462C2×C4C2×Dic47⋊C411yescharacteristic
463C2×C4C2×Dic47⋊C411yescharacteristic
464C2×C4C2×Dic47⋊C411yescharacteristic
465C2×C4C22×C4×D4711yescharacteristic
466C2×C4C22×C22⋊D4711yescharacteristic
467C2×C4C22×Dic9411yescharacteristic
468C8—41no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—942no—
473C8—942no—
474C8—942no—
475C8—942no—
476C8—1881no—
477C8—1881no—
478C8—1881no—
479C8—1881no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22C22×Dic47⋊C411yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4#1568988912yes—
501C4#1568992611yescharacteristic
502C4#1568993811yescharacteristic
503C2—41no—
504C2—41no—
505C2—41no—
506C2#2025195111yescharacteristic
507C2#2025198611yescharacteristic
508C2#2025199711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2989C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#41×C47C2×C4
cosocleC42×C47C24
hypercenter#2989D47
hypocenterC47#17825
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
3. #20242179C2semidirect
4. #20242176C2semidirect
5. #20242174C2semidirect
6. #20242171C2semidirect
7. #20242169C2semidirect
8. #20242166C2semidirect
9. #20242164C2semidirect
10. #20242162C2semidirect
11. #20242156C2semidirect
12. #20242153C2semidirect
13. #20242149C2semidirect
14. #20242146C2semidirect
317. C47#17825semidirect

Maximal subgroups

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

subgroupindex
#202525052
#202520322
#202421792
#202421762
#202421742
#202421712
#202421692
#202421662
#202421642
#202421622
#202421562
#202421532
#202421492
#202421462
C47×#29892
#1782547