Finite Group Databasebeta

← #26187134

Subgroups — #26187134

Order 12032.

544 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253971C211yesmaximal, characteristic
2#20252484C211yesmaximal, characteristic
3#20252479C211yesmaximal, characteristic
4#20242262C211yesmaximal, characteristic, complemented
5#20242259C211yesmaximal, characteristic, complemented
6#20242257C211yesmaximal, characteristic, complemented
7#20242256C211yesmaximal, characteristic, complemented
8#20242240C211yesmaximal, characteristic, complemented
9#20242239C211yesmaximal, characteristic, complemented
10#20242237C211yesmaximal, characteristic, complemented
11#20242150C211yesmaximal, characteristic
12#20241859C211yesmaximal, characteristic
13#20241859C211yesmaximal, characteristic
14#20241679C211yesmaximal, characteristic
15C47×#1584C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17#15689677C2211yescharacteristic
18#15689527C411yescharacteristic
19#15689501C411yescharacteristic
20#15689472C411yescharacteristic
21#15689472C411yescharacteristic
22#15689365C411yescharacteristic
23#15689363C411yescharacteristic
24#15689363C411yescharacteristic
25#15689361C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689253—21no—
28#15689253C2211yescharacteristic
29#15689252—21no—
30#15689251—21no—
31#15689250—21no—
32#15689250C2211yescharacteristic
33Q8×C47⋊C8C2211yescharacteristic
34C8×Dic94C2211yescharacteristic
35#15689247C2211yescharacteristic
36C4×Dic188C2211yescharacteristic
37C4×#10625337C2211yescharacteristic
38C4×#10625337C2211yescharacteristic
39#15689185—21no—
40#15689183—21no—
41#15689183—21no—
42#15689182—21no—
43#15689179C2211yescharacteristic
44#15689179C2211yescharacteristic
45#15689174C2211yescharacteristic
46#15689174C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54Q8⋊(C47⋊C8)C2211yescharacteristic
55#15688853C2211yescharacteristic
56#15688853C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688845C2211yescharacteristic
59#15688844C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Dic188C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×C8×D47C2×C411yescharacteristic
71C2×C8×D47C2×C411yescharacteristic
72#13094023C2×C411yescharacteristic
73#13094023C2×C411yescharacteristic
74#13094022C2×C411yescharacteristic
75#13094022C2×C411yescharacteristic
76#13094014—21no—
77#13094014—21no—
78#13094004C2×C411yescharacteristic
79#13094004C2×C411yescharacteristic
80#13094002—21no—
81#13094002—21no—
82#13094000C2×C411yescharacteristic
83#13094000C2×C411yescharacteristic
84C4×Dic94—21no—
85C4×Dic94—21no—
86C4×Dic94C2311yescharacteristic
87C4×Dic94C2311yescharacteristic
88#13093981—21no—
89#13093981—21no—
90C42×D47C2311yescharacteristic
91#13093958C2×C411yescharacteristic
92#13093957C2×C411yescharacteristic
93#13093957C2×C411yescharacteristic
94C4⋊(C47⋊C8)—21no—
95C4⋊(C47⋊C8)—21no—
96C4⋊(C47⋊C8)C2311yescharacteristic
97C4⋊(C47⋊C8)C2311yescharacteristic
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8D411yescharacteristic
104Dic47⋊C8D411yescharacteristic
105#13093949C2×C411yescharacteristic
106#13093949C2×C411yescharacteristic
107#13093948C2×C411yescharacteristic
108#13093948C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111(C2×D47)⋊C8—21no—
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8D411yescharacteristic
115(C2×D47)⋊C8D411yescharacteristic
116#13093935—21no—
117#13093934—21no—
118#13093934—21no—
119#13093934—21no—
120#13093934—21no—
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47C2×C411yescharacteristic
128C8×Dic47C2×C411yescharacteristic
129C2×Q16×C47C2×C411yescharacteristic
130C4×Q8×C47C2311yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132#107×C47C2×C411yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#103×C47C2×C411yescharacteristic
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×C4×D47C22×C411yescharacteristic
147C2×C4×D47C2×D411yescharacteristic
148C2×C4×D47#4111yescharacteristic
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94C22×C411yescharacteristic
152C2×Dic94C22×C411yescharacteristic
153Q16×C47—41no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47C22×C411yescharacteristic
158C2×C8×C47C22×C411yescharacteristic
159C2×C8×C47C2×D411yescharacteristic
160C2×C8×C47C2×D411yescharacteristic
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47C22×C411yescharacteristic
164C4⋊C4×C47C22×C411yescharacteristic
165C42×C47—21no—
166C42×C47—21no—
167C42×C47C2411yescharacteristic
168#10625337—41no—
169#10625337—41no—
170(C2×D47)⋊C4—21no—
171(C2×D47)⋊C4—21no—
172(C2×D47)⋊C4—21no—
173(C2×D47)⋊C4—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47C22×C411yescharacteristic
177C4⋊Dic47C22×C411yescharacteristic
178Dic47⋊C4—21no—
179Dic47⋊C4—21no—
180Dic47⋊C4—21no—
181Dic47⋊C4—21no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47C22×C411yescharacteristic
191C4×Dic47C2×D411yescharacteristic
192C4×Dic47#4111yescharacteristic
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C2×D411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200Dic188—41no—
201C8×D47—41no—
202C8×D47—41no—
203C22×D47C4×D411yescharacteristic
204Q8×C47—21no—
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47C23×C411yescharacteristic
213C2×C4×C47C22×D411yescharacteristic
214C2×C4×C47C2×#4111yescharacteristic
215C2×Dic47—21no—
216C2×Dic47—21no—
217C2×Dic47—21no—
218C2×Dic47—21no—
219C2×Dic47C4×D411yescharacteristic
220C2×Dic47C4×D411yescharacteristic
221C2×Dic47C4×D411yescharacteristic
222C4×D47—21no—
223C4×D47—21no—
224C4×D47—21no—
225C4×D47—21no—
226C4×D47—41no—
227Dic94—21no—
228Dic94—21no—
229Dic94—21no—
230Dic94—21no—
231Dic94—81no—
232Dic94—81no—
233C8×C47—21no—
234C8×C47—21no—
235C8×C47—21no—
236C8×C47—21no—
237C8×C47—41no—
238C8×C47—41no—
239C8×C47—41no—
240C47⋊C8—21no—
241C47⋊C8—21no—
242C47⋊C8—21no—
243C47⋊C8—21no—
244C47⋊C8—41no—
245C47⋊C8—41no—
246C47⋊C8—41no—
247#17991—471nomaximal, Sylow
248C22×C47C2×C4×D411yescharacteristic
249C2×D47—21no—
250C2×D47—21no—
251C2×D47—21no—
252C4×C47—21no—
253C4×C47—41no—
254C4×C47—41no—
255C4×C47—41no—
256C4×C47—41no—
257C4×C47#56811yescharacteristic
258C4×C47#56811yescharacteristic
259C4×C47#57811yescharacteristic
260C4×C47#57811yescharacteristic
261Dic47—21no—
262Dic47—21no—
263Dic47—21no—
264Dic47—41no—
265Dic47—41no—
266Dic47—41no—
267Dic47—41no—
268#3170—471no—
269#2985—471no—
270#2985—471no—
271#1587—471no—
272#1587—471no—
273#1587—471no—
274#1587—471no—
275#1584—471no—
276#1584—471no—
277#1584—471no—
278#1584D4711yescharacteristic, complemented
279#1568—471no—
280#1497—471no—
281#1497—471no—
282#1452—471no—
283C2×C47#293211yescharacteristic
284C2×C47#295011yescharacteristic
285C2×C47#295711yescharacteristic
286D47—41no—
287#533—471no—
288#533—471no—
289#500—471no—
290#494—471no—
291#487—471no—
292#487—471no—
293#467—471no—
294#467—471no—
295#467—471no—
296#467—471no—
297#446—471no—
298#446—471no—
299#446—471no—
300#446—941no—
301#446—941no—
302#446—941no—
303#446—941no—
304#446C2×D4711yescharacteristic
305C8×Q8—471no—
306C8×Q8—471no—
307C8×Q8—471no—
308C8×Q8C2×D4711yescharacteristic
309C4×Q16—471no—
310C4×Q16—471no—
311C4×Q16—471no—
312C4×Q16C2×D4711yescharacteristic
313#433—941no—
314#433—941no—
315#433—941no—
316#433—941no—
317#432—471no—
318#432—471no—
319#431—471no—
320#431—471no—
321C2×C4×C8—471no—
322#335—471no—
323#335C2×D4711yescharacteristic
324#334—471no—
325#334—471no—
326Q8⋊C8—471no—
327Q8⋊C8—471no—
328Q8⋊C8—471no—
329Q8⋊C8—471no—
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8C2×D4711yescharacteristic
333Q8⋊C8C2×D4711yescharacteristic
334#322—471no—
335#322—471no—
336#322—471no—
337#322C2×D4711yescharacteristic
338C47#1799111yescharacteristic, complemented, Sylow
339C2×Q16—471no—
340C2×Q16—471no—
341C2×Q16—471no—
342C2×Q16C4×D4711yescharacteristic
343C22×C8—471no—
344C22×C8—471no—
345C4⋊Q8—471no—
346C4⋊Q8—471no—
347C4⋊Q8—471no—
348C4⋊Q8—471no—
349#125—941no—
350#125—941no—
351C22⋊Q8—471no—
352C22⋊Q8—471no—
353C22⋊Q8—471no—
354C22⋊Q8—471no—
355C22⋊Q8—941no—
356C22⋊Q8—941no—
357C4×Q8—471no—
358C4×Q8—471no—
359C4×Q8—941no—
360C4×Q8—941no—
361C4×Q8C22×D4711yescharacteristic
362C4×Q8C22×D4711yescharacteristic
363#117—941no—
364#117—941no—
365C2×C42—471no—
366#107—471no—
367#107—471no—
368#107—471no—
369#107C4×D4711yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—471no—
373C4⋊C8—471no—
374C4⋊C8—471no—
375C4⋊C8—471no—
376C4⋊C8—941no—
377C4⋊C8—941no—
378C4⋊C8—941no—
379C4⋊C8—941no—
380C4⋊C8—941no—
381C4⋊C8—941no—
382C4⋊C8—941no—
383C4⋊C8C22×D4711yescharacteristic
384C4⋊C8C22×D4711yescharacteristic
385#103—471no—
386#103—471no—
387#103—471no—
388#103—471no—
389#103—471no—
390#103—471no—
391#103C4×D4711yescharacteristic
392#103C4×D4711yescharacteristic
393C22⋊C8—471no—
394C22⋊C8—471no—
395C22⋊C8—941no—
396C22⋊C8—941no—
397C22⋊C8—941no—
398#97—21no—
399#97—941no—
400#97—941no—
401#97—941no—
402#97—941no—
403#97—941no—
404C4×C8—21no—
405C4×C8—471no—
406C4×C8—471no—
407C4×C8—471no—
408C4×C8—471no—
409C4×C8—471no—
410C4×C8—941no—
411C4×C8—941no—
412C4×C8—941no—
413C4×C8C22×D4711yescharacteristic
414C4×C8C22×D4711yescharacteristic
415C4×C8C22×D4711yescharacteristic
416C2×Q8—471no—
417C2×Q8—471no—
418C2×Q8—941no—
419C2×Q8—941no—
420C2×Q8C2×C4×D4711yescharacteristic
421C2×Q8C2×C4×D4711yescharacteristic
422C22×C4—471no—
423C22×C4—471no—
424C22×C4—471no—
425Q16—41no—
426Q16—1881no—
427Q16—1881no—
428Q16—1881no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—471no—
433C2×C8—471no—
434C2×C8—471no—
435C2×C8—471no—
436C2×C8—941no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—1881no—
440C2×C8—1881no—
441C2×C8C2×C4×D4711yescharacteristic
442C2×C8C2×C4×D4711yescharacteristic
443C2×C8D4×D4711yescharacteristic
444C2×C8D4×D4711yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—471no—
448C4⋊C4—471no—
449C4⋊C4—941no—
450C4⋊C4—941no—
451C4⋊C4—941no—
452C4⋊C4—941no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4C2×C4×D4711yescharacteristic
462C4⋊C4C2×C4×D4711yescharacteristic
463C22⋊C4—941no—
464C22⋊C4—941no—
465C22⋊C4—941no—
466C22⋊C4—941no—
467C42—21no—
468C42—21no—
469C42—471no—
470C42—471no—
471C42—471no—
472C42—941no—
473C42—941no—
474C42C23×D4711yescharacteristic
475C23—471no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—941no—
481Q8—941no—
482Q8—941no—
483Q8—941no—
484Q8—3761no—
485Q8—3761no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—471no—
491C2×C4—471no—
492C2×C4—471no—
493C2×C4—941no—
494C2×C4—941no—
495C2×C4—941no—
496C2×C4—941no—
497C2×C4—941no—
498C2×C4—941no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—1881no—
502C2×C4C22×C4×D4711yescharacteristic
503C2×C4C2×D4×D4711yescharacteristic
504C2×C4#41×D4711yescharacteristic
505C8—21no—
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—941no—
513C8—941no—
514C8—941no—
515C8—941no—
516C8—1881no—
517C8—1881no—
518C8—1881no—
519C22—941no—
520C22—941no—
521C22—941no—
522C22C4×D4×D4711yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—941no—
529C4—941no—
530C4—941no—
531C4—1881no—
532C4—1881no—
533C4—1881no—
534C4—1881no—
535C4#1568988811yescharacteristic
536C4#1568988911yescharacteristic
537C4#1568993611yescharacteristic
538C4#1568993711yescharacteristic
539C2—1881no—
540C2#2025210211yescharacteristic
541C2#2025225111yescharacteristic
542C2#2025230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1584C2
socleC22×C47C2×C4×D4
prime radicalC22×D47C4×D4
cosocleC42×C47C24
hypercenter#1584D47
hypocenterC47#17991
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #20242262C2semidirect
5. #20242259C2semidirect
6. #20242257C2semidirect
7. #20242256C2semidirect
8. #20242240C2semidirect
9. #20242239C2semidirect
10. #20242237C2semidirect
15. C47×#1584C2semidirect
278. #1584D47semidirect
338. C47#17991semidirect

Maximal subgroups

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

subgroupindex
#202539712
#202524842
#202524792
#202422622
#202422592
#202422572
#202422562
#202422402
#202422392
#202422372
#202421502
#202418592
#202416792
C47×#15842
#1799147