Finite Group Databasebeta

← #26187423

Subgroups — #26187423

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253460C211yesmaximal, characteristic
2#20252406C211yesmaximal, characteristic
3#20252335C211yesmaximal, characteristic, complemented
4#20242292C211yesmaximal, characteristic, complemented
5#20242280C211yesmaximal, characteristic, complemented
6#20242268C211yesmaximal, characteristic, complemented
7#20242261C211yesmaximal, characteristic, complemented
8#20242240C211yesmaximal, characteristic, complemented
9#20242233C211yesmaximal, characteristic, complemented
10#20242208C211yesmaximal, characteristic, complemented
11C8×Dic188C211yesmaximal, characteristic, complemented
12#20242173C211yesmaximal, characteristic, complemented
13#20241862C211yesmaximal, characteristic, complemented
14#20241776C211yesmaximal, characteristic
15C47×#1453C211yesmaximal, characteristic, complemented
16#15689680C2211yescharacteristic
17C4×#10625350C2211yescharacteristic
18#15689465C411yescharacteristic
19#15689465C411yescharacteristic
20#15689409C411yescharacteristic
21#15689404C411yescharacteristic
22#15689334C411yescharacteristic
23#15689329C411yescharacteristic
24#15689287C411yescharacteristic
25#15689287C411yescharacteristic
26#15689253C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689251—21no—
29#15689251—21no—
30C8×Dic94C2211yescharacteristic
31C8×Dic94C2211yescharacteristic
32C8×Dic94C2211yescharacteristic
33C8×Dic94C2211yescharacteristic
34C4×Dic188C2211yescharacteristic
35C4×Dic188C2211yescharacteristic
36C4×#10625325C2211yescharacteristic
37C4×#10625325C2211yescharacteristic
38#15689202C2211yescharacteristic
39#15689202C2211yescharacteristic
40#15689199—21no—
41#15689199—21no—
42#15689180C2211yescharacteristic
43#15689178—21no—
44#15689151—21no—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46#15689081—21no—
47#15689075—21no—
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688874C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688855C2211yescharacteristic
57#15688855C2211yescharacteristic
58#15688852C2211yescharacteristic
59#15688852C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C4×M16×C47C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×#10625324—21no—
74C22×C47⋊C8—21no—
75#13094024C2×C411yescharacteristic
76#13094024C2×C411yescharacteristic
77#13094016—21no—
78#13094003—21no—
79#13094003C2×C411yescharacteristic
80#13094003C2×C411yescharacteristic
81C4×Dic94—21no—
82C4×Dic94C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×Dic94C2311yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×D188C2×C411yescharacteristic
87C4×D188C2311yescharacteristic
88C4×C22⋊D47—21no—
89C4×C22⋊D47—21no—
90#13093983—21no—
91#13093983C2×C411yescharacteristic
92#13093981—21no—
93C42×D47—21no—
94#13093958C2×C411yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093956C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093949C2×C411yescharacteristic
113#13093949C2×C411yescharacteristic
114#13093949C2×C411yescharacteristic
115#13093946C2×C411yescharacteristic
116#13093946C2×C411yescharacteristic
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120#13093935—21no—
121#13093934—21no—
122#13093934—21no—
123C8×Dic47—21no—
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C2×M16×C47D411yescharacteristic
128C2×M16×C47D411yescharacteristic
129C2×C42×C47C2311yescharacteristic
130C4⋊C8×C47—21no—
131C4⋊C8×C47C2×C411yescharacteristic
132C4⋊C8×C47C2×C411yescharacteristic
133C22⋊C8×C47—21no—
134C22⋊C8×C47C2×C411yescharacteristic
135C22⋊C8×C47C2×C411yescharacteristic
136#97×C47D411yescharacteristic
137#97×C47D411yescharacteristic
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148#10625350—22no—
149#10625350—41no—
150C2×D188C22×C411yescharacteristic
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×Dic94—21no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158M16×C47—22no—
159M16×C47—41no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C2×C8×C47C2×D411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C42×C47C22×C411yescharacteristic
171C42×C47C2×D411yescharacteristic
172C42×C47#4111yescharacteristic
173C42×C47C2411yescharacteristic
174C22⋊Dic47—21no—
175C22⋊Dic47—21no—
176C22⋊Dic47—21no—
177(C2×D47)⋊C4—21no—
178(C2×D47)⋊C4—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47C22×C411yescharacteristic
183C4⋊Dic47C22×C411yescharacteristic
184C4⋊Dic47C22×C411yescharacteristic
185C4⋊Dic47C22×C411yescharacteristic
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—42no—
202Dic188—22no—
203Dic188—22no—
204#10625325—41no—
205#10625325—41no—
206#10625324—42no—
207#10625324—42no—
208C23×C47C4×D411yescharacteristic
209C22×D47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—41no—
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C23×C411yescharacteristic
219C2×C4×C47C22×D411yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C22⋊D47—42no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229D188—21no—
230D188—21no—
231C4×D47—42no—
232C4×D47—41no—
233C4×D47—41no—
234C4×D47—81no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—21no—
240Dic94—81no—
241Dic94#13112yes—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47#13712yes—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256#18013—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47C2×C4×D411yescharacteristic
261C2×D47—41no—
262C2×D47—41no—
263C2×D47—41no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47C2×#13111yescharacteristic
269C4×C47#56811yescharacteristic
270C4×C47C2×#13711yescharacteristic
271C4×C47#57511yescharacteristic
272Dic47—22no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278Dic47—41no—
279#3107—471no—
280#2971—471no—
281#2962—471no—
282#1592—471no—
283#1590—471no—
284#1588—471no—
285#1587—471no—
286#1584—471no—
287#1583—471no—
288#1579—471no—
289C8×Q16—471no—
290#1573—471no—
291#1497—471no—
292#1477—471no—
293#1453D4711yescharacteristic, complemented
294C2×C47—41no—
295C2×C47#293311yescharacteristic
296C2×C47C4×#13711yescharacteristic
297C2×C47#295711yescharacteristic
298D47—81no—
299#533—471no—
300C4×#41—471no—
301#485—471no—
302#485—471no—
303#475—471no—
304#474—471no—
305#462—471no—
306#461—471no—
307#452—471no—
308#452—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8—471no—
316C8×Q8—471no—
317C4×Q16—471no—
318C4×Q16—471no—
319C4×SD16—471no—
320C4×SD16—471no—
321#436—471no—
322#436—471no—
323#436—941no—
324#436—941no—
325#432—471no—
326#432—941no—
327#431C2×D4711yescharacteristic
328#431C2×D4711yescharacteristic
329#424—941no—
330C2×C4⋊C8—471no—
331#405—941no—
332C4×M16—941no—
333C4×M16C2×D4711yescharacteristic
334#335—471no—
335#335—471no—
336#334—471no—
337#334—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8—471no—
343Q8⋊C8—471no—
344D4⋊C8—471no—
345D4⋊C8—471no—
346#322C2×D4711yescharacteristic
347#322C2×D4711yescharacteristic
348#322C2×D4711yescharacteristic
349C82C2×D4711yescharacteristic
350C47#1801311yescharacteristic, complemented, Sylow
351C2×#41—471no—
352C2×Q16—471no—
353C2×Q16—471no—
354C2×SD16—471no—
355C2×SD16—471no—
356C2×M16—941no—
357C2×M16—941no—
358C2×M16D18811yescharacteristic
359C2×M16D18811yescharacteristic
360C22×C8—941no—
361C4⋊Q8—471no—
362C4⋊Q8—471no—
363#125—941no—
364C22⋊Q8—471no—
365C22⋊Q8—471no—
366C22⋊Q8—941no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—471no—
370C4×Q8—471no—
371C4×Q8—941no—
372C4×D4—471no—
373C4×D4—471no—
374C4×D4—941no—
375C4×D4—941no—
376#117—471no—
377#117—941no—
378#117—941no—
379C2×C42—941no—
380C2×C42C22×D4711yescharacteristic
381#107—471no—
382#107—471no—
383#106—471no—
384#106—471no—
385C4⋊C8—21no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8—941no—
397C4⋊C8C4×D4711yescharacteristic
398C4⋊C8C4×D4711yescharacteristic
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#103—471no—
405#102—471no—
406#102—471no—
407C22⋊C8—21no—
408C22⋊C8—941no—
409C22⋊C8—941no—
410C22⋊C8—941no—
411C22⋊C8C4×D4711yescharacteristic
412C22⋊C8C4×D4711yescharacteristic
413#97—941no—
414#97—941no—
415#97—941no—
416#97D18811yescharacteristic
417#97D18811yescharacteristic
418C4×C8—941no—
419C4×C8—941no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8C22×D4711yescharacteristic
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427C4×C8C22×D4711yescharacteristic
428#41—942no—
429#41—1881no—
430C2×Q8—471no—
431C2×Q8—471no—
432C2×Q8—471no—
433C2×Q8—941no—
434C2×D4—471no—
435C2×D4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4C2×D18811yescharacteristic
441C22×C4#1062535011yescharacteristic
442Q16—942no—
443Q16—942no—
444SD16—1881no—
445SD16—1881no—
446M16—22no—
447M16—41no—
448M16—1882no—
449M16—1882no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—1882no—
457C2×C8C2×C4×D4711yescharacteristic
458C2×C8C2×C4×D4711yescharacteristic
459C2×C8C2×C4×D4711yescharacteristic
460C2×C8C2×C4×D4711yescharacteristic
461C2×C8C2×D18811yescharacteristic
462C2×C8C2×D18811yescharacteristic
463C2×C8C2×D18811yescharacteristic
464C2×C8C2×D18811yescharacteristic
465C4⋊C4—471no—
466C4⋊C4—471no—
467C4⋊C4—471no—
468C4⋊C4—471no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C22⋊C4—941no—
482C22⋊C4—941no—
483C42—941no—
484C42—941no—
485C42—941no—
486C42—941no—
487C42—941no—
488C42C2×C4×D4711yescharacteristic
489C42C2×D18811yescharacteristic
490C42#1062535011yescharacteristic
491C42C23×D4711yescharacteristic
492C23—941no—
493C23C4×D18811yescharacteristic
494Q8—472no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—941no—
499Q8—941no—
500Q8—3761no—
501D4—941no—
502D4—941no—
503D4—1882no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—3761no—
517C2×C4—1882no—
518C2×C4—1881no—
519C2×C4—1881no—
520C2×C4C4×D18811yescharacteristic
521C2×C4C4×D18811yescharacteristic
522C2×C4C4×D18811yescharacteristic
523C2×C4C22×C4×D4711yescharacteristic
524C2×C4C22×D18811yescharacteristic
525C2×C4C2×#1062535011yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—1881no—
536C8—1881no—
537C8—1881no—
538C8—1881no—
539C8#1309405712yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—1881no—
544C22—1881no—
545C22—1881no—
546C22C2×C4×D18811yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—942no—
552C4—1881no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4—1881no—
557C4—1881no—
558C4#131×D4711yescharacteristic
559C4#1568988811yescharacteristic
560C4C2×#1309405711yescharacteristic
561C4#1568992311yescharacteristic
562C2—41no—
563C2—3761no—
564C2#2025211611yescharacteristic
565C2C4×#1309405711yescharacteristic
566C2#2025230611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1453C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C2×C4
cosocleC42×C47C24
hypercenter#1453D47
hypocenterC47#18013
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #20252335C2semidirect
4. #20242292C2semidirect
5. #20242280C2semidirect
6. #20242268C2semidirect
7. #20242261C2semidirect
8. #20242240C2semidirect
9. #20242233C2semidirect
10. #20242208C2semidirect
11. C8×Dic188C2semidirect
12. #20242173C2semidirect
13. #20241862C2semidirect
15. C47×#1453C2semidirect
293. #1453D47semidirect
350. C47#18013semidirect

Maximal subgroups

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

subgroupindex
#202534602
#202524062
#202523352
#202422922
#202422802
#202422682
#202422612
#202422402
#202422332
#202422082
C8×Dic1882
#202421732
#202418622
#202417762
C47×#14532
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