Finite Group Databasebeta

← #26186372

Subgroups — #26186372

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253449C211yesmaximal, characteristic
2#20252496C211yesmaximal, characteristic, complemented
3#20252463C211yesmaximal, characteristic, complemented
4#20242268C211yesmaximal, characteristic, complemented
5#20242254C211yesmaximal, characteristic, complemented
6#20242233C211yesmaximal, characteristic, complemented
7#20242219C211yesmaximal, characteristic, complemented
8#20242213C211yesmaximal, characteristic, complemented
9#20242202C211yesmaximal, characteristic, complemented
10C8×#10625325C211yesmaximal, characteristic, complemented
11C8×D376C211yesmaximal, characteristic, complemented
12#20242173C211yesmaximal, characteristic, complemented
13#20241823C211yesmaximal, characteristic, complemented
14#20241788C211yesmaximal, characteristic, complemented
15C47×#1454C211yesmaximal, characteristic, complemented
16#15689673C2211yescharacteristic
17C4×#10625350C2211yescharacteristic
18#15689448C411yescharacteristic
19#15689448C411yescharacteristic
20#15689419C411yescharacteristic
21#15689414C411yescharacteristic
22#15689324C411yescharacteristic
23#15689319C411yescharacteristic
24#15689270C411yescharacteristic
25#15689270C411yescharacteristic
26C8×Dic94C2211yescharacteristic
27C8×Dic94C2211yescharacteristic
28C4×#10625325C2211yescharacteristic
29C4×#10625325C2211yescharacteristic
30C4×D376C2211yescharacteristic
31C4×D376C2211yescharacteristic
32#15689202C2211yescharacteristic
33#15689202C2211yescharacteristic
34#15689193—21no—
35#15689193—21no—
36C8×D188C2211yescharacteristic
37C8×D188C2211yescharacteristic
38C8×D188C2211yescharacteristic
39C8×D188C2211yescharacteristic
40(C22⋊D47)⋊C8—21no—
41(C22⋊D47)⋊C8—21no—
42#15689180C2211yescharacteristic
43#15689175—21no—
44C2×C4⋊(C47⋊C8)C2211yescharacteristic
45C4⋊C8×D47—21no—
46#15689088—21no—
47#15689088—21no—
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688874C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688852C2211yescharacteristic
57#15688852C2211yescharacteristic
58#15688852C2211yescharacteristic
59#15688852C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625350—21no—
68C2×#10625350C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×D376C2×C411yescharacteristic
72C2×D376C2×C411yescharacteristic
73C2×#10625324—21no—
74C2×#10625324—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80#13094024C2×C411yescharacteristic
81#13094021C2×C411yescharacteristic
82#13094012—21no—
83#13093998—21no—
84#13093998C2×C411yescharacteristic
85#13093998C2×C411yescharacteristic
86C4×Dic94C2×C411yescharacteristic
87C4×Dic94C2311yescharacteristic
88C4×D188—21no—
89C4×D188C2×C411yescharacteristic
90C4×D188C2311yescharacteristic
91C4×D188C2311yescharacteristic
92C4×D188C2311yescharacteristic
93C4×C22⋊D47—21no—
94C4×C22⋊D47—21no—
95#13093983C2×C411yescharacteristic
96#13093981—21no—
97C42×D47—21no—
98#13093958C2×C411yescharacteristic
99#13093958C2×C411yescharacteristic
100#13093956C2×C411yescharacteristic
101#13093956C2×C411yescharacteristic
102C4⋊(C47⋊C8)—21no—
103C4⋊(C47⋊C8)C2311yescharacteristic
104C4⋊(C47⋊C8)C2311yescharacteristic
105C4⋊(C47⋊C8)C2311yescharacteristic
106C4⋊(C47⋊C8)C2311yescharacteristic
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093946C2×C411yescharacteristic
115#13093946C2×C411yescharacteristic
116#13093946C2×C411yescharacteristic
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121(C2×D47)⋊C8—21no—
122(C2×D47)⋊C8—21no—
123(C2×D47)⋊C8—21no—
124#13093935—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C2×C42×C47C2311yescharacteristic
128C4⋊C8×C47—21no—
129C4⋊C8×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47D411yescharacteristic
133C22⋊C8×C47—21no—
134C22⋊C8×C47C2×C411yescharacteristic
135C22⋊C8×C47C2×C411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137C22⋊C8×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—
148C2×C22⋊D47—21no—
149C2×C22⋊D47—21no—
150#10625350—22no—
151#10625350—22no—
152#10625350—81no—
153#10625350—81no—
154C2×D188—21no—
155C2×D188—21no—
156C2×D188C22×C411yescharacteristic
157C2×D188C22×C411yescharacteristic
158C2×D188C22×C411yescharacteristic
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×Dic94—21no—
165C2×Dic94C22×C411yescharacteristic
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C2×C8×C47C2×D411yescharacteristic
176C42×C47C22×C411yescharacteristic
177C42×C47C2×D411yescharacteristic
178C42×C47#4111yescharacteristic
179C42×C47C2411yescharacteristic
180C22⋊Dic47—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190C4⋊Dic47C22×C411yescharacteristic
191C4⋊Dic47C22×C411yescharacteristic
192Dic47⋊C4—21no—
193Dic47⋊C4—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—81no—
202D376—22no—
203D376—22no—
204#10625325—22no—
205#10625325—22no—
206#10625324—81no—
207#10625324—81no—
208C8×D47—81no—
209C8×D47—81no—
210C8×D47—81no—
211C8×D47—81no—
212C23×C47C4×D411yescharacteristic
213C22×D47—21no—
214C22×D47—21no—
215C22×D47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—41no—
221C2×C4×C47C4×D411yescharacteristic
222C2×C4×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C23×C411yescharacteristic
225C2×C4×C47C22×D411yescharacteristic
226C2×C4×C47C2×#4111yescharacteristic
227C22⋊D47—24no—
228C22⋊D47—81no—
229C22⋊D47—81no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235D188—21no—
236D188—21no—
237D188—21no—
238D188—21no—
239D188—21no—
240D188—81no—
241D188—81no—
242D188#13112yes—
243C4×D47—24no—
244C4×D47—41no—
245C4×D47—41no—
246C4×D47—41no—
247C4×D47—41no—
248C4×D47—41no—
249C4×D47—41no—
250C4×D47—81no—
251Dic94—21no—
252Dic94—81no—
253Dic94#13112yes—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—21no—
259C8×C47—21no—
260C8×C47—21no—
261C8×C47—21no—
262C8×C47—41no—
263C8×C47—41no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#17920—471nomaximal, Sylow
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—21no—
272C22×C47C2×C4×D411yescharacteristic
273C2×D47—22no—
274C2×D47—41no—
275C2×D47—41no—
276C2×D47—41no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C2×D47—41no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47C2×#13111yescharacteristic
287C4×C47C2×#13111yescharacteristic
288C4×C47#57611yescharacteristic
289C4×C47#57711yescharacteristic
290Dic47—22no—
291Dic47—41no—
292Dic47—41no—
293Dic47—41no—
294Dic47—41no—
295#3106—471no—
296#2988—471no—
297#2981—471no—
298#1588—471no—
299#1586—471no—
300#1583—471no—
301#1581—471no—
302#1580—471no—
303SD16⋊C8—471no—
304C8×SD16—471no—
305C8×D8—471no—
306#1573—471no—
307#1488—471no—
308#1480—471no—
309#1454D4711yescharacteristic, complemented
310C2×C47—41no—
311C2×C47#292911yescharacteristic
312C2×C47#294611yescharacteristic
313C2×C47#295711yescharacteristic
314D47—42no—
315D47—81no—
316D47—81no—
317#532—471no—
318C4×#41—471no—
319#482—471no—
320#482—471no—
321#477—471no—
322#476—471no—
323#460—471no—
324#459—471no—
325#449—471no—
326#449—471no—
327C8×Q8—471no—
328C8×Q8—471no—
329C4×SD16—471no—
330C4×SD16—471no—
331C4×D8—471no—
332C4×D8—471no—
333#436—471no—
334#436—471no—
335#435—941no—
336#435—941no—
337C8×D4—471no—
338C8×D4—471no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—941no—
342C8×D4—941no—
343#432—471no—
344#431—941no—
345#431C2×D4711yescharacteristic
346#431C2×D4711yescharacteristic
347#431C2×D4711yescharacteristic
348C2×C4⋊C8—471no—
349C2×C4⋊C8—941no—
350#408—941no—
351#408—941no—
352#335—471no—
353#335—471no—
354#334—471no—
355#334—471no—
356Q8⋊C8—471no—
357Q8⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364#322C2×D4711yescharacteristic
365#322C2×D4711yescharacteristic
366#322C2×D4711yescharacteristic
367C82C2×D4711yescharacteristic
368C47#1792011yescharacteristic, complemented, Sylow
369C2×#41—471no—
370C2×#41—941no—
371C2×SD16—471no—
372C2×SD16—471no—
373C2×D8—471no—
374C2×D8—471no—
375C2×M16—941no—
376C2×M16—941no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C4⋊Q8—471no—
383#127—471no—
384#124—941no—
385#121—471no—
386#121—471no—
387#121—941no—
388C4×Q8—471no—
389C4×Q8—471no—
390C4×D4—471no—
391C4×D4—471no—
392C4×D4—471no—
393C4×D4—471no—
394C4×D4—941no—
395C4×D4—941no—
396C4×D4—941no—
397#117—471no—
398#117—941no—
399C2×C42—941no—
400C2×C42C22×D4711yescharacteristic
401#107—471no—
402#107—471no—
403#106—471no—
404#106—471no—
405C4⋊C8—21no—
406C4⋊C8—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8C4×D4711yescharacteristic
414C4⋊C8C4×D4711yescharacteristic
415C4⋊C8D18811yescharacteristic
416C4⋊C8D18811yescharacteristic
417#103—471no—
418#103—471no—
419#102—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425C22⋊C8—21no—
426C22⋊C8—941no—
427C22⋊C8—941no—
428C22⋊C8—941no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8C4×D4711yescharacteristic
434C22⋊C8C4×D4711yescharacteristic
435C22⋊C8D18811yescharacteristic
436C22⋊C8D18811yescharacteristic
437#97—941no—
438C4×C8—941no—
439C4×C8—941no—
440C4×C8C22×D4711yescharacteristic
441C4×C8C22×D4711yescharacteristic
442C4×C8C22×D4711yescharacteristic
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445C4×C8C22×D4711yescharacteristic
446#41—942no—
447#41—942no—
448#41—3761no—
449#41—3761no—
450C2×Q8—471no—
451C2×Q8—941no—
452C2×D4—471no—
453C2×D4—471no—
454C2×D4—471no—
455C2×D4—941no—
456C2×D4—941no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4C2×D18811yescharacteristic
467C22×C4#1062535011yescharacteristic
468SD16—942no—
469SD16—942no—
470D8—942no—
471D8—942no—
472M16—3761no—
473M16—3761no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—3761no—
481C2×C8—3761no—
482C2×C8—3761no—
483C2×C8—3761no—
484C2×C8—3761no—
485C2×C8C2×C4×D4711yescharacteristic
486C2×C8C2×C4×D4711yescharacteristic
487C2×C8C2×C4×D4711yescharacteristic
488C2×C8C2×C4×D4711yescharacteristic
489C2×C8C2×D18811yescharacteristic
490C2×C8C2×D18811yescharacteristic
491C2×C8C2×D18811yescharacteristic
492C2×C8C2×D18811yescharacteristic
493C4⋊C4—471no—
494C4⋊C4—471no—
495C4⋊C4—471no—
496C4⋊C4—471no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C22⋊C4—941no—
501C22⋊C4—941no—
502C22⋊C4—941no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C42—941no—
508C42—941no—
509C42—941no—
510C42C2×C4×D4711yescharacteristic
511C42C2×D18811yescharacteristic
512C42#1062535011yescharacteristic
513C42C23×D4711yescharacteristic
514C23—941no—
515C23—941no—
516C23—941no—
517C23C4×D18811yescharacteristic
518Q8—472no—
519Q8—941no—
520Q8—3761no—
521D4—472no—
522D4—944no—
523D4—941no—
524D4—941no—
525D4—941no—
526D4—941no—
527D4—941no—
528D4—3761no—
529D4—3761no—
530D4—3761no—
531D4—3761no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—944no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—3761no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4C4×D18811yescharacteristic
551C2×C4C4×D18811yescharacteristic
552C2×C4C4×D18811yescharacteristic
553C2×C4C22×C4×D4711yescharacteristic
554C2×C4C22×D18811yescharacteristic
555C2×C4C2×#1062535011yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—1881no—
567C8—1881no—
568C8—1881no—
569C8—1881no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—942no—
574C22—1881no—
575C22—1881no—
576C22—1881no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22—1881no—
581C22—1881no—
582C22C2×C4×D18811yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—942no—
588C4—1881no—
589C4—1881no—
590C4—1881no—
591C4—1881no—
592C4#131×D4711yescharacteristic
593C4#131×D4711yescharacteristic
594C4#1568992811yescharacteristic
595C4#1568993511yescharacteristic
596C2—41no—
597C2—3761no—
598C2—3761no—
599C2—1882no—
600C2#2025208411yescharacteristic
601C2#2025222211yescharacteristic
602C2#2025230611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1454C2
socleC22×C47C2×C4×D4
prime radical#20253449C2
cosocleC42×C47C24
hypercenter#1454D47
hypocenterC47#17920
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #20252496C2semidirect
3. #20252463C2semidirect
4. #20242268C2semidirect
5. #20242254C2semidirect
6. #20242233C2semidirect
7. #20242219C2semidirect
8. #20242213C2semidirect
9. #20242202C2semidirect
10. C8×#10625325C2semidirect
11. C8×D376C2semidirect
12. #20242173C2semidirect
13. #20241823C2semidirect
14. #20241788C2semidirect
15. C47×#1454C2semidirect
309. #1454D47semidirect
368. C47#17920semidirect

Maximal subgroups

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

subgroupindex
#202534492
#202524962
#202524632
#202422682
#202422542
#202422332
#202422192
#202422132
#202422022
C8×#106253252
C8×D3762
#202421732
#202418232
#202417882
C47×#14542
#1792047