Finite Group Databasebeta

← #26235756

Subgroups — #26235756

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252190C211yesmaximal, characteristic
2#20252053C211yesmaximal, characteristic, complemented
3#20251953C211yesmaximal, characteristic, complemented
4#20244099C211yesmaximal, characteristic, complemented
5#20244092C211yesmaximal, characteristic, complemented
6#20243988C211yesmaximal, characteristic, complemented
7#20243988C211yesmaximal, characteristic, complemented
8#20243714C211yesmaximal, characteristic
9#20243714C211yesmaximal, characteristic
10#20243529C211yesmaximal, characteristic, complemented
11#20243409C211yesmaximal, characteristic, complemented
12#20243409C211yesmaximal, characteristic, complemented
13#20243232C211yesmaximal, characteristic, complemented
14#20243225C211yesmaximal, characteristic, complemented
15C47×#1771C211yesmaximal, characteristic, complemented
16C2×#13094046C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18C2×#13094030C2211yescharacteristic
19C4×#10625350C2211yescharacteristic
20C4×#10625350C2211yescharacteristic
21#15689236C411yescharacteristic, complemented
22#15689236C411yescharacteristic, complemented
23#15689231C411yescharacteristic, complemented
24#15689231C411yescharacteristic, complemented
25#15689225C411yescharacteristic, complemented
26#15689225C411yescharacteristic, complemented
27#15689225C411yescharacteristic, complemented
28#15689225C411yescharacteristic, complemented
29#15689183—21no—
30#15689183—21no—
31#15689179—21no—
32#15689175—21no—
33#15689161C2211yescharacteristic
34#15689149C2211yescharacteristic
35#15689149C2211yescharacteristic
36#15689148—21no—
37#15689148—21no—
38#15689147C2211yescharacteristic
39#15689147C2211yescharacteristic
40#15689145—21no—
41C4⋊C8×D47—21no—
42C2×#13093952C2211yescharacteristic
43C2×#13093952C2211yescharacteristic
44C2×#13093952C2211yescharacteristic
45C2×#13093952C2211yescharacteristic
46#15689120C2211yescharacteristic
47#15689120C2211yescharacteristic
48#15689089C2211yescharacteristic
49#15689089C2211yescharacteristic
50#15689078C2211yescharacteristic
51#15689078C2211yescharacteristic
52#15688888C2211yescharacteristic
53#15688888C2211yescharacteristic
54#15688888C2211yescharacteristic
55#15688888C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688883C2211yescharacteristic
58#15688883C2211yescharacteristic
59#15688883C2211yescharacteristic
60C2×C4⋊C8×C47C2211yescharacteristic
61C2×#97×C47C2211yescharacteristic
62C2×#97×C47C2211yescharacteristic
63C2×C4×C8×C47C2211yescharacteristic
64C4×C4⋊C4×C47C2211yescharacteristic
65C47×#336C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68C2×#10625350C2311yescharacteristic
69#13094046—22no—
70#13094046—22no—
71C2×Dic188C2×C411yescharacteristic
72C2×#10625325C2×C411yescharacteristic
73C2×#10625325C2×C411yescharacteristic
74C2×D376C2×C411yescharacteristic
75#13094030—22no—
76#13094030—22no—
77#13094030—41no—
78#13094030—41no—
79C2×#10625329C2311yescharacteristic
80C2×#10625329C2311yescharacteristic
81C2×#10625329C2311yescharacteristic
82C2×#10625329C2311yescharacteristic
83C2×#10625324—21no—
84C2×#10625324—21no—
85C2×C8×D47—21no—
86C2×C8×D47—21no—
87C4×Dic94C2×C411yescharacteristic
88C4×Dic94C2×C411yescharacteristic
89C4×Dic94C2×C411yescharacteristic
90C4×Dic94C2×C411yescharacteristic
91C4×D188C2×C411yescharacteristic
92C4×D188C2×C411yescharacteristic
93C4×D188C2×C411yescharacteristic
94C4×D188C2×C411yescharacteristic
95C4×C22⋊D47—21no—
96C4×C22⋊D47—21no—
97C4×C22⋊D47—21no—
98C4×C22⋊D47—21no—
99#13093983C2311yescharacteristic
100#13093983C2311yescharacteristic
101#13093981—21no—
102#13093981—21no—
103C42×D47—21no—
104C42×D47—21no—
105#13093958C2×C411yescharacteristic
106#13093958C2×C411yescharacteristic
107#13093956C2×C411yescharacteristic
108#13093956C2×C411yescharacteristic
109C4⋊(C47⋊C8)—21no—
110C4⋊(C47⋊C8)—21no—
111C4⋊(C47⋊C8)—21no—
112C4⋊(C47⋊C8)—21no—
113Dic47⋊C8—21no—
114Dic47⋊C8—21no—
115Dic47⋊C8—21no—
116Dic47⋊C8—21no—
117#13093952—22no—
118#13093952—22no—
119#13093952—41no—
120#13093952—41no—
121#13093949C2×C411yescharacteristic
122#13093949C2×C411yescharacteristic
123#13093949C2×C411yescharacteristic
124#13093949C2×C411yescharacteristic
125#13093946C2×C411yescharacteristic
126#13093946C2×C411yescharacteristic
127#13093946C2×C411yescharacteristic
128#13093946C2×C411yescharacteristic
129(C2×D47)⋊C8—21no—
130(C2×D47)⋊C8—21no—
131(C2×D47)⋊C8—21no—
132(C2×D47)⋊C8—21no—
133#13093934—21no—
134#13093934—21no—
135C8×Dic47—21no—
136C8×Dic47—21no—
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140C22×C8×C47C2311yescharacteristic
141C2×C4⋊C4×C47—21no—
142C2×C42×C47C2311yescharacteristic
143C2×C42×C47C2311yescharacteristic
144C2×C42×C47C2311yescharacteristic
145C4⋊C8×C47D411yescharacteristic
146C4⋊C8×C47D411yescharacteristic
147C4⋊C8×C47D411yescharacteristic
148C4⋊C8×C47D411yescharacteristic
149#97×C47—41no—
150#97×C47C2×C411yescharacteristic
151#97×C47C2×C411yescharacteristic
152#97×C47C2×C411yescharacteristic
153#97×C47C2×C411yescharacteristic
154C4×C8×C47—41no—
155#95×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47#4111yescharacteristic
159C22×C4×C47#4111yescharacteristic
160C22×C4×C47C2411yescharacteristic
161C2×C22⋊D47—21no—
162C2×C22⋊D47—21no—
163#10625350—21no—
164#10625350—21no—
165#10625350—21no—
166#10625350—21no—
167#10625350—21no—
168#10625350—21no—
169#10625350#4112yes—
170#10625350#4112yes—
171C2×D188C22×C411yescharacteristic
172C2×D188C22×C411yescharacteristic
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×Dic94C22×C411yescharacteristic
180C2×Dic94C22×C411yescharacteristic
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47C22×C411yescharacteristic
190C2×C8×C47C22×C411yescharacteristic
191C2×C8×C47C22×C411yescharacteristic
192C2×C8×C47C22×C411yescharacteristic
193C2×C8×C47C2×D411yescharacteristic
194C2×C8×C47C2×D411yescharacteristic
195C2×C8×C47C2×D411yescharacteristic
196C2×C8×C47C2×D411yescharacteristic
197C4⋊C4×C47—42no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47C22×C411yescharacteristic
203C42×C47C22×C411yescharacteristic
204C42×C47C2×D411yescharacteristic
205C42×C47C2×D411yescharacteristic
206C22⋊Dic47—21no—
207C22⋊Dic47—21no—
208(C2×D47)⋊C4—21no—
209(C2×D47)⋊C4—21no—
210(C2×D47)⋊C4—21no—
211(C2×D47)⋊C4—21no—
212C4⋊Dic47C22×C411yescharacteristic
213C4⋊Dic47C22×C411yescharacteristic
214C4⋊Dic47C22×C411yescharacteristic
215C4⋊Dic47C22×C411yescharacteristic
216Dic47⋊C4—21no—
217Dic47⋊C4—21no—
218Dic47⋊C4—21no—
219Dic47⋊C4—21no—
220C4×Dic47—21no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226#10625329—21no—
227#10625329—21no—
228#10625329—21no—
229#10625329—21no—
230#10625329—21no—
231#10625329—21no—
232#10625329—21no—
233#10625329—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238Dic188—22no—
239D376—22no—
240#10625325—22no—
241#10625325—22no—
242#10625324—42no—
243#10625324—42no—
244C8×D47—42no—
245C8×D47—42no—
246C23×C47C2×#4111yescharacteristic
247C22×D47—21no—
248C22×D47—21no—
249C2×C4×C47—22no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47C4×D411yescharacteristic
258C2×C4×C47C4×D411yescharacteristic
259C2×C4×C47C4×D411yescharacteristic
260C2×C4×C47C4×D411yescharacteristic
261C2×C4×C47C23×C411yescharacteristic
262C2×C4×C47C22×D411yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C2×C4×C472−1+411yescharacteristic
267C22⋊D47—22no—
268C22⋊D47—22no—
269C22⋊D47—41no—
270C22⋊D47—41no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277D188—21no—
278D188—21no—
279D188—21no—
280D188#11712yes—
281C4×D47—22no—
282C4×D47—22no—
283C4×D47—42no—
284C4×D47—42no—
285C4×D47—41no—
286C4×D47—41no—
287C4×D47—81no—
288C4×D47—81no—
289Dic94—21no—
290Dic94—21no—
291Dic94—21no—
292Dic94#11712yes—
293C8×C47—21no—
294C8×C47—21no—
295C8×C47—21no—
296C8×C47—21no—
297C8×C47—21no—
298C8×C47—21no—
299C8×C47—21no—
300C8×C47—21no—
301C47⋊C8—41no—
302C47⋊C8—41no—
303C47⋊C8—41no—
304C47⋊C8—41no—
305#22784—471nomaximal, Sylow
306C22×C47—21no—
307C22×C47—21no—
308C22×C47C2×C4×D411yescharacteristic
309C22×C47#55211yescharacteristic
310C22×C47#55311yescharacteristic
311C2×D47—22no—
312C2×D47—41no—
313C2×D47—41no—
314C2×D47—41no—
315C2×D47—41no—
316C2×D47—41no—
317C4×C47—21no—
318C4×C47—21no—
319C4×C47—21no—
320C4×C47—21no—
321C4×C47—42no—
322C4×C47—81no—
323C4×C47C2×#11711yescharacteristic
324C4×C47#52011yescharacteristic
325C4×C47#54611yescharacteristic
326C4×C47#54811yescharacteristic
327Dic47—22no—
328Dic47—41no—
329Dic47—41no—
330Dic47—41no—
331Dic47—41no—
332Dic47—41no—
333#2943—471no—
334#2925—471no—
335#2906—471no—
336#1938—471no—
337#1937—471no—
338#1922—471no—
339#1922—471no—
340#1876—471no—
341#1876—471no—
342#1838—471no—
343#1806—471no—
344#1806—471no—
345#1771D4711yescharacteristic, complemented
346#1765—471no—
347#1764—471no—
348C2×C47—21no—
349C2×C47—21no—
350C2×C47#235211yescharacteristic
351C2×C47#295511yescharacteristic
352C2×C47#295611yescharacteristic
353D47—42no—
354D47—81no—
355C2×#135—471no—
356C2×#131—471no—
357C2×#131—471no—
358C4×#41—471no—
359C4×#41—471no—
360#442—471no—
361#442—471no—
362#441—471no—
363#441—471no—
364#440—471no—
365#440—471no—
366#440—471no—
367#440—471no—
368#433—941no—
369#433—941no—
370#432—941no—
371#431—941no—
372#427—471no—
373#424—471no—
374#424—471no—
375#424—941no—
376#424—941no—
377#423—471no—
378#423—471no—
379#423—941no—
380C2×C4⋊C8—941no—
381C2×C4⋊C8C2×D4711yescharacteristic
382C2×#104—471no—
383C2×#104—471no—
384C2×#104—471no—
385C2×#104—471no—
386#416—471no—
387#416—471no—
388#408—471no—
389#408—471no—
390#405—471no—
391#405—471no—
392C2×#97C2×D4711yescharacteristic
393C2×#97C2×D4711yescharacteristic
394C2×C4×C8C2×D4711yescharacteristic
395C4×C4⋊C4C2×D4711yescharacteristic
396#341—471no—
397#341—471no—
398#341—471no—
399#341—471no—
400#339—471no—
401#339—471no—
402#339—471no—
403#339—471no—
404#336C2×D4711yescharacteristic
405#336C2×D4711yescharacteristic
406C47#2278411yescharacteristic, complemented, Sylow
407C2×#41—471no—
408C2×#41—471no—
409#135—942no—
410#135—942no—
411C2×Q16—471no—
412C2×SD16—471no—
413C2×SD16—471no—
414C2×D8—471no—
415#131—942no—
416#131—942no—
417#131—1881no—
418#131—1881no—
419C2×M16—471no—
420C2×M16—471no—
421C2×M16—471no—
422C2×M16—471no—
423C2×M16—941no—
424C2×M16—941no—
425C22×C8—941no—
426C22×C8—941no—
427C22×C8C22×D4711yescharacteristic
428C22×C8C22×D4711yescharacteristic
429C22×C8C22×D4711yescharacteristic
430C22×C8C22×D4711yescharacteristic
431C4×Q8—471no—
432C4×Q8—471no—
433C4×Q8—471no—
434C4×Q8—471no—
435C4×D4—471no—
436C4×D4—471no—
437C4×D4—471no—
438C4×D4—471no—
439C4×D4—941no—
440C4×D4—941no—
441C4×D4—941no—
442C4×D4—941no—
443#117—471no—
444#117—471no—
445#117—941no—
446#117—941no—
447C2×C4⋊C4—21no—
448C2×C42—941no—
449C2×C42—941no—
450C2×C42C22×D4711yescharacteristic
451C2×C42C22×D4711yescharacteristic
452C2×C42C22×D4711yescharacteristic
453#107—471no—
454#107—471no—
455#106—471no—
456#106—471no—
457C4⋊C8—941no—
458C4⋊C8—941no—
459C4⋊C8—941no—
460C4⋊C8—941no—
461C4⋊C8—941no—
462C4⋊C8—941no—
463C4⋊C8—941no—
464C4⋊C8—941no—
465C4⋊C8D18811yescharacteristic
466C4⋊C8D18811yescharacteristic
467C4⋊C8D18811yescharacteristic
468C4⋊C8D18811yescharacteristic
469#104—942no—
470#104—942no—
471#104—1881no—
472#104—1881no—
473#103—471no—
474#103—471no—
475#103—471no—
476#103—471no—
477#102—471no—
478#102—471no—
479#102—471no—
480#102—471no—
481C22⋊C8—941no—
482C22⋊C8—941no—
483C22⋊C8—941no—
484C22⋊C8—941no—
485#97—41no—
486#97—941no—
487#97—941no—
488#97C4×D4711yescharacteristic
489#97C4×D4711yescharacteristic
490#97C4×D4711yescharacteristic
491#97C4×D4711yescharacteristic
492C4×C8—41no—
493C4×C8—941no—
494C4×C8—941no—
495#95—21no—
496#41—472no—
497#41—472no—
498#41—941no—
499#41—941no—
500#41—941no—
501#41—941no—
502#41—941no—
503#41—941no—
504C2×Q8—471no—
505C2×Q8—471no—
506C2×D4—471no—
507C2×D4—471no—
508C2×D4—941no—
509C2×D4—941no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—941no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4#1062535011yescharacteristic
519C22×C4#1062535011yescharacteristic
520C22×C4C23×D4711yescharacteristic
521Q16—942no—
522SD16—942no—
523SD16—942no—
524D8—942no—
525M16—941no—
526M16—941no—
527M16—941no—
528M16—941no—
529M16—941no—
530M16—941no—
531M16—941no—
532M16—941no—
533M16—1882no—
534M16—1882no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—941no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—1882no—
548C2×C8—1882no—
549C2×C8C2×C4×D4711yescharacteristic
550C2×C8C2×C4×D4711yescharacteristic
551C2×C8C2×C4×D4711yescharacteristic
552C2×C8C2×C4×D4711yescharacteristic
553C2×C8C2×D18811yescharacteristic
554C2×C8C2×D18811yescharacteristic
555C2×C8C2×D18811yescharacteristic
556C2×C8C2×D18811yescharacteristic
557C4⋊C4—42no—
558C4⋊C4—471no—
559C4⋊C4—471no—
560C4⋊C4—471no—
561C4⋊C4—471no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—941no—
566C22⋊C4—941no—
567C22⋊C4—941no—
568C22⋊C4—941no—
569C22⋊C4—941no—
570C22⋊C4—941no—
571C22⋊C4—941no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—941no—
577C42—941no—
578C42—941no—
579C42—941no—
580C42—941no—
581C42—941no—
582C42C2×C4×D4711yescharacteristic
583C42C2×C4×D4711yescharacteristic
584C42C2×D18811yescharacteristic
585C42C2×D18811yescharacteristic
586C23—941no—
587C23—941no—
588C23C2×#1062535011yescharacteristic
589Q8—472no—
590Q8—941no—
591Q8—941no—
592Q8—941no—
593D4—472no—
594D4—942no—
595D4—942no—
596D4—941no—
597D4—941no—
598D4—941no—
599D4—1881no—
600D4—1881no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—941no—
610C2×C4—942no—
611C2×C4—942no—
612C2×C4—941no—
613C2×C4—941no—
614C2×C4—941no—
615C2×C4—941no—
616C2×C4—941no—
617C2×C4—3761no—
618C2×C4—3761no—
619C2×C4—1882no—
620C2×C4—1882no—
621C2×C4—1881no—
622C2×C4—1881no—
623C2×C4C4×D18811yescharacteristic
624C2×C4C4×D18811yescharacteristic
625C2×C4C4×D18811yescharacteristic
626C2×C4C4×D18811yescharacteristic
627C2×C4C22×C4×D4711yescharacteristic
628C2×C4C22×D18811yescharacteristic
629C2×C4#41×D4711yescharacteristic
630C2×C4#41×D4711yescharacteristic
631C2×C4#1309406911yescharacteristic
632C2×C4#1309407211yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—1881no—
642C8—1881no—
643C8—1881no—
644C8—1881no—
645C22—21no—
646C22—21no—
647C22—942no—
648C22—1881no—
649C22—1881no—
650C22—1881no—
651C22—1881no—
652C22—1881no—
653C22C2×C4×D18811yescharacteristic
654C22#1568981411yescharacteristic
655C22#1568982311yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—42no—
661C4—81no—
662C4—942no—
663C4—1881no—
664C4—1881no—
665C4—1881no—
666C4—1881no—
667C4—1881no—
668C4#117×D4711yescharacteristic
669C4#1568960411yescharacteristic
670C4#1568976811yescharacteristic
671C4#1568978511yescharacteristic
672C2—21no—
673C2—21no—
674C2—3761no—
675C2—1882no—
676C2#2024632011yescharacteristic
677C2#2025229211yescharacteristic
678C2#2025229911yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1771C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094046C22
cosocleC22×C4×C47C24
hypercenter#1771D47
hypocenterC47#22784
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #20252053C2semidirect
3. #20251953C2semidirect
4. #20244099C2semidirect
5. #20244092C2semidirect
6. #20243988C2semidirect
7. #20243988C2semidirect
10. #20243529C2semidirect
11. #20243409C2semidirect
12. #20243409C2semidirect
13. #20243232C2semidirect
14. #20243225C2semidirect
15. C47×#1771C2semidirect
21. #15689236C4semidirect
22. #15689236C4semidirect
23. #15689231C4semidirect
24. #15689231C4semidirect
25. #15689225C4semidirect
26. #15689225C4semidirect
27. #15689225C4semidirect
28. #15689225C4semidirect
345. #1771D47semidirect
406. C47#22784semidirect

Maximal subgroups

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

subgroupindex
#202521902
#202520532
#202519532
#202440992
#202440922
#202439882
#202437142
#202435292
#202434092
#202432322
#202432252
C47×#17712
#2278447