Finite Group Databasebeta

← #26235755

Subgroups — #26235755

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#20252186C211yesmaximal, characteristic
2#20252056C211yesmaximal, characteristic, complemented
3#20251956C211yesmaximal, characteristic, complemented
4#20244100C211yesmaximal, characteristic, complemented
5#20244093C211yesmaximal, characteristic, complemented
6#20243990C211yesmaximal, characteristic, complemented
7#20243990C211yesmaximal, characteristic, complemented
8#20243713C211yesmaximal, characteristic
9#20243713C211yesmaximal, characteristic
10#20243528C211yesmaximal, characteristic, complemented
11#20243409C211yesmaximal, characteristic, complemented
12#20243263C211yesmaximal, characteristic, complemented
13#20243233C211yesmaximal, characteristic, complemented
14#20243226C211yesmaximal, characteristic, complemented
15C47×#1806C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18C2×#13094031C2211yescharacteristic
19C4×#10625350C2211yescharacteristic
20#15689233C411yescharacteristic, complemented
21#15689233C411yescharacteristic, complemented
22#15689228C411yescharacteristic, complemented
23#15689228C411yescharacteristic, complemented
24#15689223C411yescharacteristic, complemented
25#15689223C411yescharacteristic, complemented
26#15689221C411yescharacteristic, complemented
27#15689221C411yescharacteristic, complemented
28#15689183—21no—
29#15689183—21no—
30#15689179—21no—
31#15689175—21no—
32#15689159C2211yescharacteristic
33#15689150—21no—
34#15689150—21no—
35#15689150C2211yescharacteristic
36#15689150C2211yescharacteristic
37#15689147—21no—
38#15689147C2211yescharacteristic
39C2×C4⋊(C47⋊C8)—21no—
40C2×C4⋊(C47⋊C8)C2211yescharacteristic
41C2×#13093952C2211yescharacteristic
42C2×#13093952C2211yescharacteristic
43#15689119C2211yescharacteristic
44#15689117C2211yescharacteristic
45#15689091C2211yescharacteristic
46#15689091C2211yescharacteristic
47#15689081C2211yescharacteristic
48#15689081C2211yescharacteristic
49C2×#13093935C2211yescharacteristic
50C2×#13093935C2211yescharacteristic
51C2×C4×C47⋊C8C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688887C2211yescharacteristic
54#15688887C2211yescharacteristic
55#15688887C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688883C2211yescharacteristic
58#15688878C2211yescharacteristic
59#15688878C2211yescharacteristic
60C4×#41×C47C2211yescharacteristic
61C47×#423C2211yescharacteristic
62C2×#104×C47C2211yescharacteristic
63C2×#104×C47C2211yescharacteristic
64C4×C4⋊C4×C47C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094044—22no—
69#13094044—22no—
70C2×#10625337C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C2×#10625336C2×C411yescharacteristic
73C2×#10625334C2×C411yescharacteristic
74#13094031—22no—
75#13094031—22no—
76#13094031—41no—
77#13094031—41no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329C2311yescharacteristic
81C2×#10625329C2311yescharacteristic
82C22×C47⋊C8—21no—
83C22×C47⋊C8—21no—
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C4×Dic94C2×C411yescharacteristic
89C4×Dic94C2×C411yescharacteristic
90C4×D188C2×C411yescharacteristic
91C4×D188C2×C411yescharacteristic
92C4×C22⋊D47—21no—
93C4×C22⋊D47—21no—
94#13093983C2311yescharacteristic
95#13093981—21no—
96C42×D47—21no—
97#13093957C2×C411yescharacteristic
98#13093957C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101C4⋊(C47⋊C8)—21no—
102C4⋊(C47⋊C8)—21no—
103C4⋊(C47⋊C8)—21no—
104C4⋊(C47⋊C8)—21no—
105C4⋊(C47⋊C8)—21no—
106C4⋊(C47⋊C8)—21no—
107C4⋊(C47⋊C8)D411yescharacteristic
108C4⋊(C47⋊C8)D411yescharacteristic
109C4⋊(C47⋊C8)D411yescharacteristic
110C4⋊(C47⋊C8)D411yescharacteristic
111#13093952—41no—
112#13093952—41no—
113#13093948C2×C411yescharacteristic
114#13093948C2×C411yescharacteristic
115#13093947C2×C411yescharacteristic
116#13093947C2×C411yescharacteristic
117#13093945C2×C411yescharacteristic
118#13093945C2×C411yescharacteristic
119#13093944C2×C411yescharacteristic
120#13093944C2×C411yescharacteristic
121(C2×D47)⋊C8—21no—
122(C2×D47)⋊C8—21no—
123(C2×D47)⋊C8—21no—
124(C2×D47)⋊C8—21no—
125#13093935—41no—
126#13093935C2×C411yescharacteristic
127#13093935C2×C411yescharacteristic
128#13093935C2×C411yescharacteristic
129#13093935C2×C411yescharacteristic
130#13093934—21no—
131#13093934—21no—
132C4×C47⋊C8—41no—
133C8×Dic47—21no—
134C8×Dic47—21no—
135C2×#41×C47C2311yescharacteristic
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C4×Q8×C47C2×C411yescharacteristic
139C4×Q8×C47C2×C411yescharacteristic
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47C2×C411yescharacteristic
143C4×D4×C47C2×C411yescharacteristic
144#117×C47—21no—
145#117×C47C2311yescharacteristic
146C2×C4⋊C4×C47—21no—
147C2×C42×C47—21no—
148C2×C42×C47C2311yescharacteristic
149C2×C42×C47C2311yescharacteristic
150C2×C42×C47C2311yescharacteristic
151C4⋊C8×C47—21no—
152C4⋊C8×C47—21no—
153#104×C47—22no—
154#104×C47—22no—
155#95×C47—21no—
156#41×C47—21no—
157#41×C47—21no—
158#41×C47#4112yes—
159#41×C47#4112yes—
160C2×Q8×C47C22×C411yescharacteristic
161C2×D4×C47—21no—
162C2×D4×C47C22×C411yescharacteristic
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47#4111yescharacteristic
169C22×C4×C47#4111yescharacteristic
170C22×C4×C47C2411yescharacteristic
171C2×C22⋊D47—21no—
172#10625350—21no—
173#10625350—21no—
174#10625350—21no—
175#10625350—21no—
176C2×D188C22×C411yescharacteristic
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×Dic94C22×C411yescharacteristic
181M16×C47—21no—
182M16×C47—21no—
183M16×C47—21no—
184M16×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—42no—
190C4⋊C4×C47C22×C411yescharacteristic
191C4⋊C4×C47C22×C411yescharacteristic
192C22⋊C4×C47—21no—
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
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—
207#10625337—22no—
208#10625336—22no—
209#10625335—22no—
210#10625334—22no—
211(C2×D47)⋊C4—21no—
212(C2×D47)⋊C4—21no—
213C4⋊Dic47C22×C411yescharacteristic
214C4⋊Dic47C22×C411yescharacteristic
215Dic47⋊C4—21no—
216Dic47⋊C4—21no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220#10625329—21no—
221#10625329—21no—
222#10625329—21no—
223#10625329—21no—
224#10625329—42no—
225#10625329—42no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—42no—
237C2×C47⋊C8—42no—
238C2×C47⋊C8C22×C411yescharacteristic
239C2×C47⋊C8C22×C411yescharacteristic
240C2×C47⋊C8C22×C411yescharacteristic
241C2×C47⋊C8C22×C411yescharacteristic
242C2×C47⋊C8C2×D411yescharacteristic
243C2×C47⋊C8C2×D411yescharacteristic
244C2×C47⋊C8C2×D411yescharacteristic
245C2×C47⋊C8C2×D411yescharacteristic
246C23×C47—21no—
247C23×C47C2×#4111yescharacteristic
248C22×D47—21no—
249Q8×C47—21no—
250Q8×C47#11712yes—
251D4×C47—22no—
252D4×C47—22no—
253D4×C47—21no—
254D4×C47#11712yes—
255C2×C4×C47—21no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—42no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—81no—
270C2×C4×C47C4×D411yescharacteristic
271C2×C4×C47C4×D411yescharacteristic
272C2×C4×C47C4×D411yescharacteristic
273C2×C4×C47C4×D411yescharacteristic
274C2×C4×C47C23×C411yescharacteristic
275C2×C4×C47C22×D411yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47H(5,𝔽2)11yescharacteristic
279C2×C4×C472−1+411yescharacteristic
280C22⋊D47—41no—
281C22⋊D47—41no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285D188—21no—
286D188—21no—
287C4×D47—42no—
288C4×D47—41no—
289C4×D47—41no—
290C4×D47—81no—
291Dic94—21no—
292Dic94—21no—
293C8×C47—41no—
294C8×C47—41no—
295C47⋊C8—21no—
296C47⋊C8—21no—
297C47⋊C8—21no—
298C47⋊C8—21no—
299C47⋊C8—21no—
300C47⋊C8—21no—
301C47⋊C8—21no—
302C47⋊C8—21no—
303C47⋊C8—41no—
304C47⋊C8—41no—
305#22784—471nomaximal, Sylow
306C22×C47—21no—
307C22×C47—21no—
308C22×C47—22no—
309C22×C47—41no—
310C22×C47—41no—
311C22×C47C2×C4×D411yescharacteristic
312C22×C47#55211yescharacteristic
313C22×C47#55311yescharacteristic
314C2×D47—41no—
315C2×D47—41no—
316C2×D47—41no—
317C4×C47—22no—
318C4×C47—21no—
319C4×C47—21no—
320C4×C47—21no—
321C4×C47—21no—
322C4×C47—42no—
323C4×C47—41no—
324C4×C47—41no—
325C4×C47—81no—
326C4×C47C2×#11711yescharacteristic
327C4×C47#52011yescharacteristic
328C4×C47#54611yescharacteristic
329C4×C47#54811yescharacteristic
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#1806D4711yescharacteristic, complemented
345#1771—471no—
346#1765—471no—
347#1764—471no—
348C2×C47—21no—
349C2×C47—21no—
350C2×C47—42no—
351C2×C47#235211yescharacteristic
352C2×C47#295511yescharacteristic
353C2×C47#295611yescharacteristic
354D47—81no—
355C2×#135—471no—
356C2×#131—471no—
357C2×#131—471no—
358C4×#41—471no—
359C4×#41C2×D4711yescharacteristic
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—941no—
379#423C2×D4711yescharacteristic
380C2×C4⋊C8—471no—
381C2×C4⋊C8—941no—
382C2×#104—471no—
383C2×#104—471no—
384C2×#104C2×D4711yescharacteristic
385C2×#104C2×D4711yescharacteristic
386#416—471no—
387#416—471no—
388#408—471no—
389#408—471no—
390#405—471no—
391#405—471no—
392C2×#97—471no—
393C2×#97—471no—
394C2×C4×C8—471no—
395C4×C4⋊C4C2×D4711yescharacteristic
396#341—471no—
397#341—471no—
398#341—471no—
399#341—471no—
400#339—471no—
401#339—471no—
402#339C2×D4711yescharacteristic
403#339C2×D4711yescharacteristic
404#336—471no—
405#336—471no—
406C47#2278411yescharacteristic, complemented, Sylow
407C2×#41—471no—
408C2×#41C22×D4711yescharacteristic
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—941no—
422C2×M16—941no—
423C2×M16C22×D4711yescharacteristic
424C2×M16C22×D4711yescharacteristic
425C22×C8—471no—
426C22×C8—471no—
427C22×C8—471no—
428C22×C8—471no—
429C22×C8—941no—
430C22×C8—941no—
431C4×Q8—471no—
432C4×Q8—471no—
433C4×Q8C4×D4711yescharacteristic
434C4×Q8C4×D4711yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—471no—
438C4×D4—471no—
439C4×D4—941no—
440C4×D4—941no—
441C4×D4C4×D4711yescharacteristic
442C4×D4C4×D4711yescharacteristic
443#117—21no—
444#117—471no—
445#117—941no—
446#117C22×D4711yescharacteristic
447C2×C4⋊C4—21no—
448C2×C42—21no—
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—21no—
458C4⋊C8—21no—
459C4⋊C8—471no—
460C4⋊C8—471no—
461C4⋊C8—471no—
462C4⋊C8—471no—
463C4⋊C8—941no—
464C4⋊C8—941no—
465C4⋊C8—941no—
466C4⋊C8—941no—
467C4⋊C8—941no—
468C4⋊C8—941no—
469#104—22no—
470#104—22no—
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—471no—
486#97—471no—
487#97—471no—
488#97—471no—
489#97—941no—
490#97—941no—
491#97—1881no—
492C4×C8—941no—
493C4×C8—941no—
494C4×C8—1881no—
495#95—21no—
496#41—21no—
497#41—21no—
498#41—941no—
499#41—941no—
500#41—941no—
501#41—941no—
502#41#1062535212yes—
503#41#1062535412yes—
504C2×Q8—471no—
505C2×Q8C2×C4×D4711yescharacteristic
506C2×D4—21no—
507C2×D4—471no—
508C2×D4—941no—
509C2×D4C2×C4×D4711yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4#1062535211yescharacteristic
519C22×C4#1062535211yescharacteristic
520C22×C4C23×D4711yescharacteristic
521Q16—942no—
522SD16—942no—
523SD16—942no—
524D8—942no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—941no—
530M16—941no—
531M16—941no—
532M16—941no—
533M16—1882no—
534M16—1882no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—471no—
538C2×C8—471no—
539C2×C8—471no—
540C2×C8—471no—
541C2×C8—471no—
542C2×C8—471no—
543C2×C8—471no—
544C2×C8—471no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—1882no—
556C2×C8—1882no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—471no—
561C4⋊C4—471no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4C2×C4×D4711yescharacteristic
565C4⋊C4C2×C4×D4711yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—941no—
570C22⋊C4—941no—
571C22⋊C4—941no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—941no—
580C42—941no—
581C42—941no—
582C42C2×C4×D4711yescharacteristic
583C42C2×C4×D4711yescharacteristic
584C42D4×D4711yescharacteristic
585C42D4×D4711yescharacteristic
586C23—21no—
587C23—941no—
588C23C2×#1062535211yescharacteristic
589Q8—21no—
590Q8—941no—
591Q8—941no—
592Q8#1309398212yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—941no—
597D4—941no—
598D4—1881no—
599D4—1881no—
600D4#1309398212yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—81no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—941no—
619C2×C4—3761no—
620C2×C4—1882no—
621C2×C4—1881no—
622C2×C4—1881no—
623C2×C4(C22⋊D47)⋊C411yescharacteristic
624C2×C4(C22⋊D47)⋊C411yescharacteristic
625C2×C4(C22⋊D47)⋊C411yescharacteristic
626C2×C4(C22⋊D47)⋊C411yescharacteristic
627C2×C4C22×C4×D4711yescharacteristic
628C2×C4C2×D4×D4711yescharacteristic
629C2×C4C2×#1062535211yescharacteristic
630C2×C4C2×#1062535411yescharacteristic
631C2×C4#1309407011yescharacteristic
632C2×C4#1309407111yescharacteristic
633C8—41no—
634C8—41no—
635C8—941no—
636C8—941no—
637C8—941no—
638C8—941no—
639C8—941no—
640C8—941no—
641C8—941no—
642C8—941no—
643C8—1881no—
644C8—1881no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—1881no—
651C22—1881no—
652C22—1881no—
653C22C2×(C22⋊D47)⋊C411yescharacteristic
654C22#1568981511yescharacteristic
655C22#1568982511yescharacteristic
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—81no—
665C4—1881no—
666C4—1881no—
667C4—1881no—
668C4C2×#1309398211yescharacteristic
669C4#1568960311yescharacteristic
670C4#1568976411yescharacteristic
671C4#1568977911yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—3761no—
676C2#2024631911yescharacteristic
677C2#2025228711yescharacteristic
678C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1806C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenter#1806D47
hypocenterC47#22784
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #20252056C2semidirect
3. #20251956C2semidirect
4. #20244100C2semidirect
5. #20244093C2semidirect
6. #20243990C2semidirect
7. #20243990C2semidirect
10. #20243528C2semidirect
11. #20243409C2semidirect
12. #20243263C2semidirect
13. #20243233C2semidirect
14. #20243226C2semidirect
15. C47×#1806C2semidirect
20. #15689233C4semidirect
21. #15689233C4semidirect
22. #15689228C4semidirect
23. #15689228C4semidirect
24. #15689223C4semidirect
25. #15689223C4semidirect
26. #15689221C4semidirect
27. #15689221C4semidirect
344. #1806D47semidirect
406. C47#22784semidirect

Maximal subgroups

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

subgroupindex
#202521862
#202520562
#202519562
#202441002
#202440932
#202439902
#202437132
#202435282
#202434092
#202432632
#202432332
#202432262
C47×#18062
#2278447