Finite Group Databasebeta

← #25116067

Subgroups — #25116067

Order 11008.

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#19143397C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic, complemented
3#19143164C211yesmaximal, characteristic, complemented
4#19135304C211yesmaximal, characteristic, complemented
5#19135297C211yesmaximal, characteristic, complemented
6#19135193C211yesmaximal, characteristic, complemented
7#19135193C211yesmaximal, characteristic, complemented
8#19134923C211yesmaximal, characteristic
9#19134923C211yesmaximal, characteristic
10#19134612C211yesmaximal, characteristic, complemented
11#19134612C211yesmaximal, characteristic, complemented
12#19134467C211yesmaximal, characteristic, complemented
13#19134438C211yesmaximal, characteristic, complemented
14#19134431C211yesmaximal, characteristic, complemented
15C43×#1838C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20C4×#10621898C2211yescharacteristic
21#14583012C411yescharacteristic, complemented
22#14583012C411yescharacteristic, complemented
23#14583007C411yescharacteristic, complemented
24#14583007C411yescharacteristic, complemented
25#14583001C411yescharacteristic, complemented
26#14583001C411yescharacteristic, complemented
27#14583001C411yescharacteristic, complemented
28#14583001C411yescharacteristic, complemented
29#14582959—21no—
30#14582959—21no—
31#14582955—21no—
32#14582951—21no—
33#14582937C2211yescharacteristic
34#14582927C2211yescharacteristic
35#14582927C2211yescharacteristic
36#14582924—21no—
37#14582924—21no—
38#14582921—21no—
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40C4⋊C8×D43—21no—
41C2×#13063251C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45#14582896C2211yescharacteristic
46#14582896C2211yescharacteristic
47#14582867C2211yescharacteristic
48#14582867C2211yescharacteristic
49#14582857C2211yescharacteristic
50#14582857C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52C2×C8×Dic43C2211yescharacteristic
53C4×C4⋊Dic43C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582660C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C43×#423C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#341C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063347—22no—
70#13063347—22no—
71C2×Dic172C2×C411yescharacteristic
72C2×#10621873C2×C411yescharacteristic
73C2×#10621873C2×C411yescharacteristic
74C2×D344C2×C411yescharacteristic
75#13063333—22no—
76#13063333—22no—
77#13063333—41no—
78#13063333—41no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86C2×C411yescharacteristic
89C4×D172C2×C411yescharacteristic
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×D172C2×C411yescharacteristic
93C4×C22⋊D43—21no—
94C4×C22⋊D43—21no—
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97#13063284C2311yescharacteristic
98#13063284C2311yescharacteristic
99#13063282—21no—
100#13063282—21no—
101C2×C4⋊Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C42×D43—21no—
105C42×D43—21no—
106#13063259C2×C411yescharacteristic
107#13063259C2×C411yescharacteristic
108#13063257C2×C411yescharacteristic
109#13063257C2×C411yescharacteristic
110C4⋊(C43⋊C8)D411yescharacteristic
111C4⋊(C43⋊C8)D411yescharacteristic
112C4⋊(C43⋊C8)D411yescharacteristic
113C4⋊(C43⋊C8)D411yescharacteristic
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118#13063251—22no—
119#13063251—22no—
120#13063251—41no—
121#13063251—41no—
122#13063250C2×C411yescharacteristic
123#13063250C2×C411yescharacteristic
124#13063250C2×C411yescharacteristic
125#13063250C2×C411yescharacteristic
126#13063247C2×C411yescharacteristic
127#13063247C2×C411yescharacteristic
128#13063247C2×C411yescharacteristic
129#13063247C2×C411yescharacteristic
130(C2×D43)⋊C8—21no—
131(C2×D43)⋊C8—21no—
132(C2×D43)⋊C8—21no—
133(C2×D43)⋊C8—21no—
134#13063235—21no—
135#13063235—21no—
136#13063235—41no—
137C8×Dic43—21no—
138C8×Dic43—21no—
139C8×Dic43—41no—
140C43⋊#95—21no—
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C2×M16×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C4⋊C8×C43—21no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152#97×C43C2×C411yescharacteristic
153#97×C43C2×C411yescharacteristic
154#97×C43C2×C411yescharacteristic
155#97×C43C2×C411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C2×C22⋊D43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163#10621898—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898#4112yes—
170#10621898#4112yes—
171C2×D172C22×C411yescharacteristic
172C2×D172C22×C411yescharacteristic
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×Dic86C22×C411yescharacteristic
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43—21no—
187M16×C43—21no—
188M16×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C22×C411yescharacteristic
198C2×C8×C43C22×C411yescharacteristic
199C2×C8×C43C22×C411yescharacteristic
200C2×C8×C43C22×C411yescharacteristic
201C42×C43C22×C411yescharacteristic
202C42×C43C22×C411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C22⋊Dic43—21no—
206C22⋊Dic43—21no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—21no—
211C4⋊Dic43—42no—
212C4⋊Dic43C22×C411yescharacteristic
213C4⋊Dic43C22×C411yescharacteristic
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C2×D411yescharacteristic
235C2×C43⋊C8C2×D411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C2×C43⋊C8C2×D411yescharacteristic
238Dic172—22no—
239D344—22no—
240#10621873—22no—
241#10621873—22no—
242#10621872—42no—
243#10621872—42no—
244C8×D43—42no—
245C8×D43—42no—
246C23×C43C2×#4111yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C22⋊D43—22no—
262C22⋊D43—22no—
263C22⋊D43—41no—
264C22⋊D43—41no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277D172—21no—
278D172—21no—
279D172—21no—
280D172#11712yes—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—42no—
284C4×D43—42no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—81no—
288C4×D43—81no—
289Dic86—21no—
290Dic86—21no—
291Dic86—21no—
292Dic86#11712yes—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—41no—
298C8×C43—41no—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—21no—
304C43⋊C8—21no—
305#22784—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43C2×C4×D411yescharacteristic
309C22×C43#55211yescharacteristic
310C22×C43#55311yescharacteristic
311C2×D43—22no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43C2×#11711yescharacteristic
322C4×C43#52011yescharacteristic
323C4×C43#54611yescharacteristic
324C4×C43#54811yescharacteristic
325Dic43—22no—
326Dic43—42no—
327Dic43—41no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333#2943—431no—
334#2925—431no—
335#2906—431no—
336#1938—431no—
337#1937—431no—
338#1922—431no—
339#1922—431no—
340#1876—431no—
341#1876—431no—
342#1838D4311yescharacteristic, complemented
343#1806—431no—
344#1806—431no—
345#1771—431no—
346#1765—431no—
347#1764—431no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43#235211yescharacteristic
351C2×C43#295511yescharacteristic
352C2×C43#295611yescharacteristic
353D43—42no—
354D43—81no—
355C2×#135—431no—
356C2×#131—431no—
357C2×#131—431no—
358C4×#41—431no—
359C4×#41—431no—
360#442—431no—
361#442—431no—
362#441—431no—
363#441—431no—
364#440—431no—
365#440—431no—
366#440—431no—
367#440—431no—
368#433—861no—
369#433—861no—
370#432—861no—
371#431—861no—
372#427—431no—
373#424—431no—
374#424—431no—
375#424—861no—
376#424—861no—
377#423—861no—
378#423C2×D4311yescharacteristic
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—431no—
381C2×C4⋊C8—861no—
382C2×#104—431no—
383C2×#104—431no—
384C2×#104—431no—
385C2×#104—431no—
386#416—431no—
387#416—431no—
388#408—431no—
389#408—431no—
390#405—431no—
391#405—431no—
392C2×#97—431no—
393C2×#97C2×D4311yescharacteristic
394C2×C4×C8—431no—
395C4×C4⋊C4—431no—
396#341C2×D4311yescharacteristic
397#341C2×D4311yescharacteristic
398#341C2×D4311yescharacteristic
399#341C2×D4311yescharacteristic
400#339—431no—
401#339—431no—
402#339—431no—
403#339—431no—
404#336—431no—
405#336—431no—
406C43#2278411yescharacteristic, complemented, Sylow
407C2×#41—431no—
408C2×#41—431no—
409#135—862no—
410#135—862no—
411C2×Q16—431no—
412C2×SD16—431no—
413C2×SD16—431no—
414C2×D8—431no—
415#131—862no—
416#131—862no—
417#131—1721no—
418#131—1721no—
419C2×M16—861no—
420C2×M16—861no—
421C2×M16C22×D4311yescharacteristic
422C2×M16C22×D4311yescharacteristic
423C2×M16C22×D4311yescharacteristic
424C2×M16C22×D4311yescharacteristic
425C22×C8—431no—
426C22×C8—431no—
427C22×C8—861no—
428C22×C8—861no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—431no—
434C4×Q8—431no—
435C4×D4—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—861no—
443#117—431no—
444#117—431no—
445#117—861no—
446#117—861no—
447C2×C4⋊C4—861no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#107—431no—
454#107—431no—
455#106—431no—
456#106—431no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—431no—
462C4⋊C8—431no—
463C4⋊C8—431no—
464C4⋊C8—431no—
465C4⋊C8—861no—
466C4⋊C8—861no—
467C4⋊C8—861no—
468C4⋊C8—861no—
469#104—862no—
470#104—862no—
471#104—1721no—
472#104—1721no—
473#103—431no—
474#103—431no—
475#103—431no—
476#103—431no—
477#102—431no—
478#102—431no—
479#102—431no—
480#102—431no—
481C22⋊C8—861no—
482C22⋊C8—861no—
483C22⋊C8—861no—
484C22⋊C8—861no—
485#97—861no—
486#97—861no—
487#97—1721no—
488#97C4×D4311yescharacteristic
489#97C4×D4311yescharacteristic
490#97C4×D4311yescharacteristic
491#97C4×D4311yescharacteristic
492C4×C8—861no—
493C4×C8—861no—
494C4×C8—1721no—
495#95—861no—
496#41—432no—
497#41—432no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41—861no—
502#41—861no—
503#41—861no—
504C2×Q8—431no—
505C2×Q8—431no—
506C2×D4—431no—
507C2×D4—431no—
508C2×D4—861no—
509C2×D4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4#1062190211yescharacteristic
519C22×C4#1062190211yescharacteristic
520C22×C4C23×D4311yescharacteristic
521Q16—862no—
522SD16—862no—
523SD16—862no—
524D8—862no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—1722no—
534M16—1722no—
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—431no—
544C2×C8—431no—
545C2×C8—431no—
546C2×C8—431no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—1722no—
552C2×C8—1722no—
553C2×C8C2×C4×D4311yescharacteristic
554C2×C8C2×C4×D4311yescharacteristic
555C2×C8C2×C4×D4311yescharacteristic
556C2×C8C2×C4×D4311yescharacteristic
557C4⋊C4—431no—
558C4⋊C4—431no—
559C4⋊C4—431no—
560C4⋊C4—431no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—1722no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—861no—
573C42—861no—
574C42—861no—
575C42—861no—
576C42—861no—
577C42—861no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42C2×C4×D4311yescharacteristic
583C42C2×C4×D4311yescharacteristic
584C42D4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C23—861no—
587C23—861no—
588C23C2×#1062190211yescharacteristic
589Q8—432no—
590Q8—861no—
591Q8—861no—
592Q8—861no—
593D4—432no—
594D4—862no—
595D4—862no—
596D4—861no—
597D4—861no—
598D4—861no—
599D4—1721no—
600D4—1721no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—861no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—3441no—
613C2×C4—3441no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4#1306328711yescharacteristic
624C2×C4#1306328711yescharacteristic
625C2×C4#1306328711yescharacteristic
626C2×C4#1306328711yescharacteristic
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C2×D4×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#1306337111yescharacteristic
632C2×C4#1306337211yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—41no—
640C8—41no—
641C8—861no—
642C8—861no—
643C8—861no—
644C8—861no—
645C22—21no—
646C22—21no—
647C22—862no—
648C22—1721no—
649C22—1721no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22C2×#1306328711yescharacteristic
654C22#1458358711yescharacteristic
655C22#1458360211yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—862no—
661C4—3441no—
662C4—1722no—
663C4—1721no—
664C4—1721no—
665C4—1721no—
666C4—1721no—
667C4—1721no—
668C4#117×D4311yescharacteristic
669C4#1458337911yescharacteristic
670C4#1458354211yescharacteristic
671C4#1458355711yescharacteristic
672C2—21no—
673C2—21no—
674C2—3441no—
675C2—1722no—
676C2#1913752111yescharacteristic
677C2#1914349711yescharacteristic
678C2#1914350411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1838C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063347C22
cosocleC22×C4×C43C24
hypercenter#1838D43
hypocenterC43#22784
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
2. #19143263C2semidirect
3. #19143164C2semidirect
4. #19135304C2semidirect
5. #19135297C2semidirect
6. #19135193C2semidirect
7. #19135193C2semidirect
10. #19134612C2semidirect
11. #19134612C2semidirect
12. #19134467C2semidirect
13. #19134438C2semidirect
14. #19134431C2semidirect
15. C43×#1838C2semidirect
21. #14583012C4semidirect
22. #14583012C4semidirect
23. #14583007C4semidirect
24. #14583007C4semidirect
25. #14583001C4semidirect
26. #14583001C4semidirect
27. #14583001C4semidirect
28. #14583001C4semidirect
342. #1838D43semidirect
406. C43#22784semidirect

Maximal subgroups

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

subgroupindex
#191433972
#191432632
#191431642
#191353042
#191352972
#191351932
#191349232
#191346122
#191344672
#191344382
#191344312
C43×#18382
#2278443