Finite Group Databasebeta

← #25116066

Subgroups — #25116066

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#19143393C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic, complemented
3#19135305C211yesmaximal, characteristic, complemented
4#19135298C211yesmaximal, characteristic, complemented
5#19135191C211yesmaximal, characteristic, complemented
6#19135191C211yesmaximal, characteristic, complemented
7#19134922C211yesmaximal, characteristic
8#19134922C211yesmaximal, characteristic
9#19134735C211yesmaximal, characteristic, complemented
10#19134615C211yesmaximal, characteristic, complemented
11#19134612C211yesmaximal, characteristic, complemented
12#19134472C211yesmaximal, characteristic, complemented
13#19134437C211yesmaximal, characteristic, complemented
14#19134430C211yesmaximal, characteristic, complemented
15C43×#2906C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583009C411yescharacteristic, complemented
19#14583009C411yescharacteristic, complemented
20#14583004C411yescharacteristic, complemented
21#14583004C411yescharacteristic, complemented
22#14582999C411yescharacteristic, complemented
23#14582999C411yescharacteristic, complemented
24#14582997C411yescharacteristic, complemented
25#14582997C411yescharacteristic, complemented
26#14582959—21no—
27#14582959—21no—
28#14582955—21no—
29#14582951—21no—
30#14582935C2211yescharacteristic
31#14582923C2211yescharacteristic
32C2×#13063252C2211yescharacteristic
33C2×#13063252C2211yescharacteristic
34C2×#13063251C2211yescharacteristic
35C2×#13063251C2211yescharacteristic
36#14582895C2211yescharacteristic
37#14582893C2211yescharacteristic
38#14582865C2211yescharacteristic
39#14582865C2211yescharacteristic
40#14582854C2211yescharacteristic
41#14582854C2211yescharacteristic
42C2×#13063236C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582663C2211yescharacteristic
47#14582663C2211yescharacteristic
48#14582663C2211yescharacteristic
49#14582663C2211yescharacteristic
50#14582660C2211yescharacteristic
51#14582660C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#131×C43C2211yescharacteristic
57C2×#131×C43C2211yescharacteristic
58C4×#41×C43C2211yescharacteristic
59C43×#424—21no—
60C43×#424—21no—
61C43×#424C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C43×#423—21no—
64C43×#423C2211yescharacteristic
65C2×C4⋊C8×C43—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063345—22no—
69#13063345—22no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C4×Dic86C2×C411yescharacteristic
79C4×Dic86C2×C411yescharacteristic
80C4×D172C2×C411yescharacteristic
81C4×D172C2×C411yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284C2311yescharacteristic
85#13063282—21no—
86C2×C4⋊Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89C42×D43—21no—
90#13063258C2×C411yescharacteristic
91#13063258C2×C411yescharacteristic
92#13063256C2×C411yescharacteristic
93#13063256C2×C411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96#13063252—22no—
97#13063252—22no—
98#13063251—41no—
99#13063251—41no—
100#13063249C2×C411yescharacteristic
101#13063249C2×C411yescharacteristic
102#13063248C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063246C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107#13063245C2×C411yescharacteristic
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112#13063236C2×C411yescharacteristic
113#13063236C2×C411yescharacteristic
114#13063236C2×C411yescharacteristic
115#13063236C2×C411yescharacteristic
116#13063235—21no—
117#13063235—21no—
118#13063235—41no—
119C8×Dic43—21no—
120C8×Dic43—21no—
121C8×Dic43—41no—
122C43⋊#95—21no—
123C2×#41×C43C2311yescharacteristic
124#131×C43—22no—
125#131×C43—22no—
126#131×C43—41no—
127#131×C43—41no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43C2311yescharacteristic
131C2×M16×C43C2311yescharacteristic
132C22×C8×C43—21no—
133C22×C8×C43—21no—
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C4×Q8×C43C2×C411yescharacteristic
137C4×Q8×C43C2×C411yescharacteristic
138C4×D4×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43C2×C411yescharacteristic
141C4×D4×C43C2×C411yescharacteristic
142#117×C43—21no—
143#117×C43C2311yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152C4⋊C8×C43D411yescharacteristic
153C4⋊C8×C43D411yescharacteristic
154C4⋊C8×C43D411yescharacteristic
155C4⋊C8×C43D411yescharacteristic
156#41×C43—21no—
157#41×C43—21no—
158#41×C43#4112yes—
159#41×C43#4112yes—
160C2×Q8×C43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C22×C411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43#4111yescharacteristic
167C22×C4×C43#4111yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175#10621898—21no—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—42no—
186M16×C43—42no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—42no—
194C2×C8×C43—42no—
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C2×C8×C43C2×D411yescharacteristic
198C2×C8×C43C2×D411yescharacteristic
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43C22×C411yescharacteristic
202C4⋊C4×C43C22×C411yescharacteristic
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43C22×C411yescharacteristic
210C42×C43C22×C411yescharacteristic
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213C22⋊Dic43—21no—
214#10621885—22no—
215#10621884—22no—
216#10621883—22no—
217#10621882—22no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—21no—
220C4⋊Dic43—42no—
221C4⋊Dic43C22×C411yescharacteristic
222C4⋊Dic43C22×C411yescharacteristic
223Dic43⋊C4—21no—
224Dic43⋊C4—21no—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877—21no—
235#10621877—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8C22×C411yescharacteristic
243C2×C43⋊C8C22×C411yescharacteristic
244C2×C43⋊C8C22×C411yescharacteristic
245C2×C43⋊C8C22×C411yescharacteristic
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—21no—
249Q8×C43—21no—
250Q8×C43#11712yes—
251D4×C43—22no—
252D4×C43—22no—
253D4×C43—21no—
254D4×C43#11712yes—
255C2×C4×C43—21no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—42no—
263C2×C4×C43—81no—
264C2×C4×C43C4×D411yescharacteristic
265C2×C4×C43C4×D411yescharacteristic
266C2×C4×C43C4×D411yescharacteristic
267C2×C4×C43C4×D411yescharacteristic
268C2×C4×C43C23×C411yescharacteristic
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C2×C4×C432−1+411yescharacteristic
274C22⋊D43—41no—
275C22⋊D43—41no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285D172—21no—
286D172—21no—
287C4×D43—42no—
288C4×D43—41no—
289C4×D43—41no—
290C4×D43—81no—
291Dic86—21no—
292Dic86—21no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—41no—
298C8×C43—41no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#22784—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43C2×C4×D411yescharacteristic
312C22×C43#55211yescharacteristic
313C22×C43#55311yescharacteristic
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C4×C43—22no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43C2×#11711yescharacteristic
325C4×C43#52011yescharacteristic
326C4×C43#54611yescharacteristic
327C4×C43#54811yescharacteristic
328Dic43—42no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333#2943—431no—
334#2925—431no—
335#2906D4311yescharacteristic, complemented
336#1938—431no—
337#1937—431no—
338#1922—431no—
339#1922—431no—
340#1876—431no—
341#1876—431no—
342#1838—431no—
343#1806—431no—
344#1806—431no—
345#1771—431no—
346#1765—431no—
347#1764—431no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—42no—
351C2×C43#235211yescharacteristic
352C2×C43#295511yescharacteristic
353C2×C43#295611yescharacteristic
354D43—81no—
355C2×#135—431no—
356C2×#131C2×D4311yescharacteristic
357C2×#131C2×D4311yescharacteristic
358C4×#41—431no—
359C4×#41C2×D4311yescharacteristic
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—21no—
374#424—21no—
375#424C2×D4311yescharacteristic
376#424C2×D4311yescharacteristic
377#423—21no—
378#423—431no—
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—21no—
381C2×C4⋊C8C2×D4311yescharacteristic
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×#97—431no—
394C2×C4×C8—431no—
395C4×C4⋊C4—431no—
396#341—431no—
397#341—431no—
398#341—431no—
399#341—431no—
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×#41C22×D4311yescharacteristic
409#135—862no—
410#135—862no—
411C2×Q16—431no—
412C2×SD16—431no—
413C2×SD16—431no—
414C2×D8—431no—
415#131—22no—
416#131—22no—
417#131—41no—
418#131—41no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16—431no—
422C2×M16—431no—
423C2×M16C22×D4311yescharacteristic
424C2×M16C22×D4311yescharacteristic
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8C4×D4311yescharacteristic
434C4×Q8C4×D4311yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4C4×D4311yescharacteristic
442C4×D4C4×D4311yescharacteristic
443#117—21no—
444#117—431no—
445#117—861no—
446#117C22×D4311yescharacteristic
447C2×C4⋊C4—861no—
448C2×C42—21no—
449C2×C42—431no—
450C2×C42—431no—
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—21no—
462C4⋊C8—21no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465C4⋊C8C22⋊D4311yescharacteristic
466C4⋊C8C22⋊D4311yescharacteristic
467C4⋊C8C22⋊D4311yescharacteristic
468C4⋊C8C22⋊D4311yescharacteristic
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—431no—
486#97—431no—
487#97—431no—
488#97—431no—
489#97—861no—
490#97—861no—
491#97—1721no—
492C4×C8—861no—
493C4×C8—861no—
494C4×C8—1721no—
495#95—861no—
496#41—21no—
497#41—21no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41—861no—
502#41#1062190012yes—
503#41#1062190212yes—
504C2×Q8—431no—
505C2×Q8C2×C4×D4311yescharacteristic
506C2×D4—21no—
507C2×D4—431no—
508C2×D4—861no—
509C2×D4C2×C4×D4311yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4#1062189811yescharacteristic
519C22×C4#1062189811yescharacteristic
520C22×C4C23×D4311yescharacteristic
521Q16—862no—
522SD16—862no—
523SD16—862no—
524D8—862no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—42no—
531M16—861no—
532M16—861no—
533M16—861no—
534M16—861no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—42no—
542C2×C8—42no—
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—861no—
552C2×C8—861no—
553C2×C8C2×C22⋊D4311yescharacteristic
554C2×C8C2×C22⋊D4311yescharacteristic
555C2×C8C2×C22⋊D4311yescharacteristic
556C2×C8C2×C22⋊D4311yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—431no—
560C4⋊C4—431no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—1722no—
564C4⋊C4C2×C4×D4311yescharacteristic
565C4⋊C4C2×C4×D4311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—861no—
576C42—861no—
577C42—861no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42C2×C4×D4311yescharacteristic
583C42C2×C4×D4311yescharacteristic
584C42C2×C22⋊D4311yescharacteristic
585C42C2×C22⋊D4311yescharacteristic
586C23—21no—
587C23—861no—
588C23C2×#1062189811yescharacteristic
589Q8—21no—
590Q8—861no—
591Q8—861no—
592Q8#1306328312yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—861no—
597D4—861no—
598D4—1721no—
599D4—1721no—
600D4#1306328312yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—81no—
610C2×C4—862no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—3441no—
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×C4C4×C22⋊D4311yescharacteristic
624C2×C4C4×C22⋊D4311yescharacteristic
625C2×C4C4×C22⋊D4311yescharacteristic
626C2×C4C4×C22⋊D4311yescharacteristic
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C22×C22⋊D4311yescharacteristic
629C2×C4C2×#1062190011yescharacteristic
630C2×C4C2×#1062190211yescharacteristic
631C2×C4#1306337011yescharacteristic
632C2×C4#1306337311yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—861no—
640C8—861no—
641C8—861no—
642C8—861no—
643C8—1721no—
644C8—1721no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22C2×C4×C22⋊D4311yescharacteristic
654C22#1458358411yescharacteristic
655C22#1458359711yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—3441no—
664C4—1722no—
665C4—1721no—
666C4—1721no—
667C4—1721no—
668C4C2×#1306328311yescharacteristic
669C4#1458338011yescharacteristic
670C4#1458354311yescharacteristic
671C4#1458356011yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—3441no—
676C2#1913752011yescharacteristic
677C2#1914349611yescharacteristic
678C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2906C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#2906D43
hypocenterC43#22784
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #19143260C2semidirect
3. #19135305C2semidirect
4. #19135298C2semidirect
5. #19135191C2semidirect
6. #19135191C2semidirect
9. #19134735C2semidirect
10. #19134615C2semidirect
11. #19134612C2semidirect
12. #19134472C2semidirect
13. #19134437C2semidirect
14. #19134430C2semidirect
15. C43×#2906C2semidirect
18. #14583009C4semidirect
19. #14583009C4semidirect
20. #14583004C4semidirect
21. #14583004C4semidirect
22. #14582999C4semidirect
23. #14582999C4semidirect
24. #14582997C4semidirect
25. #14582997C4semidirect
335. #2906D43semidirect
406. C43#22784semidirect

Maximal subgroups

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

subgroupindex
#191433932
#191432602
#191353052
#191352982
#191351912
#191349222
#191347352
#191346152
#191346122
#191344722
#191344372
#191344302
C43×#29062
#2278443