Finite Group Databasebeta

← #25113803

Subgroups — #25113803

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582894C211yesmaximal, characteristic
2#19137487C211yesmaximal, characteristic, complemented
3#19137424C211yesmaximal, characteristic
4#19135273C211yesmaximal, characteristic, complemented
5#19135239C211yesmaximal, characteristic, complemented
6#19135233C211yesmaximal, characteristic, complemented
7#19134843C211yesmaximal, characteristic, complemented
8#19134841C211yesmaximal, characteristic, complemented
9#19134688C211yesmaximal, characteristic, complemented
10#19134623C211yesmaximal, characteristic, complemented
11#19134534C211yesmaximal, characteristic
12C4×#13063247C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14C8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23#14582894C418yescomplemented
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582791—21no—
35#14582789—21no—
36#14582777—21no—
37#14582777—21no—
38#14582766—21no—
39#14582761—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621902—22no—
61C2×#10621902—22no—
62C2×#10621902—22no—
63C2×#10621902—41no—
64C2×#10621902—41no—
65C2×#10621902C2×C414yes—
66C22×D172—21no—
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—41no—
75C2×C8×D43—41no—
76C2×C8×D43C2×C414yescomplemented
77C4×D172—22no—
78C4×D172—41no—
79#13063287—22no—
80#13063287—41no—
81#13063283—22no—
82#13063283C2×C414yescomplemented
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063258—41no—
99#13063258—41no—
100#13063249—41no—
101#13063249C2×C414yescomplemented
102#13063247—22no—
103#13063247C2×C414yes—
104#13063245—22no—
105#13063245C2×C414yes—
106(C2×D43)⋊C8—22no—
107C8×Dic43—41no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#103×C43—41no—
126#103×C43C2×C414yescomplemented
127C4×C8×C43—41no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131C23×D43—21no—
132C23×D43C2×D411yescharacteristic
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C22×C412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152#10621902—28no—
153#10621902—44no—
154#10621902—44no—
155#10621902—44no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—24no—
160C2×D172—42no—
161C2×D172—42no—
162C2×D172C22×C412yes—
163C2×D172#4112yes—
164C2×D172#4112yes—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—24no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—81no—
177C2×C4×D43—81no—
178C2×C4×D43C22×C412yes—
179C2×C4×D43#4112yes—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C22×C412yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43C22×C412yes—
193C42×C43—21no—
194C42×C43—21no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4—81no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—42no—
208C4⋊Dic43C22×C412yes—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—24no—
212C4×Dic43—81no—
213C4×Dic43—81no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C8×D43—44no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43C4×D412yes—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43#13512yes—
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C4×D412yes—
281C2×Dic43#13512yes—
282D172—22no—
283D172—22no—
284D172—22no—
285D172—48no—
286D172#11714yes—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—48no—
292C4×D43—84no—
293C4×D43—84no—
294C8×C43—22no—
295C8×C43—41no—
296C43⋊C8—22no—
297C43⋊C8—41no—
298#22576—431nomaximal, Sylow
299C22×C43C2×C4×D411yescharacteristic
300C22×C43#54611yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43#57611yescharacteristic
305C22×C43#57811yescharacteristic
306C2×D43—24no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—41no—
317C2×D43—41no—
318C2×D43—42no—
319C2×D43—42no—
320C4×C43—22no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43—81no—
326C4×C43C2×#11711yescharacteristic
327C4×C43#51811yescharacteristic
328C4×C43#55111yescharacteristic
329C4×C43#55111yescharacteristic
330Dic43—22no—
331Dic43—22no—
332Dic43—42no—
333Dic43—41no—
334Dic43—81no—
335Dic43—81no—
336C2×#416—431no—
337#2347—431no—
338#2339—431no—
339#1933—431no—
340#1933D4311yescharacteristic, complemented
341#1928—431no—
342#1928—431no—
343#1862—431no—
344#1862—431no—
345#1825—431no—
346#1808—431no—
347#1788—431no—
348C4×#102—431no—
349C4×#102—431no—
350C8×C22⋊C4—431no—
351C2×C43#234211yescharacteristic
352C2×C43C4×#13511yescharacteristic
353C2×C43#295111yescharacteristic
354C2×C43#329711yescharacteristic
355C2×C43#329711yescharacteristic
356C2×C43#330211yescharacteristic
357C2×C43#330211yescharacteristic
358D43—42no—
359D43—44no—
360C22×#41—431no—
361C23×C8—431no—
362C2×C4×D4—431no—
363C2×C4×D4—431no—
364C2×#117—431no—
365C2×#107—431no—
366C2×#107—431no—
367#416—438no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103C2×D4311yescharacteristic
371C2×#103C2×D4311yescharacteristic
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×C22⋊C8—431no—
377C2×C4×C8—431no—
378C2×C4×C8C2×D4311yescharacteristic
379#391—431no—
380#391C2×D4311yescharacteristic
381#389—431no—
382#389C2×D4311yescharacteristic
383#388—861no—
384#388—861no—
385#386—861no—
386#386—861no—
387#383—861no—
388#381—861no—
389#380—431no—
390#380—431no—
391C4×C4⋊C4—431no—
392C4×C4⋊C4—431no—
393C4×C4⋊C4—861no—
394C4×C22⋊C4—431no—
395C2×#95—861no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340C2×D4311yescharacteristic
401#340C2×D4311yescharacteristic
402#336—431no—
403#336—431no—
404C43#2257611yescharacteristic, complemented, Sylow
405C2×#41—434no—
406C2×#41—862no—
407C2×#41—862no—
408C2×#41—862no—
409C2×#41—1721no—
410C2×#41—1721no—
411C22×Q8C22×D4311yescharacteristic
412C22×D4—431no—
413C22×D4—861no—
414C23×C4—431no—
415C23×C4—861no—
416C23×C4—861no—
417C23×C4—861no—
418C22×C8—431no—
419C22×C8—434no—
420C22×C8—431no—
421C22×C8—1721no—
422C22×C8—1721no—
423C22×C8C22×D4311yescharacteristic
424C22×C8C22×D4311yescharacteristic
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—1721no—
428C4×D4—1721no—
429#117—434no—
430#117—862no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—431no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42—431no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451#107—1721no—
452#107—1721no—
453#103—41no—
454#103—434no—
455#103—1721no—
456#103C4×D4314yescomplemented
457#102—434no—
458#102—434no—
459#102—862no—
460#102—862no—
461C22⋊C8—862no—
462C4×C8—41no—
463C4×C8—1721no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—431no—
468#95—431no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—431no—
477C24—861no—
478#41—868no—
479#41—1724no—
480#41—1724no—
481#41—1724no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8C2×C4×D4312yes—
488C2×D4—432no—
489C2×D4—432no—
490C2×D4—432no—
491C2×D4—864no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—1722no—
496C2×D4—1722no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—432no—
504C22×C4—432no—
505C22×C4—431no—
506C22×C4—864no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—3441no—
515C22×C4—3441no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4D4×D4311yescharacteristic
523C22×C4D4×D4311yescharacteristic
524C22×C4C23×D4311yescharacteristic
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—432no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—1724no—
537C2×C8C2×C4×D4312yes—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—432no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—1722no—
551C4⋊C4C2×C4×D4312yes—
552C22⋊C4—862no—
553C22⋊C4—864no—
554C22⋊C4—862no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—1722no—
558C22⋊C4—1722no—
559C42—21no—
560C42—21no—
561C42—864no—
562C42—861no—
563C42—861no—
564C42—3441no—
565C42—3441no—
566C23—432no—
567C23—862no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23—862no—
573C23—861no—
574C23—862no—
575C23—861no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23C2×D4×D4311yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—41no—
584Q8—41no—
585D4—434no—
586D4—862no—
587D4—862no—
588D4—862no—
589D4—1728no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—3444no—
622C2×C4—3444no—
623C2×C4—1728no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4#1306334612yes—
633C2×C4C22×C4×D4311yescharacteristic
634C2×C4#41×D4311yescharacteristic
635C2×C4#41×D4311yescharacteristic
636C2×C4#41×D4311yescharacteristic
637C2×C4#1306337011yescharacteristic
638C2×C4#1306337111yescharacteristic
639C8—22no—
640C8—41no—
641C8—862no—
642C8—1721no—
643C22—862no—
644C22—862no—
645C22—864no—
646C22—862no—
647C22—1721no—
648C22—1722no—
649C22—1721no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22—1722no—
654C22—1721no—
655C22—1722no—
656C22—1721no—
657C22C4×D4×D4311yescharacteristic
658C22#1458353811yescharacteristic
659C22#1458354211yescharacteristic
660C22#135×D4311yescharacteristic
661C22C2×#1306334611yescharacteristic
662C22#1458370111yescharacteristic
663C22#1458371211yescharacteristic
664C4—22no—
665C4—41no—
666C4—42no—
667C4—42no—
668C4—81no—
669C4—81no—
670C4—862no—
671C4—862no—
672C4—3441no—
673C4—3441no—
674C4—1721no—
675C4—1722no—
676C4#117×D4311yescharacteristic
677C4#1458337111yescharacteristic
678C4#1458357411yescharacteristic
679C4#1458357711yescharacteristic
680C2—1722no—
681C2—1724no—
682C2#1913744311yescharacteristic
683C2C4×#1306334611yescharacteristic
684C2#1914347011yescharacteristic
685C2#1914644411yescharacteristic
686C2#1914645111yescharacteristic
687C2#1914650711yescharacteristic
688C2#1914651111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1933D43
hypocenterC43#22576
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. #19137487C2semidirect
4. #19135273C2semidirect
5. #19135239C2semidirect
6. #19135233C2semidirect
7. #19134843C2semidirect
8. #19134841C2semidirect
9. #19134688C2semidirect
10. #19134623C2semidirect
12. C4×#13063247C2semidirect
13. #19134409C2semidirect
14. C8×(C2×D43)⋊C4C2semidirect
15. C43×#1933C2semidirect
23. #14582894C4semidirect
76. C2×C8×D43C2×C4semidirect
82. #13063283C2×C4semidirect
101. #13063249C2×C4semidirect
126. #103×C43C2×C4semidirect
340. #1933D43semidirect
404. C43#22576semidirect
456. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828942
#191374872
#191374242
#191352732
#191352392
#191352332
#191348432
#191348412
#191346882
#191346232
#191345342
C4×#130632472
#191344092
C8×(C2×D43)⋊C42
C43×#19332
#2257643