Finite Group Databasebeta

← #25126263

Subgroups — #25126263

Order 11008.

876 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
1C2×#14583002C211yesmaximal, characteristic, complemented
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19137284C211yesmaximal, characteristic
4#19137279C211yesmaximal, characteristic, complemented
5#19136087C211yesmaximal, characteristic, complemented
6#19136026C211yesmaximal, characteristic, complemented
7#19135988C211yesmaximal, characteristic, complemented
8#19135964C211yesmaximal, characteristic, complemented
9#19135909C211yesmaximal, characteristic, complemented
10#19135778C211yesmaximal, characteristic
11#19135596C211yesmaximal, characteristic
12#19134495C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#2035C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583002—24no—
22#14582957—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582799—21no—
37#14582798—21no—
38#14582798C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582792—21no—
41#14582792—21no—
42#14582791—21no—
43#14582785—21no—
44#14582775—21no—
45#14582773—21no—
46#14582759C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063299—22no—
70#13063299—22no—
71Q8×Dic43—22no—
72Q8×Dic43—22no—
73#13063287—22no—
74#13063287—22no—
75#13063284—22no—
76#13063284—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43D411yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063259—22no—
98#13063258—22no—
99Dic43⋊C8—22no—
100Dic43⋊C8—22no—
101#13063249—22no—
102#13063247—22no—
103#13063247—22no—
104#13063245—22no—
105C22⋊(C43⋊C8)—22no—
106#13063235D414yescomplemented
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—22no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127#106×C43—22no—
128#103×C43—22no—
129#103×C43—22no—
130C22⋊C8×C43—22no—
131#95×C43—21no—
132C24×C43C2×D411yescharacteristic
133C23×D43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—24no—
153C2×C22⋊D43—81no—
154C2×C22⋊D43—81no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172#4112yes—
168C2×C4×D43—42no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C4⋊C4×C43—24no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43#4112yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—81no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—81no—
189#10621884—28no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43—81no—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—81no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C4×Dic43—81no—
209C4×Dic43—81no—
210C4×Dic43C2×D412yes—
211C4×Dic43#4112yes—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D412yes—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43C22×D411yescharacteristic
226C22×D43—22no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C22⋊D43—84no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43#12112yes—
283C2×Dic43#12112yes—
284D172—22no—
285D172—22no—
286D172—41no—
287D172—41no—
288C4×D43—84no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—41no—
293#23715—431nomaximal, Sylow
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43C2×#12111yescharacteristic
302C22×C43#52511yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43#57611yescharacteristic
305C22×C43#57711yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57811yescharacteristic
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C4×C43—42no—
316C4×C43—41no—
317C4×C43—42no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43#52511yescharacteristic
321C4×C43#52911yescharacteristic
322C4×C43#52911yescharacteristic
323C4×C43#53211yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—41no—
328Dic43—41no—
329Dic43—81no—
330Dic43—81no—
331C2×#440—431no—
332C2×#433—431no—
333#2324—431no—
334#2323—431no—
335#2086—431no—
336#2076—431no—
337#2068—431no—
338#2065—431no—
339#2055—431no—
340#2035D4311yescharacteristic, complemented
341#2033—431no—
342#2000—431no—
343#1776—431no—
344C4×#103—431no—
345C4×#102—431no—
346C2×C43—81no—
347C2×C43#239211yescharacteristic
348C2×C43#306211yescharacteristic
349C2×C43#306311yescharacteristic
350C2×C43#311811yescharacteristic
351C2×C43#312011yescharacteristic
352C2×C43#312411yescharacteristic
353C2×C43#312611yescharacteristic
354D43—82no—
355C22×SD16—431no—
356C2×C22⋊Q8C2×D4311yescharacteristic
357C2×#121—431no—
358C2×C4×Q8—431no—
359C2×C4×D4—431no—
360C2×#117—431no—
361#440—864no—
362#433—864no—
363C2×#107—431no—
364C2×#107—431no—
365C2×#106C2×D4311yescharacteristic
366C2×C4⋊C8—431no—
367C2×C4⋊C8—431no—
368C2×#103—431no—
369C2×#103C2×D4311yescharacteristic
370C2×#103C2×D4311yescharacteristic
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×C22⋊C8—431no—
375C2×C22⋊C8C2×D4311yescharacteristic
376C2×#97—431no—
377C2×C4×C8—431no—
378#391—431no—
379#390—431no—
380#390—861no—
381#389—431no—
382#389—431no—
383#389—861no—
384#388—861no—
385#388—861no—
386#388—861no—
387#387—861no—
388#386—861no—
389#385—861no—
390#380—431no—
391#380C2×D4311yescharacteristic
392C4×C4⋊C4—431no—
393C4×C4⋊C4—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340C2×D4311yescharacteristic
400C43#2371511yescharacteristic, complemented, Sylow
401C22×Q8C22×D4311yescharacteristic
402C22×D4—431no—
403C22×D4—861no—
404C23×C4—861no—
405C23×C4C22×D4311yescharacteristic
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—862no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415#121—862no—
416#121—862no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×D4—862no—
420C4×D4—862no—
421#117—862no—
422#117—862no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42—861no—
449#107—862no—
450#107—862no—
451#106—22no—
452C4⋊C8—862no—
453C4⋊C8—862no—
454#103—22no—
455#103—22no—
456#103—862no—
457#102—862no—
458#102—862no—
459#102—862no—
460C22⋊C8—22no—
461C22⋊C8—862no—
462#97—434no—
463C4×C8—862no—
464#95—21no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—861no—
473C24D4×D4311yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#1062190012yes—
480C2×D4—432no—
481C2×D4—864no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—3441no—
488C2×D4—3441no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—1722no—
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—868no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—432no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8D4×D4312yes—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—432no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—3441no—
539C4⋊C4—3441no—
540C4⋊C4—1722no—
541C4⋊C4#1062190012yes—
542C22⋊C4—24no—
543C22⋊C4—81no—
544C22⋊C4—864no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—3441no—
548C22⋊C4—3441no—
549C22⋊C4—3441no—
550C22⋊C4—1722no—
551C42—432no—
552C42—432no—
553C42—861no—
554C42—861no—
555C42—3441no—
556C42—3441no—
557C42—1722no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—862no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C2×D4×D4311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—862no—
578D4—862no—
579D4—3444no—
580D4—1721no—
581D4—1721no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—3444no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062190011yescharacteristic
628C2×C4C2×#1062190011yescharacteristic
629C8—22no—
630C8—41no—
631C8—862no—
632C8—1721no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—1722no—
645C22—1722no—
646C22—1722no—
647C22#121×D4311yescharacteristic
648C22#1458340511yescharacteristic
649C22#1458340711yescharacteristic
650C22#1458370111yescharacteristic
651C22#1458370511yescharacteristic
652C22#1458370811yescharacteristic
653C22#1458371511yescharacteristic
654C4—41no—
655C4—42no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—3441no—
663C4—1721no—
664C4—1722no—
665C4—1721no—
666C4#1458340911yescharacteristic
667C4#1458342611yescharacteristic
668C4#1458342811yescharacteristic
669C4#1458344411yescharacteristic
670C2—81no—
671C2—3442no—
672C2#1913783811yescharacteristic
673C2#1914426811yescharacteristic
674C2#1914428311yescharacteristic
675C2#1914478211yescharacteristic
676C2#1914481211yescharacteristic
677C2#1914485811yescharacteristic
678C2#1914488011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2035C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2035D43
hypocenterC43#23715
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
1. C2×#14583002C2semidirect
2. C2×#14582957C2semidirect
4. #19137279C2semidirect
5. #19136087C2semidirect
6. #19136026C2semidirect
7. #19135988C2semidirect
8. #19135964C2semidirect
9. #19135909C2semidirect
12. #19134495C2semidirect
13. #103×Dic43C2semidirect
14. #19134409C2semidirect
15. C43×#2035C2semidirect
106. #13063235D4semidirect
340. #2035D43semidirect
400. C43#23715semidirect

Maximal subgroups

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

subgroupindex
C2×#145830022
C2×#145829572
#191372842
#191372792
#191360872
#191360262
#191359882
#191359642
#191359092
#191357782
#191355962
#191344952
#103×Dic432
#191344092
C43×#20352
#2371543