Finite Group Databasebeta

← #25976714

Subgroups — #25976714

Order 11008.

1730 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148400C211yesmaximal, characteristic, complemented
2#19147431C214yesmaximal, complemented
3#19147394C214yesmaximal, complemented
4#19147357C214yesmaximal, complemented
5#19147331C214yesmaximal, complemented
6#19144960C212yesmaximal, complemented
7#19144940C211yesmaximal, characteristic
8#19144457C212yesmaximal, complemented
9#19144400C211yesmaximal, characteristic, complemented
10#19144121C212yesmaximal, complemented
11#19144063C211yesmaximal, characteristic
12#19143536C211yesmaximal, characteristic, complemented
13#19143434C212yesmaximal, complemented
14C2×#14583004C211yesmaximal, characteristic, complemented
15C43×#3507C211yesmaximal, characteristic
16C2×#13063355C2212yes—
17C22×#10621885C2211yescharacteristic
18Q8×Dic86C2212yes—
19#14583629—21no—
20#14583627C2214yes—
21#14583627C2212yes—
22#14583626—22no—
23#14583624—21no—
24#14583528—22no—
25#14583527C2212yes—
26#14583456C2211yescharacteristic
27#14583451—22no—
28#14583376C2212yes—
29C2×C4×Dic86C2211yescharacteristic
30#14583267C2214yes—
31#14583267C2212yes—
32#14583263C2212yes—
33#14583258C2214yes—
34#14583258C2212yes—
35#14583258C2212yes—
36#14583253C2214yes—
37#14583249C2214yes—
38#14583206C2214yes—
39#14583206C2214yes—
40#14583199C2214yes—
41#14583194C2212yes—
42#14583189C2214yes—
43#14583184C2214yes—
44#14583184C2212yes—
45#14583118C2214yes—
46#14583118C2214yes—
47#14583118C2214yes—
48#14583106C2214yes—
49#14583106C2212yes—
50#14583106C2214yes—
51#14583096C2212yes—
52#14583030C2214yes—
53#14583030C2214yes—
54#14583004C2214yes—
55#14583004C2214yes—
56#14583004C2214yes—
57#14582999C2214yes—
58C4×#10621885C2214yes—
59C4×#10621883C2214yes—
60#14582939C2212yes—
61C2×#13063256C2211yescharacteristic
62#14582926C2212yes—
63#14582923C2211yescharacteristic
64#14582908C2212yes—
65#14582900C2212yes—
66#14582895C2212yes—
67#14582895C2212yes—
68C2×#13063249C2211yescharacteristic
69C2×#13063248C2211yescharacteristic
70#14582855C2212yes—
71C2×#13063236C2211yescharacteristic
72C43×#559C2212yes—
73C43×#557C2212yes—
74C43×#556—21no—
75C43×#556C2214yes—
76C43×#554—21no—
77C43×#552—22no—
78C43×#539—22no—
79C43×#536C2212yes—
80C43×#533C2211yescharacteristic
81C43×#532C2211yescharacteristic
82C43×#529—22no—
83C43×#520C2212yes—
84C2×C4×Q8×C43C2211yescharacteristic
85C22×Dic86C2311yescharacteristic
86#13063355—28no—
87C2×#10621885—24no—
88C2×#10621885C2314yes—
89C2×#10621885C2314yes—
90C2×#10621883C2314yes—
91C2×#10621877C2312yes—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063325C2311yescharacteristic
95#13063325C2314yes—
96#13063325C2311yescharacteristic
97#13063324—22no—
98#13063324—24no—
99#13063324—22no—
100#13063323—22no—
101#13063323—24no—
102#13063317C2314yes—
103#13063317C2312yes—
104#13063316—22no—
105#13063315—24no—
106#13063315—24no—
107#13063315—24no—
108#13063304—21no—
109#13063304—21no—
110#13063302—24no—
111Q8×Dic43—22no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86—21no—
115C4×Dic86—21no—
116C4×Dic86C2312yes—
117C4×Dic86C2314yes—
118C4×Dic86C2314yes—
119C4×Dic86C2312yes—
120#13063290—22no—
121#13063290—24no—
122#13063290—22no—
123#13063290—22no—
124#13063284C2312yes—
125#13063281—24no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×C4×Dic43—21no—
129#13063258C2314yes—
130#13063256C2314yes—
131#13063256C2314yes—
132C4⋊(C43⋊C8)C2312yes—
133C4⋊(C43⋊C8)C2314yes—
134C4⋊(C43⋊C8)C2314yes—
135C4⋊(C43⋊C8)C2312yes—
136#13063249C2312yes—
137#13063249C2312yes—
138#13063249C2314yes—
139#13063249C2314yes—
140#13063249C2314yes—
141#13063249C2314yes—
142#13063249C2312yes—
143#13063249C2312yes—
144#13063248C2314yes—
145#13063246C2314yes—
146#13063246C2312yes—
147#13063246C2312yes—
148#13063246C2312yes—
149#13063246C2312yes—
150#13063236C2312yes—
151#13063236C2312yes—
152#13063236C2314yes—
153C4×C43⋊C8C2314yes—
154C2×#41×C43C2312yes—
155C22×Q8×C43C2311yescharacteristic
156C4⋊Q8×C43D411yescharacteristic
157C4⋊Q8×C43D411yescharacteristic
158C4⋊Q8×C43C2311yescharacteristic
159C4⋊Q8×C43C2314yes—
160#127×C43C2311yescharacteristic
161#126×C43—24no—
162#126×C43—24no—
163#125×C43—22no—
164#125×C43—24no—
165#125×C43D412yes—
166#124×C43—22no—
167#124×C43C2312yes—
168#124×C43C2314yes—
169#123×C43—24no—
170#123×C43—24no—
171C22⋊Q8×C43—24no—
172C22⋊Q8×C43—22no—
173C22⋊Q8×C43—22no—
174C22⋊Q8×C43D412yes—
175C22⋊Q8×C43D412yes—
176#121×C43—21no—
177#121×C43—21no—
178C4×Q8×C43—22no—
179C4×Q8×C43—21no—
180C4×Q8×C43—21no—
181C4×Q8×C43C2312yes—
182C4×Q8×C43C2312yes—
183C4×Q8×C43C2314yes—
184C4×Q8×C43C2312yes—
185C4×Q8×C43C2312yes—
186C4×D4×C43—22no—
187C4×D4×C43—24no—
188C4×D4×C43—21no—
189C4×D4×C43—21no—
190C4×D4×C43C2314yes—
191#117×C43—22no—
192#117×C43—24no—
193#117×C43C2312yes—
194C2×C4⋊C4×C43—21no—
195C2×C4⋊C4×C43—22no—
196C2×C4⋊C4×C43C2311yescharacteristic
197C2×C42×C43—21no—
198C2×C42×C43C2311yescharacteristic
199#41×C43—24no—
200#41×C43—24no—
201C2×Q8×C43—21no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43C2×D412yes—
205C2×Q8×C43C2×D412yes—
206C2×Q8×C43C2412yes—
207C2×Q8×C43C2412yes—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—22no—
211C2×D4×C43C2412yes—
212C22×C4×C43—22no—
213C22×C4×C43—24no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C22×Dic43—21no—
220C22×Dic43—21no—
221C2×Dic86—21no—
222C2×Dic86—22no—
223C2×Dic86—21no—
224C2×Dic86—24no—
225C2×Dic86—21no—
226C2×Dic86#4114yes—
227C2×Dic86C2412yes—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—22no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43C2×D412yes—
237C4⋊C4×C43C2×D412yes—
238C4⋊C4×C43C2×D414yes—
239C4⋊C4×C43C2×D412yes—
240C4⋊C4×C43C2×D414yes—
241C4⋊C4×C43C2×D412yes—
242C4⋊C4×C43C2412yes—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—24no—
248C22⋊C4×C43C2×D414yes—
249C42×C43—22no—
250C42×C43—22no—
251C42×C43—24no—
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C42×C43C2411yescharacteristic
255C42×C43C2411yescharacteristic
256C42×C43C2414yes—
257C22⋊Dic43—22no—
258#10621885—28no—
259#10621885—28no—
260#10621883—28no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—24no—
265C4⋊Dic43C2412yes—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268Dic43⋊C4—22no—
269Dic43⋊C4—22no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—22no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—22no—
276C4×Dic43—22no—
277C4×Dic43—22no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43—22no—
281#10621877—24no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2414yes—
286C2×C43⋊C8C2412yes—
287C23×C43—22no—
288C23×C43C22×D411yescharacteristic
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—42no—
294Q8×C43—42no—
295Q8×C43—42no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—42no—
299D4×C43—44no—
300D4×C43—81no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—42no—
307C2×C4×C43—44no—
308C2×C4×C43—84no—
309C2×C4×C43—81no—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D414yes—
313C2×C4×C43C22×D414yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4112yes—
318C2×C4×C432−1+412yes—
319C2×C4×C43C2511yescharacteristic
320C2×Dic43—24no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—81no—
326Dic86—24no—
327Dic86—22no—
328Dic86—42no—
329Dic86—81no—
330Dic86—84no—
331Dic86C2×#4114yes—
332C43⋊C8—22no—
333C43⋊C8—24no—
334C43⋊C8—22no—
335#61335—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43#54812yes—
342C22×C43C23×D411yescharacteristic
343C4×C43—21no—
344C4×C43—21no—
345C4×C43—24no—
346C4×C43—21no—
347C4×C43—21no—
348C4×C43—24no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43#54812yes—
353C4×C43C22×#4111yescharacteristic
354C4×C43C2×2−1+411yescharacteristic
355Dic43—24no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359#3507D4311yescharacteristic
360#3502—431no—
361#3377—434no—
362#3374—434no—
363#3371—434no—
364#3369—434no—
365#3137—432no—
366#3135—431no—
367#3084—432no—
368#3078—431no—
369#3044—432no—
370#3037—431no—
371#2961—431no—
372#2947—432no—
373C2×#441—431no—
374C2×C43—22no—
375C2×C43—82no—
376C2×C43C2×#54811yescharacteristic
377C2×C43#358611yescharacteristic
378C2×C43#358611yescharacteristic
379C2×#137—432no—
380C22×Q16—431no—
381#559C2×D4312yes—
382Q82—432no—
383Q82—861no—
384#557—434no—
385#557—432no—
386#557—861no—
387#557—862no—
388#557C2×D4312yes—
389#556—21no—
390#556C2×D4314yes—
391#554—21no—
392#552—22no—
393#544—432no—
394#544—862no—
395#539—22no—
396#536C2×D4312yes—
397#533—431no—
398#533—862no—
399#533C2×D4311yescharacteristic
400#532C2×D4311yescharacteristic
401#529—22no—
402#520C2×D4312yes—
403#519—432no—
404C2×C4×Q8—431no—
405C2×C4×Q8C2×D4311yescharacteristic
406#491—432no—
407#491—434no—
408#490—432no—
409#489—432no—
410#489—434no—
411#489—432no—
412#488—434no—
413#487—434no—
414#479—434no—
415#479—434no—
416#478—434no—
417#477—432no—
418#476—434no—
419#475—432no—
420#475—434no—
421#464—434no—
422#464—434no—
423#464—434no—
424#462—434no—
425#462—432no—
426#462—434no—
427#460—432no—
428#446—434no—
429#446—434no—
430#441—434no—
431#441—434no—
432#441—434no—
433#440—434no—
434C4×Q16—434no—
435C4×SD16—434no—
436#428—432no—
437C2×#106—431no—
438#424—432no—
439#423—431no—
440#419—432no—
441#417—432no—
442#416—432no—
443#416—432no—
444C2×#103—431no—
445C2×#103—431no—
446#405—432no—
447C2×#97—431no—
448C43#6133511yescharacteristic, complemented, Sylow
449C2×#41C22×D4312yes—
450C22×Q8—431no—
451C22×Q8C22×D4311yescharacteristic
452#137—868no—
453C2×Q16—434no—
454C2×Q16—434no—
455C2×Q16—864no—
456C2×SD16—434no—
457C2×M16—432no—
458C22×C8—431no—
459C22×C8—431no—
460C4⋊Q8—431no—
461C4⋊Q8—431no—
462C4⋊Q8—434no—
463C4⋊Q8—862no—
464C4⋊Q8—864no—
465C4⋊Q8—862no—
466C4⋊Q8—862no—
467C4⋊Q8—864no—
468C4⋊Q8C22⋊D4311yescharacteristic
469C4⋊Q8C22⋊D4311yescharacteristic
470C4⋊Q8C22×D4311yescharacteristic
471C4⋊Q8C22×D4314yes—
472#127C22×D4311yescharacteristic
473#126—24no—
474#126—24no—
475#125—22no—
476#125—24no—
477#125—432no—
478#125—434no—
479#125—864no—
480#125—862no—
481#125—864no—
482#125—864no—
483#125C22⋊D4312yes—
484#124—22no—
485#124C22×D4312yes—
486#124C22×D4314yes—
487#123—24no—
488#123—24no—
489C22⋊Q8—24no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—861no—
493C22⋊Q8—861no—
494C22⋊Q8—864no—
495C22⋊Q8C22⋊D4312yes—
496C22⋊Q8C22⋊D4312yes—
497#121—21no—
498#121—21no—
499C4×Q8—22no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—432no—
503C4×Q8—432no—
504C4×Q8—434no—
505C4×Q8—434no—
506C4×Q8—862no—
507C4×Q8—862no—
508C4×Q8—862no—
509C4×Q8—864no—
510C4×Q8—862no—
511C4×Q8—861no—
512C4×Q8—861no—
513C4×Q8—861no—
514C4×Q8—861no—
515C4×Q8C22×D4312yes—
516C4×Q8C22×D4312yes—
517C4×Q8C22×D4314yes—
518C4×Q8C22×D4312yes—
519C4×Q8C22×D4312yes—
520C4×D4—22no—
521C4×D4—24no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4C22×D4314yes—
525#117—22no—
526#117—24no—
527#117—432no—
528#117—864no—
529#117C22×D4312yes—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C42—21no—
536C2×C42—861no—
537C2×C42C22×D4311yescharacteristic
538#107—434no—
539#106—434no—
540#106—434no—
541C4⋊C8—432no—
542C4⋊C8—432no—
543C4⋊C8—434no—
544C4⋊C8—434no—
545#103—434no—
546#103—432no—
547#103—432no—
548#103—432no—
549#103—432no—
550#103—434no—
551#103—434no—
552#103—434no—
553#103—434no—
554#102—432no—
555#102—432no—
556#102—432no—
557#102—432no—
558#102—434no—
559#97—432no—
560#97—432no—
561#97—434no—
562C4×C8—434no—
563#41—24no—
564#41—24no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—434no—
569C2×Q8—432no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—864no—
573C2×Q8—861no—
574C2×Q8—862no—
575C2×Q8C2×C22⋊D4312yes—
576C2×Q8C2×C22⋊D4312yes—
577C2×Q8C23×D4312yes—
578C2×Q8C23×D4312yes—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4C23×D4312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592Q16—868no—
593Q16—868no—
594SD16—868no—
595M16—864no—
596C2×C8—432no—
597C2×C8—434no—
598C2×C8—432no—
599C2×C8—862no—
600C2×C8—862no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—24no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—861no—
613C4⋊C4—862no—
614C4⋊C4—862no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—862no—
618C4⋊C4—861no—
619C4⋊C4—864no—
620C4⋊C4—862no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—864no—
624C4⋊C4C2×C22⋊D4312yes—
625C4⋊C4C2×C22⋊D4312yes—
626C4⋊C4C2×C22⋊D4314yes—
627C4⋊C4C2×C22⋊D4312yes—
628C4⋊C4C2×C22⋊D4314yes—
629C4⋊C4C2×C22⋊D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—22no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—24no—
636C22⋊C4—862no—
637C22⋊C4C2×C22⋊D4314yes—
638C42—22no—
639C42—22no—
640C42—24no—
641C42—862no—
642C42—862no—
643C42—862no—
644C42—864no—
645C42—864no—
646C42C2×C22⋊D4311yescharacteristic
647C42C2×C22⋊D4311yescharacteristic
648C42C23×D4314yes—
649C42C23×D4311yescharacteristic
650C42C23×D4311yescharacteristic
651C23—22no—
652C23C22×C22⋊D4311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—434no—
661Q8—864no—
662Q8—862no—
663Q8—3441no—
664Q8—3444no—
665Q8—1722no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—44no—
670D4—81no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—84no—
679C2×C4—81no—
680C2×C4—864no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—3441no—
686C2×C4C22×C22⋊D4311yescharacteristic
687C2×C4C22×C22⋊D4311yescharacteristic
688C2×C4C22×C22⋊D4314yes—
689C2×C4C22×C22⋊D4311yescharacteristic
690C2×C4C22×C22⋊D4311yescharacteristic
691C2×C4C22×C22⋊D4314yes—
692C2×C4C22×C22⋊D4311yescharacteristic
693C2×C4#41×D4312yes—
694C2×C4#1306337212yes—
695C2×C4C24×D4311yescharacteristic
696C8—862no—
697C8—864no—
698C8—862no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22#1458355612yes—
705C22C23×C22⋊D4311yescharacteristic
706C4—21no—
707C4—21no—
708C4—24no—
709C4—21no—
710C4—21no—
711C4—24no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—864no—
716C4—1722no—
717C4—1722no—
718C4—1722no—
719C4#1458355612yes—
720C4C2×#41×D4311yescharacteristic
721C4C2×#1306337211yescharacteristic
722C2—22no—
723C2—82no—
724C2C2×#1458355611yescharacteristic
725C2#1914938111yescharacteristic
726C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3507C2
socleC22×C43C23×D4
prime radicalC43×#532C22
hypercenter#3507D43
hypocenterC43#61335
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #533 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #19148400C2semidirect
2. #19147431C2semidirect
3. #19147394C2semidirect
4. #19147357C2semidirect
5. #19147331C2semidirect
6. #19144960C2semidirect
8. #19144457C2semidirect
9. #19144400C2semidirect
10. #19144121C2semidirect
12. #19143536C2semidirect
13. #19143434C2semidirect
14. C2×#14583004C2semidirect
448. C43#61335semidirect

Maximal subgroups

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

subgroupindex
#191484002
#191474312
#191473942
#191473572
#191473312
#191449602
#191449402
#191444572
#191444002
#191441212
#191440632
#191435362
#191434342
C2×#145830042
C43×#35072
#6133543