Finite Group Databasebeta

← #25967390

Subgroups — #25967390

Order 11008.

2130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583470C211yesmaximal, characteristic, complemented
2#19145486C214yesmaximal, complemented
3#19145471C218yesmaximal, complemented
4#19145467C214yesmaximal, complemented
5#19144543C212yesmaximal, complemented
6#19144524C212yesmaximal, complemented
7#19144227C214yesmaximal, complemented
8#19143855C212yesmaximal, complemented
9#19143828C212yesmaximal, complemented
10#19143040C211yesmaximal, characteristic, complemented
11C43×#3449C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic, complemented
13C2×#13063355C2214yes—
14C22×#10621877C2212yescomplemented
15#14583470—22no—
16#14583470—22no—
17#14583470C2214yes—
18#14583470C2214yescomplemented
19C2×#13063323—21no—
20C2×#13063312—21no—
21C2×#13063306—21no—
22C2×#13063306—21no—
23C2×#13063304C2212yes—
24C2×#13063304C2212yescomplemented
25C2×#13063284C2211yescharacteristic, complemented
26#14583240C2218yescomplemented
27#14583237C2218yescomplemented
28#14583234C2214yescomplemented
29#14583229C2214yescomplemented
30#14583220C2218yescomplemented
31#14583155C2218yescomplemented
32#14583143C2218yescomplemented
33#14583138C2218yescomplemented
34#14583126C2218yescomplemented
35#14583061C2218yescomplemented
36#14583055C2214yescomplemented
37#14583054C2218yescomplemented
38#14583050C2214yescomplemented
39#14583037C2218yescomplemented
40#14582942C2214yescomplemented
41#14582907C2214yescomplemented
42#14582900C2214yes—
43#14582866C2214yes—
44#14582866C2214yescomplemented
45#14582863C2212yes—
46#14582863C2212yescomplemented
47C22×#41×C43C2211yescharacteristic
48C22×#41×C43C2211yescharacteristic
49C43×#537C2214yes—
50C43×#536—21no—
51C43×#536C2212yes—
52C43×#535—21no—
53C43×#535C2212yes—
54C43×#534—21no—
55C43×#534—21no—
56C43×#532—22no—
57C43×#525—22no—
58C43×#525C2212yes—
59C43×#525C2212yes—
60C2×#117×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—22no—
63C22×Dic86—44no—
64C22×Dic86C2312yes—
65C22×Dic86C2314yes—
66C23×Dic43—21no—
67#13063355—48no—
68C2×#10621885C2318yes—
69C2×#10621883C2318yes—
70C2×#10621877—44no—
71C2×#10621877C2314yes—
72C2×#10621877C2314yes—
73C22×C43⋊C8C2314yes—
74#13063323—24no—
75#13063323—24no—
76#13063312—24no—
77#13063312—24no—
78#13063306—24no—
79#13063306—24no—
80#13063306—24no—
81#13063306—24no—
82#13063304—22no—
83#13063304—22no—
84#13063304—24no—
85#13063304C2314yes—
86#13063304C2314yes—
87#13063304C2318yes—
88#13063284—22no—
89#13063284C2314yes—
90C2×C4⋊Dic43C2312yes—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C4×Dic43—21no—
97#13063258C2318yes—
98#13063256C2318yes—
99#13063249C2318yes—
100#13063248C2318yes—
101#13063248C2318yes—
102#13063246C2318yes—
103C22⋊(C43⋊C8)C2314yes—
104C22⋊(C43⋊C8)C2318yes—
105C22⋊(C43⋊C8)C2314yes—
106C2×#41×C43—21no—
107C2×#41×C43—21no—
108C2×#41×C43—44no—
109C2×#41×C43—44no—
110C2×#41×C43D412yes—
111C2×#41×C43D412yes—
112C2×#41×C43C2312yes—
113C2×#41×C43C2312yes—
114C2×#41×C43C2312yes—
115C2×#41×C43C2312yes—
116C22×Q8×C43D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—21no—
119C22×D4×C43D411yescharacteristic
120C22×D4×C43D411yescharacteristic
121C22×D4×C43D411yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C4⋊Q8×C43—22no—
128#127×C43—22no—
129#124×C43—22no—
130#124×C43—22no—
131#123×C43—22no—
132#123×C43—22no—
133#123×C43—22no—
134#123×C43—22no—
135C22⋊Q8×C43—24no—
136C22⋊Q8×C43C2314yes—
137C22⋊Q8×C43C2314yes—
138#121×C43—24no—
139#121×C43—24no—
140#121×C43—24no—
141#121×C43C2314yes—
142#121×C43C2314yes—
143#120×C43—22no—
144#120×C43—22no—
145#120×C43—22no—
146#120×C43—22no—
147C4×D4×C43—24no—
148C4×D4×C43—24no—
149#117×C43—21no—
150#117×C43—21no—
151#117×C43C2312yes—
152#117×C43C2312yes—
153C2×C4⋊C4×C43C2312yes—
154C2×C22⋊C4×C43—21no—
155C2×C42×C43—21no—
156C24×C43—21no—
157C24×C43C2×D411yescharacteristic
158C24×C43C2×D411yescharacteristic
159C24×C43C2×D411yescharacteristic
160#41×C43—28no—
161#41×C43—44no—
162#41×C43—44no—
163#41×C43—42no—
164#41×C43—42no—
165#41×C43—42no—
166#41×C43—42no—
167#41×C43—44no—
168#41×C43—44no—
169#41×C43—44no—
170C2×Q8×C43—21no—
171C2×Q8×C43—42no—
172C2×Q8×C43—42no—
173C2×Q8×C43C2×D412yes—
174C2×Q8×C43C2×D412yes—
175C2×Q8×C43C2412yes—
176C2×D4×C43—21no—
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—24no—
180C2×D4×C43—24no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—44no—
185C2×D4×C43—42no—
186C2×D4×C43C2×D412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43C2×D412yes—
189C2×D4×C43C2×D412yes—
190C2×D4×C43C2×D412yes—
191C2×D4×C43C2×D412yes—
192C2×D4×C43C2412yes—
193C22×C4×C43—24no—
194C22×C4×C43—24no—
195C22×C4×C43—24no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—21no—
199C22×C4×C43—22no—
200C22×C4×C43—44no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—24no—
216C22×Dic43—44no—
217C2×Dic86—28no—
218C2×Dic86—22no—
219C2×Dic86—24no—
220C2×Dic86—44no—
221C2×Dic86—44no—
222C2×Dic86—44no—
223C2×Dic86—48no—
224C2×Dic86C2414yes—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43C2414yes—
229C22⋊C4×C43—24no—
230C22⋊C4×C43—24no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C42×C43—22no—
236C42×C43—22no—
237C22⋊Dic43—24no—
238C22⋊Dic43—24no—
239C22⋊Dic43—28no—
240C22⋊Dic43—24no—
241#10621885—48no—
242#10621883—48no—
243C4⋊Dic43—22no—
244C4⋊Dic43C2414yes—
245Dic43⋊C4—24no—
246Dic43⋊C4—28no—
247Dic43⋊C4—24no—
248C4×Dic43—24no—
249#10621877—28no—
250#10621877—44no—
251C2×C43⋊C8—44no—
252C2×C43⋊C8C2418yes—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—42no—
258C23×C43—42no—
259C23×C43—42no—
260C23×C43—42no—
261C23×C43—82no—
262C23×C43C22×D411yescharacteristic
263C23×C43C22×D412yes—
264C23×C43C22×D411yescharacteristic
265C23×C43C22×D412yes—
266C23×C43C22×D411yescharacteristic
267Q8×C43—24no—
268Q8×C43—42no—
269Q8×C43—42no—
270Q8×C43—42no—
271D4×C43—24no—
272D4×C43—42no—
273D4×C43—42no—
274D4×C43—42no—
275D4×C43—42no—
276D4×C43—42no—
277D4×C43—42no—
278D4×C43—42no—
279D4×C43—44no—
280D4×C43—44no—
281D4×C43—84no—
282D4×C43—84no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—24no—
287C2×C4×C43—22no—
288C2×C4×C43—24no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—44no—
299C2×C4×C43—42no—
300C2×C4×C43—44no—
301C2×C4×C43—82no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43H(5,𝔽2)14yes—
308C2×C4×C43C2511yescharacteristic
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—48no—
312C2×Dic43—44no—
313C2×Dic43—44no—
314Dic86—28no—
315Dic86—48no—
316Dic86—44no—
317C43⋊C8—28no—
318#60754—431nomaximal, Sylow
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—24no—
323C22×C43—24no—
324C22×C43—21no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—21no—
328C22×C43—44no—
329C22×C43—44no—
330C22×C43—42no—
331C22×C43—82no—
332C22×C43—82no—
333C22×C43—84no—
334C22×C43#53412yes—
335C22×C43C23×D411yescharacteristic
336C4×C43—22no—
337C4×C43—21no—
338C4×C43—21no—
339C4×C43—22no—
340C4×C43—44no—
341C4×C43—42no—
342C4×C43#53412yes—
343C4×C43C2×H(5,𝔽2)12yes—
344Dic43—44no—
345Dic43—44no—
346#3449D4311yescharacteristic
347C2×#536—431no—
348#3202—434no—
349#3201—438no—
350#3200—434no—
351#3095—432no—
352#3093—432no—
353#3056—434no—
354#3007—432no—
355#3004—432no—
356#2879—431no—
357C2×C43—22no—
358C2×C43—42no—
359C2×C43—41no—
360C2×C43—42no—
361C2×C43—41no—
362C2×C43—82no—
363C2×C43C2×#53411yescharacteristic
364C2×C43#358612yes—
365C22×#41C2×D4311yescharacteristic
366C22×#41C2×D4311yescharacteristic
367C23×Q8—431no—
368C2×#137—434no—
369C22×M16—432no—
370#537C2×D4314yes—
371#536—21no—
372#536—434no—
373#536—434no—
374#536—862no—
375#536—862no—
376#536C2×D4312yes—
377#535—21no—
378#535C2×D4312yes—
379#534—21no—
380#534—21no—
381#532—22no—
382C2×C4⋊Q8—861no—
383C2×#124—861no—
384#525—22no—
385#525C2×D4312yes—
386#525C2×D4312yes—
387C2×#123—861no—
388C2×#123—861no—
389C2×C22⋊Q8—432no—
390C2×C22⋊Q8—432no—
391C2×#117—431no—
392C2×#117C2×D4311yescharacteristic
393#485—438no—
394#485—438no—
395#484—434no—
396#483—434no—
397#482—438no—
398#470—438no—
399#468—438no—
400#467—438no—
401#465—438no—
402#452—438no—
403#451—434no—
404#451—438no—
405#450—434no—
406#448—438no—
407#428—434no—
408#419—434no—
409#417—434no—
410#408—434no—
411#408—434no—
412#407—432no—
413#407—432no—
414C43#6075411yescharacteristic, complemented, Sylow
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—44no—
418C2×#41—44no—
419C2×#41C22⋊D4312yes—
420C2×#41C22⋊D4312yes—
421C2×#41C22×D4312yes—
422C2×#41C22×D4312yes—
423C2×#41C22×D4312yes—
424C2×#41C22×D4312yes—
425C22×Q8—432no—
426C22×Q8—434no—
427C22×Q8—861no—
428C22×Q8—862no—
429C22×Q8—1724no—
430C22×Q8C22⋊D4311yescharacteristic
431C22×Q8C22×D4311yescharacteristic
432C22×D4—21no—
433C22×D4C22⋊D4311yescharacteristic
434C22×D4C22⋊D4311yescharacteristic
435C22×D4C22⋊D4311yescharacteristic
436C22×D4C22×D4311yescharacteristic
437C23×C4—21no—
438C23×C4—861no—
439C23×C4C22×D4311yescharacteristic
440C23×C4C22×D4311yescharacteristic
441C23×C4C22×D4311yescharacteristic
442#137—1728no—
443C2×Q16—438no—
444C2×SD16—438no—
445C2×M16—434no—
446C2×M16—434no—
447C2×M16—1724no—
448C22×C8—434no—
449C4⋊Q8—22no—
450C4⋊Q8—864no—
451C4⋊Q8—864no—
452#127—22no—
453#124—22no—
454#124—22no—
455#124—864no—
456#124—864no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—22no—
461#123—864no—
462#123—864no—
463#123—864no—
464#123—864no—
465C22⋊Q8—24no—
466C22⋊Q8—434no—
467C22⋊Q8—434no—
468C22⋊Q8—438no—
469C22⋊Q8—862no—
470C22⋊Q8—862no—
471C22⋊Q8—864no—
472C22⋊Q8C22×D4314yes—
473C22⋊Q8C22×D4314yes—
474#121—24no—
475#121—24no—
476#121—24no—
477#121C22×D4314yes—
478#121C22×D4314yes—
479#120—22no—
480#120—22no—
481#120—22no—
482#120—22no—
483C4×D4—24no—
484C4×D4—24no—
485#117—21no—
486#117—21no—
487#117—434no—
488#117—862no—
489#117C22×D4312yes—
490#117C22×D4312yes—
491C2×C4⋊C4—432no—
492C2×C4⋊C4—862no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4C22×D4312yes—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—862no—
498C2×C22⋊C4—862no—
499C2×C42—21no—
500C2×C42—861no—
501#107—438no—
502#106—438no—
503#103—438no—
504#103—438no—
505#103—438no—
506#102—438no—
507C22⋊C8—438no—
508C22⋊C8—434no—
509C22⋊C8—434no—
510C24—21no—
511C24C2×C22⋊D4311yescharacteristic
512C24C2×C22⋊D4311yescharacteristic
513C24C2×C22⋊D4311yescharacteristic
514#41—28no—
515#41—42no—
516#41—42no—
517#41—42no—
518#41—42no—
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—434no—
528C2×Q8—862no—
529C2×Q8—864no—
530C2×Q8—868no—
531C2×Q8—1724no—
532C2×Q8—1724no—
533C2×Q8—1724no—
534C2×Q8—1728no—
535C2×Q8C2×C22⋊D4312yes—
536C2×Q8C2×C22⋊D4312yes—
537C2×Q8C23×D4312yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—44no—
548C2×D4C2×C22⋊D4312yes—
549C2×D4C2×C22⋊D4312yes—
550C2×D4C2×C22⋊D4312yes—
551C2×D4C2×C22⋊D4312yes—
552C2×D4C2×C22⋊D4312yes—
553C2×D4C2×C22⋊D4312yes—
554C2×D4C23×D4312yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—864no—
566C22×C4—1724no—
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C2×C22⋊D4311yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C2×C22⋊D4312yes—
573C22×C4C2×C22⋊D4312yes—
574C22×C4C23×D4311yescharacteristic
575C22×C4C23×D4312yes—
576C22×C4C23×D4311yescharacteristic
577C22×C4C23×D4312yes—
578C22×C4C23×D4311yescharacteristic
579Q16—1728no—
580SD16—1728no—
581M16—868no—
582M16—1724no—
583C2×C8—438no—
584C2×C8—1724no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—434no—
589C4⋊C4—862no—
590C4⋊C4—864no—
591C4⋊C4—868no—
592C4⋊C4—864no—
593C4⋊C4C23×D4314yes—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—868no—
603C22⋊C4—864no—
604C42—22no—
605C42—22no—
606C42—864no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—82no—
616C23C22×C22⋊D4311yescharacteristic
617C23C22×C22⋊D4312yes—
618C23C22×C22⋊D4312yes—
619C23C22×C22⋊D4311yescharacteristic
620C23C22×C22⋊D4311yescharacteristic
621Q8—24no—
622Q8—42no—
623Q8—42no—
624Q8—42no—
625Q8—868no—
626Q8—1728no—
627Q8—1724no—
628D4—24no—
629D4—42no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—42no—
634D4—42no—
635D4—42no—
636D4—44no—
637D4—44no—
638D4—84no—
639D4—84no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—42no—
657C2×C4—44no—
658C2×C4—82no—
659C2×C4—864no—
660C2×C4—864no—
661C2×C4—1728no—
662C2×C4—1724no—
663C2×C4—1724no—
664C2×C4C22×C22⋊D4311yescharacteristic
665C2×C4C22×C22⋊D4312yes—
666C2×C4C22×C22⋊D4312yes—
667C2×C4C22×C22⋊D4311yescharacteristic
668C2×C4C22×C22⋊D4311yescharacteristic
669C2×C4#1306337014yes—
670C2×C4C24×D4311yescharacteristic
671C8—868no—
672C22—22no—
673C22—22no—
674C22—24no—
675C22—24no—
676C22—22no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—22no—
681C22—44no—
682C22—44no—
683C22—42no—
684C22—82no—
685C22—82no—
686C22—84no—
687C22#1458345812yes—
688C22C23×C22⋊D4311yescharacteristic
689C4—21no—
690C4—21no—
691C4—22no—
692C4—22no—
693C4—44no—
694C4—42no—
695C4—1724no—
696C4—1724no—
697C4#1458345812yes—
698C4C2×#1306337012yes—
699C2—22no—
700C2—42no—
701C2—41no—
702C2—41no—
703C2—42no—
704C2—82no—
705C2C2×#1458345811yescharacteristic
706C2#1914938112yes—
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC43×#3449C2
socleC22×C43C23×D4
hypercenter#3449D43
hypocenterC43#60754
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#14583470C2semidirect
2. #19145486C2semidirect
3. #19145471C2semidirect
4. #19145467C2semidirect
5. #19144543C2semidirect
6. #19144524C2semidirect
7. #19144227C2semidirect
8. #19143855C2semidirect
9. #19143828C2semidirect
10. #19143040C2semidirect
12. C23×Dic86C22semidirect
14. C22×#10621877C22semidirect
18. #14583470C22semidirect
24. C2×#13063304C22semidirect
25. C2×#13063284C22semidirect
26. #14583240C22semidirect
27. #14583237C22semidirect
28. #14583234C22semidirect
29. #14583229C22semidirect
30. #14583220C22semidirect
31. #14583155C22semidirect
32. #14583143C22semidirect
33. #14583138C22semidirect
34. #14583126C22semidirect
35. #14583061C22semidirect
36. #14583055C22semidirect
37. #14583054C22semidirect
38. #14583050C22semidirect
39. #14583037C22semidirect
40. #14582942C22semidirect
41. #14582907C22semidirect
44. #14582866C22semidirect
46. #14582863C22semidirect
414. C43#60754semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
#191454862
#191454712
#191454672
#191445432
#191445242
#191442272
#191438552
#191438282
#191430402
C43×#34492
#6075443