Finite Group Databasebeta

← #25967396

Subgroups — #25967396

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
1#19147924C211yesmaximal, characteristic
2C2×#14583470C211yesmaximal, characteristic, complemented
3#19145490C214yesmaximal, complemented
4#19145479C218yesmaximal, complemented
5#19145468C214yesmaximal, complemented
6#19144544C212yesmaximal, complemented
7#19144528C212yesmaximal, complemented
8#19144225C214yesmaximal, complemented
9#19143857C212yesmaximal, complemented
10#19143832C212yesmaximal, complemented
11C43×#2879C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C23×Dic86C2211yescharacteristic, complemented
14C2×#13063358C2214yes—
15#14583477C2214yes—
16#14583473—21no—
17#14583470—22no—
18#14583470—22no—
19#14583470C2212yes—
20#14583470C2214yes—
21#14583470C2214yescomplemented
22#14583466—21no—
23#14583463C2212yes—
24#14583458—21no—
25#14583458—21no—
26#14583445—22no—
27C2×#13063323—21no—
28C2×#13063312—21no—
29#14583410C2212yes—
30#14583410C2212yes—
31#14583406—22no—
32C2×#13063306—21no—
33C2×#13063306—21no—
34C2×#13063304C2212yes—
35C2×#13063304C2212yescomplemented
36C2×#13063284C2211yescharacteristic
37C2×#13063284C2211yescharacteristic, complemented
38#14583241C2218yescomplemented
39#14583241C2218yescomplemented
40#14583235C2214yescomplemented
41#14583230C2214yescomplemented
42#14583224C2218yescomplemented
43#14583157C2218yescomplemented
44#14583145C2218yescomplemented
45#14583140C2218yescomplemented
46#14583128C2218yescomplemented
47#14583063C2218yescomplemented
48#14583057C2218yescomplemented
49#14583057C2214yescomplemented
50#14583052C2214yescomplemented
51#14583040C2218yescomplemented
52#14582941C2214yescomplemented
53#14582909C2214yescomplemented
54#14582901C2214yes—
55C22×#41×C43C2211yescharacteristic
56C22×M16×C43C2212yescomplemented
57C43×#408C2214yes—
58C43×#408C2214yescomplemented
59C43×#407C2212yes—
60C43×#407C2212yescomplemented
61C2×#10621898—21no—
62C2×#10621898—21no—
63C2×#10621898—44no—
64C2×#10621898C2312yes—
65C2×#10621898C2312yes—
66C22×Dic86—21no—
67C22×Dic86—22no—
68C22×Dic86—44no—
69C22×Dic86C2312yes—
70C22×Dic86C2314yes—
71C22×Dic86C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76#13063358—48no—
77C2×Dic172C2318yes—
78C2×#10621873C2318yes—
79#13063323—24no—
80#13063323—24no—
81#13063323—22no—
82#13063321—22no—
83#13063314—22no—
84#13063312—24no—
85#13063312—24no—
86#13063312—22no—
87#13063308—22no—
88#13063308—22no—
89#13063306—24no—
90#13063306—24no—
91#13063306—24no—
92#13063306—24no—
93#13063306—22no—
94#13063306—22no—
95#13063304—22no—
96#13063304—22no—
97#13063304—24no—
98#13063304C2314yes—
99#13063304C2314yes—
100#13063304C2314yes—
101#13063304C2318yes—
102#13063304C2314yes—
103#13063301—24no—
104#13063299C2314yes—
105#13063299C2314yes—
106#13063297—24no—
107#13063297—24no—
108#13063296—24no—
109#13063294—22no—
110#13063294—22no—
111#13063293—22no—
112#13063293—22no—
113C4×C22⋊D43—24no—
114C4×C22⋊D43—24no—
115#13063284—21no—
116#13063284—21no—
117#13063284—22no—
118#13063284C2312yes—
119#13063284C2312yes—
120#13063284C2314yes—
121C2×C4⋊Dic43C2312yes—
122C2×C4⋊Dic43C2312yes—
123C2×Dic43⋊C4—22no—
124C2×Dic43⋊C4—22no—
125C2×C22⋊Dic43—21no—
126C2×C22⋊Dic43—21no—
127C2×C22⋊Dic43—22no—
128C2×C22⋊Dic43—22no—
129C2×C4×Dic43—21no—
130C2×C4×Dic43—21no—
131#13063259C2318yes—
132#13063257C2318yes—
133#13063250C2318yes—
134#13063250C2318yes—
135#13063250C2318yes—
136#13063247C2318yes—
137C2×#41×C43—44no—
138C2×#41×C43D412yes—
139C2×#41×C43D412yes—
140C2×#41×C43C2312yes—
141C2×#41×C43C2312yes—
142C22×Q8×C43D411yescharacteristic
143C22×D4×C43D411yescharacteristic
144C22×D4×C43D411yescharacteristic
145C22×D4×C43D411yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C2×M16×C43—44no—
150C2×M16×C43C2314yes—
151C2×M16×C43C2314yes—
152C22×C8×C43C2314yes—
153C22⋊C8×C43C2318yes—
154C22⋊C8×C43C2314yes—
155C22⋊C8×C43C2314yes—
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158C24×C43C2×D411yescharacteristic
159C23×D43—21no—
160#41×C43—44no—
161#41×C43—44no—
162#41×C43—42no—
163#41×C43—42no—
164#41×C43—42no—
165#41×C43—42no—
166C2×Q8×C43—42no—
167C2×Q8×C43C2×D412yes—
168C2×Q8×C43C2×D412yes—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43C2×D412yes—
173C2×D4×C43C2×D412yes—
174C2×D4×C43C2×D412yes—
175C2×D4×C43C2×D412yes—
176C2×D4×C43C2×D412yes—
177C2×D4×C43C2×D412yes—
178C22×C4×C43—24no—
179C22×C4×C43—24no—
180C22×C4×C43—24no—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2411yescharacteristic
189C22×C4×C43C2412yes—
190C22×C4×C43C2411yescharacteristic
191C22×C4×C43C2412yes—
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—44no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—21no—
201C22×Dic43—24no—
202C22×Dic43—22no—
203C22×Dic43—44no—
204#10621898—28no—
205#10621898—44no—
206#10621898—44no—
207#10621898—44no—
208C2×D172—21no—
209C2×D172—42no—
210C2×D172C2412yes—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43—44no—
214C2×Dic86—28no—
215C2×Dic86—22no—
216C2×Dic86—24no—
217C2×Dic86—21no—
218C2×Dic86—44no—
219C2×Dic86—44no—
220C2×Dic86—42no—
221C2×Dic86—44no—
222C2×Dic86—48no—
223C2×Dic86C2414yes—
224C2×Dic86C2412yes—
225M16×C43—28no—
226M16×C43—44no—
227C2×C8×C43—44no—
228C2×C8×C43C2418yes—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—24no—
232C22⋊Dic43—24no—
233C22⋊Dic43—28no—
234C22⋊Dic43—24no—
235C22⋊Dic43—24no—
236C22⋊Dic43—24no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4—24no—
239C4⋊Dic43—22no—
240C4⋊Dic43—22no—
241C4⋊Dic43C2414yes—
242C4⋊Dic43C2414yes—
243Dic43⋊C4—24no—
244Dic43⋊C4—28no—
245Dic43⋊C4—24no—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248C4×Dic43—22no—
249C4×Dic43—24no—
250C4×Dic43—22no—
251Dic172—48no—
252#10621873—48no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—42no—
257C23×C43—42no—
258C23×C43—42no—
259C23×C43C22×D411yescharacteristic
260C23×C43C22×D412yes—
261C23×C43C22×D411yescharacteristic
262C23×C43C22×D412yes—
263C23×C43C22×D411yescharacteristic
264C22×D43—22no—
265C22×D43—42no—
266C22×D43—82no—
267Q8×C43—42no—
268Q8×C43—42no—
269D4×C43—42no—
270D4×C43—42no—
271D4×C43—42no—
272D4×C43—42no—
273D4×C43—42no—
274D4×C43—42no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—24no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—24no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C22×D412yes—
290C2×C4×C43C22×D412yes—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43H(5,𝔽2)14yes—
294C2×C4×C43C2511yescharacteristic
295C22⋊D43—44no—
296C22⋊D43—44no—
297C22⋊D43—84no—
298C22⋊D43—84no—
299C2×Dic43—24no—
300C2×Dic43—24no—
301C2×Dic43—24no—
302C2×Dic43—22no—
303C2×Dic43—48no—
304C2×Dic43—42no—
305C2×Dic43—44no—
306C2×Dic43—44no—
307C2×Dic43—82no—
308D172—24no—
309D172—42no—
310C4×D43—44no—
311C4×D43—44no—
312Dic86—28no—
313Dic86—24no—
314Dic86—48no—
315Dic86—42no—
316Dic86—44no—
317C8×C43—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—21no—
327C22×C43—22no—
328C22×C43—44no—
329C22×C43—82no—
330C22×C43—82no—
331C22×C43#53412yes—
332C22×C43C23×D411yescharacteristic
333C2×D43—44no—
334C2×D43—42no—
335C2×D43—84no—
336C4×C43—22no—
337C4×C43—21no—
338C4×C43—21no—
339C4×C43—22no—
340C4×C43#53412yes—
341C4×C43C2×H(5,𝔽2)12yes—
342Dic43—44no—
343Dic43—44no—
344Dic43—44no—
345Dic43—42no—
346#3449—431no—
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#2879D4311yescharacteristic, complemented
357C2×C43—22no—
358C2×C43—41no—
359C2×C43—42no—
360C2×C43—41no—
361C2×C43—42no—
362C2×C43C2×#53411yescharacteristic
363C2×C43#358612yes—
364D43—82no—
365C22×#41—431no—
366C22×#41C2×D4311yescharacteristic
367C23×Q8—431no—
368C2×#137—434no—
369C22×M16C2×D4312yescomplemented
370#537—434no—
371#536—434no—
372#536—434no—
373#536—432no—
374#536—862no—
375#536—862no—
376#536—861no—
377#535—432no—
378#535—861no—
379#534—861no—
380#534—861no—
381#532—862no—
382C2×C4⋊Q8—861no—
383C2×#124—861no—
384#525—432no—
385#525—432no—
386#525—862no—
387C2×#123—861no—
388C2×#123—861no—
389C2×C22⋊Q8—432no—
390C2×C22⋊Q8—432no—
391C2×#117—431no—
392C2×#117—431no—
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—438no—
404#451—434no—
405#450—434no—
406#448—438no—
407#428—434no—
408#419—434no—
409#417—434no—
410#408C2×D4314yes—
411#408C2×D4314yescomplemented
412#407C2×D4312yes—
413#407C2×D4312yescomplemented
414C43#6075411yescharacteristic, complemented, Sylow
415C2×#41—44no—
416C2×#41—432no—
417C2×#41—432no—
418C2×#41—861no—
419C2×#41—861no—
420C2×#41—1724no—
421C2×#41D17212yes—
422C2×#41D17212yes—
423C2×#41C22×D4312yes—
424C2×#41C22×D4312yes—
425C22×Q8—432no—
426C22×Q8—434no—
427C22×Q8—431no—
428C22×Q8—861no—
429C22×Q8—862no—
430C22×Q8—1724no—
431C22×Q8D17211yescharacteristic
432C22×D4—431no—
433C22×D4—861no—
434C22×D4D17211yescharacteristic
435C22×D4D17211yescharacteristic
436C22×D4D17211yescharacteristic
437C23×C4—861no—
438C23×C4—861no—
439C23×C4C22×D4311yescharacteristic
440C23×C4C22×D4311yescharacteristic
441C23×C4C22×D4311yescharacteristic
442#137—1728no—
443C2×Q16—438no—
444C2×SD16—438no—
445C2×M16—44no—
446C2×M16C22×D4314yes—
447C2×M16C22×D4314yes—
448C22×C8C22×D4314yes—
449C4⋊Q8—864no—
450C4⋊Q8—864no—
451C4⋊Q8—862no—
452#127—862no—
453#124—862no—
454#124—864no—
455#124—864no—
456#124—862no—
457#123—864no—
458#123—864no—
459#123—864no—
460#123—864no—
461#123—862no—
462#123—862no—
463#123—862no—
464#123—862no—
465C22⋊Q8—434no—
466C22⋊Q8—434no—
467C22⋊Q8—438no—
468C22⋊Q8—434no—
469C22⋊Q8—434no—
470C22⋊Q8—864no—
471C22⋊Q8—862no—
472C22⋊Q8—862no—
473C22⋊Q8—864no—
474#121—434no—
475#121—434no—
476#121—864no—
477#121—864no—
478#121—864no—
479#120—862no—
480#120—862no—
481#120—862no—
482#120—862no—
483C4×D4—864no—
484C4×D4—864no—
485#117—432no—
486#117—432no—
487#117—434no—
488#117—861no—
489#117—861no—
490#117—862no—
491C2×C4⋊C4—432no—
492C2×C4⋊C4—432no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—862no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—862no—
498C2×C22⋊C4—862no—
499C2×C42—861no—
500C2×C42—861no—
501#107—438no—
502#106—438no—
503#103—438no—
504#103—438no—
505#103—438no—
506#102—438no—
507C22⋊C8C22×D4314yes—
508C22⋊C8C22×D4314yes—
509C22⋊C8C22×D4318yes—
510C24—861no—
511C24C2×D17211yescharacteristic
512C24C2×D17211yescharacteristic
513C24C2×D17211yescharacteristic
514#41—42no—
515#41—42no—
516#41—42no—
517#41—42no—
518#41—44no—
519#41—44no—
520#41—868no—
521#41—1724no—
522#41—1724no—
523#41—1724no—
524C2×Q8—42no—
525C2×Q8—434no—
526C2×Q8—432no—
527C2×Q8—862no—
528C2×Q8—864no—
529C2×Q8—861no—
530C2×Q8—868no—
531C2×Q8—1724no—
532C2×Q8—1724no—
533C2×Q8—1722no—
534C2×Q8—1724no—
535C2×Q8—1728no—
536C2×Q8C2×D17212yes—
537C2×Q8C2×D17212yes—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—432no—
542C2×D4—864no—
543C2×D4—864no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—861no—
547C2×D4—1722no—
548C2×D4—1724no—
549C2×D4C2×D17212yes—
550C2×D4C2×D17212yes—
551C2×D4C2×D17212yes—
552C2×D4C2×D17212yes—
553C2×D4C2×D17212yes—
554C2×D4C2×D17212yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—861no—
562C22×C4—864no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—1724no—
566C22×C4—1724no—
567C22×C4C2×D17211yescharacteristic
568C22×C4C2×D17211yescharacteristic
569C22×C4C2×D17211yescharacteristic
570C22×C4C2×D17211yescharacteristic
571C22×C4C2×D17212yes—
572C22×C4C2×D17211yescharacteristic
573C22×C4C2×D17212yes—
574C22×C4C23×D4311yescharacteristic
575C22×C4C23×D4312yes—
576C22×C4C23×D4311yescharacteristic
577C22×C4C23×D4312yes—
578C22×C4C23×D4311yescharacteristic
579Q16—1728no—
580SD16—1728no—
581M16—28no—
582M16—44no—
583C2×C8—44no—
584C2×C8C23×D4318yes—
585C4⋊C4—434no—
586C4⋊C4—434no—
587C4⋊C4—862no—
588C4⋊C4—862no—
589C4⋊C4—864no—
590C4⋊C4—868no—
591C4⋊C4—864no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C22⋊C4—862no—
595C22⋊C4—862no—
596C22⋊C4—864no—
597C22⋊C4—864no—
598C22⋊C4—868no—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C42—862no—
605C42—862no—
606C42—864no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—862no—
614C23—3442no—
615C23—1722no—
616C23C22×D17211yescharacteristic
617C23C22×D17212yes—
618C23C22×D17211yescharacteristic
619C23C22×D17212yes—
620C23C22×D17211yescharacteristic
621Q8—42no—
622Q8—42no—
623Q8—868no—
624Q8—864no—
625Q8—1728no—
626Q8—1722no—
627Q8—1724no—
628D4—42no—
629D4—42no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—42no—
634D4—864no—
635D4—3444no—
636D4—3444no—
637D4—1722no—
638D4—1724no—
639D4—1724no—
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—864no—
654C2×C4—864no—
655C2×C4—862no—
656C2×C4—864no—
657C2×C4—3442no—
658C2×C4—1724no—
659C2×C4—1722no—
660C2×C4—1728no—
661C2×C4—1724no—
662C2×C4—1724no—
663C2×C4—1724no—
664C2×C4C22×D17212yes—
665C2×C4C22×D17211yescharacteristic
666C2×C4C22×D17212yes—
667C2×C4C22×D17211yescharacteristic
668C2×C4C22×D17211yescharacteristic
669C2×C4#1306337014yes—
670C2×C4C24×D4311yescharacteristic
671C8—28no—
672C22—22no—
673C22—22no—
674C22—24no—
675C22—24no—
676C22—22no—
677C22—22no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—44no—
682C22—82no—
683C22—82no—
684C22—3444no—
685C22—1724no—
686C22—1722no—
687C22#1458346112yes—
688C22C23×D17211yescharacteristic
689C4—21no—
690C4—21no—
691C4—22no—
692C4—22no—
693C4—1724no—
694C4—1724no—
695C4—1722no—
696C4—1724no—
697C4#1458346112yes—
698C4C2×#1306337012yes—
699C2—22no—
700C2—42no—
701C2—41no—
702C2—41no—
703C2—42no—
704C2—3442no—
705C2C2×#1458346111yescharacteristic
706C2#1914938312yes—
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2879C2
socleC22×C43C23×D4
prime radical#19147924C2
hypercenter#2879D43
hypocenterC43#60754
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2879

Complements

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

NH ≅ G/Ntype
2. C2×#14583470C2semidirect
3. #19145490C2semidirect
4. #19145479C2semidirect
5. #19145468C2semidirect
6. #19144544C2semidirect
7. #19144528C2semidirect
8. #19144225C2semidirect
9. #19143857C2semidirect
10. #19143832C2semidirect
11. C43×#2879C2semidirect
13. C23×Dic86C22semidirect
21. #14583470C22semidirect
35. C2×#13063304C22semidirect
37. C2×#13063284C22semidirect
38. #14583241C22semidirect
39. #14583241C22semidirect
40. #14583235C22semidirect
41. #14583230C22semidirect
42. #14583224C22semidirect
43. #14583157C22semidirect
44. #14583145C22semidirect
45. #14583140C22semidirect
46. #14583128C22semidirect
47. #14583063C22semidirect
48. #14583057C22semidirect
49. #14583057C22semidirect
50. #14583052C22semidirect
51. #14583040C22semidirect
52. #14582941C22semidirect
53. #14582909C22semidirect
56. C22×M16×C43C22semidirect
58. C43×#408C22semidirect
60. C43×#407C22semidirect
356. #2879D43semidirect
369. C22×M16C2×D43semidirect
411. #408C2×D43semidirect
413. #407C2×D43semidirect
414. C43#60754semidirect

Maximal subgroups

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

subgroupindex
#191479242
C2×#145834702
#191454902
#191454792
#191454682
#191445442
#191445282
#191442252
#191438572
#191438322
C43×#28792
#6075443