Finite Group Databasebeta

← #25196804

Subgroups — #25196804

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140420C211yesmaximal, characteristic, complemented
2#19137284C211yesmaximal, characteristic
3#19136167C211yesmaximal, characteristic, complemented
4#19136117C211yesmaximal, characteristic, complemented
5#19135926C211yesmaximal, characteristic, complemented
6#19135730C211yesmaximal, characteristic, complemented
7#19135175C211yesmaximal, characteristic, complemented
8#19135164C211yesmaximal, characteristic, complemented
9#19135031C211yesmaximal, characteristic
10#19135023C211yesmaximal, characteristic
11#19134857C211yesmaximal, characteristic, complemented
12#19134853C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic, complemented
14#19134291C211yesmaximal, characteristic, complemented
15C43×#1807C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27#14582841—21no—
28#14582835—21no—
29#14582820—21no—
30#14582811—21no—
31#14582800C2211yescharacteristic
32#14582799—21no—
33#14582798C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582791—21no—
37#14582775—21no—
38#14582773—21no—
39#14582764C2211yescharacteristic
40#14582759C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—41no—
69#13063324—41no—
70#13063299—22no—
71#13063299Q814yescomplemented
72#13063287—41no—
73#13063287—41no—
74#13063284—41no—
75#13063284—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
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×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063256—41no—
97#13063247—22no—
98#13063247—41no—
99#13063245—22no—
100#13063245—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43—22no—
110C22×C8×C43—22no—
111C22×C8×C43—41no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120#106×C43—22no—
121#106×C43—41no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×Q812yes—
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—81no—
140C2×C22⋊D43—81no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C2×Q812yes—
154C2×C4×D43—42no—
155C2×C4×D43—81no—
156C2×C4×D43—81no—
157C2×Dic86—42no—
158C2×Dic86—81no—
159C2×Dic86—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—44no—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C22⋊Dic43—81no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43—81no—
192C4⋊Dic43C2×Q812yes—
193Dic43⋊C4—42no—
194Dic43⋊C4—81no—
195Dic43⋊C4—81no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—81no—
201#10621877—44no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8#4112yes—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C22⋊Q812yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C22⋊Q812yes—
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C22⋊D43—84no—
249C2×Dic43—22no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275Dic86—84no—
276C8×C43—22no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280#29174—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43C2×C22⋊Q811yescharacteristic
289C22×C43#53211yescharacteristic
290C22×C43#53411yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57711yescharacteristic
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C4×C43—22no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#55111yescharacteristic
308C4×C43#55111yescharacteristic
309C4×C43#55411yescharacteristic
310C4×C43#55411yescharacteristic
311Dic43—42no—
312Dic43—41no—
313Dic43—41no—
314Dic43—41no—
315Dic43—41no—
316Dic43—81no—
317Dic43—81no—
318#2628—431no—
319#2324—431no—
320#2101—431no—
321#2092—431no—
322#2058—431no—
323#2023—431no—
324#1919—431no—
325#1918—431no—
326#1895—431no—
327#1893—431no—
328#1864—431no—
329#1864—431no—
330#1809—431no—
331#1807D4311yescharacteristic, complemented
332#1729—431no—
333C2×C43—42no—
334C2×C43#256411yescharacteristic
335C2×C43#308111yescharacteristic
336C2×C43#308411yescharacteristic
337C2×C43#317311yescharacteristic
338C2×C43#317911yescharacteristic
339C2×C43#319811yescharacteristic
340C2×C43#320011yescharacteristic
341D43—82no—
342C22×M16—431no—
343C23×C8C2×D4311yescharacteristic
344C2×C4⋊Q8—431no—
345C2×#121—431no—
346C2×C4×D4—431no—
347C2×#117—431no—
348C2×#107—431no—
349C2×#106—431no—
350C2×#106C2×D4311yescharacteristic
351C2×#106C2×D4311yescharacteristic
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356#400—861no—
357#399—861no—
358#395—861no—
359#393—861no—
360#390—431no—
361#390—861no—
362#389—431no—
363#389—431no—
364#389—431no—
365#388—861no—
366#386—861no—
367#385—861no—
368#382—431no—
369#380—431no—
370#380C2×D4311yescharacteristic
371#380C2×D4311yescharacteristic
372C4×C4⋊C4—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340C2×D4311yescharacteristic
380#340C2×D4311yescharacteristic
381#336—431no—
382#336—431no—
383#336—431no—
384#336—431no—
385C43#2917411yescharacteristic, complemented, Sylow
386C22×Q8—861no—
387C22×D4—431no—
388C22×D4—861no—
389C23×C4—861no—
390C23×C4C22×D4311yescharacteristic
391C2×M16—862no—
392C2×M16—862no—
393C2×M16—1721no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—41no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C4⋊Q8—1721no—
402C4⋊Q8—1721no—
403#121—434no—
404#121—862no—
405C4×D4—1721no—
406C4×D4—1721no—
407#117—1721no—
408#117—1721no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—861no—
434#107—862no—
435#106—22no—
436#106—41no—
437#106—1721no—
438#102—862no—
439#102—862no—
440#102—1721no—
441#102—1721no—
442#95—21no—
443#95—21no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451C24—861no—
452C24D4×D4311yescharacteristic
453C2×Q8—3441no—
454C2×Q8—3441no—
455C2×Q8—1722no—
456C2×D4—432no—
457C2×D4—864no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—3441no—
464C2×D4—3441no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—3441no—
481C22×C4—3441no—
482C22×C4—1722no—
483C22×C4#1062189812yes—
484C22×C4D4×D4311yescharacteristic
485C22×C4Q8×D4312yes—
486C22×C4C23×D4311yescharacteristic
487M16—1724no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—44no—
494C2×C8—432no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8#1062190012yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—432no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4—1722no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—864no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—1722no—
528C22⋊C4—1721no—
529C22⋊C4—1721no—
530C42—861no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42—3441no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23#1306330312yes—
549C23C2×D4×D4311yescharacteristic
550Q8—3444no—
551D4—862no—
552D4—862no—
553D4—3444no—
554D4—1721no—
555D4—1721no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4#1306330312yes—
597C2×C4C2×Q8×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4C2×#1062190011yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C2×C4#1306337011yescharacteristic
602C2×C4#1306337111yescharacteristic
603C8—22no—
604C8—41no—
605C8—862no—
606C8—1721no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22C2×#1306330311yescharacteristic
622C22#1458344411yescharacteristic
623C22#1458345711yescharacteristic
624C22#1458370111yescharacteristic
625C22#1458370511yescharacteristic
626C22#1458370511yescharacteristic
627C22#1458370611yescharacteristic
628C4—22no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—3441no—
634C4—3441no—
635C4—1721no—
636C4—1721no—
637C4—1722no—
638C4—1721no—
639C4—1721no—
640C4#1458357311yescharacteristic
641C4#1458357511yescharacteristic
642C4#1458360311yescharacteristic
643C4#1458360711yescharacteristic
644C2—42no—
645C2—3442no—
646C2#1913977311yescharacteristic
647C2#1914442911yescharacteristic
648C2#1914446211yescharacteristic
649C2#1914520511yescharacteristic
650C2#1914527311yescharacteristic
651C2#1914545011yescharacteristic
652C2#1914546111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1807C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1807D43
hypocenterC43#29174
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
1. #19140420C2semidirect
3. #19136167C2semidirect
4. #19136117C2semidirect
5. #19135926C2semidirect
6. #19135730C2semidirect
7. #19135175C2semidirect
8. #19135164C2semidirect
11. #19134857C2semidirect
12. #19134853C2semidirect
13. #19134626C2semidirect
14. #19134291C2semidirect
15. C43×#1807C2semidirect
71. #13063299Q8semidirect
331. #1807D43semidirect
385. C43#29174semidirect

Maximal subgroups

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

subgroupindex
#191404202
#191372842
#191361672
#191361172
#191359262
#191357302
#191351752
#191351642
#191350312
#191350232
#191348572
#191348532
#191346262
#191342912
C43×#18072
#2917443