Finite Group Databasebeta

← #25137940

Subgroups — #25137940

Order 11008.

802 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
1C2×#14583176C211yesmaximal, characteristic, complemented
2C2×#14582959C211yesmaximal, characteristic, complemented
3#19140417C211yesmaximal, characteristic, complemented
4#19137289C211yesmaximal, characteristic
5#19136027C211yesmaximal, characteristic, complemented
6#19136022C211yesmaximal, characteristic, complemented
7#19135787C211yesmaximal, characteristic
8#19135780C211yesmaximal, characteristic
9#19135363C211yesmaximal, characteristic, complemented
10#19135337C211yesmaximal, characteristic, complemented
11#19135327C211yesmaximal, characteristic, complemented
12#19135290C211yesmaximal, characteristic, complemented
13#19135276C211yesmaximal, characteristic, complemented
14#19134606C211yesmaximal, characteristic, complemented
15C43×#1987C211yesmaximal, characteristic, complemented
16C2×#13063300C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19#14583176—24no—
20#14582959—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582837—21no—
35#14582834—21no—
36#14582818—21no—
37#14582810—21no—
38#14582801—21no—
39#14582800C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582790—21no—
44#14582777—21no—
45#14582773—21no—
46#14582765C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582756C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4⋊Q8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D172—21no—
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063300—22no—
68#13063300—22no—
69C4×D172—22no—
70C4×D172—22no—
71#13063282—22no—
72#13063282—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—22no—
92#13063258—22no—
93#13063258—22no—
94#13063256—22no—
95C4⋊(C43⋊C8)D414yescomplemented
96#13063247—22no—
97#13063247—22no—
98#13063245—22no—
99#13063245—22no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102#13063235—22no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4⋊Q8×C43—22no—
116C4⋊Q8×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C4⋊C8×C43—22no—
125#95×C43—21no—
126C23×D43—21no—
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—42no—
129C2×Q8×C43—81no—
130C2×Q8×C43—81no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×D172—21no—
145C2×D172—24no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—81no—
151C2×D172—81no—
152C2×D172#4112yes—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×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—
175C4⋊C4×C43—42no—
176C4⋊C4×C43#4112yes—
177C42×C43—81no—
178C42×C43C2×D412yes—
179C42×C43#4112yes—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—81no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C2×D412yes—
207C2×C43⋊C8C2×D412yes—
208C23×C43C22×D411yescharacteristic
209C22×D43—21no—
210C22×D43—22no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223Q8×C43—84no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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#12112yes—
241C2×C4×C43#12112yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266D172—22no—
267D172—22no—
268D172—41no—
269D172—41no—
270D172—84no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—84no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—22no—
280#24712—431nomaximal, Sylow
281C22×C43C2×#12111yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43#53611yescharacteristic
284C22×C43#57611yescharacteristic
285C22×C43#57611yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57811yescharacteristic
288C2×D43—41no—
289C2×D43—42no—
290C2×D43—41no—
291C2×D43—42no—
292C2×D43—41no—
293C2×D43—42no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#54711yescharacteristic
309C4×C43#54811yescharacteristic
310C4×C43#55211yescharacteristic
311C4×C43#55611yescharacteristic
312Dic43—41no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318C2×#474—431no—
319C2×#433—431no—
320#2628—431no—
321#2324—431no—
322#2076—431no—
323#2075—431no—
324#2034—431no—
325#2033—431no—
326#1987D4311yescharacteristic, complemented
327#1949—431no—
328#1944—431no—
329#1942—431no—
330#1936—431no—
331#1934—431no—
332#1804—431no—
333C2×C43#241511yescharacteristic
334C2×C43#305811yescharacteristic
335C2×C43#306311yescharacteristic
336C2×C43#311811yescharacteristic
337C2×C43#312411yescharacteristic
338C2×C43#324111yescharacteristic
339C2×C43#324311yescharacteristic
340D43—81no—
341D43—82no—
342C2×C4⋊Q8C2×D4311yescharacteristic
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×#117—431no—
346#474—864no—
347#433—864no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#107—431no—
351C2×#106—431no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8C2×D4311yescharacteristic
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×C22⋊C8—431no—
359C2×C22⋊C8—431no—
360C2×#97—431no—
361C2×C4×C8—431no—
362#400—861no—
363#399—861no—
364#395—861no—
365#393—861no—
366#390—431no—
367#390—861no—
368#389—431no—
369#389—431no—
370#389—431no—
371#388—861no—
372#386—861no—
373#385—861no—
374#382—431no—
375#380—431no—
376#380—431no—
377#380—431no—
378C4×C4⋊C4C2×D4311yescharacteristic
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#340C2×D4311yescharacteristic
385#340C2×D4311yescharacteristic
386#340C2×D4311yescharacteristic
387C43#2471211yescharacteristic, complemented, Sylow
388C22×Q8—21no—
389C22×D4—431no—
390C22×D4—861no—
391C23×C4—431no—
392C23×C4—861no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399#121—862no—
400#121—862no—
401C4×D4—862no—
402C4×D4—862no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—431no—
419C2×C22⋊C4—431no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—21no—
428C2×C42—431no—
429C2×C42C22×D4311yescharacteristic
430#107—862no—
431#107—862no—
432#107—862no—
433#106—862no—
434C4⋊C8—22no—
435C4⋊C8—434no—
436#102—862no—
437#102—862no—
438#102—862no—
439#102—862no—
440C22⋊C8—862no—
441C22⋊C8—862no—
442#97—862no—
443C4×C8—862no—
444#95—21no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453C24—431no—
454C24—861no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×Q8—81no—
458C2×D4—432no—
459C2×D4—864no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—3441no—
466C2×D4—3441no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—432no—
496C2×C8—432no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4#1062190212yes—
521C22⋊C4—864no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C42—81no—
531C42—861no—
532C42—861no—
533C42#1062189812yes—
534C42D4×D4312yes—
535C23—861no—
536C23—862no—
537C23—861no—
538C23—861no—
539C23—861no—
540C23—861no—
541C23—861no—
542C23—861no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23C2×D4×D4311yescharacteristic
550Q8—84no—
551D4—862no—
552D4—862no—
553D4—3444no—
554D4—1721no—
555D4—1721no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
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—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—3444no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4#1306329812yes—
596C2×C4#1306329812yes—
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4C2×#1062189811yescharacteristic
600C2×C4C2×#1062190211yescharacteristic
601C2×C4#1306337211yescharacteristic
602C2×C4#1306337311yescharacteristic
603C8—41no—
604C8—41no—
605C8—862no—
606C8—862no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—1721no—
612C22—1721no—
613C22—1722no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1722no—
619C22—1721no—
620C22—1722no—
621C22C2×#1306329811yescharacteristic
622C22#1458341211yescharacteristic
623C22#1458347211yescharacteristic
624C22#1458370311yescharacteristic
625C22#1458370311yescharacteristic
626C22#1458370511yescharacteristic
627C22#1458371211yescharacteristic
628C4—22no—
629C4—22no—
630C4—42no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—1721no—
638C4—1721no—
639C4—1721no—
640C4#1458355211yescharacteristic
641C4#1458355711yescharacteristic
642C4#1458359011yescharacteristic
643C4#1458362211yescharacteristic
644C2—3442no—
645C2—3441no—
646C2#1913802711yescharacteristic
647C2#1914424211yescharacteristic
648C2#1914428411yescharacteristic
649C2#1914478411yescharacteristic
650C2#1914486411yescharacteristic
651C2#1914584711yescharacteristic
652C2#1914588311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1987C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1987D43
hypocenterC43#24712
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
2. C2×#14582959C2semidirect
3. #19140417C2semidirect
5. #19136027C2semidirect
6. #19136022C2semidirect
9. #19135363C2semidirect
10. #19135337C2semidirect
11. #19135327C2semidirect
12. #19135290C2semidirect
13. #19135276C2semidirect
14. #19134606C2semidirect
15. C43×#1987C2semidirect
95. C4⋊(C43⋊C8)D4semidirect
326. #1987D43semidirect
387. C43#24712semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
C2×#145829592
#191404172
#191372892
#191360272
#191360222
#191357872
#191357802
#191353632
#191353372
#191353272
#191352902
#191352762
#191346062
C43×#19872
#2471243