Finite Group Databasebeta

← #25259284

Subgroups — #25259284

Order 11008.

2568 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583640C211yesmaximal, characteristic
2#19137788C211yesmaximal, characteristic, complemented
3#19137771C211yesmaximal, characteristic, complemented
4#19137751C213yesmaximal, complemented
5#19137750C213yesmaximal, complemented
6#19137740C213yesmaximal, complemented
7#19137735C213yesmaximal, complemented
8#19137157C211yesmaximal, characteristic, complemented
9#126×Dic43C211yesmaximal, characteristic, complemented
10#19137143C211yesmaximal, characteristic, complemented
11#19137116C213yesmaximal, complemented
12#19137107C213yesmaximal, complemented
13#19137103C213yesmaximal, complemented
14#19137096C213yesmaximal, complemented
15C43×#2383C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17#14583640C4116yescomplemented
18C2×#13063322C2211yescharacteristic
19C2×#13063319C2211yescharacteristic
20C2×#13063310C2213yes—
21C2×#13063300C2213yes—
22C2×#13063298C2213yes—
23C2×#13063295C2213yes—
24C2×#13063287C2213yes—
25C2×#13063287C2213yes—
26C2×#13063287C2213yescomplemented
27C2×(C22⋊D43)⋊C4C2213yes—
28C2×C42×D43C2213yescomplemented
29#14582801C2213yes—
30#14582800C2213yes—
31#14582800C2213yescomplemented
32#14582799C2213yes—
33#14582794C2213yescomplemented
34#14582792C2213yes—
35#14582791C2213yes—
36#14582790C2213yes—
37#14582790C2213yescomplemented
38#14582789C2213yes—
39#14582789C2213yescomplemented
40#14582788C2213yes—
41#14582785C2213yescomplemented
42#14582781C2213yescomplemented
43#14582780C2213yescomplemented
44#14582778C2213yes—
45#14582777C2213yes—
46#14582777C2213yes—
47#14582777C2213yes—
48#14582777C2213yes—
49#14582777C2213yescomplemented
50#14582777C2213yescomplemented
51#14582775C2213yes—
52#14582773C2213yescomplemented
53#14582770C2213yes—
54#14582770C2213yes—
55#14582767C2211yescharacteristic, complemented
56#14582761C2213yescomplemented
57#14582758C2213yescomplemented
58#14582756C2213yescomplemented
59#14582754C2213yes—
60C4⋊C4×Dic43C2213yescomplemented
61#14582750C2213yescomplemented
62C22⋊C4×Dic43C2213yes—
63#14582746C2213yes—
64#14582746C2213yes—
65#14582746C2213yescomplemented
66C42×Dic43C2211yescharacteristic, complemented
67C2×#126×C43C2211yescharacteristic
68C43×#389C2213yescomplemented
69C43×#388C2213yes—
70C43×#387C2213yescomplemented
71C43×#385C2213yes—
72C43×#384C2211yescharacteristic, complemented
73C43×#383C2211yescharacteristic, complemented
74C24×D43C2311yescharacteristic
75C22×D172C2313yes—
76C22×D172C2313yes—
77C22×D172C2313yes—
78C22×C22⋊D43C2313yes—
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—46no—
81C22×C4×D43C2313yes—
82C22×C4×D43C2311yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C22×C4×D43C2313yes—
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2313yes—
88#13063322C2×C418yescomplemented
89#13063319C2×C418yescomplemented
90#13063310C2×C4124yescomplemented
91#13063300C2×C4124yescomplemented
92#13063298C2×C4124yescomplemented
93#13063295C2×C4124yescomplemented
94#13063287—46no—
95#13063287—46no—
96#13063287—46no—
97(C22⋊D43)⋊C4—46no—
98C2×C4⋊Dic43C2313yes—
99C2×Dic43⋊C4C2313yes—
100C2×Dic43⋊C4C2313yes—
101C2×Dic43⋊C4C2313yes—
102C2×C22⋊Dic43C2313yes—
103C2×(C2×D43)⋊C4C2313yes—
104C2×(C2×D43)⋊C4C2313yes—
105C2×(C2×D43)⋊C4C2313yes—
106C2×(C2×D43)⋊C4C2313yes—
107C2×(C2×D43)⋊C4C2313yes—
108C2×(C2×D43)⋊C4C2313yes—
109C2×(C2×D43)⋊C4C2313yes—
110C2×(C2×D43)⋊C4C2313yes—
111C2×(C2×D43)⋊C4C2313yes—
112C2×(C2×D43)⋊C4C2313yes—
113C2×(C2×D43)⋊C4C2313yes—
114C2×(C2×D43)⋊C4C2313yes—
115C2×(C2×D43)⋊C4C2313yes—
116C2×C4×Dic43C2313yes—
117C2×C4×Dic43C2313yes—
118C2×C4×Dic43C2313yes—
119C2×C4×Dic43C2313yes—
120C2×C4×Dic43C2313yes—
121C42×D43—46no—
122C43⋊#95C2313yes—
123C43⋊#95C2313yes—
124C43⋊#95C2313yes—
125C43⋊#95C2313yes—
126C43⋊#95C2313yes—
127C43⋊#95C2313yes—
128C43⋊#95C2313yes—
129C43⋊#95C2313yes—
130C23×C4×C43C2311yescharacteristic
131#126×C43C2×C418yescomplemented
132C2×C4⋊C4×C43C2313yes—
133C2×C4⋊C4×C43C2313yes—
134C2×C4⋊C4×C43C2313yes—
135C2×C4⋊C4×C43C2313yes—
136C2×C22⋊C4×C43C2313yes—
137C2×C22⋊C4×C43C2313yes—
138C2×C42×C43C2313yes—
139C2×C42×C43C2311yescharacteristic
140#95×C43C2313yes—
141#95×C43C2313yes—
142#95×C43C2313yes—
143#95×C43C2313yes—
144C24×C43C2411yescharacteristic
145C23×D43—43no—
146C23×D43—43no—
147C23×D43C22×C414yes—
148C23×D43C2411yescharacteristic
149C23×D43C2411yescharacteristic
150C23×D43C2413yes—
151C22×C4×C43—43no—
152C22×C4×C43C2413yes—
153C22×C4×C43C2411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×C4×C43C2413yes—
156C22×C4×C43C2413yes—
157C22×C4×C43C2413yes—
158C2×C22⋊D43—43no—
159C2×C22⋊D43—43no—
160C2×C22⋊D43C22×C4112yes—
161C22×Dic43—26no—
162C22×Dic43C2413yes—
163C22×Dic43C2411yescharacteristic
164C22×Dic43C2413yes—
165C22×Dic43C2413yes—
166C22×Dic43C2411yescharacteristic
167C2×D172—43no—
168C2×D172—43no—
169C2×D172—43no—
170C2×D172—43no—
171C2×D172—43no—
172C2×D172—43no—
173C2×D172C22×C4112yes—
174C2×D172C22×C4112yes—
175C2×D172C22×C4112yescomplemented
176C2×C4×D43—26no—
177C2×C4×D43—26no—
178C2×C4×D43—26no—
179C2×C4×D43—26no—
180C2×C4×D43—26no—
181C2×C4×D43—43no—
182C2×C4×D43—43no—
183C2×C4×D43—43no—
184C2×C4×D43—43no—
185C2×C4×D43—43no—
186C2×C4×D43—43no—
187C2×C4×D43—43no—
188C2×C4×D43—416no—
189C2×C4×D43C22×C4112yescomplemented
190C4⋊C4×C43—43no—
191C4⋊C4×C43—43no—
192C4⋊C4×C43—43no—
193C4⋊C4×C43C22×C4112yescomplemented
194C22⋊C4×C43—43no—
195C22⋊C4×C43C22×C4112yes—
196C42×C43—43no—
197C42×C43C22×C414yescomplemented
198C22⋊Dic43—43no—
199(C2×D43)⋊C4—43no—
200(C2×D43)⋊C4—43no—
201(C2×D43)⋊C4—43no—
202(C2×D43)⋊C4—43no—
203(C2×D43)⋊C4—43no—
204(C2×D43)⋊C4—43no—
205(C2×D43)⋊C4—43no—
206(C2×D43)⋊C4—43no—
207(C2×D43)⋊C4—43no—
208(C2×D43)⋊C4—43no—
209(C2×D43)⋊C4C22×C4112yes—
210(C2×D43)⋊C4C22×C4112yes—
211(C2×D43)⋊C4C22×C4112yescomplemented
212C4⋊Dic43—43no—
213Dic43⋊C4—43no—
214Dic43⋊C4—43no—
215Dic43⋊C4C22×C4112yescomplemented
216C4×Dic43—26no—
217C4×Dic43—26no—
218C4×Dic43—26no—
219C4×Dic43—43no—
220C4×Dic43—43no—
221C23×C43—23no—
222C23×C43—23no—
223C23×C43C23×C412yes—
224C23×C43C2511yescharacteristic
225C22×D43—23no—
226C22×D43—23no—
227C22×D43—23no—
228C22×D43—23no—
229C22×D43—23no—
230C22×D43—23no—
231C22×D43—23no—
232C22×D43—23no—
233C22×D43—23no—
234C22×D43—23no—
235C22×D43—412no—
236C22×D43—44no—
237C22×D43—412no—
238C22×D43C23×C412yes—
239C22×D43C23×C412yes—
240C22×D43C23×C416yes—
241C2×C4×C43—23no—
242C2×C4×C43—23no—
243C2×C4×C43—23no—
244C2×C4×C43—23no—
245C2×C4×C43—23no—
246C2×C4×C43—23no—
247C2×C4×C43—23no—
248C2×C4×C43—23no—
249C2×C4×C43—23no—
250C2×C4×C43—23no—
251C2×C4×C43—23no—
252C2×C4×C43—23no—
253C2×C4×C43—44no—
254C2×C4×C43C23×C416yes—
255C2×C4×C43C23×C416yes—
256C22⋊D43—412no—
257C2×Dic43—23no—
258C2×Dic43—23no—
259C2×Dic43—23no—
260C2×Dic43—23no—
261C2×Dic43—23no—
262C2×Dic43—23no—
263C2×Dic43—23no—
264C2×Dic43—23no—
265C2×Dic43—23no—
266C2×Dic43—44no—
267C2×Dic43C23×C416yes—
268C2×Dic43H(5,𝔽2)16yes—
269D172—412no—
270D172—412no—
271D172—412no—
272C4×D43—412no—
273C4×D43—412no—
274C4×D43—44no—
275C4×D43—44no—
276C4×D43—412no—
277C4×D43—44no—
278C4×D43—44no—
279C4×#560—431nomaximal, Sylow
280C22×C43—26no—
281C22×C43—41no—
282C22×C43—43no—
283C22×C43C24×C411yescharacteristic
284C22×C43C2×H(5,𝔽2)13yes—
285C22×C43#58513yes—
286C2×D43—26no—
287C2×D43—26no—
288C2×D43—26no—
289C2×D43—26no—
290C2×D43—26no—
291C2×D43—416no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—43no—
295C2×D43—43no—
296C2×D43—43no—
297C2×D43—43no—
298C2×D43—43no—
299C2×D43—43no—
300C4×C43—26no—
301C4×C43—26no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—43no—
305C4×C43—43no—
306Dic43—26no—
307Dic43—41no—
308Dic43—43no—
309Dic43—43no—
310Dic43#56014yescomplemented
311C2×#560—431no—
312#2383—431no—
313#2383D4311yescharacteristic, complemented
314#2380—431no—
315#2377—433no—
316#2377—433no—
317#2376—433no—
318#2375—433no—
319C4×#127—431no—
320C4×#126—431no—
321C4×#126—431no—
322C4×#123—433no—
323C4×#121—433no—
324C4×#121—433no—
325C4×#120—433no—
326C2×C43—42no—
327C2×C43C4×H(5,𝔽2)13yes—
328C2×C43C2×#56011yescharacteristic
329C2×C43#352913yes—
330D43—46no—
331D43—42no—
332D43—42no—
333C24×C4—431no—
334#560—4316no—
335C2×#127—431no—
336C2×#126—431no—
337C2×#126C2×D4311yescharacteristic
338C2×#123—433no—
339C2×#121—433no—
340C2×#121—433no—
341C2×#120—433no—
342C2×C4×D4—433no—
343C2×C4×D4—433no—
344C2×C4×D4—433no—
345C2×C4×D4—433no—
346C22×C42—433no—
347#390—433no—
348#390—433no—
349#390—433no—
350#390—433no—
351#389—433no—
352#389C2×D4313yescomplemented
353#388—433no—
354#388—433no—
355#388—433no—
356#388—433no—
357#388—433no—
358#388—433no—
359#388—433no—
360#388C2×D4313yes—
361#387—433no—
362#387—433no—
363#387—433no—
364#387C2×D4313yescomplemented
365#386—433no—
366#386—433no—
367#386—433no—
368#386—433no—
369#386—433no—
370#386—433no—
371#386—433no—
372#386—433no—
373#385—433no—
374#385—433no—
375#385—433no—
376#385C2×D4313yes—
377#384C2×D4311yescharacteristic, complemented
378#383—431no—
379#383C2×D4311yescharacteristic, complemented
380#381—433no—
381#380—433no—
382#380—433no—
383#379—433no—
384C4×C4⋊C4—433no—
385C4×C4⋊C4—433no—
386C4×C22⋊C4—433no—
387C4×C22⋊C4—433no—
388C4×C22⋊C4—433no—
389C4×C22⋊C4—433no—
390C43—431no—
391C43C4×#56011yescharacteristic, complemented, Sylow
392C25—431no—
393C22×D4—433no—
394C22×D4—433no—
395C22×D4—433no—
396C22×D4—433no—
397C23×C4—433no—
398C23×C4—431no—
399C23×C4—433no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—431no—
404C23×C4—433no—
405C23×C4—1726no—
406C23×C4C22×D4311yescharacteristic
407#127—438no—
408#126—438no—
409#126C4×D4318yescomplemented
410#123—4324no—
411#121—4324no—
412#121—4324no—
413#120—4324no—
414C4×D4—1726no—
415C4×D4—1726no—
416C4×D4—1726no—
417C4×D4—1726no—
418C2×C4⋊C4—433no—
419C2×C4⋊C4—433no—
420C2×C4⋊C4—433no—
421C2×C4⋊C4—433no—
422C2×C4⋊C4C22×D4313yes—
423C2×C4⋊C4C22×D4313yes—
424C2×C4⋊C4C22×D4313yes—
425C2×C4⋊C4C22×D4313yes—
426C2×C22⋊C4—433no—
427C2×C22⋊C4—433no—
428C2×C22⋊C4—433no—
429C2×C22⋊C4—433no—
430C2×C22⋊C4—433no—
431C2×C22⋊C4—433no—
432C2×C22⋊C4—433no—
433C2×C22⋊C4—433no—
434C2×C22⋊C4—433no—
435C2×C22⋊C4—433no—
436C2×C22⋊C4—433no—
437C2×C22⋊C4—433no—
438C2×C22⋊C4—433no—
439C2×C22⋊C4—433no—
440C2×C22⋊C4C22×D4313yes—
441C2×C22⋊C4C22×D4313yes—
442C2×C42—433no—
443C2×C42—433no—
444C2×C42—433no—
445C2×C42—433no—
446C2×C42—433no—
447C2×C42—1726no—
448C2×C42C22×D4313yes—
449C2×C42C22×D4311yescharacteristic
450#95—433no—
451#95—433no—
452#95—433no—
453#95—433no—
454#95—433no—
455#95—433no—
456#95—433no—
457#95—433no—
458#95C22×D4313yes—
459#95C22×D4313yes—
460#95C22×D4313yes—
461#95C22×D4313yes—
462C24—431no—
463C24—431no—
464C24—433no—
465C24—434no—
466C24—1723no—
467C24—1723no—
468C24C23×D4311yescharacteristic
469C2×D4—4312no—
470C2×D4—4312no—
471C2×D4—4312no—
472C2×D4—4312no—
473C2×D4—1723no—
474C2×D4—1723no—
475C2×D4—1723no—
476C2×D4—1723no—
477C2×D4—1723no—
478C2×D4—1723no—
479C2×D4—1723no—
480C2×D4—1723no—
481C22×C4—43no—
482C22×C4—431no—
483C22×C4—433no—
484C22×C4—4312no—
485C22×C4—433no—
486C22×C4—431no—
487C22×C4—433no—
488C22×C4—866no—
489C22×C4—866no—
490C22×C4—866no—
491C22×C4—866no—
492C22×C4—866no—
493C22×C4—866no—
494C22×C4—1723no—
495C22×C4—1723no—
496C22×C4—1723no—
497C22×C4—1723no—
498C22×C4—1723no—
499C22×C4—1723no—
500C22×C4—1723no—
501C22×C4—17216no—
502C22×C4C23×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504C22×C4C23×D4313yes—
505C22×C4C23×D4313yes—
506C22×C4C23×D4313yes—
507C22×C4C23×D4313yes—
508C4⋊C4—43no—
509C4⋊C4—43no—
510C4⋊C4—43no—
511C4⋊C4—4312no—
512C4⋊C4—1723no—
513C4⋊C4—1723no—
514C4⋊C4—1723no—
515C4⋊C4C2×C4×D43112yescomplemented
516C22⋊C4—43no—
517C22⋊C4—4312no—
518C22⋊C4—4312no—
519C22⋊C4—4312no—
520C22⋊C4—1723no—
521C22⋊C4—1723no—
522C22⋊C4—1723no—
523C22⋊C4—1723no—
524C22⋊C4—1723no—
525C22⋊C4—1723no—
526C22⋊C4—1723no—
527C22⋊C4—1723no—
528C22⋊C4—1723no—
529C22⋊C4—1723no—
530C22⋊C4—1723no—
531C22⋊C4C2×C4×D43112yes—
532C42—43no—
533C42—866no—
534C42—866no—
535C42—866no—
536C42—1723no—
537C42—1723no—
538C42C2×C4×D4314yescomplemented
539C23—23no—
540C23—23no—
541C23—432no—
542C23—432no—
543C23—436no—
544C23—863no—
545C23—863no—
546C23—863no—
547C23—863no—
548C23—863no—
549C23—863no—
550C23—863no—
551C23—863no—
552C23—863no—
553C23—863no—
554C23—17212no—
555C23—1724no—
556C23—17212no—
557C23C22×C4×D4312yes—
558C23C24×D4311yescharacteristic
559D4—17212no—
560D4—17212no—
561D4—17212no—
562D4—17212no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—44no—
576C2×C4—436no—
577C2×C4—436no—
578C2×C4—863no—
579C2×C4—863no—
580C2×C4—863no—
581C2×C4—863no—
582C2×C4—863no—
583C2×C4—863no—
584C2×C4—863no—
585C2×C4—863no—
586C2×C4—863no—
587C2×C4—17212no—
588C2×C4—1724no—
589C2×C4—1724no—
590C2×C4—17212no—
591C2×C4—1724no—
592C2×C4—1724no—
593C2×C4—17212no—
594C2×C4—1724no—
595C2×C4C22×C4×D4316yes—
596C2×C4C22×C4×D4316yes—
597C22—26no—
598C22—41no—
599C22—43no—
600C22—866no—
601C22—866no—
602C22—866no—
603C22—866no—
604C22—866no—
605C22—17216no—
606C22—1721no—
607C22—1721no—
608C22—1723no—
609C22—1723no—
610C22—1723no—
611C22—1723no—
612C22—1723no—
613C22—1723no—
614C22C23×C4×D4311yescharacteristic
615C22H(5,𝔽2)×D4313yes—
616C22#1458373613yes—
617C4—26no—
618C4—26no—
619C4—41no—
620C4—41no—
621C4—43no—
622C4—43no—
623C4—434no—
624C4—866no—
625C4—1721no—
626C4—1723no—
627C4—1723no—
628C2—42no—
629C2—1722no—
630C2—1722no—
631C2—1726no—
632C2#1914780113yes—
633C2#560×D4311yescharacteristic
634C2#1914873613yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2383C2
socle, cosocleC23×C43C25
prime radicalC2×#14583640C2
hypercenter#2383D43
hypocenterC43C4×#560
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2383

Complements

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

NH ≅ G/Ntype
2. #19137788C2semidirect
3. #19137771C2semidirect
4. #19137751C2semidirect
5. #19137750C2semidirect
6. #19137740C2semidirect
7. #19137735C2semidirect
8. #19137157C2semidirect
9. #126×Dic43C2semidirect
10. #19137143C2semidirect
11. #19137116C2semidirect
12. #19137107C2semidirect
13. #19137103C2semidirect
14. #19137096C2semidirect
15. C43×#2383C2semidirect
17. #14583640C4semidirect
26. C2×#13063287C22semidirect
28. C2×C42×D43C22semidirect
31. #14582800C22semidirect
33. #14582794C22semidirect
37. #14582790C22semidirect
39. #14582789C22semidirect
41. #14582785C22semidirect
42. #14582781C22semidirect
43. #14582780C22semidirect
49. #14582777C22semidirect
50. #14582777C22semidirect
52. #14582773C22semidirect
55. #14582767C22semidirect
56. #14582761C22semidirect
57. #14582758C22semidirect
58. #14582756C22semidirect
60. C4⋊C4×Dic43C22semidirect
61. #14582750C22semidirect
65. #14582746C22semidirect
66. C42×Dic43C22semidirect
68. C43×#389C22semidirect
70. C43×#387C22semidirect
72. C43×#384C22semidirect
73. C43×#383C22semidirect
88. #13063322C2×C4semidirect
89. #13063319C2×C4semidirect
90. #13063310C2×C4semidirect
91. #13063300C2×C4semidirect
92. #13063298C2×C4semidirect
93. #13063295C2×C4semidirect
131. #126×C43C2×C4semidirect
175. C2×D172C22×C4semidirect
189. C2×C4×D43C22×C4semidirect
193. C4⋊C4×C43C22×C4semidirect
197. C42×C43C22×C4semidirect
211. (C2×D43)⋊C4C22×C4semidirect
215. Dic43⋊C4C22×C4semidirect
310. Dic43#560semidirect
313. #2383D43semidirect
352. #389C2×D43semidirect
364. #387C2×D43semidirect
377. #384C2×D43semidirect
379. #383C2×D43semidirect
391. C43C4×#560semidirect
409. #126C4×D43semidirect
515. C4⋊C4C2×C4×D43semidirect
538. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836402
#191377882
#191377712
#191377512
#191377502
#191377402
#191377352
#191371572
#126×Dic432
#191371432
#191371162
#191371072
#191371032
#191370962
C43×#23832
C4×#56043