Finite Group Databasebeta

← #25165107

Subgroups — #25165107

Order 11008.

832 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#19139114C211yesmaximal, characteristic, complemented
2#19137659C211yesmaximal, characteristic
3#19136002C211yesmaximal, characteristic, complemented
4#19135978C211yesmaximal, characteristic, complemented
5#19135830C211yesmaximal, characteristic
6#19135829C211yesmaximal, characteristic
7#19135279C211yesmaximal, characteristic, complemented
8#19135214C211yesmaximal, characteristic, complemented
9#19135166C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134843C211yesmaximal, characteristic, complemented
12#19134843C211yesmaximal, characteristic, complemented
13#19134594C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1918C211yesmaximal, characteristic, complemented
16C2×#13063322C2211yescharacteristic
17C2×#13063316—21no—
18C2×C4×D172—21no—
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582841—21no—
33#14582832—21no—
34#14582801—21no—
35#14582800C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582786—21no—
41#14582777—21no—
42#14582777—21no—
43#14582768C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063322—22no—
68#13063322—22no—
69#13063316—44no—
70C4×D172—44no—
71#13063287—22no—
72#13063287—22no—
73#13063287—41no—
74#13063287—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊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)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—22no—
94Dic43⋊C8—41no—
95#13063247—22no—
96#13063247—22no—
97#13063247—41no—
98#13063247—41no—
99#13063245—22no—
100#13063245—22no—
101#13063245—22no—
102#13063245—22no—
103C8×Dic43—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#107×C43—22no—
120#95×C43—21no—
121#95×C43—21no—
122C23×D43—21no—
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C2×D172—24no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—24no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—42no—
150C2×D172—42no—
151C2×D172—81no—
152C2×D172—81no—
153C2×D172#4112yes—
154C2×D172#4112yes—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
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—42no—
174C4⋊C4×C43#4112yes—
175C4⋊C4×C43#4112yes—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43—42no—
191C4⋊Dic43—42no—
192C4⋊Dic43D814yes—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C23×C43C22×D411yescharacteristic
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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×C43C2×D812yes—
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
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—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43C2×D812yes—
263C2×Dic43C2×D812yes—
264D172—22no—
265D172—22no—
266D172—22no—
267D172—22no—
268D172—48no—
269D172—41no—
270D172—41no—
271D172—41no—
272D172—41no—
273D172—84no—
274C4×D43—84no—
275C4×D43—84no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#26752—431nomaximal, Sylow
281C22×C43#52511yescharacteristic
282C22×C43#54611yescharacteristic
283C22×C43#54811yescharacteristic
284C22×C43C22×D811yescharacteristic
285C22×C43#57511yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57711yescharacteristic
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C4×C43—22no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—42no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#52911yescharacteristic
309C4×C43#53911yescharacteristic
310C4×C43#55211yescharacteristic
311C4×C43#55311yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—41no—
315Dic43—41no—
316Dic43—81no—
317Dic43—81no—
318#2506—431no—
319#2366—431no—
320#2071—431no—
321#2067—431no—
322#2041—431no—
323#2041—431no—
324#1934—431no—
325#1925—431no—
326#1918—431no—
327#1918D4311yescharacteristic, complemented
328#1916—431no—
329#1862—431no—
330#1862—431no—
331#1802—431no—
332C4×#102—431no—
333C2×C43#246011yescharacteristic
334C2×C43#310011yescharacteristic
335C2×C43#312311yescharacteristic
336C2×C43#329411yescharacteristic
337C2×C43#331711yescharacteristic
338C2×C43#335811yescharacteristic
339C2×C43#337111yescharacteristic
340D43—82no—
341D43—82no—
342C2×#127—431no—
343C2×#125—861no—
344C2×C4×D4—431no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C2×#107—431no—
348C2×#107C2×D4311yescharacteristic
349C2×C4⋊C8—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×C4×C8—431no—
359#400—861no—
360#398—861no—
361#390—431no—
362#390—431no—
363#390—861no—
364#389—431no—
365#389—431no—
366#389—431no—
367#389C2×D4311yescharacteristic
368#387—861no—
369#386—861no—
370#386—861no—
371#384—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4C2×D4311yescharacteristic
375#340—431no—
376#340—431no—
377#340—431no—
378#340C2×D4311yescharacteristic
379#340C2×D4311yescharacteristic
380#340C2×D4311yescharacteristic
381#336—431no—
382#336—431no—
383#336—431no—
384#336C2×D4311yescharacteristic
385C43#2675211yescharacteristic, complemented, Sylow
386C22×D4—431no—
387C22×D4—431no—
388C22×D4—861no—
389C22×D4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8C22×D4311yescharacteristic
395C22×C8C22×D4311yescharacteristic
396#127—862no—
397#127—862no—
398#125—1724no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—1724no—
402C4×D4—1721no—
403C4×D4—1721no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
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—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—21no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429#107—22no—
430#107—862no—
431C4⋊C8—1721no—
432#102—862no—
433#102—862no—
434#102—862no—
435#102—862no—
436#102—862no—
437#102—862no—
438#102—1721no—
439#102—1721no—
440C4×C8—1721no—
441#95—21no—
442#95—21no—
443#95—431no—
444#95—431no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449C24—861no—
450C24—861no—
451C2×D4—432no—
452C2×D4—432no—
453C2×D4—864no—
454C2×D4—864no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—3441no—
466C2×D4—3441no—
467C2×D4—1722no—
468C2×D4—1722no—
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—3441no—
480C22×C4—3441no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4D4×D4311yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4C23×D4311yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—434no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1721no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4#1062189812yes—
519C4⋊C4#1062190212yes—
520C22⋊C4—3441no—
521C22⋊C4—3441no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—861no—
533C42—1722no—
534C23—862no—
535C23—862no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23C2×D4×D4311yescharacteristic
549D4—862no—
550D4—862no—
551D4—862no—
552D4—862no—
553D4—3444no—
554D4—1728no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
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—41no—
575C2×C4—41no—
576C2×C4—432no—
577C2×C4—432no—
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—861no—
588C2×C4—3444no—
589C2×C4—3444no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4D8×D4312yes—
597C2×C4#41×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4C2×#1062189811yescharacteristic
600C2×C4C2×#1062190211yescharacteristic
601C2×C4#1306337111yescharacteristic
602C2×C4#1306337211yescharacteristic
603C8—41no—
604C8—41no—
605C8—1721no—
606C8—1721no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22#1458340711yescharacteristic
622C22#1458354011yescharacteristic
623C22#1458355811yescharacteristic
624C22C2×D8×D4311yescharacteristic
625C22#1458369811yescharacteristic
626C22#1458370611yescharacteristic
627C22#1458370811yescharacteristic
628C4—22no—
629C4—41no—
630C4—42no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—862no—
635C4—862no—
636C4—3441no—
637C4—3441no—
638C4—1721no—
639C4—1721no—
640C4#1458343611yescharacteristic
641C4#1458349011yescharacteristic
642C4#1458358711yescharacteristic
643C4#1458359311yescharacteristic
644C2—3442no—
645C2—3442no—
646C2#1913854611yescharacteristic
647C2#1914459211yescharacteristic
648C2#1914484311yescharacteristic
649C2#1914640511yescharacteristic
650C2#1914671811yescharacteristic
651C2#1914722811yescharacteristic
652C2#1914736411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1918C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#1918D43
hypocenterC43#26752
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
1. #19139114C2semidirect
3. #19136002C2semidirect
4. #19135978C2semidirect
7. #19135279C2semidirect
8. #19135214C2semidirect
9. #19135166C2semidirect
10. #19135151C2semidirect
11. #19134843C2semidirect
12. #19134843C2semidirect
13. #19134594C2semidirect
14. #19134409C2semidirect
15. C43×#1918C2semidirect
327. #1918D43semidirect
385. C43#26752semidirect

Maximal subgroups

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

subgroupindex
#191391142
#191376592
#191360022
#191359782
#191358302
#191358292
#191352792
#191352142
#191351662
#191351512
#191348432
#191345942
#191344092
C43×#19182
#2675243