Finite Group Databasebeta

← #25165108

Subgroups — #25165108

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#19139105C211yesmaximal, characteristic, complemented
2#19137657C211yesmaximal, characteristic
3#19136001C211yesmaximal, characteristic, complemented
4#19135979C211yesmaximal, characteristic, complemented
5#19135828C211yesmaximal, characteristic
6#19135827C211yesmaximal, characteristic
7#19135278C211yesmaximal, characteristic, complemented
8#19135215C211yesmaximal, characteristic, complemented
9#19135169C211yesmaximal, characteristic, complemented
10#19135164C211yesmaximal, characteristic, complemented
11#19135152C211yesmaximal, characteristic, complemented
12#19134843C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134594C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C2×#13063321C2211yescharacteristic
17C2×#13063317—21no—
18C2×#13063287C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29#14582841—21no—
30#14582833—21no—
31#14582802C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582799—21no—
34#14582798C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582783—21no—
39#14582778—21no—
40#14582775—21no—
41#14582768C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063321—22no—
66#13063321—22no—
67#13063317—44no—
68#13063287—22no—
69#13063287—41no—
70C4×C22⋊D43—44no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—22no—
91#13063258—22no—
92Dic43⋊C8—41no—
93#13063247—22no—
94#13063247—41no—
95#13063246—22no—
96#13063246—41no—
97#13063245—22no—
98#13063245—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C4×D4×C43—22no—
111C4×D4×C43—41no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#102×C43—22no—
119#102×C43—22no—
120C4×C8×C43—41no—
121#95×C43—21no—
122C24×C43—21no—
123C23×D43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43#4112yes—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43—81no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C2×C22⋊D43—42no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—81no—
144C2×C22⋊D43—81no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172#4112yes—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
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#4112yes—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—42no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177C22⋊Dic43—42no—
178C22⋊Dic43—81no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—81no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189C4⋊Dic43—42no—
190Dic43⋊C4—41no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4D814yes—
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×C43—22no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
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—84no—
241C2×C4×C43C2×D812yes—
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C22⋊D43—48no—
249C22⋊D43—84no—
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—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43C2×D812yes—
270C2×Dic43C2×D812yes—
271D172—22no—
272D172—22no—
273D172—41no—
274D172—41no—
275C4×D43—84no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#26752—431nomaximal, Sylow
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43#52511yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43#54811yescharacteristic
291C22×C43C22×D811yescharacteristic
292C22×C43#57511yescharacteristic
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—42no—
304C4×C43—42no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#53911yescharacteristic
309C4×C43#55211yescharacteristic
310C4×C43#55311yescharacteristic
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
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#1918—431no—
328#1916—431no—
329#1862—431no—
330#1862—431no—
331#1802—431no—
332C4×#102D4311yescharacteristic, complemented
333C2×C43—82no—
334C2×C43#246011yescharacteristic
335C2×C43#310011yescharacteristic
336C2×C43#312311yescharacteristic
337C2×C43#329411yescharacteristic
338C2×C43#331711yescharacteristic
339C2×C43#335811yescharacteristic
340C2×C43#337111yescharacteristic
341D43—82no—
342C2×#127—431no—
343C2×#125—861no—
344C2×C4×D4—431no—
345C2×C4×D4—861no—
346C2×C4×D4C2×D4311yescharacteristic
347C2×#107—431no—
348C2×#107—431no—
349C2×C4⋊C8—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×#102C2×D4311yescharacteristic
358C2×C4×C8C2×D4311yescharacteristic
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#389—431no—
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#340—431no—
379#340C2×D4311yescharacteristic
380#340C2×D4311yescharacteristic
381#336—431no—
382#336—431no—
383#336—431no—
384#336—431no—
385C43#2675211yescharacteristic, complemented, Sylow
386C22×D4—431no—
387C22×D4—861no—
388C22×D4—861no—
389C22×D4C22×D4311yescharacteristic
390C23×C4—21no—
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—22no—
400C4×D4—41no—
401C4×D4—862no—
402C4×D4—1721no—
403C4×D4—1724no—
404C2×C4⋊C4—431no—
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⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
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—862no—
430#107—862no—
431C4⋊C8—1721no—
432#102—22no—
433#102—22no—
434#102—862no—
435#102—862no—
436#102—862no—
437#102—862no—
438#102—1721no—
439#102—1721no—
440C4×C8—41no—
441#95—21no—
442#95—431no—
443#95—431no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449C24—21no—
450C24—861no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—432no—
457C2×D4—864no—
458C2×D4—864no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—3441no—
465C2×D4—3441no—
466C2×D4—1722no—
467C2×D4—1722no—
468C2×D4#1062189812yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—81no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—3441no—
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—434no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1721no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4#1062189812yes—
519C4⋊C4#1062189812yes—
520C22⋊C4—42no—
521C22⋊C4—3441no—
522C22⋊C4—3441no—
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—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23C2×D4×D4311yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—862no—
554D4—862no—
555D4—3444no—
556D4—1728no—
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—84no—
574C2×C4—432no—
575C2×C4—432no—
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—3444no—
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—1721no—
596C2×C4D8×D4312yes—
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4C2×#1062189811yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C2×C4#1306337011yescharacteristic
602C2×C4#1306337211yescharacteristic
603C8—41no—
604C8—41no—
605C8—1721no—
606C8—1721no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22#1458340811yescharacteristic
622C22#1458353911yescharacteristic
623C22#1458355811yescharacteristic
624C22C2×D8×D4311yescharacteristic
625C22#1458369611yescharacteristic
626C22#1458370511yescharacteristic
627C22#1458370611yescharacteristic
628C4—22no—
629C4—42no—
630C4—42no—
631C4—41no—
632C4—81no—
633C4—862no—
634C4—862no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—1721no—
639C4—1721no—
640C4#1458343311yescharacteristic
641C4#1458349111yescharacteristic
642C4#1458358811yescharacteristic
643C4#1458359911yescharacteristic
644C2—82no—
645C2—3442no—
646C2#1913854711yescharacteristic
647C2#1914459311yescharacteristic
648C2#1914484411yescharacteristic
649C2#1914640411yescharacteristic
650C2#1914671711yescharacteristic
651C2#1914722811yescharacteristic
652C2#1914735911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenterC4×#102D43
hypocenterC43#26752
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #19139105C2semidirect
3. #19136001C2semidirect
4. #19135979C2semidirect
7. #19135278C2semidirect
8. #19135215C2semidirect
9. #19135169C2semidirect
10. #19135164C2semidirect
11. #19135152C2semidirect
12. #19134843C2semidirect
13. #19134842C2semidirect
14. #19134594C2semidirect
15. C4×#102×C43C2semidirect
332. C4×#102D43semidirect
385. C43#26752semidirect

Maximal subgroups

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

subgroupindex
#191391052
#191376572
#191360012
#191359792
#191358282
#191358272
#191352782
#191352152
#191351692
#191351642
#191351522
#191348432
#191348422
#191345942
C4×#102×C432
#2675243