Finite Group Databasebeta

← #25140957

Subgroups — #25140957

Order 11008.

754 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
1#19138890C211yesmaximal, characteristic
2#19137527C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136076C211yesmaximal, characteristic, complemented
5#19136034C211yesmaximal, characteristic, complemented
6#19136022C211yesmaximal, characteristic, complemented
7#19135166C211yesmaximal, characteristic, complemented
8#19134886C211yesmaximal, characteristic
9#19134791C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, characteristic, complemented
11#19134688C211yesmaximal, characteristic, complemented
12#19134684C211yesmaximal, characteristic, complemented
13#19134623C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27#14582828—21no—
28#14582816—21no—
29#14582797C2211yescharacteristic
30#14582790—21no—
31#14582788—21no—
32#14582785—21no—
33#14582784—21no—
34#14582777—21no—
35#14582765C2211yescharacteristic
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4×(C2×D43)⋊C4—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172D411yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C2×C8×D43—22no—
66C2×C8×D43—22no—
67C2×C8×D43—41no—
68C4×D172—22no—
69C4×D172—22no—
70#13063283—22no—
71#13063283—22no—
72#13063283—22no—
73#13063283—41no—
74C2×C4⋊Dic43D411yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C4⋊C4×D43—22no—
82C4⋊C4×D43—41no—
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)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063258—22no—
95#13063258—41no—
96#13063256—41no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—22no—
99(C2×D43)⋊C8—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43C2×D411yescharacteristic
121C23×D43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—22no—
136C2×D172—22no—
137C2×D172—41no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—81no—
151C2×C4×D43#4112yes—
152C2×C4×D43#4112yes—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43#4112yes—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—81no—
171(C2×D43)⋊C4—22no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—22no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191C4×Dic43—42no—
192C4×Dic43—42no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8#4112yes—
199C8×D43—44no—
200C23×C43C22×D411yescharacteristic
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43#12312yes—
214C22×D43#13512yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43#12312yes—
257D172—44no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—84no—
267C8×C43—41no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#24934—431nomaximal, Sylow
272C22×C43C2×#12311yescharacteristic
273C22×C43#54611yescharacteristic
274C22×C43#54711yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57611yescharacteristic
278C22×C43#57811yescharacteristic
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—42no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43#52911yescharacteristic
300C4×C43#53911yescharacteristic
301C4×C43#55111yescharacteristic
302C4×C43#55211yescharacteristic
303Dic43—22no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309#2485—431no—
310#2352—431no—
311#2101—431no—
312#2085—431no—
313#2077—431no—
314#2075—431no—
315#1921D4311yescharacteristic, complemented
316#1918—431no—
317#1869—431no—
318#1854—431no—
319#1852—431no—
320#1825—431no—
321#1824—431no—
322#1808—431no—
323#1735—431no—
324C2×C43#241911yescharacteristic
325C2×C43#309111yescharacteristic
326C2×C43#309811yescharacteristic
327C2×C43#330011yescharacteristic
328C2×C43#331911yescharacteristic
329C2×C43#333911yescharacteristic
330C2×C43#334911yescharacteristic
331D43—42no—
332D43—42no—
333C23×C8—431no—
334C2×C4×D4—431no—
335C2×#117—431no—
336C2×#117—431no—
337C22×C4⋊C4—431no—
338C2×#107—431no—
339C2×#107—431no—
340C2×#107C2×D4311yescharacteristic
341C2×#106—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—431no—
345#397—861no—
346#394—861no—
347#389—431no—
348#389C2×D4311yescharacteristic
349#388—861no—
350#388—861no—
351#387—861no—
352#387—861no—
353#386—861no—
354#382—431no—
355#380—431no—
356#380—431no—
357#380—431no—
358#380—431no—
359#380—431no—
360C4×C4⋊C4C2×D4311yescharacteristic
361C4×C22⋊C4—861no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#336—431no—
375#336C2×D4311yescharacteristic
376C43#2493411yescharacteristic, complemented, Sylow
377C22×D4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—861no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—862no—
384C22×C8—862no—
385C22×C8—1721no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C4×D4—862no—
389C4×D4—862no—
390#117—862no—
391#117—862no—
392#117—862no—
393#117—1721no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—1721no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—431no—
409C2×C22⋊C4—431no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—21no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421#107—22no—
422#107—862no—
423#107—1721no—
424#106—1721no—
425C22⋊C8—862no—
426C22⋊C8—862no—
427C22⋊C8—1721no—
428#95—21no—
429#95—21no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24—431no—
439C24—431no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—1721no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—431no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—3441no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4D4×D4311yescharacteristic
469C22×C4D4×D4311yescharacteristic
470C22×C4C23×D4311yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—432no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—1724no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—862no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—3441no—
502C4⋊C4—1722no—
503C4⋊C4#1062189812yes—
504C22⋊C4—862no—
505C22⋊C4—862no—
506C22⋊C4—3441no—
507C22⋊C4—3441no—
508C22⋊C4—3441no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—81no—
516C42—1722no—
517C42—1722no—
518C23—432no—
519C23—432no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23—861no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23C2×D4×D4311yescharacteristic
533D4—1724no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—432no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—3444no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062189811yescharacteristic
583C2×C4#1306337111yescharacteristic
584C2×C4#1306337311yescharacteristic
585C8—41no—
586C8—41no—
587C8—862no—
588C8—1721no—
589C22—862no—
590C22—862no—
591C22—862no—
592C22—862no—
593C22—862no—
594C22—862no—
595C22—1721no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22—1721no—
603C22#123×D4311yescharacteristic
604C22#1458354511yescharacteristic
605C22#1458355111yescharacteristic
606C22#135×D4311yescharacteristic
607C22#1458369511yescharacteristic
608C22#1458370311yescharacteristic
609C22#1458371211yescharacteristic
610C4—42no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—862no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—3441no—
621C4—1721no—
622C4#1458342711yescharacteristic
623C4#1458349711yescharacteristic
624C4#1458357411yescharacteristic
625C4#1458359011yescharacteristic
626C2—1722no—
627C2—1722no—
628C2#1913807711yescharacteristic
629C2#1914450711yescharacteristic
630C2#1914457411yescharacteristic
631C2#1914648711yescharacteristic
632C2#1914675611yescharacteristic
633C2#1914699411yescharacteristic
634C2#1914712211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenter#1921D43
hypocenterC43#24934
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
3. #19136164C2semidirect
4. #19136076C2semidirect
5. #19136034C2semidirect
6. #19136022C2semidirect
7. #19135166C2semidirect
9. #19134791C2semidirect
10. #19134781C2semidirect
11. #19134688C2semidirect
12. #19134684C2semidirect
13. #19134623C2semidirect
14. #19134310C2semidirect
15. C43×#1921C2semidirect
315. #1921D43semidirect
376. C43#24934semidirect

Maximal subgroups

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

subgroupindex
#191388902
#191375272
#191361642
#191360762
#191360342
#191360222
#191351662
#191348862
#191347912
#191347812
#191346882
#191346842
#191346232
#191343102
C43×#19212
#2493443