Finite Group Databasebeta

← #25200138

Subgroups — #25200138

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142936C211yesmaximal, characteristic
2#19137133C211yesmaximal, characteristic
3#19136019C211yesmaximal, characteristic
4#19135790C211yesmaximal, characteristic
5#19135790C211yesmaximal, characteristic
6#19135602C211yesmaximal, characteristic
7#19135323C211yesmaximal, characteristic, complemented
8#19135274C211yesmaximal, characteristic, complemented
9#19135274C211yesmaximal, characteristic, complemented
10#19135231C211yesmaximal, characteristic, complemented
11#19135168C211yesmaximal, characteristic, complemented
12#19134938C211yesmaximal, characteristic, complemented
13#19134865C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic
15C43×#1969C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C42×D43C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582806C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582786—21no—
34#14582782—21no—
35#14582781—21no—
36#14582773—21no—
37#14582773—21no—
38#14582761—21no—
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42#14582750—21no—
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063301—22no—
65#13063301—22no—
66#13063301—41no—
67#13063301—41no—
68Q8×Dic43—41no—
69Q8×Dic43—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
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×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89C42×D43—41no—
90C42×D43—41no—
91#13063257—22no—
92#13063257—41no—
93#13063249—22no—
94#13063249—22no—
95#13063249—41no—
96#13063249—41no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—22no—
99C4×C43⋊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×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C2×Q16×C43—22no—
111C2×Q16×C43—22no—
112C2×Q16×C43—41no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#103×C43—22no—
120#103×C43—22no—
121C4×C8×C43—41no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165Q16×C43—44no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43#4112yes—
171C2×C8×C43#4112yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—42no—
190C4⋊Dic43—42no—
191C4⋊Dic43#4112yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C23×C43C22×D411yescharacteristic
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43#13512yes—
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
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#13712yes—
241C2×C4×C43#13712yes—
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
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—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43#13512yes—
269C4×D43—44no—
270C4×D43—44no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C8×C43—22no—
276C8×C43—22no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#29463—431nomaximal, Sylow
280C22×C43#52511yescharacteristic
281C22×C43#53211yescharacteristic
282C22×C43#53411yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×#13711yescharacteristic
286C22×C43C2×#13711yescharacteristic
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C4×C43—22no—
295C4×C43—22no—
296C4×C43—42no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43#55111yescharacteristic
301C4×C43#55311yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55911yescharacteristic
304Dic43—22no—
305Dic43—42no—
306Dic43—41no—
307Dic43—41no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311#2855—431no—
312C4×C22⋊Q8—431no—
313#2075—431no—
314#2035—431no—
315#2035—431no—
316#2001—431no—
317#1969D4311yescharacteristic, complemented
318#1941—431no—
319#1933—431no—
320#1933—431no—
321#1927—431no—
322#1918—431no—
323#1878—431no—
324#1865—431no—
325C4×C22⋊C8—431no—
326C2×C43#260211yescharacteristic
327C2×C43#310711yescharacteristic
328C2×C43#310811yescharacteristic
329C2×C43#316811yescharacteristic
330C2×C43#318511yescharacteristic
331C2×C43#319011yescharacteristic
332C2×C43#319011yescharacteristic
333D43—42no—
334C22×Q16C2×D4311yescharacteristic
335C2×C22⋊Q8—431no—
336C2×C22⋊Q8—431no—
337C2×C4×Q8—431no—
338C22×C42—431no—
339C2×#107C2×D4311yescharacteristic
340C2×#106—431no—
341C2×#106—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103C2×D4311yescharacteristic
347C2×#103C2×D4311yescharacteristic
348C2×C22⋊C8—431no—
349C2×C22⋊C8—431no—
350C2×C4×C8—431no—
351C2×C4×C8C2×D4311yescharacteristic
352#391—431no—
353#391C2×D4311yescharacteristic
354#391C2×D4311yescharacteristic
355#389—431no—
356#389—431no—
357#389—431no—
358#387—861no—
359#387—861no—
360#387—861no—
361#385—861no—
362#385—861no—
363#381—861no—
364#380—431no—
365#380—431no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—861no—
368C4×C22⋊C4—861no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#336—431no—
376#336—431no—
377C43#2946311yescharacteristic, complemented, Sylow
378C22×Q8C22×D4311yescharacteristic
379C22×Q8C22×D4311yescharacteristic
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C2×Q16—22no—
384C2×Q16—22no—
385C2×Q16—41no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8—1721no—
393C22⋊Q8—1721no—
394C4×Q8—1721no—
395C4×Q8—1721no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42—1721no—
418C2×C42—1721no—
419C2×C42C22×D4311yescharacteristic
420#107—22no—
421#106—862no—
422#106—1721no—
423#103—22no—
424#103—22no—
425#103—862no—
426#103—862no—
427#103—1721no—
428#103—1721no—
429C22⋊C8—862no—
430C22⋊C8—862no—
431C4×C8—41no—
432C4×C8—1721no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—431no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8#1062189812yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—861no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—1721no—
480C22×C4—1721no—
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484Q16—44no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8#1062190012yes—
496C2×C8#1062190012yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—432no—
502C4⋊C4—864no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C22⋊C4—864no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—861no—
522C42—861no—
523C42—1721no—
524C42—1721no—
525C42—1722no—
526C42—1722no—
527C23—432no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23C2×D4×D4311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—432no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—862no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—1724no—
570C2×C4—1724no—
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—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4#1306335712yes—
587C2×C4#1306335712yes—
588C2×C4#41×D4311yescharacteristic
589C2×C4C2×#1062190011yescharacteristic
590C2×C4C2×#1062190011yescharacteristic
591C2×C4C2×#1062189811yescharacteristic
592C2×C4#1306337011yescharacteristic
593C2×C4#1306337111yescharacteristic
594C8—22no—
595C8—22no—
596C8—1721no—
597C8—1721no—
598C22—862no—
599C22—862no—
600C22—862no—
601C22—1721no—
602C22—1721no—
603C22—1721no—
604C22—1721no—
605C22#1458340811yescharacteristic
606C22#1458344711yescharacteristic
607C22#1458345711yescharacteristic
608C22#135×D4311yescharacteristic
609C22#135×D4311yescharacteristic
610C22C2×#1306335711yescharacteristic
611C22C2×#1306335711yescharacteristic
612C4—22no—
613C4—22no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—862no—
619C4—3441no—
620C4—3441no—
621C4—3441no—
622C4—1721no—
623C4—1721no—
624C4—1722no—
625C4#1458357511yescharacteristic
626C4#1458359211yescharacteristic
627C4#1458359511yescharacteristic
628C4#1458363111yescharacteristic
629C2—1722no—
630C2#1914020411yescharacteristic
631C2#1914466411yescharacteristic
632C2#1914467911yescharacteristic
633C2#1914516211yescharacteristic
634C2#1914533811yescharacteristic
635C2#1914537711yescharacteristic
636C2#1914537711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1969C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1969D43
hypocenterC43#29463
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
7. #19135323C2semidirect
8. #19135274C2semidirect
9. #19135274C2semidirect
10. #19135231C2semidirect
11. #19135168C2semidirect
12. #19134938C2semidirect
13. #19134865C2semidirect
15. C43×#1969C2semidirect
317. #1969D43semidirect
377. C43#29463semidirect

Maximal subgroups

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

subgroupindex
#191429362
#191371332
#191360192
#191357902
#191356022
#191353232
#191352742
#191352312
#191351682
#191349382
#191348652
C4×(C2×D43)⋊C82
C43×#19692
#2946343