Finite Group Databasebeta

← #25199732

Subgroups — #25199732

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140556C211yesmaximal, characteristic, complemented
2#19137238C211yesmaximal, characteristic, complemented
3#19136090C211yesmaximal, characteristic, complemented
4#19135979C211yesmaximal, characteristic, complemented
5#19135979C211yesmaximal, characteristic, complemented
6#19135903C211yesmaximal, characteristic
7#19135462C211yesmaximal, characteristic
8#19135327C211yesmaximal, characteristic, complemented
9#19135294C211yesmaximal, characteristic, complemented
10#19135289C211yesmaximal, characteristic, complemented
11#19135212C211yesmaximal, characteristic, complemented
12#19135188C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134451C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic
16C2×#13063259C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×Dic43⋊C8C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582827—21no—
28#14582827—21no—
29#14582824—21no—
30#14582822—21no—
31#14582802C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582792—21no—
41#14582792—21no—
42#14582762—21no—
43#14582759—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45#14582745C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×D8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2311yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81#13063259—22no—
82#13063258—22no—
83#13063258—41no—
84Dic43⋊C8—22no—
85Dic43⋊C8—22no—
86#13063246—22no—
87#13063246—22no—
88#13063246—22no—
89#13063246—41no—
90#13063235—41no—
91C8×Dic43—41no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95D411yescharacteristic
99C43⋊#95D411yescharacteristic
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C23×C4×C43—21no—
105C2×D8×C43—22no—
106C2×D8×C43—22no—
107C2×D8×C43—41no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#102×C43—22no—
119#102×C43—41no—
120C24×C43—21no—
121C24×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43#4112yes—
134C22×C4×C43—24no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—81no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150D8×C43—44no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43#4112yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43#4112yes—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—81no—
163C22⋊C4×C43—81no—
164C42×C43—21no—
165C42×C43—21no—
166C22⋊Dic43—81no—
167C22⋊Dic43—81no—
168C22⋊Dic43—81no—
169C22⋊Dic43—81no—
170C22⋊Dic43—81no—
171C22⋊Dic43—81no—
172C22⋊Dic43—81no—
173C22⋊Dic43—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—81no—
183C4⋊Dic43—81no—
184C4⋊Dic43—81no—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—81no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8#4112yes—
198C23×C43—22no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43C22×D411yescharacteristic
213D4×C43—22no—
214D4×C43—22no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—84no—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C8×C43—22no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268#29436—431nomaximal, Sylow
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43#52511yescharacteristic
284C22×C43#53211yescharacteristic
285C22×C43#53711yescharacteristic
286C22×C43#57611yescharacteristic
287C22×C43#57611yescharacteristic
288C22×C43#57611yescharacteristic
289C22×C43#57811yescharacteristic
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43#55111yescharacteristic
295C4×C43#55211yescharacteristic
296C4×C43#55311yescharacteristic
297C4×C43#55611yescharacteristic
298Dic43—41no—
299Dic43—41no—
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305Dic43—81no—
306#2644—431no—
307#2319—431no—
308#2087—431no—
309#2067—431no—
310#2067—431no—
311#2054—431no—
312#1970—431no—
313#1942—431no—
314#1936—431no—
315#1936—431no—
316#1925—431no—
317#1921—431no—
318#1879D4311yescharacteristic
319#1862—431no—
320#1768—431no—
321C2×C43—82no—
322C2×C43—161no—
323C2×C43#260111yescharacteristic
324C2×C43#312211yescharacteristic
325C2×C43#312411yescharacteristic
326C2×C43#317511yescharacteristic
327C2×C43#317611yescharacteristic
328C2×C43#325911yescharacteristic
329C2×C43#326211yescharacteristic
330C22×D8C2×D4311yescharacteristic
331C2×C4×D4C2×D4311yescharacteristic
332C2×#107—431no—
333C2×#107—431no—
334C2×#107—431no—
335C2×C4⋊C8—431no—
336C2×C4⋊C8—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102C2×D4311yescharacteristic
342C2×#102C2×D4311yescharacteristic
343C2×#97—431no—
344C2×C4×C8—431no—
345#397—861no—
346#397—861no—
347#397—861no—
348#396—861no—
349#390—431no—
350#390—431no—
351#390—431no—
352#390—431no—
353#390C2×D4311yescharacteristic
354#389—431no—
355#389—431no—
356#389—431no—
357#389—431no—
358#389—431no—
359#388—861no—
360#388—861no—
361#381—861no—
362#380—861no—
363C4×C4⋊C4—431no—
364#376—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#336—431no—
372#336C2×D4311yescharacteristic
373C43#2943611yescharacteristic, complemented, Sylow
374C22×D4C22×D4311yescharacteristic
375C22×D4C22×D4311yescharacteristic
376C23×C4—21no—
377C2×D8—22no—
378C2×D8—22no—
379C2×D8—41no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C4×D4—22no—
385C4×D4—22no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412#107—862no—
413#107—862no—
414#107—1721no—
415C4⋊C8—862no—
416C4⋊C8—862no—
417#102—22no—
418#102—41no—
419#102—862no—
420#102—862no—
421#102—862no—
422#102—1721no—
423#97—1721no—
424C4×C8—1721no—
425#95—431no—
426#95—431no—
427#95—431no—
428#95—431no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24—21no—
436C24—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4#1062190012yes—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4D4×D4311yescharacteristic
463C22×C4D4×D4311yescharacteristic
464C22×C4C23×D4311yescharacteristic
465D8—44no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8#1062189812yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—3441no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4#1062190012yes—
495C22⋊C4—24no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—3441no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C22⋊C4—3441no—
505C22⋊C4—3441no—
506C42—21no—
507C42—21no—
508C42—861no—
509C42—861no—
510C42—861no—
511C42—861no—
512C42—3441no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C2×D4×D4311yescharacteristic
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—1721no—
562C2×C4—1721no—
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#41×D4311yescharacteristic
574C2×C4C2×#1062190011yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C2×C4C2×#1062189811yescharacteristic
577C2×C4#1306337011yescharacteristic
578C2×C4#1306337211yescharacteristic
579C8—22no—
580C8—41no—
581C8—862no—
582C8—1721no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#1458340511yescharacteristic
598C22#1458344611yescharacteristic
599C22#1458347811yescharacteristic
600C22#1458370011yescharacteristic
601C22#1458370311yescharacteristic
602C22#1458370311yescharacteristic
603C22#1458371311yescharacteristic
604C4—41no—
605C4—42no—
606C4—41no—
607C4—81no—
608C4—3441no—
609C4—3441no—
610C4—3441no—
611C4—3441no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4—1721no—
616C4#1458357511yescharacteristic
617C4#1458358611yescharacteristic
618C4#1458359611yescharacteristic
619C4#1458361911yescharacteristic
620C2—82no—
621C2—161no—
622C2#1914018811yescharacteristic
623C2#1914483211yescharacteristic
624C2#1914485011yescharacteristic
625C2#1914523011yescharacteristic
626C2#1914524311yescharacteristic
627C2#1914603211yescharacteristic
628C2#1914605311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#1879D43
hypocenterC43#29436
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. #19140556C2semidirect
2. #19137238C2semidirect
3. #19136090C2semidirect
4. #19135979C2semidirect
5. #19135979C2semidirect
8. #19135327C2semidirect
9. #19135294C2semidirect
10. #19135289C2semidirect
11. #19135212C2semidirect
12. #19135188C2semidirect
13. #19134842C2semidirect
14. #19134451C2semidirect
373. C43#29436semidirect

Maximal subgroups

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

subgroupindex
#191405562
#191372382
#191360902
#191359792
#191359032
#191354622
#191353272
#191352942
#191352892
#191352122
#191351882
#191348422
#191344512
C43×#18792
#2943643