Finite Group Databasebeta

← #25157035

Subgroups — #25157035

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583006C211yesmaximal, characteristic, complemented
2#19138389C211yesmaximal, characteristic
3#19137513C211yesmaximal, characteristic, complemented
4#19136118C211yesmaximal, characteristic
5#19136093C211yesmaximal, characteristic, complemented
6#19136016C211yesmaximal, characteristic, complemented
7#19135831C211yesmaximal, characteristic
8#19135289C211yesmaximal, characteristic
9#19135156C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic
11#19134952C211yesmaximal, characteristic
12#19134938C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14#19134847C211yesmaximal, characteristic, complemented
15C2×C43×#464C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19#14583006—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29#14582835—21no—
30#14582824—21no—
31#14582806C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582797—21no—
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795—21no—
38#14582795C2211yescharacteristic
39#14582787—21no—
40#14582787—21no—
41#14582764—21no—
42#14582764C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×Q16×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#464—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63Q8×Dic43—22no—
64Q8×Dic43—22no—
65Q8×Dic43—22no—
66Q8×Dic43—22no—
67Q8×Dic43—41no—
68Q8×Dic43—41no—
69C2×C4⋊Dic43—21no—
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⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—41no—
91#13063257—22no—
92#13063249—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249—22no—
96#13063246—22no—
97#13063246—41no—
98#13063235—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C2×Q16×C43—22no—
112C2×Q16×C43—22no—
113C2×Q16×C43D414yes—
114C2×SD16×C43—22no—
115C2×SD16×C43—22no—
116C2×SD16×C43—22no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119#124×C43—22no—
120#124×C43—41no—
121C4×Q8×C43—22no—
122C4×Q8×C43—41no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130#103×C43—22no—
131#102×C43—22no—
132C24×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—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C2×D412yes—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C2×Q8×C43#4112yes—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165Q16×C43—28no—
166SD16×C43—44no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D412yes—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—42no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—42no—
181C22⋊Dic43—42no—
182C22⋊Dic43—42no—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185C4⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43—42no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201C4×Dic43—24no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43#12314yes—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C8×C43—22no—
280C8×C43—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283#26189—431nomaximal, Sylow
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43#52511yescharacteristic
292C22×C43D4211yescharacteristic
293C22×C43#54811yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57511yescharacteristic
296C22×C43#57711yescharacteristic
297C22×C43#57811yescharacteristic
298C4×C43—24no—
299C4×C43—42no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43C2×#12311yescharacteristic
304C4×C43#53911yescharacteristic
305C4×C43#54711yescharacteristic
306C4×C43#55311yescharacteristic
307Dic43—41no—
308Dic43—42no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315C2×#464D4311yescharacteristic
316C2×#441—431no—
317#2448—431no—
318#2351—431no—
319#2092—431no—
320#2088—431no—
321#2074—431no—
322#2042—431no—
323#1936—431no—
324#1917—431no—
325#1880—431no—
326#1880—431no—
327#1878—431no—
328#1863—431no—
329#1863—431no—
330C2×C43—161no—
331C2×C43#244311yescharacteristic
332C2×C43#311111yescharacteristic
333C2×C43#312111yescharacteristic
334C2×C43#327111yescharacteristic
335C2×C43#327711yescharacteristic
336C2×C43#337111yescharacteristic
337C2×C43#337711yescharacteristic
338C22×Q16C2×D4311yescharacteristic
339C22×SD16C2×D4311yescharacteristic
340C2×#124C2×D4311yescharacteristic
341C2×C4×Q8—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8C2×D4311yescharacteristic
345#464—24no—
346#441—864no—
347C2×#107—431no—
348C2×#106—431no—
349C2×C4⋊C8C2×D4311yescharacteristic
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103C2×D4311yescharacteristic
355C2×#102—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#97—431no—
359#399—861no—
360#397—861no—
361#391—431no—
362#390—431no—
363#390—431no—
364#389—431no—
365#389—431no—
366#389—431no—
367#389—861no—
368#389—861no—
369#388—861no—
370#388—861no—
371#382—431no—
372#382—861no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—861no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#336—431no—
380#336—431no—
381#336—431no—
382#336—431no—
383C43#2618911yescharacteristic, complemented, Sylow
384C22×Q8C22×D4311yescharacteristic
385C22×Q8C22×D4311yescharacteristic
386C22×D4C22×D4311yescharacteristic
387C2×Q16—22no—
388C2×Q16—22no—
389C2×Q16C22⋊D4314yes—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—22no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#124—22no—
398#124—41no—
399C4×Q8—22no—
400C4×Q8—41no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—21no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#107—1721no—
435#106—862no—
436C4⋊C8—22no—
437#103—22no—
438#103—862no—
439#103—862no—
440#103—862no—
441#103—862no—
442#102—22no—
443#102—862no—
444#102—1721no—
445#97—862no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455C24—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8#1062190012yes—
465C2×Q8#1062190012yes—
466C2×Q8C2×C22⋊D4312yes—
467C2×Q8C2×C22⋊D4312yes—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4D4×D4311yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4C23×D4311yescharacteristic
488Q16—28no—
489SD16—44no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8C2×C22⋊D4312yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—432no—
506C4⋊C4—864no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—3441no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—3441no—
524C22⋊C4—3441no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—864no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—1722no—
536C42—1722no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C2×D4×D4311yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8#1306330614yes—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—861no—
573C2×C4—862no—
574C2×C4—861no—
575C2×C4—861no—
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—1721no—
586C2×C4—1721no—
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×C4C22×C22⋊D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062190011yescharacteristic
599C2×C4C2×#1062190011yescharacteristic
600C2×C4#1306337011yescharacteristic
601C2×C4#1306337211yescharacteristic
602C8—22no—
603C8—41no—
604C8—1721no—
605C8—1721no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#1458340911yescharacteristic
614C22D4×C22⋊D4311yescharacteristic
615C22#1458355511yescharacteristic
616C22#1458369611yescharacteristic
617C22#1458369811yescharacteristic
618C22#1458370611yescharacteristic
619C22#1458371511yescharacteristic
620C4—24no—
621C4—41no—
622C4—42no—
623C4—41no—
624C4—81no—
625C4—3441no—
626C4—3441no—
627C4—3441no—
628C4—1721no—
629C4—1721no—
630C4—1721no—
631C4—1721no—
632C4—1722no—
633C4C2×#1306330611yescharacteristic
634C4#1458349411yescharacteristic
635C4#1458354811yescharacteristic
636C4#1458359211yescharacteristic
637C2—161no—
638C2#1913832611yescharacteristic
639C2#1914470311yescharacteristic
640C2#1914482111yescharacteristic
641C2#1914618011yescharacteristic
642C2#1914624611yescharacteristic
643C2#1914736011yescharacteristic
644C2#1914744111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#464D43
hypocenterC43#26189
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583006C2semidirect
3. #19137513C2semidirect
5. #19136093C2semidirect
6. #19136016C2semidirect
9. #19135156C2semidirect
12. #19134938C2semidirect
13. #19134849C2semidirect
14. #19134847C2semidirect
383. C43#26189semidirect

Maximal subgroups

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

subgroupindex
C2×#145830062
#191383892
#191375132
#191361182
#191360932
#191360162
#191358312
#191352892
#191351562
#191349522
#191349382
#191348492
#191348472
C2×C43×#4642
#2618943