Finite Group Databasebeta

← #25164734

Subgroups — #25164734

Order 11008.

790 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138945C211yesmaximal, characteristic
2#19137605C211yesmaximal, characteristic, complemented
3#19135796C211yesmaximal, characteristic, complemented
4#19135746C211yesmaximal, characteristic, complemented
5#19135595C211yesmaximal, characteristic
6#19135550C211yesmaximal, characteristic, complemented
7#19135275C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19135200C211yesmaximal, characteristic, complemented
10#19135185C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic, complemented
12#19134909C211yesmaximal, characteristic
13#19134680C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#2055C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582827—21no—
30#14582814—21no—
31#14582802C2211yescharacteristic
32#14582799—21no—
33#14582796—21no—
34#14582795C2211yescharacteristic
35#14582787—21no—
36#14582781—21no—
37#14582773—21no—
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×(C2×D43)⋊C4C2211yescharacteristic
42#14582746—21no—
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063317—22no—
65#13063317—41no—
66#13063301—22no—
67#13063301—22no—
68#13063296—22no—
69#13063296—41no—
70Q8×Dic43—22no—
71Q8×Dic43—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C4⋊C4×D43—22no—
83C4⋊C4×D43—41no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063249—22no—
97#13063249—41no—
98#13063246—22no—
99#13063246—22no—
100(C2×D43)⋊C8—41no—
101(C2×D43)⋊C8—41no—
102C8×Dic43—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C2×SD16×C43—22no—
112C2×SD16×C43—41no—
113C2×SD16×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C4⋊C8×C43—41no—
122#103×C43—22no—
123#102×C43—41no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×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
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—81no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—81no—
165SD16×C43—44no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C22⋊C4×C43—81no—
177C22⋊C4×C43—81no—
178C42×C43—21no—
179C42×C43—21no—
180C22⋊Dic43—42no—
181C22⋊Dic43—42no—
182C22⋊Dic43—81no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—81no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—42no—
193C4⋊Dic43#4112yes—
194C4⋊Dic43#4112yes—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—42no—
204C4×Dic43—81no—
205C4×Dic43—81no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43#13512yes—
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—41no—
230Q8×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C22⋊D43—84no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—22no—
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#13712yes—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—84no—
283C8×C43—41no—
284C8×C43—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#26727—431nomaximal, Sylow
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43#52511yescharacteristic
296C22×C43#54611yescharacteristic
297C22×C43#54611yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57611yescharacteristic
301C22×C43#57711yescharacteristic
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C4×C43—41no—
310C4×C43—42no—
311C4×C43—41no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43#52911yescharacteristic
315C4×C43#53811yescharacteristic
316C4×C43#55511yescharacteristic
317C4×C43#55911yescharacteristic
318Dic43—22no—
319Dic43—42no—
320Dic43—41no—
321Dic43—42no—
322Dic43—42no—
323Dic43—41no—
324Dic43—81no—
325#2490—431no—
326#2360—431no—
327#2055D4311yescharacteristic, complemented
328#2036—431no—
329#2026—431no—
330#2000—431no—
331#1989—431no—
332#1934—431no—
333#1925—431no—
334#1923—431no—
335#1921—431no—
336#1880—431no—
337#1874—431no—
338#1823—431no—
339C4×#103—431no—
340C2×C43—161no—
341C2×C43#245911yescharacteristic
342C2×C43#310811yescharacteristic
343C2×C43#311911yescharacteristic
344C2×C43#329611yescharacteristic
345C2×C43#329711yescharacteristic
346C2×C43#332011yescharacteristic
347C2×C43#333311yescharacteristic
348D43—42no—
349C22×SD16C2×D4311yescharacteristic
350C2×#125—431no—
351C2×C22⋊Q8—431no—
352C2×#121—431no—
353C2×C4×Q8—431no—
354C22×C4⋊C4—431no—
355C2×#107—431no—
356C2×C4⋊C8C2×D4311yescharacteristic
357C2×#103—431no—
358C2×#103—431no—
359C2×#103C2×D4311yescharacteristic
360C2×#102—431no—
361C2×#102—431no—
362C2×#102C2×D4311yescharacteristic
363C2×C22⋊C8—431no—
364C2×C22⋊C8—431no—
365C2×C4×C8—431no—
366#397—861no—
367#394—861no—
368#391C2×D4311yescharacteristic
369#390—431no—
370#390—861no—
371#390C2×D4311yescharacteristic
372#389—431no—
373#389—861no—
374#388—861no—
375#387—861no—
376#385—861no—
377#380—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C22⋊C4—431no—
381C4×C22⋊C4—861no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#336—431no—
391#336—431no—
392C43#2672711yescharacteristic, complemented, Sylow
393C22×Q8C22×D4311yescharacteristic
394C22×D4—861no—
395C22×D4C22×D4311yescharacteristic
396C23×C4—431no—
397C23×C4—861no—
398C2×SD16—22no—
399C2×SD16—41no—
400C2×SD16—41no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405#125—862no—
406#125—1721no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409#121—862no—
410#121—1721no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—1721no—
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441#107—862no—
442C4⋊C8—41no—
443#103—22no—
444#103—862no—
445#103—1721no—
446#102—41no—
447#102—862no—
448#102—862no—
449C22⋊C8—1721no—
450C22⋊C8—1721no—
451C4×C8—1721no—
452#95—21no—
453#95—21no—
454#95—431no—
455#95—431no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—21no—
461C24—431no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8#1062190012yes—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—3441no—
475C2×D4—1722no—
476C2×D4—1722no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—3441no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499SD16—44no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—432no—
517C4⋊C4—432no—
518C4⋊C4—432no—
519C4⋊C4—864no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—3441no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4—1722no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—864no—
535C22⋊C4—3441no—
536C22⋊C4—3441no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C42—21no—
540C42—21no—
541C42—861no—
542C42—861no—
543C42—3441no—
544C42—3441no—
545C42—1722no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—432no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23C2×D4×D4311yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—41no—
564Q8—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—3444no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—432no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—862no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—3444no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4#1306337011yescharacteristic
616C2×C4#1306337011yescharacteristic
617C8—41no—
618C8—41no—
619C8—1721no—
620C8—1721no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—1721no—
632C22—1721no—
633C22—1721no—
634C22—1721no—
635C22#1458340911yescharacteristic
636C22#1458353811yescharacteristic
637C22#1458354611yescharacteristic
638C22#135×D4311yescharacteristic
639C22#137×D4311yescharacteristic
640C22#1458370311yescharacteristic
641C22#1458370511yescharacteristic
642C4—41no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—862no—
648C4—3441no—
649C4—1722no—
650C4—1722no—
651C4—1721no—
652C4—1722no—
653C4—1721no—
654C4#1458342611yescharacteristic
655C4#1458348411yescharacteristic
656C4#1458361111yescharacteristic
657C4#1458363311yescharacteristic
658C2—161no—
659C2—1722no—
660C2#1913853311yescharacteristic
661C2#1914467411yescharacteristic
662C2#1914479311yescharacteristic
663C2#1914642511yescharacteristic
664C2#1914645211yescharacteristic
665C2#1914677311yescharacteristic
666C2#1914692811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2055C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2055D43
hypocenterC43#26727
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. #19137605C2semidirect
3. #19135796C2semidirect
4. #19135746C2semidirect
6. #19135550C2semidirect
7. #19135275C2semidirect
8. #19135212C2semidirect
9. #19135200C2semidirect
10. #19135185C2semidirect
11. #19134952C2semidirect
13. #19134680C2semidirect
14. #103×Dic43C2semidirect
15. C43×#2055C2semidirect
327. #2055D43semidirect
392. C43#26727semidirect

Maximal subgroups

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

subgroupindex
#191389452
#191376052
#191357962
#191357462
#191355952
#191355502
#191352752
#191352122
#191352002
#191351852
#191349522
#191349092
#191346802
#103×Dic432
C43×#20552
#2672743