Finite Group Databasebeta

← #25103865

Subgroups — #25103865

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583233C211yesmaximal, characteristic
2#19137271C211yesmaximal, characteristic
3#19136949C211yesmaximal, characteristic
4#19135238C211yesmaximal, characteristic, complemented
5#19135232C211yesmaximal, characteristic, complemented
6#19135186C211yesmaximal, characteristic, complemented
7#19135164C211yesmaximal, characteristic, complemented
8#19134904C211yesmaximal, characteristic
9#19134797C211yesmaximal, characteristic
10#19134680C211yesmaximal, characteristic
11#19134493C211yesmaximal, characteristic, complemented
12C4×#13063259C211yesmaximal, characteristic, complemented
13#19134425C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20#14583233C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582794—21no—
33#14582790—21no—
34#14582789—21no—
35#14582783—21no—
36#14582756C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×Dic43⋊C4—21no—
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582750—21no—
43C4×(C2×D43)⋊C4—21no—
44#14582746—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063301—22no—
65#13063301C2×C414yes—
66#13063283—22no—
67#13063283—22no—
68#13063282—22no—
69#13063282—22no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C4⋊C4×D43—22no—
80C4⋊C4×D43C2×C414yes—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92#13063259—22no—
93#13063259C2×C414yes—
94#13063258C2×C414yes—
95#13063256—22no—
96#13063249—22no—
97#13063249C2×C414yes—
98(C2×D43)⋊C8—22no—
99(C2×D43)⋊C8C2×C414yes—
100#13063236—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×Q8×C43—22no—
113C4×Q8×C43—22no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#103×C43—22no—
122#103×C43C2×C414yes—
123C4×C8×C43—22no—
124#95×C43—21no—
125C23×D43C2×D411yescharacteristic
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—24no—
151C2×C4×D43—81no—
152C2×C4×D43—81no—
153C2×C4×D43C22×C412yes—
154C2×C4×D43#4112yes—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C412yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43C22×C412yes—
167C4⋊C4×C43#4112yes—
168C42×C43—42no—
169C42×C43—81no—
170C42×C43#4112yes—
171C42×C43#4112yes—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—22no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—81no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C22×C412yes—
183C4⋊Dic43C22×C412yes—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—24no—
188Dic43⋊C4—24no—
189Dic43⋊C4—81no—
190C4×Dic43—24no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—81no—
194C4×Dic43—81no—
195C4×Dic43—81no—
196C4×Dic43—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C412yes—
203C23×C43C22×D411yescharacteristic
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43C4×D412yes—
211Q8×C43—22no—
212Q8×C43—22no—
213Q8×C43—41no—
214Q8×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
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#12312yes—
232C2×C4×C43#12312yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C4×D412yes—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—84no—
265C8×C43—22no—
266C8×C43—41no—
267C43⋊C8—22no—
268C43⋊C8—41no—
269#21585—431nomaximal, Sylow
270C22×C43C2×C4×D411yescharacteristic
271C22×C43C2×#12311yescharacteristic
272C22×C43#52511yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C22×C43#57811yescharacteristic
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—42no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—81no—
290C4×C43C4×#4111yescharacteristic
291C4×C43C4×#4111yescharacteristic
292C4×C43#52911yescharacteristic
293C4×C43#52911yescharacteristic
294Dic43—22no—
295Dic43—41no—
296Dic43—41no—
297Dic43—42no—
298Dic43—42no—
299Dic43—42no—
300Dic43—81no—
301C2×#484—431no—
302#2323—431no—
303#2274—431no—
304#1928—431no—
305#1927—431no—
306#1921—431no—
307#1918—431no—
308#1873—431no—
309#1854—431no—
310#1823—431no—
311#1776—431no—
312C4×#107—431no—
313#1763—431no—
314C4×#103D4311yescharacteristic, complemented
315#1750—431no—
316C2×C43C4×#12311yescharacteristic
317C2×C43#294611yescharacteristic
318C2×C43#295011yescharacteristic
319C2×C43#309711yescharacteristic
320C2×C43#309811yescharacteristic
321C2×C43#312011yescharacteristic
322C2×C43#312411yescharacteristic
323D43—42no—
324C2×C22⋊Q8—431no—
325C2×C4×Q8C2×D4311yescharacteristic
326C2×#117—431no—
327C2×#117—431no—
328C22×C4⋊C4—431no—
329#484—438no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#107—431no—
333C2×#106—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103C2×D4311yescharacteristic
337C2×#103C2×D4311yescharacteristic
338C2×C22⋊C8—431no—
339C2×C22⋊C8—431no—
340C2×#97—431no—
341C2×C4×C8C2×D4311yescharacteristic
342#391—431no—
343#389—431no—
344#389—861no—
345#388—861no—
346#388—861no—
347#387—861no—
348#380—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—861no—
354C4×C4⋊C4—861no—
355C4×C4⋊C4C2×D4311yescharacteristic
356C4×C22⋊C4—861no—
357C4×C22⋊C4—861no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340C2×D4311yescharacteristic
365#340C2×D4311yescharacteristic
366#336—431no—
367#336—431no—
368C43#2158511yescharacteristic, complemented, Sylow
369C22×Q8C22×D4311yescharacteristic
370C23×C4—431no—
371C23×C4—861no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376C22⋊Q8—434no—
377C22⋊Q8—862no—
378C4×Q8—22no—
379C4×Q8—22no—
380#117—862no—
381#117—862no—
382#117—862no—
383#117—862no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—434no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—431no—
400C2×C22⋊C4—431no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—434no—
414#107—434no—
415#107—862no—
416#106—862no—
417#103—22no—
418#103—434no—
419#103—862no—
420#103C4×D4314yes—
421C22⋊C8—434no—
422C22⋊C8—862no—
423#97—862no—
424C4×C8—22no—
425#95—21no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—431no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×C4×D4312yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—431no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—864no—
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—3441no—
460C22×C4—3441no—
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—432no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8C2×C4×D4312yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—432no—
482C4⋊C4—432no—
483C4⋊C4—432no—
484C4⋊C4—864no—
485C4⋊C4—864no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—3441no—
494C4⋊C4C2×C4×D4312yes—
495C4⋊C4#1062189812yes—
496C22⋊C4—864no—
497C22⋊C4—864no—
498C22⋊C4—862no—
499C22⋊C4—862no—
500C22⋊C4—3441no—
501C42—42no—
502C42—81no—
503C42—864no—
504C42—861no—
505C42—861no—
506C42—3441no—
507C42—3441no—
508C42—3441no—
509C42—3441no—
510C42#1062189812yes—
511C42#1062190012yes—
512C23—432no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23C2×D4×D4311yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—432no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—3444no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4#1306330712yes—
567C2×C4#1306330712yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062190011yescharacteristic
572C2×C4C2×#1062189811yescharacteristic
573C2×C4C2×#1062189811yescharacteristic
574C8—22no—
575C8—41no—
576C8—862no—
577C8—1721no—
578C22—862no—
579C22—862no—
580C22—862no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22C4×D4×D4311yescharacteristic
586C22C2×#1306330711yescharacteristic
587C22#1458340811yescharacteristic
588C22#1458370111yescharacteristic
589C22#1458370511yescharacteristic
590C22#1458371211yescharacteristic
591C22#1458371311yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—862no—
599C4—3441no—
600C4—1721no—
601C4—1721no—
602C4—1722no—
603C4—1722no—
604C4—1722no—
605C4C4×#1062190011yescharacteristic
606C4C4×#1062189811yescharacteristic
607C4#1458342711yescharacteristic
608C4#1458343111yescharacteristic
609C2—1722no—
610C2C4×#1306330711yescharacteristic
611C2#1914342211yescharacteristic
612C2#1914345811yescharacteristic
613C2#1914456011yescharacteristic
614C2#1914457111yescharacteristic
615C2#1914480511yescharacteristic
616C2#1914486311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43#21585
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. #19135238C2semidirect
5. #19135232C2semidirect
6. #19135186C2semidirect
7. #19135164C2semidirect
11. #19134493C2semidirect
12. C4×#13063259C2semidirect
13. #19134425C2semidirect
15. C4×#103×C43C2semidirect
20. #14583233C4semidirect
314. C4×#103D43semidirect
368. C43#21585semidirect

Maximal subgroups

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

subgroupindex
C2×#145832332
#191372712
#191369492
#191352382
#191352322
#191351862
#191351642
#191349042
#191347972
#191346802
#191344932
C4×#130632592
#191344252
#191343622
C4×#103×C432
#2158543