Finite Group Databasebeta

← #25003149

Subgroups — #25003149

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063325C211yesmaximal, characteristic
2C2×#14582909C211yesmaximal, characteristic
3C2×#14582907C211yesmaximal, characteristic
4C22×#13063243C211yesmaximal, characteristic
5#19137179C211yesmaximal, characteristic
6C2×#14582659C211yesmaximal, characteristic
7C2×C43×#339C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9C23×Dic86C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063325—22no—
12C2×#13063325—22no—
13C2×#13063325—22no—
14C2×#13063325—22no—
15C2×#13063325—22no—
16C2×#13063325C414yescomplemented
17C2×#13063284C2211yescharacteristic
18C22×C4⋊Dic43—22no—
19#14582909—22no—
20#14582909—22no—
21#14582907—22no—
22#14582907—22no—
23C2×#13063250—22no—
24C2×#13063248—22no—
25C2×#13063243—22no—
26C2×#13063243—22no—
27C2×#13063243—22no—
28#14582805—22no—
29#14582804—22no—
30#14582760—22no—
31#14582659—22no—
32C22×M16×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic
35C43×#339—22no—
36C22×Dic86—21no—
37C22×Dic86—21no—
38C22×Dic86—21no—
39C22×Dic86—21no—
40C22×Dic86—21no—
41C22×Dic86—21no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—21no—
45C22×Dic86—21no—
46C22×Dic86—21no—
47C22×Dic86—21no—
48C22×Dic86—21no—
49C22×Dic86—21no—
50C22×Dic86—21no—
51C22×Dic86—21no—
52C22×Dic86—21no—
53C22×Dic86—21no—
54C22×Dic86—21no—
55C22×Dic86—21no—
56C22×Dic86—21no—
57C22×Dic86—21no—
58C22×Dic86—21no—
59C22×Dic86C2×C412yes—
60C22×Dic86C2×C412yes—
61C22×Dic86D412yes—
62C22×Dic86D412yes—
63C22×Dic86D412yes—
64C23×Dic43—21no—
65C23×Dic43D412yes—
66C2×#10621877—21no—
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877D412yes—
72C22×C43⋊C8—21no—
73#13063325—28no—
74#13063325—28no—
75#13063325—28no—
76#13063325—28no—
77#13063284—21no—
78#13063284—21no—
79#13063284—21no—
80#13063284—21no—
81C2×C4⋊Dic43—28no—
82C2×C4⋊Dic43—28no—
83C2×C4⋊Dic43—28no—
84C2×C4⋊Dic43D412yes—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87#13063250—28no—
88#13063248—28no—
89#13063243—28no—
90C43⋊#95—28no—
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43—21no—
97C2×M16×C43—21no—
98C2×M16×C43D412yes—
99C22×C8×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104C2×C4⋊C4×C43D412yes—
105C2×C22⋊C4×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43—21no—
109C2×C42×C43—21no—
110C2×C42×C43C2×C412yes—
111C2×C42×C43D412yes—
112C2×C42×C43D412yes—
113C24×C43C2×D411yescharacteristic
114C22×C4×C43—28no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43—41no—
146C22×Dic43—41no—
147C22×Dic43C22⋊C414yes—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—22no—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86—22no—
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—22no—
159C2×Dic86—22no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—22no—
166C2×Dic86—22no—
167C2×Dic86—22no—
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—41no—
176C2×Dic86—41no—
177C2×Dic86—41no—
178C2×Dic86—41no—
179C2×Dic86—41no—
180C2×Dic86—41no—
181C2×Dic86—41no—
182C2×Dic86—41no—
183C2×Dic86—41no—
184C2×Dic86—41no—
185C2×Dic86—41no—
186C2×Dic86—41no—
187C2×Dic86—41no—
188C2×Dic86—41no—
189C2×Dic86—41no—
190C2×Dic86—41no—
191C2×Dic86—41no—
192C2×Dic86—41no—
193C2×Dic86—41no—
194C2×Dic86—41no—
195C2×Dic86—41no—
196C2×Dic86—41no—
197C2×Dic86—41no—
198C2×Dic86—41no—
199C2×Dic86—41no—
200C2×Dic86—41no—
201C2×Dic86—41no—
202C2×Dic86—41no—
203C2×Dic86C22⋊C414yes—
204M16×C43—22no—
205M16×C43—22no—
206M16×C43—41no—
207M16×C43—41no—
208C2×C8×C43—22no—
209C2×C8×C43—41no—
210C2×C8×C43—41no—
211C4⋊C4×C43—22no—
212C4⋊C4×C43—22no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C42×C43—22no—
216C42×C43—22no—
217C42×C43—22no—
218C42×C43—41no—
219C42×C43—41no—
220C42×C43C22⋊C414yes—
221C22⋊Dic43—41no—
222C22⋊Dic43—41no—
223C4⋊Dic43—232no—
224C4⋊Dic43—22no—
225C4⋊Dic43—22no—
226C4×Dic43—41no—
227C4×Dic43—41no—
228#10621877—22no—
229#10621877—22no—
230#10621877—41no—
231#10621877—41no—
232C2×C43⋊C8—22no—
233C2×C43⋊C8—41no—
234C2×C43⋊C8—41no—
235C23×C43—24no—
236C23×C43C2×C22⋊C411yescharacteristic
237C23×C43#12011yescharacteristic
238C23×C43#12011yescharacteristic
239C23×C43#12011yescharacteristic
240C23×C43#12111yescharacteristic
241C23×C43#12111yescharacteristic
242C23×C43#12311yescharacteristic
243C2×C4×C43—28no—
244C2×C4×C43—28no—
245C2×C4×C43—28no—
246C2×C4×C43—24no—
247C2×C4×C43—42no—
248C2×C4×C43—44no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12011yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43#12111yescharacteristic
265C2×C4×C43#12111yescharacteristic
266C2×C4×C43#12111yescharacteristic
267C2×C4×C43#12111yescharacteristic
268C2×C4×C43#12111yescharacteristic
269C2×C4×C43#12111yescharacteristic
270C2×C4×C43#12311yescharacteristic
271C2×C4×C43#12311yescharacteristic
272C2×C4×C43#12311yescharacteristic
273C2×C4×C43#12411yescharacteristic
274C2×C4×C43#12411yescharacteristic
275C2×C4×C43#12711yescharacteristic
276C2×C4×C43#12711yescharacteristic
277C2×Dic43—24no—
278C2×Dic43—24no—
279C2×Dic43—24no—
280C2×Dic43—24no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292C2×Dic43—44no—
293Dic86—24no—
294Dic86—24no—
295Dic86—42no—
296Dic86—42no—
297Dic86—42no—
298Dic86—42no—
299Dic86—42no—
300Dic86—42no—
301Dic86—42no—
302Dic86—42no—
303Dic86—42no—
304Dic86—42no—
305Dic86—42no—
306Dic86—42no—
307Dic86—42no—
308Dic86—42no—
309C8×C43—42no—
310C43⋊C8—42no—
311#10978—431nomaximal, Sylow
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—22no—
318C22×C43#37911yescharacteristic
319C22×C43#38611yescharacteristic
320C22×C43#38611yescharacteristic
321C22×C43#39211yescharacteristic
322C22×C43#39211yescharacteristic
323C22×C43#39411yescharacteristic
324C22×C43#39411yescharacteristic
325C22×C43#45614yes—
326C4×C43—28no—
327C4×C43—82no—
328C4×C43#38611yescharacteristic
329C4×C43#38611yescharacteristic
330C4×C43#39011yescharacteristic
331C4×C43#39011yescharacteristic
332C4×C43#39211yescharacteristic
333C4×C43#39211yescharacteristic
334C4×C43#39411yescharacteristic
335C4×C43#39411yescharacteristic
336Dic43—44no—
337Dic43—44no—
338Dic43—82no—
339C22×C4⋊Q8—431no—
340C2×#419—431no—
341C2×#419—431no—
342C22×#101—431no—
343#2310—431no—
344C2×#339—431no—
345C2×#339D4311yescharacteristic
346C2×C43—21no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43#143811yescharacteristic
351C2×C43#188612yes—
352C2×C43#200512yes—
353C2×C43#200512yes—
354C23×Q8—431no—
355C23×Q8—431no—
356C22×M16—431no—
357C22×M16C2×D4311yescharacteristic
358C2×C4⋊Q8—434no—
359C2×C4⋊Q8—862no—
360C2×C4⋊Q8—862no—
361C2×C4⋊Q8—862no—
362C2×C4⋊Q8—862no—
363C2×C4⋊Q8—862no—
364C2×#117—431no—
365C2×#117C2×D4311yescharacteristic
366C22×C4⋊C4—862no—
367C22×C42C2×D4311yescharacteristic
368#419—862no—
369#419—862no—
370#419—862no—
371#419—862no—
372C2×#103—862no—
373C2×#103—862no—
374C2×#101—862no—
375C2×#101—862no—
376C2×#101—862no—
377#391—862no—
378#391—862no—
379#381—862no—
380#339—22no—
381#339—862no—
382C43#1097811yescharacteristic, complemented, Sylow
383C22×Q8—432no—
384C22×Q8—432no—
385C22×Q8—432no—
386C22×Q8—432no—
387C22×Q8—432no—
388C22×Q8—861no—
389C22×Q8—861no—
390C22×Q8—861no—
391C22×Q8—861no—
392C22×Q8—861no—
393C22×Q8—861no—
394C22×Q8—861no—
395C22×Q8—861no—
396C22×Q8—861no—
397C22×Q8—861no—
398C22×Q8—861no—
399C22×Q8—861no—
400C22×Q8—861no—
401C22×Q8—861no—
402C22×Q8—861no—
403C22×Q8—861no—
404C22×Q8—861no—
405C22×Q8—861no—
406C22×Q8—861no—
407C22×Q8—861no—
408C22×Q8—861no—
409C22×Q8—861no—
410C22×Q8—861no—
411C23×C4—21no—
412C23×C4—432no—
413C23×C4—861no—
414C23×C4C22×D4311yescharacteristic
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—432no—
421C2×M16—861no—
422C2×M16—861no—
423C2×M16—861no—
424C2×M16—861no—
425C2×M16—861no—
426C2×M16D17212yes—
427C22×C8—21no—
428C22×C8—861no—
429C4⋊Q8—868no—
430C4⋊Q8—868no—
431C4⋊Q8—868no—
432C4⋊Q8—868no—
433#117—21no—
434#117—21no—
435#117—21no—
436#117—21no—
437#117—861no—
438#117—861no—
439#117—861no—
440#117—861no—
441C2×C4⋊C4—432no—
442C2×C4⋊C4—868no—
443C2×C4⋊C4—868no—
444C2×C4⋊C4—868no—
445C2×C4⋊C4D17212yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—861no—
453C2×C42C4×D4312yes—
454C2×C42D17212yes—
455C2×C42C22⋊D4312yes—
456#103—868no—
457#103—868no—
458#101—868no—
459#95—868no—
460C24D4×D4311yescharacteristic
461C2×Q8—434no—
462C2×Q8—862no—
463C2×Q8—862no—
464C2×Q8—862no—
465C2×Q8—862no—
466C2×Q8—862no—
467C2×Q8—862no—
468C2×Q8—862no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×Q8—862no—
475C2×Q8—862no—
476C2×Q8—862no—
477C2×Q8—862no—
478C2×Q8—862no—
479C2×Q8—862no—
480C2×Q8—862no—
481C2×Q8—862no—
482C2×Q8—862no—
483C2×Q8—862no—
484C2×Q8—862no—
485C2×Q8—862no—
486C2×Q8—862no—
487C2×Q8—862no—
488C2×Q8—862no—
489C2×Q8—1721no—
490C2×Q8—1721no—
491C2×Q8—1721no—
492C2×Q8—1721no—
493C2×Q8—1721no—
494C2×Q8—1721no—
495C2×Q8—1721no—
496C2×Q8—1721no—
497C2×Q8—1721no—
498C2×Q8—1721no—
499C2×Q8—1721no—
500C2×Q8—1721no—
501C2×Q8—1721no—
502C2×Q8—1721no—
503C2×Q8—1721no—
504C2×Q8—1721no—
505C2×Q8—1721no—
506C2×Q8—1721no—
507C2×Q8—1721no—
508C2×Q8—1721no—
509C2×Q8—1721no—
510C2×Q8—1721no—
511C2×Q8—1721no—
512C2×Q8—1721no—
513C2×Q8—1721no—
514C2×Q8—1721no—
515C2×Q8—1721no—
516C2×Q8—1721no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—434no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—1721no—
534C22×C4—1721no—
535C22×C4—1721no—
536C22×C4—1721no—
537C22×C4C2×C4×D4311yescharacteristic
538C22×C4C2×D17211yescharacteristic
539C22×C4C2×D17211yescharacteristic
540C22×C4C2×D17211yescharacteristic
541C22×C4#1062189811yescharacteristic
542C22×C4#1062189811yescharacteristic
543C22×C4D4×D4311yescharacteristic
544C22×C4D4×D4311yescharacteristic
545C22×C4D4×D4311yescharacteristic
546C22×C4D4×D4311yescharacteristic
547C22×C4D4×D4311yescharacteristic
548C22×C4#1062190211yescharacteristic
549C22×C4#1062190211yescharacteristic
550C22×C4C2×C22⋊D4311yescharacteristic
551M16—22no—
552M16—22no—
553M16—41no—
554M16—41no—
555M16—862no—
556M16—862no—
557M16—1721no—
558M16—1721no—
559C2×C8—22no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—862no—
563C2×C8—1721no—
564C2×C8—1721no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—8632no—
568C4⋊C4—862no—
569C4⋊C4—862no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—1721no—
573C22⋊C4—1721no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—41no—
578C42—41no—
579C42—1721no—
580C42—1721no—
581C42(C2×D43)⋊C414yes—
582C23—24no—
583C23C22⋊C4×D4311yescharacteristic
584C23#1306329311yescharacteristic
585C23#1306329511yescharacteristic
586C23#1306329511yescharacteristic
587C23#1306329811yescharacteristic
588C23#1306330011yescharacteristic
589C23#1306331011yescharacteristic
590Q8—864no—
591Q8—864no—
592Q8—1722no—
593Q8—1722no—
594Q8—1722no—
595Q8—1722no—
596Q8—1722no—
597Q8—1722no—
598Q8—1722no—
599Q8—1722no—
600Q8—1722no—
601Q8—1722no—
602Q8—1722no—
603Q8—1722no—
604Q8—1722no—
605Q8—1722no—
606C2×C4—28no—
607C2×C4—28no—
608C2×C4—28no—
609C2×C4—24no—
610C2×C4—42no—
611C2×C4—44no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—864no—
615C2×C4—864no—
616C2×C4—1722no—
617C2×C4—1724no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4C22⋊C4×D4311yescharacteristic
629C2×C4C2×(C2×D43)⋊C411yescharacteristic
630C2×C4#1306328711yescharacteristic
631C2×C4#1306328711yescharacteristic
632C2×C4C4×D17211yescharacteristic
633C2×C4C4×D17211yescharacteristic
634C2×C4#1306329311yescharacteristic
635C2×C4#1306329511yescharacteristic
636C2×C4#1306329511yescharacteristic
637C2×C4#1306329511yescharacteristic
638C2×C4#1306329511yescharacteristic
639C2×C4#1306329811yescharacteristic
640C2×C4#1306329811yescharacteristic
641C2×C4#1306329811yescharacteristic
642C2×C4#1306329911yescharacteristic
643C2×C4#1306329911yescharacteristic
644C2×C4#1306330011yescharacteristic
645C2×C4#1306330011yescharacteristic
646C2×C4#1306330011yescharacteristic
647C2×C4#1306330011yescharacteristic
648C2×C4#1306330011yescharacteristic
649C2×C4#1306331011yescharacteristic
650C2×C4#1306331011yescharacteristic
651C2×C4#1306331011yescharacteristic
652C2×C4#1306331311yescharacteristic
653C2×C4#1306331411yescharacteristic
654C2×C4#1306332111yescharacteristic
655C2×C4#1306332211yescharacteristic
656C8—42no—
657C8—1722no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22#1458275411yescharacteristic
665C22#1458277711yescharacteristic
666C22#1458277711yescharacteristic
667C22#1458280811yescharacteristic
668C22#1458280911yescharacteristic
669C22#1458281611yescharacteristic
670C22#1458281711yescharacteristic
671C22#1458308314yes—
672C4—28no—
673C4—82no—
674C4—3442no—
675C4—1724no—
676C4—1724no—
677C4#1458277711yescharacteristic
678C4#1458277711yescharacteristic
679C4#1458280011yescharacteristic
680C4#1458280111yescharacteristic
681C4#1458280811yescharacteristic
682C4#1458280911yescharacteristic
683C4#1458281611yescharacteristic
684C4#1458281711yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2#1913283511yescharacteristic
690C2#1913498712yes—
691C2#1913563012yes—
692C2#1913563412yes—
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#10978
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
16. C2×#13063325C4semidirect
382. C43#10978semidirect

Maximal subgroups

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

subgroupindex
C22×#130633252
C2×#145829092
C2×#145829072
C22×#130632432
#191371792
C2×#145826592
C2×C43×#3392
#1097843