Finite Group Databasebeta

← #25003147

Subgroups — #25003147

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×#13063323C211yesmaximal, characteristic
2C2×#14582908C211yesmaximal, characteristic
3C22×#13063243C211yesmaximal, characteristic
4#19137179C211yesmaximal, characteristic
5C2×#14582660C211yesmaximal, characteristic
6C2×#14582658C211yesmaximal, characteristic
7C2×C43×#419C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063323—22no—
11C2×#13063323—22no—
12C2×#13063323—22no—
13C2×#13063323—22no—
14C2×#13063323—22no—
15C2×#13063323C414yescomplemented
16C2×#13063284C2211yescharacteristic
17C22×Dic43⋊C4—22no—
18C22×C4×Dic43C2211yescharacteristic
19#14582908—22no—
20#14582908—22no—
21C2×#13063249—22no—
22C2×#13063243—22no—
23C2×#13063243—22no—
24C2×#13063243—22no—
25#14582805—22no—
26#14582804—22no—
27#14582760—22no—
28#14582660—22no—
29#14582658—22no—
30C23×Q8×C43C2211yescharacteristic
31C22×M16×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C43×#419—22no—
34C43×#419—22no—
35C2×#103×C43—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×Dic86C2×C412yes—
49C22×Dic86D412yes—
50C23×Dic43—21no—
51C23×Dic43D412yes—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877D412yes—
58C22×C43⋊C8—21no—
59#13063323—28no—
60#13063323—28no—
61#13063323—28no—
62#13063323—28no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66#13063284—21no—
67C2×C4⋊Dic43D412yes—
68C2×Dic43⋊C4—28no—
69C2×Dic43⋊C4—28no—
70C2×Dic43⋊C4—28no—
71C2×C22⋊Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43C2×C412yes—
77C2×C4×Dic43D412yes—
78C2×C4×Dic43D412yes—
79#13063249—28no—
80#13063243—28no—
81C43⋊#95—28no—
82C22×Q8×C43—21no—
83C22×Q8×C43—21no—
84C22×Q8×C43—21no—
85C22×Q8×C43—21no—
86C22×Q8×C43—21no—
87C22×Q8×C43—21no—
88C22×Q8×C43—21no—
89C22×Q8×C43—21no—
90C22×Q8×C43—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43C2×C412yes—
94C22×Q8×C43D412yes—
95C22×Q8×C43D412yes—
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C2×M16×C43—21no—
99C2×M16×C43—21no—
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43—21no—
103C2×M16×C43D412yes—
104C22×C8×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107#117×C43—21no—
108#117×C43—21no—
109C2×C4⋊C4×C43D412yes—
110C2×C22⋊C4×C43—21no—
111C2×C42×C43—21no—
112#103×C43—28no—
113C24×C43C2×D411yescharacteristic
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—22no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—41no—
130C2×Q8×C43—41no—
131C2×Q8×C43—41no—
132C2×Q8×C43—41no—
133C2×Q8×C43—41no—
134C2×Q8×C43—41no—
135C2×Q8×C43—41no—
136C2×Q8×C43—41no—
137C2×Q8×C43—41no—
138C2×Q8×C43—41no—
139C2×Q8×C43—41no—
140C2×Q8×C43—41no—
141C2×Q8×C43C22⋊C414yes—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—41no—
147C22×C4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C22×C4×C43#4111yescharacteristic
164C22×Dic43—28no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43C22⋊C414yes—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—22no—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C2×Dic86—22no—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—22no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—22no—
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×Dic86—41no—
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—41no—
216C42×C43—41no—
217C22⋊Dic43—41no—
218C22⋊Dic43—41no—
219C4⋊Dic43—22no—
220C4⋊Dic43—22no—
221Dic43⋊C4—232no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43—22no—
225C4×Dic43—41no—
226C4×Dic43—41no—
227C4×Dic43C22⋊C414yes—
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
243Q8×C43—24no—
244Q8×C43—24no—
245Q8×C43—42no—
246Q8×C43—42no—
247Q8×C43—42no—
248Q8×C43—42no—
249Q8×C43—42no—
250Q8×C43—42no—
251C2×C4×C43—24no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—44no—
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C4×D411yescharacteristic
263C2×C4×C43C4×D411yescharacteristic
264C2×C4×C43C4×D411yescharacteristic
265C2×C4×C43C4×D411yescharacteristic
266C2×C4×C43#12011yescharacteristic
267C2×C4×C43#12011yescharacteristic
268C2×C4×C43#12011yescharacteristic
269C2×C4×C43#12011yescharacteristic
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43#12111yescharacteristic
272C2×C4×C43#12111yescharacteristic
273C2×C4×C43#12111yescharacteristic
274C2×C4×C43#12111yescharacteristic
275C2×C4×C43#12111yescharacteristic
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43#12111yescharacteristic
278C2×C4×C43#12111yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12311yescharacteristic
282C2×C4×C43#12311yescharacteristic
283C2×C4×C43#12311yescharacteristic
284C2×C4×C43#12411yescharacteristic
285C2×C4×C43#12411yescharacteristic
286C2×C4×C43#12711yescharacteristic
287C2×C4×C43#12711yescharacteristic
288C2×Dic43—28no—
289C2×Dic43—28no—
290C2×Dic43—28no—
291C2×Dic43—24no—
292C2×Dic43—24no—
293C2×Dic43—24no—
294C2×Dic43—24no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—44no—
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—44no—
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—28no—
337Dic43—44no—
338Dic43—82no—
339C22×C4⋊Q8—431no—
340C2×#419—431no—
341C2×#419D4311yescharacteristic
342C22×#101—431no—
343#2310—431no—
344C2×#339—431no—
345C2×#339—431no—
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×Q8C2×D4311yescharacteristic
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×C42—431no—
368#419—22no—
369#419—22no—
370#419—862no—
371#419—862no—
372C2×#103—22no—
373C2×#103—862no—
374C2×#101—862no—
375C2×#101—862no—
376C2×#101—862no—
377#391—862no—
378#391—862no—
379#381—862no—
380#339—862no—
381#339—862no—
382C43#1097811yescharacteristic, complemented, Sylow
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—432no—
395C22×Q8—432no—
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×Q8C4×D4312yes—
409C22×Q8D17212yes—
410C22×Q8C22⋊D4312yes—
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×M16C22⋊D4312yes—
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⋊C4C22⋊D4312yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C42—21no—
449C2×C42—432no—
450C2×C42—432no—
451C2×C42—432no—
452C2×C42—861no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42—861no—
456#103—28no—
457#103—868no—
458#101—868no—
459#95—868no—
460C24D4×D4311yescharacteristic
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—862no—
489C2×Q8—862no—
490C2×Q8—862no—
491C2×Q8—862no—
492C2×Q8—862no—
493C2×Q8—862no—
494C2×Q8—862no—
495C2×Q8—862no—
496C2×Q8—862no—
497C2×Q8—862no—
498C2×Q8—862no—
499C2×Q8—862no—
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(C2×D43)⋊C414yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—434no—
526C22×C4—868no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4C2×C4×D4311yescharacteristic
538C22×C4C2×D17211yescharacteristic
539C22×C4#1062189811yescharacteristic
540C22×C4#1062189811yescharacteristic
541C22×C4D4×D4311yescharacteristic
542C22×C4D4×D4311yescharacteristic
543C22×C4D4×D4311yescharacteristic
544C22×C4D4×D4311yescharacteristic
545C22×C4D4×D4311yescharacteristic
546C22×C4#1062190011yescharacteristic
547C22×C4#1062190011yescharacteristic
548C22×C4C2×C22⋊D4311yescharacteristic
549C22×C4C2×C22⋊D4311yescharacteristic
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—41no—
575C42—41no—
576C42—434no—
577C42—862no—
578C42—862no—
579C42—862no—
580C42—1721no—
581C42—1721no—
582C23—24no—
583C23C22⋊C4×D4311yescharacteristic
584C23#1306329311yescharacteristic
585C23#1306329311yescharacteristic
586C23#1306329511yescharacteristic
587C23#1306329611yescharacteristic
588C23#1306329811yescharacteristic
589C23#1306330711yescharacteristic
590Q8—24no—
591Q8—24no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597Q8—42no—
598Q8—1722no—
599Q8—1722no—
600Q8—1722no—
601Q8—1722no—
602Q8—1722no—
603Q8—1722no—
604Q8—1722no—
605Q8—1722no—
606C2×C4—24no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—868no—
616C2×C4—868no—
617C2×C4—868no—
618C2×C4—864no—
619C2×C4—864no—
620C2×C4—864no—
621C2×C4—864no—
622C2×C4—1722no—
623C2×C4—1724no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4C22⋊C4×D4311yescharacteristic
629C2×C4C2×(C2×D43)⋊C411yescharacteristic
630C2×C4(C22⋊D43)⋊C411yescharacteristic
631C2×C4(C22⋊D43)⋊C411yescharacteristic
632C2×C4C4×C22⋊D4311yescharacteristic
633C2×C4C4×C22⋊D4311yescharacteristic
634C2×C4#1306329311yescharacteristic
635C2×C4#1306329311yescharacteristic
636C2×C4#1306329411yescharacteristic
637C2×C4#1306329511yescharacteristic
638C2×C4#1306329511yescharacteristic
639C2×C4#1306329611yescharacteristic
640C2×C4#1306329711yescharacteristic
641C2×C4#1306329711yescharacteristic
642C2×C4#1306329711yescharacteristic
643C2×C4#1306329711yescharacteristic
644C2×C4#1306329811yescharacteristic
645C2×C4#1306329811yescharacteristic
646C2×C4#1306329811yescharacteristic
647C2×C4#1306329911yescharacteristic
648C2×C4#1306329911yescharacteristic
649C2×C4#1306330711yescharacteristic
650C2×C4#1306330811yescharacteristic
651C2×C4#1306330911yescharacteristic
652C2×C4#1306331111yescharacteristic
653C2×C4#1306331111yescharacteristic
654C2×C4#1306332111yescharacteristic
655C2×C4#1306332111yescharacteristic
656C8—42no—
657C8—1722no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22#1458275411yescharacteristic
665C22#1458277511yescharacteristic
666C22#1458277511yescharacteristic
667C22#1458280711yescharacteristic
668C22#1458280811yescharacteristic
669C22#1458281411yescharacteristic
670C22#1458281511yescharacteristic
671C22#1458308014yes—
672C4—44no—
673C4—82no—
674C4—868no—
675C4—3442no—
676C4—1724no—
677C4#1458277611yescharacteristic
678C4#1458277811yescharacteristic
679C4#1458279911yescharacteristic
680C4#1458279911yescharacteristic
681C4#1458280711yescharacteristic
682C4#1458280811yescharacteristic
683C4#1458281411yescharacteristic
684C4#1458281511yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2#1913283411yescharacteristic
690C2#1913498512yes—
691C2#1913562812yes—
692C2#1913563212yes—
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#419C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#419D43
hypocenterC43#10978
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
15. C2×#13063323C4semidirect
382. C43#10978semidirect

Maximal subgroups

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

subgroupindex
C22×#130633232
C2×#145829082
C22×#130632432
#191371792
C2×#145826602
C2×#145826582
C2×C43×#4192
#1097843