Finite Group Databasebeta

← #25003684

Subgroups — #25003684

Order 11008.

1018 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143158C211yesmaximal, characteristic, complemented
2C2×#14582862C211yesmaximal, characteristic
3C2×#14582862C211yesmaximal, characteristic
4#19136974C211yesmaximal, characteristic
5C2×#14582669C211yesmaximal, characteristic, complemented
6#19134333C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582927—22no—
13#14582925—22no—
14#14582922—22no—
15#14582862—22no—
16#14582862—22no—
17#14582862—22no—
18#14582862—22no—
19C2×(C2×D43)⋊C8—22no—
20C2×(C2×D43)⋊C8—22no—
21#14582760C412yes—
22#14582756—22no—
23#14582754C412yes—
24C4×(C2×D43)⋊C4—22no—
25#14582669—22no—
26#14582667—22no—
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C43×#344—22no—
31C24×D43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C22×C4×D43—21no—
34C22×C4×D43—21no—
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43D412yes—
46C22×C4×D43Q812yes—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877D412yes—
59C22×C43⋊C8—21no—
60C22×C43⋊C8D412yes—
61#13063284—21no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65C2×C4⋊Dic43D412yes—
66C2×C22⋊Dic43C2×C412yes—
67C2×(C2×D43)⋊C4—24no—
68C2×C4×Dic43D412yes—
69Dic43⋊C8—28no—
70(C2×D43)⋊C8—28no—
71(C2×D43)⋊C8—28no—
72C43⋊#95—24no—
73C23×C4×C43C2311yescharacteristic
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43D412yes—
86C22×C8×C43—21no—
87C22×C8×C43D412yes—
88#117×C43—21no—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C22⋊C4×C43C2×C412yes—
94C2×C42×C43—21no—
95C24×C43C22×C411yescharacteristic
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—21no—
99C23×D43—21no—
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—44no—
103C23×D43C4⋊C412yes—
104C22×C4×C43—22no—
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×Q811yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43C22⋊C414yes—
126C22×Dic43C4⋊C412yes—
127C2×C4×D43—22no—
128C2×C4×D43—22no—
129C2×C4×D43—22no—
130C2×C4×D43—22no—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—22no—
134C2×C4×D43—22no—
135C2×C4×D43—22no—
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—41no—
140C2×C4×D43—41no—
141C2×C4×D43—41no—
142C2×C4×D43—41no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—41no—
158M16×C43—41no—
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—41no—
162M16×C43—41no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—41no—
168C2×C8×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C42×C43—41no—
174C42×C43—41no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177(C2×D43)⋊C4—48no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4×Dic43—22no—
181C4×Dic43—22no—
182#10621877—22no—
183#10621877—22no—
184#10621877—41no—
185#10621877—41no—
186#10621877—41no—
187#10621877—41no—
188#10621877—41no—
189#10621877—41no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C23×C43—42no—
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43C2×C4⋊C411yescharacteristic
199C23×C43#11711yescharacteristic
200C23×C43C4×D411yescharacteristic
201C23×C43C4×D411yescharacteristic
202C23×C43C4×D411yescharacteristic
203C23×C43C4×D411yescharacteristic
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—24no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—44no—
211C22×D43—44no—
212C22×D43—44no—
213C22×D43—44no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C2×C4×C43—44no—
222C2×C4×C43—42no—
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43C22⋊Q811yescharacteristic
235C2×C4×C43C22⋊Q811yescharacteristic
236C2×C4×C43C22⋊Q811yescharacteristic
237C2×C4×C43C22⋊Q811yescharacteristic
238C2×C4×C43C22⋊Q811yescharacteristic
239C2×C4×C43C22⋊Q811yescharacteristic
240C2×C4×C43#12311yescharacteristic
241C2×C4×C43#12311yescharacteristic
242C2×C4×C43#12311yescharacteristic
243C2×C4×C43#12311yescharacteristic
244C2×C4×C43#12311yescharacteristic
245C2×C4×C43#12411yescharacteristic
246C2×C4×C43#12411yescharacteristic
247C2×C4×C43#12411yescharacteristic
248C2×C4×C43#12611yescharacteristic
249C2×C4×C43#12611yescharacteristic
250C2×C4×C43#12711yescharacteristic
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—44no—
260C4×D43—42no—
261C4×D43—42no—
262C4×D43—42no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267C4×D43—42no—
268C8×C43—42no—
269C8×C43—42no—
270C43⋊C8—42no—
271C43⋊C8—42no—
272#11071—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43#38011yescharacteristic
281C22×C43#38511yescharacteristic
282C22×C43#38511yescharacteristic
283C22×C43#38611yescharacteristic
284C22×C43#38811yescharacteristic
285C22×C43#38811yescharacteristic
286C22×C43#39011yescharacteristic
287C2×D43—24no—
288C2×D43—24no—
289C2×D43—24no—
290C2×D43—44no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—44no—
295C2×D43—44no—
296C2×D43—44no—
297C2×D43—42no—
298C4×C43—82no—
299C4×C43#39211yescharacteristic
300C4×C43#39311yescharacteristic
301C4×C43#39411yescharacteristic
302C4×C43#39411yescharacteristic
303C4×C43#39611yescharacteristic
304C4×C43#39611yescharacteristic
305C4×C43#39711yescharacteristic
306C4×C43#39911yescharacteristic
307Dic43—44no—
308Dic43—42no—
309#2905—431no—
310C2×#407—431no—
311C2×#407—431no—
312#2280—431no—
313C2×#344—431no—
314C2×#344D4311yescharacteristic, complemented
315#1742—431no—
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43#143911yescharacteristic
323C2×C43#189112yes—
324D43—44no—
325C24×C4—431no—
326C22×M16—431no—
327C22×M16—431no—
328C22×M16C2×D4311yescharacteristic
329C22×M16C2×D4311yescharacteristic
330C2×#117—431no—
331C2×#117C2×D4311yescharacteristic
332#424—862no—
333#424—862no—
334#423—862no—
335#407—862no—
336#407—862no—
337#407—862no—
338#407—862no—
339C2×C22⋊C8—862no—
340C2×C22⋊C8—862no—
341#381—432no—
342#380—862no—
343#379—432no—
344C4×C22⋊C4—862no—
345#344—22no—
346#344—862no—
347#343—862no—
348C43#1107111yescharacteristic, complemented, Sylow
349C25—431no—
350C23×C4—431no—
351C23×C4—432no—
352C23×C4—432no—
353C23×C4—861no—
354C23×C4—861no—
355C23×C4—861no—
356C23×C4—861no—
357C23×C4—861no—
358C23×C4—861no—
359C23×C4—861no—
360C23×C4—861no—
361C23×C4—861no—
362C23×C4—861no—
363C23×C4—861no—
364C23×C4—861no—
365C23×C4C22×D4311yescharacteristic
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—432no—
378C2×M16—861no—
379C2×M16—861no—
380C2×M16—861no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16C22⋊D4312yes—
390C22×C8—21no—
391C22×C8—432no—
392C22×C8—861no—
393C22×C8D17212yes—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—861no—
399#117—861no—
400#117—861no—
401#117—861no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—432no—
404C2×C22⋊C4—432no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4C4×D4312yes—
407C2×C42—21no—
408C2×C42—432no—
409C4⋊C8—868no—
410C22⋊C8—868no—
411C22⋊C8—868no—
412#95—864no—
413C24—432no—
414C24—861no—
415C24—861no—
416C24—861no—
417C24—861no—
418C24—861no—
419C24—861no—
420C24—1724no—
421C24C2×C4×D4311yescharacteristic
422C22×C4—22no—
423C22×C4—432no—
424C22×C4—434no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1721no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4C2×D17211yescharacteristic
460C22×C4#1062189811yescharacteristic
461C22×C4#1062189811yescharacteristic
462C22×C4#1062189811yescharacteristic
463C22×C4#1062189811yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4#1062190011yescharacteristic
470C22×C4Q8×D4311yescharacteristic
471C22×C4#1062190211yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—862no—
482M16—862no—
483M16—1721no—
484M16—1721no—
485M16—1721no—
486M16—1721no—
487M16—1721no—
488M16—1721no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—862no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—862no—
499C2×C8—1721no—
500C2×C8—1721no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—1728no—
510C42—41no—
511C42—41no—
512C42—862no—
513C42—862no—
514C23—42no—
515C23—864no—
516C23—864no—
517C23—864no—
518C23—862no—
519C23—862no—
520C23—862no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23—1724no—
525C23—1724no—
526C23—1724no—
527C23—1724no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23C22⋊C4×D4311yescharacteristic
533C23C4⋊C4×D4311yescharacteristic
534C23#1306328211yescharacteristic
535C23(C22⋊D43)⋊C411yescharacteristic
536C23C4×C22⋊D4311yescharacteristic
537C23#1306328711yescharacteristic
538C23C4×D17211yescharacteristic
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—864no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1724no—
558C2×C4#1306329311yescharacteristic
559C2×C4#1306329511yescharacteristic
560C2×C4#1306329511yescharacteristic
561C2×C4#1306329711yescharacteristic
562C2×C4#1306329811yescharacteristic
563C2×C4#1306329811yescharacteristic
564C2×C4#1306329811yescharacteristic
565C2×C4#1306329811yescharacteristic
566C2×C4#1306329811yescharacteristic
567C2×C4#1306329911yescharacteristic
568C2×C4#1306330011yescharacteristic
569C2×C4#1306330111yescharacteristic
570C2×C4#1306330311yescharacteristic
571C2×C4#1306330311yescharacteristic
572C2×C4#1306330311yescharacteristic
573C2×C4#1306330311yescharacteristic
574C2×C4#1306330511yescharacteristic
575C2×C4#1306330711yescharacteristic
576C2×C4#1306330811yescharacteristic
577C2×C4#1306331011yescharacteristic
578C2×C4#1306331011yescharacteristic
579C2×C4#1306331011yescharacteristic
580C2×C4#1306331111yescharacteristic
581C2×C4#1306331111yescharacteristic
582C2×C4#1306331311yescharacteristic
583C2×C4#1306331911yescharacteristic
584C2×C4#1306332011yescharacteristic
585C2×C4#1306332111yescharacteristic
586C8—42no—
587C8—42no—
588C8—1722no—
589C8—1722no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—864no—
598C22—864no—
599C22—864no—
600C22—1724no—
601C22—1722no—
602C22—1722no—
603C22—1722no—
604C22—1724no—
605C22—1724no—
606C22—1724no—
607C22—1722no—
608C22#1458275811yescharacteristic
609C22#1458277011yescharacteristic
610C22#1458277311yescharacteristic
611C22#1458277711yescharacteristic
612C22#1458278811yescharacteristic
613C22#1458279011yescharacteristic
614C22#1458279911yescharacteristic
615C4—82no—
616C4—1724no—
617C4—1722no—
618C4#1458280811yescharacteristic
619C4#1458281211yescharacteristic
620C4#1458281411yescharacteristic
621C4#1458281711yescharacteristic
622C4#1458282111yescharacteristic
623C4#1458282311yescharacteristic
624C4#1458282811yescharacteristic
625C4#1458283411yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—1724no—
633C2#1913283911yescharacteristic
634C2#1913501212yes—
subgroupG/H
centerC2×C4#13063295
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#11071
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. #19143158C2semidirect
5. C2×#14582669C2semidirect
6. #19134333C2semidirect
7. C2×C43×#344C2semidirect
314. C2×#344D43semidirect
348. C43#11071semidirect

Maximal subgroups

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

subgroupindex
#191431582
C2×#145828622
#191369742
C2×#145826692
#191343332
C2×C43×#3442
#1107143