Finite Group Databasebeta

← #25003679

Subgroups — #25003679

Order 11008.

1202 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137207C211yesmaximal, characteristic
2C2×#14582760C211yesmaximal, characteristic
3C2×#14582760C211yesmaximal, characteristic
4C2×#14582760C211yesmaximal, characteristic
5C2×#14582665C211yesmaximal, characteristic
6C2×#14582665C211yesmaximal, characteristic
7C2×C43×#342C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12#14582772—22no—
13#14582771—22no—
14#14582760—22no—
15#14582760—22no—
16#14582760—22no—
17#14582760—22no—
18#14582760—22no—
19#14582760C414yescomplemented
20#14582757—22no—
21C2×C43⋊#95—22no—
22C2×C43⋊#95—22no—
23C2×C43⋊#95—22no—
24#14582665—22no—
25#14582665—22no—
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C43×#342—22no—
30C23×Dic43—21no—
31C23×Dic43—21no—
32C23×Dic43—21no—
33C23×Dic43—21no—
34C23×Dic43—21no—
35C23×Dic43—21no—
36C23×Dic43—21no—
37C23×Dic43—21no—
38C23×Dic43—21no—
39C23×Dic43—21no—
40C23×Dic43—21no—
41C23×Dic43—21no—
42C23×Dic43—21no—
43C23×Dic43C2×C412yes—
44C23×Dic43D412yes—
45C23×Dic43D412yes—
46C23×Dic43D412yes—
47C23×Dic43Q812yes—
48C2×Dic43⋊C4—24no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43C2×C412yes—
65C2×C22⋊Dic43D412yes—
66C2×C22⋊Dic43D412yes—
67C43⋊#95—28no—
68C43⋊#95—28no—
69C43⋊#95—24no—
70C43⋊#95—28no—
71C25×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43D412yes—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43C2×C412yes—
92C2×C22⋊C4×C43D412yes—
93C24×C43—44no—
94C24×C43C22×C411yescharacteristic
95C24×C43C2×D411yescharacteristic
96C24×C43C2×D411yescharacteristic
97C24×C43C2×D411yescharacteristic
98C24×C43C2×D411yescharacteristic
99C24×C43C2×D411yescharacteristic
100C24×C43C2×D411yescharacteristic
101C24×C43C2×D411yescharacteristic
102C24×C43C2×Q811yescharacteristic
103C24×C43#4111yescharacteristic
104C24×C43#4111yescharacteristic
105C24×C43#4111yescharacteristic
106C24×C43#4111yescharacteristic
107C24×C43#4111yescharacteristic
108C24×C43#4111yescharacteristic
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—44no—
115C22×C4×C43—44no—
116C22×C4×C43—44no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
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—22no—
144C22×Dic43—22no—
145C22×Dic43—44no—
146C22×Dic43—44no—
147C22×Dic43—44no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C22×Dic43—41no—
165C22×Dic43—41no—
166C22×Dic43C22⋊C414yes—
167C22×Dic43C4⋊C414yescomplemented
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189C22⋊Dic43—41no—
190C22⋊Dic43—41no—
191C22⋊Dic43—41no—
192Dic43⋊C4—84no—
193C23×C43—24no—
194C23×C43—24no—
195C23×C43—24no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43C2×C22⋊C411yescharacteristic
209C23×C43C2×C4⋊C411yescharacteristic
210C23×C43#11711yescharacteristic
211C23×C43C4×D411yescharacteristic
212C23×C43C4×D411yescharacteristic
213C23×C43C4×D411yescharacteristic
214C23×C43C4×D411yescharacteristic
215C23×C43#12011yescharacteristic
216C23×C43#12011yescharacteristic
217C23×C43#12011yescharacteristic
218C23×C43#12111yescharacteristic
219C23×C43#12111yescharacteristic
220C23×C43#12111yescharacteristic
221C23×C43#12111yescharacteristic
222C23×C43#12111yescharacteristic
223C23×C43#12111yescharacteristic
224C23×C43#12111yescharacteristic
225C23×C43#12111yescharacteristic
226C23×C43C22⋊Q811yescharacteristic
227C23×C43C22⋊Q811yescharacteristic
228C23×C43C22⋊Q811yescharacteristic
229C23×C43C22⋊Q811yescharacteristic
230C23×C43C22⋊Q811yescharacteristic
231C23×C43C22⋊Q811yescharacteristic
232C23×C43#12311yescharacteristic
233C23×C43#12311yescharacteristic
234C23×C43#12311yescharacteristic
235C23×C43#12311yescharacteristic
236C23×C43#12311yescharacteristic
237C23×C43#12411yescharacteristic
238C23×C43#12411yescharacteristic
239C23×C43#12411yescharacteristic
240C23×C43#12611yescharacteristic
241C23×C43#12611yescharacteristic
242C23×C43#12711yescharacteristic
243C2×C4×C43—44no—
244C2×C4×C43—44no—
245C2×C4×C43—44no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—44no—
250C2×C4×C43—82no—
251C2×C4×C43—82no—
252C2×C4×C43—82no—
253C2×C4×C43—82no—
254C2×C4×C43—82no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—44no—
272C2×Dic43—44no—
273C2×Dic43—44no—
274C2×Dic43—44no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—44no—
278C2×Dic43—82no—
279C2×Dic43—82no—
280C2×Dic43—82no—
281C2×Dic43—82no—
282#11070—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43#38011yescharacteristic
318C22×C43#38511yescharacteristic
319C22×C43#38511yescharacteristic
320C22×C43#38611yescharacteristic
321C22×C43#38811yescharacteristic
322C22×C43#38811yescharacteristic
323C22×C43#39011yescharacteristic
324C22×C43#39211yescharacteristic
325C22×C43#39311yescharacteristic
326C22×C43#39411yescharacteristic
327C22×C43#39411yescharacteristic
328C22×C43#39611yescharacteristic
329C22×C43#39611yescharacteristic
330C22×C43#39711yescharacteristic
331C22×C43#39911yescharacteristic
332C22×C43#45814yes—
333C4×C43—82no—
334C4×C43—82no—
335C4×C43—82no—
336Dic43—44no—
337Dic43—44no—
338Dic43—82no—
339Dic43—82no—
340#2315—431no—
341C2×#381—431no—
342C2×#381—431no—
343C2×#381—431no—
344C2×#342—431no—
345C2×#342—431no—
346C2×#342D4311yescharacteristic
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—21no—
353C2×C43—21no—
354C2×C43—21no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—21no—
358C2×C43—21no—
359C2×C43#143911yescharacteristic
360C2×C43#189012yes—
361C2×C43#202212yes—
362C2×C43#203012yes—
363C24×C4—431no—
364C22×C22⋊C4—431no—
365C22×C22⋊C4—431no—
366C22×C22⋊C4—431no—
367C22×C22⋊C4C2×D4311yescharacteristic
368C22×C22⋊C4C2×D4311yescharacteristic
369C22×C22⋊C4C2×D4311yescharacteristic
370#385—862no—
371#385—862no—
372#381—434no—
373#381—862no—
374#381—862no—
375#381—862no—
376#381—862no—
377#381—862no—
378#380—862no—
379C2×#95—862no—
380C2×#95—862no—
381C2×#95—862no—
382#342—22no—
383#342—862no—
384#342—862no—
385C43#1107011yescharacteristic, complemented, Sylow
386C25C22×D4311yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—432no—
390C23×C4—432no—
391C23×C4—432no—
392C23×C4—432no—
393C23×C4—432no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C23×C4—861no—
402C23×C4—861no—
403C23×C4—861no—
404C23×C4—861no—
405C23×C4—861no—
406C23×C4—861no—
407C23×C4D17212yes—
408C2×C4⋊C4—864no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—432no—
426C2×C22⋊C4—432no—
427C2×C22⋊C4—432no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4C4×D4312yes—
444C2×C22⋊C4C22⋊D4312yes—
445#95—868no—
446#95—868no—
447#95—868no—
448#95—864no—
449C24—44no—
450C24C2×C4×D4311yescharacteristic
451C24C2×D17211yescharacteristic
452C24#1062189811yescharacteristic
453C24#1062189811yescharacteristic
454C24#1062189811yescharacteristic
455C24#1062189811yescharacteristic
456C24D4×D4311yescharacteristic
457C24D4×D4311yescharacteristic
458C24D4×D4311yescharacteristic
459C24D4×D4311yescharacteristic
460C24D4×D4311yescharacteristic
461C24#1062190011yescharacteristic
462C24Q8×D4311yescharacteristic
463C24#1062190211yescharacteristic
464C24C2×C22⋊D4311yescharacteristic
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—434no—
478C22×C4—434no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—1724no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1724no—
507C22×C4—1724no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4—1721no—
511C22×C4—1721no—
512C22×C4—1721no—
513C22×C4—1721no—
514C22×C4—1721no—
515C22×C4—1721no—
516C22×C4—1721no—
517C22×C4—1721no—
518C22×C4—1721no—
519C22×C4—1721no—
520C22×C4—1721no—
521C22×C4—1721no—
522C22×C4—1721no—
523C22×C4—1721no—
524C4⋊C4—3444no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—1721no—
544C22⋊C4—1721no—
545C22⋊C4—1721no—
546C22⋊C4—1721no—
547C22⋊C4—1721no—
548C22⋊C4—1721no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23C22⋊C4×D4311yescharacteristic
565C23C4⋊C4×D4311yescharacteristic
566C23#1306328211yescharacteristic
567C23(C22⋊D43)⋊C411yescharacteristic
568C23C4×C22⋊D4311yescharacteristic
569C23#1306328711yescharacteristic
570C23C4×D17211yescharacteristic
571C23#1306329311yescharacteristic
572C23#1306329511yescharacteristic
573C23#1306329511yescharacteristic
574C23#1306329711yescharacteristic
575C23#1306329811yescharacteristic
576C23#1306329811yescharacteristic
577C23#1306329811yescharacteristic
578C23#1306329811yescharacteristic
579C23#1306329811yescharacteristic
580C23#1306329911yescharacteristic
581C23#1306330011yescharacteristic
582C23#1306330111yescharacteristic
583C23#1306330311yescharacteristic
584C23#1306330311yescharacteristic
585C23#1306330311yescharacteristic
586C23#1306330311yescharacteristic
587C23#1306330511yescharacteristic
588C23#1306330711yescharacteristic
589C23#1306330811yescharacteristic
590C23#1306331011yescharacteristic
591C23#1306331011yescharacteristic
592C23#1306331011yescharacteristic
593C23#1306331111yescharacteristic
594C23#1306331111yescharacteristic
595C23#1306331311yescharacteristic
596C23#1306331911yescharacteristic
597C23#1306332011yescharacteristic
598C23#1306332111yescharacteristic
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—82no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—864no—
615C2×C4—3442no—
616C2×C4—3442no—
617C2×C4—3442no—
618C2×C4—3442no—
619C2×C4—1724no—
620C2×C4—1724no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1724no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1722no—
634C2×C4—1722no—
635C2×C4—1724no—
636C2×C4—1722no—
637C2×C4—1724no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22#1458275811yescharacteristic
673C22#1458277011yescharacteristic
674C22#1458277311yescharacteristic
675C22#1458277711yescharacteristic
676C22#1458278811yescharacteristic
677C22#1458279011yescharacteristic
678C22#1458279911yescharacteristic
679C22#1458280811yescharacteristic
680C22#1458281211yescharacteristic
681C22#1458281411yescharacteristic
682C22#1458281711yescharacteristic
683C22#1458282111yescharacteristic
684C22#1458282311yescharacteristic
685C22#1458282811yescharacteristic
686C22#1458283411yescharacteristic
687C22#1458309014yes—
688C4—82no—
689C4—82no—
690C4—82no—
691C4—3442no—
692C4—3442no—
693C4—1724no—
694C4—1724no—
695C2—21no—
696C2—21no—
697C2—21no—
698C2—21no—
699C2—21no—
700C2—21no—
701C2—21no—
702C2—21no—
703C2—21no—
704C2—21no—
705C2—21no—
706C2—21no—
707C2#1913283911yescharacteristic
708C2#1913500712yes—
709C2#1913572512yes—
710C2#1913576312yes—
subgroupG/H
centerC23#13063295
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43#120
prime radical, cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#11070
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
19. #14582760C4semidirect
167. C22×Dic43C4⋊C4semidirect
385. C43#11070semidirect

Maximal subgroups

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

subgroupindex
#191372072
C2×#145827602
C2×#145826652
C2×C43×#3422
#1107043