Finite Group Databasebeta

← #25002077

Subgroups — #25002077

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2C2×#14582917C211yesmaximal, characteristic
3C2×#14582915C211yesmaximal, characteristic
4#19134333C211yesmaximal, characteristic, complemented
5#19134327C211yesmaximal, characteristic, complemented
6#19134314C211yesmaximal, characteristic, complemented
7C43×#1736C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583380—22no—
11#14583380—22no—
12#14583380—22no—
13#14583380—22no—
14C2×#13063290C412yescomplemented
15C2×#13063287C412yescomplemented
16C2×C4×C22⋊D43—22no—
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063283—21no—
20C2×C4⋊C4×D43—21no—
21#14582917—22no—
22#14582917C414yescomplemented
23#14582915—22no—
24#14582915C414yescomplemented
25C2×#13063253—22no—
26C2×#13063251—22no—
27#14582667—21no—
28#14582667—21no—
29#14582665—22no—
30#14582661—22no—
31C22×M16×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#340—22no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898C2×C412yes—
42C2×#10621898C2×C412yes—
43C2×#10621898D412yes—
44C2×#10621898D412yes—
45C2×#10621898D412yes—
46C2×#10621898Q812yes—
47C22×Dic86C2×C411yescharacteristic
48C22×D172C2×C411yescharacteristic
49C22×C22⋊D43—21no—
50C22×C4×D43—21no—
51C22×C4×D43—22no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877C2×C412yescomplemented
58C22×C43⋊C8—21no—
59#13063290—24no—
60#13063290—24no—
61#13063287—24no—
62#13063287—24no—
63C4×C22⋊D43—28no—
64C4×C22⋊D43—28no—
65#13063284—21no—
66#13063284—21no—
67#13063284—21no—
68#13063284—21no—
69#13063284—21no—
70#13063284—21no—
71#13063284—21no—
72#13063284C2×C412yescomplemented
73#13063283—24no—
74#13063283—24no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43D411yescharacteristic
78C2×Dic43⋊C4—22no—
79C4⋊C4×D43—24no—
80C4⋊C4×D43—24no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43D412yes—
83C2×(C2×D43)⋊C4—22no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2×C412yes—
87#13063253—28no—
88#13063251—28no—
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43C2×C412yescomplemented
97C22×C8×C43—21no—
98#117×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43C2×C412yescomplemented
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2×C412yes—
107C2×C4⋊C4×C43D412yes—
108C2×C4⋊C4×C43D412yes—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—41no—
117C22×C4×C43—82no—
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C22×C411yescharacteristic
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×Q811yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C22×Dic43—21no—
139C22×Dic43—41no—
140C22×Dic43C22⋊C412yes—
141C22×Dic43C22⋊C412yes—
142#10621898—22no—
143#10621898—22no—
144#10621898—22no—
145#10621898—22no—
146#10621898—22no—
147#10621898—22no—
148#10621898—22no—
149#10621898—22no—
150#10621898—22no—
151#10621898—22no—
152#10621898—22no—
153#10621898—22no—
154#10621898C22⋊C414yes—
155#10621898C22⋊C414yes—
156#10621898C4⋊C414yes—
157#10621898C4⋊C414yes—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172C4212yes—
162C2×D172C22⋊C412yes—
163C2×D172C4⋊C412yes—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—28no—
171C2×C4×D43—84no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86C4212yes—
176C2×Dic86C22⋊C412yes—
177C2×Dic86C4⋊C412yes—
178M16×C43—22no—
179M16×C43—22no—
180M16×C43—41no—
181M16×C43—41no—
182C2×C8×C43—22no—
183C2×C8×C43—41no—
184C2×C8×C43—41no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43C22⋊C414yes—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—41no—
193C42×C43—22no—
194C42×C43—41no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—41no—
199(C2×D43)⋊C4—28no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—41no—
206Dic43⋊C4—28no—
207C4×Dic43—28no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—41no—
212#10621877—22no—
213#10621877—22no—
214#10621877—41no—
215#10621877—41no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—41no—
218C2×C43⋊C8—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C2×C22⋊C411yescharacteristic
222C23×C43C4×D411yescharacteristic
223C23×C43C4×D411yescharacteristic
224C23×C43#12011yescharacteristic
225C23×C43#12011yescharacteristic
226C23×C43#12111yescharacteristic
227C23×C43C22⋊Q811yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—42no—
232C22×D43—42no—
233C2×C4×C43—24no—
234C2×C4×C43—44no—
235C2×C4×C43—42no—
236C2×C4×C43—82no—
237C2×C4×C43—82no—
238C2×C4×C43—81no—
239C2×C4×C43—81no—
240C2×C4×C43C2×C4211yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C4⋊C411yescharacteristic
246C2×C4×C43C2×C4⋊C411yescharacteristic
247C2×C4×C43C2×C4⋊C411yescharacteristic
248C2×C4×C43#11711yescharacteristic
249C2×C4×C43#11711yescharacteristic
250C2×C4×C43C4×D411yescharacteristic
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C4×D411yescharacteristic
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12111yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43C22⋊Q811yescharacteristic
262C2×C4×C43C22⋊Q811yescharacteristic
263C2×C4×C43C22⋊Q811yescharacteristic
264C2×C4×C43#12311yescharacteristic
265C2×C4×C43#12311yescharacteristic
266C2×C4×C43#12311yescharacteristic
267C2×C4×C43#12311yescharacteristic
268C22⋊D43—24no—
269C22⋊D43—24no—
270C22⋊D43—24no—
271C22⋊D43—24no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282D172—22no—
283D172—22no—
284D172—22no—
285D172#9514yes—
286C4×D43—24no—
287C4×D43—24no—
288C4×D43—24no—
289C4×D43—24no—
290C4×D43—88no—
291Dic86—22no—
292Dic86—22no—
293Dic86—22no—
294Dic86#9514yes—
295C8×C43—42no—
296C43⋊C8—42no—
297#10775—431nomaximal, Sylow
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43C4×C22⋊C411yescharacteristic
309C22×C43#37911yescharacteristic
310C22×C43#38011yescharacteristic
311C22×C43#38511yescharacteristic
312C22×C43#38511yescharacteristic
313C22×C43#38611yescharacteristic
314C22×C43#38611yescharacteristic
315C2×D43—24no—
316C2×D43—44no—
317C2×D43—44no—
318C2×D43—42no—
319C2×D43—42no—
320C4×C43—44no—
321C4×C43—82no—
322C4×C43C2×#9511yescharacteristic
323C4×C43C4×C22⋊C411yescharacteristic
324C4×C43#38011yescharacteristic
325C4×C43#38111yescharacteristic
326C4×C43#38511yescharacteristic
327C4×C43#38511yescharacteristic
328C4×C43#38611yescharacteristic
329C4×C43#38611yescharacteristic
330Dic43—24no—
331Dic43—42no—
332Dic43—42no—
333Dic43—82no—
334C2×#520—431no—
335C2×#421—431no—
336C2×#421—431no—
337#1742—431no—
338#1740—431no—
339#1736—431no—
340#1736D4311yescharacteristic, complemented
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43C22⋊#9511yescharacteristic
348C2×C43#179511yescharacteristic
349C2×C43#179611yescharacteristic
350D43—44no—
351C22×#41—431no—
352C22×M16—431no—
353C22×M16C2×D4311yescharacteristic
354#520—862no—
355#520—862no—
356#520—862no—
357#520—862no—
358C2×C4×Q8—432no—
359C2×C4×D4—432no—
360C2×C4×D4—862no—
361C2×#117—431no—
362C2×#117—431no—
363C2×#117—861no—
364C2×#117C2×D4311yescharacteristic
365C22×C4⋊C4—861no—
366C22×C4⋊C4C2×D4311yescharacteristic
367#421—434no—
368#421—434no—
369#421—862no—
370#421—862no—
371C2×#104—862no—
372C2×#104—862no—
373#343—861no—
374#343—861no—
375#342—862no—
376#340—22no—
377#340—862no—
378C43#1077511yescharacteristic, complemented, Sylow
379C2×#41—432no—
380C2×#41—432no—
381C2×#41—432no—
382C2×#41—432no—
383C2×#41—432no—
384C2×#41—432no—
385C2×#41—861no—
386C2×#41—861no—
387C2×#41—861no—
388C2×#41—861no—
389C2×#41—861no—
390C2×#41—861no—
391C22×Q8—431no—
392C22×D4—431no—
393C22×D4—861no—
394C23×C4—21no—
395C23×C4—862no—
396C23×C4—861no—
397C23×C4C22×D4311yescharacteristic
398C2×M16—21no—
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—432no—
404C2×M16—861no—
405C2×M16—861no—
406C2×M16—861no—
407C2×M16—861no—
408C2×M16—861no—
409C2×M16C4×D4312yescomplemented
410C22×C8—21no—
411C22×C8—861no—
412C4×Q8—864no—
413C4×Q8—864no—
414C4×D4—864no—
415C4×D4—868no—
416C4×D4—868no—
417C4×D4—864no—
418#117—21no—
419#117—21no—
420#117—21no—
421#117—432no—
422#117—864no—
423#117—864no—
424#117—861no—
425#117—861no—
426#117—861no—
427#117—861no—
428#117—861no—
429#117—861no—
430#117—861no—
431#117C4×D4312yescomplemented
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—864no—
439C2×C4⋊C4—864no—
440C2×C4⋊C4—862no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4C4×D4312yes—
443C2×C4⋊C4D17212yes—
444C2×C4⋊C4C22⋊D4312yes—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—432no—
447C2×C22⋊C4—862no—
448C2×C22⋊C4—861no—
449C2×C42—21no—
450C2×C42—432no—
451C2×C42—862no—
452C2×C42—861no—
453#104—868no—
454#104—868no—
455C24—861no—
456C24D4×D4311yescharacteristic
457#41—434no—
458#41—434no—
459#41—434no—
460#41—434no—
461#41—862no—
462#41—862no—
463#41—862no—
464#41—862no—
465#41—862no—
466#41—862no—
467#41—862no—
468#41—862no—
469#41—862no—
470#41—862no—
471#41—862no—
472#41—862no—
473C2×Q8—432no—
474C2×Q8—432no—
475C2×Q8—432no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×D4—432no—
480C2×D4—432no—
481C2×D4—432no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4—862no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—41no—
495C22×C4—82no—
496C22×C4—432no—
497C22×C4—432no—
498C22×C4—868no—
499C22×C4—861no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—3444no—
507C22×C4—1721no—
508C22×C4C2×C4×D4311yescharacteristic
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4C2×C4×D4311yescharacteristic
511C22×C4C2×D17211yescharacteristic
512C22×C4#1062189811yescharacteristic
513C22×C4#1062189811yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4#1062190011yescharacteristic
519C22×C4Q8×D4311yescharacteristic
520C22×C4#1062190211yescharacteristic
521C22×C4C2×C22⋊D4311yescharacteristic
522M16—22no—
523M16—22no—
524M16—41no—
525M16—41no—
526M16—862no—
527M16—862no—
528M16—1721no—
529M16—1721no—
530C2×C8—22no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—862no—
534C2×C8—1721no—
535C2×C8—1721no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—868no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—862no—
547C4⋊C4—1721no—
548C4⋊C4(C2×D43)⋊C414yes—
549C22⋊C4—22no—
550C22⋊C4—41no—
551C22⋊C4—868no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—1721no—
556C42—22no—
557C42—41no—
558C42—868no—
559C42—862no—
560C42—862no—
561C42—862no—
562C42—1721no—
563C23—41no—
564C23—41no—
565C23—862no—
566C23—862no—
567C23—862no—
568C23—1722no—
569C23—1722no—
570C23C22⋊C4×D4311yescharacteristic
571C23(C22⋊D43)⋊C411yescharacteristic
572C23#1306328711yescharacteristic
573C23#1306329311yescharacteristic
574C23#1306329511yescharacteristic
575C23#1306329811yescharacteristic
576C23#1306330311yescharacteristic
577Q8—434no—
578Q8—862no—
579Q8—862no—
580Q8—862no—
581D4—434no—
582D4—864no—
583D4—864no—
584D4—864no—
585D4—864no—
586D4—862no—
587D4—862no—
588D4—862no—
589C2×C4—24no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—3448no—
606C2×C4—3441no—
607C2×C4—3441no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4C42×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C2×(C2×D43)⋊C411yescharacteristic
616C2×C4C4⋊C4×D4311yescharacteristic
617C2×C4C4⋊C4×D4311yescharacteristic
618C2×C4C4⋊C4×D4311yescharacteristic
619C2×C4#1306328211yescharacteristic
620C2×C4#1306328311yescharacteristic
621C2×C4(C22⋊D43)⋊C411yescharacteristic
622C2×C4C4×C22⋊D4311yescharacteristic
623C2×C4C4×C22⋊D4311yescharacteristic
624C2×C4#1306328711yescharacteristic
625C2×C4C4×D17211yescharacteristic
626C2×C4C4×D17211yescharacteristic
627C2×C4#1306329311yescharacteristic
628C2×C4#1306329511yescharacteristic
629C2×C4#1306329611yescharacteristic
630C2×C4#1306329811yescharacteristic
631C2×C4#1306330011yescharacteristic
632C2×C4#1306330111yescharacteristic
633C2×C4#1306330311yescharacteristic
634C2×C4#1306330511yescharacteristic
635C2×C4#1306330711yescharacteristic
636C2×C4#1306330711yescharacteristic
637C2×C4#1306331011yescharacteristic
638C2×C4#1306331011yescharacteristic
639C8—42no—
640C8—1722no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—864no—
652C22—1724no—
653C22—1724no—
654C22—1722no—
655C22—1722no—
656C22#1458274611yescharacteristic
657C22#1458275411yescharacteristic
658C22#1458275811yescharacteristic
659C22#1458277011yescharacteristic
660C22#1458277311yescharacteristic
661C22#1458277511yescharacteristic
662C22#1458277711yescharacteristic
663C4—44no—
664C4—82no—
665C4—864no—
666C4—3442no—
667C4—1722no—
668C4—1722no—
669C4#95×D4311yescharacteristic
670C4C4×(C2×D43)⋊C411yescharacteristic
671C4#1458275611yescharacteristic
672C4#1458276111yescharacteristic
673C4#1458277011yescharacteristic
674C4#1458277311yescharacteristic
675C4#1458277511yescharacteristic
676C4#1458277711yescharacteristic
677C2—21no—
678C2—21no—
679C2—21no—
680C2—21no—
681C2—21no—
682C2—21no—
683C2—1724no—
684C2(C2×D43)⋊#9511yescharacteristic
685C2#1913456211yescharacteristic
686C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1736C2
socleC22×C43#379
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1736D43
hypocenterC43#10775
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #19134333C2semidirect
5. #19134327C2semidirect
6. #19134314C2semidirect
7. C43×#1736C2semidirect
14. C2×#13063290C4semidirect
15. C2×#13063287C4semidirect
22. #14582917C4semidirect
24. #14582915C4semidirect
57. C2×#10621877C2×C4semidirect
72. #13063284C2×C4semidirect
96. C2×M16×C43C2×C4semidirect
101. #117×C43C2×C4semidirect
340. #1736D43semidirect
378. C43#10775semidirect
409. C2×M16C4×D43semidirect
431. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833802
C2×#145829172
C2×#145829152
#191343332
#191343272
#191343142
C43×#17362
#1077543