Finite Group Databasebeta

← #25002064

Subgroups — #25002064

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2C2×#14582915C211yesmaximal, characteristic
3#19143115C211yesmaximal, characteristic
4#19134327C211yesmaximal, characteristic, complemented
5C2×#14582660C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583367—22no—
10#14583367—22no—
11#14583367—22no—
12#14583367C414yescomplemented
13C2×#13063290—21no—
14C2×#13063287—21no—
15C2×(C22⋊D43)⋊C4—22no—
16C2×#13063284C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063282—21no—
19C22×C4×Dic43C2211yescharacteristic
20C2×C42×D43—21no—
21#14582915—22no—
22#14582915C414yescomplemented
23C2×#13063251—22no—
24#14582909—21no—
25#14582905—21no—
26#14582901C414yescomplemented
27#14582896—22no—
28#14582665—22no—
29#14582660—21no—
30#14582660—21no—
31#14582660—22no—
32C22×M16×C43C2211yescharacteristic
33C22×M16×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C43×#344—22no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898C2×C412yes—
43C2×#10621898C2×C412yes—
44C2×#10621898C2×C412yes—
45C2×#10621898D412yes—
46C2×#10621898D412yes—
47C2×#10621898Q812yes—
48C22×Dic86D411yescharacteristic
49C22×D172D411yescharacteristic
50C22×C22⋊D43—21no—
51C23×Dic43—21no—
52C22×C4×D43—21no—
53C22×C4×D43—22no—
54#13063290—24no—
55#13063290—24no—
56#13063287—24no—
57#13063287—24no—
58(C22⋊D43)⋊C4—28no—
59(C22⋊D43)⋊C4—28no—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66#13063284—21no—
67#13063284C2×C412yescomplemented
68#13063282—24no—
69#13063282—24no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2×C412yescomplemented
72C2×Dic43⋊C4—22no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×(C2×D43)⋊C4—22no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2×C412yes—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D412yes—
86C42×D43—24no—
87C42×D43—24no—
88#13063251—28no—
89#13063250—24no—
90#13063247—24no—
91C23×C4×C43C2311yescharacteristic
92C2×M16×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43—21no—
97C2×M16×C43—21no—
98C2×M16×C43—21no—
99C2×M16×C43—21no—
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43C2×C412yescomplemented
103C2×M16×C43C2×C412yescomplemented
104C22×C8×C43—21no—
105C22×C8×C43—21no—
106#117×C43—21no—
107#117×C43—21no—
108#117×C43C2×C412yes—
109#117×C43D412yes—
110C2×C4⋊C4×C43—21no—
111C2×C22⋊C4×C43D412yes—
112C2×C42×C43—21no—
113C24×C43C2×D411yescharacteristic
114C23×D43—21no—
115C22×C4×C43—22no—
116C22×C4×C43C22×C411yescharacteristic
117C22×C4×C43C22×C411yescharacteristic
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×Q811yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—44no—
143C22×Dic43—41no—
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#10621898—22no—
155#10621898—22no—
156#10621898C4214yes—
157#10621898C22⋊C414yes—
158#10621898C4⋊C414yes—
159#10621898C4⋊C414yes—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22⋊C412yes—
164C2×D172C22⋊C412yes—
165C2×D172C4⋊C412yes—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—28no—
173C2×C4×D43—48no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86C22⋊C412yes—
178C2×Dic86C22⋊C412yes—
179C2×Dic86C4⋊C412yes—
180M16×C43—22no—
181M16×C43—22no—
182M16×C43—22no—
183M16×C43—22no—
184M16×C43—41no—
185M16×C43—41no—
186M16×C43—41no—
187M16×C43—41no—
188C2×C8×C43—22no—
189C2×C8×C43—22no—
190C2×C8×C43—41no—
191C2×C8×C43—41no—
192C2×C8×C43—41no—
193C2×C8×C43—41no—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—22no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43C22⋊C414yes—
198C42×C43—22no—
199C42×C43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—41no—
202C22⋊Dic43—41no—
203C22⋊Dic43—41no—
204(C2×D43)⋊C4—28no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43—22no—
208C4⋊Dic43—41no—
209Dic43⋊C4—28no—
210C4×Dic43—28no—
211C4×Dic43—22no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—41no—
217C4×Dic43—41no—
218C4×Dic43—41no—
219C4×Dic43C22⋊C412yes—
220C4×Dic43C22⋊C412yes—
221C23×C43—42no—
222C23×C43C2×C22⋊C411yescharacteristic
223C23×C43C4×D411yescharacteristic
224C23×C43C4×D411yescharacteristic
225C23×C43#12011yescharacteristic
226C23×C43#12011yescharacteristic
227C23×C43#12111yescharacteristic
228C23×C43C22⋊Q811yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—44no—
233C2×C4×C43—24no—
234C2×C4×C43—44no—
235C2×C4×C43C2×C4211yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C4⋊C411yescharacteristic
241C2×C4×C43C2×C4⋊C411yescharacteristic
242C2×C4×C43C2×C4⋊C411yescharacteristic
243C2×C4×C43#11711yescharacteristic
244C2×C4×C43#11711yescharacteristic
245C2×C4×C43C4×D411yescharacteristic
246C2×C4×C43C4×D411yescharacteristic
247C2×C4×C43C4×D411yescharacteristic
248C2×C4×C43C4×D411yescharacteristic
249C2×C4×C43C4×D411yescharacteristic
250C2×C4×C43C4×D411yescharacteristic
251C2×C4×C43#12011yescharacteristic
252C2×C4×C43#12011yescharacteristic
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43C22⋊Q811yescharacteristic
257C2×C4×C43C22⋊Q811yescharacteristic
258C2×C4×C43C22⋊Q811yescharacteristic
259C2×C4×C43#12311yescharacteristic
260C2×C4×C43#12311yescharacteristic
261C2×C4×C43#12311yescharacteristic
262C2×C4×C43#12311yescharacteristic
263C22⋊D43—24no—
264C22⋊D43—24no—
265C22⋊D43—24no—
266C22⋊D43—24no—
267C2×Dic43—24no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—44no—
274C2×Dic43—44no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—82no—
279C2×Dic43—82no—
280D172—22no—
281D172—22no—
282D172—22no—
283D172#9514yes—
284C4×D43—24no—
285C4×D43—24no—
286C4×D43—24no—
287C4×D43—24no—
288C4×D43—416no—
289Dic86—22no—
290Dic86—22no—
291Dic86—22no—
292Dic86#9514yes—
293C8×C43—42no—
294C8×C43—42no—
295#10772—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43C4×C22⋊C411yescharacteristic
304C22×C43#37911yescharacteristic
305C22×C43#38011yescharacteristic
306C22×C43#38511yescharacteristic
307C22×C43#38511yescharacteristic
308C22×C43#38611yescharacteristic
309C22×C43#38611yescharacteristic
310C2×D43—24no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—44no—
314C4×C43—44no—
315C4×C43C2×#9511yescharacteristic
316C4×C43C4×C22⋊C411yescharacteristic
317C4×C43#38011yescharacteristic
318C4×C43#38111yescharacteristic
319C4×C43#38511yescharacteristic
320C4×C43#38511yescharacteristic
321C4×C43#38611yescharacteristic
322C4×C43#38611yescharacteristic
323Dic43—24no—
324Dic43—24no—
325Dic43—42no—
326Dic43—82no—
327Dic43—82no—
328C2×C4×#41—431no—
329C2×#421—431no—
330#2896—431no—
331C2×#344D4311yescharacteristic, complemented
332#1740—431no—
333C2×#339—431no—
334C2×#339—431no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43C22⋊#9511yescharacteristic
342C2×C43#190612yes—
343D43—44no—
344C22×#41—431no—
345C22×M16C2×D4311yescharacteristic
346C22×M16C2×D4311yescharacteristic
347C4×#41—434no—
348C4×#41—862no—
349C4×#41—862no—
350C4×#41—862no—
351C2×C4×Q8—861no—
352C2×C4×D4—861no—
353C2×C4×D4—862no—
354C2×#117—431no—
355C2×#117—431no—
356C2×#117—861no—
357C2×#117C2×D4311yescharacteristic
358C22×C42—431no—
359C22×C42—861no—
360#421—434no—
361#421—862no—
362C2×#104—862no—
363#419—861no—
364#418—861no—
365#417—434no—
366#416—862no—
367#344—22no—
368#342—862no—
369#339—861no—
370#339—862no—
371#339—861no—
372C43#1077211yescharacteristic, complemented, Sylow
373C2×#41—432no—
374C2×#41—432no—
375C2×#41—432no—
376C2×#41—432no—
377C2×#41—432no—
378C2×#41—432no—
379C2×#41—861no—
380C2×#41—861no—
381C2×#41—861no—
382C2×#41—861no—
383C2×#41—861no—
384C2×#41—861no—
385C22×Q8—431no—
386C22×D4—431no—
387C22×D4—861no—
388C23×C4—862no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4C22×D4311yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—21no—
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16C4×D4312yescomplemented
403C2×M16C4×D4312yescomplemented
404C22×C8—21no—
405C22×C8—21no—
406C4×Q8—864no—
407C4×Q8—864no—
408C4×D4—868no—
409C4×D4—864no—
410C4×D4—864no—
411C4×D4—868no—
412#117—21no—
413#117—21no—
414#117—432no—
415#117—864no—
416#117—864no—
417#117—861no—
418#117—861no—
419#117—861no—
420#117—861no—
421#117—861no—
422#117—861no—
423#117—861no—
424#117C4×D4312yes—
425#117C22⋊D4312yes—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—432no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4—861no—
430C2×C22⋊C4—862no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4D17212yes—
434C2×C42—21no—
435C2×C42—432no—
436C2×C42—431no—
437C2×C42—432no—
438C2×C42—431no—
439C2×C42—864no—
440C2×C42—864no—
441C2×C42—862no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447#104—868no—
448#103—864no—
449#102—864no—
450C24—861no—
451C24C2×D17211yescharacteristic
452#41—434no—
453#41—434no—
454#41—434no—
455#41—434no—
456#41—862no—
457#41—862no—
458#41—862no—
459#41—862no—
460#41—862no—
461#41—862no—
462#41—862no—
463#41—862no—
464#41—862no—
465#41—862no—
466#41—862no—
467#41—862no—
468C2×Q8—432no—
469C2×Q8—432no—
470C2×Q8—432no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—432no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—862no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C22×C4—22no—
487C22×C4—868no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—1728no—
501C22×C4—1724no—
502C22×C4—1721no—
503C22×C4C2×C4×D4311yescharacteristic
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4#1062189811yescharacteristic
507C22×C4#1062189811yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512C22×C4D4×D4311yescharacteristic
513C22×C4#1062190011yescharacteristic
514C22×C4Q8×D4311yescharacteristic
515C22×C4#1062190211yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517M16—22no—
518M16—22no—
519M16—22no—
520M16—22no—
521M16—41no—
522M16—41no—
523M16—41no—
524M16—41no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—868no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—1721no—
538C22⋊C4—22no—
539C22⋊C4—868no—
540C22⋊C4—862no—
541C22⋊C4—1721no—
542C22⋊C4—1721no—
543C22⋊C4—1721no—
544C22⋊C4(C2×D43)⋊C414yes—
545C42—22no—
546C42—22no—
547C42—432no—
548C42—432no—
549C42—868no—
550C42—862no—
551C42—861no—
552C42—861no—
553C42—862no—
554C42—862no—
555C42—1721no—
556C42—1721no—
557C42—1721no—
558C23—42no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—1724no—
563C23C2×(C2×D43)⋊C411yescharacteristic
564C23C4×D17211yescharacteristic
565C23C4×D17211yescharacteristic
566C23#1306329511yescharacteristic
567C23#1306329511yescharacteristic
568C23#1306330011yescharacteristic
569C23#1306330511yescharacteristic
570Q8—434no—
571Q8—862no—
572Q8—862no—
573Q8—862no—
574D4—434no—
575D4—864no—
576D4—864no—
577D4—864no—
578D4—864no—
579D4—862no—
580D4—862no—
581D4—862no—
582C2×C4—24no—
583C2×C4—44no—
584C2×C4—864no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—864no—
593C2×C4—862no—
594C2×C4—3442no—
595C2×C4—3442no—
596C2×C4—17216no—
597C2×C4—1724no—
598C2×C4—1724no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4C42×D4311yescharacteristic
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C4⋊C4×D4311yescharacteristic
608C2×C4C4⋊C4×D4311yescharacteristic
609C2×C4C4⋊C4×D4311yescharacteristic
610C2×C4#1306328211yescharacteristic
611C2×C4#1306328311yescharacteristic
612C2×C4(C22⋊D43)⋊C411yescharacteristic
613C2×C4(C22⋊D43)⋊C411yescharacteristic
614C2×C4C4×C22⋊D4311yescharacteristic
615C2×C4C4×C22⋊D4311yescharacteristic
616C2×C4#1306328711yescharacteristic
617C2×C4#1306328711yescharacteristic
618C2×C4#1306329311yescharacteristic
619C2×C4#1306329311yescharacteristic
620C2×C4#1306329611yescharacteristic
621C2×C4#1306329811yescharacteristic
622C2×C4#1306329811yescharacteristic
623C2×C4#1306330111yescharacteristic
624C2×C4#1306330311yescharacteristic
625C2×C4#1306330311yescharacteristic
626C2×C4#1306330711yescharacteristic
627C2×C4#1306330711yescharacteristic
628C2×C4#1306331011yescharacteristic
629C2×C4#1306331011yescharacteristic
630C8—42no—
631C8—42no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—864no—
640C22—1724no—
641C22—1724no—
642C22—1724no—
643C22C4×(C2×D43)⋊C411yescharacteristic
644C22#1458275411yescharacteristic
645C22#1458275611yescharacteristic
646C22#1458277311yescharacteristic
647C22#1458277311yescharacteristic
648C22#1458277711yescharacteristic
649C22#1458277711yescharacteristic
650C4—44no—
651C4—864no—
652C4—864no—
653C4—3442no—
654C4—3442no—
655C4—1722no—
656C4#95×D4311yescharacteristic
657C4#1458274611yescharacteristic
658C4#1458275811yescharacteristic
659C4#1458276111yescharacteristic
660C4#1458277011yescharacteristic
661C4#1458277011yescharacteristic
662C4#1458277511yescharacteristic
663C4#1458277511yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—1724no—
671C2(C2×D43)⋊#9511yescharacteristic
672C2#1913509712yes—
subgroupG/H
centerC2×C4#13063298
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#10772
LCSG ▷ C2×C4×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
4. #19134327C2semidirect
5. C2×#14582660C2semidirect
6. C2×#14582660C2semidirect
7. C2×C43×#344C2semidirect
12. #14583367C4semidirect
22. #14582915C4semidirect
26. #14582901C4semidirect
67. #13063284C2×C4semidirect
71. C2×C4⋊Dic43C2×C4semidirect
102. C2×M16×C43C2×C4semidirect
103. C2×M16×C43C2×C4semidirect
331. C2×#344D43semidirect
372. C43#10772semidirect
402. C2×M16C4×D43semidirect
403. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
C2×#145829152
#191431152
#191343272
C2×#145826602
C2×C43×#3442
#1077243