Finite Group Databasebeta

← #25096428

Subgroups — #25096428

Order 11008.

1470 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4#19134693C218yesmaximal, complemented
5#19134306C211yesmaximal, characteristic, complemented
6#19134305C211yesmaximal, characteristic, complemented
7#19134304C211yesmaximal, characteristic, complemented
8C43×#1733C211yesmaximal, characteristic, complemented
9C23×C4×D43C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C2×#13063284C2211yescharacteristic
13C2×#13063283C412yescomplemented
14C2×#13063282—21no—
15C2×#13063281—21no—
16#117×D43—22no—
17#117×D43—22no—
18#117×D43C414yescomplemented
19#117×D43C2214yes—
20C2×C4⋊C4×D43C412yescomplemented
21C2×C22⋊C4×D43—21no—
22C2×C42×D43—21no—
23#14582862—21no—
24#14582862—21no—
25#14582862C2214yes—
26C2×(C2×D43)⋊C8—22no—
27#14582760—21no—
28#14582756—22no—
29#14582754—21no—
30C4×(C2×D43)⋊C4C2214yes—
31#14582660C2214yescomplemented
32#14582659C2214yescomplemented
33#14582658C2214yescomplemented
34C22×M16×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C2×#117×C43C2211yescharacteristic
37C43×#339C2214yescomplemented
38C24×D43D411yescharacteristic
39C23×Dic43D411yescharacteristic
40C22×C4×D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—22no—
43C22×C4×D43—22no—
44C22×C4×D43—22no—
45C22×C4×D43C2×C411yescharacteristic
46C22×C4×D43C2×C412yes—
47C22×C4×D43C2×C411yescharacteristic
48C22×C4×D43D412yes—
49C22×C4×D43D411yescharacteristic
50C22×C4×D43D412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43C2312yes—
53C2×#10621877—21no—
54C2×#10621877—22no—
55C2×#10621877—22no—
56C2×#10621877C2312yes—
57C22×C43⋊C8—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284—22no—
61#13063284—22no—
62#13063284C2×C412yes—
63#13063284C2312yes—
64#13063283—24no—
65#13063283C2×C418yes—
66#13063282—24no—
67#13063282—24no—
68#13063281—24no—
69#13063281—24no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2×C412yes—
72C2×Dic43⋊C4—22no—
73C4⋊C4×D43—22no—
74C4⋊C4×D43—22no—
75C4⋊C4×D43C2×C414yes—
76C4⋊C4×D43C2×C414yes—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—24no—
81C22⋊C4×D43—24no—
82C22⋊C4×D43—24no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43C2312yes—
86C42×D43—24no—
87C42×D43—24no—
88(C2×D43)⋊C8—24no—
89(C2×D43)⋊C8—24no—
90C43⋊#95—24no—
91C23×C4×C43C2311yescharacteristic
92C2×M16×C43—21no—
93C2×M16×C43—22no—
94C2×M16×C43—22no—
95C2×M16×C43C2312yes—
96C22×C8×C43—21no—
97#117×C43—21no—
98#117×C43—21no—
99#117×C43—22no—
100#117×C43—22no—
101#117×C43C2×C412yes—
102#117×C43C2312yes—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2×C412yes—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C23×D43—22no—
111C23×D43—22no—
112C23×D43—44no—
113C23×D43C22⋊C411yescharacteristic
114C23×D43C22⋊C412yes—
115C23×D43C22⋊C411yescharacteristic
116C23×D43C2×D412yes—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C22×C411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×C4×C43#4112yes—
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43C22⋊C411yescharacteristic
134C22×Dic43C22⋊C411yescharacteristic
135C22×Dic43C22⋊C412yes—
136C22×Dic43C2×D412yes—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—24no—
140C2×C4×D43—22no—
141C2×C4×D43—24no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—24no—
146C2×C4×D43—24no—
147C2×C4×D43—24no—
148C2×C4×D43—22no—
149C2×C4×D43—24no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—48no—
158C2×C4×D43C22⋊C412yes—
159C2×C4×D43C22⋊C412yes—
160C2×C4×D43C22⋊C412yes—
161C2×C4×D43C22⋊C412yes—
162C2×C4×D43C22×C412yes—
163C2×C4×D43C22×C412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×D412yes—
166M16×C43—22no—
167M16×C43—22no—
168M16×C43—42no—
169C2×C8×C43—22no—
170C2×C8×C43—42no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43C22×C414yes—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—42no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—28no—
185(C2×D43)⋊C4—48no—
186C4⋊Dic43—22no—
187C4⋊Dic43—42no—
188C4⋊Dic43C22×C414yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—28no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196#10621877—22no—
197#10621877—22no—
198#10621877—42no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—42no—
201C23×C43—42no—
202C23×C43C2×C22⋊C411yescharacteristic
203C23×C43C2×C22⋊C411yescharacteristic
204C23×C43#12312yes—
205C23×C43#12312yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—24no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—24no—
212C22×D43—22no—
213C22×D43—24no—
214C22×D43—24no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—48no—
219C22×D43—48no—
220C22×D43C2×C22⋊C412yes—
221C22×D43C2×C22⋊C412yes—
222C2×C4×C43—24no—
223C2×C4×C43—44no—
224C2×C4×C43—44no—
225C2×C4×C43—42no—
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43#11712yes—
229C2×C4×C43#11712yes—
230C2×C4×C43#11712yes—
231C2×C4×C43#11712yes—
232C2×C4×C43#12312yes—
233C2×C4×C43#12312yes—
234C2×C4×C43#12312yes—
235C2×C4×C43#12312yes—
236C2×C4×C43#12312yes—
237C2×C4×C43#12312yes—
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—44no—
251C2×Dic43—44no—
252C2×Dic43—42no—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—24no—
264C4×D43—24no—
265C4×D43—24no—
266C4×D43—24no—
267C4×D43—48no—
268C4×D43—48no—
269C8×C43—42no—
270C43⋊C8—42no—
271#20705—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43#38112yes—
278C22×C43#38112yes—
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43C2×#12311yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C2×D43—28no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—44no—
289C2×D43—44no—
290C2×D43—48no—
291C2×D43—44no—
292C2×D43#42114yes—
293C4×C43—44no—
294C4×C43—82no—
295C4×C43#38112yes—
296C4×C43#38112yes—
297C4×C43C2×#11711yescharacteristic
298C4×C43C2×#11711yescharacteristic
299C4×C43C2×#12311yescharacteristic
300C4×C43C2×#12311yescharacteristic
301Dic43—22no—
302Dic43—22no—
303Dic43—44no—
304Dic43—82no—
305C22×#117—431no—
306C2×#407—431no—
307#2280—431no—
308#1826—438no—
309#1733—431no—
310#1733—431no—
311#1733—431no—
312#1733D4311yescharacteristic, complemented
313C2×C43—21no—
314C2×C43—21no—
315C2×C43—22no—
316C2×C43—22no—
317C2×C43C2×#38111yescharacteristic
318C2×C43C2×#42112yes—
319D43—24no—
320D43—42no—
321C24×C4—431no—
322C22×M16—431no—
323C22×M16C2×D4311yescharacteristic
324C2×#117—431no—
325C2×#117—431no—
326C2×#117—434no—
327C2×#117—434no—
328C2×#117—432no—
329C2×#117—861no—
330C2×#117—861no—
331C2×#117—862no—
332C2×#117—862no—
333C2×#117C2×D4311yescharacteristic
334C2×#117C2×D4311yescharacteristic
335C22×C4⋊C4—432no—
336C22×C22⋊C4—861no—
337C22×C42—861no—
338#407—434no—
339#407—861no—
340#407—861no—
341C2×C22⋊C8—862no—
342#381—861no—
343#380—862no—
344#379—861no—
345C4×C22⋊C4—434no—
346#339—434no—
347#339—434no—
348#339—434no—
349#339C2×D4314yescomplemented
350C43#2070511yescharacteristic, complemented, Sylow
351C25—431no—
352C23×C4—431no—
353C23×C4—431no—
354C23×C4—431no—
355C23×C4—432no—
356C23×C4—432no—
357C23×C4—432no—
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—432no—
361C23×C4—862no—
362C23×C4—862no—
363C23×C4—862no—
364C23×C4—862no—
365C23×C4—862no—
366C23×C4C22×D4311yescharacteristic
367C2×M16—21no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—432no—
371C2×M16—861no—
372C2×M16—862no—
373C2×M16—862no—
374C2×M16C22×D4312yes—
375C22×C8—21no—
376C22×C8—861no—
377#117—21no—
378#117—21no—
379#117—22no—
380#117—22no—
381#117—432no—
382#117—432no—
383#117—438no—
384#117—864no—
385#117—864no—
386#117—864no—
387#117—864no—
388#117—864no—
389#117—861no—
390#117—861no—
391#117—862no—
392#117—862no—
393#117C4×D4312yes—
394#117C22×D4312yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—434no—
398C2×C4⋊C4—434no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C4×D4312yes—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—864no—
411C2×C22⋊C4—861no—
412C2×C42—21no—
413C2×C42—432no—
414C2×C42—864no—
415C2×C42—864no—
416C2×C42—862no—
417C2×C42—861no—
418C2×C42C22×D4312yes—
419C22⋊C8—864no—
420C22⋊C8—864no—
421#95—864no—
422C24—431no—
423C24—432no—
424C24—432no—
425C24—431no—
426C24—862no—
427C24—862no—
428C24—1724no—
429C24D4×D4311yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—432no—
444C22×C4—864no—
445C22×C4—864no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—864no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—864no—
454C22×C4—864no—
455C22×C4—864no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—864no—
459C22×C4—864no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—1728no—
469C22×C4C2×C4×D4311yescharacteristic
470C22×C4C2×C4×D4311yescharacteristic
471C22×C4#1062189812yes—
472C22×C4#1062189812yes—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4#1062190012yes—
477C22×C4#1062190212yes—
478C22×C4C23×D4311yescharacteristic
479M16—22no—
480M16—22no—
481M16—42no—
482M16—862no—
483M16—862no—
484M16—1722no—
485C2×C8—22no—
486C2×C8—42no—
487C2×C8—862no—
488C2×C8—1722no—
489C4⋊C4—22no—
490C4⋊C4—42no—
491C4⋊C4—434no—
492C4⋊C4—864no—
493C4⋊C4—864no—
494C4⋊C4—862no—
495C4⋊C4—1722no—
496C4⋊C4C2×C4×D4314yes—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—42no—
500C22⋊C4—868no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C22⋊C4—1728no—
504C22⋊C4—1722no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—22no—
509C42—868no—
510C42—862no—
511C42—862no—
512C42—862no—
513C42—862no—
514C23—42no—
515C23—432no—
516C23—432no—
517C23—864no—
518C23—864no—
519C23—864no—
520C23—862no—
521C23—862no—
522C23—862no—
523C23—864no—
524C23—862no—
525C23—1722no—
526C23—1722no—
527C23—1722no—
528C23—1728no—
529C23—1728no—
530C23C22⋊C4×D4311yescharacteristic
531C23C22⋊C4×D4311yescharacteristic
532C23#1306330712yes—
533C23#1306331012yes—
534C23C2×D4×D4311yescharacteristic
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—864no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—864no—
559C2×C4—1728no—
560C2×C4—1728no—
561C2×C4—1724no—
562C2×C4—1722no—
563C2×C4—1724no—
564C2×C4C22⋊C4×D4311yescharacteristic
565C2×C4C22⋊C4×D4311yescharacteristic
566C2×C4#1306328212yes—
567C2×C4#1306328212yes—
568C2×C4#1306328312yes—
569C2×C4#1306328312yes—
570C2×C4#1306330712yes—
571C2×C4#1306330712yes—
572C2×C4#1306330712yes—
573C2×C4#1306331012yes—
574C2×C4#1306331012yes—
575C2×C4#1306331012yes—
576C2×C4C22×C4×D4311yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4C2×#1062189811yescharacteristic
581C2×C4C2×#1062190211yescharacteristic
582C8—42no—
583C8—1722no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—434no—
590C22—868no—
591C22—862no—
592C22—862no—
593C22—862no—
594C22—862no—
595C22—862no—
596C22—1724no—
597C22—1724no—
598C22—1728no—
599C22—1724no—
600C22#1458276112yes—
601C22#1458276112yes—
602C22C2×C22⋊C4×D4311yescharacteristic
603C22C2×#1306330711yescharacteristic
604C22C2×#1306331011yescharacteristic
605C4—44no—
606C4—82no—
607C4—862no—
608C4—862no—
609C4—3442no—
610C4—1724no—
611C4#1458276112yes—
612C4#1458276112yes—
613C4C2×#1306328211yescharacteristic
614C4C2×#1306328311yescharacteristic
615C4C2×#1306330711yescharacteristic
616C4C2×#1306331011yescharacteristic
617C2—21no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—864no—
622C2—1722no—
623C2C2×#1458276111yescharacteristic
624C2#421×D4312yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1733C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1733D43
hypocenterC43#20705
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #19134693C2semidirect
5. #19134306C2semidirect
6. #19134305C2semidirect
7. #19134304C2semidirect
8. C43×#1733C2semidirect
13. C2×#13063283C4semidirect
18. #117×D43C4semidirect
20. C2×C4⋊C4×D43C4semidirect
31. #14582660C22semidirect
32. #14582659C22semidirect
33. #14582658C22semidirect
37. C43×#339C22semidirect
312. #1733D43semidirect
349. #339C2×D43semidirect
350. C43#20705semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
C2×#145828622
#191369742
#191346932
#191343062
#191343052
#191343042
C43×#17332
#2070543