Finite Group Databasebeta

← #25018473

Subgroups — #25018473

Order 11008.

3686 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063281C211yesmaximal, characteristic, complemented
2C23×(C2×D43)⋊C4C211yesmaximal, characteristic
3C2×#14582760C211yesmaximal, characteristic, complemented
4C2×#14582754C211yesmaximal, characteristic
5C2×#14582754C211yesmaximal, characteristic
6#19132839C214yesmaximal, complemented
7#19132831C214yesmaximal, complemented
8#19132818C211yesmaximal, characteristic, complemented
9C43×C22⋊#95C211yesmaximal, characteristic, complemented
10C25×D43C2211yescharacteristic
11C24×Dic43C2211yescharacteristic
12C2×#13063281—24no—
13C2×#13063281—24no—
14C2×#13063281—24no—
15C22×Dic43⋊C4C2212yescomplemented
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×(C2×D43)⋊C4—24no—
19C22×(C2×D43)⋊C4—24no—
20C22×(C2×D43)⋊C4C418yescomplemented
21C22×(C2×D43)⋊C4C2214yes—
22C22×(C2×D43)⋊C4C2214yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2212yes—
25C22×C4×Dic43C2212yescomplemented
26#14582760—24no—
27#14582754—24no—
28#14582754—24no—
29C2×C43⋊#95C2212yescomplemented
30C2×C43⋊#95C2212yescomplemented
31C2×C43⋊#95C2214yescomplemented
32C24×C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C2×#95×C43C2214yescomplemented
36C24×D43—22no—
37C24×D43—22no—
38C24×D43—28no—
39C24×D43—22no—
40C24×D43—22no—
41C24×D43—22no—
42C24×D43—22no—
43C24×D43—44no—
44C24×D43C2×C414yes—
45C24×D43C2312yes—
46C23×Dic43—22no—
47C23×Dic43—22no—
48C23×Dic43—22no—
49C23×Dic43—22no—
50C23×Dic43C2×C414yes—
51C23×Dic43D414yes—
52C23×Dic43D414yes—
53C23×Dic43C2312yes—
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57#13063281—232no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—22no—
66C2×C22⋊Dic43D414yes—
67C2×(C2×D43)⋊C4—232no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—28no—
73C2×(C2×D43)⋊C4—28no—
74C2×(C2×D43)⋊C4—28no—
75C2×(C2×D43)⋊C4—28no—
76C2×(C2×D43)⋊C4—44no—
77C2×(C2×D43)⋊C4—44no—
78C2×(C2×D43)⋊C4C2×C418yes—
79C2×(C2×D43)⋊C4C2×C418yes—
80C2×C4×Dic43—24no—
81C2×C4×Dic43—24no—
82C2×C4×Dic43—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—44no—
86C25×C43C2311yescharacteristic
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43—44no—
90C23×C4×C43C2×C414yes—
91C23×C4×C43C2312yes—
92C23×C4×C43C2312yes—
93C23×C4×C43C2312yes—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—22no—
96C2×C22⋊C4×C43—22no—
97C2×C22⋊C4×C43—22no—
98C2×C22⋊C4×C43—22no—
99C2×C22⋊C4×C43D414yes—
100#95×C43—44no—
101C24×C43—24no—
102C24×C43—24no—
103C24×C43C22×C412yes—
104C24×C43C2×D412yes—
105C24×C43C2×D412yes—
106C24×C43C2×D412yes—
107C24×C43C2×D412yes—
108C24×C43#4112yes—
109C24×C43#4112yes—
110C24×C43C2411yescharacteristic
111C23×D43—216no—
112C23×D43—216no—
113C23×D43—28no—
114C23×D43—22no—
115C23×D43—22no—
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—24no—
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—24no—
122C23×D43—24no—
123C23×D43—216no—
124C23×D43—28no—
125C23×D43—28no—
126C23×D43—48no—
127C23×D43—416no—
128C23×D43—416no—
129C23×D43—416no—
130C23×D43—416no—
131C23×D43—48no—
132C23×D43—48no—
133C23×D43—44no—
134C23×D43—44no—
135C23×D43—44no—
136C23×D43—44no—
137C23×D43C22×C414yes—
138C23×D43#4118yes—
139C22×C4×C43—28no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—24no—
147C22×C4×C43—22no—
148C22×C4×C43—24no—
149C22×C4×C43—24no—
150C22×C4×C43—24no—
151C22×C4×C43—24no—
152C22×C4×C43—24no—
153C22×C4×C43—48no—
154C22×C4×C43—48no—
155C22×C4×C43—48no—
156C22×C4×C43C22×C414yes—
157C22×C4×C43C2×D414yes—
158C22×Dic43—28no—
159C22×Dic43—28no—
160C22×Dic43—28no—
161C22×Dic43—28no—
162C22×Dic43—28no—
163C22×Dic43—28no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—24no—
177C22×Dic43—24no—
178C22×Dic43—22no—
179C22×Dic43—24no—
180C22×Dic43—24no—
181C22×Dic43C22⋊C4116yescomplemented
182C22×Dic43C22×C412yes—
183C22×Dic43C22×C412yes—
184C22×Dic43C2×D414yes—
185C22×Dic43C2×D412yes—
186C22×Dic43C2×D412yes—
187C22×Dic43C2×D412yes—
188C22×Dic43C2×D412yes—
189C22⋊C4×C43—28no—
190C22⋊C4×C43—44no—
191C22⋊Dic43—28no—
192C22⋊Dic43—44no—
193(C2×D43)⋊C4—216no—
194(C2×D43)⋊C4—216no—
195(C2×D43)⋊C4—416no—
196(C2×D43)⋊C4—416no—
197Dic43⋊C4—216no—
198C4×Dic43—216no—
199C23×C43—24no—
200C23×C43—24no—
201C23×C43—24no—
202C23×C43—24no—
203C23×C43—24no—
204C23×C43—24no—
205C23×C43—28no—
206C23×C43—28no—
207C23×C43—28no—
208C23×C43—28no—
209C23×C43C2×C22⋊C414yes—
210C23×C43C4×D414yes—
211C23×C43C4×D414yes—
212C23×C43#12014yes—
213C23×C43#12114yes—
214C23×C43#12114yes—
215C23×C43#12314yes—
216C23×C43C23×C411yescharacteristic
217C23×C43C22×D411yescharacteristic
218C23×C43C22×D411yescharacteristic
219C23×C43C22×D411yescharacteristic
220C23×C43C22×D411yescharacteristic
221C23×C43C2×#4114yes—
222C23×C43C2×#4111yescharacteristic
223C23×C43C2×#4111yescharacteristic
224C23×C43H(5,𝔽2)14yes—
225C22×D43—232no—
226C22×D43—24no—
227C22×D43—24no—
228C22×D43—24no—
229C22×D43—24no—
230C22×D43—24no—
231C22×D43—24no—
232C22×D43—28no—
233C22×D43—28no—
234C22×D43—28no—
235C22×D43—28no—
236C22×D43—28no—
237C22×D43—28no—
238C22×D43—432no—
239C22×D43—432no—
240C22×D43—416no—
241C22×D43—432no—
242C22×D43—432no—
243C22×D43—432no—
244C22×D43—432no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43—42no—
249C22×D43—44no—
250C22×D43—44no—
251C22×D43—44no—
252C22×D43—44no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—416no—
256C22×D43#11718yescomplemented
257C2×C4×C43—24no—
258C2×C4×C43—24no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—28no—
262C2×C4×C43—416no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—44no—
266C2×C4×C43—44no—
267C2×C4×C43—44no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—44no—
272C2×C4×C43—44no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—232no—
286C2×Dic43—24no—
287C2×Dic43—28no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C2×Dic43—44no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293C2×Dic43—42no—
294C2×Dic43—44no—
295C2×Dic43—44no—
296C2×Dic43C2×C22⋊C414yes—
297C2×Dic43C2×C22⋊C414yes—
298#13868—431nomaximal, Sylow
299C22×C43—24no—
300C22×C43—28no—
301C22×C43—28no—
302C22×C43—28no—
303C22×C43—28no—
304C22×C43—28no—
305C22×C43—28no—
306C22×C43—24no—
307C22×C43#38618yes—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43C2×#11712yes—
310C22×C43C2×C4×D411yescharacteristic
311C22×C43C2×C4×D411yescharacteristic
312C22×C43#51812yes—
313C22×C43C2×#12011yescharacteristic
314C22×C43C2×#12111yescharacteristic
315C22×C43C2×#12111yescharacteristic
316C22×C43C2×#12311yescharacteristic
317C22×C43#52512yes—
318C22×C43#52512yes—
319C22×C43#53512yes—
320C22×C43#53512yes—
321C22×C43#54614yes—
322C22×C43#54614yes—
323C22×C43#55114yes—
324C22×C43#55114yes—
325C2×D43—28no—
326C2×D43—28no—
327C2×D43—28no—
328C2×D43—464no—
329C2×D43—44no—
330C2×D43—44no—
331C2×D43—44no—
332C2×D43—48no—
333C2×D43—48no—
334C2×D43—48no—
335C2×D43—48no—
336C2×D43—44no—
337C4×C43—44no—
338C4×C43—44no—
339C4×C43—82no—
340Dic43—24no—
341Dic43—24no—
342Dic43—44no—
343Dic43—82no—
344C22×#117—431no—
345C23×C22⋊C4—431no—
346C2×#381—431no—
347C2×#379—431no—
348C2×#379—431no—
349#1439—434no—
350#1437—434no—
351C22⋊#95—431no—
352C22⋊#95D4311yescharacteristic, complemented
353C2×C43—28no—
354C2×C43#228011yescharacteristic
355C2×C43C2×#38611yescharacteristic
356C2×C43#230911yescharacteristic
357C2×C43#234212yes—
358C2×C43#234212yes—
359C2×C43#240412yes—
360C2×C43#241112yes—
361C2×C43#241112yes—
362C2×C43#248212yes—
363D43—48no—
364C26—431no—
365C24×C4—431no—
366C24×C4C2×D4311yescharacteristic
367C2×#117—864no—
368C2×#117—864no—
369C2×#117—864no—
370C22×C4⋊C4—432no—
371C22×C22⋊C4—431no—
372C22×C22⋊C4—432no—
373C22×C22⋊C4—432no—
374C22×C22⋊C4—438no—
375C22×C22⋊C4—431no—
376C22×C22⋊C4—434no—
377C22×C22⋊C4—434no—
378C22×C22⋊C4—864no—
379C22×C22⋊C4—864no—
380C22×C22⋊C4C2×D4311yescharacteristic
381C22×C22⋊C4C2×D4311yescharacteristic
382C22×C42—432no—
383#381—864no—
384#379—864no—
385#379—864no—
386C2×#95—432no—
387C2×#95—432no—
388C2×#95—434no—
389C2×#95C2×D4314yescomplemented
390C43#1386811yescharacteristic, complemented, Sylow
391C25—432no—
392C25—434no—
393C25—868no—
394C25—862no—
395C25—862no—
396C25—862no—
397C25—862no—
398C25—862no—
399C25—862no—
400C25—1724no—
401C25C22×D4311yescharacteristic
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—44no—
405C23×C4—434no—
406C23×C4—434no—
407C23×C4—434no—
408C23×C4—431no—
409C23×C4—431no—
410C23×C4—432no—
411C23×C4—432no—
412C23×C4—862no—
413C23×C4—862no—
414C23×C4—862no—
415C23×C4—862no—
416C23×C4C4×D4314yes—
417C23×C4C22×D4312yes—
418C23×C4C22×D4312yes—
419C23×C4C22×D4312yes—
420#117—8632no—
421C2×C4⋊C4—864no—
422C2×C4⋊C4—864no—
423C2×C4⋊C4—864no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—434no—
430C2×C22⋊C4—438no—
431C2×C22⋊C4—438no—
432C2×C22⋊C4—8632no—
433C2×C22⋊C4—864no—
434C2×C22⋊C4—864no—
435C2×C22⋊C4—864no—
436C2×C22⋊C4—864no—
437C2×C22⋊C4—862no—
438C2×C22⋊C4—862no—
439C2×C22⋊C4—868no—
440C2×C22⋊C4—868no—
441C2×C22⋊C4—868no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C22⋊C4—862no—
445C2×C22⋊C4—868no—
446C2×C22⋊C4—1724no—
447C2×C22⋊C4—1724no—
448C2×C22⋊C4D17214yes—
449C2×C42—864no—
450C2×C42—864no—
451C2×C42—864no—
452#95—44no—
453#95—864no—
454#95—864no—
455#95—1724no—
456C24—24no—
457C24—24no—
458C24—434no—
459C24—438no—
460C24—8616no—
461C24—8616no—
462C24—8616no—
463C24—868no—
464C24—862no—
465C24—862no—
466C24—862no—
467C24—862no—
468C24—864no—
469C24—862no—
470C24—862no—
471C24—864no—
472C24—864no—
473C24—868no—
474C24—868no—
475C24—1728no—
476C24—17216no—
477C24—17216no—
478C24—17216no—
479C24—17216no—
480C24—1728no—
481C24—1728no—
482C24—1724no—
483C24—1724no—
484C24—1724no—
485C24—1724no—
486C24C2×C4×D4312yes—
487C24C2×D17212yes—
488C24#1062189812yes—
489C24D4×D4312yes—
490C24D4×D4312yes—
491C24D4×D4312yes—
492C24#1062190212yes—
493C24C23×D4311yescharacteristic
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—4316no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—432no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—434no—
519C22×C4—868no—
520C22×C4—868no—
521C22×C4—868no—
522C22×C4—868no—
523C22×C4—868no—
524C22×C4—868no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—864no—
536C22×C4—864no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—864no—
540C22×C4—862no—
541C22×C4—864no—
542C22×C4C2×C4×D4314yes—
543C22×C4C2×D17214yes—
544C4⋊C4—8616no—
545C22⋊C4—28no—
546C22⋊C4—44no—
547C22⋊C4—8616no—
548C22⋊C4—8616no—
549C22⋊C4—868no—
550C22⋊C4—17216no—
551C22⋊C4—17216no—
552C22⋊C4—1724no—
553C42—8616no—
554C23—28no—
555C23—28no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—28no—
563C23—28no—
564C23—438no—
565C23—8632no—
566C23—868no—
567C23—868no—
568C23—864no—
569C23—864no—
570C23—864no—
571C23—864no—
572C23—864no—
573C23—864no—
574C23—868no—
575C23—868no—
576C23—868no—
577C23—868no—
578C23—17232no—
579C23—17232no—
580C23—17232no—
581C23—17232no—
582C23—17216no—
583C23—17232no—
584C23—17232no—
585C23—1724no—
586C23—1724no—
587C23—1722no—
588C23—1722no—
589C23—1722no—
590C23—1722no—
591C23—1724no—
592C23—1724no—
593C23—1724no—
594C23—1724no—
595C23—17216no—
596C23C22⋊C4×D4314yes—
597C23#1306328714yes—
598C23C4×D17214yes—
599C23#1306329514yes—
600C23#1306329814yes—
601C23#1306330014yes—
602C23#1306331014yes—
603C23C22×C4×D4311yescharacteristic
604C23C2×D4×D4311yescharacteristic
605C23C2×D4×D4311yescharacteristic
606C23C2×D4×D4311yescharacteristic
607C23C22×D17211yescharacteristic
608C23#41×D4314yes—
609C23C2×#1062189811yescharacteristic
610C23C2×#1062190211yescharacteristic
611C23#1306337014yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—28no—
617C2×C4—416no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—42no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—44no—
628C2×C4—434no—
629C2×C4—434no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—8632no—
643C2×C4—864no—
644C2×C4—868no—
645C2×C4—1724no—
646C2×C4—1722no—
647C2×C4—1722no—
648C2×C4—1722no—
649C2×C4—1724no—
650C2×C4—1722no—
651C2×C4—1722no—
652C2×C4—1724no—
653C22—28no—
654C22—28no—
655C22—24no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22—28no—
660C22—24no—
661C22—868no—
662C22—868no—
663C22—868no—
664C22—17264no—
665C22—1728no—
666C22—1728no—
667C22—1724no—
668C22—1724no—
669C22—1724no—
670C22—1728no—
671C22—1728no—
672C22—1724no—
673C22#1458277718yes—
674C22C2×C22⋊C4×D4311yescharacteristic
675C22#117×D4312yes—
676C22C2×#1306328711yescharacteristic
677C22C2×C4×D17211yescharacteristic
678C22#1458337212yes—
679C22C2×#1306329511yescharacteristic
680C22C2×#1306329811yescharacteristic
681C22C2×#1306330011yescharacteristic
682C22C2×#1306331011yescharacteristic
683C22#1458340712yes—
684C22#1458340712yes—
685C22#1458346412yes—
686C22#1458346412yes—
687C22#1458353814yes—
688C22#1458354414yes—
689C22#1458357614yes—
690C22#1458357814yes—
691C4—44no—
692C4—44no—
693C4—82no—
694C4—864no—
695C4—864no—
696C4—3442no—
697C4—1724no—
698C2—28no—
699C2—1728no—
700C2#1913697511yescharacteristic
701C2C2×#1458277711yescharacteristic
702C2#1913717611yescharacteristic
703C2#1913744112yes—
704C2#1913744712yes—
705C2#1913791312yes—
706C2#1913797812yes—
707C2#1913798312yes—
708C2#1913886812yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenterC22⋊#95D43
hypocenterC43#13868
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#13063281C2semidirect
3. C2×#14582760C2semidirect
6. #19132839C2semidirect
7. #19132831C2semidirect
8. #19132818C2semidirect
9. C43×C22⋊#95C2semidirect
15. C22×Dic43⋊C4C22semidirect
20. C22×(C2×D43)⋊C4C4semidirect
25. C22×C4×Dic43C22semidirect
29. C2×C43⋊#95C22semidirect
30. C2×C43⋊#95C22semidirect
31. C2×C43⋊#95C22semidirect
35. C2×#95×C43C22semidirect
181. C22×Dic43C22⋊C4semidirect
256. C22×D43#117semidirect
352. C22⋊#95D43semidirect
389. C2×#95C2×D43semidirect
390. C43#13868semidirect

Maximal subgroups

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

subgroupindex
C22×#130632812
C23×(C2×D43)⋊C42
C2×#145827602
C2×#145827542
#191328392
#191328312
#191328182
C43×C22⋊#952
#1386843