Finite Group Databasebeta

← #25019676

Subgroups — #25019676

Order 11008.

1918 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582774C211yesmaximal, characteristic
2C2×#14582760C211yesmaximal, characteristic
3C2×#14582760C211yesmaximal, characteristic
4C2×C4×C22⋊Dic43C211yesmaximal, characteristic
5C22×C43⋊#95C211yesmaximal, characteristic
6#19132855C212yesmaximal, complemented
7#19132851C212yesmaximal, complemented
8#19132829C212yesmaximal, complemented
9#19132819C212yesmaximal, complemented
10#19132817C211yesmaximal, characteristic
11C43×C22⋊#95C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2212yes—
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C4×Dic43C2211yescharacteristic
18C22×C4×Dic43C2211yescharacteristic
19#14582774—24no—
20#14582760—24no—
21#14582760C418yescomplemented
22C4×C22⋊Dic43—24no—
23C2×C43⋊#95—24no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C23×Dic43—22no—
41C23×Dic43—22no—
42C23×Dic43—22no—
43C23×Dic43—22no—
44C23×Dic43—22no—
45C23×Dic43—22no—
46C23×Dic43—22no—
47C23×Dic43—24no—
48C23×Dic43—22no—
49C23×Dic43—22no—
50C23×Dic43—42no—
51C23×Dic43C2×C414yes—
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2312yes—
58C2×C4⋊Dic43—24no—
59C2×C4⋊Dic43—24no—
60C2×C4⋊Dic43—42no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43C2×C414yes—
66C2×C22⋊Dic43D414yes—
67C2×C4×Dic43—22no—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—42no—
71C43⋊#95—24no—
72C43⋊#95—24no—
73C43⋊#95—22no—
74C43⋊#95—22no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—42no—
80C43⋊#95C2×C418yescomplemented
81C43⋊#95C2×C418yescomplemented
82C25×C43C2311yescharacteristic
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—24no—
86C23×C4×C43—42no—
87C23×C4×C43D414yes—
88C23×C4×C43C2312yes—
89C23×C4×C43C2312yes—
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—22no—
96C2×C22⋊C4×C43—22no—
97C2×C22⋊C4×C43C2×C414yes—
98#95×C43—24no—
99#95×C43—42no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43—22no—
103C24×C43—22no—
104C24×C43C22×C412yes—
105C24×C43C2×D412yes—
106C24×C43C2×D412yes—
107C24×C43#4112yes—
108C24×C43#4112yes—
109C24×C43#4112yes—
110C24×C43#4112yes—
111C24×C43C2411yescharacteristic
112C22×C4×C43—28no—
113C22×C4×C43—28no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—44no—
135C22×C4×C43—48no—
136C22×C4×C43—48no—
137C22×C4×C43C22×C414yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43#4114yes—
141C22×Dic43—28no—
142C22×Dic43—28no—
143C22×Dic43—28no—
144C22×Dic43—28no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—48no—
174C22×Dic43—48no—
175C22×Dic43—44no—
176C22×Dic43—44no—
177C22×Dic43—44no—
178C22×Dic43—44no—
179C22×Dic43—44no—
180C22×Dic43—44no—
181C22×Dic43C22×C412yes—
182C22×Dic43C22×C412yes—
183C22×Dic43C22×C414yes—
184C22×Dic43C2×D412yes—
185C22×Dic43C2×D412yes—
186C22×Dic43#4114yes—
187C22⋊C4×C43—28no—
188C22⋊C4×C43—44no—
189C22⋊Dic43—28no—
190C22⋊Dic43—28no—
191C4⋊Dic43—48no—
192C4×Dic43—44no—
193C4×Dic43—44no—
194C23×C43—24no—
195C23×C43—24no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43—24no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—24no—
202C23×C43—24no—
203C23×C43—24no—
204C23×C43—24no—
205C23×C43—24no—
206C23×C43—24no—
207C23×C43—24no—
208C23×C43—24no—
209C23×C43—24no—
210C23×C43#11714yes—
211C23×C43C4×D414yes—
212C23×C43C4×D414yes—
213C23×C43#12114yes—
214C23×C43#12314yes—
215C23×C43#12414yes—
216C23×C43#12614yes—
217C23×C43C23×C411yescharacteristic
218C23×C43C22×D411yescharacteristic
219C23×C43C22×D411yescharacteristic
220C23×C43C2×#4112yes—
221C23×C43C2×#4111yescharacteristic
222C23×C43C2×#4111yescharacteristic
223C23×C43C2×#4112yes—
224C23×C43C2×#4111yescharacteristic
225C23×C43C2×#4111yescharacteristic
226C23×C43H(5,𝔽2)12yes—
227C23×C432−1+412yes—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—416no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43#12314yes—
253C2×Dic43—24no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—24no—
266C2×Dic43—24no—
267C2×Dic43—416no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—42no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—42no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43—416no—
289#13992—431nomaximal, Sylow
290C22×C43—24no—
291C22×C43—28no—
292C22×C43—28no—
293C22×C43—24no—
294C22×C43—24no—
295C22×C43—24no—
296C22×C43—28no—
297C22×C43—28no—
298C22×C43—24no—
299C22×C43—24no—
300C22×C43#38818yes—
301C22×C43C2×#11711yescharacteristic
302C22×C43C2×C4×D411yescharacteristic
303C22×C43C2×C4×D411yescharacteristic
304C22×C43C4×#4112yes—
305C22×C43#52012yes—
306C22×C43C2×#12111yescharacteristic
307C22×C43C2×#12311yescharacteristic
308C22×C43C2×#12311yescharacteristic
309C22×C43#52511yescharacteristic
310C22×C43C2×#12411yescharacteristic
311C22×C43C2×#12611yescharacteristic
312C22×C43#52912yes—
313C22×C43#53411yescharacteristic
314C22×C43#53611yescharacteristic
315C22×C43#53912yes—
316C22×C43#54612yes—
317C22×C43#54712yes—
318C22×C43#55112yes—
319C22×C43#55112yes—
320C22×C43#55112yes—
321C22×C43#55212yes—
322C22×C43#55212yes—
323C22×C43#55212yes—
324C4×C43—24no—
325C4×C43—44no—
326C4×C43—42no—
327C4×C43—82no—
328Dic43—42no—
329Dic43—42no—
330Dic43—42no—
331Dic43—44no—
332Dic43—44no—
333Dic43—42no—
334C2×#385—431no—
335C2×#381—431no—
336C2×#381—431no—
337C2×C4×C22⋊C4—431no—
338C22×#95—431no—
339#1443—432no—
340#1442—432no—
341#1436—432no—
342#1434—432no—
343C22⋊#95—431no—
344C22⋊#95D4311yescharacteristic
345C2×C43—28no—
346C2×C43C2×#38811yescharacteristic
347C2×C43C4×#12311yescharacteristic
348C2×C43#232211yescharacteristic
349C2×C43#234312yes—
350C2×C43#235912yes—
351C2×C43#248311yescharacteristic
352C2×C43#248411yescharacteristic
353C2×C43#248611yescharacteristic
354C2×C43#248812yes—
355C2×C43#249312yes—
356C2×C43#253411yescharacteristic
357C24×C4—431no—
358C24×C4—431no—
359C24×C4C2×D4311yescharacteristic
360C22×C4⋊C4—432no—
361C22×C22⋊C4—431no—
362C22×C22⋊C4—431no—
363C22×C22⋊C4C2×D4311yescharacteristic
364C22×C22⋊C4C2×D4311yescharacteristic
365C22×C42—431no—
366C22×C42—431no—
367#385—864no—
368#381—438no—
369#381—864no—
370C4×C22⋊C4—864no—
371C2×#95—432no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95—432no—
375C2×#95—432no—
376C2×#95—432no—
377C2×#95—432no—
378C2×#95—431no—
379C2×#95—432no—
380C2×#95—431no—
381C2×#95—432no—
382C2×#95—864no—
383C2×#95C2×D4312yes—
384C2×#95C2×D4312yes—
385C43#1399211yescharacteristic, complemented, Sylow
386C25C22×D4311yescharacteristic
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—42no—
391C23×C4—434no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—432no—
397C23×C4—432no—
398C23×C4—864no—
399C23×C4—862no—
400C23×C4—862no—
401C23×C4—862no—
402C23×C4—862no—
403C23×C4—862no—
404C23×C4—862no—
405C23×C4—862no—
406C23×C4—862no—
407C23×C4—862no—
408C23×C4—1722no—
409C23×C4D17214yes—
410C23×C4C22×D4312yes—
411C23×C4C22×D4312yes—
412C23×C4C22×D4311yescharacteristic
413C23×C4C22×D4311yescharacteristic
414C2×C4⋊C4—864no—
415C2×C4⋊C4—864no—
416C2×C4⋊C4—1722no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—434no—
423C2×C22⋊C4—434no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—862no—
427C2×C22⋊C4—862no—
428C2×C22⋊C4C4×D4314yes—
429C2×C42—862no—
430C2×C42—862no—
431C2×C42—864no—
432C2×C42—1722no—
433#95—24no—
434#95—42no—
435#95—438no—
436#95—438no—
437#95—864no—
438#95—864no—
439#95—864no—
440#95—864no—
441#95—864no—
442#95—864no—
443#95—862no—
444#95—862no—
445#95—1722no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24C2×C4×D4312yes—
451C24C2×D17212yes—
452C24#1062189812yes—
453C24D4×D4312yes—
454C24#1062190012yes—
455C24#1062190012yes—
456C24#1062190212yes—
457C24C23×D4311yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—28no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—44no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—432no—
484C22×C4—432no—
485C22×C4—434no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—434no—
489C22×C4—868no—
490C22×C4—868no—
491C22×C4—868no—
492C22×C4—868no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—862no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—1728no—
522C22×C4—1728no—
523C22×C4—1724no—
524C22×C4—1724no—
525C22×C4—1724no—
526C22×C4—1724no—
527C22×C4—1724no—
528C22×C4—1724no—
529C22×C4C2×C4×D4314yes—
530C22×C4C2×D17212yes—
531C22×C4C2×D17212yes—
532C22×C4#1062190014yes—
533C4⋊C4—1728no—
534C22⋊C4—28no—
535C22⋊C4—44no—
536C22⋊C4—868no—
537C22⋊C4—868no—
538C42—1724no—
539C42—1724no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—22no—
549C23—22no—
550C23—24no—
551C23—22no—
552C23—22no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23#1306328314yes—
557C23(C22⋊D43)⋊C414yes—
558C23C4×D17214yes—
559C23#1306330014yes—
560C23#1306330914yes—
561C23#1306331114yes—
562C23#1306332014yes—
563C23C22×C4×D4311yescharacteristic
564C23C2×D4×D4311yescharacteristic
565C23C22×D17211yescharacteristic
566C23#41×D4312yes—
567C23C2×#1062190011yescharacteristic
568C23C2×#1062190011yescharacteristic
569C23C2×#1062190012yes—
570C23C2×#1062189811yescharacteristic
571C23C2×#1062190211yescharacteristic
572C23#1306337012yes—
573C23#1306337212yes—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—416no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—864no—
609C2×C4—864no—
610C2×C4—864no—
611C2×C4—864no—
612C2×C4—17216no—
613C2×C4—17216no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1722no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1722no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1722no—
633C2×C4—1722no—
634C2×C4#1306330914yes—
635C22—28no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—24no—
640C22—28no—
641C22—24no—
642C22—28no—
643C22—28no—
644C22—24no—
645C22#1458279118yes—
646C22C2×#1306328311yescharacteristic
647C22C2×(C22⋊D43)⋊C411yescharacteristic
648C22C2×C4×D17211yescharacteristic
649C22C4×#1062190012yes—
650C22#1458337812yes—
651C22C2×#1306330011yescharacteristic
652C22C2×#1306330911yescharacteristic
653C22C2×#1306330911yescharacteristic
654C22#1458341111yescharacteristic
655C22C2×#1306331111yescharacteristic
656C22C2×#1306332011yescharacteristic
657C22#1458342912yes—
658C22#1458346111yescharacteristic
659C22#1458347511yescharacteristic
660C22#1458349112yes—
661C22#1458353812yes—
662C22#1458354912yes—
663C22#1458357612yes—
664C22#1458358012yes—
665C22#1458358012yes—
666C22#1458358612yes—
667C22#1458358612yes—
668C22#1458359112yes—
669C4—24no—
670C4—44no—
671C4—42no—
672C4—82no—
673C4—1724no—
674C4—1722no—
675C4—1722no—
676C4—1724no—
677C4—1722no—
678C4—1722no—
679C2—28no—
680C2C2×#1458279111yescharacteristic
681C2C4×#1306330911yescharacteristic
682C2#1913726611yescharacteristic
683C2#1913745312yes—
684C2#1913759312yes—
685C2#1913887611yescharacteristic
686C2#1913888411yescharacteristic
687C2#1913890411yescharacteristic
688C2#1913892312yes—
689C2#1913898212yes—
690C2#1913948711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13992
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. #19132855C2semidirect
7. #19132851C2semidirect
8. #19132829C2semidirect
9. #19132819C2semidirect
21. #14582760C4semidirect
80. C43⋊#95C2×C4semidirect
81. C43⋊#95C2×C4semidirect
385. C43#13992semidirect

Maximal subgroups

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

subgroupindex
C2×#145827742
C2×#145827602
C2×C4×C22⋊Dic432
C22×C43⋊#952
#191328552
#191328512
#191328292
#191328192
#191328172
C43×C22⋊#952
#1399243