Finite Group Databasebeta

← #25018398

Subgroups — #25018398

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063290C211yesmaximal, characteristic, complemented
2C2×#14582811C211yesmaximal, characteristic
3C2×C22⋊C4×Dic43C212yesmaximal
4C2×C22⋊C4×Dic43C211yesmaximal, characteristic
5#19132865C211yesmaximal, characteristic, complemented
6#19132854C211yesmaximal, characteristic, complemented
7#19132850C212yesmaximal, complemented
8#19132838C212yesmaximal
9#95×Dic43C212yesmaximal, complemented
10#95×Dic43C211yesmaximal, characteristic, complemented
11C43×#1439C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C2×#13063290—28no—
15C2×#13063290—24no—
16C22×Dic43⋊C4C2212yes—
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C4×Dic43C2211yescharacteristic
20C22×C4×Dic43C2212yes—
21C22×C4×Dic43C2212yes—
22C22×C4×Dic43C2211yescharacteristic
23#14582811C418yescomplemented
24C22⋊C4×Dic43—28no—
25C22⋊C4×Dic43—24no—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2212yes—
37C22×C22⋊C4×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C22×Dic86—22no—
41C22×Dic86—22no—
42C22×Dic86—24no—
43C22×Dic86—24no—
44C22×Dic86C2×C414yescomplemented
45C23×Dic43—24no—
46C23×Dic43—22no—
47C23×Dic43—24no—
48C23×Dic43—22no—
49C23×Dic43Q814yescomplemented
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56#13063290—232no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—24no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—24no—
65C2×C22⋊Dic43C2×C418yes—
66C2×C4×Dic43—24no—
67C2×C4×Dic43—24no—
68C2×C4×Dic43—24no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—24no—
74C2×C4×Dic43D414yes—
75C2×C4×Dic43D418yes—
76C43⋊#95—24no—
77C43⋊#95—22no—
78C43⋊#95—24no—
79C43⋊#95—22no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95C2×C414yescomplemented
84C43⋊#95C2×C418yescomplemented
85C25×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2312yes—
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43—24no—
91C2×C4⋊C4×C43—22no—
92C2×C22⋊C4×C43—24no—
93C2×C22⋊C4×C43—24no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—24no—
96C2×C22⋊C4×C43—22no—
97C2×C22⋊C4×C43C2×C414yes—
98#95×C43—24no—
99#95×C43—22no—
100C24×C43—22no—
101C24×C43—21no—
102C24×C43—21no—
103C24×C43—22no—
104C24×C43—22no—
105C24×C43—21no—
106C24×C43—22no—
107C24×C43—21no—
108C24×C43C22×C412yes—
109C24×C43C2×Q812yes—
110C24×C43#4112yes—
111C24×C43C2411yescharacteristic
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
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×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C2×D414yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43#4114yes—
135C22×C4×C43#4112yes—
136C22×Dic43—28no—
137C22×Dic43—216no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—44no—
161C22×Dic43—44no—
162C22×Dic43—48no—
163C22×Dic43C22×C414yes—
164C22×Dic43C22×C414yes—
165C22×Dic43C2×D412yes—
166C22×Dic43C2×D414yes—
167C22×Dic43C2×D414yes—
168C22×Dic43C2×D412yes—
169C22×Dic43C2×Q812yes—
170C22×Dic43C2×Q812yes—
171C22×Dic43#4112yes—
172C22×Dic43#4114yes—
173C22×Dic43#4114yes—
174C22×Dic43#4112yes—
175C2×Dic86—28no—
176C2×Dic86—216no—
177C2×Dic86—28no—
178C2×Dic86—28no—
179C2×Dic86—216no—
180C4⋊C4×C43—28no—
181C22⋊C4×C43—216no—
182C22⋊C4×C43—28no—
183C22⋊Dic43—28no—
184C22⋊Dic43—216no—
185Dic43⋊C4—216no—
186C4×Dic43—216no—
187C4×Dic43—28no—
188C4×Dic43—44no—
189C4×Dic43—48no—
190C23×C43—24no—
191C23×C43—22no—
192C23×C43—24no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—24no—
196C23×C43—22no—
197C23×C43—24no—
198C23×C43—24no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—24no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43—41no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—41no—
212C23×C43C4×Q814yescomplemented
213C23×C43C23×C411yescharacteristic
214C23×C43C22×D412yes—
215C23×C43C22×D411yescharacteristic
216C23×C43C22×Q811yescharacteristic
217C23×C43C2×#4112yes—
218C23×C43C2×#4112yes—
219C23×C43C2×#4111yescharacteristic
220C23×C43C2×#4111yescharacteristic
221C23×C43C2×#4111yescharacteristic
222C23×C43C2×#4111yescharacteristic
223C23×C43C2×#4112yes—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—41no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43C4×D414yes—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—24no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—41no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—416no—
277C2×Dic43C4×D418yes—
278C2×Dic43#12014yes—
279C2×Dic43C22⋊Q814yes—
280C2×Dic43C22⋊Q818yes—
281C2×Dic43#12414yes—
282C2×Dic43#12418yes—
283Dic86—232no—
284C4×#393—431nomaximal, Sylow
285C22×C43—24no—
286C22×C43—28no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—44no—
291C22×C43—42no—
292C22×C43—44no—
293C22×C43—42no—
294C22×C43—44no—
295C22×C43—42no—
296C22×C43C2×C4×D412yes—
297C22×C43C2×C4×D411yescharacteristic
298C22×C43C2×C4×Q811yescharacteristic
299C22×C43C4×#4112yes—
300C22×C43C4×#4111yescharacteristic
301C22×C43C2×#12011yescharacteristic
302C22×C43C2×C22⋊Q811yescharacteristic
303C22×C43C2×C22⋊Q812yes—
304C22×C43#52512yes—
305C22×C43#52511yescharacteristic
306C22×C43#52511yescharacteristic
307C22×C43#52512yes—
308C22×C43C2×#12411yescharacteristic
309C22×C43C2×#12412yes—
310C22×C43#52912yes—
311C22×C43#52912yes—
312C22×C43#52912yes—
313C22×C43#52911yescharacteristic
314C22×C43#52912yes—
315C22×C43#53212yes—
316C22×C43#53211yescharacteristic
317C22×C43#53312yes—
318C22×C43#53311yescharacteristic
319C4×C43—24no—
320C4×C43—44no—
321C4×C43—44no—
322C4×C43—42no—
323Dic43—28no—
324Dic43—42no—
325Dic43—42no—
326Dic43—42no—
327Dic43—44no—
328Dic43#39318yescomplemented
329C22×C4×Q8—431no—
330C2×#393—431no—
331C2×C4×C22⋊C4—432no—
332C2×C4×C22⋊C4—431no—
333#1446—431no—
334#1442—432no—
335#1442—431no—
336#1439—432no—
337#1439D4311yescharacteristic
338C4×#95—431no—
339C4×#95—432no—
340C2×C43—44no—
341C2×C43C4×#12011yescharacteristic
342C2×C43C4×C22⋊Q811yescharacteristic
343C2×C43C4×C22⋊Q812yes—
344C2×C43C4×#12412yes—
345C2×C43C4×#12411yescharacteristic
346C2×C43C2×#39311yescharacteristic
347C2×C43#238811yescharacteristic
348C2×C43#239611yescharacteristic
349C2×C43#239612yes—
350C2×C43#239811yescharacteristic
351C2×C43#239812yes—
352C23×Q8—431no—
353C24×C4—431no—
354C2×C4×Q8—864no—
355C2×C4×Q8—868no—
356C22×C4⋊C4—432no—
357C22×C4⋊C4C2×D4311yescharacteristic
358C22×C22⋊C4—432no—
359C22×C22⋊C4—431no—
360C22×C22⋊C4C2×D4312yes—
361C22×C22⋊C4C2×D4311yescharacteristic
362C22×C42—432no—
363C22×C42—431no—
364C22×C42—431no—
365C22×C42—432no—
366#393—438no—
367C4×C22⋊C4—868no—
368C4×C22⋊C4—864no—
369C2×#95—432no—
370C2×#95—431no—
371C2×#95—432no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95—431no—
375C2×#95—432no—
376C2×#95—432no—
377C2×#95—431no—
378C2×#95C2×D4312yes—
379C2×#95C2×D4311yescharacteristic
380C43C4×#39311yescharacteristic, complemented, Sylow
381C25C22×D4311yescharacteristic
382C22×Q8—434no—
383C22×Q8—864no—
384C22×Q8—864no—
385C22×Q8—862no—
386C22×Q8—862no—
387C23×C4—431no—
388C23×C4—432no—
389C23×C4—434no—
390C23×C4—431no—
391C23×C4—432no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—864no—
395C23×C4—862no—
396C23×C4—864no—
397C23×C4—862no—
398C23×C4C22×D4311yescharacteristic
399C23×C4C22×D4312yes—
400C23×C4C22×D4312yes—
401C23×C4C22×D4311yescharacteristic
402C4×Q8—8632no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—864no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—438no—
414C2×C22⋊C4—864no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4—864no—
417C2×C22⋊C4—862no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4C4×D4314yes—
420C2×C42—438no—
421C2×C42—434no—
422C2×C42—864no—
423C2×C42—864no—
424C2×C42—864no—
425C2×C42—862no—
426C2×C42—864no—
427C2×C42—864no—
428C2×C42—864no—
429C2×C42—864no—
430#95—24no—
431#95—22no—
432#95—438no—
433#95—434no—
434#95—864no—
435#95—864no—
436#95—864no—
437#95—862no—
438#95—864no—
439#95—862no—
440#95—864no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24C2×C4×D4312yes—
450C24#1062190012yes—
451C24Q8×D4312yes—
452C24C23×D4311yescharacteristic
453C2×Q8—8616no—
454C2×Q8—868no—
455C2×Q8—868no—
456C2×Q8—8616no—
457C2×Q8—868no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—434no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—434no—
480C22×C4—432no—
481C22×C4—434no—
482C22×C4—434no—
483C22×C4—434no—
484C22×C4—434no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—868no—
489C22×C4—8616no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—861no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—861no—
506C22×C4—862no—
507C22×C4—861no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—1724no—
513C22×C4—1724no—
514C22×C4—1728no—
515C22×C4C2×C4×D4312yes—
516C22×C4C2×C4×D4312yes—
517C22×C4D4×D4314yes—
518C22×C4D4×D4312yes—
519C22×C4#1062190014yes—
520C22×C4#1062190012yes—
521C4⋊C4—28no—
522C4⋊C4—8616no—
523C22⋊C4—216no—
524C22⋊C4—28no—
525C22⋊C4—8616no—
526C22⋊C4—868no—
527C42—868no—
528C42—8616no—
529C42—1728no—
530C42—1724no—
531C23—24no—
532C23—22no—
533C23—24no—
534C23—22no—
535C23—22no—
536C23—24no—
537C23—24no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—22no—
542C23—24no—
543C23—41no—
544C23—41no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—41no—
553C23#1306329014yescomplemented
554C23C22×C4×D4311yescharacteristic
555C23C2×D4×D4312yes—
556C23C2×D4×D4311yescharacteristic
557C23C2×Q8×D4311yescharacteristic
558C23#41×D4312yes—
559C23#41×D4312yes—
560C23#41×D4311yescharacteristic
561C23#41×D4311yescharacteristic
562C23C2×#1062190011yescharacteristic
563C23C2×#1062190011yescharacteristic
564C23C2×#1062190012yes—
565Q8—8632no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—434no—
590C2×C4—434no—
591C2×C4—438no—
592C2×C4—434no—
593C2×C4—438no—
594C2×C4—438no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—864no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—864no—
610C2×C4—862no—
611C2×C4—17216no—
612C2×C4—1721no—
613C2×C4—1722no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1722no—
617C2×C4—1721no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4(C22⋊D43)⋊C414yes—
625C22—24no—
626C22—28no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—44no—
632C22—42no—
633C22—44no—
634C22—44no—
635C22—42no—
636C22C4×D4×D4312yes—
637C22C2×(C22⋊D43)⋊C411yescharacteristic
638C22C2×#1306329011yescharacteristic
639C22C4×#1062190012yes—
640C22#1458336711yescharacteristic
641C22#120×D4311yescharacteristic
642C22C22⋊Q8×D4311yescharacteristic
643C22C22⋊Q8×D4312yes—
644C22#1458340512yes—
645C22#1458340711yescharacteristic
646C22#1458340911yescharacteristic
647C22#1458340912yes—
648C22#124×D4311yescharacteristic
649C22#124×D4312yes—
650C22#1458342612yes—
651C22#1458342612yes—
652C22#1458343012yes—
653C22#1458343011yescharacteristic
654C22#1458343212yes—
655C22#1458344412yes—
656C22#1458344711yescharacteristic
657C22#1458345112yes—
658C22#1458345111yescharacteristic
659C4—24no—
660C4—44no—
661C4—44no—
662C4—42no—
663C4—438no—
664C4—868no—
665C4—1722no—
666C4—1722no—
667C4—1722no—
668C4—1724no—
669C2—44no—
670C2#1913710011yescharacteristic
671C2#1913712311yescharacteristic
672C2#1913712712yes—
673C2#1913713612yes—
674C2#1913714211yescharacteristic
675C2#393×D4311yescharacteristic
676C2#1913780711yescharacteristic
677C2#1913786411yescharacteristic
678C2#1913787012yes—
679C2#1913788011yescharacteristic
680C2#1913788312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43C4×#393
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#13063290C2semidirect
5. #19132865C2semidirect
6. #19132854C2semidirect
7. #19132850C2semidirect
9. #95×Dic43C2semidirect
10. #95×Dic43C2semidirect
23. #14582811C4semidirect
44. C22×Dic86C2×C4semidirect
49. C23×Dic43Q8semidirect
83. C43⋊#95C2×C4semidirect
84. C43⋊#95C2×C4semidirect
212. C23×C43C4×Q8semidirect
328. Dic43#393semidirect
380. C43C4×#393semidirect
553. C23#13063290semidirect

Maximal subgroups

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

subgroupindex
C22×#130632902
C2×#145828112
C2×C22⋊C4×Dic432
#191328652
#191328542
#191328502
#191328382
#95×Dic432
C43×#14392
C4×#39343