Finite Group Databasebeta

← #25027890

Subgroups — #25027890

Order 11008.

2734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063305C211yesmaximal, characteristic
2C22×C42×D43C211yesmaximal, characteristic
3C2×#14582805C211yesmaximal, characteristic, complemented
4C2×#14582804C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic
6#19132829C214yesmaximal, complemented
7#19132824C211yesmaximal, characteristic, complemented
8(C2×D43)⋊#95C214yesmaximal
9C43×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×Dic86C2211yescharacteristic
11C23×C4×D43C2212yes—
12C23×C4×D43C2211yescharacteristic
13C2×#13063305—24no—
14C2×#13063305—24no—
15C2×#13063305C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×C4×Dic43C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22C2×C42×D43—24no—
23C2×C42×D43—24no—
24C2×C42×D43—24no—
25#14582805—24no—
26#14582804—24no—
27#14582756—24no—
28C2×C43⋊#95C2214yes—
29C2×C43⋊#95C2214yes—
30C2×C43⋊#95C2214yes—
31C2×C43⋊#95C2212yes—
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic
35C2×#95×C43C2214yes—
36C24×D43C2311yescharacteristic
37C22×Dic86—22no—
38C22×Dic86—22no—
39C22×Dic86—22no—
40C22×Dic86—22no—
41C22×Dic86—22no—
42C22×Dic86—22no—
43C22×Dic86C2×C414yescomplemented
44C23×Dic43C2312yes—
45C23×Dic43C2312yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2312yes—
48C22×C4×D43—24no—
49C22×C4×D43—24no—
50C22×C4×D43—24no—
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—24no—
55C22×C4×D43—22no—
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43C2×C414yes—
59C22×C4×D43D414yes—
60C22×C4×D43D414yes—
61C22×C4×D43Q818yescomplemented
62#13063305—232no—
63C2×C4⋊Dic43—24no—
64C2×C4⋊Dic43—24no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43C2×C418yescomplemented
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—28no—
73C2×(C2×D43)⋊C4C2×C418yes—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—22no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43D414yes—
80C42×D43—232no—
81C43⋊#95—28no—
82C43⋊#95—28no—
83C43⋊#95—24no—
84C43⋊#95—28no—
85C23×C4×C43C2312yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43C2×C414yescomplemented
95C2×C42×C43—22no—
96C2×C42×C43—22no—
97C2×C42×C43D414yes—
98#95×C43—28no—
99C24×C43C2411yescharacteristic
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—21no—
103C23×D43—21no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43C22×C412yes—
107C23×D43C2×D412yes—
108C23×D43C2×D412yes—
109C23×D43C2×Q814yes—
110C23×D43#4114yes—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—24no—
120C22×C4×C43—24no—
121C22×C4×C43—24no—
122C22×C4×C43—22no—
123C22×C4×C43—24no—
124C22×C4×C43C22×C414yes—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D414yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×Q814yes—
132C22×C4×C43#4112yes—
133C22×C4×C43#4114yes—
134C22×C4×C43#4112yes—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—24no—
152C22×Dic43—24no—
153C22×Dic43—22no—
154C22×Dic43C22×C414yes—
155C22×Dic43C22×C412yes—
156C22×Dic43C2×D412yes—
157C22×Dic43C2×D412yes—
158C22×Dic43C2×D414yes—
159C22×Dic43C2×Q814yes—
160C22×Dic43#4114yes—
161C2×C4×D43—216no—
162C2×C4×D43—216no—
163C2×C4×D43—216no—
164C2×C4×D43—216no—
165C2×C4×D43—28no—
166C2×C4×D43—28no—
167C2×C4×D43—28no—
168C2×C4×D43—28no—
169C2×C4×D43—28no—
170C2×C4×D43—216no—
171C2×C4×D43—28no—
172C2×C4×D43—216no—
173C2×C4×D43—216no—
174C2×C4×D43C22⋊C4116yes—
175C2×Dic86—28no—
176C2×Dic86—28no—
177C2×Dic86—28no—
178C2×Dic86—44no—
179C2×Dic86—44no—
180C2×Dic86—44no—
181C2×Dic86—44no—
182C4⋊C4×C43—28no—
183C4⋊C4×C43—44no—
184C42×C43—28no—
185(C2×D43)⋊C4—216no—
186(C2×D43)⋊C4—48no—
187C4⋊Dic43—216no—
188C4⋊Dic43—44no—
189C4×Dic43—216no—
190C4×Dic43—28no—
191C23×C43C23×C411yescharacteristic
192C23×C43C22×D411yescharacteristic
193C23×C43C22×D411yescharacteristic
194C23×C43C22×D411yescharacteristic
195C23×C43C22×D411yescharacteristic
196C23×C43C22×Q812yes—
197C23×C43C2×#4112yes—
198C23×C43C2×#4112yes—
199C23×C43C2×#4112yes—
200C23×C43C2×#4111yescharacteristic
201C23×C43C2×#4111yescharacteristic
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—24no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—24no—
209C22×D43—24no—
210C22×D43—22no—
211C22×D43—24no—
212C22×D43—24no—
213C22×D43—24no—
214C22×D43—24no—
215C22×D43—24no—
216C22×D43—22no—
217C22×D43—22no—
218C22×D43—24no—
219C22×D43—24no—
220C22×D43C2×C22⋊C414yes—
221C22×D43C4×Q818yes—
222C22×D43C22⋊Q818yes—
223C22×D43#12414yes—
224C22×D43C4⋊Q814yes—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—28no—
233C2×C4×C43—44no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—44no—
238C2×C4×C43—42no—
239C2×C4×C43—44no—
240C2×C4×C43—42no—
241C2×C4×C43C2×C22⋊C414yes—
242C2×C4×C43C4×D414yes—
243C2×C4×C43C4×D414yes—
244C2×C4×C43#12014yes—
245C2×C4×C43#12114yes—
246C2×C4×C43#12114yes—
247C2×C4×C43C22⋊Q818yescomplemented
248C2×C4×C43#12314yes—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—24no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—22no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—44no—
270C2×Dic43—42no—
271C2×Dic43—44no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C414yes—
274C2×Dic43C22⋊Q818yescomplemented
275C4×D43—264no—
276C4×D43—232no—
277Dic86—416no—
278#14702—431nomaximal, Sylow
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×C4×D411yescharacteristic
282C22×C43C2×C4×Q812yes—
283C22×C43C4×#4112yes—
284C22×C43C2×#12011yescharacteristic
285C22×C43C2×#12111yescharacteristic
286C22×C43C2×#12111yescharacteristic
287C22×C43C2×C22⋊Q812yes—
288C22×C43C2×C22⋊Q812yes—
289C22×C43C2×C22⋊Q812yes—
290C22×C43C2×#12311yescharacteristic
291C22×C43#52512yes—
292C22×C43#52512yes—
293C22×C43#52512yes—
294C22×C43C2×#12411yescharacteristic
295C22×C43#52912yes—
296C22×C43#52912yes—
297C22×C43C2×C4⋊Q811yescharacteristic
298C22×C43#53211yescharacteristic
299C22×C43#53211yescharacteristic
300C22×C43#53312yes—
301C22×C43#53312yes—
302C2×D43—28no—
303C2×D43—24no—
304C2×D43—24no—
305C2×D43—28no—
306C2×D43—24no—
307C2×D43—24no—
308C2×D43—24no—
309C2×D43—24no—
310C2×D43—28no—
311C2×D43—28no—
312C2×D43#39118yescomplemented
313C4×C43—28no—
314C4×C43—44no—
315C4×C43—82no—
316C4×C43#38618yes—
317Dic43—28no—
318Dic43—24no—
319Dic43—44no—
320Dic43—82no—
321C22×C22⋊Q8—431no—
322C23×C42—431no—
323C2×#391—431no—
324C2×#391—431no—
325C2×#380—431no—
326#1436—434no—
327C4⋊#95—431no—
328C4⋊#95D4311yescharacteristic, complemented
329C22⋊#95—434no—
330C2×C43C2×#38611yescharacteristic
331C2×C43C2×#39111yescharacteristic
332C2×C43#229711yescharacteristic
333C2×C43C4×C22⋊Q812yes—
334C2×C43C4×C22⋊Q812yes—
335C2×C43#284812yes—
336C2×C43#285011yescharacteristic
337C2×C43#285011yescharacteristic
338C2×C43#285512yes—
339C2×C43#285711yescharacteristic
340C2×C43#285711yescharacteristic
341D43—28no—
342C23×Q8—431no—
343C24×C4—431no—
344C24×C4—432no—
345C2×C22⋊Q8—438no—
346C2×C22⋊Q8—864no—
347C2×C22⋊Q8—864no—
348C22×C4⋊C4—432no—
349C22×C4⋊C4—431no—
350C22×C4⋊C4C2×D4311yescharacteristic
351C22×C4⋊C4C2×D4311yescharacteristic
352C22×C22⋊C4—432no—
353C22×C22⋊C4—432no—
354C22×C42—431no—
355C22×C42—432no—
356C22×C42—864no—
357C22×C42—864no—
358C22×C42—864no—
359C22×C42C2×D4311yescharacteristic
360#391—864no—
361#391—864no—
362#380—864no—
363C2×#95—434no—
364C2×#95—434no—
365C2×#95—434no—
366C2×#95—432no—
367C2×#95C2×D4314yes—
368C43#1470211yescharacteristic, complemented, Sylow
369C25—431no—
370C22×Q8—434no—
371C22×Q8—862no—
372C22×Q8—862no—
373C22×Q8—862no—
374C22×Q8—862no—
375C22×Q8—862no—
376C22×Q8—862no—
377C23×C4—431no—
378C23×C4—432no—
379C23×C4—434no—
380C23×C4—434no—
381C23×C4—434no—
382C23×C4—432no—
383C23×C4—438no—
384C23×C4—432no—
385C23×C4—864no—
386C23×C4—864no—
387C23×C4—864no—
388C23×C4—864no—
389C23×C4—864no—
390C23×C4—862no—
391C23×C4—862no—
392C23×C4—862no—
393C23×C4—864no—
394C23×C4—862no—
395C23×C4C22×D4312yes—
396C23×C4C22×D4312yes—
397C23×C4C22×D4312yes—
398C23×C4C22×D4311yescharacteristic
399C22⋊Q8—8632no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—438no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—864no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—862no—
410C2×C4⋊C4—862no—
411C2×C4⋊C4C4×D4314yescomplemented
412C2×C22⋊C4—438no—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—864no—
415C2×C22⋊C4—868no—
416C2×C22⋊C4—864no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—434no—
420C2×C42—8632no—
421C2×C42—864no—
422C2×C42—864no—
423C2×C42—864no—
424C2×C42—862no—
425C2×C42—862no—
426C2×C42D17214yes—
427#95—28no—
428#95—868no—
429#95—864no—
430#95—868no—
431#95—868no—
432C24—432no—
433C24—432no—
434C24—432no—
435C24—434no—
436C24—434no—
437C24—861no—
438C24—861no—
439C24—862no—
440C24—862no—
441C24—861no—
442C24—861no—
443C24C23×D4311yescharacteristic
444C2×Q8—868no—
445C2×Q8—868no—
446C2×Q8—868no—
447C2×Q8—1724no—
448C2×Q8—1724no—
449C2×Q8—1724no—
450C2×Q8—1724no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—432no—
465C22×C4—434no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—434no—
469C22×C4—434no—
470C22×C4—4316no—
471C22×C4—434no—
472C22×C4—8616no—
473C22×C4—8616no—
474C22×C4—8616no—
475C22×C4—8616no—
476C22×C4—8616no—
477C22×C4—8616no—
478C22×C4—861no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—868no—
487C22×C4—868no—
488C22×C4—868no—
489C22×C4—868no—
490C22×C4—868no—
491C22×C4—8616no—
492C22×C4—868no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—864no—
502C22×C4—864no—
503C22×C4—862no—
504C22×C4C2×C4×D4314yes—
505C22×C4C2×C4×D4312yes—
506C22×C4C2×D17214yes—
507C22×C4C2×D17212yes—
508C22×C4#1062189812yes—
509C22×C4D4×D4312yes—
510C22×C4D4×D4312yes—
511C22×C4D4×D4312yes—
512C22×C4#1062190014yes—
513C22×C4Q8×D4314yes—
514C22×C4#1062190212yes—
515C4⋊C4—28no—
516C4⋊C4—44no—
517C4⋊C4—8616no—
518C4⋊C4—1724no—
519C22⋊C4—8616no—
520C22⋊C4—1728no—
521C42—28no—
522C42—8616no—
523C42—868no—
524C23—434no—
525C23—438no—
526C23—438no—
527C23—434no—
528C23—434no—
529C23—862no—
530C23—862no—
531C23—864no—
532C23—862no—
533C23—862no—
534C23—862no—
535C23—864no—
536C23—864no—
537C23—862no—
538C23—864no—
539C23—864no—
540C23—864no—
541C23—864no—
542C23—864no—
543C23—862no—
544C23—862no—
545C23—864no—
546C23—864no—
547C23C22×C4×D4311yescharacteristic
548C23C2×D4×D4311yescharacteristic
549C23C2×D4×D4311yescharacteristic
550C23C2×D4×D4311yescharacteristic
551C23C22×D17211yescharacteristic
552C23C2×Q8×D4312yes—
553C23#41×D4312yes—
554C23#41×D4312yes—
555C23C2×#1062190012yes—
556C23C2×#1062189811yescharacteristic
557C23C2×#1062190211yescharacteristic
558Q8—17216no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—28no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—434no—
576C2×C4—438no—
577C2×C4—8664no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—864no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—862no—
587C2×C4—864no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—8632no—
591C2×C4—864no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—1722no—
595C2×C4—1724no—
596C2×C4—1722no—
597C2×C4—1724no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4C22⋊C4×D4314yes—
604C2×C4#1306328714yes—
605C2×C4C4×D17214yes—
606C2×C4#1306329514yes—
607C2×C4#1306329814yes—
608C2×C4#1306330014yes—
609C2×C4#1306330518yescomplemented
610C2×C4#1306331014yes—
611C22—438no—
612C22—868no—
613C22—864no—
614C22—864no—
615C22—864no—
616C22—868no—
617C22—868no—
618C22—868no—
619C22—864no—
620C22—864no—
621C22—864no—
622C22C2×C22⋊C4×D4311yescharacteristic
623C22C2×#1306328711yescharacteristic
624C22C2×C4×D17211yescharacteristic
625C22C4×Q8×D4312yes—
626C22C4×#1062190012yes—
627C22C2×#1306329511yescharacteristic
628C22C2×#1306329811yescharacteristic
629C22C2×#1306330011yescharacteristic
630C22C22⋊Q8×D4312yes—
631C22C22⋊Q8×D4312yes—
632C22C2×#1306330512yes—
633C22C2×#1306331011yescharacteristic
634C22#1458340912yes—
635C22#1458340912yes—
636C22#1458341112yes—
637C22#124×D4311yescharacteristic
638C22#1458343112yes—
639C22#1458343412yes—
640C22C4⋊Q8×D4311yescharacteristic
641C22#1458344711yescharacteristic
642C22#1458344811yescharacteristic
643C22#1458345312yes—
644C22#1458345412yes—
645C4—28no—
646C4—44no—
647C4—82no—
648C4—868no—
649C4—864no—
650C4—3442no—
651C4—1724no—
652C4#1458277718yes—
653C2—868no—
654C2C2×#1458277711yescharacteristic
655C2#391×D4311yescharacteristic
656C2#1913708211yescharacteristic
657C2#1913712512yes—
658C2C4×#1306330512yes—
659C2#1914288312yes—
660C2#1914289511yescharacteristic
661C2#1914289711yescharacteristic
662C2#1914293312yes—
663C2#1914294411yescharacteristic
664C2#1914294811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4⋊#95D43
hypocenterC43#14702
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#14582805C2semidirect
4. C2×#14582804C2semidirect
6. #19132829C2semidirect
7. #19132824C2semidirect
9. C43×C4⋊#95C2semidirect
15. C2×#13063305C4semidirect
43. C22×Dic86C2×C4semidirect
61. C22×C4×D43Q8semidirect
68. C2×C4⋊Dic43C2×C4semidirect
94. C2×C4⋊C4×C43C2×C4semidirect
247. C2×C4×C43C22⋊Q8semidirect
274. C2×Dic43C22⋊Q8semidirect
312. C2×D43#391semidirect
328. C4⋊#95D43semidirect
368. C43#14702semidirect
411. C2×C4⋊C4C4×D43semidirect
609. C2×C4#13063305semidirect

Maximal subgroups

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

subgroupindex
C22×#130633052
C22×C42×D432
C2×#145828052
C2×#145828042
C2×#145827562
#191328292
#191328242
(C2×D43)⋊#952
C43×C4⋊#952
#1470243