Finite Group Databasebeta

← #24988427

Subgroups — #24988427

Order 11008.

1040 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134913C211yesmaximal, characteristic, complemented
2#19134903C211yesmaximal, characteristic, complemented
3C2×#14582636C211yesmaximal, characteristic, complemented
4C2×#14582633C211yesmaximal, characteristic, complemented
5C2×#14582623C211yesmaximal, characteristic, complemented
6#19132840C211yesmaximal, characteristic, complemented
7C2×C43×#538C211yesmaximal, characteristic
8C22×C4⋊Dic43C2211yescharacteristic
9C22×C22⋊Dic43—21no—
10C2×#13063249—21no—
11C2×#13063246—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×C43⋊#95—21no—
15C2×C43⋊#95C2211yescharacteristic
16#14582661—21no—
17#14582661—21no—
18#14582636—22no—
19#14582633—22no—
20#14582623—22no—
21C43×#538—22no—
22C43×#538—22no—
23C43×#538—22no—
24C43×#538C414yescomplemented
25C2×#126×C43—21no—
26C2×#124×C43—21no—
27C2×#123×C43—21no—
28C2×C22⋊Q8×C43C2211yescharacteristic
29C2×#121×C43—21no—
30C2×#121×C43C2211yescharacteristic
31C2×#120×C43—21no—
32C2×C4×D4×C43—21no—
33C22×C22⋊C4×C43C2211yescharacteristic
34C23×Dic43—21no—
35C23×Dic43—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—42no—
41C2×C22⋊Dic43—42no—
42C2×C22⋊Dic43—42no—
43C2×C22⋊Dic43—42no—
44#13063249—42no—
45#13063246—42no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—42no—
53C25×C43D411yescharacteristic
54C22×Q8×C43D411yescharacteristic
55C22×D4×C43—21no—
56C22×D4×C43—21no—
57C22×D4×C43—21no—
58C22×D4×C43D411yescharacteristic
59C23×C4×C43—21no—
60C23×C4×C43D411yescharacteristic
61C23×C4×C43C2311yescharacteristic
62#126×C43—24no—
63#126×C43—24no—
64#124×C43—24no—
65#124×C43—24no—
66#123×C43—24no—
67#123×C43—24no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43C2×C412yes—
71C22⋊Q8×C43D412yes—
72#121×C43—24no—
73#121×C43—24no—
74#121×C43—21no—
75#121×C43—21no—
76#121×C43C2×C412yes—
77#121×C43D412yes—
78#120×C43—24no—
79#120×C43—24no—
80C4×D4×C43—24no—
81C4×D4×C43—24no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C4⋊C4×C43D411yescharacteristic
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43C2×C412yes—
96C2×C22⋊C4×C43D412yes—
97C2×C42×C43—21no—
98C24×C43—21no—
99C24×C43—21no—
100C24×C43—21no—
101C24×C43—21no—
102C24×C43—21no—
103C24×C43—21no—
104C24×C43—21no—
105C24×C43—41no—
106C24×C43—41no—
107C24×C43—41no—
108C24×C43—41no—
109C24×C43C22⋊C412yes—
110C24×C43C2×D411yescharacteristic
111C2×Q8×C43—21no—
112C2×Q8×C43—41no—
113C2×Q8×C43—41no—
114C2×Q8×C43C22⋊C412yescomplemented
115C2×D4×C43—24no—
116C2×D4×C43—24no—
117C2×D4×C43—21no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—41no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C2×D4×C43—41no—
126C2×D4×C43—81no—
127C2×D4×C43—81no—
128C2×D4×C43—81no—
129C2×D4×C43—81no—
130C2×D4×C43C22⋊C412yescomplemented
131C22×C4×C43—24no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43—81no—
142C22×C4×C43—81no—
143C22×C4×C43C22⋊C412yes—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22⋊C412yescomplemented
170C4⋊C4×C43C22⋊C412yescomplemented
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C42×C43—24no—
183C22⋊Dic43—48no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—41no—
187C4⋊Dic43—41no—
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8—41no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—81no—
223C23×C43—81no—
224C23×C43—81no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43—81no—
228C23×C43C2×C22⋊C411yescharacteristic
229C23×C43#12011yescharacteristic
230C23×C43#12011yescharacteristic
231C23×C43#13511yescharacteristic
232C23×C43#13511yescharacteristic
233C23×C43AGL(1,ℤ/8)11yescharacteristic
234C23×C43#13711yescharacteristic
235Q8×C43—42no—
236Q8×C43—81no—
237D4×C43—42no—
238D4×C43—42no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—42no—
242D4×C43—81no—
243D4×C43—84no—
244D4×C43—84no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—42no—
266C2×C4×C43—81no—
267C2×C4×C43—84no—
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43#12011yescharacteristic
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—81no—
279C2×Dic43—81no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282C2×Dic43—81no—
283C2×Dic43—81no—
284C2×Dic43—81no—
285C2×Dic43—81no—
286C43⋊C8—81no—
287C43⋊C8—81no—
288#8408—431nomaximal, Sylow
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—44no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—82no—
309C22×C43—82no—
310C22×C43—82no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43#37911yescharacteristic
320C22×C43#41611yescharacteristic
321C22×C43#41711yescharacteristic
322C22×C43#44911yescharacteristic
323C22×C43#44911yescharacteristic
324C22×C43#45211yescharacteristic
325C22×C43#45211yescharacteristic
326C22×C43#45311yescharacteristic
327C22×C43#45511yescharacteristic
328C22×C43B(4,𝔽2)11yescharacteristic
329C22×C43#45811yescharacteristic
330C4×C43—21no—
331C4×C43—21no—
332C4×C43—21no—
333C4×C43—21no—
334C4×C43—42no—
335C4×C43—42no—
336C4×C43—42no—
337C4×C43—42no—
338Dic43—82no—
339Dic43—82no—
340C2×#538D4311yescharacteristic
341#1874—431no—
342#1872—431no—
343C2×#328—431no—
344C2×#327—431no—
345C2×#323—431no—
346#1439—431no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—21no—
351C2×C43—82no—
352C2×C43—82no—
353C2×C43#160011yescharacteristic
354C2×C43#160611yescharacteristic
355C2×C43#161211yescharacteristic
356C2×C43#161811yescharacteristic
357C2×C43#178811yescharacteristic
358C2×C43#179011yescharacteristic
359C2×C43#179211yescharacteristic
360#538—22no—
361#538—22no—
362#538—22no—
363#538Dic4314yescomplemented
364C2×#126—21no—
365C2×#124—21no—
366C2×#123—21no—
367C2×C22⋊Q8C2×D4311yescharacteristic
368C2×#121—21no—
369C2×#121C2×D4311yescharacteristic
370C2×#120—21no—
371C2×C4×D4—21no—
372C22×C4⋊C4—431no—
373C22×C22⋊C4—861no—
374C22×C22⋊C4C2×D4311yescharacteristic
375C2×#103—861no—
376C2×#102—861no—
377C2×C22⋊C8—431no—
378C2×C22⋊C8—431no—
379C2×#95—431no—
380C2×#95—861no—
381#340—861no—
382#340—861no—
383#328—862no—
384#327—862no—
385#323—862no—
386C43#840811yescharacteristic, complemented, Sylow
387C25C22⋊D4311yescharacteristic
388C22×Q8C22⋊D4311yescharacteristic
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4C22⋊D4311yescharacteristic
393C23×C4—21no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4C22⋊D4311yescharacteristic
397C23×C4C22×D4311yescharacteristic
398C22×C8—861no—
399C22×C8—861no—
400#126—24no—
401#126—24no—
402#124—24no—
403#124—24no—
404#123—24no—
405#123—24no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8C2×Dic4312yes—
409C22⋊Q8C22⋊D4312yes—
410#121—24no—
411#121—24no—
412#121—21no—
413#121—21no—
414#121C2×Dic4312yes—
415#121C22⋊D4312yes—
416#120—24no—
417#120—24no—
418C4×D4—24no—
419C4×D4—24no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—1722no—
425C2×C4⋊C4C22⋊D4311yescharacteristic
426C2×C4⋊C4C22⋊D4311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—1722no—
437C2×C22⋊C4—1722no—
438C2×C22⋊C4—1722no—
439C2×C22⋊C4C2×Dic4312yes—
440C2×C22⋊C4C22⋊D4312yes—
441C2×C42—21no—
442#103—1722no—
443#102—1722no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448#95—861no—
449#95—861no—
450#95—1722no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24C22⋊Dic4312yes—
463C24C2×C22⋊D4311yescharacteristic
464C2×Q8—21no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8C22⋊Dic4312yescomplemented
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4C22⋊Dic4312yescomplemented
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—1721no—
499C22×C4—1721no—
500C22×C4—1721no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4—1721no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4C22⋊Dic4312yes—
511C22×C4C22×Dic4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C2×C8—1721no—
518C2×C8—1721no—
519C2×C8—1721no—
520C2×C8—1721no—
521C2×C8—1721no—
522C2×C8—1721no—
523C4⋊C4—24no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—1721no—
531C4⋊C4—1721no—
532C4⋊C4C22⋊Dic4312yescomplemented
533C4⋊C4C22⋊Dic4312yescomplemented
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—1728no—
546C42—24no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23C2×C22⋊Dic4311yescharacteristic
582C23#1306329411yescharacteristic
583C23#1306329411yescharacteristic
584C23#1306334511yescharacteristic
585C23#1306334511yescharacteristic
586C23#1306335011yescharacteristic
587C23#1306335511yescharacteristic
588Q8—42no—
589Q8—81no—
590D4—42no—
591D4—42no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—81no—
596D4—84no—
597D4—84no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—81no—
620C2×C4—84no—
621C2×C4—3441no—
622C2×C4—3441no—
623C2×C4—3441no—
624C2×C4—3441no—
625C2×C4—3441no—
626C2×C4—3441no—
627C2×C4—3441no—
628C2×C4—3441no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1722no—
634C2×C4—1722no—
635C2×C4C2×C22⋊Dic4311yescharacteristic
636C2×C4C2×C22⋊Dic4311yescharacteristic
637C2×C4#1306329411yescharacteristic
638C2×C4#1306329411yescharacteristic
639C8—3441no—
640C8—3441no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—44no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—82no—
661C22—82no—
662C22—82no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22#1458275511yescharacteristic
672C22#1458289511yescharacteristic
673C22#1458290011yescharacteristic
674C22#1458304411yescharacteristic
675C22#1458304411yescharacteristic
676C22#1458306111yescharacteristic
677C22#1458306111yescharacteristic
678C22#1458306711yescharacteristic
679C22#1458307711yescharacteristic
680C22#1458308611yescharacteristic
681C22#1458308911yescharacteristic
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—3442no—
691C4—3442no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—21no—
696C2—82no—
697C2—82no—
698C2#1913354111yescharacteristic
699C2#1913357511yescharacteristic
700C2#1913360911yescharacteristic
701C2#1913364311yescharacteristic
702C2#1913453511yescharacteristic
703C2#1913454311yescharacteristic
704C2#1913454911yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#538C2
socleC23×C43#120
cosocleC23×C4×C43C23
hypercenterC2×#538D43
hypocenterC43#8408
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #19134913C2semidirect
2. #19134903C2semidirect
3. C2×#14582636C2semidirect
4. C2×#14582633C2semidirect
5. C2×#14582623C2semidirect
6. #19132840C2semidirect
24. C43×#538C4semidirect
114. C2×Q8×C43C22⋊C4semidirect
130. C2×D4×C43C22⋊C4semidirect
169. C4⋊C4×C43C22⋊C4semidirect
170. C4⋊C4×C43C22⋊C4semidirect
363. #538Dic43semidirect
386. C43#8408semidirect
467. C2×Q8C22⋊Dic43semidirect
483. C2×D4C22⋊Dic43semidirect
532. C4⋊C4C22⋊Dic43semidirect
533. C4⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
#191349132
#191349032
C2×#145826362
C2×#145826332
C2×#145826232
#191328402
C2×C43×#5382
#840843