Finite Group Databasebeta

← #25018573

Subgroups — #25018573

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063284C211yesmaximal, characteristic
2C2×#14582769C211yesmaximal, characteristic, complemented
3C2×#14582765C211yesmaximal, characteristic, complemented
4C2×#14582759C211yesmaximal, characteristic
5#19132840C214yesmaximal
6#19132829C214yesmaximal, complemented
7#19132825C211yesmaximal, characteristic, complemented
8#19132825C211yesmaximal, characteristic, complemented
9C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
10C2×#13063284—24no—
11C2×#13063284—24no—
12C2×#13063284—24no—
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4⋊Dic43C2214yes—
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2212yes—
20C22×C4×Dic43C2212yes—
21#14582769—24no—
22#14582765—24no—
23#14582759—24no—
24C2×C43⋊#95C2214yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2214yes—
27C2×C43⋊#95C2214yes—
28C24×C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C22×C42×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C4×C22⋊C4×C43C418yescomplemented
33C2×#95×C43C2212yes—
34C23×Dic43C2312yes—
35C23×Dic43C2312yes—
36C23×Dic43C2312yes—
37C23×Dic43C2312yes—
38#13063284—232no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43—22no—
41C2×C4⋊Dic43—22no—
42C2×C4⋊Dic43—22no—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—28no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—28no—
51C2×C4⋊Dic43—44no—
52C2×C4⋊Dic43D414yes—
53C2×C4⋊Dic43D414yes—
54C2×C22⋊Dic43—24no—
55C2×C22⋊Dic43—24no—
56C2×C22⋊Dic43—24no—
57C2×C22⋊Dic43—24no—
58C2×C22⋊Dic43—44no—
59C2×C4×Dic43—24no—
60C2×C4×Dic43—24no—
61C2×C4×Dic43—24no—
62C43⋊#95—24no—
63C43⋊#95—28no—
64C43⋊#95—28no—
65C43⋊#95—44no—
66C25×C43C2311yescharacteristic
67C23×C4×C43—22no—
68C23×C4×C43—22no—
69C23×C4×C43—22no—
70C23×C4×C43—22no—
71C23×C4×C43C2×C414yes—
72C23×C4×C43D414yes—
73C23×C4×C43Q814yes—
74C23×C4×C43C2312yes—
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2312yes—
77C23×C4×C43C2311yescharacteristic
78C2×C22⋊C4×C43—24no—
79C2×C22⋊C4×C43—24no—
80C2×C22⋊C4×C43C2×C418yes—
81C2×C42×C43—22no—
82C2×C42×C43—22no—
83C2×C42×C43—22no—
84C2×C42×C43—22no—
85C2×C42×C43C2×C414yes—
86C2×C42×C43C2×C414yes—
87#95×C43C2×C418yes—
88C24×C43—21no—
89C24×C43—21no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—21no—
93C24×C43—21no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43C22×C412yes—
97C24×C43C2×D412yes—
98C24×C43C2×Q812yes—
99C24×C43C2411yescharacteristic
100C22×C4×C43—28no—
101C22×C4×C43—28no—
102C22×C4×C43—28no—
103C22×C4×C43—28no—
104C22×C4×C43—28no—
105C22×C4×C43—28no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
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—22no—
120C22×C4×C43C4⋊C4116yescomplemented
121C22×C4×C43C22×C414yes—
122C22×C4×C43C22×C412yes—
123C22×C4×C43C22×C414yes—
124C22×C4×C43C22×C412yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×Q812yes—
130C22×C4×C43C2×Q812yes—
131C22×C4×C43#4114yes—
132C22×C4×C43#4114yes—
133C22×C4×C43#4112yes—
134C22×C4×C43#4112yes—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—24no—
144C22×Dic43—24no—
145C22×Dic43—24no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—24no—
149C22×Dic43—24no—
150C22×Dic43—24no—
151C22×Dic43—24no—
152C22×Dic43—24no—
153C22×Dic43C2×D414yes—
154C22×Dic43C2×D414yes—
155C22⋊C4×C43—216no—
156C42×C43—28no—
157C42×C43—28no—
158C22⋊Dic43—216no—
159C22⋊Dic43—48no—
160C4⋊Dic43—28no—
161C4⋊Dic43—28no—
162C4⋊Dic43—416no—
163C4⋊Dic43—44no—
164C4⋊Dic43—44no—
165C4×Dic43—216no—
166C23×C43—24no—
167C23×C43—22no—
168C23×C43—22no—
169C23×C43—24no—
170C23×C43—22no—
171C23×C43—22no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—22no—
176C23×C43—24no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—24no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43C2×C4⋊C414yes—
189C23×C43C23×C411yescharacteristic
190C23×C43C22×D411yescharacteristic
191C23×C43C22×D411yescharacteristic
192C23×C43C22×D411yescharacteristic
193C23×C43C22×Q811yescharacteristic
194C23×C43C2×#4111yescharacteristic
195C23×C43C2×#4111yescharacteristic
196C23×C43C2×#4112yes—
197C23×C43C2×#4112yes—
198C23×C43H(5,𝔽2)12yes—
199C23×C432−1+412yes—
200C2×C4×C43—24no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—24no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—24no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—232no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43C2×C4⋊C414yes—
221C2×C4×C43C2×C4⋊C414yes—
222C2×C4×C43#11718yescomplemented
223C2×C4×C43C4×D414yes—
224C2×C4×C43C4×D414yes—
225C2×C4×C43#12014yes—
226C2×C4×C43C22⋊Q814yes—
227C2×C4×C43C22⋊Q814yes—
228C2×C4×C43#12314yes—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—28no—
232C2×Dic43—28no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—44no—
238C2×Dic43—44no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—44no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249#13879—431nomaximal, Sylow
250C22×C43—24no—
251C22×C43—24no—
252C22×C43—24no—
253C22×C43—44no—
254C22×C43—44no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—44no—
258C22×C43—44no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43C22×C4⋊C411yescharacteristic
262C22×C43C2×#11712yes—
263C22×C43C2×C4×D411yescharacteristic
264C22×C43C2×C4×D411yescharacteristic
265C22×C43#52012yes—
266C22×C43C2×#12011yescharacteristic
267C22×C43C2×C22⋊Q811yescharacteristic
268C22×C43C2×C22⋊Q811yescharacteristic
269C22×C43C2×#12311yescharacteristic
270C22×C43#53211yescharacteristic
271C22×C43#53211yescharacteristic
272C22×C43#53312yes—
273C22×C43#53511yescharacteristic
274C22×C43#53611yescharacteristic
275C22×C43#54412yes—
276C22×C43#54612yes—
277C22×C43#54712yes—
278C22×C43#54812yes—
279C22×C43#55012yes—
280C22×C43#55212yes—
281C22×C43#55312yes—
282C22×C43#55512yes—
283C22×C43#55612yes—
284C4×C43—28no—
285C4×C43—24no—
286C4×C43—44no—
287C4×C43#38518yes—
288Dic43—44no—
289Dic43—44no—
290Dic43—82no—
291Dic43—82no—
292C22×#117—431no—
293C2×#384—431no—
294C2×#382—431no—
295C2×#380—431no—
296C2×C4×C22⋊C4D4311yescharacteristic
297#1439—434no—
298#1436—434no—
299C4⋊#95—431no—
300C4⋊#95—431no—
301C2×C43—44no—
302C2×C43#228511yescharacteristic
303C2×C43C2×#38511yescharacteristic
304C2×C43#231711yescharacteristic
305C2×C43#235212yes—
306C2×C43#235412yes—
307C2×C43#243111yescharacteristic
308C2×C43#243211yescharacteristic
309C2×C43#243912yes—
310C2×C43#244112yes—
311C2×C43#249911yescharacteristic
312C2×C43#250011yescharacteristic
313C24×C4C2×D4311yescharacteristic
314C2×#117—864no—
315C2×#117—864no—
316C2×#117—864no—
317C22×C4⋊C4—431no—
318C22×C4⋊C4—431no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4—431no—
321C22×C4⋊C4—434no—
322C22×C22⋊C4—432no—
323C22×C22⋊C4—432no—
324C22×C22⋊C4C2×D4312yes—
325C22×C42—432no—
326C22×C42C2×D4311yescharacteristic
327C22×C42C2×D4311yescharacteristic
328#384—864no—
329#382—864no—
330#380—864no—
331C4×C22⋊C4Dic4318yescomplemented
332C2×#95—434no—
333C2×#95—432no—
334C2×#95—434no—
335C2×#95—434no—
336C2×#95C2×D4312yes—
337C43#1387911yescharacteristic, complemented, Sylow
338C25C22×D4311yescharacteristic
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—432no—
344C23×C4—432no—
345C23×C4—432no—
346C23×C4—432no—
347C23×C4Dic8614yes—
348C23×C4D17214yes—
349C23×C4C2×Dic4314yes—
350C23×C4C22×D4312yes—
351C23×C4C22×D4311yescharacteristic
352C23×C4C22×D4312yes—
353C23×C4C22×D4311yescharacteristic
354#117—8632no—
355C2×C4⋊C4—434no—
356C2×C4⋊C4—434no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—868no—
362C2×C4⋊C4—862no—
363C2×C4⋊C4—862no—
364C2×C4⋊C4—868no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—1724no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—864no—
373C2×C22⋊C4—864no—
374C2×C22⋊C4—864no—
375C2×C22⋊C4—864no—
376C2×C22⋊C4—1724no—
377C2×C22⋊C4C2×Dic4318yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—864no—
383C2×C42—864no—
384C2×C42—864no—
385C2×C42C2×Dic4314yes—
386C2×C42C2×Dic4314yes—
387#95—868no—
388#95—864no—
389#95—868no—
390#95—1724no—
391#95C2×Dic4318yes—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24C2×Dic8612yes—
401C24C2×D17212yes—
402C24C22×Dic4312yes—
403C24C23×D4311yescharacteristic
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—434no—
425C22×C4—434no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—864no—
431C22×C4—864no—
432C22×C4—864no—
433C22×C4—864no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—864no—
441C22×C4—864no—
442C22×C4—864no—
443C22×C4—864no—
444C22×C4C4⋊Dic43116yescomplemented
445C22×C4C2×Dic8612yes—
446C22×C4C2×Dic8612yes—
447C22×C4C2×D17212yes—
448C22×C4C2×D17212yes—
449C22×C4#1062189814yes—
450C22×C4#1062189814yes—
451C22×C4D4×D4312yes—
452C22×C4D4×D4312yes—
453C22×C4#1062190012yes—
454C22×C4#1062190012yes—
455C22×C4C22×Dic4314yes—
456C22×C4C22×Dic4312yes—
457C22×C4C22×Dic4314yes—
458C22×C4C22×Dic4312yes—
459C4⋊C4—868no—
460C4⋊C4—868no—
461C4⋊C4—17216no—
462C4⋊C4—1724no—
463C4⋊C4—1724no—
464C22⋊C4—216no—
465C22⋊C4—8616no—
466C22⋊C4—1728no—
467C42—28no—
468C42—28no—
469C42—8616no—
470C23—24no—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C2×C4⋊Dic4314yes—
493C23C23×Dic4311yescharacteristic
494C23C2×D4×D4311yescharacteristic
495C23C2×D4×D4311yescharacteristic
496C23C22×D17211yescharacteristic
497C23C22×Dic8611yescharacteristic
498C23C2×#1062190011yescharacteristic
499C23C2×#1062190011yescharacteristic
500C23C2×#1062189812yes—
501C23C2×#1062189812yes—
502C23#1306337112yes—
503C23#1306337212yes—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—232no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—868no—
525C2×C4—864no—
526C2×C4—864no—
527C2×C4—868no—
528C2×C4—1724no—
529C2×C4—1724no—
530C2×C4—1724no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1724no—
538C2×C4—1724no—
539C2×C4—1724no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4C2×C4⋊Dic4314yes—
545C2×C4C2×C4⋊Dic4314yes—
546C2×C4#1306328418yescomplemented
547C2×C4D4×Dic4314yes—
548C2×C4D4×Dic4314yes—
549C2×C4#1306329514yes—
550C2×C4#1306330214yes—
551C2×C4#1306330214yes—
552C2×C4#1306330914yes—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—44no—
557C22—44no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—44no—
562C22—42no—
563C22—44no—
564C22C22×C4⋊Dic4311yescharacteristic
565C22C2×#1306328412yes—
566C22C2×D4×Dic4311yescharacteristic
567C22C2×D4×Dic4311yescharacteristic
568C22#1458338212yes—
569C22C2×#1306329511yescharacteristic
570C22C2×#1306330211yescharacteristic
571C22C2×#1306330211yescharacteristic
572C22C2×#1306330911yescharacteristic
573C22#1458344911yescharacteristic
574C22#1458344911yescharacteristic
575C22#1458345612yes—
576C22#1458346811yescharacteristic
577C22#1458347511yescharacteristic
578C22#1458352712yes—
579C22#1458354512yes—
580C22#1458355412yes—
581C22#1458355812yes—
582C22#1458357012yes—
583C22#1458358912yes—
584C22#1458359512yes—
585C22#1458361412yes—
586C22#1458361912yes—
587C4—24no—
588C4—28no—
589C4—44no—
590C4—3442no—
591C4—3442no—
592C4—1724no—
593C4—1724no—
594C4#1458277418yes—
595C2—44no—
596C2#1913700211yescharacteristic
597C2C2×#1458277411yescharacteristic
598C2#1913721811yescharacteristic
599C2#1913752412yes—
600C2#1913754412yes—
601C2#1913821411yescharacteristic
602C2#1913822311yescharacteristic
603C2#1913828612yes—
604C2#1913830812yes—
605C2#1913904811yescharacteristic
606C2#1913905711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13879
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14582769C2semidirect
3. C2×#14582765C2semidirect
6. #19132829C2semidirect
7. #19132825C2semidirect
8. #19132825C2semidirect
32. C4×C22⋊C4×C43C4semidirect
120. C22×C4×C43C4⋊C4semidirect
222. C2×C4×C43#117semidirect
331. C4×C22⋊C4Dic43semidirect
337. C43#13879semidirect
444. C22×C4C4⋊Dic43semidirect
546. C2×C4#13063284semidirect

Maximal subgroups

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

subgroupindex
C22×#130632842
C2×#145827692
C2×#145827652
C2×#145827592
#191328402
#191328292
#191328252
C2×C4×C22⋊C4×C432
#1387943