Finite Group Databasebeta

← #25019253

Subgroups — #25019253

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063282C211yesmaximal, characteristic
2C2×#14582796C212yesmaximal, complemented
3C2×#14582758C211yesmaximal, characteristic
4C2×#14582746C211yesmaximal, characteristic
5#19132841C212yesmaximal
6#19132839C212yesmaximal
7#19132825C211yesmaximal, characteristic, complemented
8Dic43⋊#95C212yesmaximal, complemented
9Dic43⋊#95C211yesmaximal, characteristic, complemented
10#19132821C211yesmaximal, characteristic, complemented
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C2×#13063282—28no—
14C2×#13063282C418yescomplemented
15C22×C4⋊Dic43C2212yes—
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2212yes—
24C22×C4×Dic43C2212yes—
25C22×C4×Dic43C2211yescharacteristic
26#14582796—28no—
27#14582758—24no—
28#14582746—24no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C42×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—24no—
47C22×C4×D43—24no—
48C22×C4×D43C2×C414yes—
49C22×C4×D43D414yes—
50C22×C4×D43Q814yes—
51#13063282—232no—
52C2×C4⋊Dic43—24no—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43—42no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—42no—
62C2×Dic43⋊C4C2×C414yes—
63C2×Dic43⋊C4C2×C414yes—
64C2×Dic43⋊C4D418yes—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—24no—
67C2×(C2×D43)⋊C4—24no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—42no—
72C2×(C2×D43)⋊C4—42no—
73C2×(C2×D43)⋊C4C2×C414yes—
74C2×(C2×D43)⋊C4C2×C414yes—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—24no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43C2×C414yes—
80C43⋊#95—22no—
81C43⋊#95—22no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—42no—
85C43⋊#95—42no—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C2×C42×C43—24no—
92C2×C42×C43C2×C414yes—
93#95×C43—24no—
94#95×C43—22no—
95#95×C43—22no—
96#95×C43—24no—
97C24×C43C2411yescharacteristic
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—21no—
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43C22×C412yes—
107C23×D43C2×D412yes—
108C23×D43C2×Q812yes—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
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—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C2×D414yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×Q812yes—
137C22×C4×C43#4114yes—
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—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
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×Dic43C22×C412yes—
159C22×Dic43C22×C412yes—
160C22×Dic43C22×C412yes—
161C22×Dic43C2×D414yes—
162C22×Dic43C2×D414yes—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×Q812yes—
165C22×Dic43#4114yes—
166C22×Dic43#4114yes—
167C2×C4×D43—28no—
168C2×C4×D43—28no—
169C2×C4×D43—216no—
170C2×C4×D43—216no—
171C2×C4×D43C4⋊C4116yescomplemented
172C42×C43—28no—
173(C2×D43)⋊C4—216no—
174(C2×D43)⋊C4—28no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—48no—
177C4⋊Dic43—48no—
178Dic43⋊C4—28no—
179Dic43⋊C4—48no—
180Dic43⋊C4—48no—
181Dic43⋊C4C22⋊C4116yescomplemented
182C4×Dic43—28no—
183C4×Dic43—48no—
184C23×C43C23×C411yescharacteristic
185C23×C43C22×D412yes—
186C23×C43C22×D411yescharacteristic
187C23×C43C22×Q811yescharacteristic
188C23×C43C2×#4112yes—
189C23×C43C2×#4112yes—
190C23×C43C2×#4112yes—
191C23×C43H(5,𝔽2)11yescharacteristic
192C23×C43H(5,𝔽2)11yescharacteristic
193C23×C432−1+411yescharacteristic
194C23×C432−1+411yescharacteristic
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43C2×C4⋊C414yes—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
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×C43C2×C22⋊C414yes—
246C2×C4×C43C2×C4⋊C414yes—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43C2×C22⋊C414yes—
271C2×Dic43C2×C22⋊C414yes—
272C2×Dic43C2×C4⋊C414yes—
273C2×Dic43#11714yes—
274C2×Dic43#12118yes—
275C2×Dic43C22⋊Q818yes—
276C4×D43—232no—
277#13951—431nomaximal, Sylow
278C22×C43C22×C22⋊C411yescharacteristic
279C22×C43C22×C4⋊C411yescharacteristic
280C22×C43C2×#11711yescharacteristic
281C22×C43C4×#4111yescharacteristic
282C22×C43C4×#4111yescharacteristic
283C22×C43#52011yescharacteristic
284C22×C43#52011yescharacteristic
285C22×C43C2×#12112yes—
286C22×C43C2×C22⋊Q812yes—
287C22×C43#52512yes—
288C22×C43#53312yes—
289C22×C43#53511yescharacteristic
290C22×C43#53611yescharacteristic
291C22×C43#54411yescharacteristic
292C22×C43#54411yescharacteristic
293C22×C43#54612yes—
294C22×C43#54712yes—
295C22×C43#54812yes—
296C22×C43#55012yes—
297C22×C43#55212yes—
298C22×C43#55312yes—
299C22×C43#55512yes—
300C22×C43#55612yes—
301C2×D43—24no—
302C2×D43—24no—
303C2×D43—24no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—44no—
311C2×D43—44no—
312C4×C43—24no—
313C4×C43—24no—
314C4×C43—42no—
315C4×C43—44no—
316C4×C43—82no—
317Dic43—24no—
318Dic43—42no—
319Dic43—44no—
320Dic43—82no—
321Dic43#38018yes—
322C22×#117—431no—
323C2×#389—432no—
324C2×#380—431no—
325C2×C4×C22⋊C4—431no—
326#1439—432no—
327#1439—432no—
328C4⋊#95—431no—
329C4⋊#95—432no—
330C4⋊#95—431no—
331#1434—431no—
332#1434D4311yescharacteristic, complemented
333C2×C43C2×#38011yescharacteristic
334C2×C43#229611yescharacteristic
335C2×C43#231711yescharacteristic
336C2×C43#233911yescharacteristic
337C2×C43#234111yescharacteristic
338C2×C43#234611yescharacteristic
339C2×C43#234711yescharacteristic
340C2×C43#241412yes—
341C2×C43#241512yes—
342C2×C43#243912yes—
343C2×C43#244112yes—
344D43—44no—
345C24×C4—431no—
346C2×#117—438no—
347C2×#117—868no—
348C22×C4⋊C4—431no—
349C22×C4⋊C4—431no—
350C22×C4⋊C4—432no—
351C22×C4⋊C4—432no—
352C22×C4⋊C4—432no—
353C22×C22⋊C4—431no—
354C22×C22⋊C4—431no—
355C22×C22⋊C4—432no—
356C22×C22⋊C4—432no—
357C22×C42—431no—
358C22×C42—432no—
359C22×C42C2×D4311yescharacteristic
360#389—868no—
361#380—864no—
362C4×C22⋊C4—864no—
363C2×#95—432no—
364C2×#95—431no—
365C2×#95—432no—
366C2×#95—431no—
367C2×#95—432no—
368C2×#95—432no—
369C2×#95C2×D4311yescharacteristic
370C2×#95C2×D4312yes—
371C2×#95C2×D4311yescharacteristic
372C2×#95C2×D4312yes—
373C43#1395111yescharacteristic, complemented, Sylow
374C25—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—434no—
378C23×C4—434no—
379C23×C4—434no—
380C23×C4—432no—
381C23×C4—431no—
382C23×C4—432no—
383C23×C4—864no—
384C23×C4—864no—
385C23×C4C22×D4312yes—
386C23×C4C22×D4311yescharacteristic
387C23×C4C22×D4312yes—
388C23×C4C22×D4311yescharacteristic
389C23×C4C22×D4311yescharacteristic
390#117—8632no—
391C2×C4⋊C4—434no—
392C2×C4⋊C4—438no—
393C2×C4⋊C4—434no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—864no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—864no—
402C2×C4⋊C4—1722no—
403C2×C4⋊C4—1722no—
404C2×C22⋊C4—434no—
405C2×C22⋊C4—434no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—864no—
410C2×C22⋊C4—864no—
411C2×C22⋊C4—864no—
412C2×C22⋊C4—1722no—
413C2×C22⋊C4—1722no—
414C2×C42—24no—
415C2×C42—434no—
416C2×C42—864no—
417C2×C42—864no—
418C2×C42—864no—
419C2×C42—864no—
420C2×C42C4×D4314yes—
421#95—24no—
422#95—22no—
423#95—22no—
424#95—24no—
425#95—864no—
426#95—864no—
427#95—862no—
428#95—862no—
429#95—1722no—
430#95—1722no—
431C24—432no—
432C24—432no—
433C24—432no—
434C24—862no—
435C24—862no—
436C24—862no—
437C24—862no—
438C24—861no—
439C24—861no—
440C24—861no—
441C24—861no—
442C24C23×D4311yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—434no—
468C22×C4—432no—
469C22×C4—434no—
470C22×C4—432no—
471C22×C4—434no—
472C22×C4—4316no—
473C22×C4—432no—
474C22×C4—434no—
475C22×C4—868no—
476C22×C4—868no—
477C22×C4—8616no—
478C22×C4—8616no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—862no—
491C22×C4—861no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4C2×C4×D4312yes—
500C22×C4C2×C4×D4312yes—
501C22×C4C2×C4×D4312yes—
502C22×C4#1062189814yes—
503C22×C4D4×D4314yes—
504C22×C4D4×D4312yes—
505C22×C4Q8×D4312yes—
506C4⋊C4—4316no—
507C4⋊C4—868no—
508C4⋊C4—1728no—
509C4⋊C4—1728no—
510C4⋊C4—1728no—
511C22⋊C4—868no—
512C22⋊C4—8616no—
513C22⋊C4—868no—
514C22⋊C4—1728no—
515C42—28no—
516C42—868no—
517C42—1728no—
518C23—434no—
519C23—862no—
520C23—862no—
521C23—862no—
522C23—862no—
523C23—862no—
524C23—862no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—862no—
530C23—862no—
531C23—862no—
532C23—862no—
533C23—1722no—
534C23—1722no—
535C23—1722no—
536C23—1722no—
537C23—1722no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23C22×C4×D4311yescharacteristic
542C23C2×D4×D4312yes—
543C23C2×D4×D4311yescharacteristic
544C23C2×Q8×D4311yescharacteristic
545C23#41×D4312yes—
546C23#41×D4312yes—
547C23C2×#1062189812yes—
548C23#1306337111yescharacteristic
549C23#1306337111yescharacteristic
550C23#1306337211yescharacteristic
551C23#1306337211yescharacteristic
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—434no—
580C2×C4—434no—
581C2×C4—434no—
582C2×C4—438no—
583C2×C4—438no—
584C2×C4—434no—
585C2×C4—8632no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4C22⋊C4×D4314yes—
610C2×C4C4⋊C4×D4314yes—
611C22—864no—
612C22—864no—
613C22—864no—
614C22—1724no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1724no—
620C22—1724no—
621C22—1724no—
622C22C2×C22⋊C4×D4311yescharacteristic
623C22C2×C4⋊C4×D4311yescharacteristic
624C22#117×D4311yescharacteristic
625C22#1458336711yescharacteristic
626C22C4×#1062189811yescharacteristic
627C22#1458337911yescharacteristic
628C22#1458337911yescharacteristic
629C22#121×D4312yes—
630C22C22⋊Q8×D4312yes—
631C22#1458340812yes—
632C22#1458345312yes—
633C22#1458346711yescharacteristic
634C22#1458346911yescharacteristic
635C22#1458352911yescharacteristic
636C22#1458352911yescharacteristic
637C22#1458354112yes—
638C22#1458354712yes—
639C22#1458355812yes—
640C22#1458357012yes—
641C22#1458358212yes—
642C22#1458360012yes—
643C22#1458361212yes—
644C22#1458361612yes—
645C4—24no—
646C4—24no—
647C4—42no—
648C4—44no—
649C4—82no—
650C4—438no—
651C4—864no—
652C4—3442no—
653C4—1722no—
654C4—1724no—
655C2—1724no—
656C2#380×D4311yescharacteristic
657C2#1913707511yescharacteristic
658C2#1913722011yescharacteristic
659C2#1913741911yescharacteristic
660C2#1913743511yescharacteristic
661C2#1913748111yescharacteristic
662C2#1913748311yescharacteristic
663C2#1913801212yes—
664C2#1913802112yes—
665C2#1913828512yes—
666C2#1913830712yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1434D43
hypocenterC43#13951
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#14582796C2semidirect
7. #19132825C2semidirect
8. Dic43⋊#95C2semidirect
9. Dic43⋊#95C2semidirect
10. #19132821C2semidirect
11. C43×#1434C2semidirect
14. C2×#13063282C4semidirect
171. C2×C4×D43C4⋊C4semidirect
181. Dic43⋊C4C22⋊C4semidirect
332. #1434D43semidirect
373. C43#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#130632822
C2×#145827962
C2×#145827582
C2×#145827462
#191328412
#191328392
#191328252
Dic43⋊#952
#191328212
C43×#14342
#1395143