Finite Group Databasebeta

← #25019222

Subgroups — #25019222

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582787C212yesmaximal
2C2×C4×C22⋊Dic43C211yesmaximal, characteristic
3#19132853C212yesmaximal, complemented
4#19132838C212yesmaximal
5#19132830C212yesmaximal, complemented
6Dic43⋊#95C211yesmaximal, characteristic, complemented
7Dic43⋊#95C211yesmaximal, characteristic, complemented
8#19132820C211yesmaximal, characteristic, complemented
9#19132818C211yesmaximal, characteristic
10#95×Dic43C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic
12C22×Dic43⋊C4C2212yes—
13C22×Dic43⋊C4C2212yes—
14C22×C22⋊Dic43C2212yes—
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C4×Dic43C2212yes—
18C22×C4×Dic43C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20#14582787—28no—
21C4×C22⋊Dic43C418yescomplemented
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C24×C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2212yes—
34C2×#95×C43C2211yescharacteristic
35C2×#95×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C23×Dic43C2312yes—
38C23×Dic43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C2×Dic43⋊C4—24no—
44C2×Dic43⋊C4—24no—
45C2×Dic43⋊C4—24no—
46C2×Dic43⋊C4—24no—
47C2×Dic43⋊C4—42no—
48C2×Dic43⋊C4—42no—
49C2×C22⋊Dic43—22no—
50C2×C22⋊Dic43—22no—
51C2×C22⋊Dic43—24no—
52C2×C22⋊Dic43—24no—
53C2×C22⋊Dic43—42no—
54C2×C22⋊Dic43C2×C414yes—
55C2×C22⋊Dic43C2×C414yes—
56C2×C22⋊Dic43D414yes—
57C2×C22⋊Dic43Q814yes—
58C2×C4×Dic43—24no—
59C2×C4×Dic43—24no—
60C2×C4×Dic43—42no—
61C2×C4×Dic43—42no—
62C2×C4×Dic43—42no—
63C2×C4×Dic43C2×C414yes—
64C2×C4×Dic43C2×C414yes—
65C43⋊#95—22no—
66C43⋊#95—22no—
67C43⋊#95—24no—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—24no—
71C43⋊#95—42no—
72C43⋊#95—42no—
73C43⋊#95C2×C414yes—
74C43⋊#95C2×C414yes—
75C25×C43C2311yescharacteristic
76C23×C4×C43—22no—
77C23×C4×C43—22no—
78C23×C4×C43—42no—
79C23×C4×C43—42no—
80C23×C4×C43C2×C414yes—
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C2×C22⋊C4×C43—24no—
86C2×C22⋊C4×C43—24no—
87C2×C22⋊C4×C43—42no—
88#95×C43—22no—
89#95×C43—22no—
90#95×C43—42no—
91C24×C43—22no—
92C24×C43—21no—
93C24×C43—21no—
94C24×C43—21no—
95C24×C43—21no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43C22×C412yes—
100C24×C43C2×D412yes—
101C24×C43C2×Q812yes—
102C24×C43C2411yescharacteristic
103C22×C4×C43—28no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
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—44no—
124C22×C4×C43—44no—
125C22×C4×C43—48no—
126C22×C4×C43—48no—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43#4114yes—
130C22×C4×C43#4112yes—
131C22×C4×C43#4112yes—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
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×Dic43C22×C412yes—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C22×C412yes—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×Q812yes—
162C22×Dic43C2×Q812yes—
163C22×Dic43#4114yes—
164C22×Dic43#4112yes—
165C22×Dic43#4112yes—
166C22⋊C4×C43—48no—
167C22⋊Dic43—28no—
168C22⋊Dic43—48no—
169C22⋊Dic43C4⋊C4116yescomplemented
170Dic43⋊C4—48no—
171Dic43⋊C4—48no—
172C4×Dic43—44no—
173C4×Dic43—44no—
174C4×Dic43—48no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—24no—
186C23×C43—24no—
187C23×C43—24no—
188C23×C43—24no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43C2×C4⋊C414yes—
198C23×C43C23×C411yescharacteristic
199C23×C43C22×D411yescharacteristic
200C23×C43C22×Q811yescharacteristic
201C23×C43C2×#4111yescharacteristic
202C23×C43C2×#4111yescharacteristic
203C23×C43C2×#4112yes—
204C23×C43C2×#4111yescharacteristic
205C23×C43C2×#4111yescharacteristic
206C23×C43C2×#4112yes—
207C23×C43H(5,𝔽2)12yes—
208C23×C43H(5,𝔽2)12yes—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—416no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43#11714yes—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
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×Dic43C2×C4⋊C414yes—
266C2×Dic43C2×C4⋊C414yes—
267C2×Dic43#11714yes—
268#13948—431nomaximal, Sylow
269C22×C43—24no—
270C22×C43—24no—
271C22×C43—24no—
272C22×C43—42no—
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—44no—
279C22×C43—44no—
280C22×C43C22×C4⋊C411yescharacteristic
281C22×C43C2×#11711yescharacteristic
282C22×C43C2×#11711yescharacteristic
283C22×C43C4×#4111yescharacteristic
284C22×C43C4×#4111yescharacteristic
285C22×C43#51811yescharacteristic
286C22×C43#51811yescharacteristic
287C22×C43#52912yes—
288C22×C43#52912yes—
289C22×C43#53211yescharacteristic
290C22×C43#53211yescharacteristic
291C22×C43#53311yescharacteristic
292C22×C43#53311yescharacteristic
293C22×C43#53812yes—
294C22×C43#53812yes—
295C22×C43#54612yes—
296C22×C43#54612yes—
297C22×C43#55112yes—
298C22×C43#55312yes—
299C22×C43#55312yes—
300C22×C43#55412yes—
301C22×C43#55412yes—
302C22×C43#55912yes—
303C4×C43—24no—
304C4×C43—42no—
305C4×C43—44no—
306C4×C43—82no—
307Dic43—24no—
308Dic43—24no—
309Dic43—24no—
310Dic43—42no—
311Dic43—44no—
312Dic43—82no—
313C2×#388—432no—
314C2×C4×C22⋊C4—431no—
315#1442—432no—
316#1439—432no—
317#1436—432no—
318C4⋊#95—431no—
319C4⋊#95—431no—
320#1434—431no—
321C22⋊#95—431no—
322C22⋊#95D4311yescharacteristic
323C4×#95—431no—
324C2×C43—44no—
325C2×C43#228511yescharacteristic
326C2×C43#229811yescharacteristic
327C2×C43#231211yescharacteristic
328C2×C43#234911yescharacteristic
329C2×C43#234911yescharacteristic
330C2×C43#235311yescharacteristic
331C2×C43#235711yescharacteristic
332C2×C43#255712yes—
333C2×C43#255912yes—
334C2×C43#258712yes—
335C2×C43#258912yes—
336C24×C4C2×D4311yescharacteristic
337C22×C4⋊C4—432no—
338C22×C4⋊C4—432no—
339C22×C22⋊C4—431no—
340C22×C22⋊C4—431no—
341C22×C22⋊C4—432no—
342C22×C22⋊C4C2×D4312yes—
343C22×C42—431no—
344C22×C42—431no—
345C22×C42—432no—
346#388—868no—
347C4×C22⋊C4—438no—
348C2×#95—431no—
349C2×#95—431no—
350C2×#95—431no—
351C2×#95—432no—
352C2×#95—431no—
353C2×#95—432no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95C2×D4311yescharacteristic
359C2×#95C2×D4311yescharacteristic
360C2×#95C2×D4312yes—
361C43#1394811yescharacteristic, complemented, Sylow
362C25C22×D4311yescharacteristic
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—432no—
371C23×C4—431no—
372C23×C4—432no—
373C23×C4C4×D4314yes—
374C23×C4C22×D4312yes—
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4312yes—
377C23×C4C22×D4311yescharacteristic
378C2×C4⋊C4—864no—
379C2×C4⋊C4—864no—
380C2×C4⋊C4—864no—
381C2×C4⋊C4—864no—
382C2×C4⋊C4—1722no—
383C2×C4⋊C4—1722no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—434no—
388C2×C22⋊C4—434no—
389C2×C22⋊C4—434no—
390C2×C22⋊C4—434no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—864no—
394C2×C22⋊C4—864no—
395C2×C22⋊C4—1722no—
396C2×C42—434no—
397C2×C42—434no—
398C2×C42—864no—
399C2×C42—864no—
400C2×C42—1722no—
401C2×C42—1722no—
402C2×C42—1722no—
403#95—22no—
404#95—22no—
405#95—42no—
406#95—434no—
407#95—434no—
408#95—864no—
409#95—864no—
410#95—864no—
411#95—864no—
412#95—862no—
413#95—862no—
414#95—1722no—
415#95—1722no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24C2×C4×D4312yes—
425C24D4×D4312yes—
426C24Q8×D4312yes—
427C24C23×D4311yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—28no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—432no—
462C22×C4—434no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4C2×C4×D4312yes—
487C22×C4C2×C4×D4312yes—
488C22×C4#1062189814yes—
489C22×C4#1062190012yes—
490C22×C4#1062190012yes—
491C4⋊C4—1728no—
492C4⋊C4—1728no—
493C22⋊C4—48no—
494C22⋊C4—4316no—
495C22⋊C4—868no—
496C22⋊C4—1728no—
497C42—1724no—
498C42—1724no—
499C42—1728no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C4⋊C4×D4314yes—
523C23C22×C4×D4311yescharacteristic
524C23C2×D4×D4311yescharacteristic
525C23C2×Q8×D4311yescharacteristic
526C23#41×D4311yescharacteristic
527C23#41×D4311yescharacteristic
528C23#41×D4312yes—
529C23C2×#1062190011yescharacteristic
530C23C2×#1062190011yescharacteristic
531C23C2×#1062189812yes—
532C23#1306337012yes—
533C23#1306337012yes—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—416no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—434no—
559C2×C4—434no—
560C2×C4—434no—
561C2×C4—864no—
562C2×C4—864no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—864no—
572C2×C4—864no—
573C2×C4—864no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4#1306328114yes—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22C2×C4⋊C4×D4311yescharacteristic
605C22#117×D4311yescharacteristic
606C22C2×#1306328111yescharacteristic
607C22#1458336711yescharacteristic
608C22C4×#1062189811yescharacteristic
609C22#1458337211yescharacteristic
610C22#1458337211yescharacteristic
611C22#1458342912yes—
612C22#1458343112yes—
613C22#1458344411yescharacteristic
614C22#1458344411yescharacteristic
615C22#1458345111yescharacteristic
616C22#1458345111yescharacteristic
617C22#1458348412yes—
618C22#1458348412yes—
619C22#1458353812yes—
620C22#1458353912yes—
621C22#1458357812yes—
622C22#1458359412yes—
623C22#1458359912yes—
624C22#1458360312yes—
625C22#1458360412yes—
626C22#1458363312yes—
627C4—24no—
628C4—44no—
629C4—42no—
630C4—82no—
631C4—864no—
632C4—864no—
633C4—864no—
634C4—3442no—
635C4—1722no—
636C4—1724no—
637C2—44no—
638C2#1913699711yescharacteristic
639C2#1913709111yescharacteristic
640C2#1913719111yescharacteristic
641C2#1913749911yescharacteristic
642C2#1913750211yescharacteristic
643C2#1913753811yescharacteristic
644C2#1913756311yescharacteristic
645C2#1913969112yes—
646C2#1913972312yes—
647C2#1914001312yes—
648C2#1914004512yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13948
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. #19132853C2semidirect
5. #19132830C2semidirect
6. Dic43⋊#95C2semidirect
7. Dic43⋊#95C2semidirect
8. #19132820C2semidirect
10. #95×Dic43C2semidirect
21. C4×C22⋊Dic43C4semidirect
169. C22⋊Dic43C4⋊C4semidirect
361. C43#13948semidirect

Maximal subgroups

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

subgroupindex
C2×#145827872
C2×C4×C22⋊Dic432
#191328532
#191328382
#191328302
Dic43⋊#952
#191328202
#191328182
#95×Dic432
C43×C22⋊#952
#1394843