Finite Group Databasebeta

← #25023560

Subgroups — #25023560

Order 11008.

1558 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582836C211yesmaximal, characteristic
2C2×#14582797C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
4#19132862C211yesmaximal, characteristic, complemented
5#19132852C211yesmaximal, characteristic, complemented
6#19132847C212yesmaximal, complemented
7#19132841C211yesmaximal, characteristic
8#19132839C212yesmaximal
9#19132829C212yesmaximal, complemented
10(C2×D43)⋊#95C212yesmaximal
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4⋊Dic43C2212yes—
16C22×Dic43⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22#14582836C418yescomplemented
23#14582797—24no—
24C4×(C2×D43)⋊C4—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C22×C42×C43C2211yescharacteristic
34C2×#95×C43C2212yes—
35C2×#95×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—22no—
45C22×C4×D43—22no—
46C22×C4×D43—42no—
47C22×C4×D43—42no—
48C22×C4×D43Q814yes—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—42no—
53C2×C4⋊Dic43—42no—
54C2×C4⋊Dic43—42no—
55C2×C4⋊Dic43C2×C414yescomplemented
56C2×C4⋊Dic43C2×C418yescomplemented
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—42no—
59C2×Dic43⋊C4—42no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4—42no—
70C2×(C2×D43)⋊C4C2×C414yes—
71C2×(C2×D43)⋊C4C2×C418yes—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—42no—
74C43⋊#95—24no—
75C43⋊#95—22no—
76C43⋊#95—22no—
77C43⋊#95—24no—
78C43⋊#95—42no—
79C43⋊#95—42no—
80C43⋊#95—42no—
81C43⋊#95—42no—
82C23×C4×C43C2312yes—
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C2×C42×C43—42no—
88C2×C42×C43D414yes—
89#95×C43—22no—
90#95×C43—24no—
91#95×C43—42no—
92#95×C43C2×C414yescomplemented
93C24×C43C2411yescharacteristic
94C23×D43—21no—
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43C22×C412yes—
103C23×D43C2×Q812yes—
104C23×D43#4112yes—
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—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43C22×C414yes—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×Q812yes—
132C22×C4×C43#4112yes—
133C22×C4×C43#4112yes—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
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×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43C22×C414yes—
160C22×Dic43C22×C412yes—
161C22×Dic43C2×Q812yes—
162C22×Dic43#4112yes—
163C2×C4×D43—28no—
164C2×C4×D43—48no—
165C2×C4×D43—44no—
166C2×C4×D43—44no—
167C2×C4×D43—48no—
168C42×C43—44no—
169(C2×D43)⋊C4—28no—
170(C2×D43)⋊C4—28no—
171(C2×D43)⋊C4—48no—
172(C2×D43)⋊C4—48no—
173C4⋊Dic43—28no—
174C4⋊Dic43—48no—
175C4⋊Dic43—44no—
176Dic43⋊C4—48no—
177C4×Dic43—44no—
178C23×C43C23×C411yescharacteristic
179C23×C43C22×D411yescharacteristic
180C23×C43C22×Q811yescharacteristic
181C23×C43C2×#4111yescharacteristic
182C23×C43C2×#4111yescharacteristic
183C23×C43C2×#4111yescharacteristic
184C23×C43C2×#4111yescharacteristic
185C23×C43H(5,𝔽2)12yes—
186C23×C43H(5,𝔽2)12yes—
187C23×C43H(5,𝔽2)12yes—
188C23×C432−1+412yes—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—24no—
192C22×D43—24no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—24no—
200C22×D43—24no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43C4×Q814yes—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
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—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43C4×D414yes—
240C2×C4×C43C22⋊Q814yes—
241C2×Dic43—24no—
242C2×Dic43—22no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—41no—
257C2×Dic43—41no—
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—
270C4×D43—416no—
271#14317—431nomaximal, Sylow
272C22×C43C2×C4×D411yescharacteristic
273C22×C43C2×C4×Q811yescharacteristic
274C22×C43C4×#4111yescharacteristic
275C22×C43#51812yes—
276C22×C43#52012yes—
277C22×C43C2×C22⋊Q811yescharacteristic
278C22×C43#52511yescharacteristic
279C22×C43#52911yescharacteristic
280C22×C43#53311yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43#53511yescharacteristic
283C22×C43#53511yescharacteristic
284C22×C43#53611yescharacteristic
285C22×C43#53812yes—
286C22×C43#53812yes—
287C22×C43#53912yes—
288C22×C43#53912yes—
289C22×C43#53912yes—
290C22×C43#54012yes—
291C22×C43#54012yes—
292C22×C43#54212yes—
293C22×C43#54312yes—
294C22×C43#54412yes—
295C2×D43—28no—
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—44no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—44no—
305C2×D43—44no—
306C4×C43—24no—
307C4×C43—24no—
308C4×C43—44no—
309C4×C43—42no—
310C4×C43—82no—
311Dic43—44no—
312Dic43—42no—
313Dic43—42no—
314Dic43—42no—
315Dic43—82no—
316C2×#399—431no—
317C2×#389—431no—
318C2×C4×C22⋊C4—431no—
319#1445—431no—
320#1442—431no—
321#1441—432no—
322#1439—432no—
323#1439—431no—
324#1436—432no—
325#1434D4311yescharacteristic, complemented
326C22⋊#95—432no—
327C2×C43C4×C22⋊Q811yescharacteristic
328C2×C43#232211yescharacteristic
329C2×C43#232811yescharacteristic
330C2×C43#232912yes—
331C2×C43#233512yes—
332C2×C43#262611yescharacteristic
333C2×C43#262811yescharacteristic
334C2×C43#263311yescharacteristic
335C2×C43#263511yescharacteristic
336C2×C43#264912yes—
337C2×C43#266712yes—
338D43—44no—
339C24×C4—431no—
340C22×C4⋊C4—431no—
341C22×C4⋊C4—432no—
342C22×C4⋊C4—432no—
343C22×C4⋊C4—431no—
344C22×C22⋊C4—431no—
345C22×C22⋊C4—432no—
346C22×C22⋊C4—431no—
347C22×C22⋊C4—432no—
348C22×C42—431no—
349C22×C42C2×D4311yescharacteristic
350#399—438no—
351#389—864no—
352C4×C22⋊C4—864no—
353C2×#95—432no—
354C2×#95—432no—
355C2×#95—431no—
356C2×#95—431no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95—432no—
361C2×#95C2×D4312yes—
362C2×#95C2×D4311yescharacteristic
363C2×#95C2×D4312yes—
364C2×#95C2×D4311yescharacteristic
365C43#1431711yescharacteristic, complemented, Sylow
366C25—431no—
367C23×C4—432no—
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—434no—
372C23×C4—432no—
373C23×C4—862no—
374C23×C4—862no—
375C23×C4—1722no—
376C23×C4—1722no—
377C23×C4C22×D4312yes—
378C23×C4C22×D4312yes—
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C23×C4C22×D4311yescharacteristic
382C2×C4⋊C4—434no—
383C2×C4⋊C4—438no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—1722no—
389C2×C4⋊C4—1722no—
390C2×C4⋊C4—1722no—
391C2×C4⋊C4—1722no—
392C2×C4⋊C4—1722no—
393C2×C22⋊C4—434no—
394C2×C22⋊C4—438no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—862no—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—862no—
399C2×C22⋊C4—862no—
400C2×C22⋊C4—864no—
401C2×C22⋊C4—1722no—
402C2×C22⋊C4—1722no—
403C2×C22⋊C4—1722no—
404C2×C22⋊C4—1722no—
405C2×C42—42no—
406C2×C42—862no—
407C2×C42—1722no—
408C2×C42D17214yes—
409#95—22no—
410#95—24no—
411#95—42no—
412#95—864no—
413#95—862no—
414#95—862no—
415#95—864no—
416#95—1722no—
417#95—1722no—
418#95—1722no—
419#95—1722no—
420#95C4×D4314yescomplemented
421C24—432no—
422C24—432no—
423C24—432no—
424C24—861no—
425C24—861no—
426C24—861no—
427C24—861no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—862no—
432C24C23×D4311yescharacteristic
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—432no—
455C22×C4—434no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—862no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—868no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—1728no—
485C22×C4—1724no—
486C22×C4—1724no—
487C22×C4—1728no—
488C22×C4C2×C4×D4314yes—
489C22×C4C2×C4×D4312yes—
490C22×C4C2×D17212yes—
491C22×C4C2×D17212yes—
492C22×C4C2×D17212yes—
493C22×C4#1062189812yes—
494C22×C4#1062190012yes—
495C22×C4Q8×D4312yes—
496C4⋊C4—868no—
497C4⋊C4—1728no—
498C4⋊C4—1728no—
499C4⋊C4—1724no—
500C22⋊C4—868no—
501C22⋊C4—868no—
502C22⋊C4—1728no—
503C22⋊C4—1728no—
504C42—44no—
505C42—1724no—
506C23—434no—
507C23—862no—
508C23—862no—
509C23—864no—
510C23—864no—
511C23—862no—
512C23—862no—
513C23—862no—
514C23—862no—
515C23—864no—
516C23—864no—
517C23—864no—
518C23—864no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1722no—
524C23—1722no—
525C23—1722no—
526C23—1722no—
527C23—1722no—
528C23—1722no—
529C23C22×C4×D4311yescharacteristic
530C23C22×D17211yescharacteristic
531C23C2×Q8×D4311yescharacteristic
532C23#41×D4311yescharacteristic
533C23#41×D4311yescharacteristic
534C23C2×#1062190011yescharacteristic
535C23C2×#1062189811yescharacteristic
536C23#1306337012yes—
537C23#1306337112yes—
538C23#1306337112yes—
539C23#1306337212yes—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—862no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—864no—
571C2×C4—864no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—864no—
575C2×C4—864no—
576C2×C4—17216no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1722no—
588C2×C4—1721no—
589C2×C4—1722no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4C4×D17214yes—
598C2×C4#1306330514yes—
599C22—868no—
600C22—864no—
601C22—1722no—
602C22—1722no—
603C22—1722no—
604C22—1724no—
605C22—1722no—
606C22—1722no—
607C22—1724no—
608C22—1722no—
609C22—1724no—
610C22C2×C4×D17211yescharacteristic
611C22C4×Q8×D4311yescharacteristic
612C22C4×#1062190011yescharacteristic
613C22#1458337312yes—
614C22#1458337812yes—
615C22C2×#1306330511yescharacteristic
616C22#1458341111yescharacteristic
617C22#1458343111yescharacteristic
618C22#1458345311yescharacteristic
619C22#1458346111yescharacteristic
620C22#1458346811yescharacteristic
621C22#1458346811yescharacteristic
622C22#1458347511yescharacteristic
623C22#1458348512yes—
624C22#1458348612yes—
625C22#1458349012yes—
626C22#1458349012yes—
627C22#1458349112yes—
628C22#1458350112yes—
629C22#1458350412yes—
630C22#1458351812yes—
631C22#1458352412yes—
632C22#1458352912yes—
633C4—24no—
634C4—24no—
635C4—44no—
636C4—42no—
637C4—82no—
638C4—3442no—
639C4—1722no—
640C4—1724no—
641C4—1722no—
642C4—1722no—
643C2—1724no—
644C2C4×#1306330511yescharacteristic
645C2#1913726611yescharacteristic
646C2#1913732011yescharacteristic
647C2#1913732412yes—
648C2#1913737812yes—
649C2#1914040311yescharacteristic
650C2#1914041911yescharacteristic
651C2#1914046611yescharacteristic
652C2#1914048211yescharacteristic
653C2#1914060212yes—
654C2#1914079512yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1434D43
hypocenterC43#14317
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#14582797C2semidirect
4. #19132862C2semidirect
5. #19132852C2semidirect
6. #19132847C2semidirect
9. #19132829C2semidirect
11. C43×#1434C2semidirect
22. #14582836C4semidirect
55. C2×C4⋊Dic43C2×C4semidirect
56. C2×C4⋊Dic43C2×C4semidirect
92. #95×C43C2×C4semidirect
325. #1434D43semidirect
365. C43#14317semidirect
420. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828362
C2×#145827972
C2×C4×(C2×D43)⋊C42
#191328622
#191328522
#191328472
#191328412
#191328392
#191328292
(C2×D43)⋊#952
C43×#14342
#1431743