Finite Group Databasebeta

← #25024994

Subgroups — #25024994

Order 11008.

2018 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
1C2×#14582801C211yesmaximal, characteristic
2C2×#14582777C212yesmaximal
3C2×#14582773C212yesmaximal, complemented
4#19132847C212yesmaximal, complemented
5#19132841C212yesmaximal, complemented
6#19132839C212yesmaximal, complemented
7#19132825C211yesmaximal, characteristic, complemented
8(C2×D43)⋊#95C212yesmaximal, complemented
9C43×#1434C211yesmaximal, characteristic, complemented
10C23×D172C2211yescharacteristic
11C23×C4×D43C2212yes—
12C22×C4⋊Dic43C2212yes—
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20#14582801C418yescomplemented
21#14582777—28no—
22#14582773—28no—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C22×C42×C43C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2212yes—
32C2×#95×C43C2212yes—
33C2×#95×C43C2211yescharacteristic
34C24×D43C2312yes—
35C22×D172—42no—
36C22×D172—42no—
37C22×D172C2×C414yes—
38C22×D172D414yes—
39C22×D172Q814yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C22×C4×D43—24no—
44C22×C4×D43—24no—
45C22×C4×D43—24no—
46C22×C4×D43—42no—
47C22×C4×D43—42no—
48C22×C4×D43—42no—
49C22×C4×D43—42no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—24no—
52C2×C4⋊Dic43—42no—
53C2×C4⋊Dic43—42no—
54C2×C4⋊Dic43C2×C414yescomplemented
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—42no—
57C2×Dic43⋊C4—42no—
58C2×(C2×D43)⋊C4—24no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—42no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4—42no—
70C2×(C2×D43)⋊C4—42no—
71C2×(C2×D43)⋊C4C2×C418yescomplemented
72C2×(C2×D43)⋊C4C2×C418yescomplemented
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—42no—
76C43⋊#95—42no—
77C43⋊#95—41no—
78C43⋊#95—41no—
79C23×C4×C43C2312yes—
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C2×C42×C43—42no—
85C2×C42×C43C2×C414yescomplemented
86#95×C43—24no—
87#95×C43—22no—
88#95×C43—42no—
89#95×C43D414yescomplemented
90C24×C43C2411yescharacteristic
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—22no—
94C23×D43—22no—
95C23×D43—22no—
96C23×D43—22no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—22no—
103C23×D43C22×C414yes—
104C23×D43C2×D414yes—
105C23×D43C2×Q814yes—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
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—21no—
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—21no—
126C22×C4×C43—22no—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D414yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×Q812yes—
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—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×Dic43C22×C414yes—
155C22×Dic43#4114yes—
156C2×D172—44no—
157C2×D172—44no—
158C2×D172—48no—
159C2×D172—48no—
160C2×D172C4⋊C4116yescomplemented
161C2×C4×D43—48no—
162C2×C4×D43—48no—
163C2×C4×D43—48no—
164C2×C4×D43—48no—
165C2×C4×D43—48no—
166C2×C4×D43—48no—
167C2×C4×D43—48no—
168C42×C43—44no—
169(C2×D43)⋊C4—216no—
170(C2×D43)⋊C4—48no—
171(C2×D43)⋊C4—48no—
172(C2×D43)⋊C4—48no—
173(C2×D43)⋊C4—48no—
174C4⋊Dic43—44no—
175C4⋊Dic43—48no—
176Dic43⋊C4—48no—
177C23×C43C23×C411yescharacteristic
178C23×C43C22×D411yescharacteristic
179C23×C43C22×D411yescharacteristic
180C23×C43C22×Q811yescharacteristic
181C23×C43C2×#4112yes—
182C23×C43C2×#4111yescharacteristic
183C23×C43H(5,𝔽2)12yes—
184C23×C43H(5,𝔽2)12yes—
185C23×C43H(5,𝔽2)12yes—
186C23×C43H(5,𝔽2)11yescharacteristic
187C23×C432−1+411yescharacteristic
188C22×D43—24no—
189C22×D43—24no—
190C22×D43—24no—
191C22×D43—24no—
192C22×D43—24no—
193C22×D43—24no—
194C22×D43—24no—
195C22×D43—24no—
196C22×D43—24no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—24no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
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×D43—42no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43C2×C4⋊C418yes—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
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×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43C2×C4⋊C414yes—
251C2×C4×C43C4×D414yes—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
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×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273D172—416no—
274C4×D43—432no—
275#14438—431nomaximal, Sylow
276C22×C43C22×C4⋊C411yescharacteristic
277C22×C43C2×C4×D411yescharacteristic
278C22×C43C4×#4111yescharacteristic
279C22×C43#51811yescharacteristic
280C22×C43#51811yescharacteristic
281C22×C43#51811yescharacteristic
282C22×C43#52011yescharacteristic
283C22×C43#53412yes—
284C22×C43#53512yes—
285C22×C43#53812yes—
286C22×C43#54012yes—
287C22×C43#54212yes—
288C22×C43#54312yes—
289C22×C43D4211yescharacteristic
290C22×C43#54612yes—
291C22×C43#54612yes—
292C22×C43#54711yescharacteristic
293C22×C43D4×Q811yescharacteristic
294C22×C43#55312yes—
295C22×C43#55412yes—
296C22×C43#55411yescharacteristic
297C22×C43#56012yes—
298C22×C43#56212yes—
299C2×D43—28no—
300C2×D43—28no—
301C2×D43—28no—
302C2×D43—44no—
303C2×D43—44no—
304C2×D43—44no—
305C2×D43—44no—
306C2×D43—44no—
307C2×D43—44no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—44no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—44no—
314C4×C43—24no—
315C4×C43—24no—
316C4×C43—42no—
317C4×C43—44no—
318C4×C43—82no—
319Dic43—44no—
320Dic43—44no—
321Dic43—82no—
322C2×#390—431no—
323C2×#386—432no—
324C2×#385—432no—
325#1441—432no—
326#1439—432no—
327#1439—432no—
328C4⋊#95—431no—
329#1434D4311yescharacteristic, complemented
330C22⋊#95—432no—
331C2×C43#231511yescharacteristic
332C2×C43#232811yescharacteristic
333C2×C43#233711yescharacteristic
334C2×C43D4×C4⋊C411yescharacteristic
335C2×C43#234911yescharacteristic
336C2×C43#236411yescharacteristic
337C2×C43#237711yescharacteristic
338C2×C43#267812yes—
339C2×C43#269212yes—
340C2×C43#270112yes—
341C2×C43#278012yes—
342D43—48no—
343C23×D4—431no—
344C24×C4—432no—
345C22×C4⋊C4—431no—
346C22×C4⋊C4—432no—
347C22×C4⋊C4—432no—
348C22×C22⋊C4—432no—
349C22×C22⋊C4—432no—
350C22×C22⋊C4—432no—
351C22×C22⋊C4—432no—
352C22×C22⋊C4—432no—
353C22×C42C2×D4311yescharacteristic
354#390—438no—
355#386—868no—
356#385—868no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—431no—
360C2×#95—432no—
361C2×#95—431no—
362C2×#95—432no—
363C2×#95C2×D4311yescharacteristic
364C2×#95C2×D4312yes—
365C2×#95C2×D4312yes—
366C2×#95C2×D4311yescharacteristic
367C43#1443811yescharacteristic, complemented, Sylow
368C25—432no—
369C22×D4—434no—
370C22×D4—434no—
371C22×D4—434no—
372C22×D4—1722no—
373C22×D4—1722no—
374C23×C4—432no—
375C23×C4—432no—
376C23×C4—432no—
377C23×C4—864no—
378C23×C4—864no—
379C23×C4—864no—
380C23×C4—1722no—
381C23×C4—1722no—
382C23×C4—1722no—
383C23×C4—1722no—
384C23×C4C22×D4312yes—
385C23×C4C22×D4311yescharacteristic
386C23×C4C22×D4312yes—
387C23×C4C22×D4311yescharacteristic
388C23×C4C22×D4311yescharacteristic
389C2×C4⋊C4—434no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—864no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—1722no—
394C2×C4⋊C4—1722no—
395C2×C4⋊C4—1722no—
396C2×C4⋊C4—1722no—
397C2×C22⋊C4—438no—
398C2×C22⋊C4—438no—
399C2×C22⋊C4—864no—
400C2×C22⋊C4—864no—
401C2×C22⋊C4—864no—
402C2×C22⋊C4—864no—
403C2×C22⋊C4—864no—
404C2×C22⋊C4—864no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4—1722no—
407C2×C22⋊C4—1722no—
408C2×C22⋊C4—1722no—
409C2×C22⋊C4—1722no—
410C2×C22⋊C4—1722no—
411C2×C22⋊C4—1722no—
412C2×C42—42no—
413C2×C42C4×D4314yescomplemented
414#95—22no—
415#95—24no—
416#95—42no—
417#95—864no—
418#95—864no—
419#95—1721no—
420#95—1721no—
421#95—1722no—
422#95—1722no—
423#95D17214yescomplemented
424C24—434no—
425C24—434no—
426C24—434no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—862no—
432C24—862no—
433C24—862no—
434C24—862no—
435C24—862no—
436C24—862no—
437C24—862no—
438C24—862no—
439C24C23×D4311yescharacteristic
440C2×D4—4316no—
441C2×D4—1724no—
442C2×D4—1724no—
443C2×D4—1728no—
444C2×D4—1728no—
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—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—434no—
467C22×C4—434no—
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—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×C4—862no—
487C22×C4—1728no—
488C22×C4—1728no—
489C22×C4—1728no—
490C22×C4—1728no—
491C22×C4—1728no—
492C22×C4—1728no—
493C22×C4—1728no—
494C22×C4C2×C4×D4312yes—
495C22×C4C2×C4×D4312yes—
496C22×C4C2×C4×D4312yes—
497C22×C4C2×D17214yes—
498C22×C4C2×D17212yes—
499C22×C4#1062189812yes—
500C22×C4D4×D4312yes—
501C22×C4Q8×D4312yes—
502C4⋊C4—1724no—
503C4⋊C4—1728no—
504C4⋊C4—1728no—
505C22⋊C4—8616no—
506C22⋊C4—1728no—
507C22⋊C4—1728no—
508C22⋊C4—1728no—
509C22⋊C4—1728no—
510C42—44no—
511C23—438no—
512C23—864no—
513C23—864no—
514C23—864no—
515C23—864no—
516C23—864no—
517C23—864no—
518C23—864no—
519C23—864no—
520C23—864no—
521C23—864no—
522C23—864no—
523C23—864no—
524C23—864no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—864no—
530C23—1722no—
531C23—1722no—
532C23—1722no—
533C23—1722no—
534C23—1722no—
535C23—1722no—
536C23—1722no—
537C23—1722no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23C22×C4×D4311yescharacteristic
547C23C2×D4×D4311yescharacteristic
548C23C22×D17211yescharacteristic
549C23C2×Q8×D4311yescharacteristic
550C23#41×D4312yes—
551C23C2×#1062189811yescharacteristic
552C23#1306337012yes—
553C23#1306337112yes—
554C23#1306337111yescharacteristic
555C23#1306337112yes—
556C23#1306337211yescharacteristic
557D4—17216no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—864no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—17232no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
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×C4C4⋊C4×D4314yes—
608C2×C4C4×D17214yes—
609C22—868no—
610C22—868no—
611C22—868no—
612C22—1724no—
613C22—1724no—
614C22—1724no—
615C22—1724no—
616C22—1724no—
617C22—1724no—
618C22—1724no—
619C22—1724no—
620C22—1724no—
621C22—1724no—
622C22—1724no—
623C22—1724no—
624C22C2×C4⋊C4×D4311yescharacteristic
625C22C2×C4×D17211yescharacteristic
626C22#1458336711yescharacteristic
627C22#1458337211yescharacteristic
628C22#1458337311yescharacteristic
629C22#1458337311yescharacteristic
630C22#1458337911yescharacteristic
631C22#1458345712yes—
632C22#1458346812yes—
633C22#1458348812yes—
634C22#1458350412yes—
635C22#1458351512yes—
636C22#1458352412yes—
637C22D4×D17211yescharacteristic
638C22#1458354212yes—
639C22#1458354412yes—
640C22#1458355411yescharacteristic
641C22Q8×D17211yescharacteristic
642C22#1458359812yes—
643C22#1458360512yes—
644C22#1458360911yescharacteristic
645C22#1458363912yes—
646C22#1458364612yes—
647C4—24no—
648C4—24no—
649C4—44no—
650C4—42no—
651C4—82no—
652C4—3442no—
653C4—1724no—
654C4—1724no—
655C2—1728no—
656C2#1913720811yescharacteristic
657C2#1913732011yescharacteristic
658C2#1913740511yescharacteristic
659C2C4⋊C4×D17211yescharacteristic
660C2#1913750311yescharacteristic
661C2#1913764511yescharacteristic
662C2#1913775411yescharacteristic
663C2#1914091812yes—
664C2#1914108912yes—
665C2#1914120512yes—
666C2#1914224612yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#14438
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#14582773C2semidirect
4. #19132847C2semidirect
5. #19132841C2semidirect
6. #19132839C2semidirect
7. #19132825C2semidirect
8. (C2×D43)⋊#95C2semidirect
9. C43×#1434C2semidirect
20. #14582801C4semidirect
54. C2×C4⋊Dic43C2×C4semidirect
71. C2×(C2×D43)⋊C4C2×C4semidirect
72. C2×(C2×D43)⋊C4C2×C4semidirect
85. C2×C42×C43C2×C4semidirect
89. #95×C43D4semidirect
160. C2×D172C4⋊C4semidirect
329. #1434D43semidirect
367. C43#14438semidirect
413. C2×C42C4×D43semidirect
423. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827772
C2×#145827732
#191328472
#191328412
#191328392
#191328252
(C2×D43)⋊#952
C43×#14342
#1443843