Finite Group Databasebeta

← #25025141

Subgroups — #25025141

Order 11008.

1450 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19132857C212yesmaximal, complemented
2#19132848C212yesmaximal, complemented
3#19132840C212yesmaximal
4#19132832C212yesmaximal
5#19132829C212yesmaximal, complemented
6#19132827C212yesmaximal, complemented
7#19132818C211yesmaximal, characteristic
8#19132818C211yesmaximal, characteristic
9C2×C43×#380C211yesmaximal, characteristic
10C22×C4⋊Dic43C2212yes—
11C22×C22⋊Dic43C2212yes—
12C22×C22⋊Dic43C2211yescharacteristic
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C4×Dic43C2212yes—
15C2×C43⋊#95C2212yes—
16C2×C43⋊#95C2212yes—
17C2×C43⋊#95C2212yes—
18C2×C43⋊#95C2211yescharacteristic
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2211yescharacteristic
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C24×C4×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C43×#380C418yescomplemented
31C2×#95×C43C2212yes—
32C23×Dic43C2312yes—
33C23×Dic43C2312yes—
34C23×Dic43C2312yes—
35C23×Dic43C2312yes—
36C2×C4⋊Dic43—24no—
37C2×C4⋊Dic43—42no—
38C2×C4⋊Dic43—42no—
39C2×C22⋊Dic43—24no—
40C2×C22⋊Dic43—22no—
41C2×C22⋊Dic43—24no—
42C2×C22⋊Dic43—41no—
43C2×C22⋊Dic43—41no—
44C2×C22⋊Dic43—42no—
45C2×C22⋊Dic43—41no—
46C2×C22⋊Dic43—41no—
47C2×C22⋊Dic43Q814yes—
48C2×C4×Dic43—42no—
49C2×C4×Dic43—42no—
50C2×C4×Dic43—42no—
51C43⋊#95—24no—
52C43⋊#95—24no—
53C43⋊#95—24no—
54C43⋊#95—42no—
55C43⋊#95—42no—
56C43⋊#95—42no—
57C43⋊#95—42no—
58C43⋊#95—41no—
59C43⋊#95—41no—
60C43⋊#95—42no—
61C43⋊#95—42no—
62C25×C43C2311yescharacteristic
63C23×C4×C43—24no—
64C23×C4×C43—41no—
65C23×C4×C43—41no—
66C23×C4×C43—42no—
67C23×C4×C43C2×C414yes—
68C23×C4×C43C2312yes—
69C23×C4×C43C2312yes—
70C23×C4×C43C2311yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C2×C4⋊C4×C43—41no—
73C2×C4⋊C4×C43—42no—
74C2×C4⋊C4×C43—41no—
75C2×C4⋊C4×C43C2×C414yes—
76C2×C4⋊C4×C43C2×C414yes—
77C2×C22⋊C4×C43—42no—
78C2×C22⋊C4×C43—42no—
79C2×C22⋊C4×C43C2×C418yes—
80#95×C43C2×C418yes—
81C24×C43—22no—
82C24×C43—22no—
83C24×C43—22no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—22no—
87C24×C43—21no—
88C24×C43—21no—
89C24×C43C22×C412yes—
90C24×C43C2×Q812yes—
91C24×C43#4112yes—
92C24×C43C2411yescharacteristic
93C22×C4×C43—28no—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43—22no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—44no—
114C22×C4×C43—44no—
115C22×C4×C43—48no—
116C22×C4×C43—48no—
117C22×C4×C43C22×C412yes—
118C22×C4×C43C22×C414yes—
119C22×C4×C43C22×C414yes—
120C22×C4×C43C22×C412yes—
121C22×C4×C43#4114yes—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
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—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43C2×Q814yes—
149C22×Dic43#4114yes—
150C4⋊C4×C43—44no—
151C4⋊C4×C43—44no—
152C22⋊C4×C43—48no—
153C22⋊Dic43—44no—
154C22⋊Dic43—48no—
155C22⋊Dic43—44no—
156C4⋊Dic43—48no—
157C4×Dic43—48no—
158C23×C43—22no—
159C23×C43—22no—
160C23×C43—22no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—22no—
166C23×C43—22no—
167C23×C43—22no—
168C23×C43—24no—
169C23×C43—24no—
170C23×C43—24no—
171C23×C43—24no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43C4×Q814yes—
181C23×C43C23×C411yescharacteristic
182C23×C43C22×Q811yescharacteristic
183C23×C43C2×#4112yes—
184C23×C43C2×#4112yes—
185C23×C43C2×#4111yescharacteristic
186C23×C43H(5,𝔽2)11yescharacteristic
187C23×C43H(5,𝔽2)11yescharacteristic
188C23×C43H(5,𝔽2)12yes—
189C23×C43H(5,𝔽2)12yes—
190C23×C43H(5,𝔽2)11yescharacteristic
191C23×C432−1+411yescharacteristic
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—24no—
195C2×C4×C43—24no—
196C2×C4×C43—22no—
197C2×C4×C43—24no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—24no—
205C2×C4×C43—416no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43#11714yes—
217C2×Dic43—24no—
218C2×Dic43—24no—
219C2×Dic43—24no—
220C2×Dic43—24no—
221C2×Dic43—24no—
222C2×Dic43—24no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245#14453—431nomaximal, Sylow
246C22×C43—24no—
247C22×C43—24no—
248C22×C43—24no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—44no—
254C22×C43—44no—
255C22×C43—44no—
256C22×C43—44no—
257C22×C43C2×#11711yescharacteristic
258C22×C43C2×C4×Q811yescharacteristic
259C22×C43C4×#4111yescharacteristic
260C22×C43#51811yescharacteristic
261C22×C43#51811yescharacteristic
262C22×C43#51811yescharacteristic
263C22×C43#52011yescharacteristic
264C22×C43#53812yes—
265C22×C43#53812yes—
266C22×C43#53812yes—
267C22×C43#53811yescharacteristic
268C22×C43#53911yescharacteristic
269C22×C43#54012yes—
270C22×C43#54311yescharacteristic
271C22×C43#54411yescharacteristic
272C22×C43#55112yes—
273C22×C43#55312yes—
274C22×C43#55312yes—
275C22×C43#55412yes—
276C22×C43#55412yes—
277C22×C43#55612yes—
278C22×C43#56012yes—
279C22×C43#56212yes—
280C4×C43—24no—
281C4×C43—42no—
282C4×C43—44no—
283C4×C43—44no—
284Dic43—44no—
285Dic43—44no—
286Dic43—82no—
287Dic43—82no—
288C2×#380D4311yescharacteristic
289#1443—432no—
290#1441—432no—
291#1439—432no—
292#1437—432no—
293#1436—432no—
294#1436—432no—
295C22⋊#95—431no—
296C22⋊#95—431no—
297C2×C43—44no—
298C2×C43#231211yescharacteristic
299C2×C43#232911yescharacteristic
300C2×C43#233311yescharacteristic
301C2×C43#234511yescharacteristic
302C2×C43#234711yescharacteristic
303C2×C43#236811yescharacteristic
304C2×C43#237711yescharacteristic
305C2×C43#277812yes—
306C2×C43#278012yes—
307C2×C43#278612yes—
308C2×C43#278812yes—
309C24×C4C2×D4311yescharacteristic
310C22×C4⋊C4—432no—
311C22×C4⋊C4C2×D4311yescharacteristic
312C22×C4⋊C4C2×D4311yescharacteristic
313C22×C22⋊C4—431no—
314C22×C22⋊C4—432no—
315C22×C22⋊C4—431no—
316C22×C22⋊C4C2×D4312yes—
317C22×C42—432no—
318#380Dic4318yescomplemented
319C2×#95—432no—
320C2×#95—432no—
321C2×#95—432no—
322C2×#95—431no—
323C2×#95—432no—
324C2×#95—431no—
325C2×#95—432no—
326C2×#95—432no—
327C2×#95—432no—
328C2×#95—432no—
329C2×#95—432no—
330C2×#95C2×D4312yes—
331C43#1445311yescharacteristic, complemented, Sylow
332C25C22×D4311yescharacteristic
333C23×C4—24no—
334C23×C4—42no—
335C23×C4—41no—
336C23×C4—41no—
337C23×C4—432no—
338C23×C4—432no—
339C23×C4—432no—
340C23×C4—432no—
341C23×C4C2×Dic4314yes—
342C23×C4C22×D4312yes—
343C23×C4C22×D4312yes—
344C23×C4C22×D4311yescharacteristic
345C23×C4C22×D4311yescharacteristic
346C2×C4⋊C4—41no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—864no—
350C2×C4⋊C4—1722no—
351C2×C4⋊C4—1722no—
352C2×C4⋊C4C2×Dic4314yes—
353C2×C4⋊C4C2×Dic4314yes—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—434no—
357C2×C22⋊C4—864no—
358C2×C22⋊C4—864no—
359C2×C22⋊C4—862no—
360C2×C22⋊C4—1721no—
361C2×C22⋊C4—1721no—
362C2×C22⋊C4—1722no—
363C2×C22⋊C4—1721no—
364C2×C22⋊C4—1721no—
365C2×C22⋊C4C2×Dic4318yes—
366C2×C42—1722no—
367C2×C42—1722no—
368C2×C42—1722no—
369#95—864no—
370#95—864no—
371#95—864no—
372#95—1722no—
373#95—1722no—
374#95—1722no—
375#95—1722no—
376#95—1722no—
377#95—1721no—
378#95—1721no—
379#95—1722no—
380#95C2×Dic4318yes—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24Q8×D4312yes—
390C24#1062190212yes—
391C24C22×Dic4312yes—
392C24C23×D4311yescharacteristic
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—48no—
416C22×C4—48no—
417C22×C4—434no—
418C22×C4—434no—
419C22×C4—862no—
420C22×C4—862no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4#1062189814yes—
446C22×C4C22×Dic4312yes—
447C22×C4C22×Dic4314yes—
448C22×C4C22×Dic4314yes—
449C22×C4C22×Dic4312yes—
450C4⋊C4—44no—
451C4⋊C4—44no—
452C4⋊C4—1728no—
453C22⋊C4—48no—
454C22⋊C4—1724no—
455C22⋊C4—1728no—
456C22⋊C4—1724no—
457C42—1728no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23Q8×Dic4314yes—
481C23C23×Dic4311yescharacteristic
482C23C2×Q8×D4311yescharacteristic
483C23#41×D4312yes—
484C23C2×#1062189812yes—
485C23C2×#1062190211yescharacteristic
486C23#1306337012yes—
487C23#1306337012yes—
488C23#1306337011yescharacteristic
489C23#1306337011yescharacteristic
490C23#1306337111yescharacteristic
491C23#1306337211yescharacteristic
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—416no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—864no—
517C2×C4—864no—
518C2×C4—864no—
519C2×C4—864no—
520C2×C4—864no—
521C2×C4—864no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4#1306328414yes—
545C22—24no—
546C22—24no—
547C22—24no—
548C22—44no—
549C22—42no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22C2×#1306328411yescharacteristic
557C22C2×Q8×Dic4311yescharacteristic
558C22#41×Dic4311yescharacteristic
559C22#1458337411yescharacteristic
560C22#1458337411yescharacteristic
561C22#1458337411yescharacteristic
562C22#1458338211yescharacteristic
563C22#1458348112yes—
564C22#1458348712yes—
565C22#1458348712yes—
566C22#1458348911yescharacteristic
567C22#1458349811yescharacteristic
568C22#1458349912yes—
569C22#1458352411yescharacteristic
570C22#1458352811yescharacteristic
571C22#1458357612yes—
572C22#1458359312yes—
573C22#1458359712yes—
574C22#1458360312yes—
575C22#1458360412yes—
576C22#1458361712yes—
577C22#1458363712yes—
578C22#1458364412yes—
579C4—24no—
580C4—44no—
581C4—42no—
582C4—44no—
583C4—3442no—
584C4—3442no—
585C4—1724no—
586C4—1724no—
587C2—44no—
588C2#1913719311yescharacteristic
589C2#1913733011yescharacteristic
590C2#1913736211yescharacteristic
591C2#1913747211yescharacteristic
592C2#1913748811yescharacteristic
593C2#1913768011yescharacteristic
594C2#1913775211yescharacteristic
595C2#1914220912yes—
596C2#1914223912yes—
597C2#1914230712yes—
598C2#1914233712yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#380C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#380D43
hypocenterC43#14453
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. #19132857C2semidirect
2. #19132848C2semidirect
5. #19132829C2semidirect
6. #19132827C2semidirect
30. C43×#380C4semidirect
318. #380Dic43semidirect
331. C43#14453semidirect

Maximal subgroups

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

subgroupindex
#191328572
#191328482
#191328402
#191328322
#191328292
#191328272
#191328182
C2×C43×#3802
#1445343