Finite Group Databasebeta

← #25025547

Subgroups — #25025547

Order 11008.

1918 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582800C211yesmaximal, characteristic
2C2×#14582777C212yesmaximal
3#19132848C211yesmaximal, characteristic, complemented
4#19132841C212yesmaximal, complemented
5#19132837C212yesmaximal, complemented
6#19132821C212yesmaximal, complemented
7(C2×D43)⋊#95C212yesmaximal, complemented
8(C2×D43)⋊#95C212yesmaximal, complemented
9C43×#1441C211yesmaximal, characteristic, complemented
10C23×D172C2211yescharacteristic
11C23×C4×D43C2212yes—
12C22×C4⋊Dic43C2211yescharacteristic
13C22×(C2×D43)⋊C4C2212yes—
14C22×(C2×D43)⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×C4×Dic43C2211yescharacteristic
19#14582800C418yescomplemented
20#14582777—28no—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C2×#95×C43C2212yes—
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C24×D43C2312yes—
34C22×D172—41no—
35C22×D172—41no—
36C22×D172—41no—
37C22×D172—41no—
38C22×D172C2×C414yes—
39C22×D172D414yes—
40C22×D172Q814yes—
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C22×C4×D43—24no—
45C22×C4×D43—24no—
46C22×C4×D43—24no—
47C22×C4×D43—42no—
48C22×C4×D43—42no—
49C22×C4×D43—42no—
50C22×C4×D43—42no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43—41no—
53C2×(C2×D43)⋊C4—24no—
54C2×(C2×D43)⋊C4—24no—
55C2×(C2×D43)⋊C4—24no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—42no—
59C2×(C2×D43)⋊C4—42no—
60C2×(C2×D43)⋊C4—42no—
61C2×(C2×D43)⋊C4—42no—
62C2×(C2×D43)⋊C4—42no—
63C2×(C2×D43)⋊C4—42no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4—42no—
66C2×(C2×D43)⋊C4C2×C418yescomplemented
67C2×(C2×D43)⋊C4C2×C418yescomplemented
68C2×C4×Dic43—41no—
69C2×C4×Dic43—41no—
70C2×C4×Dic43C2×C414yescomplemented
71C43⋊#95—24no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C43⋊#95—41no—
77C43⋊#95—42no—
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43—41no—
84C2×C4⋊C4×C43—41no—
85C2×C4⋊C4×C43—41no—
86C2×C4⋊C4×C43—42no—
87C2×C4⋊C4×C43C2×C414yescomplemented
88#95×C43—24no—
89#95×C43—41no—
90#95×C43—42no—
91C24×C43C2411yescharacteristic
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×D43—22no—
104C23×D43C22×C414yes—
105C23×D43C2×D414yes—
106C23×D43C2×Q814yes—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C22×C412yes—
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—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43C22×C414yes—
158C22×Dic43#4114yes—
159C2×D172—44no—
160C2×D172—44no—
161C2×D172—44no—
162C2×D172—44no—
163C2×D172—44no—
164C2×D172—44no—
165C2×D172C4⋊C4116yescomplemented
166C2×C4×D43—48no—
167C2×C4×D43—48no—
168C2×C4×D43—48no—
169C2×C4×D43—48no—
170C2×C4×D43—48no—
171C2×C4×D43—48no—
172C2×C4×D43—48no—
173C4⋊C4×C43—44no—
174C4⋊C4×C43—44no—
175(C2×D43)⋊C4—48no—
176(C2×D43)⋊C4—48no—
177(C2×D43)⋊C4—48no—
178(C2×D43)⋊C4—48no—
179(C2×D43)⋊C4—48no—
180C4⋊Dic43—44no—
181C4×Dic43—44no—
182C23×C43C23×C411yescharacteristic
183C23×C43C22×D411yescharacteristic
184C23×C43C22×Q811yescharacteristic
185C23×C43C2×#4112yes—
186C23×C43C2×#4112yes—
187C23×C43H(5,𝔽2)11yescharacteristic
188C23×C43H(5,𝔽2)11yescharacteristic
189C23×C43H(5,𝔽2)12yes—
190C23×C43H(5,𝔽2)11yescharacteristic
191C23×C43H(5,𝔽2)11yescharacteristic
192C23×C43H(5,𝔽2)12yes—
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—24no—
207C22×D43—24no—
208C22×D43—24no—
209C22×D43—24no—
210C22×D43—24no—
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×D43—42no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43—42no—
227C22×D43C2×C4⋊C418yes—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—24no—
239C2×C4×C43—24no—
240C2×C4×C43—24no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43C2×C4⋊C414yes—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280D172—416no—
281C4×D43—432no—
282#14486—431nomaximal, Sylow
283C22×C43C22×C4⋊C411yescharacteristic
284C22×C43C4×#4112yes—
285C22×C43#51812yes—
286C22×C43#51811yescharacteristic
287C22×C43#51811yescharacteristic
288C22×C43#53411yescharacteristic
289C22×C43#53411yescharacteristic
290C22×C43#53812yes—
291C22×C43#53812yes—
292C22×C43#54012yes—
293C22×C43#54012yes—
294C22×C43#54311yescharacteristic
295C22×C43#54311yescharacteristic
296C22×C43#54612yes—
297C22×C43#54612yes—
298C22×C43#55112yes—
299C22×C43#55412yes—
300C22×C43#55412yes—
301C22×C43#55511yescharacteristic
302C22×C43#55511yescharacteristic
303C22×C43#56012yes—
304C22×C43#56011yescharacteristic
305C22×C43#56011yescharacteristic
306C2×D43—28no—
307C2×D43—28no—
308C2×D43—28no—
309C2×D43—44no—
310C2×D43—44no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—44no—
314C2×D43—44no—
315C2×D43—44no—
316C2×D43—44no—
317C2×D43—44no—
318C2×D43—44no—
319C2×D43—44no—
320C2×D43—44no—
321C4×C43—24no—
322C4×C43—42no—
323C4×C43—42no—
324C4×C43—44no—
325C4×C43—82no—
326Dic43—44no—
327Dic43—44no—
328Dic43—82no—
329C2×#390—431no—
330C2×#386—432no—
331#1441—431no—
332#1441D4311yescharacteristic, complemented
333#1439—432no—
334#1439—432no—
335#1434—432no—
336C22⋊#95—432no—
337C22⋊#95—432no—
338C2×C43#231511yescharacteristic
339C2×C43#233312yes—
340C2×C43#234912yes—
341C2×C43#237211yescharacteristic
342C2×C43#238011yescharacteristic
343C2×C43#269712yes—
344C2×C43#269911yescharacteristic
345C2×C43#269911yescharacteristic
346C2×C43#274812yes—
347C2×C43#278411yescharacteristic
348C2×C43#278411yescharacteristic
349D43—48no—
350C23×D4—431no—
351C24×C4—432no—
352C22×C4⋊C4—431no—
353C22×C4⋊C4C2×D4311yescharacteristic
354C22×C4⋊C4C2×D4311yescharacteristic
355C22×C22⋊C4—432no—
356C22×C22⋊C4—432no—
357C22×C22⋊C4—432no—
358C22×C22⋊C4—432no—
359C22×C22⋊C4—432no—
360C22×C42—431no—
361#390—438no—
362#386—868no—
363C2×#95—432no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95—431no—
368C2×#95—432no—
369C2×#95—432no—
370C2×#95C2×D4312yes—
371C2×#95C2×D4311yescharacteristic
372C2×#95C2×D4312yes—
373C43#1448611yescharacteristic, complemented, Sylow
374C25—432no—
375C22×D4—434no—
376C22×D4—434no—
377C22×D4—434no—
378C22×D4—1721no—
379C22×D4—1721no—
380C22×D4—1721no—
381C22×D4—1721no—
382C23×C4—432no—
383C23×C4—432no—
384C23×C4—432no—
385C23×C4—864no—
386C23×C4—864no—
387C23×C4—864no—
388C23×C4—1722no—
389C23×C4—1722no—
390C23×C4—1722no—
391C23×C4—1722no—
392C23×C4C22×D4312yes—
393C23×C4C22×D4311yescharacteristic
394C23×C4C22×D4311yescharacteristic
395C23×C4C22×D4312yes—
396C23×C4C22×D4311yescharacteristic
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—1721no—
402C2×C4⋊C4—1722no—
403C2×C4⋊C4C4×D4314yescomplemented
404C2×C22⋊C4—438no—
405C2×C22⋊C4—438no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—864no—
410C2×C22⋊C4—864no—
411C2×C22⋊C4—1722no—
412C2×C22⋊C4—1722no—
413C2×C22⋊C4—1722no—
414C2×C22⋊C4—1722no—
415C2×C22⋊C4—1722no—
416C2×C22⋊C4—1722no—
417C2×C22⋊C4—1722no—
418C2×C22⋊C4—1722no—
419C2×C42—434no—
420C2×C42—1721no—
421C2×C42—1721no—
422#95—24no—
423#95—42no—
424#95—41no—
425#95—864no—
426#95—864no—
427#95—864no—
428#95—1721no—
429#95—1722no—
430#95—1722no—
431#95—1722no—
432C24—434no—
433C24—434no—
434C24—434no—
435C24—862no—
436C24—862no—
437C24—862no—
438C24—862no—
439C24—862no—
440C24—862no—
441C24—862no—
442C24—862no—
443C24—862no—
444C24—862no—
445C24—862no—
446C24—862no—
447C24C23×D4311yescharacteristic
448C2×D4—4316no—
449C2×D4—1724no—
450C2×D4—1724no—
451C2×D4—1724no—
452C2×D4—1724no—
453C2×D4—1724no—
454C2×D4—1724no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—434no—
481C22×C4—434no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—1728no—
502C22×C4—1728no—
503C22×C4—1728no—
504C22×C4—1728no—
505C22×C4—1728no—
506C22×C4—1728no—
507C22×C4—1728no—
508C22×C4C2×C4×D4312yes—
509C22×C4C2×C4×D4312yes—
510C22×C4C2×C4×D4312yes—
511C22×C4D4×D4312yes—
512C22×C4Q8×D4312yes—
513C22×C4#1062190214yes—
514C4⋊C4—44no—
515C4⋊C4—44no—
516C4⋊C4—1724no—
517C22⋊C4—1728no—
518C22⋊C4—1728no—
519C22⋊C4—1728no—
520C22⋊C4—1728no—
521C22⋊C4—1728no—
522C42—1724no—
523C23—438no—
524C23—864no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—864no—
530C23—864no—
531C23—864no—
532C23—864no—
533C23—864no—
534C23—864no—
535C23—864no—
536C23—864no—
537C23—864no—
538C23—864no—
539C23—864no—
540C23—864no—
541C23—864no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23—1722no—
547C23—1722no—
548C23—1722no—
549C23—1722no—
550C23—1722no—
551C23—1722no—
552C23—1722no—
553C23—1722no—
554C23—1722no—
555C23—1722no—
556C23—1722no—
557C23—1722no—
558C23C22×C4×D4311yescharacteristic
559C23C2×D4×D4311yescharacteristic
560C23C2×Q8×D4311yescharacteristic
561C23#41×D4312yes—
562C23C2×#1062190212yes—
563C23#1306337011yescharacteristic
564C23#1306337012yes—
565C23#1306337011yescharacteristic
566C23#1306337112yes—
567C23#1306337111yescharacteristic
568C23#1306337111yescharacteristic
569D4—17216no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—17232no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4C4⋊C4×D4314yes—
623C22—868no—
624C22—868no—
625C22—868no—
626C22—1724no—
627C22—1724no—
628C22—1724no—
629C22—1724no—
630C22—1724no—
631C22—1724no—
632C22—1724no—
633C22—1724no—
634C22—1724no—
635C22—1724no—
636C22—1724no—
637C22—1724no—
638C22C2×C4⋊C4×D4311yescharacteristic
639C22C4×#1062190212yes—
640C22#1458337112yes—
641C22#1458337211yescharacteristic
642C22#1458337311yescharacteristic
643C22#1458345711yescharacteristic
644C22#1458345711yescharacteristic
645C22#1458348812yes—
646C22#1458348912yes—
647C22#1458350112yes—
648C22#1458350512yes—
649C22#1458352411yescharacteristic
650C22#1458352411yescharacteristic
651C22#1458354012yes—
652C22#1458354612yes—
653C22#1458357612yes—
654C22#1458360512yes—
655C22#1458361012yes—
656C22#1458361111yescharacteristic
657C22#1458361511yescharacteristic
658C22#1458363712yes—
659C22#1458363811yescharacteristic
660C22#1458363911yescharacteristic
661C4—24no—
662C4—44no—
663C4—42no—
664C4—42no—
665C4—82no—
666C4—3442no—
667C4—1724no—
668C4—1724no—
669C2—1728no—
670C2#1913720811yescharacteristic
671C2#1913735912yes—
672C2#1913750412yes—
673C2#1913770611yescharacteristic
674C2#1913777011yescharacteristic
675C2#1914115312yes—
676C2#1914117711yescharacteristic
677C2#1914118111yescharacteristic
678C2#1914180712yes—
679C2#1914229511yescharacteristic
680C2#1914229811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1441C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1441D43
hypocenterC43#14486
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #19132848C2semidirect
4. #19132841C2semidirect
5. #19132837C2semidirect
6. #19132821C2semidirect
7. (C2×D43)⋊#95C2semidirect
8. (C2×D43)⋊#95C2semidirect
9. C43×#1441C2semidirect
19. #14582800C4semidirect
66. C2×(C2×D43)⋊C4C2×C4semidirect
67. C2×(C2×D43)⋊C4C2×C4semidirect
70. C2×C4×Dic43C2×C4semidirect
87. C2×C4⋊C4×C43C2×C4semidirect
165. C2×D172C4⋊C4semidirect
332. #1441D43semidirect
373. C43#14486semidirect
403. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828002
C2×#145827772
#191328482
#191328412
#191328372
#191328212
(C2×D43)⋊#952
C43×#14412
#1448643