Finite Group Databasebeta

← #25112753

Subgroups — #25112753

Order 11008.

1322 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583550C211yesmaximal, characteristic
2M16×C22⋊D43C212yesmaximal, complemented
3#19135582C212yesmaximal, complemented
4#19135058C212yesmaximal, complemented
5#19135057C212yesmaximal, complemented
6#19134675C211yesmaximal, characteristic, complemented
7#19134674C211yesmaximal, characteristic, complemented
8#19134586C211yesmaximal, characteristic, complemented
9#19134386C211yesmaximal, characteristic, complemented
10#343×D43C211yesmaximal, characteristic, complemented
11C2×C43×#343C211yesmaximal, characteristic, complemented
12C22×#10621898C412yes—
13C2×M16×D43C2212yes—
14#14583550—22no—
15#14583550—22no—
16#14583550—22no—
17#14583550—22no—
18C2×#13063324C2211yescharacteristic
19C2×#13063310C412yes—
20C2×#13063308C412yes—
21C2×#13063303C412yes—
22C2×#13063300C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×C4⋊C4×D43C2211yescharacteristic
27#14582975—22no—
28#14582970—22no—
29#14582968—22no—
30C8×C22⋊D43—22no—
31#14582922C2212yes—
32C2×#13063241C2212yes—
33C2×#13063241C2212yes—
34#14582863C2212yes—
35#14582862C2212yes—
36M16×Dic43C2212yes—
37#14582668C2212yes—
38#14582668C2211yescharacteristic
39#14582668C2211yescharacteristic
40#14582667C2212yes—
41#14582667C2212yes—
42C22×M16×C43C2212yes—
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#343C2212yes—
45C43×#343C2211yescharacteristic
46C43×#343C2211yescharacteristic
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—48no—
52C22×Dic86C2×C412yes—
53C22×D172C2×C412yes—
54C22×D172C2311yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43C2×C412yes—
57C22×C4×D43C2×C412yes—
58C22×C4×D43C2×C412yes—
59C22×C4×D43C2311yescharacteristic
60C2×#10621877C2312yes—
61C2×#10621877C2312yes—
62C2×#10621872—22no—
63M16×D43—24no—
64M16×D43—42no—
65C2×C8×D43—22no—
66#13063324—22no—
67#13063324—22no—
68#13063310—24no—
69#13063310—24no—
70#13063308—24no—
71#13063308—24no—
72#13063303—24no—
73#13063303—24no—
74#13063300—22no—
75#13063300—22no—
76#13063299—22no—
77#13063299—22no—
78#13063287—22no—
79#13063287—22no—
80C4×C22⋊D43D412yes—
81C4×C22⋊D43D412yes—
82C4×C22⋊D43D412yes—
83C4×C22⋊D43D412yes—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4C2×C412yes—
86C2×Dic43⋊C4C2×C412yes—
87C2×Dic43⋊C4C2×C411yescharacteristic
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C2×C22⋊Dic43C2×C411yescharacteristic
91C2×(C2×D43)⋊C4C2×C412yes—
92C2×(C2×D43)⋊C4C2×C412yes—
93C2×(C2×D43)⋊C4C2×C412yes—
94C2×(C2×D43)⋊C4C2×C411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96Dic43⋊C8—22no—
97Dic43⋊C8—22no—
98#13063241—24no—
99#13063241—42no—
100C22⋊(C43⋊C8)—22no—
101C22⋊(C43⋊C8)—22no—
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8—22no—
104#13063235—22no—
105C8×Dic43—22no—
106C23×C4×C43C2×C412yes—
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43—22no—
109C2×M16×C43—24no—
110C2×M16×C43—42no—
111C2×M16×C43C2312yes—
112C2×M16×C43C2312yes—
113C22×C8×C43—22no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43C2×C412yes—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C24×C43C22×C411yescharacteristic
120C23×D43C22×C411yescharacteristic
121C23×D43C22×C412yes—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—44no—
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C22×C412yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—44no—
138C2×C22⋊D43C22⋊C411yescharacteristic
139C2×C22⋊D43C22⋊C411yescharacteristic
140C2×C22⋊D43C22⋊C411yescharacteristic
141C2×C22⋊D43C22⋊C411yescharacteristic
142C22×Dic43C22×C411yescharacteristic
143C22×Dic43C22×C411yescharacteristic
144C22×Dic43C22×C412yes—
145C22×Dic43C22×C411yescharacteristic
146#10621898—48no—
147#10621898—48no—
148#10621898—48no—
149#10621898—48no—
150C2×D172—22no—
151C2×D172—22no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—44no—
157C2×C4×D43—22no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—44no—
165C2×C4×D43—44no—
166C2×C4×D43C2×D412yes—
167C2×C4×D43C2×D412yes—
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—44no—
171M16×C43—22no—
172M16×C43—22no—
173M16×C43—22no—
174M16×C43—44no—
175M16×C43#4114yescomplemented
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—44no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C22⋊Dic43C22⋊C412yes—
183C22⋊Dic43C22⋊C412yes—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4C22⋊C412yes—
188(C2×D43)⋊C4C22⋊C412yes—
189C4⋊Dic43—22no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192Dic43⋊C4C22⋊C412yes—
193Dic43⋊C4C22⋊C412yes—
194C4×Dic43C2×D412yes—
195C4×Dic43C2×D412yes—
196#10621877—22no—
197#10621877—22no—
198#10621877—22no—
199#10621877—22no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202#10621872—44no—
203C8×D43—44no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43C2×C22⋊C411yescharacteristic
209C23×C43C2×C22⋊C411yescharacteristic
210C23×C43C23×C411yescharacteristic
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—22no—
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43C2×C22⋊C411yescharacteristic
221C22×D43C2×C22⋊C411yescharacteristic
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—44no—
231C2×C4×C43—44no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43C2×C22⋊C412yes—
235C2×C4×C43C22×D412yes—
236C2×C4×C43C2×#4112yes—
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C22⋊D43—22no—
240C22⋊D43—22no—
241C22⋊D43—22no—
242C22⋊D43—44no—
243C22⋊D43—44no—
244C22⋊D43#10014yescomplemented
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—41no—
250C2×Dic43—42no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C411yescharacteristic
255D172—44no—
256D172—44no—
257D172—42no—
258D172—42no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—44no—
264C4×D43—44no—
265C4×D43—44no—
266C4×D43—44no—
267Dic86—44no—
268Dic86—44no—
269C8×C43—24no—
270C8×C43—42no—
271C43⋊C8—42no—
272C43⋊C8—42no—
273#22479—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43C2×#10012yes—
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43C4×#4111yescharacteristic
286C22×C43#52011yescharacteristic
287C2×D43—21no—
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—82no—
298C2×D43—82no—
299C2×D43C2×#10012yes—
300C4×C43—22no—
301C4×C43—42no—
302C4×C43—42no—
303C4×C43#54612yes—
304C4×C43#54712yes—
305Dic43—22no—
306Dic43—21no—
307Dic43—22no—
308Dic43—42no—
309Dic43C2×#10012yes—
310C2×#547—431no—
311D4×M16—432no—
312#1997—432no—
313#1900—432no—
314#1900—432no—
315#1821—431no—
316#1821—431no—
317#1800—431no—
318C4×#100—431no—
319C2×#343—431no—
320C2×#343D4311yescharacteristic, complemented
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—22no—
324C2×C43—41no—
325C2×C43#233911yescharacteristic
326C2×C43C22×#10011yescharacteristic
327C2×C43#288911yescharacteristic
328D43—22no—
329D43—41no—
330D43—82no—
331C22×#41—432no—
332C22×M16—432no—
333C22×M16C2×D4312yes—
334#547—862no—
335#547—862no—
336#547—862no—
337#547—862no—
338C2×C4⋊Q8—431no—
339C2×#123—432no—
340C2×#123—432no—
341C2×C22⋊Q8—432no—
342C2×#121—431no—
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×C4×D4—431no—
346C22×C4⋊C4—431no—
347C22×C4⋊C4C2×D4311yescharacteristic
348#436—862no—
349#435—862no—
350#435—862no—
351C8×D4—862no—
352#423—432no—
353C2×#100—432no—
354C2×#100—432no—
355#407—432no—
356#407—432no—
357C4×M16—432no—
358#343—432no—
359#343—432no—
360#343—431no—
361#343—431no—
362#343—432no—
363#343C2×D4311yescharacteristic
364#343C2×D4312yes—
365#343C2×D4311yescharacteristic
366C43#2247911yescharacteristic, complemented, Sylow
367C2×#41—862no—
368C2×#41—862no—
369C2×#41—862no—
370C2×#41—862no—
371C2×#41—1728no—
372C22×Q8—432no—
373C22×D4—431no—
374C22×D4—432no—
375C22×D4—432no—
376C22×D4—431no—
377C23×C4—431no—
378C23×C4—432no—
379C23×C4—432no—
380C23×C4C4×D4312yes—
381C23×C4C22×D4311yescharacteristic
382C2×M16—22no—
383C2×M16—24no—
384C2×M16—42no—
385C2×M16—432no—
386C2×M16—432no—
387C2×M16—862no—
388C2×M16—864no—
389C2×M16—1722no—
390C2×M16C22×D4312yes—
391C2×M16C22×D4312yes—
392C22×C8—22no—
393C22×C8—862no—
394C4⋊Q8—862no—
395C4⋊Q8—862no—
396#123—864no—
397#123—864no—
398#123—864no—
399#123—864no—
400C22⋊Q8—864no—
401C22⋊Q8—864no—
402#121—862no—
403#121—862no—
404#121—862no—
405#121—862no—
406C4×D4—432no—
407C4×D4—432no—
408C4×D4—432no—
409C4×D4—432no—
410C4×D4—862no—
411C4×D4—862no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—432no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4C4×D4312yes—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—431no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—432no—
426C2×C22⋊C4—432no—
427C2×C22⋊C4—432no—
428C2×C42—431no—
429C4⋊C8—862no—
430C4⋊C8—862no—
431#100—864no—
432#100—1722no—
433C22⋊C8—862no—
434C22⋊C8—862no—
435C22⋊C8—862no—
436C22⋊C8—862no—
437#97—862no—
438C4×C8—862no—
439C24—431no—
440C24—432no—
441C24C2×C4×D4311yescharacteristic
442#41—1728no—
443#41—1728no—
444#41—1728no—
445#41—1728no—
446C2×Q8—862no—
447C2×Q8—862no—
448C2×Q8—1724no—
449C2×D4—431no—
450C2×D4—431no—
451C2×D4—431no—
452C2×D4—431no—
453C2×D4—862no—
454C2×D4—862no—
455C2×D4—864no—
456C2×D4—862no—
457C2×D4—862no—
458C2×D4—862no—
459C2×D4—862no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—1724no—
463C2×D4—1724no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—44no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—432no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—1724no—
484C22×C4—1724no—
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×C4×D4312yes—
487C22×C4C2×C4×D4312yes—
488C22×C4D4×D4312yes—
489C22×C4D4×D4312yes—
490C22×C4C23×D4311yescharacteristic
491M16—22no—
492M16—22no—
493M16—22no—
494M16—44no—
495M16—862no—
496M16—862no—
497M16—862no—
498M16—862no—
499M16—1724no—
500M16#1062189814yescomplemented
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—44no—
504C2×C8—862no—
505C2×C8—862no—
506C2×C8—1724no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—864no—
513C4⋊C4—864no—
514C4⋊C4—862no—
515C22⋊C4—432no—
516C22⋊C4—432no—
517C22⋊C4—432no—
518C22⋊C4—432no—
519C22⋊C4—864no—
520C22⋊C4—864no—
521C22⋊C4—864no—
522C42—432no—
523C42—432no—
524C23—21no—
525C23—21no—
526C23—22no—
527C23—41no—
528C23—431no—
529C23—431no—
530C23—862no—
531C23—861no—
532C23—861no—
533C23—862no—
534C23—862no—
535C23—862no—
536C23—1721no—
537C23—1722no—
538C23—1722no—
539C23C22⋊C4×D4311yescharacteristic
540C23C22⋊C4×D4311yescharacteristic
541C23C22×C4×D4311yescharacteristic
542Q8—1724no—
543Q8—1724no—
544D4—434no—
545D4—862no—
546D4—862no—
547D4—862no—
548D4—1724no—
549D4—1724no—
550D4—1724no—
551D4—1724no—
552D4—1722no—
553D4—1722no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—431no—
567C2×C4—432no—
568C2×C4—431no—
569C2×C4—432no—
570C2×C4—862no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—1724no—
579C2×C4—1724no—
580C2×C4—1724no—
581C2×C4—1724no—
582C2×C4—1721no—
583C2×C4—1722no—
584C2×C4C22⋊C4×D4312yes—
585C2×C4C2×D4×D4312yes—
586C2×C4C2×#1062189812yes—
587C2×C4#1306337011yescharacteristic
588C2×C4#1306337311yescharacteristic
589C8—24no—
590C8—42no—
591C8—1722no—
592C8—1722no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—42no—
602C22—432no—
603C22—861no—
604C22—861no—
605C22—861no—
606C22—861no—
607C22—861no—
608C22—3442no—
609C22—3442no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22#100×D4312yes—
616C22C2×C22⋊C4×D4311yescharacteristic
617C22C4×#1062189811yescharacteristic
618C22#1458338011yescharacteristic
619C4—22no—
620C4—42no—
621C4—42no—
622C4—432no—
623C4—862no—
624C4—861no—
625C4—862no—
626C4—1722no—
627C4#1458353912yes—
628C4#1458355012yes—
629C2—21no—
630C2—21no—
631C2—22no—
632C2—41no—
633C2—862no—
634C2—3442no—
635C2—1721no—
636C2#1913742211yescharacteristic
637C2C2×#100×D4311yescharacteristic
638C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#343C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583550C2
cosocleC22×C4×C43C24
hypercenterC2×#343D43
hypocenterC43#22479
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. #19135582C2semidirect
4. #19135058C2semidirect
5. #19135057C2semidirect
6. #19134675C2semidirect
7. #19134674C2semidirect
8. #19134586C2semidirect
9. #19134386C2semidirect
10. #343×D43C2semidirect
11. C2×C43×#343C2semidirect
175. M16×C43#41semidirect
244. C22⋊D43#100semidirect
320. C2×#343D43semidirect
366. C43#22479semidirect
500. M16#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835502
M16×C22⋊D432
#191355822
#191350582
#191350572
#191346752
#191346742
#191345862
#191343862
#343×D432
C2×C43×#3432
#2247943