Finite Group Databasebeta

← #25113883

Subgroups — #25113883

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582901C211yesmaximal, characteristic
2#19137466C211yesmaximal, characteristic, complemented
3#19137423C211yesmaximal, characteristic
4#19135283C211yesmaximal, characteristic, complemented
5#19135269C211yesmaximal, characteristic, complemented
6#19135235C211yesmaximal, characteristic, complemented
7#19135228C211yesmaximal, characteristic, complemented
8#19134853C211yesmaximal, characteristic, complemented
9#19134839C211yesmaximal, characteristic, complemented
10#19134683C211yesmaximal, characteristic, complemented
11#19134533C211yesmaximal, characteristic
12#19134419C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C43×#1809C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063287C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063281—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21#14582901C418yescomplemented
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582782—21no—
38#14582782—21no—
39#14582775—21no—
40#14582775—21no—
41#14582761—21no—
42#14582760—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46#95×D43—21no—
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621898—22no—
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898C2×C414yes—
66C22×Dic86C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063287—22no—
76#13063287—22no—
77#13063287—41no—
78#13063287—41no—
79#13063281—44no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43C2×C414yescomplemented
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43D411yescharacteristic
88C2×C22⋊Dic43D411yescharacteristic
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063250C2×C414yescomplemented
96#13063250C2×C414yescomplemented
97#13063248—41no—
98#13063248—41no—
99#13063247C2×C414yes—
100#13063247C2×C414yes—
101#13063245—22no—
102#13063245—22no—
103C22⋊(C43⋊C8)—22no—
104#13063235—41no—
105C8×Dic43—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C2×M16×C43—41no—
118C2×M16×C43—41no—
119C2×M16×C43C2×C414yescomplemented
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128#107×C43—41no—
129#106×C43—41no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43C2×D411yescharacteristic
133C23×D43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C22×C412yes—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43#4112yes—
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—24no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159#10621898—28no—
160#10621898—44no—
161#10621898—44no—
162#10621898—44no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172C22×C412yes—
167C2×D172#4112yes—
168C2×D172#4112yes—
169C2×C4×D43—24no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—81no—
177C2×C4×D43—81no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86C22×C412yes—
184M16×C43—44no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C22×C412yes—
190C2×C8×C43C22×C412yes—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C22⋊C4×C43—42no—
200C22⋊C4×C43—81no—
201C22⋊Dic43—22no—
202C22⋊Dic43—41no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—42no—
205C4⋊Dic43—24no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43C22×C412yes—
209C4⋊Dic43C22×C412yes—
210Dic43⋊C4—42no—
211Dic43⋊C4—42no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—42no—
217C4×Dic43—42no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43C4×D412yes—
231C23×C43C22×D411yescharacteristic
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C4×D412yes—
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C22⋊D43—48no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—48no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43AGL(1,ℤ/8)12yes—
287D172—22no—
288D172—22no—
289D172—22no—
290D172#11714yescomplemented
291C4×D43—48no—
292C4×D43—84no—
293C4×D43—84no—
294Dic86—22no—
295Dic86—22no—
296Dic86—41no—
297Dic86—41no—
298C8×C43—22no—
299C8×C43—22no—
300C43⋊C8—41no—
301C43⋊C8—41no—
302#22582—431nomaximal, Sylow
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43C2×C4×D411yescharacteristic
311C22×C43#54611yescharacteristic
312C22×C43#54611yescharacteristic
313C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C43#57511yescharacteristic
315C22×C43#57711yescharacteristic
316C22×C43#57811yescharacteristic
317C2×D43—24no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C4×C43—22no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43C2×#11711yescharacteristic
330C4×C43#51811yescharacteristic
331C4×C43#55111yescharacteristic
332C4×C43#55111yescharacteristic
333Dic43—22no—
334Dic43—41no—
335Dic43—42no—
336Dic43—42no—
337Dic43—42no—
338Dic43—41no—
339Dic43—41no—
340C2×#417—431no—
341#2344—431no—
342#2339—431no—
343#1935—431no—
344#1933—431no—
345#1928—431no—
346#1927—431no—
347#1864—431no—
348#1862—431no—
349#1824—431no—
350#1809D4311yescharacteristic, complemented
351#1788—431no—
352#1762—431no—
353C4×#102—431no—
354#1753—431no—
355C2×C43—42no—
356C2×C43#234211yescharacteristic
357C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
358C2×C43#294711yescharacteristic
359C2×C43#330611yescharacteristic
360C2×C43#331511yescharacteristic
361C2×C43#332311yescharacteristic
362C2×C43#333011yescharacteristic
363D43—44no—
364C22×#41—431no—
365C22×M16C2×D4311yescharacteristic
366C2×C4×D4—431no—
367C2×C4×D4—431no—
368C2×#117—861no—
369C22×C4⋊C4—431no—
370C2×#107C2×D4311yescharacteristic
371C2×#106C2×D4311yescharacteristic
372#417—438no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×C22⋊C8—431no—
382C2×#97—431no—
383C2×C4×C8—431no—
384#391—431no—
385#391—431no—
386#389—431no—
387#389—431no—
388#387—861no—
389#387—861no—
390#386—861no—
391#386—861no—
392#381—861no—
393#381—861no—
394#380C2×D4311yescharacteristic
395#380C2×D4311yescharacteristic
396C4×C4⋊C4—431no—
397C4×C4⋊C4—431no—
398C4×C22⋊C4—431no—
399C2×#95—861no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340C2×D4311yescharacteristic
405#340C2×D4311yescharacteristic
406#336—431no—
407#336—431no—
408C43#2258211yescharacteristic, complemented, Sylow
409C2×#41—434no—
410C2×#41—862no—
411C2×#41—862no—
412C2×#41—862no—
413C2×#41—1721no—
414C2×#41—1721no—
415C22×Q8—431no—
416C22×D4—431no—
417C22×D4—861no—
418C23×C4—861no—
419C23×C4—861no—
420C23×C4—861no—
421C23×C4—861no—
422C23×C4C22×D4311yescharacteristic
423C2×M16—41no—
424C2×M16—41no—
425C2×M16C4×D4314yescomplemented
426C22×C8—431no—
427C22×C8—431no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—1721no—
433C4×D4—1721no—
434#117—1724no—
435C2×C4⋊C4—434no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—862no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—431no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—861no—
456#107—41no—
457#106—41no—
458#103—434no—
459#103—434no—
460#103—1721no—
461#103—1721no—
462#102—434no—
463#102—434no—
464#102—862no—
465#102—862no—
466C22⋊C8—862no—
467#97—1721no—
468C4×C8—1721no—
469#95—21no—
470#95—21no—
471#95—431no—
472#95—431no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—861no—
482C24D4×D4311yescharacteristic
483#41—868no—
484#41—1724no—
485#41—1724no—
486#41—1724no—
487C2×Q8—432no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×D4—432no—
494C2×D4—432no—
495C2×D4—432no—
496C2×D4—864no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—1722no—
501C2×D4—1722no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—864no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—864no—
519C22×C4—3441no—
520C22×C4—3441no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4C2×C4×D4312yes—
530C22×C4D4×D4311yescharacteristic
531C22×C4#1062190212yes—
532C22×C4C23×D4311yescharacteristic
533M16—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8C2×C4×D4312yes—
545C2×C8C2×C4×D4312yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—432no—
555C4⋊C4—432no—
556C4⋊C4—864no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—862no—
564C22⋊C4—1722no—
565C22⋊C4—1722no—
566C22⋊C4—1721no—
567C42—861no—
568C42—861no—
569C42—861no—
570C42—861no—
571C42—1722no—
572C42—1722no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—862no—
580C23—862no—
581C23—862no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23#1306328712yes—
587C23C2×D4×D4311yescharacteristic
588Q8—862no—
589Q8—862no—
590Q8—1721no—
591Q8—1721no—
592D4—434no—
593D4—862no—
594D4—862no—
595D4—862no—
596D4—1728no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—432no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—3444no—
631C2×C4—3444no—
632C2×C4—1728no—
633C2×C4—1728no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4#1306328712yes—
641C2×C4C22×C4×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4C2×#1062190211yescharacteristic
645C2×C4#1306337011yescharacteristic
646C2×C4#1306337011yescharacteristic
647C8—22no—
648C8—22no—
649C8—1721no—
650C8—1721no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—864no—
659C22—1722no—
660C22—1722no—
661C22—1722no—
662C22—1722no—
663C22—1722no—
664C22—1722no—
665C22C2×#1306328711yescharacteristic
666C22#1458353811yescharacteristic
667C22#1458353811yescharacteristic
668C22AGL(1,ℤ/8)×D4311yescharacteristic
669C22#1458369811yescharacteristic
670C22#1458370911yescharacteristic
671C22#1458371511yescharacteristic
672C4—22no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—862no—
678C4—1721no—
679C4—1721no—
680C4—1722no—
681C4—1721no—
682C4—1722no—
683C4—1722no—
684C4#117×D4311yescharacteristic
685C4#1458337211yescharacteristic
686C4#1458357611yescharacteristic
687C4#1458357611yescharacteristic
688C2—42no—
689C2—1724no—
690C2#1913744111yescharacteristic
691C2#1914340211yescharacteristic
692C2#1914343611yescharacteristic
693C2#1914655111yescharacteristic
694C2#1914668611yescharacteristic
695C2#1914680611yescharacteristic
696C2#1914689511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1809C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1809D43
hypocenterC43#22582
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. #19137466C2semidirect
4. #19135283C2semidirect
5. #19135269C2semidirect
6. #19135235C2semidirect
7. #19135228C2semidirect
8. #19134853C2semidirect
9. #19134839C2semidirect
10. #19134683C2semidirect
12. #19134419C2semidirect
13. #19134409C2semidirect
14. #19134376C2semidirect
15. C43×#1809C2semidirect
21. #14582901C4semidirect
82. C2×C4⋊Dic43C2×C4semidirect
95. #13063250C2×C4semidirect
96. #13063250C2×C4semidirect
119. C2×M16×C43C2×C4semidirect
290. D172#117semidirect
350. #1809D43semidirect
408. C43#22582semidirect
425. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829012
#191374662
#191374232
#191352832
#191352692
#191352352
#191352282
#191348532
#191348392
#191346832
#191345332
#191344192
#191344092
#191343762
C43×#18092
#2258243