Finite Group Databasebeta

← #25113830

Subgroups — #25113830

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582900C211yesmaximal, characteristic
2#19137474C211yesmaximal, characteristic, complemented
3#19137425C211yesmaximal, characteristic
4#19135282C211yesmaximal, characteristic, complemented
5#19135268C211yesmaximal, characteristic, complemented
6#19135239C211yesmaximal, characteristic, complemented
7#19135232C211yesmaximal, characteristic, complemented
8#19134854C211yesmaximal, characteristic, complemented
9#19134840C211yesmaximal, characteristic, complemented
10#19134682C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22#14582900C418yescomplemented
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582806C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582784—21no—
34#14582784—21no—
35#14582779—21no—
36#14582779—21no—
37#14582762—21no—
38#14582759C2211yescharacteristic
39#14582757—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C22⋊C4×Dic43—21no—
43C4×C22⋊Dic43C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C2×#10621877—41no—
64C2×#10621877—41no—
65C2×#10621877C2×C414yescomplemented
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71D4×Dic43—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43C2×C414yescomplemented
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43D411yescharacteristic
85C2×C22⋊Dic43D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—41no—
91#13063256—41no—
92#13063249C2×C414yescomplemented
93#13063249C2×C414yescomplemented
94#13063246C2×C414yes—
95#13063246C2×C414yes—
96#13063235—41no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C2×#41×C43—22no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—41no—
113C2×#41×C43—41no—
114C2×#41×C43C2×C414yes—
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125#103×C43—41no—
126#103×C43—41no—
127#102×C43—22no—
128#102×C43—22no—
129C22⋊C8×C43—22no—
130#95×C43—21no—
131C24×C43—21no—
132C24×C43C2×D411yescharacteristic
133#41×C43—28no—
134#41×C43—44no—
135#41×C43—44no—
136#41×C43—44no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—24no—
147C2×D4×C43—42no—
148C2×D4×C43—42no—
149C2×D4×C43C22×C412yes—
150C2×D4×C43#4112yes—
151C2×D4×C43#4112yes—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—24no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43C22×C412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4112yes—
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—24no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—42no—
174C22×Dic43—42no—
175C22×Dic43—81no—
176C22×Dic43—81no—
177C22×Dic43—81no—
178C22×Dic43—81no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C22⋊C4×C43—42no—
194C22⋊Dic43—22no—
195C22⋊Dic43—41no—
196C22⋊Dic43—42no—
197C22⋊Dic43—42no—
198C22⋊Dic43—81no—
199C4⋊Dic43—24no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C22×C412yes—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—81no—
209Dic43⋊C4—81no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—81no—
215C4×Dic43—81no—
216#10621877—44no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C22×C412yes—
222C2×C43⋊C8C22×C412yes—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43C4×D412yes—
237C23×C43C22×D411yescharacteristic
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—41no—
241Q8×C43—41no—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—48no—
246D4×C43#11714yes—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—48no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43C4×D412yes—
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43H(5,𝔽2)11yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—84no—
294C2×Dic43—84no—
295C2×Dic43—84no—
296C2×Dic43#13712yes—
297C8×C43—41no—
298C8×C43—41no—
299C43⋊C8—22no—
300C43⋊C8—22no—
301#22578—431nomaximal, Sylow
302C22×C43—24no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—41no—
307C22×C43—42no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—41no—
311C22×C43—42no—
312C22×C43—41no—
313C22×C43—42no—
314C22×C43—41no—
315C22×C43—42no—
316C22×C43C2×C4×D411yescharacteristic
317C22×C43#54611yescharacteristic
318C22×C43#54611yescharacteristic
319C22×C43C2×#13711yescharacteristic
320C22×C43#57511yescharacteristic
321C22×C43#57611yescharacteristic
322C22×C43#57711yescharacteristic
323C4×C43—22no—
324C4×C43—42no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43C2×#11711yescharacteristic
328C4×C43#51811yescharacteristic
329C4×C43#55111yescharacteristic
330C4×C43#55111yescharacteristic
331Dic43—22no—
332Dic43—41no—
333Dic43—42no—
334Dic43—42no—
335Dic43—41no—
336Dic43—41no—
337Dic43—81no—
338Dic43—81no—
339C2×#417—431no—
340#2345—431no—
341#2339—431no—
342#1935—431no—
343#1933—431no—
344#1928—431no—
345#1927—431no—
346#1864—431no—
347#1862—431no—
348#1823—431no—
349#1809—431no—
350#1788D4311yescharacteristic
351#1762—431no—
352C4×#102—431no—
353#1753—431no—
354C2×C43—42no—
355C2×C43—44no—
356C2×C43#234211yescharacteristic
357C2×C43C4×#13711yescharacteristic
358C2×C43#294611yescharacteristic
359C2×C43#330711yescharacteristic
360C2×C43#331411yescharacteristic
361C2×C43#332211yescharacteristic
362C2×C43#333111yescharacteristic
363C22×#41C2×D4311yescharacteristic
364C22×M16—431no—
365C2×C4×D4—431no—
366C2×C4×D4—431no—
367C22×C4⋊C4—431no—
368C2×#107—431no—
369C2×#106—431no—
370#417—438no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103C2×D4311yescharacteristic
374C2×#103C2×D4311yescharacteristic
375C2×#102—431no—
376C2×#102—431no—
377C2×#102C2×D4311yescharacteristic
378C2×#102C2×D4311yescharacteristic
379C2×C22⋊C8C2×D4311yescharacteristic
380C2×#97—431no—
381C2×C4×C8—431no—
382#391—431no—
383#391—431no—
384#389—431no—
385#389—431no—
386#387—861no—
387#387—861no—
388#386—861no—
389#386—861no—
390#381—861no—
391#380—431no—
392#380—861no—
393#380C2×D4311yescharacteristic
394C4×C4⋊C4—431no—
395C4×C4⋊C4—431no—
396C4×C22⋊C4—431no—
397C4×C22⋊C4—861no—
398C2×#95—861no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#336—431no—
406#336—431no—
407C43#2257811yescharacteristic, complemented, Sylow
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—41no—
412C2×#41—41no—
413C2×#41C4×D4314yes—
414C22×Q8C22×D4311yescharacteristic
415C22×D4—21no—
416C22×D4C22×D4311yescharacteristic
417C23×C4—21no—
418C23×C4—861no—
419C23×C4—861no—
420C23×C4—861no—
421C23×C4C22×D4311yescharacteristic
422C2×M16—434no—
423C2×M16—1721no—
424C2×M16—1721no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—1721no—
432C4×D4—1721no—
433C2×C4⋊C4—434no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
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×C22⋊C4—21no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4—431no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—861no—
453C2×C42—861no—
454#107—1721no—
455#106—1721no—
456#103—41no—
457#103—41no—
458#103—434no—
459#103—434no—
460#102—22no—
461#102—22no—
462#102—434no—
463#102—434no—
464C22⋊C8—22no—
465#97—1721no—
466C4×C8—1721no—
467#95—21no—
468#95—431no—
469#95—431no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—21no—
480C24D4×D4311yescharacteristic
481#41—28no—
482#41—44no—
483#41—44no—
484#41—44no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C2×C4×D4312yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C2×C4×D4312yes—
498C2×D4#1062190012yes—
499C2×D4#1062190012yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—42no—
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—861no—
519C22×C4—3441no—
520C22×C4—3441no—
521C22×C4—3441no—
522C22×C4—3441no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4C2×C4×D4312yes—
528C22×C4D4×D4311yescharacteristic
529C22×C4#1062190012yes—
530C22×C4C23×D4311yescharacteristic
531M16—1724no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—432no—
539C2×C8—432no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—432no—
549C4⋊C4—432no—
550C4⋊C4—864no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—3441no—
558C4⋊C4—3441no—
559C22⋊C4—42no—
560C22⋊C4—862no—
561C22⋊C4—3441no—
562C22⋊C4—1721no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—861no—
566C42—861no—
567C42—861no—
568C42—861no—
569C42—3441no—
570C42—3441no—
571C23—22no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23(C22⋊D43)⋊C412yes—
585C23C2×D4×D4311yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4#1306328114yes—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—48no—
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—432no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—3444no—
626C2×C4—3444no—
627C2×C4—3444no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4(C22⋊D43)⋊C412yes—
639C2×C4C22×C4×D4311yescharacteristic
640C2×C4C2×#1062190011yescharacteristic
641C2×C4C2×#1062190011yescharacteristic
642C2×C4C2×#1062190011yescharacteristic
643C2×C4#1306337011yescharacteristic
644C2×C4#1306337011yescharacteristic
645C8—41no—
646C8—41no—
647C8—862no—
648C8—862no—
649C22—22no—
650C22—22no—
651C22—24no—
652C22—22no—
653C22—42no—
654C22—42no—
655C22—41no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—42no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22C2×(C22⋊D43)⋊C411yescharacteristic
664C22#1458353611yescharacteristic
665C22#1458353611yescharacteristic
666C22#137×D4311yescharacteristic
667C22#1458369511yescharacteristic
668C22#1458370111yescharacteristic
669C22#1458370611yescharacteristic
670C4—22no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—862no—
675C4—3441no—
676C4—3441no—
677C4—1722no—
678C4—1722no—
679C4—1721no—
680C4—1721no—
681C4—1721no—
682C4C2×#1306328111yescharacteristic
683C4#1458337211yescharacteristic
684C4#1458358011yescharacteristic
685C4#1458358011yescharacteristic
686C2—42no—
687C2—44no—
688C2#1913744611yescharacteristic
689C2#1914341911yescharacteristic
690C2#1914343011yescharacteristic
691C2#1914656411yescharacteristic
692C2#1914666911yescharacteristic
693C2#1914678911yescharacteristic
694C2#1914690411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22578
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. #19137474C2semidirect
4. #19135282C2semidirect
5. #19135268C2semidirect
6. #19135239C2semidirect
7. #19135232C2semidirect
8. #19134854C2semidirect
9. #19134840C2semidirect
10. #19134682C2semidirect
11. #19134626C2semidirect
12. #19134422C2semidirect
13. #102×Dic43C2semidirect
14. #19134381C2semidirect
22. #14582900C4semidirect
65. C2×#10621877C2×C4semidirect
74. C2×C4⋊Dic43C2×C4semidirect
92. #13063249C2×C4semidirect
93. #13063249C2×C4semidirect
407. C43#22578semidirect

Maximal subgroups

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

subgroupindex
C2×#145829002
#191374742
#191374252
#191352822
#191352682
#191352392
#191352322
#191348542
#191348402
#191346822
#191346262
#191344222
#102×Dic432
#191343812
C43×#17882
#2257843