Finite Group Databasebeta

← #25164663

Subgroups — #25164663

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138967C211yesmaximal, characteristic, complemented
2#19137613C211yesmaximal, characteristic
3#19135910C211yesmaximal, characteristic, complemented
4#19135786C211yesmaximal, characteristic
5#19135732C211yesmaximal, characteristic, complemented
6#19135597C211yesmaximal, characteristic
7#19135543C211yesmaximal, characteristic, complemented
8#19135273C211yesmaximal, characteristic, complemented
9#19135202C211yesmaximal, characteristic, complemented
10#19135175C211yesmaximal, characteristic, complemented
11#19134926C211yesmaximal, characteristic, complemented
12#19134899C211yesmaximal, characteristic, complemented
13#19134680C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1927C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×C4×D172—21no—
21C2×#13063287C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582841—21no—
32#14582812—21no—
33#14582806C2211yescharacteristic
34#14582803—21no—
35#14582801C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582791—21no—
38#14582790—21no—
39#14582777—21no—
40#14582773—21no—
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43C2311yescharacteristic
65C2×#10621884—22no—
66C2×#10621884—41no—
67C2×#10621884—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063325—22no—
71#13063325—41no—
72#13063301—22no—
73#13063301—41no—
74#13063300—22no—
75#13063300—22no—
76C4×D172—44no—
77#13063287—22no—
78#13063287—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—41no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C4⋊(C43⋊C8)—41no—
99#13063249—41no—
100#13063247—22no—
101#13063247—41no—
102#13063245—22no—
103(C2×D43)⋊C8—41no—
104(C2×D43)⋊C8—41no—
105C8×Dic43—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×Q8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#106×C43—22no—
122#103×C43—22no—
123#103×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127C23×D43—21no—
128C23×D43C2×D411yescharacteristic
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—24no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—42no—
155C2×D172—42no—
156C2×D172#4112yes—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×Dic86—42no—
170C2×Dic86—42no—
171C2×Dic86—81no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43#4112yes—
183C4⋊C4×C43#4112yes—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187#10621884—44no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4SD1614yescomplemented
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43—42no—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—81no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43C2×SD1612yes—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
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×C43C2×SD1612yes—
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43C2×SD1612yes—
276D172—22no—
277D172—22no—
278D172—48no—
279D172—41no—
280D172—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—41no—
285C4×D43—84no—
286C4×D43—84no—
287Dic86—84no—
288C8×C43—41no—
289C8×C43—41no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292#26722—431nomaximal, Sylow
293C22×C43#52511yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43C22×SD1611yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57811yescharacteristic
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—22no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43#52911yescharacteristic
321C4×C43#53811yescharacteristic
322C4×C43#55511yescharacteristic
323C4×C43#55911yescharacteristic
324Dic43—22no—
325Dic43—41no—
326Dic43—41no—
327Dic43—42no—
328Dic43—81no—
329Dic43—81no—
330#2492—431no—
331#2361—431no—
332#2055—431no—
333#2034—431no—
334#2023—431no—
335#2000—431no—
336#1987—431no—
337#1933—431no—
338#1927D4311yescharacteristic, complemented
339#1923—431no—
340#1919—431no—
341#1877—431no—
342#1872—431no—
343#1823—431no—
344C4×#102—431no—
345C2×C43#245911yescharacteristic
346C2×C43#310111yescharacteristic
347C2×C43#312411yescharacteristic
348C2×C43#329511yescharacteristic
349C2×C43#329811yescharacteristic
350C2×C43#331311yescharacteristic
351C2×C43#332211yescharacteristic
352D43—42no—
353D43—82no—
354C22×SD16—431no—
355C2×C4⋊Q8—431no—
356C2×C22⋊Q8—431no—
357C2×#121—431no—
358C2×C4×D4—431no—
359C2×C4×D4—861no—
360C22×C4⋊C4—431no—
361C2×#106C2×D4311yescharacteristic
362C2×C4⋊C8—431no—
363C2×#103—431no—
364C2×#103C2×D4311yescharacteristic
365C2×#103C2×D4311yescharacteristic
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×C22⋊C8—431no—
370C2×C22⋊C8—431no—
371C2×C4×C8—431no—
372#400—861no—
373#393—861no—
374#391—431no—
375#391—861no—
376#391C2×D4311yescharacteristic
377#390—431no—
378#389—431no—
379#388—861no—
380#388—861no—
381#386—861no—
382#385—861no—
383#380—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4C2×D4311yescharacteristic
386C4×C22⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#336—431no—
396#336C2×D4311yescharacteristic
397C43#2672211yescharacteristic, complemented, Sylow
398C22×Q8—861no—
399C22×Q8C22×D4311yescharacteristic
400C22×D4—431no—
401C22×D4—861no—
402C23×C4—431no—
403C23×C4—861no—
404C23×C4—861no—
405C2×SD16—862no—
406C2×SD16—1721no—
407C2×SD16—1721no—
408C22×C8—431no—
409C22×C8—431no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C4⋊Q8—862no—
413C4⋊Q8—1721no—
414C22⋊Q8—862no—
415C22⋊Q8—1721no—
416#121—862no—
417#121—862no—
418C4×D4—862no—
419C4×D4—1724no—
420C4×D4—1721no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—1721no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—431no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#106—22no—
446C4⋊C8—1721no—
447#103—22no—
448#103—22no—
449#103—1721no—
450#102—862no—
451#102—862no—
452#102—1721no—
453C22⋊C8—1721no—
454C22⋊C8—1721no—
455C4×C8—1721no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—431no—
460#95—431no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—431no—
467C24—861no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—3441no—
475C2×Q8—1722no—
476C2×Q8—1722no—
477C2×D4—432no—
478C2×D4—864no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—1722no—
485C2×D4—1722no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—3441no—
503C22×C4—3441no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—1724no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—432no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4#1062189812yes—
539C4⋊C4#1062190012yes—
540C22⋊C4—434no—
541C22⋊C4—864no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—1721no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—861no—
552C42—861no—
553C42—3441no—
554C23—432no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23—862no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23C2×D4×D4311yescharacteristic
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—3444no—
574D4—862no—
575D4—862no—
576D4—1728no—
577D4—1721no—
578D4—1721no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—432no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—862no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—3444no—
607C2×C4—3444no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4SD16×D4312yes—
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4#1306337111yescharacteristic
626C2×C4#1306337111yescharacteristic
627C8—41no—
628C8—41no—
629C8—1721no—
630C8—1721no—
631C22—862no—
632C22—862no—
633C22—862no—
634C22—3441no—
635C22—3441no—
636C22—3441no—
637C22—3441no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22#1458340911yescharacteristic
646C22#1458354111yescharacteristic
647C22#1458354511yescharacteristic
648C22C2×SD16×D4311yescharacteristic
649C22#1458369811yescharacteristic
650C22#1458370111yescharacteristic
651C22#1458371511yescharacteristic
652C4—22no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—862no—
659C4—3441no—
660C4—3441no—
661C4—1722no—
662C4—1721no—
663C4—1721no—
664C4#1458342711yescharacteristic
665C4#1458348811yescharacteristic
666C4#1458361411yescharacteristic
667C4#1458363111yescharacteristic
668C2—3442no—
669C2—1722no—
670C2#1913853711yescharacteristic
671C2#1914460211yescharacteristic
672C2#1914485611yescharacteristic
673C2#1914642111yescharacteristic
674C2#1914645811yescharacteristic
675C2#1914666611yescharacteristic
676C2#1914679411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1927D43
hypocenterC43#26722
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
1. #19138967C2semidirect
3. #19135910C2semidirect
5. #19135732C2semidirect
7. #19135543C2semidirect
8. #19135273C2semidirect
9. #19135202C2semidirect
10. #19135175C2semidirect
11. #19134926C2semidirect
12. #19134899C2semidirect
13. #19134680C2semidirect
14. #19134409C2semidirect
15. C43×#1927C2semidirect
195. (C2×D43)⋊C4SD16semidirect
338. #1927D43semidirect
397. C43#26722semidirect

Maximal subgroups

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

subgroupindex
#191389672
#191376132
#191359102
#191357862
#191357322
#191355972
#191355432
#191352732
#191352022
#191351752
#191349262
#191348992
#191346802
#191344092
C43×#19272
#2672243