Finite Group Databasebeta

← #25164657

Subgroups — #25164657

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#19138971C211yesmaximal, characteristic, complemented
2#19137611C211yesmaximal, characteristic
3#19135909C211yesmaximal, characteristic, complemented
4#19135785C211yesmaximal, characteristic
5#19135730C211yesmaximal, characteristic, complemented
6#19135596C211yesmaximal, characteristic
7#19135541C211yesmaximal, characteristic, complemented
8#19135268C211yesmaximal, characteristic, complemented
9#19135231C211yesmaximal, characteristic, complemented
10#19135204C211yesmaximal, characteristic, complemented
11#19135172C211yesmaximal, characteristic, complemented
12#19134926C211yesmaximal, characteristic, complemented
13#19134681C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×C4×C22⋊D43—21no—
21C2×#13063257C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582837—21no—
30#14582811—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582804—21no—
34#14582800C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582793—21no—
37#14582789—21no—
38#14582778—21no—
39#14582770—21no—
40#14582759C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C22⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621884—22no—
64C2×#10621884—41no—
65C2×#10621884—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324—41no—
70#13063299—22no—
71#13063299—22no—
72#13063287—22no—
73#13063287—41no—
74C4×C22⋊D43—44no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43D411yescharacteristic
82C2×C22⋊Dic43D411yescharacteristic
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063257—22no—
92Dic43⋊C8—41no—
93#13063249—22no—
94#13063247—22no—
95#13063247—41no—
96#13063245—22no—
97C22⋊(C43⋊C8)—41no—
98C8×Dic43—41no—
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
109C22×Q8×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—41no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—41no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124#103×C43—22no—
125#103×C43—41no—
126C22⋊C8×C43—41no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
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×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—81no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172#4112yes—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
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—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43#4112yes—
185C4⋊C4×C43#4112yes—
186C22⋊C4×C43—42no—
187C22⋊Dic43—41no—
188C22⋊Dic43—81no—
189C22⋊Dic43SD1614yescomplemented
190#10621884—44no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
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×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43C2×SD1612yes—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
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×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—84no—
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C22⋊D43—48no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C2×SD1612yes—
281C2×Dic43C2×SD1612yes—
282D172—22no—
283D172—22no—
284D172—41no—
285D172—41no—
286C4×D43—84no—
287Dic86—84no—
288C8×C43—41no—
289C8×C43—41no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292#26722—431nomaximal, Sylow
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43#52511yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43#54611yescharacteristic
303C22×C43C22×SD1611yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57811yescharacteristic
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—41no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#52911yescharacteristic
320C4×C43#53811yescharacteristic
321C4×C43#55511yescharacteristic
322C4×C43#55911yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—42no—
326Dic43—41no—
327Dic43—41no—
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#1927—431no—
339#1923—431no—
340#1919—431no—
341#1877—431no—
342#1872D4311yescharacteristic, complemented
343#1823—431no—
344C4×#102—431no—
345C2×C43—42no—
346C2×C43#245911yescharacteristic
347C2×C43#310111yescharacteristic
348C2×C43#312411yescharacteristic
349C2×C43#329511yescharacteristic
350C2×C43#329811yescharacteristic
351C2×C43#331311yescharacteristic
352C2×C43#332211yescharacteristic
353D43—82no—
354C22×SD16—431no—
355C2×C4⋊Q8—431no—
356C2×C22⋊Q8C2×D4311yescharacteristic
357C2×#121—431no—
358C2×C4×D4—431no—
359C2×C4×D4—861no—
360C22×C4⋊C4C2×D4311yescharacteristic
361C2×#106—431no—
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⋊C8C2×D4311yescharacteristic
371C2×C4×C8—431no—
372#400—861no—
373#393—861no—
374#391—431no—
375#391—431no—
376#391—861no—
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⋊C4—431no—
386C4×C22⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340C2×D4311yescharacteristic
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397C43#2672211yescharacteristic, complemented, Sylow
398C22×Q8—861no—
399C22×Q8C22×D4311yescharacteristic
400C22×D4—431no—
401C22×D4—861no—
402C23×C4—21no—
403C23×C4—861no—
404C23×C4C22×D4311yescharacteristic
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—22no—
415C22⋊Q8—41no—
416#121—862no—
417#121—862no—
418C4×D4—862no—
419C4×D4—1721no—
420C4×D4—1724no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42—861no—
445#106—862no—
446C4⋊C8—1721no—
447#103—22no—
448#103—41no—
449#103—862no—
450#102—862no—
451#102—862no—
452#102—1721no—
453C22⋊C8—41no—
454C22⋊C8—1721no—
455C4×C8—1721no—
456#95—431no—
457#95—431no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—861no—
467C24D4×D4311yescharacteristic
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—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—1722no—
508C22×C4—1722no—
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—42no—
529C4⋊C4—42no—
530C4⋊C4—432no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4#1062189812yes—
539C4⋊C4#1062190012yes—
540C22⋊C4—42no—
541C22⋊C4—434no—
542C22⋊C4—864no—
543C22⋊C4—3441no—
544C22⋊C4—3441no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1721no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—3441no—
553C42—1722no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—862no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23SD16×D4312yes—
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—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
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—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—432no—
600C2×C4—432no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—862no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—3444no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337011yescharacteristic
627C8—41no—
628C8—41no—
629C8—1721no—
630C8—1721no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458340711yescharacteristic
646C22#1458353611yescharacteristic
647C22#1458353911yescharacteristic
648C22C2×SD16×D4311yescharacteristic
649C22#1458369811yescharacteristic
650C22#1458370311yescharacteristic
651C22#1458371211yescharacteristic
652C4—42no—
653C4—42no—
654C4—41no—
655C4—81no—
656C4—81no—
657C4—862no—
658C4—862no—
659C4—3441no—
660C4—3441no—
661C4—1721no—
662C4—1722no—
663C4—1721no—
664C4#1458343111yescharacteristic
665C4#1458348111yescharacteristic
666C4#1458361311yescharacteristic
667C4#1458363211yescharacteristic
668C2—42no—
669C2—3442no—
670C2#1913853111yescharacteristic
671C2#1914460011yescharacteristic
672C2#1914486011yescharacteristic
673C2#1914641211yescharacteristic
674C2#1914645611yescharacteristic
675C2#1914665411yescharacteristic
676C2#1914679711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1872D43
hypocenterC43#26722
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. #19138971C2semidirect
3. #19135909C2semidirect
5. #19135730C2semidirect
7. #19135541C2semidirect
8. #19135268C2semidirect
9. #19135231C2semidirect
10. #19135204C2semidirect
11. #19135172C2semidirect
12. #19134926C2semidirect
13. #19134681C2semidirect
14. #19134409C2semidirect
15. C43×#1872C2semidirect
189. C22⋊Dic43SD16semidirect
342. #1872D43semidirect
397. C43#26722semidirect

Maximal subgroups

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

subgroupindex
#191389712
#191376112
#191359092
#191357852
#191357302
#191355962
#191355412
#191352682
#191352312
#191352042
#191351722
#191349262
#191346812
#191344092
C43×#18722
#2672243