Finite Group Databasebeta

← #25200151

Subgroups — #25200151

Order 11008.

850 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#19142935C211yesmaximal, characteristic, complemented
2#19137101C211yesmaximal, characteristic
3#19135791C211yesmaximal, characteristic, complemented
4#19135784C211yesmaximal, characteristic
5#19135600C211yesmaximal, characteristic
6#19135447C211yesmaximal, characteristic, complemented
7#19135322C211yesmaximal, characteristic, complemented
8#19135279C211yesmaximal, characteristic, complemented
9#19135269C211yesmaximal, characteristic, complemented
10#19135227C211yesmaximal, characteristic, complemented
11#19135182C211yesmaximal, characteristic, complemented
12#19134930C211yesmaximal, characteristic, complemented
13#19134857C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#2077C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C22×C4×Dic43C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582788—21no—
40#14582784—21no—
41#14582784—21no—
42#14582776—21no—
43#14582774—21no—
44#14582760—21no—
45C4⋊C4×Dic43C2211yescharacteristic
46#14582746—21no—
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063304—41no—
71#13063304—41no—
72#13063299—22no—
73#13063299—22no—
74#13063287—41no—
75#13063287—41no—
76(C22⋊D43)⋊C4—44no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—41no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063256—22no—
96#13063256—41no—
97#13063250—22no—
98#13063248—22no—
99#13063248—41no—
100#13063247—41no—
101#13063245—22no—
102#13063245—22no—
103C22⋊(C43⋊C8)—22no—
104C8×Dic43—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—
114C23×C4×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123#106×C43—22no—
124C22⋊C8×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43SD1614yescomplemented
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172#4112yes—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43#4112yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—42no—
188C22⋊Dic43—42no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43—42no—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—41no—
206C4×Dic43—41no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8#4112yes—
214#10621873—44no—
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—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C22⋊D43—48no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—44no—
267C2×Dic43—44no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43C2×SD1612yes—
277C2×Dic43C2×SD1612yes—
278C2×Dic43#13512yes—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283C4×D43—84no—
284Dic86—41no—
285Dic86—41no—
286Dic86—41no—
287Dic86—41no—
288C8×C43—22no—
289C8×C43—41no—
290C43⋊C8—22no—
291C43⋊C8—41no—
292#29464—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#53211yescharacteristic
302C22×C43#53411yescharacteristic
303C22×C43C22×SD1611yescharacteristic
304C22×C43C2×#13511yescharacteristic
305C22×C43#57511yescharacteristic
306C22×C43#57511yescharacteristic
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—81no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#55111yescharacteristic
320C4×C43#55311yescharacteristic
321C4×C43#55311yescharacteristic
322C4×C43#55911yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330#2855—431no—
331C4×#121—431no—
332#2077D4311yescharacteristic, complemented
333#2035—431no—
334#2034—431no—
335#2000—431no—
336#1968—431no—
337#1941—431no—
338#1934—431no—
339#1933—431no—
340#1927—431no—
341#1920—431no—
342#1877—431no—
343#1864—431no—
344C4×C22⋊C8—431no—
345C2×C43—42no—
346C2×C43#260211yescharacteristic
347C2×C43#310111yescharacteristic
348C2×C43#310211yescharacteristic
349C2×C43#316711yescharacteristic
350C2×C43#318311yescharacteristic
351C2×C43#318711yescharacteristic
352C2×C43#319111yescharacteristic
353D43—82no—
354C22×SD16—431no—
355C2×C22⋊Q8—431no—
356C2×#121—431no—
357C2×C4×D4—431no—
358C2×C4×D4—861no—
359C22×C42—431no—
360C2×#106—431no—
361C2×#106—431no—
362C2×#106C2×D4311yescharacteristic
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×C22⋊C8—431no—
370C2×C22⋊C8C2×D4311yescharacteristic
371C2×C4×C8—431no—
372C2×C4×C8—431no—
373#391—431no—
374#391—431no—
375#390—431no—
376#389—431no—
377#389—431no—
378#389—431no—
379#388—861no—
380#387—861no—
381#387—861no—
382#386—861no—
383#385—861no—
384#381—861no—
385#380C2×D4311yescharacteristic
386#380C2×D4311yescharacteristic
387C4×C4⋊C4—431no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#340C2×D4311yescharacteristic
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397C43#2946411yescharacteristic, complemented, Sylow
398C22×Q8—431no—
399C22×D4—431no—
400C22×D4—861no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—861no—
404C23×C4C22×D4311yescharacteristic
405C2×SD16—862no—
406C2×SD16—862no—
407C2×SD16—1721no—
408C22×C8—431no—
409C22×C8—431no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C22⋊Q8—1721no—
413C22⋊Q8—1721no—
414#121—862no—
415#121—862no—
416C4×D4—1721no—
417C4×D4—1721no—
418C4×D4—1724no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42—1721no—
442C2×C42—1721no—
443#106—22no—
444#106—862no—
445#106—1721no—
446#103—862no—
447#103—862no—
448#103—1721no—
449#102—862no—
450#102—862no—
451#102—1721no—
452C22⋊C8—22no—
453C22⋊C8—862no—
454C4×C8—1721no—
455C4×C8—1721no—
456#95—21no—
457#95—21no—
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—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×D4—432no—
475C2×D4—864no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—1722no—
482C2×D4—1722no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—434no—
497C22×C4—431no—
498C22×C4—862no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
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—432no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8#1062190012yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—432no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—864no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C42—861no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—1721no—
552C42—1721no—
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—1721no—
570Q8—1721no—
571Q8—1721no—
572Q8—1721no—
573D4—862no—
574D4—862no—
575D4—1728no—
576D4—1721no—
577D4—1721no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
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—432no—
598C2×C4—432no—
599C2×C4—432no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—862no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—3444no—
611C2×C4—1724no—
612C2×C4—1724no—
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×C4#41×D4311yescharacteristic
624C2×C4C2×#1062190011yescharacteristic
625C2×C4#1306337111yescharacteristic
626C2×C4#1306337111yescharacteristic
627C8—22no—
628C8—41no—
629C8—862no—
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#1458344411yescharacteristic
647C22#1458346011yescharacteristic
648C22C2×SD16×D4311yescharacteristic
649C22#135×D4311yescharacteristic
650C22#1458369511yescharacteristic
651C22#1458369811yescharacteristic
652C4—41no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—862no—
658C4—862no—
659C4—862no—
660C4—3441no—
661C4—3441no—
662C4—1722no—
663C4—1721no—
664C4#1458357211yescharacteristic
665C4#1458360011yescharacteristic
666C4#1458360011yescharacteristic
667C4#1458363111yescharacteristic
668C2—42no—
669C2—3442no—
670C2#1914020211yescharacteristic
671C2#1914460011yescharacteristic
672C2#1914460811yescharacteristic
673C2#1914514911yescharacteristic
674C2#1914531711yescharacteristic
675C2#1914535411yescharacteristic
676C2#1914539011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2077C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2077D43
hypocenterC43#29464
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. #19142935C2semidirect
3. #19135791C2semidirect
6. #19135447C2semidirect
7. #19135322C2semidirect
8. #19135279C2semidirect
9. #19135269C2semidirect
10. #19135227C2semidirect
11. #19135182C2semidirect
12. #19134930C2semidirect
13. #19134857C2semidirect
14. C22⋊C8×Dic43C2semidirect
15. C43×#2077C2semidirect
152. C22×Dic43SD16semidirect
332. #2077D43semidirect
397. C43#29464semidirect

Maximal subgroups

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

subgroupindex
#191429352
#191371012
#191357912
#191357842
#191356002
#191354472
#191353222
#191352792
#191352692
#191352272
#191351822
#191349302
#191348572
C22⋊C8×Dic432
C43×#20772
#2946443