Finite Group Databasebeta

← #25164587

Subgroups — #25164587

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138376C211yesmaximal, characteristic
2#19137690C211yesmaximal, characteristic, complemented
3#19136094C211yesmaximal, characteristic, complemented
4#19135834C211yesmaximal, characteristic
5#19135745C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic
7#19135526C211yesmaximal, characteristic
8#19135284C211yesmaximal, characteristic, complemented
9#19135230C211yesmaximal, characteristic, complemented
10#19135228C211yesmaximal, characteristic, complemented
11#19135224C211yesmaximal, characteristic
12#19135172C211yesmaximal, characteristic, complemented
13#19135157C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic
15C43×#1864C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×#13063257C2211yescharacteristic
19C2×Dic43⋊C8C2211yescharacteristic
20C2×#13063250C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063236C2211yescharacteristic
27#14582827—21no—
28#14582827—21no—
29#14582805C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582794—21no—
35#14582784—21no—
36#14582781—21no—
37#14582772—21no—
38#14582762—21no—
39C4⋊C4×Dic43—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063316—22no—
63#13063316—22no—
64#13063312—22no—
65#13063312—41no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4D411yescharacteristic
74C2×Dic43⋊C4D411yescharacteristic
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063257—22no—
85Dic43⋊C8—41no—
86#13063250—22no—
87#13063250—22no—
88#13063248—22no—
89#13063248—41no—
90#13063246—22no—
91#13063246—22no—
92#13063236—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#106×C43—41no—
117#102×C43—22no—
118#102×C43—22no—
119#95×C43—21no—
120C24×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43—81no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43#4112yes—
163C22⋊C4×C43—42no—
164C42×C43—21no—
165C42×C43—21no—
166C22⋊Dic43—42no—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169C22⋊Dic43—81no—
170C4⋊Dic43—24no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43#4112yes—
176C4⋊Dic43#4112yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—41no—
179Dic43⋊C4—41no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—42no—
187C4×Dic43—81no—
188C4×Dic43—81no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203D4×C43—22no—
204D4×C43—22no—
205D4×C43—41no—
206D4×C43—41no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—84no—
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—22no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—22no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—41no—
256Dic86—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#26717—431nomaximal, Sylow
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43#52511yescharacteristic
270C22×C43#54611yescharacteristic
271C22×C43#54811yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57511yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57711yescharacteristic
276C4×C43—42no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#52911yescharacteristic
282C4×C43#54211yescharacteristic
283C4×C43#55211yescharacteristic
284C4×C43#55911yescharacteristic
285Dic43—41no—
286Dic43—42no—
287Dic43—41no—
288Dic43—42no—
289Dic43—41no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293#2447—431no—
294#2370—431no—
295#2088—431no—
296#2042—431no—
297#2026—431no—
298#2025—431no—
299#1983—431no—
300#1935—431no—
301#1927—431no—
302#1927—431no—
303#1926—431no—
304#1919—431no—
305#1917—431no—
306#1864D4311yescharacteristic
307#1762—431no—
308C2×C43—82no—
309C2×C43#245811yescharacteristic
310C2×C43#311111yescharacteristic
311C2×C43#312511yescharacteristic
312C2×C43#330711yescharacteristic
313C2×C43#332311yescharacteristic
314C2×C43#337111yescharacteristic
315C2×C43#337611yescharacteristic
316C2×#125—431no—
317C2×#124—431no—
318C2×C4×D4C2×D4311yescharacteristic
319C2×#106—431no—
320C2×#106C2×D4311yescharacteristic
321C2×C4⋊C8—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#102—431no—
327C2×#102—431no—
328C2×#102C2×D4311yescharacteristic
329C2×#102C2×D4311yescharacteristic
330C2×#97—431no—
331#397—861no—
332#397—861no—
333#391—431no—
334#391—431no—
335#390—431no—
336#389—431no—
337#389—431no—
338#389—861no—
339#389C2×D4311yescharacteristic
340#387—861no—
341#387—861no—
342#385—861no—
343#381—861no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—861no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340C2×D4311yescharacteristic
355#336—431no—
356#336—431no—
357#336—431no—
358#336C2×D4311yescharacteristic
359C43#2671711yescharacteristic, complemented, Sylow
360C22×Q8—431no—
361C22×D4C22×D4311yescharacteristic
362C23×C4—21no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367#125—862no—
368#125—862no—
369#124—862no—
370#124—1721no—
371C4×D4—22no—
372C4×D4—41no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—431no—
392C2×C42—431no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42C22×D4311yescharacteristic
397#106—41no—
398#106—862no—
399C4⋊C8—1721no—
400#103—862no—
401#103—862no—
402#103—862no—
403#103—1721no—
404#102—22no—
405#102—22no—
406#102—862no—
407#102—862no—
408#97—1721no—
409#95—21no—
410#95—431no—
411#95—431no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421C24—21no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4#1062190012yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—864no—
472C4⋊C4—864no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4#1062189812yes—
482C22⋊C4—42no—
483C22⋊C4—3441no—
484C22⋊C4—1722no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—861no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—3441no—
494C42—3441no—
495C42—1722no—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C2×D4×D4311yescharacteristic
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—84no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—862no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4#41×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4C2×#1062190011yescharacteristic
555C2×C4C2×#1062189811yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—41no—
559C8—41no—
560C8—1721no—
561C8—1721no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1458340811yescharacteristic
570C22#1458353611yescharacteristic
571C22#1458355911yescharacteristic
572C22#1458369511yescharacteristic
573C22#1458369511yescharacteristic
574C22#1458370511yescharacteristic
575C22#1458370611yescharacteristic
576C4—41no—
577C4—41no—
578C4—42no—
579C4—81no—
580C4—81no—
581C4—3441no—
582C4—3441no—
583C4—1721no—
584C4—1721no—
585C4—1722no—
586C4—1721no—
587C4—1722no—
588C4—1721no—
589C4#1458342611yescharacteristic
590C4#1458351911yescharacteristic
591C4#1458358411yescharacteristic
592C4#1458363211yescharacteristic
593C2—82no—
594C2#1913852111yescharacteristic
595C2#1914470011yescharacteristic
596C2#1914487811yescharacteristic
597C2#1914656411yescharacteristic
598C2#1914681511yescharacteristic
599C2#1914737011yescharacteristic
600C2#1914742511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1864D43
hypocenterC43#26717
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #19137690C2semidirect
3. #19136094C2semidirect
5. #19135745C2semidirect
8. #19135284C2semidirect
9. #19135230C2semidirect
10. #19135228C2semidirect
12. #19135172C2semidirect
13. #19135157C2semidirect
359. C43#26717semidirect

Maximal subgroups

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

subgroupindex
#191383762
#191376902
#191360942
#191358342
#191357452
#191357392
#191355262
#191352842
#191352302
#191352282
#191352242
#191351722
#191351572
#191344202
C43×#18642
#2671743