Finite Group Databasebeta

← #25164616

Subgroups — #25164616

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138395C211yesmaximal, characteristic
2#19137696C211yesmaximal, characteristic, complemented
3#19135836C211yesmaximal, characteristic
4#19135745C211yesmaximal, characteristic, complemented
5#19135740C211yesmaximal, characteristic
6#19135525C211yesmaximal, characteristic
7#19135290C211yesmaximal, characteristic
8#19135234C211yesmaximal, characteristic, complemented
9#19135214C211yesmaximal, characteristic
10#19135213C211yesmaximal, characteristic
11#19135184C211yesmaximal, characteristic, complemented
12#19135156C211yesmaximal, characteristic, complemented
13#19134846C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#2086C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×#13063313C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063250C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29#14582834—21no—
30#14582828—21no—
31#14582804C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582795—21no—
35#14582795C2211yescharacteristic
36#14582789—21no—
37#14582788—21no—
38#14582784—21no—
39#14582780—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582750—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063316—22no—
64#13063316—22no—
65#13063313—22no—
66#13063313—41no—
67#13063290—22no—
68#13063290—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4D411yescharacteristic
76C2×Dic43⋊C4D411yescharacteristic
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063258—22no—
90#13063250—22no—
91#13063250—22no—
92#13063248—22no—
93#13063248—22no—
94#13063247—22no—
95#13063247—22no—
96#13063245—22no—
97#13063245—41no—
98#13063235—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—41no—
117C4⋊C8×C43—41no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86#4112yes—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—81no—
161C4⋊C4×C43—81no—
162C4⋊C4×C43#4112yes—
163C42×C43—21no—
164C42×C43—21no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—42no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—81no—
170(C2×D43)⋊C4—81no—
171C4⋊Dic43—24no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43#4112yes—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—41no—
178Dic43⋊C4—41no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—42no—
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×C43C22×D411yescharacteristic
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C2×C4×C43—22no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252Dic86—22no—
253Dic86—22no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#26719—431nomaximal, Sylow
261C22×C43#52511yescharacteristic
262C22×C43#54611yescharacteristic
263C22×C43#54811yescharacteristic
264C22×C43#57511yescharacteristic
265C22×C43#57511yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57811yescharacteristic
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—42no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#52911yescharacteristic
282C4×C43#54211yescharacteristic
283C4×C43#55211yescharacteristic
284C4×C43#55911yescharacteristic
285Dic43—41no—
286Dic43—42no—
287Dic43—42no—
288Dic43—41no—
289Dic43—42no—
290Dic43—41no—
291Dic43—41no—
292#2448—431no—
293#2370—431no—
294#2086D4311yescharacteristic, complemented
295#2042—431no—
296#2026—431no—
297#2025—431no—
298#1983—431no—
299#1936—431no—
300#1928—431no—
301#1925—431no—
302#1925—431no—
303#1921—431no—
304#1917—431no—
305#1863—431no—
306#1763—431no—
307C2×C43#245811yescharacteristic
308C2×C43#311111yescharacteristic
309C2×C43#312411yescharacteristic
310C2×C43#330911yescharacteristic
311C2×C43#332711yescharacteristic
312C2×C43#337011yescharacteristic
313C2×C43#337711yescharacteristic
314D43—161no—
315C2×#125—431no—
316C2×#124—431no—
317C2×C4×Q8—431no—
318C2×#107—431no—
319C2×#107C2×D4311yescharacteristic
320C2×C4⋊C8C2×D4311yescharacteristic
321C2×#103—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#102—431no—
326C2×#102—431no—
327C2×#102—431no—
328C2×#102—431no—
329C2×#97—431no—
330#399—861no—
331#397—861no—
332#391—431no—
333#390—431no—
334#390—431no—
335#389—431no—
336#389—861no—
337#389C2×D4311yescharacteristic
338#389C2×D4311yescharacteristic
339#388—861no—
340#388—861no—
341#387—861no—
342#387—861no—
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—861no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354#336—431no—
355#336—431no—
356#336—431no—
357#336—431no—
358C43#2671911yescharacteristic, complemented, Sylow
359C22×Q8—431no—
360C22×D4—431no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365#125—862no—
366#125—862no—
367#124—862no—
368#124—1721no—
369C4×Q8—862no—
370C4×Q8—1721no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
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×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#107—41no—
399#107—862no—
400C4⋊C8—41no—
401#103—862no—
402#103—862no—
403#103—862no—
404#103—862no—
405#102—862no—
406#102—862no—
407#102—862no—
408#102—1721no—
409#97—1721no—
410#95—21no—
411#95—21no—
412#95—431no—
413#95—431no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420C24—861no—
421C2×Q8—432no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4D4×D4311yescharacteristic
445C22×C4D4×D4311yescharacteristic
446C22×C4C23×D4311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—432no—
469C4⋊C4—432no—
470C4⋊C4—864no—
471C4⋊C4—864no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4#1062190212yes—
479C22⋊C4—3441no—
480C22⋊C4—3441no—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C22⋊C4—1722no—
485C42—21no—
486C42—21no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42—3441no—
492C42—3441no—
493C42—1722no—
494C42—1722no—
495C23—1721no—
496C23—1721no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23—1721no—
501C23—1721no—
502C23C2×D4×D4311yescharacteristic
503Q8—862no—
504Q8—862no—
505Q8—1721no—
506Q8—1721no—
507D4—1721no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
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—41no—
528C2×C4—41no—
529C2×C4—862no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—862no—
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—861no—
543C2×C4—862no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4#41×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4#41×D4311yescharacteristic
553C2×C4C2×#1062190211yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337311yescharacteristic
556C8—41no—
557C8—41no—
558C8—1721no—
559C8—1721no—
560C22—3441no—
561C22—3441no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22#1458341211yescharacteristic
568C22#1458353811yescharacteristic
569C22#1458355911yescharacteristic
570C22#1458369611yescharacteristic
571C22#1458369811yescharacteristic
572C22#1458370011yescharacteristic
573C22#1458371511yescharacteristic
574C4—41no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—1721no—
581C4—1722no—
582C4—1722no—
583C4—1721no—
584C4—1721no—
585C4—1721no—
586C4—1722no—
587C4#1458343411yescharacteristic
588C4#1458352311yescharacteristic
589C4#1458358111yescharacteristic
590C4#1458363311yescharacteristic
591C2—6881no—
592C2#1913852011yescharacteristic
593C2#1914471111yescharacteristic
594C2#1914486211yescharacteristic
595C2#1914660711yescharacteristic
596C2#1914685811yescharacteristic
597C2#1914735511yescharacteristic
598C2#1914743511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2086C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2086D43
hypocenterC43#26719
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

Complements

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

NH ≅ G/Ntype
2. #19137696C2semidirect
4. #19135745C2semidirect
8. #19135234C2semidirect
11. #19135184C2semidirect
12. #19135156C2semidirect
13. #19134846C2semidirect
14. #19134424C2semidirect
15. C43×#2086C2semidirect
294. #2086D43semidirect
358. C43#26719semidirect

Maximal subgroups

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

subgroupindex
#191383952
#191376962
#191358362
#191357452
#191357402
#191355252
#191352902
#191352342
#191352142
#191352132
#191351842
#191351562
#191348462
#191344242
C43×#20862
#2671943