Finite Group Databasebeta

← #25164618

Subgroups — #25164618

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#19138389C211yesmaximal, characteristic
2#19137693C211yesmaximal, characteristic, complemented
3#19136083C211yesmaximal, characteristic, complemented
4#19135831C211yesmaximal, characteristic
5#19135744C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic
7#19135294C211yesmaximal, characteristic
8#19135239C211yesmaximal, characteristic, complemented
9#19135218C211yesmaximal, characteristic
10#19135217C211yesmaximal, characteristic
11#19135187C211yesmaximal, characteristic, complemented
12#19135156C211yesmaximal, characteristic, complemented
13#19134851C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1983C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063235C2211yescharacteristic
25#14582835—21no—
26#14582824—21no—
27#14582806C2211yescharacteristic
28#14582802C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582787—21no—
35#14582787—21no—
36#14582783—21no—
37#14582782—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×Dic43⋊C4C2211yescharacteristic
41C4×C4⋊Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61#13063316—22no—
62#13063316—22no—
63Q8×Dic43—22no—
64Q8×Dic43—41no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
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×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063259—41no—
87#13063258—22no—
88#13063249—22no—
89#13063249—22no—
90#13063246—22no—
91#13063246—41no—
92#13063235—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×Q8×C43C2311yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106#124×C43—22no—
107#124×C43—41no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—41no—
115#103×C43—22no—
116#103×C43—22no—
117#102×C43—22no—
118#102×C43—22no—
119#95×C43—21no—
120C24×C43—21no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43#4112yes—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
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#4112yes—
156C4⋊C4×C43#4112yes—
157C22⋊C4×C43—42no—
158C22⋊C4×C43—42no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—42no—
162C22⋊Dic43—42no—
163C22⋊Dic43—42no—
164C22⋊Dic43—81no—
165C22⋊Dic43—81no—
166C4⋊Dic43—24no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—42no—
175C4⋊Dic43—42no—
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—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—41no—
206Q8×C43—41no—
207D4×C43—41no—
208D4×C43—41no—
209D4×C43—41no—
210D4×C43—41no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×C4×C432−1+411yescharacteristic
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—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#26719—431nomaximal, Sylow
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43#52511yescharacteristic
269C22×C43#54611yescharacteristic
270C22×C43#54811yescharacteristic
271C22×C43#57511yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57811yescharacteristic
275C4×C43—42no—
276C4×C43—42no—
277C4×C43—42no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43#52911yescharacteristic
281C4×C43#54211yescharacteristic
282C4×C43#55211yescharacteristic
283C4×C43#55911yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—42no—
287Dic43—41no—
288Dic43—41no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292#2448—431no—
293#2370—431no—
294#2086—431no—
295#2042—431no—
296#2026—431no—
297#2025—431no—
298#1983D4311yescharacteristic
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—161no—
308C2×C43#245811yescharacteristic
309C2×C43#311111yescharacteristic
310C2×C43#312411yescharacteristic
311C2×C43#330911yescharacteristic
312C2×C43#332711yescharacteristic
313C2×C43#337011yescharacteristic
314C2×C43#337711yescharacteristic
315C2×#125—431no—
316C2×#124C2×D4311yescharacteristic
317C2×C4×Q8—431no—
318C2×#107—431no—
319C2×#107—431no—
320C2×C4⋊C8C2×D4311yescharacteristic
321C2×#103—431no—
322C2×#103—431no—
323C2×#103C2×D4311yescharacteristic
324C2×#103C2×D4311yescharacteristic
325C2×#102—431no—
326C2×#102—431no—
327C2×#102C2×D4311yescharacteristic
328C2×#102C2×D4311yescharacteristic
329C2×#97—431no—
330#399—861no—
331#397—861no—
332#391—431no—
333#390—431no—
334#390—431no—
335#389—431no—
336#389—431no—
337#389—431no—
338#389—861no—
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—861no—
347C4×C4⋊C4C2×D4311yescharacteristic
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#336—431no—
355#336—431no—
356#336—431no—
357#336—431no—
358C43#2671911yescharacteristic, complemented, Sylow
359C22×Q8C22×D4311yescharacteristic
360C22×D4C22×D4311yescharacteristic
361C22×C8—431no—
362C22×C8—431no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365#125—862no—
366#125—862no—
367#124—22no—
368#124—41no—
369C4×Q8—862no—
370C4×Q8—1721no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
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⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—21no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#107—862no—
399#107—1721no—
400C4⋊C8—41no—
401#103—22no—
402#103—22no—
403#103—862no—
404#103—862no—
405#102—22no—
406#102—22no—
407#102—862no—
408#102—1721no—
409#97—1721no—
410#95—21no—
411#95—431no—
412#95—431no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420C24—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#1062189812yes—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—861no—
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—432no—
462C4⋊C4—864no—
463C4⋊C4—864no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—3441no—
472C4⋊C4—3441no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4#1062190012yes—
478C4⋊C4#1062190012yes—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—3441no—
482C22⋊C4—3441no—
483C22⋊C4—1722no—
484C22⋊C4—1722no—
485C42—21no—
486C42—21no—
487C42—42no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42—861no—
492C42—3441no—
493C42—3441no—
494C42—1722no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C2×D4×D4311yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
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#41×D4311yescharacteristic
551C2×C4C2×#1062190011yescharacteristic
552C2×C4C2×#1062190011yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337211yescharacteristic
556C8—41no—
557C8—41no—
558C8—1721no—
559C8—1721no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#1458340911yescharacteristic
568C22#1458353911yescharacteristic
569C22#1458355511yescharacteristic
570C22#1458369511yescharacteristic
571C22#1458369611yescharacteristic
572C22#1458370111yescharacteristic
573C22#1458371511yescharacteristic
574C4—42no—
575C4—41no—
576C4—41no—
577C4—42no—
578C4—42no—
579C4—3441no—
580C4—3441no—
581C4—3441no—
582C4—1721no—
583C4—1721no—
584C4—1721no—
585C4—1722no—
586C4—1721no—
587C4#1458342911yescharacteristic
588C4#1458351311yescharacteristic
589C4#1458358911yescharacteristic
590C4#1458363511yescharacteristic
591C2—161no—
592C2#1913852211yescharacteristic
593C2#1914470111yescharacteristic
594C2#1914485611yescharacteristic
595C2#1914659711yescharacteristic
596C2#1914686411yescharacteristic
597C2#1914734511yescharacteristic
598C2#1914744111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1983D43
hypocenterC43#26719
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. #19137693C2semidirect
3. #19136083C2semidirect
5. #19135744C2semidirect
8. #19135239C2semidirect
11. #19135187C2semidirect
12. #19135156C2semidirect
13. #19134851C2semidirect
14. #19134427C2semidirect
358. C43#26719semidirect

Maximal subgroups

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

subgroupindex
#191383892
#191376932
#191360832
#191358312
#191357442
#191357392
#191352942
#191352392
#191352182
#191352172
#191351872
#191351562
#191348512
#191344272
C43×#19832
#2671943