Finite Group Databasebeta

← #25169697

Subgroups — #25169697

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139030C211yesmaximal, characteristic
2#19137626C211yesmaximal, characteristic
3#19136006C211yesmaximal, characteristic, complemented
4#19135986C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic
6#19135355C211yesmaximal, characteristic, complemented
7#19135337C211yesmaximal, characteristic, complemented
8#19135205C211yesmaximal, characteristic
9#19135183C211yesmaximal, characteristic, complemented
10#19135182C211yesmaximal, characteristic, complemented
11#19134861C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic
13#19134691C211yesmaximal, characteristic
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2035C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26#14582840—21no—
27#14582822—21no—
28#14582806C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582793—21no—
33#14582792—21no—
34#14582792—21no—
35#14582785—21no—
36#14582784—21no—
37#14582768C2211yescharacteristic
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C22⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61Q8×Dic43—22no—
62Q8×Dic43—41no—
63#13063284—22no—
64#13063284—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×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43D411yescharacteristic
78C2×C22⋊Dic43D411yescharacteristic
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2311yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85#13063258—41no—
86#13063256—22no—
87#13063256—22no—
88Dic43⋊C8—22no—
89#13063249—22no—
90#13063249—22no—
91C22⋊(C43⋊C8)—22no—
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⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×Q8×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115#106×C43—22no—
116#103×C43—22no—
117#103×C43—41no—
118C22⋊C8×C43—41no—
119#95×C43—21no—
120C24×C43C2×D411yescharacteristic
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—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×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—24no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43#4112yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—81no—
162C22⋊Dic43—22no—
163C22⋊Dic43—41no—
164C22⋊Dic43—42no—
165C22⋊Dic43—81no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—42no—
174C4⋊Dic43—42no—
175C4⋊Dic43—42no—
176C4⋊Dic43#4112yes—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43—42no—
187C4×Dic43—81no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8#4112yes—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43C22×D411yescharacteristic
202Q8×C43—22no—
203Q8×C43—22no—
204Q8×C43—41no—
205Q8×C43—41no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
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×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
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—
253C2×Dic43—41no—
254C2×Dic43#13712yes—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—22no—
258C43⋊C8—41no—
259#27060—431nomaximal, Sylow
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43#52511yescharacteristic
268C22×C43#54611yescharacteristic
269C22×C43#54711yescharacteristic
270C22×C43C2×#13711yescharacteristic
271C22×C43#57511yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57711yescharacteristic
274C4×C43—42no—
275C4×C43—41no—
276C4×C43—42no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43#52911yescharacteristic
280C4×C43#53911yescharacteristic
281C4×C43#55311yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—22no—
284Dic43—41no—
285Dic43—42no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290Dic43—81no—
291#2497—431no—
292#2362—431no—
293#2072—431no—
294#2068—431no—
295#2035—431no—
296#2035D4311yescharacteristic
297#1948—431no—
298#1944—431no—
299#1924—431no—
300#1920—431no—
301#1920—431no—
302#1865—431no—
303#1854—431no—
304#1825—431no—
305#1763—431no—
306C2×C43—81no—
307C2×C43#246611yescharacteristic
308C2×C43#311611yescharacteristic
309C2×C43#312611yescharacteristic
310C2×C43#332111yescharacteristic
311C2×C43#333111yescharacteristic
312C2×C43#334411yescharacteristic
313C2×C43#335011yescharacteristic
314C2×C22⋊Q8C2×D4311yescharacteristic
315C2×C4×Q8—431no—
316C2×#117—431no—
317C2×#107—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×#106C2×D4311yescharacteristic
321C2×C4⋊C8—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103C2×D4311yescharacteristic
325C2×#103C2×D4311yescharacteristic
326C2×C22⋊C8—431no—
327C2×C22⋊C8C2×D4311yescharacteristic
328C2×#97—431no—
329#400—861no—
330#396—861no—
331#391—431no—
332#389—431no—
333#389—431no—
334#389—431no—
335#388—861no—
336#388—861no—
337#388—861no—
338#387—861no—
339#387—861no—
340#384—431no—
341#380—431no—
342#380C2×D4311yescharacteristic
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—861no—
346C4×C22⋊C4—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340C2×D4311yescharacteristic
355#336—431no—
356#336—431no—
357C43#2706011yescharacteristic, complemented, Sylow
358C22×Q8C22×D4311yescharacteristic
359C23×C4C22×D4311yescharacteristic
360C22×C8—431no—
361C22×C8—431no—
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C4×Q8—862no—
367C4×Q8—1721no—
368#117—862no—
369#117—1721no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
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×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—431no—
387C2×C22⋊C4—431no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C42—431no—
391C2×C42—431no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42—861no—
396#107—1721no—
397#106—22no—
398#106—862no—
399#106—862no—
400C4⋊C8—862no—
401#103—22no—
402#103—41no—
403#103—862no—
404#103—862no—
405C22⋊C8—41no—
406C22⋊C8—862no—
407#97—1721no—
408#95—21no—
409#95—431no—
410#95—431no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419C24D4×D4311yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8#1062190012yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—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×C4C23×D4311yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—432no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C4⋊C4—24no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—432no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—3441no—
473C4⋊C4—3441no—
474C4⋊C4—3441no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4#1062190012yes—
479C22⋊C4—24no—
480C22⋊C4—81no—
481C22⋊C4—862no—
482C22⋊C4—3441no—
483C22⋊C4—1721no—
484C22⋊C4—1722no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—3441no—
490C42—1722no—
491C42—1722no—
492C42—1722no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×D4×D4311yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—432no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—862no—
536C2×C4—861no—
537C2×C4—1721no—
538C2×C4—1721no—
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#41×D4311yescharacteristic
549C2×C4#41×D4311yescharacteristic
550C2×C4C2×#1062190011yescharacteristic
551C2×C4C2×#1062190011yescharacteristic
552C2×C4#1306337011yescharacteristic
553C2×C4#1306337211yescharacteristic
554C8—41no—
555C8—41no—
556C8—862no—
557C8—1721no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22#1458340511yescharacteristic
566C22#1458353811yescharacteristic
567C22#1458354711yescharacteristic
568C22#137×D4311yescharacteristic
569C22#1458369611yescharacteristic
570C22#1458370511yescharacteristic
571C22#1458370811yescharacteristic
572C4—42no—
573C4—41no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—862no—
578C4—3441no—
579C4—3441no—
580C4—3441no—
581C4—1721no—
582C4—1721no—
583C4—1721no—
584C4—1722no—
585C4#1458342611yescharacteristic
586C4#1458349411yescharacteristic
587C4#1458359611yescharacteristic
588C4#1458361811yescharacteristic
589C2—81no—
590C2#1913862411yescharacteristic
591C2#1914475011yescharacteristic
592C2#1914488011yescharacteristic
593C2#1914678711yescharacteristic
594C2#1914690611yescharacteristic
595C2#1914705311yescharacteristic
596C2#1914713811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2035C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2035D43
hypocenterC43#27060
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
3. #19136006C2semidirect
4. #19135986C2semidirect
6. #19135355C2semidirect
7. #19135337C2semidirect
9. #19135183C2semidirect
10. #19135182C2semidirect
11. #19134861C2semidirect
14. #19134427C2semidirect
357. C43#27060semidirect

Maximal subgroups

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

subgroupindex
#191390302
#191376262
#191360062
#191359862
#191357882
#191353552
#191353372
#191352052
#191351832
#191351822
#191348612
#191347922
#191346912
#191344272
C43×#20352
#2706043