Finite Group Databasebeta

← #25169700

Subgroups — #25169700

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#19137620C211yesmaximal, characteristic
2#19136004C211yesmaximal, characteristic, complemented
3#19135987C211yesmaximal, characteristic, complemented
4#19135791C211yesmaximal, characteristic
5#19135791C211yesmaximal, characteristic
6#19135356C211yesmaximal, characteristic, complemented
7#19135335C211yesmaximal, characteristic, complemented
8#19135210C211yesmaximal, characteristic
9#19135180C211yesmaximal, characteristic, complemented
10#19135177C211yesmaximal, characteristic, complemented
11#19134862C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic
13#19134687C211yesmaximal, characteristic
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2497C211yesmaximal, characteristic
16C2×#13063304C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582793—21no—
34#14582787—21no—
35#14582781—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582750—21no—
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#400—21no—
49C43×#396—21no—
50C43×#389C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#388—21no—
53C43×#387—21no—
54C43×#384C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063304—22no—
65#13063304—22no—
66C4×Dic86—22no—
67C4×Dic86—41no—
68#13063284—22no—
69#13063284—41no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81#13063258—41no—
82#13063256—22no—
83#13063256—22no—
84#13063256—22no—
85C4⋊(C43⋊C8)—22no—
86#13063248—22no—
87#13063248—22no—
88#13063248—22no—
89#13063248—41no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—41no—
92#13063236—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C23×C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43D411yescharacteristic
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86#4112yes—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43—81no—
157C4⋊C4×C43—81no—
158C4⋊C4×C43—81no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—41no—
161C22⋊C4×C43—81no—
162C22⋊C4×C43—81no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—81no—
168C22⋊Dic43—24no—
169C22⋊Dic43—42no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43#4112yes—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—42no—
178Dic43⋊C4—42no—
179C4×Dic43—42no—
180C4×Dic43—42no—
181C4×Dic43—42no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
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
202C2×C4×C43—21no—
203C2×C4×C43—21no—
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—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
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×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#13712yes—
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251Dic86—22no—
252Dic86—22no—
253Dic86—41no—
254Dic86—41no—
255C43⋊C8—22no—
256C43⋊C8—41no—
257C43⋊C8—41no—
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—22no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#52911yescharacteristic
284C4×C43#53911yescharacteristic
285C4×C43#55311yescharacteristic
286C4×C43#55611yescharacteristic
287Dic43—42no—
288Dic43—42no—
289Dic43—42no—
290Dic43—81no—
291#2497D4311yescharacteristic
292#2362—431no—
293#2072—431no—
294#2068—431no—
295#2035—431no—
296#2035—431no—
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⋊Q8—431no—
315C2×C4×Q8—431no—
316C2×#117—431no—
317C2×#107—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×C4⋊C8—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×C22⋊C8—431no—
327C2×C22⋊C8—431no—
328C2×#97—431no—
329#400—21no—
330#396—21no—
331#391—431no—
332#389—431no—
333#389C2×D4311yescharacteristic
334#389C2×D4311yescharacteristic
335#388—21no—
336#388—861no—
337#388—861no—
338#387—21no—
339#387—861no—
340#384C2×D4311yescharacteristic
341#380C2×D4311yescharacteristic
342#380C2×D4311yescharacteristic
343C4×C4⋊C4—431no—
344C4×C4⋊C4—861no—
345C4×C4⋊C4C2×D4311yescharacteristic
346C4×C22⋊C4C2×D4311yescharacteristic
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#336—431no—
356#336—431no—
357C43#2706011yescharacteristic, complemented, Sylow
358C22×Q8—431no—
359C23×C4C22×D4311yescharacteristic
360C22×C8—431no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—431no—
364C22⋊Q8—862no—
365C22⋊Q8—862no—
366C4×Q8—862no—
367C4×Q8—1721no—
368#117—862no—
369#117—1721no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4C22⋊D4311yescharacteristic
389C2×C22⋊C4C22⋊D4311yescharacteristic
390C2×C42—21no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395C2×C42C22×D4311yescharacteristic
396#107—1721no—
397#106—862no—
398#106—862no—
399#106—862no—
400C4⋊C8—862no—
401#103—862no—
402#103—862no—
403#103—862no—
404#103—1721no—
405C22⋊C8—862no—
406C22⋊C8—1721no—
407#97—1721no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95C22⋊D4311yescharacteristic
418#95C22⋊D4311yescharacteristic
419C24C2×C22⋊D4311yescharacteristic
420C2×Q8—432no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
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—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C23×D4311yescharacteristic
446C2×C8—432no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—432no—
471C4⋊C4—432no—
472C4⋊C4—864no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C22⋊C4—22no—
480C22⋊C4—41no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C22⋊C4—864no—
484C22⋊C4—1722no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—81no—
490C42—1722no—
491C42—1722no—
492C42—1722no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C22×C22⋊D4311yescharacteristic
501Q8—862no—
502Q8—862no—
503Q8—1721no—
504Q8—1721no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
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—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—862no—
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#1306335612yes—
548C2×C4#41×D4311yescharacteristic
549C2×C4#41×D4311yescharacteristic
550C2×C4#41×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4#1306337111yescharacteristic
553C2×C4#1306337211yescharacteristic
554C8—862no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22#1458340611yescharacteristic
566C22#1458353711yescharacteristic
567C22#1458354811yescharacteristic
568C22C2×#1306335611yescharacteristic
569C22#1458369711yescharacteristic
570C22#1458371011yescharacteristic
571C22#1458371011yescharacteristic
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—3441no—
582C4—1722no—
583C4—1722no—
584C4—1722no—
585C4#1458343211yescharacteristic
586C4#1458349011yescharacteristic
587C4#1458360011yescharacteristic
588C4#1458361611yescharacteristic
589C2—81no—
590C2#1913862711yescharacteristic
591C2#1914475111yescharacteristic
592C2#1914488111yescharacteristic
593C2#1914677511yescharacteristic
594C2#1914690511yescharacteristic
595C2#1914704411yescharacteristic
596C2#1914713411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2497C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2497D43
hypocenterC43#27060
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2497

Complements

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

NH ≅ G/Ntype
2. #19136004C2semidirect
3. #19135987C2semidirect
6. #19135356C2semidirect
7. #19135335C2semidirect
9. #19135180C2semidirect
10. #19135177C2semidirect
11. #19134862C2semidirect
14. #19134428C2semidirect
357. C43#27060semidirect

Maximal subgroups

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

subgroupindex
#191376202
#191360042
#191359872
#191357912
#191353562
#191353352
#191352102
#191351802
#191351772
#191348622
#191347922
#191346872
#191344282
C43×#24972
#2706043