Finite Group Databasebeta

← #25169675

Subgroups — #25169675

Order 11008.

700 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#19139020C211yesmaximal, characteristic
2#19137627C211yesmaximal, characteristic
3#19135976C211yesmaximal, characteristic, complemented
4#19135796C211yesmaximal, characteristic
5#19135796C211yesmaximal, characteristic
6#19135351C211yesmaximal, characteristic, complemented
7#19135332C211yesmaximal, characteristic, complemented
8#19135209C211yesmaximal, characteristic
9#19135185C211yesmaximal, characteristic, complemented
10#19135167C211yesmaximal, characteristic, complemented
11#19134851C211yesmaximal, characteristic, complemented
12#19134797C211yesmaximal, characteristic
13#19134688C211yesmaximal, characteristic
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2072C211yesmaximal, characteristic, complemented
16C2×#13063320—21no—
17C2×#13063301C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30#14582837—21no—
31#14582825—21no—
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582791—21no—
36#14582788—21no—
37#14582786—21no—
38#14582785—21no—
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582750—21no—
44C4×(C2×D43)⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#103×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063320—44no—
63#13063301—22no—
64#13063301—22no—
65Q8×Dic43—22no—
66Q8×Dic43—41no—
67#13063283—22no—
68#13063283—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊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)⋊C4D411yescharacteristic
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063258—22no—
91#13063258—22no—
92#13063256—41no—
93C4⋊(C43⋊C8)—22no—
94#13063249—22no—
95#13063249—41no—
96(C2×D43)⋊C8—22no—
97(C2×D43)⋊C8—41no—
98#13063235—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#103×C43—22no—
118#103×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43C2×D411yescharacteristic
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×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—42no—
161C4⋊C4×C43—42no—
162C42×C43—21no—
163C42×C43—21no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—22no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—42no—
177C4⋊Dic43—42no—
178C4⋊Dic43#4112yes—
179C4⋊Dic43#4112yes—
180Dic43⋊C4—24no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—42no—
186C4×Dic43—42no—
187C4×Dic43—42no—
188C4×Dic43—42no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8#4112yes—
195C23×C43C22×D411yescharacteristic
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—41no—
206Q8×C43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
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×C43AGL(1,ℤ/8)12yes—
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—22no—
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—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—
251C2×Dic43—41no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—22no—
259C43⋊C8—41no—
260#27058—431nomaximal, Sylow
261C22×C43#52511yescharacteristic
262C22×C43#54611yescharacteristic
263C22×C43#54711yescharacteristic
264C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C43#57511yescharacteristic
266C22×C43#57811yescharacteristic
267C22×C43#57811yescharacteristic
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—22no—
276C4×C43—41no—
277C4×C43—42no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#52911yescharacteristic
282C4×C43#53911yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55611yescharacteristic
285Dic43—41no—
286Dic43—42no—
287Dic43—42no—
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292#2496—431no—
293#2362—431no—
294#2072D4311yescharacteristic, complemented
295#2066—431no—
296#2036—431no—
297#2036—431no—
298#1947—431no—
299#1943—431no—
300#1924—431no—
301#1921—431no—
302#1918—431no—
303#1863—431no—
304#1854—431no—
305#1825—431no—
306#1763—431no—
307C2×C43#246611yescharacteristic
308C2×C43#311511yescharacteristic
309C2×C43#312711yescharacteristic
310C2×C43#331311yescharacteristic
311C2×C43#333011yescharacteristic
312C2×C43#334311yescharacteristic
313C2×C43#334911yescharacteristic
314D43—81no—
315C2×#126—861no—
316C2×C22⋊Q8—431no—
317C2×C4×Q8—431no—
318C2×#117—431no—
319C2×#107—431no—
320C2×#107—431no—
321C2×#107—431no—
322C2×#106—431no—
323C2×C4⋊C8—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103C2×D4311yescharacteristic
327C2×#103C2×D4311yescharacteristic
328C2×C22⋊C8—431no—
329C2×C22⋊C8—431no—
330C2×#97—431no—
331#400—861no—
332#397—861no—
333#391C2×D4311yescharacteristic
334#389—431no—
335#389—431no—
336#389—431no—
337#388—861no—
338#388—861no—
339#387—861no—
340#387—861no—
341#384C2×D4311yescharacteristic
342#380—431no—
343#380—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—861no—
347C4×C22⋊C4—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340C2×D4311yescharacteristic
355#340C2×D4311yescharacteristic
356#336—431no—
357#336C2×D4311yescharacteristic
358C43#2705811yescharacteristic, complemented, Sylow
359C22×Q8C22×D4311yescharacteristic
360C23×C4—431no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365#126—1724no—
366C22⋊Q8—862no—
367C22⋊Q8—862no—
368C4×Q8—862no—
369C4×Q8—1721no—
370#117—862no—
371#117—1721no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
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×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—431no—
387C2×C22⋊C4—431no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#107—862no—
399#107—862no—
400#107—862no—
401#106—1721no—
402C4⋊C8—862no—
403#103—22no—
404#103—22no—
405#103—862no—
406#103—1721no—
407C22⋊C8—862no—
408C22⋊C8—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—
420#95—861no—
421C24—431no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8#1062190012yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4C23×D4311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—432no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—432no—
469C4⋊C4—432no—
470C4⋊C4—864no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C22⋊C4—864no—
482C22⋊C4—862no—
483C22⋊C4—1721no—
484C22⋊C4—1722no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—861no—
490C42—861no—
491C42—1722no—
492C42—1722no—
493C42—1722no—
494C42—1722no—
495C23—861no—
496C23—861no—
497C23—861no—
498C23—861no—
499C23—861no—
500C23—861no—
501C23—861no—
502C23C2×D4×D4311yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
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—862no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—862no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—1721no—
536C2×C4—1721no—
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—1721no—
549C2×C4#1306335212yes—
550C2×C4#41×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4#41×D4311yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C2×C4#1306337111yescharacteristic
555C2×C4#1306337211yescharacteristic
556C8—41no—
557C8—41no—
558C8—862no—
559C8—1721no—
560C22—1721no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22—1721no—
566C22—1721no—
567C22#1458340911yescharacteristic
568C22#1458354211yescharacteristic
569C22#1458354711yescharacteristic
570C22C2×#1306335211yescharacteristic
571C22#1458369511yescharacteristic
572C22#1458371211yescharacteristic
573C22#1458371511yescharacteristic
574C4—22no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—3441no—
581C4—3441no—
582C4—1722no—
583C4—1721no—
584C4—1721no—
585C4—1722no—
586C4—1721no—
587C4#1458342611yescharacteristic
588C4#1458349311yescharacteristic
589C4#1458360011yescharacteristic
590C4#1458361611yescharacteristic
591C2—3441no—
592C2#1913863211yescharacteristic
593C2#1914474511yescharacteristic
594C2#1914489311yescharacteristic
595C2#1914666011yescharacteristic
596C2#1914689911yescharacteristic
597C2#1914703311yescharacteristic
598C2#1914711811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2072C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2072D43
hypocenterC43#27058
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #19135976C2semidirect
6. #19135351C2semidirect
7. #19135332C2semidirect
9. #19135185C2semidirect
10. #19135167C2semidirect
11. #19134851C2semidirect
14. #19134427C2semidirect
15. C43×#2072C2semidirect
294. #2072D43semidirect
358. C43#27058semidirect

Maximal subgroups

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

subgroupindex
#191390202
#191376272
#191359762
#191357962
#191353512
#191353322
#191352092
#191351852
#191351672
#191348512
#191347972
#191346882
#191344272
C43×#20722
#2705843