Finite Group Databasebeta

← #25154597

Subgroups — #25154597

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138311C211yesmaximal, characteristic
2#19137460C211yesmaximal, characteristic
3#19136157C211yesmaximal, characteristic, complemented
4#19136094C211yesmaximal, characteristic, complemented
5#19136083C211yesmaximal, characteristic, complemented
6#19135935C211yesmaximal, characteristic, complemented
7#19135551C211yesmaximal, characteristic, complemented
8#19135186C211yesmaximal, characteristic, complemented
9#19135166C211yesmaximal, characteristic, complemented
10#19134793C211yesmaximal, characteristic
11#19134776C211yesmaximal, characteristic
12#19134684C211yesmaximal, characteristic
13#19134625C211yesmaximal, characteristic
14#19134313C211yesmaximal, characteristic
15C43×#1948C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063282—21no—
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25#14582834—21no—
26#14582821—21no—
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582795C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582794—21no—
32#14582785—21no—
33#14582783—21no—
34#14582781—21no—
35#14582761—21no—
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×(C2×D43)⋊C4C2211yescharacteristic
40#14582662C2211yescharacteristic
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×#10621872—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063316—22no—
67#13063316—41no—
68#13063283—22no—
69#13063283—41no—
70#13063282—44no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C4⋊C4×D43—22no—
83C4⋊C4×D43Q814yes—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92#13063259—22no—
93#13063258—22no—
94Dic43⋊C8—41no—
95(C2×D43)⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—41no—
116#106×C43—41no—
117C4⋊C8×C43—22no—
118#95×C43—21no—
119C23×D43C2×D411yescharacteristic
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—24no—
139C2×C4×D43—42no—
140C2×C4×D43—42no—
141C2×C4×D43C2×Q812yes—
142C2×C4×D43#4112yes—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43#4112yes—
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—21no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—81no—
158C4⋊C4×C43C2×Q812yes—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—42no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—42no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—81no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—42no—
174C4⋊Dic43C2×Q812yes—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—42no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—81no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192#10621872—44no—
193C23×C43C22×D411yescharacteristic
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43C22⋊Q812yes—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
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×C43AGL(1,ℤ/8)12yes—
219C2×C4×C43C22×Q811yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—22no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—22no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43C22⋊Q812yes—
246C4×D43—22no—
247C4×D43—22no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—48no—
251C8×C43—22no—
252C8×C43—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#26014—431nomaximal, Sylow
256C22×C43C2×C22⋊Q811yescharacteristic
257C22×C43#54611yescharacteristic
258C22×C43#54711yescharacteristic
259C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C43#57511yescharacteristic
261C22×C43#57711yescharacteristic
262C22×C43#57811yescharacteristic
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—22no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—22no—
271C4×C43—42no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43#53311yescharacteristic
277C4×C43#54411yescharacteristic
278C4×C43#55111yescharacteristic
279C4×C43#55211yescharacteristic
280Dic43—22no—
281Dic43—41no—
282Dic43—42no—
283Dic43—42no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#2441—431no—
288#2344—431no—
289#2100—431no—
290#2088—431no—
291#2086—431no—
292#2059—431no—
293#1989—431no—
294#1948D4311yescharacteristic, complemented
295#1921—431no—
296#1918—431no—
297#1854—431no—
298#1851—431no—
299#1824—431no—
300#1809—431no—
301#1736—431no—
302C2×C43#243811yescharacteristic
303C2×C43#307711yescharacteristic
304C2×C43#308211yescharacteristic
305C2×C43#331711yescharacteristic
306C2×C43#333011yescharacteristic
307C2×C43#334511yescharacteristic
308C2×C43#335211yescharacteristic
309D43—42no—
310C22×M16—431no—
311C2×#125—431no—
312C2×#117—431no—
313C2×#117—861no—
314C22×C4⋊C4—431no—
315C2×#107—431no—
316C2×#107—431no—
317C2×#106C2×D4311yescharacteristic
318C2×#106C2×D4311yescharacteristic
319C2×C4⋊C8—431no—
320C2×C4⋊C8C2×D4311yescharacteristic
321C2×C22⋊C8—431no—
322#399—861no—
323#396—861no—
324#389—431no—
325#389—431no—
326#389—431no—
327#389—431no—
328#389—861no—
329#387—861no—
330#387—861no—
331#387—861no—
332#384C2×D4311yescharacteristic
333#381—861no—
334#380—431no—
335#380—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4C2×D4311yescharacteristic
338C4×C22⋊C4—431no—
339#340—431no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340C2×D4311yescharacteristic
350#340C2×D4311yescharacteristic
351#336—431no—
352#336—431no—
353C43#2601411yescharacteristic, complemented, Sylow
354C23×C4—431no—
355C23×C4—861no—
356C2×M16—862no—
357C2×M16—862no—
358C2×M16—1721no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8C22×D4311yescharacteristic
362C22×C8C22×D4311yescharacteristic
363#125—862no—
364#125—1721no—
365#117—862no—
366#117—1724no—
367#117—1721no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—434no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—861no—
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×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—431no—
388C2×C22⋊C4—431no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—21no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42C22×D4311yescharacteristic
397#107—862no—
398#107—862no—
399#106—41no—
400#106—41no—
401C4⋊C8—22no—
402C4⋊C8—1721no—
403C22⋊C8—862no—
404#95—21no—
405#95—431no—
406#95—431no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—431no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—431no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—864no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—1722no—
434C22×C4—1722no—
435C22×C4D4×D4311yescharacteristic
436C22×C4D4×D4311yescharacteristic
437C22×C4C23×D4311yescharacteristic
438M16—1724no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8#1062189812yes—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—81no—
460C4⋊C4—432no—
461C4⋊C4—432no—
462C4⋊C4—864no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—3441no—
470C4⋊C4—1722no—
471C4⋊C4—1722no—
472C4⋊C4—1722no—
473C4⋊C4—1722no—
474C4⋊C4—1722no—
475C4⋊C4Q8×D4312yes—
476C22⋊C4—862no—
477C22⋊C4—3441no—
478C22⋊C4—1721no—
479C22⋊C4—1722no—
480C22⋊C4—1722no—
481C42—21no—
482C42—21no—
483C42—42no—
484C42—861no—
485C42—861no—
486C42—1722no—
487C42—1722no—
488C23—432no—
489C23—861no—
490C23—861no—
491C23—861no—
492C23—861no—
493C23—861no—
494C23—861no—
495C23C2×D4×D4311yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—432no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—862no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—862no—
528C2×C4—1728no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306335212yes—
540C2×C4C2×Q8×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C2×C4C2×#1062189811yescharacteristic
544C2×C4#1306337011yescharacteristic
545C2×C4#1306337311yescharacteristic
546C8—22no—
547C8—41no—
548C8—1721no—
549C8—1721no—
550C22—862no—
551C22—862no—
552C22—862no—
553C22—1721no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22C22⋊Q8×D4311yescharacteristic
558C22#1458354611yescharacteristic
559C22#1458355011yescharacteristic
560C22C2×#1306335211yescharacteristic
561C22#1458369511yescharacteristic
562C22#1458370511yescharacteristic
563C22#1458371511yescharacteristic
564C4—22no—
565C4—41no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—862no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4—1722no—
575C4—1722no—
576C4—1721no—
577C4#1458345311yescharacteristic
578C4#1458352611yescharacteristic
579C4#1458357811yescharacteristic
580C4#1458358111yescharacteristic
581C2—1722no—
582C2#1913827811yescharacteristic
583C2#1914439311yescharacteristic
584C2#1914443011yescharacteristic
585C2#1914672811yescharacteristic
586C2#1914690311yescharacteristic
587C2#1914706111yescharacteristic
588C2#1914716611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1948C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1948D43
hypocenterC43#26014
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #19136157C2semidirect
4. #19136094C2semidirect
5. #19136083C2semidirect
6. #19135935C2semidirect
7. #19135551C2semidirect
8. #19135186C2semidirect
9. #19135166C2semidirect
15. C43×#1948C2semidirect
294. #1948D43semidirect
353. C43#26014semidirect

Maximal subgroups

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

subgroupindex
#191383112
#191374602
#191361572
#191360942
#191360832
#191359352
#191355512
#191351862
#191351662
#191347932
#191347762
#191346842
#191346252
#191343132
C43×#19482
#2601443