Finite Group Databasebeta

← #25165277

Subgroups — #25165277

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139116C211yesmaximal, characteristic, complemented
2#19137671C211yesmaximal, characteristic
3#19136002C211yesmaximal, characteristic
4#19135978C211yesmaximal, characteristic
5#19135833C211yesmaximal, characteristic
6#19135832C211yesmaximal, characteristic
7#19135274C211yesmaximal, characteristic, complemented
8#19135172C211yesmaximal, characteristic, complemented
9#19135168C211yesmaximal, characteristic, complemented
10#19135150C211yesmaximal, characteristic, complemented
11#19134865C211yesmaximal, characteristic, complemented
12#19134859C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic
15C43×#1928C211yesmaximal, characteristic, complemented
16C2×#13063314C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582833—21no—
29#14582833—21no—
30#14582800C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582797—21no—
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582791—21no—
37#14582788—21no—
38#14582783—21no—
39#14582773—21no—
40#14582768C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063314—22no—
64#13063314—22no—
65Q8×Dic43—22no—
66Q8×Dic43—41no—
67C4×D172—22no—
68C4×D172—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063257—22no—
91Dic43⋊C8—41no—
92#13063249—22no—
93#13063249—41no—
94#13063247—22no—
95#13063247—41no—
96#13063245—22no—
97#13063245—22no—
98C4×C43⋊C8—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114#107×C43—22no—
115#103×C43—22no—
116#103×C43—22no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—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—
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×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172#4112yes—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43#4112yes—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—81no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—81no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—42no—
176C4⋊Dic43—42no—
177C4⋊Dic43—81no—
178C4⋊Dic43#4112yes—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
184Dic43⋊C4—81no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—81no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C23×C43C22×D411yescharacteristic
198C22×D43—22no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205Q8×C43—22no—
206Q8×C43—22no—
207Q8×C43—41no—
208Q8×C43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
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#13712yes—
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
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#13512yes—
254D172—22no—
255D172—22no—
256D172—41no—
257D172—41no—
258C4×D43—84no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#26763—431nomaximal, Sylow
264C22×C43#52511yescharacteristic
265C22×C43#54611yescharacteristic
266C22×C43#54811yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—22no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43#52911yescharacteristic
285C4×C43#53911yescharacteristic
286C4×C43#55211yescharacteristic
287C4×C43#55311yescharacteristic
288Dic43—22no—
289Dic43—41no—
290Dic43—41no—
291Dic43—42no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#2507—431no—
296#2367—431no—
297#2071—431no—
298#2067—431no—
299#2042—431no—
300#2042—431no—
301#1933—431no—
302#1928D4311yescharacteristic, complemented
303#1919—431no—
304#1918—431no—
305#1916—431no—
306#1865—431no—
307#1864—431no—
308#1803—431no—
309C4×#102—431no—
310C2×C43#246011yescharacteristic
311C2×C43#310711yescharacteristic
312C2×C43#311911yescharacteristic
313C2×C43#330111yescharacteristic
314C2×C43#331411yescharacteristic
315C2×C43#336111yescharacteristic
316C2×C43#336911yescharacteristic
317D43—82no—
318C2×#124—431no—
319C2×C4×Q8—431no—
320C2×C4×D4—431no—
321C2×#107C2×D4311yescharacteristic
322C2×#106—431no—
323C2×C4⋊C8—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103C2×D4311yescharacteristic
327C2×#103C2×D4311yescharacteristic
328C2×#102—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×C4×C8—431no—
333#398—861no—
334#398—861no—
335#391C2×D4311yescharacteristic
336#390—431no—
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389—861no—
342#388—861no—
343#388—861no—
344#387—861no—
345#385—861no—
346#384—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4C2×D4311yescharacteristic
350C4×C22⋊C4—861no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340C2×D4311yescharacteristic
357#336—431no—
358#336—431no—
359#336—431no—
360#336C2×D4311yescharacteristic
361C43#2676311yescharacteristic, complemented, Sylow
362C22×Q8C22×D4311yescharacteristic
363C22×D4—431no—
364C23×C4—861no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369#124—862no—
370#124—862no—
371C4×Q8—862no—
372C4×Q8—1721no—
373C4×D4—862no—
374C4×D4—1721no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C42—21no—
396C2×C42—431no—
397C2×C42—431no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—22no—
402#106—862no—
403C4⋊C8—1721no—
404#103—22no—
405#103—22no—
406#103—862no—
407#103—1721no—
408#102—862no—
409#102—862no—
410#102—862no—
411#102—1721no—
412C4×C8—1721no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—431no—
417#95—431no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423C24—861no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8#1062189812yes—
430C2×D4—432no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—3441no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4C23×D4311yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—432no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—3441no—
479C4⋊C4—3441no—
480C4⋊C4—3441no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4#1062190012yes—
486C22⋊C4—864no—
487C22⋊C4—864no—
488C22⋊C4—3441no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C42—21no—
492C42—21no—
493C42—81no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—3441no—
499C42—1722no—
500C23—862no—
501C23—1721no—
502C23—1721no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23C2×D4×D4311yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—862no—
513D4—862no—
514D4—1721no—
515D4—1721no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
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—432no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—862no—
546C2×C4—3444no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4#1306335712yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4C2×#1062190011yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337111yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—41no—
563C8—41no—
564C8—1721no—
565C8—1721no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22—3441no—
570C22—1722no—
571C22—1722no—
572C22—1722no—
573C22#1458340811yescharacteristic
574C22#1458354111yescharacteristic
575C22#1458355511yescharacteristic
576C22#135×D4311yescharacteristic
577C22C2×#1306335711yescharacteristic
578C22#1458370311yescharacteristic
579C22#1458370811yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4—1721no—
591C4—1722no—
592C4—1721no—
593C4#1458342811yescharacteristic
594C4#1458349011yescharacteristic
595C4#1458358211yescharacteristic
596C4#1458359511yescharacteristic
597C2—3442no—
598C2#1913855111yescharacteristic
599C2#1914466411yescharacteristic
600C2#1914479211yescharacteristic
601C2#1914650011yescharacteristic
602C2#1914667411yescharacteristic
603C2#1914725011yescharacteristic
604C2#1914733911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1928C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1928D43
hypocenterC43#26763
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
1. #19139116C2semidirect
7. #19135274C2semidirect
8. #19135172C2semidirect
9. #19135168C2semidirect
10. #19135150C2semidirect
11. #19134865C2semidirect
13. #19134598C2semidirect
15. C43×#1928C2semidirect
302. #1928D43semidirect
361. C43#26763semidirect

Maximal subgroups

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

subgroupindex
#191391162
#191376712
#191360022
#191359782
#191358332
#191358322
#191352742
#191351722
#191351682
#191351502
#191348652
#191348592
#191345982
C4×#130632452
C43×#19282
#2676343