Finite Group Databasebeta

← #25154768

Subgroups — #25154768

Order 11008.

706 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#19139610C211yesmaximal, characteristic, complemented
2#19137568C211yesmaximal, characteristic
3#19135979C211yesmaximal, characteristic
4#19135965C211yesmaximal, characteristic
5#19135739C211yesmaximal, characteristic
6#19135729C211yesmaximal, characteristic
7#19135551C211yesmaximal, characteristic, complemented
8#19135545C211yesmaximal, characteristic, complemented
9#19135363C211yesmaximal, characteristic, complemented
10#19135313C211yesmaximal, characteristic, complemented
11#19135190C211yesmaximal, characteristic, complemented
12#19135183C211yesmaximal, characteristic, complemented
13#19134726C211yesmaximal, characteristic, complemented
14#19134605C211yesmaximal, characteristic
15C4×#102×C43C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25#14582831—21no—
26#14582820—21no—
27#14582805—21no—
28#14582802C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582797—21no—
33#14582792—21no—
34#14582792—21no—
35#14582765C2211yescharacteristic
36#14582765C2211yescharacteristic
37#14582762—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C22⋊Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063324—22no—
63#13063324—41no—
64#13063316—22no—
65#13063316—41no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2311yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85#13063258—22no—
86#13063256—22no—
87C4⋊(C43⋊C8)—22no—
88Dic43⋊C8—41no—
89Dic43⋊C8—41no—
90#13063246—41no—
91#13063246—41no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C4×D4×C43—22no—
107C4×D4×C43Q814yescomplemented
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114#102×C43—22no—
115#102×C43—22no—
116C4×C8×C43—22no—
117#95×C43—21no—
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—24no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—81no—
130C22×C4×C43—81no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×Dic86—42no—
143C2×Dic86—42no—
144C2×Dic86—81no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43C2×Q812yes—
155C4⋊C4×C43#4112yes—
156C4⋊C4×C43#4112yes—
157C22⋊C4×C43—24no—
158C42×C43—81no—
159C42×C43C2×Q812yes—
160C42×C43#4112yes—
161C22⋊Dic43—42no—
162C22⋊Dic43—42no—
163C22⋊Dic43—81no—
164C22⋊Dic43—81no—
165C4⋊Dic43—22no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—41no—
175C4⋊Dic43—42no—
176C4⋊Dic43—42no—
177C4⋊Dic43—81no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—81no—
185C4×Dic43—81no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
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—84no—
218C2×C4×C43C22⋊Q812yes—
219C2×C4×C43C22⋊Q812yes—
220C2×C4×C43C22×Q811yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
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×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43#13512yes—
250Dic86—84no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#26028—431nomaximal, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43#54611yescharacteristic
265C22×C43#54811yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43#57511yescharacteristic
268C22×C43#57611yescharacteristic
269C22×C43#57711yescharacteristic
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—42no—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43#53311yescharacteristic
276C4×C43#54411yescharacteristic
277C4×C43#55511yescharacteristic
278C4×C43#55611yescharacteristic
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287#2550—431no—
288#2357—431no—
289#2067—431no—
290#2065—431no—
291#2025—431no—
292#2023—431no—
293#1989—431no—
294#1988—431no—
295#1949—431no—
296#1939—431no—
297#1921—431no—
298#1920—431no—
299#1835—431no—
300#1804—431no—
301C4×#102D4311yescharacteristic
302C2×C43—82no—
303C2×C43#243911yescharacteristic
304C2×C43#307611yescharacteristic
305C2×C43#308111yescharacteristic
306C2×C43#329711yescharacteristic
307C2×C43#332611yescharacteristic
308C2×C43#336511yescharacteristic
309C2×C43#337011yescharacteristic
310C2×C4⋊Q8—431no—
311C2×#125—431no—
312C2×C4×D4C2×D4311yescharacteristic
313C2×#107—431no—
314C2×#106—431no—
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×C4⋊C8—431no—
318C2×#102—431no—
319C2×#102—431no—
320C2×#102C2×D4311yescharacteristic
321C2×#102C2×D4311yescharacteristic
322C2×C4×C8C2×D4311yescharacteristic
323#398—861no—
324#395—861no—
325#391—861no—
326#390—431no—
327#390—431no—
328#389—431no—
329#389—431no—
330#389—861no—
331#388—861no—
332#388—861no—
333#382—431no—
334#382—431no—
335#381—861no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4C2×D4311yescharacteristic
340C4×C22⋊C4—861no—
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#2602811yescharacteristic, complemented, Sylow
354C22×Q8—861no—
355C22×D4C22×D4311yescharacteristic
356C23×C4—21no—
357C22×C8—431no—
358C22×C8—431no—
359C22×C8C22×D4311yescharacteristic
360C22×C8C22×D4311yescharacteristic
361C4⋊Q8—862no—
362C4⋊Q8—1721no—
363#125—862no—
364#125—1721no—
365C4×D4—22no—
366C4×D4Dic8614yescomplemented
367C2×C4⋊C4—431no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—21no—
387C2×C42—431no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42C22×D4311yescharacteristic
392#107—862no—
393#106—862no—
394C4⋊C8—862no—
395C4⋊C8—1721no—
396C4⋊C8—1721no—
397#102—22no—
398#102—22no—
399#102—1721no—
400#102—1721no—
401C4×C8—22no—
402#95—21no—
403#95—431no—
404#95—431no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413C24—21no—
414C2×Q8—3441no—
415C2×Q8—1722no—
416C2×Q8—1722no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Dic8612yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—862no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—3441no—
465C4⋊C4—1721no—
466C4⋊C4—1722no—
467C4⋊C4—1722no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4C2×Dic8612yes—
471C4⋊C4#1062189812yes—
472C4⋊C4#1062189812yes—
473C22⋊C4—24no—
474C22⋊C4—3441no—
475C22⋊C4—3441no—
476C22⋊C4—1722no—
477C22⋊C4—1722no—
478C42—81no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—3441no—
484C42—3441no—
485C42C2×Dic8612yes—
486C42#1062190012yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C2×D4×D4311yescharacteristic
495Q8—3444no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—84no—
514C2×C4—432no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
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#1306330212yes—
539C2×C4#1306330212yes—
540C2×C4C22×Dic8611yescharacteristic
541C2×C4C2×#1062190011yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C2×C4C2×#1062189811yescharacteristic
544C2×C4#1306337111yescharacteristic
545C2×C4#1306337211yescharacteristic
546C8—41no—
547C8—41no—
548C8—1721no—
549C8—1721no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#1306330211yescharacteristic
558C22#1458354511yescharacteristic
559C22#1458355811yescharacteristic
560C22#135×D4311yescharacteristic
561C22#1458369611yescharacteristic
562C22#1458370011yescharacteristic
563C22#1458370511yescharacteristic
564C4—22no—
565C4—22no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—862no—
570C4—3441no—
571C4—3441no—
572C4—3441no—
573C4—3441no—
574C4—1721no—
575C4—1721no—
576C4—1721no—
577C4#1458345611yescharacteristic
578C4#1458352711yescharacteristic
579C4#1458361411yescharacteristic
580C4#1458361911yescharacteristic
581C2—82no—
582C2#1913828611yescharacteristic
583C2#1914437911yescharacteristic
584C2#1914442211yescharacteristic
585C2#1914645011yescharacteristic
586C2#1914685311yescharacteristic
587C2#1914729211yescharacteristic
588C2#1914734411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC4×#102D43
hypocenterC43#26028
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #19139610C2semidirect
7. #19135551C2semidirect
8. #19135545C2semidirect
9. #19135363C2semidirect
10. #19135313C2semidirect
11. #19135190C2semidirect
12. #19135183C2semidirect
13. #19134726C2semidirect
107. C4×D4×C43Q8semidirect
353. C43#26028semidirect
366. C4×D4Dic86semidirect

Maximal subgroups

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

subgroupindex
#191396102
#191375682
#191359792
#191359652
#191357392
#191357292
#191355512
#191355452
#191353632
#191353132
#191351902
#191351832
#191347262
#191346052
C4×#102×C432
#2602843