Finite Group Databasebeta

← #25067767

Subgroups — #25067767

Order 11008.

640 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#19144651C211yesmaximal, characteristic
2#19143718C211yesmaximal, characteristic, complemented
3#19143660C211yesmaximal, characteristic, complemented
4#19133484C211yesmaximal, characteristic, complemented
5#19133483C211yesmaximal, characteristic, complemented
6#19133456C211yesmaximal, characteristic, complemented
7#19133454C211yesmaximal, characteristic, complemented
8#19133449C211yesmaximal, characteristic, complemented
9D8×C43⋊C8C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133382C211yesmaximal, characteristic, complemented
12#19133044C211yesmaximal, characteristic, complemented
13#19132974C211yesmaximal, characteristic, complemented
14#19132880C211yesmaximal, characteristic, complemented
15C43×#1586C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17C4×#10621900C2211yescharacteristic
18#14583226C411yescharacteristic
19#14583222C411yescharacteristic
20#14583193C411yescharacteristic
21#14583187C411yescharacteristic
22#14583098C411yescharacteristic
23#14583092C411yescharacteristic
24#14583045C411yescharacteristic
25#14583041C411yescharacteristic
26#14583029C2211yescharacteristic
27#14583026C2211yescharacteristic
28C4×#10621873C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582976C2211yescharacteristic
32#14582975—21no—
33#14582970—21no—
34#14582967—21no—
35C8×D172C2211yescharacteristic
36D4×C43⋊C8C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38(C22⋊D43)⋊C8—21no—
39#14582953—21no—
40#14582951C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582921C2211yescharacteristic
44C2×Dic43⋊C8—21no—
45#14582867—21no—
46#14582864—21no—
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582628C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582620C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621900C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063324C2×C411yescharacteristic
79#13063321C2×C411yescharacteristic
80#13063311—21no—
81#13063300C2×C411yescharacteristic
82#13063298—21no—
83#13063296C2×C411yescharacteristic
84C4×Dic86C2311yescharacteristic
85#13063290C2×C411yescharacteristic
86C4×D172C2311yescharacteristic
87D4×Dic43C2×C411yescharacteristic
88C4×C22⋊D43—21no—
89C4×C22⋊D43—21no—
90(C22⋊D43)⋊C4—21no—
91#13063283C2×C411yescharacteristic
92#13063281—21no—
93C2×C4×Dic43—21no—
94C42×D43C2311yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063257C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8C2×C411yescharacteristic
119(C2×D43)⋊C8C2×C411yescharacteristic
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×D8×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43C2×C411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154#10621900—22no—
155#10621900—41no—
156#10621898—81no—
157#10621898—81no—
158C2×D172—21no—
159C2×D172C22×C411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43C22×C411yescharacteristic
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43#4111yescharacteristic
164C2×Dic86—21no—
165C2×Dic86C22×C411yescharacteristic
166D8×C43—22no—
167M16×C43—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—81no—
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C22×C411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C4⋊C4×C43C22×C411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182C22⋊Dic43—21no—
183#10621883—41no—
184#10621882—22no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621873—41no—
209#10621872—81no—
210#10621872—81no—
211C8×D43—24no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43C4×D411yescharacteristic
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43#13112yes—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—42no—
231C22⋊D43—42no—
232C22⋊D43—81no—
233C22⋊D43—81no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43C4×D411yescharacteristic
240C2×Dic43C4×D411yescharacteristic
241C2×Dic43C4×D411yescharacteristic
242D172—21no—
243D172—21no—
244D172—81no—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—22no—
250C4×D43—41no—
251C4×D43—41no—
252Dic86—21no—
253Dic86—21no—
254Dic86—81no—
255C8×C43—22no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—22no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#18015—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×C4×D411yescharacteristic
277C2×D43—21no—
278C2×D43—21no—
279C2×D43—21no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—21no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43C2×#13111yescharacteristic
287C4×C43#56811yescharacteristic
288C4×C43#57611yescharacteristic
289C4×C43#57711yescharacteristic
290Dic43—21no—
291Dic43—21no—
292Dic43—41no—
293Dic43—41no—
294Dic43—41no—
295Dic43#44312yes—
296#3106—431no—
297#2990—431no—
298#2979—431no—
299#1590—431no—
300#1590—431no—
301#1586—431no—
302#1586D4311yescharacteristic, complemented
303#1585—431no—
304#1585—431no—
305C8×D8—431no—
306C8×D8—431no—
307#1574—431no—
308#1492—431no—
309#1476—431no—
310#1450—431no—
311C2×C43—42no—
312C2×C43—81no—
313C2×C43#293311yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43C2×#44311yescharacteristic
316D43—41no—
317D43—81no—
318#532—431no—
319C4×#41—431no—
320#482—431no—
321#482—431no—
322#477—431no—
323#476—431no—
324#460—431no—
325#459—431no—
326#449—431no—
327#449—431no—
328#446—431no—
329#446—431no—
330C4×SD16—431no—
331C4×SD16—431no—
332C4×D8—431no—
333C4×D8C2×D4311yescharacteristic
334#436—431no—
335#436—861no—
336#436C2×D4311yescharacteristic
337#435—861no—
338#435—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342C8×D4—861no—
343C8×D4C2×D4311yescharacteristic
344#432—861no—
345#431—431no—
346#431—431no—
347#431—431no—
348#423—431no—
349C2×C4⋊C8—861no—
350#408—861no—
351#408—861no—
352C2×C4×C8—431no—
353#335—431no—
354#335—431no—
355#334—431no—
356#334C2×D4311yescharacteristic
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8C2×D4311yescharacteristic
364D4⋊C8C2×D4311yescharacteristic
365#322—431no—
366#322C2×D4311yescharacteristic
367C82—431no—
368C82—431no—
369C43#1801511yescharacteristic, complemented, Sylow
370C2×#41—431no—
371C2×#41—861no—
372C2×SD16—431no—
373C2×SD16—431no—
374C2×D8—431no—
375C2×D8C4×D4311yescharacteristic
376C2×M16—21no—
377C2×M16—861no—
378C2×M16—861no—
379C22×C8—21no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C4⋊Q8—431no—
385#127—431no—
386#124—861no—
387#121—431no—
388#121—431no—
389#121—861no—
390C4×Q8—431no—
391C4×Q8—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4C22×D4311yescharacteristic
398C4×D4C22×D4311yescharacteristic
399#117—431no—
400#117—861no—
401C2×C42—431no—
402C2×C42—861no—
403#107—431no—
404#107C4×D4311yescharacteristic
405#106—431no—
406#106—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418#103—431no—
419#103—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102C4×D4311yescharacteristic
425#102C4×D4311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C22⋊C8—431no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—861no—
438#97—861no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447#41—862no—
448#41—3441no—
449#41—3441no—
450#41—1721no—
451C2×Q8—431no—
452C2×Q8—861no—
453C2×D4—431no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4C2×C4×D4311yescharacteristic
460C2×D4C2×C4×D4311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469SD16—1721no—
470SD16—1721no—
471D8—22no—
472D8—862no—
473M16—81no—
474M16—3441no—
475M16—3441no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—864no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8—3441no—
491C2×C8C2×C4×D4311yescharacteristic
492C2×C8C2×C4×D4311yescharacteristic
493C2×C8D4×D4311yescharacteristic
494C2×C8D4×D4311yescharacteristic
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4C2×C4×D4311yescharacteristic
501C4⋊C4C2×C4×D4311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—21no—
518C23—431no—
519C23—861no—
520Q8—861no—
521Q8—861no—
522Q8—3441no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—861no—
527D4—861no—
528D4—3441no—
529D4—3441no—
530D4—3441no—
531D4—1722no—
532D4—1722no—
533D4#1306333312yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—431no—
541C2×C4—431no—
542C2×C4—431no—
543C2×C4—862no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4C22×C4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—862no—
566C8—861no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—1721no—
571C8—1721no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—861no—
579C22—861no—
580C22—861no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22C4×D4×D4311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—432no—
589C4—861no—
590C4—861no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4C2×#1306333311yescharacteristic
595C4#1458366411yescharacteristic
596C4#1458370311yescharacteristic
597C4#1458370911yescharacteristic
598C2—42no—
599C2—81no—
600C2—3441no—
601C2—1721no—
602C2#1914332111yescharacteristic
603C2#1914342411yescharacteristic
604C2#443×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1586C2
socleC22×C43C2×C4×D4
prime radical#19144651C2
cosocleC42×C43C24
hypercenter#1586D43
hypocenterC43#18015
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #19143718C2semidirect
3. #19143660C2semidirect
4. #19133484C2semidirect
5. #19133483C2semidirect
6. #19133456C2semidirect
7. #19133454C2semidirect
8. #19133449C2semidirect
9. D8×C43⋊C8C2semidirect
10. C8×#10621882C2semidirect
11. #19133382C2semidirect
12. #19133044C2semidirect
13. #19132974C2semidirect
14. #19132880C2semidirect
15. C43×#1586C2semidirect
302. #1586D43semidirect
369. C43#18015semidirect

Maximal subgroups

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

subgroupindex
#191446512
#191437182
#191436602
#191334842
#191334832
#191334562
#191334542
#191334492
D8×C43⋊C82
C8×#106218822
#191333822
#191330442
#191329742
#191328802
C43×#15862
#1801543