Finite Group Databasebeta

← D9×#911 #13149895

Subgroups — D9×#911 #13149895

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D9×#237C211yesmaximal, characteristic, complemented
2D3×D4×D9C211yesmaximal, characteristic, complemented
3#11721790C211yesmaximal, characteristic, complemented
4C9×#911C211yesmaximal, characteristic, complemented
5C3×D8×D9C211yesmaximal, characteristic, complemented
6#11721187C211yesmaximal, characteristic, complemented
7D9×#214C211yesmaximal, characteristic, complemented
8#11721175C211yesmaximal, characteristic, complemented
9D9×#213C211yesmaximal, characteristic, complemented
10#11721168C211yesmaximal, characteristic, complemented
11#11721167C211yesmaximal, characteristic, complemented
12#11720820C211yesmaximal, characteristic, complemented
13D9×#204C211yesmaximal, characteristic, complemented
14#11720805C211yesmaximal, characteristic, complemented
15D9×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16D3×#911—31nomaximal
17D9×AGL(1,ℤ/8)—31nomaximal
18C22×D3×D9—21no—
19#88742C2211yescharacteristic, complemented
20D4×C3⋊D9C2211yescharacteristic, complemented
21C9×#237C2211yescharacteristic, complemented
22D3×D4×C9C2211yescharacteristic, complemented
23C3×D4×D9C2211yescharacteristic
24C3×D4×D9C2211yescharacteristic, complemented
25#88668—21no—
26D9×#67—21no—
27D9×#67—21no—
28D3×#611—21no—
29#88663—21no—
30#88658—21no—
31C2×Dic3×D9—21no—
32#88646C2211yescharacteristic, complemented
33D9×D12C2211yescharacteristic
34D3×D36C2211yescharacteristic, complemented
35C4×D3×D9C2211yescharacteristic
36#88641C2211yescharacteristic, complemented
37#88634C2211yescharacteristic, complemented
38D9×Dic6C2211yescharacteristic, complemented
39C3×C9×D8C2211yescharacteristic, complemented
40#88544C2211yescharacteristic, complemented
41#88543C2211yescharacteristic, complemented
42#88524C2211yescharacteristic, complemented
43#88523C2211yescharacteristic, complemented
44C9×#214C2211yescharacteristic, complemented
45C9×#213C2211yescharacteristic, complemented
46C3×#3673C2211yescharacteristic, complemented
47C3×#3673C2211yescharacteristic, complemented
48C9×#204C2211yescharacteristic, complemented
49C9×ΓL(1,𝔽25)C2211yescharacteristic, complemented
50C3×D72C2211yescharacteristic, complemented
51C3×C8×D9C2211yescharacteristic, complemented
52#88426C2211yescharacteristic, complemented
53#88425C2211yescharacteristic, complemented
54#88424C2211yescharacteristic, complemented
55#88421C2211yescharacteristic, complemented
56#88420C2211yescharacteristic, complemented
57#88417C2211yescharacteristic, complemented
58#88415C2211yescharacteristic, complemented
59#88414C2211yescharacteristic, complemented
60D9×C3⋊C8C2211yescharacteristic, complemented
61D3×#237—31no—
62D32×D4—31no—
63#64120—31no—
64C3×#911D311yescharacteristic
65C3×D3×D8—31no—
66#63937—31no—
67#63932—31no—
68D3×#214—31no—
69#63927—31no—
70#63925—31no—
71D3×#213—31no—
72#63798—31no—
73#63795—31no—
74D3×#204—31no—
75D3×ΓL(1,𝔽25)—31no—
76#41×D9—31no—
77C2×D4×D9—31no—
78C9×AGL(1,ℤ/8)—31no—
79#63512—31no—
80#63495—31no—
81#63476—31no—
82#63476—31no—
83SD16×D9—31no—
84SD16×D9—31no—
85#63473—31no—
86#63473—31no—
87#63473—61no—
88D8×D9—31no—
89D8×D9D311yescharacteristic, complemented
90#63470—31no—
91M16×D9—31no—
92C22×C3⋊D9—21no—
93C22×D3×C9—21no—
94C22×C3×D9—21no—
95C22×C3×D9—21no—
96C2×D3×D9—21no—
97C2×D3×D9—21no—
98C2×D3×D9—21no—
99C2×D3×D9—44no—
100C2×D3×D9D411yescharacteristic
101C3×D4×C9C2311yescharacteristic
102C3×D4×C9C2311yescharacteristic, complemented
103#6233—21no—
104#6233—21no—
105C2×C3⋊Dic9—21no—
106C4⋊(C3⋊D9)C2311yescharacteristic
107C4×C3⋊D9C2311yescharacteristic
108#6226C2311yescharacteristic, complemented
109C9×#67—21no—
110C9×#67—21no—
111C3×#611—21no—
112C3×#611—21no—
113C2×C9×Dic3—21no—
114C9×D12C2311yescharacteristic
115C4×D3×C9C2311yescharacteristic
116C3×D36C2311yescharacteristic
117C3×D36C2311yescharacteristic, complemented
118C3×C4×D9C2311yescharacteristic
119C9×Dic6C2311yescharacteristic, complemented
120#6195—21no—
121#6194—21no—
122#6194—21no—
123D3×Dic9D411yescharacteristic
124#6192—21no—
125#6192—21no—
126(C3⋊D9)⋊C4D411yescharacteristic
127Dic3×D9—21no—
128Dic3×D9—21no—
129Dic3×D9—21no—
130Dic3×D9D411yescharacteristic
131#6189—21no—
132C3×C8×C9C2311yescharacteristic, complemented
133C3⋊(C9⋊C8)C2311yescharacteristic, complemented
134C9×C3⋊C8C2311yescharacteristic, complemented
135C3×C9⋊C8C2311yescharacteristic, complemented
136D3×AGL(1,ℤ/8)—91no—
137C2×#911—91no—
138C22×D32—61no—
139#3830—31no—
140D4×C3⋊D3—31no—
141C3×#237C2×D311yescharacteristic
142C3×D3×D4—31no—
143C3×D3×D4—31no—
144C3×D3×D4C2×D311yescharacteristic
145#3811—61no—
146D3×#67—61no—
147D3×#67—61no—
148D3×#67—61no—
149#3805—61no—
150#3804—61no—
151C2×D3×Dic3—61no—
152#3802—31no—
153D3×D12—31no—
154D3×D12—31no—
155C4×D32—31no—
156#3796—31no—
157#3795—31no—
158D3×Dic6—31no—
159C23×D9—61no—
160C32×D8C2×D311yescharacteristic
161#3754—31no—
162#3753—31no—
163#3744—31no—
164#3743—31no—
165C3×#214C2×D311yescharacteristic
166C3×#213—31no—
167C3×#213—31no—
168C3×#213C2×D311yescharacteristic
169C3×D24—31no—
170C3×#204C2×D311yescharacteristic
171C3×ΓL(1,𝔽25)C2×D311yescharacteristic
172C3×D3×C8—31no—
173#3717—31no—
174#3716—31no—
175#3716—31no—
176#3715—31no—
177#3714—31no—
178#3713—31no—
179#3712—31no—
180#3711—31no—
181D3×C3⋊C8—31no—
182C9×#41—31no—
183C2×D4×C9—31no—
184C2×#611—61no—
185#3701—31no—
186Q8×D9—31no—
187#3699—31no—
188#3699—61no—
189#3699—61no—
190D4×D9—31no—
191D4×D9—31no—
192D4×D9—31no—
193D4×D9—61no—
194D4×D9—61no—
195D4×D9—61no—
196D4×D9—61no—
197D4×D9C2×D311yescharacteristic
198D4×D9C2×D311yescharacteristic, complemented
199#3697—31no—
200#3697—61no—
201C2×D36—31no—
202C2×C4×D9—31no—
203C2×C4×D9—61no—
204C9×SD16—31no—
205C9×SD16—31no—
206C9×D8—21no—
207C9×D8—31no—
208C9×D8C2×D311yescharacteristic, complemented
209C9×M16—31no—
210#3675—31no—
211#3675—31no—
212#3673—31no—
213#3673—31no—
214#3673—61no—
215#3673C2×D311yescharacteristic, complemented
216#3673C2×D311yescharacteristic, complemented
217#3672—31no—
218#3672—31no—
219#3672—61no—
220#3667—31no—
221D72—31no—
222D72C2×D311yescharacteristic, complemented
223#3664—31no—
224#3664—31no—
225#3664—61no—
226#3663—31no—
227#3663—31no—
228#3663—61no—
229C8×D9—31no—
230C8×D9C2×D311yescharacteristic, complemented
231C22×C3×C9—21no—
232C22×C3×C9—21no—
233C2×C3⋊D9—21no—
234C2×C3⋊D9—42no—
235C2×C3⋊D9C2×D411yescharacteristic
236C2×D3×C9—21no—
237C2×D3×C9—42no—
238C2×D3×C9C2×D411yescharacteristic
239C2×C3×D9—21no—
240C2×C3×D9—21no—
241C2×C3×D9—42no—
242C2×C3×D9—42no—
243C2×C3×D9C2×D411yescharacteristic
244D3×D9—22no—
245D3×D9—42no—
246D3×D9—42no—
247D3×D9—42no—
248C3×C4×C9C2411yescharacteristic
249C3⋊Dic9—21no—
250C3⋊Dic9C2×D411yescharacteristic
251C9×Dic3—21no—
252C9×Dic3C2×D411yescharacteristic
253C3×Dic9C2×D411yescharacteristic
254D3×#41—91no—
255C2×#237—91no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C3×AGL(1,ℤ/8)—31no—
259C2×C3×D8—91no—
260#949—91no—
261C2×#214—91no—
262#932—91no—
263C2×#213—91no—
264#914—91no—
265#914—91no—
266D3×SD16—91no—
267D3×SD16—91no—
268#911—91no—
269#911—91no—
270#911—91no—
271#911—91no—
272#911—91no—
273#911—91no—
274#911—91no—
275#911—91no—
276#911—91no—
277#911—181no—
278#911D911yescharacteristic, direct product factor
279D3×D8—31no—
280D3×D8—91no—
281#908—91no—
282D3×M16—91no—
283C2×#204—91no—
284C2×ΓL(1,𝔽25)—91no—
285C22×C3⋊D3—61no—
286C22×C3×D3—21no—
287C22×C3×D3—61no—
288C22×C3×D3—61no—
289C2×D32—31no—
290C2×D32—61no—
291C2×D32—61no—
292C2×D32—61no—
293C2×D32—124no—
294C32×D4C22×D311yescharacteristic
295C32×D4C22×D311yescharacteristic
296#638—61no—
297#638—61no—
298C2×C3⋊Dic3—61no—
299C4⋊(C3⋊D3)—31no—
300C4×C3⋊D3—31no—
301#634—31no—
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—61no—
305C3×#67—61no—
306C2×C3×Dic3—21no—
307C3×D12—31no—
308C3×D12—31no—
309C3×D12C22×D311yescharacteristic
310C3×C4×D3—31no—
311C3×C4×D3C22×D311yescharacteristic
312C3×Dic6C22×D311yescharacteristic
313#627—61no—
314#626—61no—
315#626—61no—
316#626—61no—
317#625—61no—
318#625—61no—
319#624—31no—
320D3×Dic3—31no—
321D3×Dic3—31no—
322D3×Dic3—61no—
323D3×Dic3—61no—
324D3×Dic3—61no—
325C23×C9—61no—
326C22×D9—21no—
327C22×D9—21no—
328C22×D9—31no—
329C22×D9—61no—
330C22×D9—61no—
331C22×D9—61no—
332C22×D9—61no—
333C22×D9—121no—
334C22×D9—124no—
335C32×C8C22×D311yescharacteristic
336C3⋊(C3⋊C8)—31no—
337C3×C3⋊C8—31no—
338C3×C3⋊C8C22×D311yescharacteristic
339Q8×C9—31no—
340D4×C9—21no—
341D4×C9—21no—
342D4×C9—31no—
343D4×C9—61no—
344D4×C9—61no—
345D4×C9C22×D311yescharacteristic
346D4×C9C22×D311yescharacteristic, complemented
347C2×C4×C9—31no—
348C2×C4×C9—61no—
349#611—21no—
350#611—21no—
351#611—61no—
352#611—61no—
353#611—61no—
354#611—61no—
355#611—61no—
356#611—121no—
357#611—121no—
358C2×Dic9—31no—
359C2×Dic9—61no—
360C2×Dic9—121no—
361D36—31no—
362D36—61no—
363D36—61no—
364D36—61no—
365D36C22×D311yescharacteristic
366D36C22×D311yescharacteristic, complemented
367C4×D9—31no—
368C4×D9—31no—
369C4×D9—31no—
370C4×D9—61no—
371C4×D9—61no—
372C4×D9—61no—
373C4×D9—61no—
374C4×D9C22×D311yescharacteristic
375Dic18—31no—
376Dic18—61no—
377Dic18—61no—
378C8×C9—21no—
379C8×C9—31no—
380C8×C9C22×D311yescharacteristic, complemented
381C9⋊C8—31no—
382C9⋊C8—61no—
383C9⋊C8C22×D311yescharacteristic, complemented
384C2×AGL(1,ℤ/8)—271noSylow
385C2×C3×C9—41no—
386C2×C3×C9—41no—
387C2×C3×C9C22×D411yescharacteristic
388C3⋊D9—21no—
389C3⋊D9—41no—
390D3×C9—21no—
391D3×C9—41no—
392C3×D9—41no—
393C3×D9—41no—
394C3×D9AGL(1,ℤ/8)12yescomplemented
395C23×D3—181no—
396C23×D3—181no—
397C3×#41—31no—
398C2×C3×D4—31no—
399C2×C3×D4—91no—
400C2×C3×D4—91no—
401C2×#67—181no—
402C2×#67—181no—
403C2×#67—181no—
404C22×Dic3—181no—
405#239—91no—
406D3×Q8—91no—
407#237—91no—
408#237—91no—
409#237—91no—
410#237—91no—
411#237—181no—
412#237—181no—
413#237—181no—
414#237—181no—
415#237C2×D911yescharacteristic, complemented
416D3×D4—31no—
417D3×D4—31no—
418D3×D4—91no—
419D3×D4—91no—
420D3×D4—91no—
421D3×D4—91no—
422D3×D4—91no—
423D3×D4—91no—
424D3×D4—181no—
425D3×D4—181no—
426D3×D4—181no—
427D3×D4—181no—
428D3×D4—181no—
429D3×D4—181no—
430D3×D4C2×D911yescharacteristic, complemented
431#235—91no—
432#235—181no—
433C2×D12—91no—
434C2×D12—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—181no—
438C2×Dic6—91no—
439C3×SD16—31no—
440C3×SD16—31no—
441C3×D8—21no—
442C3×D8—31no—
443C3×D8—91no—
444C3×D8—91no—
445C3×D8—91no—
446C3×D8C2×D911yescharacteristic, complemented
447C3×D8D3211yescharacteristic
448C3×M16—31no—
449C2×C3×C8—91no—
450#215—91no—
451#215—91no—
452#214—91no—
453#214—91no—
454#214—91no—
455#214—91no—
456#214—91no—
457#214—181no—
458#214C2×D911yescharacteristic, complemented
459#213—31no—
460#213—31no—
461#213—91no—
462#213—91no—
463#213—91no—
464#213—91no—
465#213—91no—
466#213—181no—
467#213C2×D911yescharacteristic, complemented
468#208—91no—
469C2×C3⋊C8—91no—
470D24—31no—
471D24—91no—
472#204—91no—
473#204—91no—
474#204—91no—
475#204—91no—
476#204—91no—
477#204—181no—
478#204C2×D911yescharacteristic, complemented
479ΓL(1,𝔽25)—91no—
480ΓL(1,𝔽25)—91no—
481ΓL(1,𝔽25)—91no—
482ΓL(1,𝔽25)—91no—
483ΓL(1,𝔽25)—91no—
484ΓL(1,𝔽25)—181no—
485ΓL(1,𝔽25)C2×D911yescharacteristic, complemented
486D3×C8—31no—
487D3×C8—91no—
488C22×C32—21no—
489C22×C32—21no—
490C2×C3⋊D3—31no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—122no—
493C2×C3×D3—21no—
494C2×C3×D3—31no—
495C2×C3×D3—42no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—122no—
499C2×C3×D3—122no—
500C2×C3×D3D3×D411yescharacteristic
501D32—62no—
502D32—122no—
503D32—122no—
504D32—122no—
505C32×C4C23×D311yescharacteristic
506C3⋊Dic3—31no—
507C3⋊Dic3—61no—
508C3×Dic3—21no—
509C3×Dic3—31no—
510C3×Dic3D3×D411yescharacteristic
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—31no—
514C22×C9—41no—
515C22×C9—41no—
516C22×C9—61no—
517C22×C9—122no—
518C2×D9—21no—
519C2×D9—21no—
520C2×D9—31no—
521C2×D9—42no—
522C2×D9—42no—
523C2×D9—61no—
524C2×D9—62no—
525C2×D9—61no—
526C2×D9—121no—
527C2×D9—122no—
528C2×D9—122no—
529C2×D9—122no—
530C2×D9—122no—
531C2×D9—242no—
532C2×D9D3×D411yescharacteristic
533C4×C9—21no—
534C4×C9—31no—
535C4×C9—61no—
536C4×C9C23×D311yescharacteristic
537Dic9—31no—
538Dic9—61no—
539Dic9—61no—
540Dic9—121no—
541Dic9D3×D411yescharacteristic
542C2×#41—271no—
543C22×D4—271no—
544AGL(1,ℤ/8)—31no—
545AGL(1,ℤ/8)—271no—
546AGL(1,ℤ/8)—271no—
547AGL(1,ℤ/8)—271no—
548AGL(1,ℤ/8)—271no—
549AGL(1,ℤ/8)—271no—
550AGL(1,ℤ/8)—271no—
551AGL(1,ℤ/8)—271no—
552C2×SD16—271no—
553C2×SD16—271no—
554C2×D8—91no—
555C2×D8—271no—
556C2×M16—271no—
557C3×C9C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
558C23×C3—61no—
559C23×C3—181no—
560C23×C3—181no—
561C22×D3—21no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—181no—
567C22×D3—181no—
568C22×D3—181no—
569C22×D3—181no—
570C22×D3—181no—
571C22×D3—181no—
572C22×D3—181no—
573C22×D3—181no—
574C22×D3—361no—
575C22×D3—364no—
576C22×D3—364no—
577C3×Q8—31no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—31no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—91no—
584C3×D4—91no—
585C3×D4—181no—
586C3×D4—181no—
587C3×D4C22×D911yescharacteristic
588C3×D4C22×D911yescharacteristic, complemented
589C3×D4C2×D3211yescharacteristic
590C3×D4C2×D3211yescharacteristic
591C2×C3×C4—31no—
592C2×C3×C4—61no—
593C2×C3×C4—91no—
594#67—21no—
595#67—21no—
596#67—61no—
597#67—61no—
598#67—181no—
599#67—181no—
600#67—181no—
601#67—181no—
602#67—181no—
603#67—181no—
604#67—181no—
605#67—181no—
606#67—181no—
607#67—181no—
608#67—181no—
609#67—361no—
610#67—361no—
611C2×Dic3—21no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—181no—
615C2×Dic3—181no—
616C2×Dic3—181no—
617C2×Dic3—181no—
618C2×Dic3—181no—
619C2×Dic3—361no—
620D12—31no—
621D12—31no—
622D12—91no—
623D12—91no—
624D12—181no—
625D12—181no—
626D12—181no—
627D12—181no—
628D12C22×D911yescharacteristic
629C4×D3—31no—
630C4×D3—91no—
631C4×D3—91no—
632C4×D3—91no—
633C4×D3—91no—
634C4×D3—91no—
635C4×D3—91no—
636C4×D3—181no—
637C4×D3—181no—
638C4×D3—181no—
639C4×D3—181no—
640C4×D3C22×D911yescharacteristic
641Dic6—91no—
642Dic6—91no—
643Dic6—181no—
644Dic6—181no—
645Dic6—181no—
646Dic6C22×D911yescharacteristic, complemented
647C3×C8—21no—
648C3×C8—31no—
649C3×C8—91no—
650C3×C8C22×D911yescharacteristic, complemented
651C3×C8C2×D3211yescharacteristic
652C3⋊C8—31no—
653C3⋊C8—91no—
654C3⋊C8—91no—
655C3⋊C8—181no—
656C3⋊C8C22×D911yescharacteristic, complemented
657C2×C32—41no—
658C2×C32—41no—
659C2×C32C2×D3×D411yescharacteristic
660C3⋊D3—61no—
661C3⋊D3—121no—
662C3×D3—21no—
663C3×D3—32no—
664C3×D3—41no—
665C3×D3—121no—
666C3×D3—121no—
667C2×C9—21no—
668C2×C9—41no—
669C2×C9—41no—
670C2×C9—61no—
671C2×C9—81no—
672C2×C9—81no—
673C2×C9—121no—
674C2×C9C2×D3×D411yescharacteristic
675D9—41no—
676D9—41no—
677D9—61no—
678D9—121no—
679D9—121no—
680D9—241no—
681D9#91112yesdirect product factor
682C24—541no—
683#41—31no—
684#41—271no—
685#41—271no—
686#41—271no—
687#41—541no—
688#41—541no—
689C2×Q8—271no—
690C2×D4—31no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—271no—
694C2×D4—271no—
695C2×D4—271no—
696C2×D4—271no—
697C2×D4—541no—
698C2×D4—541no—
699C2×D4—541no—
700C2×D4—541no—
701C22×C4—271no—
702C22×C4—541no—
703SD16—31no—
704SD16—31no—
705SD16—271no—
706SD16—271no—
707SD16—271no—
708SD16—271no—
709SD16—271no—
710SD16—271no—
711D8—31no—
712D8—91no—
713D8—91no—
714D8—91no—
715D8—271no—
716D8—271no—
717D8—271no—
718D8D3×D911yescharacteristic, complemented
719M16—31no—
720M16—271no—
721M16—271no—
722M16—271no—
723C2×C8—91no—
724C2×C8—271no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—31no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—91no—
734C22×C3—122no—
735C22×C3—181no—
736C22×C3—181no—
737C22×C3—362no—
738C22×C3—362no—
739C2×D3—21no—
740C2×D3—31no—
741C2×D3—42no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—91no—
745C2×D3—91no—
746C2×D3—122no—
747C2×D3—122no—
748C2×D3—181no—
749C2×D3—182no—
750C2×D3—182no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—361no—
754C2×D3—362no—
755C2×D3—362no—
756C2×D3—362no—
757C2×D3—362no—
758C2×D3—362no—
759C2×D3—362no—
760C2×D3—362no—
761C2×D3—362no—
762C2×D3—722no—
763C2×D3D4×D911yescharacteristic
764C3×C4—21no—
765C3×C4—31no—
766C3×C4—61no—
767C3×C4—91no—
768C3×C4C23×D911yescharacteristic
769C3×C4C22×D3211yescharacteristic
770Dic3—21no—
771Dic3—31no—
772Dic3—91no—
773Dic3—91no—
774Dic3—181no—
775Dic3—181no—
776Dic3—181no—
777Dic3—361no—
778Dic3D4×D911yescharacteristic
779C32D3×AGL(1,ℤ/8)11yescharacteristic
780C9—21no—
781C9C2×#91111yescharacteristic, complemented
782C23—61no—
783C23—181no—
784C23—181no—
785C23—271no—
786C23—541no—
787C23—541no—
788C23—541no—
789C23—541no—
790C23—1084no—
791Q8—31no—
792Q8—271no—
793Q8—541no—
794D4—31no—
795D4—61no—
796D4—61no—
797D4—91no—
798D4—91no—
799D4—181no—
800D4—181no—
801D4—271no—
802D4—541no—
803D4—541no—
804D4—541no—
805D4—541no—
806D4—541no—
807D4—541no—
808D4—541no—
809D4C2×D3×D911yescharacteristic
810D4C2×D3×D911yescharacteristic, complemented
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—271no—
815C2×C4—271no—
816C2×C4—271no—
817C2×C4—271no—
818C2×C4—541no—
819C2×C4—541no—
820C2×C4—541no—
821C2×C4—541no—
822C8—31no—
823C8—91no—
824C8—271no—
825C8C2×D3×D911yescharacteristic, complemented
826C2×C3—21no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—61no—
832C2×C3—81no—
833C2×C3—81no—
834C2×C3—92no—
835C2×C3—121no—
836C2×C3—361no—
837C2×C3—361no—
838C2×C3C2×D4×D911yescharacteristic
839C2×C3D32×D411yescharacteristic
840D3—21no—
841D3—32no—
842D3—41no—
843D3—121no—
844D3—121no—
845D3—181no—
846D3—181no—
847D3—361no—
848D3—361no—
849D3—361no—
850D3—721no—
851C22—21no—
852C22—21no—
853C22—31no—
854C22—61no—
855C22—91no—
856C22—122no—
857C22—181no—
858C22—181no—
859C22—271no—
860C22—362no—
861C22—362no—
862C22—542no—
863C22—541no—
864C22—1082no—
865C22—1082no—
866C22—1082no—
867C22—1082no—
868C4—31no—
869C4—61no—
870C4—91no—
871C4—271no—
872C4—541no—
873C4C22×D3×D911yescharacteristic
874C3—21no—
875C3D9×AGL(1,ℤ/8)11yescharacteristic, complemented
876C3D3×#91111yescharacteristic
877C2—41no—
878C2—41no—
879C2—61no—
880C2—92no—
881C2—121no—
882C2—361no—
883C2—361no—
884C2—541no—
885C2—1081no—
886C2D3×D4×D911yescharacteristic
subgroupG/H
centerC2D3×D4×D9
commutator, cosocleC3×C4×C9C24
FrattiniC3×C4C22×D32
FittingC3×C9×D8C22
socleC2×C32C2×D3×D4
hypercenterD8D3×D9
hypocenterC3×C9C2×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D9×#237C2semidirect
2. D3×D4×D9C2semidirect
3. #11721790C2semidirect
4. C9×#911C2semidirect
5. C3×D8×D9C2semidirect
6. #11721187C2semidirect
7. D9×#214C2semidirect
8. #11721175C2semidirect
9. D9×#213C2semidirect
10. #11721168C2semidirect
11. #11721167C2semidirect
12. #11720820C2semidirect
13. D9×#204C2semidirect
14. #11720805C2semidirect
15. D9×ΓL(1,𝔽25)C2semidirect
19. #88742C22semidirect
20. D4×C3⋊D9C22semidirect
21. C9×#237C22semidirect
22. D3×D4×C9C22semidirect
24. C3×D4×D9C22semidirect
32. #88646C22semidirect
34. D3×D36C22semidirect
36. #88641C22semidirect
37. #88634C22semidirect
38. D9×Dic6C22semidirect
39. C3×C9×D8C22semidirect
40. #88544C22semidirect
41. #88543C22semidirect
42. #88524C22semidirect
43. #88523C22semidirect
44. C9×#214C22semidirect
45. C9×#213C22semidirect
46. C3×#3673C22semidirect
47. C3×#3673C22semidirect
48. C9×#204C22semidirect
49. C9×ΓL(1,𝔽25)C22semidirect
50. C3×D72C22semidirect
51. C3×C8×D9C22semidirect
52. #88426C22semidirect
53. #88425C22semidirect
54. #88424C22semidirect
55. #88421C22semidirect
56. #88420C22semidirect
57. #88417C22semidirect
58. #88415C22semidirect
59. #88414C22semidirect
60. D9×C3⋊C8C22semidirect
89. D8×D9D3semidirect
102. C3×D4×C9C23semidirect
108. #6226C23semidirect
117. C3×D36C23semidirect
119. C9×Dic6C23semidirect
132. C3×C8×C9C23semidirect
133. C3⋊(C9⋊C8)C23semidirect
134. C9×C3⋊C8C23semidirect
135. C3×C9⋊C8C23semidirect
198. D4×D9C2×D3semidirect
208. C9×D8C2×D3semidirect
215. #3673C2×D3semidirect
216. #3673C2×D3semidirect
222. D72C2×D3semidirect
230. C8×D9C2×D3semidirect
278. #911D9direct (N × H)
346. D4×C9C22×D3semidirect
366. D36C22×D3semidirect
380. C8×C9C22×D3semidirect
383. C9⋊C8C22×D3semidirect
394. C3×D9AGL(1,ℤ/8)semidirect
415. #237C2×D9semidirect
430. D3×D4C2×D9semidirect
446. C3×D8C2×D9semidirect
458. #214C2×D9semidirect
467. #213C2×D9semidirect
478. #204C2×D9semidirect
485. ΓL(1,𝔽25)C2×D9semidirect
557. C3×C9C2×AGL(1,ℤ/8)semidirect
588. C3×D4C22×D9semidirect
646. Dic6C22×D9semidirect
650. C3×C8C22×D9semidirect
656. C3⋊C8C22×D9semidirect
681. D9#911direct (N × H)
718. D8D3×D9semidirect
781. C9C2×#911semidirect
810. D4C2×D3×D9semidirect
825. C8C2×D3×D9semidirect
875. C3D9×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
D9×#2372
D3×D4×D92
#117217902
C9×#9112
C3×D8×D92
#117211872
D9×#2142
#117211752
D9×#2132
#117211682
#117211672
#117208202
D9×#2042
#117208052
D9×ΓL(1,𝔽25)2
D3×#9113
D9×AGL(1,ℤ/8)3