Finite Group Databasebeta

← #13164709

Subgroups — #13164709

Order 1728.

2594 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C2×C9×#235C211yesmaximal, characteristic, complemented
3C2×C3×#3697C211yesmaximal, characteristic, complemented
4#11722535C214yesmaximal, complemented
5#11722478C212yesmaximal, complemented
6#11722477C212yesmaximal, complemented
7#11722476C212yesmaximal, complemented
8#11722475C214yesmaximal, complemented
9D9×#235C214yesmaximal, complemented
10D3×#3697C214yesmaximal, complemented
11#11722465C212yesmaximal, complemented
12#11722464C212yesmaximal, complemented
13#11722458C212yesmaximal, complemented
14#10596669—31nomaximal
15#10593139—31nomaximal
16C22×C3×C4×C9C2211yescharacteristic, complemented
17C2×#6233C2212yescomplemented
18#88736C2212yescomplemented
19#88736C2212yescomplemented
20#88736C2212yescomplemented
21#88736C2212yescomplemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2212yescomplemented
24C2×#6226C2211yescharacteristic, complemented
25C2×C9×#67C2212yescomplemented
26C2×C3×#611C2212yescomplemented
27C9×#235C2212yescomplemented
28C9×#235C2212yescomplemented
29C9×#235C2212yescomplemented
30C9×#235C2212yescomplemented
31C2×C9×D12C2211yescharacteristic, complemented
32C2×C4×D3×C9C2212yescomplemented
33C3×#3697C2212yescomplemented
34C3×#3697C2212yescomplemented
35C3×#3697C2212yescomplemented
36C3×#3697C2212yescomplemented
37C2×C3×D36C2211yescharacteristic, complemented
38C2×C3×C4×D9C2212yescomplemented
39C2×C9×Dic6C2211yescharacteristic, complemented
40C2×C3×Dic18C2211yescharacteristic, complemented
41#88668C2218yescomplemented
42D9×#67C2218yescomplemented
43D3×#611C2218yescomplemented
44#88663C2218yescomplemented
45#88662C2218yescomplemented
46#88658C2218yescomplemented
47#88646C2214yescomplemented
48D9×D12C2214yescomplemented
49D3×D36C2214yescomplemented
50C4×D3×D9C2218yescomplemented
51#88642C2214yescomplemented
52#88641C2214yescomplemented
53#88640C2218yescomplemented
54#88639C2214yescomplemented
55#88638C2214yescomplemented
56D3×Dic18C2214yescomplemented
57(C3⋊D9)⋊Q8C2214yescomplemented
58#88635C2214yescomplemented
59#88634C2214yescomplemented
60D9×Dic6C2214yescomplemented
61C2×#3828—31no—
62C2×C3×#235—31no—
63C2×C3×#235D311yescharacteristic
64#64330—34no—
65#64308—32no—
66#64307—32no—
67#64307—32no—
68#64306—34no—
69D3×#235—34no—
70D3×#235—34no—
71#64298—32no—
72#64297—32no—
73#64297—32no—
74C2×C9×#41—31no—
75#63716—32no—
76#63716—32no—
77#63715—32no—
78#63715—32no—
79#41×D9—34no—
80#41×D9—34no—
81#63713—32no—
82#63710—34no—
83#63710—32no—
84C2×#3697—31no—
85C2×#3697—34no—
86C2×#3697—61no—
87C2×#3697D311yescharacteristic, complemented
88C23×C3×C9C2311yescharacteristic
89C22×C3⋊D9C2312yes—
90C22×D3×C9C2312yes—
91C22×C3×D9C2312yes—
92C2×D3×D9C2318yes—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99#6233C2314yes—
100#6233C2314yes—
101C2×C3⋊Dic9C2312yes—
102C4⋊(C3⋊D9)C2312yes—
103C4⋊(C3⋊D9)C2312yes—
104C4×C3⋊D9C2314yes—
105C4×C3⋊D9C2314yes—
106#6226C2312yes—
107#6226C2312yes—
108C9×#67C2314yes—
109C9×#67C2314yes—
110C3×#611C2314yes—
111C3×#611C2314yes—
112C2×C9×Dic3C2312yes—
113C2×C3×Dic9C2312yes—
114C9×D12C2312yes—
115C9×D12C2312yes—
116C4×D3×C9C2314yes—
117C4×D3×C9C2314yes—
118C3×D36C2312yes—
119C3×D36C2312yes—
120C3×C4×D9C2314yes—
121C3×C4×D9C2314yes—
122C9×Dic6C2312yes—
123C9×Dic6C2312yes—
124C3×Dic18C2312yes—
125C3×Dic18C2312yes—
126#6195C2318yes—
127#6194C2318yes—
128D3×Dic9C2318yes—
129#6192C2318yes—
130(C3⋊D9)⋊C4C2318yes—
131Dic3×D9C2318yes—
132#6189C2318yes—
133#5964—91no—
134#5964—91no—
135C22×C32×C4C2×D311yescharacteristic
136C2×#638—32no—
137#3828—32no—
138#3828—32no—
139#3828—32no—
140#3828—32no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4×C3⋊D3—32no—
143C2×#634—31no—
144C2×C3×#67—32no—
145C2×C3×#67C2×D312yes—
146C3×#235—32no—
147C3×#235—32no—
148C3×#235—32no—
149C3×#235—32no—
150C3×#235C2×D312yes—
151C3×#235C2×D312yes—
152C3×#235C2×D312yes—
153C3×#235C2×D312yes—
154C2×C3×D12—31no—
155C2×C3×D12C2×D311yescharacteristic
156C2×C3×C4×D3—32no—
157C2×C3×C4×D3C2×D312yes—
158C2×C3×Dic6—31no—
159C2×C3×Dic6C2×D311yescharacteristic
160#3811—38no—
161D3×#67—38no—
162D3×#67—38no—
163#3805—38no—
164#3804—38no—
165#3804—38no—
166#3802—34no—
167D3×D12—34no—
168D3×D12—34no—
169C4×D32—38no—
170#3799—34no—
171#3799—34no—
172#3798—38no—
173#3797—34no—
174#3796—34no—
175#3796—34no—
176#3795—34no—
177#3795—34no—
178D3×Dic6—34no—
179D3×Dic6—34no—
180C9×#41—32no—
181C9×#41—32no—
182C9×#41—32no—
183C9×#41—32no—
184C2×Q8×C9—31no—
185C2×D4×C9—32no—
186C2×D4×C9—31no—
187C22×C4×C9—21no—
188C22×C4×C9—32no—
189C22×C4×C9C2×D311yescharacteristic, complemented
190C2×#611—32no—
191C2×#611—38no—
192C2×#611—62no—
193C2×#611C2×D312yescomplemented
194#3701—34no—
195#3701—34no—
196Q8×D9—34no—
197Q8×D9—34no—
198#3699—38no—
199#3699—38no—
200#3699—34no—
201#3699—34no—
202D4×D9—38no—
203D4×D9—38no—
204D4×D9—34no—
205D4×D9—34no—
206#3697—32no—
207#3697—32no—
208#3697—32no—
209#3697—32no—
210#3697—38no—
211#3697—34no—
212#3697—38no—
213#3697—34no—
214#3697—62no—
215#3697—62no—
216#3697—62no—
217#3697—62no—
218#3697C2×D312yescomplemented
219#3697C2×D312yescomplemented
220#3697C2×D312yescomplemented
221#3697C2×D312yescomplemented
222C2×D36—31no—
223C2×D36—34no—
224C2×D36—61no—
225C2×D36C2×D311yescharacteristic, complemented
226C2×C4×D9—32no—
227C2×C4×D9—38no—
228C2×C4×D9—62no—
229C2×C4×D9C2×D312yescomplemented
230C2×Dic18—31no—
231C2×Dic18—34no—
232C2×Dic18—61no—
233C2×Dic18C2×D311yescharacteristic, complemented
234C22×C3×C9—41no—
235C22×C3×C9C2411yescharacteristic
236C22×C3×C9C2411yescharacteristic
237C22×C3×C9C2411yescharacteristic
238C2×C3⋊D9—42no—
239C2×C3⋊D9C2414yes—
240C2×D3×C9—42no—
241C2×D3×C9C2414yes—
242C2×C3×D9—42no—
243C2×C3×D9C2414yes—
244D3×D9—48no—
245C3×C4×C9C2411yescharacteristic
246C3×C4×C9C2411yescharacteristic
247C3×C4×C9C2411yescharacteristic
248C3×C4×C9C2411yescharacteristic
249C3⋊Dic9C2414yes—
250C9×Dic3C2414yes—
251C3×Dic9C2414yes—
252C2×C3×#41—31no—
253C2×C3×#41—91no—
254#1010—92no—
255#1010—92no—
256#1010—92no—
257#1010—92no—
258#1009—92no—
259#1009—92no—
260#1009—92no—
261#1009—92no—
262D3×#41—94no—
263D3×#41—94no—
264D3×#41—94no—
265D3×#41—94no—
266#1007—92no—
267#1007—92no—
268#1004—92no—
269#1004—94no—
270#1004—94no—
271#1004—92no—
272C2×#235—31no—
273C2×#235—94no—
274C2×#235—91no—
275C2×#235—91no—
276C2×#235—94no—
277C2×#235—181no—
278C2×#235D911yescharacteristic, complemented
279C23×C32C22×D311yescharacteristic
280C22×C3⋊D3—32no—
281C22×C3×D3—32no—
282C22×C3×D3C22×D312yes—
283C2×D32—38no—
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290#638—34no—
291#638—34no—
292C2×C3⋊Dic3—32no—
293C4⋊(C3⋊D3)—32no—
294C4⋊(C3⋊D3)—32no—
295C4×C3⋊D3—34no—
296C4×C3⋊D3—34no—
297#634—32no—
298#634—32no—
299C3×#67—34no—
300C3×#67—34no—
301C3×#67C22×D314yes—
302C3×#67C22×D314yes—
303C2×C3×Dic3—32no—
304C2×C3×Dic3C22×D312yes—
305C3×D12—32no—
306C3×D12—32no—
307C3×D12C22×D312yes—
308C3×D12C22×D312yes—
309C3×C4×D3—34no—
310C3×C4×D3—34no—
311C3×C4×D3C22×D314yes—
312C3×C4×D3C22×D314yes—
313C3×Dic6—32no—
314C3×Dic6—32no—
315C3×Dic6C22×D312yes—
316C3×Dic6C22×D312yes—
317#627—38no—
318#626—38no—
319#626—38no—
320#625—38no—
321#624—38no—
322D3×Dic3—38no—
323D3×Dic3—38no—
324C23×C9—21no—
325C23×C9—32no—
326C23×C9C22×D311yescharacteristic
327C22×D9—32no—
328C22×D9—38no—
329C22×D9—62no—
330C22×D9C22×D312yes—
331Q8×C9—32no—
332Q8×C9—32no—
333D4×C9—34no—
334D4×C9—34no—
335D4×C9—32no—
336D4×C9—32no—
337C2×C4×C9—21no—
338C2×C4×C9—21no—
339C2×C4×C9—21no—
340C2×C4×C9—21no—
341C2×C4×C9—21no—
342C2×C4×C9—21no—
343C2×C4×C9—32no—
344C2×C4×C9—34no—
345C2×C4×C9—34no—
346C2×C4×C9C22×D311yescharacteristic
347C2×C4×C9C22×D311yescharacteristic
348C2×C4×C9C22×D311yescharacteristic
349C2×C4×C9C22×D311yescharacteristic
350C2×C4×C9C22×D311yescharacteristic
351C2×C4×C9C22×D311yescharacteristic
352#611—34no—
353#611—34no—
354#611—38no—
355#611—38no—
356#611—64no—
357#611—64no—
358#611C22×D314yes—
359#611C22×D314yes—
360C2×Dic9—32no—
361C2×Dic9—38no—
362C2×Dic9—62no—
363C2×Dic9C22×D312yes—
364D36—38no—
365D36—32no—
366D36—32no—
367D36—62no—
368D36—62no—
369D36C22×D312yes—
370D36C22×D312yes—
371C4×D9—38no—
372C4×D9—34no—
373C4×D9—34no—
374C4×D9—38no—
375C4×D9—64no—
376C4×D9—64no—
377C4×D9C22×D314yes—
378C4×D9C22×D314yes—
379Dic18—32no—
380Dic18—32no—
381Dic18—38no—
382Dic18—62no—
383Dic18—62no—
384Dic18C22×D312yes—
385Dic18C22×D312yes—
386#585—271noSylow
387C2×C3×C9—21no—
388C2×C3×C9—21no—
389C2×C3×C9—21no—
390C2×C3×C9C2511yescharacteristic
391C3⋊D9—24no—
392D3×C9—24no—
393C3×D9—24no—
394C3×#41—32no—
395C3×#41—32no—
396C3×#41—32no—
397C3×#41—32no—
398C3×#41—92no—
399C3×#41—92no—
400C3×#41—92no—
401C3×#41—92no—
402C2×C3×Q8—31no—
403C2×C3×Q8—91no—
404C2×C3×D4—32no—
405C2×C3×D4—31no—
406C2×C3×D4—92no—
407C2×C3×D4—91no—
408C22×C3×C4—21no—
409C22×C3×C4—32no—
410C22×C3×C4—92no—
411C22×C3×C4C2×D911yescharacteristic, complemented
412C22×C3×C4D3211yescharacteristic
413C2×#67—32no—
414C2×#67—98no—
415C2×#67—92no—
416C2×#67—92no—
417C2×#67—98no—
418C2×#67—182no—
419C2×#67C2×D912yescomplemented
420#239—94no—
421#239—94no—
422#239—94no—
423#239—94no—
424D3×Q8—94no—
425D3×Q8—94no—
426D3×Q8—94no—
427D3×Q8—94no—
428#237—94no—
429#237—94no—
430#237—98no—
431#237—98no—
432#237—98no—
433#237—98no—
434#237—94no—
435#237—94no—
436D3×D4—94no—
437D3×D4—94no—
438D3×D4—98no—
439D3×D4—98no—
440D3×D4—98no—
441D3×D4—98no—
442D3×D4—94no—
443D3×D4—94no—
444#235—32no—
445#235—32no—
446#235—32no—
447#235—32no—
448#235—94no—
449#235—98no—
450#235—94no—
451#235—98no—
452#235—92no—
453#235—92no—
454#235—92no—
455#235—92no—
456#235—92no—
457#235—92no—
458#235—92no—
459#235—92no—
460#235—98no—
461#235—94no—
462#235—98no—
463#235—94no—
464#235—182no—
465#235—182no—
466#235—182no—
467#235—182no—
468#235C2×D912yescomplemented
469#235C2×D912yescomplemented
470#235C2×D912yescomplemented
471#235C2×D912yescomplemented
472C2×D12—31no—
473C2×D12—94no—
474C2×D12—91no—
475C2×D12—91no—
476C2×D12—94no—
477C2×D12—181no—
478C2×D12C2×D911yescharacteristic, complemented
479C2×C4×D3—32no—
480C2×C4×D3—98no—
481C2×C4×D3—92no—
482C2×C4×D3—92no—
483C2×C4×D3—98no—
484C2×C4×D3—182no—
485C2×C4×D3C2×D912yescomplemented
486C2×Dic6—31no—
487C2×Dic6—94no—
488C2×Dic6—91no—
489C2×Dic6—91no—
490C2×Dic6—94no—
491C2×Dic6—181no—
492C2×Dic6C2×D911yescharacteristic, complemented
493C22×C32—41no—
494C22×C32C23×D311yescharacteristic
495C22×C32C23×D311yescharacteristic
496C22×C32C23×D311yescharacteristic
497C2×C3⋊D3—34no—
498C2×C3⋊D3—122no—
499C2×C3×D3—34no—
500C2×C3×D3—42no—
501C2×C3×D3—122no—
502C2×C3×D3C23×D314yes—
503D32—128no—
504C32×C4C23×D311yescharacteristic
505C32×C4C23×D311yescharacteristic
506C32×C4C23×D311yescharacteristic
507C32×C4C23×D311yescharacteristic
508C3⋊Dic3—34no—
509C3×Dic3—34no—
510C3×Dic3C23×D314yes—
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—21no—
514C22×C9—34no—
515C22×C9—41no—
516C22×C9—42no—
517C22×C9—122no—
518C22×C9C23×D311yescharacteristic
519C22×C9C23×D311yescharacteristic
520C22×C9C23×D311yescharacteristic
521C2×D9—34no—
522C2×D9—42no—
523C2×D9—64no—
524C2×D9—128no—
525C2×D9—122no—
526C2×D9—124no—
527C2×D9C23×D314yes—
528C4×C9—21no—
529C4×C9—21no—
530C4×C9—21no—
531C4×C9—21no—
532C4×C9—34no—
533C4×C9C23×D311yescharacteristic
534C4×C9C23×D311yescharacteristic
535C4×C9C23×D311yescharacteristic
536C4×C9C23×D311yescharacteristic
537Dic9—34no—
538Dic9—64no—
539Dic9C23×D314yes—
5402−1+4—272no—
5412−1+4—272no—
5422−1+4—272no—
543H(5,𝔽2)—274no—
544H(5,𝔽2)—272no—
545H(5,𝔽2)—272no—
546H(5,𝔽2)—272no—
547C2×#41—31no—
548C2×#41—91no—
549C2×#41—274no—
550C2×#41—274no—
551C2×#41—274no—
552C2×#41—271no—
553C3×C9#58511yescharacteristic, complemented, Sylow
554C23×C3—21no—
555C23×C3—32no—
556C23×C3—92no—
557C23×C3C22×D911yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C22×D3—32no—
560C22×D3—98no—
561C22×D3—92no—
562C22×D3—92no—
563C22×D3—98no—
564C22×D3—182no—
565C22×D3C22×D912yes—
566C3×Q8—32no—
567C3×Q8—32no—
568C3×Q8—92no—
569C3×Q8—92no—
570C3×D4—34no—
571C3×D4—34no—
572C3×D4—32no—
573C3×D4—32no—
574C3×D4—94no—
575C3×D4—94no—
576C3×D4—92no—
577C3×D4—92no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—32no—
585C2×C3×C4—34no—
586C2×C3×C4—34no—
587C2×C3×C4—92no—
588C2×C3×C4—94no—
589C2×C3×C4—94no—
590C2×C3×C4C22×D911yescharacteristic
591C2×C3×C4C22×D911yescharacteristic
592C2×C3×C4C22×D911yescharacteristic
593C2×C3×C4C22×D911yescharacteristic
594C2×C3×C4C22×D911yescharacteristic
595C2×C3×C4C22×D911yescharacteristic
596C2×C3×C4C2×D3211yescharacteristic
597C2×C3×C4C2×D3211yescharacteristic
598C2×C3×C4C2×D3211yescharacteristic
599C2×C3×C4C2×D3211yescharacteristic
600C2×C3×C4C2×D3211yescharacteristic
601C2×C3×C4C2×D3211yescharacteristic
602#67—34no—
603#67—34no—
604#67—98no—
605#67—98no—
606#67—94no—
607#67—94no—
608#67—94no—
609#67—94no—
610#67—98no—
611#67—98no—
612#67—184no—
613#67—184no—
614#67C22×D914yes—
615#67C22×D914yes—
616C2×Dic3—32no—
617C2×Dic3—98no—
618C2×Dic3—92no—
619C2×Dic3—92no—
620C2×Dic3—98no—
621C2×Dic3—182no—
622C2×Dic3C22×D912yes—
623D12—32no—
624D12—32no—
625D12—98no—
626D12—98no—
627D12—92no—
628D12—92no—
629D12—92no—
630D12—92no—
631D12—182no—
632D12—182no—
633D12C22×D912yes—
634D12C22×D912yes—
635C4×D3—34no—
636C4×D3—34no—
637C4×D3—98no—
638C4×D3—98no—
639C4×D3—98no—
640C4×D3—94no—
641C4×D3—94no—
642C4×D3—94no—
643C4×D3—94no—
644C4×D3—98no—
645C4×D3—184no—
646C4×D3—184no—
647C4×D3C22×D914yes—
648C4×D3C22×D914yes—
649Dic6—32no—
650Dic6—32no—
651Dic6—98no—
652Dic6—92no—
653Dic6—92no—
654Dic6—92no—
655Dic6—92no—
656Dic6—98no—
657Dic6—182no—
658Dic6—182no—
659Dic6C22×D912yes—
660Dic6C22×D912yes—
661C2×C32—21no—
662C2×C32—21no—
663C2×C32—21no—
664C2×C32C24×D311yescharacteristic
665C3⋊D3—64no—
666C3×D3—24no—
667C3×D3—64no—
668C2×C9—22no—
669C2×C9—21no—
670C2×C9—21no—
671C2×C9—21no—
672C2×C9—21no—
673C2×C9—41no—
674C2×C9—41no—
675C2×C9—64no—
676C2×C9C24×D311yescharacteristic
677D9—24no—
678D9—64no—
679D9—124no—
680#41—32no—
681#41—32no—
682#41—32no—
683#41—32no—
684#41—92no—
685#41—92no—
686#41—92no—
687#41—92no—
688#41—278no—
689#41—278no—
690#41—274no—
691#41—274no—
692#41—278no—
693#41—274no—
694#41—274no—
695#41—278no—
696#41—274no—
697#41—274no—
698#41—272no—
699#41—272no—
700#41—272no—
701#41—272no—
702C2×Q8—31no—
703C2×Q8—91no—
704C2×Q8—274no—
705C2×Q8—274no—
706C2×Q8—274no—
707C2×Q8—271no—
708C2×D4—32no—
709C2×D4—31no—
710C2×D4—92no—
711C2×D4—91no—
712C2×D4—274no—
713C2×D4—274no—
714C2×D4—278no—
715C2×D4—274no—
716C2×D4—278no—
717C2×D4—278no—
718C2×D4—272no—
719C2×D4—271no—
720C22×C4—32no—
721C22×C4—92no—
722C22×C4—278no—
723C22×C4—272no—
724C22×C4D3×D911yescharacteristic, complemented
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—34no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—42no—
732C22×C3—94no—
733C22×C3—122no—
734C22×C3—362no—
735C22×C3C23×D911yescharacteristic
736C22×C3C23×D911yescharacteristic
737C22×C3C23×D911yescharacteristic
738C22×C3C22×D3211yescharacteristic
739C22×C3C22×D3211yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C2×D3—34no—
742C2×D3—42no—
743C2×D3—94no—
744C2×D3—94no—
745C2×D3—122no—
746C2×D3—184no—
747C2×D3—368no—
748C2×D3—368no—
749C2×D3—362no—
750C2×D3—362no—
751C2×D3—364no—
752C2×D3C23×D914yes—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—34no—
758C3×C4—94no—
759C3×C4C23×D911yescharacteristic
760C3×C4C23×D911yescharacteristic
761C3×C4C23×D911yescharacteristic
762C3×C4C23×D911yescharacteristic
763C3×C4C22×D3211yescharacteristic
764C3×C4C22×D3211yescharacteristic
765C3×C4C22×D3211yescharacteristic
766C3×C4C22×D3211yescharacteristic
767Dic3—34no—
768Dic3—94no—
769Dic3—94no—
770Dic3—184no—
771Dic3C23×D914yes—
772C32#596411yescharacteristic
773C9—21no—
774C9#596411yescharacteristic, complemented
775C23—32no—
776C23—92no—
777C23—278no—
778C23—272no—
779C23C2×D3×D911yescharacteristic
780Q8—32no—
781Q8—32no—
782Q8—92no—
783Q8—92no—
784Q8—278no—
785Q8—272no—
786Q8—272no—
787D4—34no—
788D4—34no—
789D4—32no—
790D4—32no—
791D4—94no—
792D4—94no—
793D4—92no—
794D4—92no—
795D4—278no—
796D4—278no—
797D4—278no—
798D4—274no—
799D4—274no—
800D4—272no—
801D4—272no—
802C2×C4—32no—
803C2×C4—34no—
804C2×C4—34no—
805C2×C4—92no—
806C2×C4—94no—
807C2×C4—94no—
808C2×C4—278no—
809C2×C4—278no—
810C2×C4—278no—
811C2×C4—272no—
812C2×C4—274no—
813C2×C4—274no—
814C2×C4C2×D3×D911yescharacteristic
815C2×C4C2×D3×D911yescharacteristic
816C2×C4C2×D3×D911yescharacteristic
817C2×C4C2×D3×D911yescharacteristic
818C2×C4C2×D3×D911yescharacteristic
819C2×C4C2×D3×D911yescharacteristic
820C2×C3—22no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—64no—
831C2×C3—184no—
832C2×C3C24×D911yescharacteristic
833C2×C3C23×D3211yescharacteristic
834D3—24no—
835D3—64no—
836D3—184no—
837D3—184no—
838D3—364no—
839C22—34no—
840C22—41no—
841C22—94no—
842C22—122no—
843C22—274no—
844C22—362no—
845C22—1082no—
846C22—1088no—
847C22C22×D3×D911yescharacteristic
848C22C22×D3×D911yescharacteristic
849C22C22×D3×D911yescharacteristic
850C4—34no—
851C4—94no—
852C4—274no—
853C4C22×D3×D911yescharacteristic
854C4C22×D3×D911yescharacteristic
855C4C22×D3×D911yescharacteristic
856C4C22×D3×D911yescharacteristic
857C3—21no—
858C3#1059313911yescharacteristic, complemented
859C3#1059666911yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—64no—
864C2—184no—
865C2—544no—
866C2C23×D3×D911yescharacteristic
subgroupG/H
centerC4C22×D3×D9
commutator, cosocleC2×C3×C9C25
FrattiniC2×C3C23×D32
FittingC22×C3×C4×C9C22
socleC2×C32C24×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#585
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88736C2semidirect
2. C2×C9×#235C2semidirect
3. C2×C3×#3697C2semidirect
4. #11722535C2semidirect
5. #11722478C2semidirect
6. #11722477C2semidirect
7. #11722476C2semidirect
8. #11722475C2semidirect
9. D9×#235C2semidirect
10. D3×#3697C2semidirect
11. #11722465C2semidirect
12. #11722464C2semidirect
13. #11722458C2semidirect
16. C22×C3×C4×C9C22semidirect
17. C2×#6233C22semidirect
18. #88736C22semidirect
19. #88736C22semidirect
20. #88736C22semidirect
21. #88736C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
23. C2×C4×C3⋊D9C22semidirect
24. C2×#6226C22semidirect
25. C2×C9×#67C22semidirect
26. C2×C3×#611C22semidirect
27. C9×#235C22semidirect
28. C9×#235C22semidirect
29. C9×#235C22semidirect
30. C9×#235C22semidirect
31. C2×C9×D12C22semidirect
32. C2×C4×D3×C9C22semidirect
33. C3×#3697C22semidirect
34. C3×#3697C22semidirect
35. C3×#3697C22semidirect
36. C3×#3697C22semidirect
37. C2×C3×D36C22semidirect
38. C2×C3×C4×D9C22semidirect
39. C2×C9×Dic6C22semidirect
40. C2×C3×Dic18C22semidirect
41. #88668C22semidirect
42. D9×#67C22semidirect
43. D3×#611C22semidirect
44. #88663C22semidirect
45. #88662C22semidirect
46. #88658C22semidirect
47. #88646C22semidirect
48. D9×D12C22semidirect
49. D3×D36C22semidirect
50. C4×D3×D9C22semidirect
51. #88642C22semidirect
52. #88641C22semidirect
53. #88640C22semidirect
54. #88639C22semidirect
55. #88638C22semidirect
56. D3×Dic18C22semidirect
57. (C3⋊D9)⋊Q8C22semidirect
58. #88635C22semidirect
59. #88634C22semidirect
60. D9×Dic6C22semidirect
87. C2×#3697D3semidirect
189. C22×C4×C9C2×D3semidirect
193. C2×#611C2×D3semidirect
218. #3697C2×D3semidirect
219. #3697C2×D3semidirect
220. #3697C2×D3semidirect
221. #3697C2×D3semidirect
225. C2×D36C2×D3semidirect
229. C2×C4×D9C2×D3semidirect
233. C2×Dic18C2×D3semidirect
278. C2×#235D9semidirect
411. C22×C3×C4C2×D9semidirect
419. C2×#67C2×D9semidirect
468. #235C2×D9semidirect
469. #235C2×D9semidirect
470. #235C2×D9semidirect
471. #235C2×D9semidirect
478. C2×D12C2×D9semidirect
485. C2×C4×D3C2×D9semidirect
492. C2×Dic6C2×D9semidirect
553. C3×C9#585semidirect
724. C22×C4D3×D9semidirect
774. C9#5964semidirect
858. C3#10593139semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C2×C9×#2352
C2×C3×#36972
#117225352
#117224782
#117224772
#117224762
#117224752
D9×#2352
D3×#36972
#117224652
#117224642
#117224582
#105966693
#105931393