Finite Group Databasebeta

← #13167819

Subgroups — #13167819

Order 1728.

1308 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724384C212yesmaximal, complemented
2#11723654C211yesmaximal, characteristic, complemented
3#11723337C211yesmaximal, characteristic, complemented
4C3⋊D3×D24C211yesmaximal, characteristic, complemented
5D3×#3745C211yesmaximal, characteristic, complemented
6C3×#63807C211yesmaximal, characteristic, complemented
7C3×#63803C211yesmaximal, characteristic, complemented
8C3×D3×D24C211yesmaximal, characteristic, complemented
9#11722879C212yesmaximal, complemented
10#11722870C212yesmaximal, complemented
11#11722868C212yesmaximal, complemented
12#10594734—31nomaximal
13#10594680—31nomaximal
14#10594678—31nomaximal
15#89041C2212yescomplemented
16C3⋊D3×D12C2212yescomplemented
17D3×C4⋊(C3⋊D3)C2212yescomplemented
18#89022C2212yescomplemented
19C3×D3×D12C2212yescomplemented
20C3×#3798C2211yescharacteristic
21C3×#3795C2212yescomplemented
22#88962—22no—
23#88954—22no—
24#88952—22no—
25D3×#626—22no—
26#88852C2211yescharacteristic, complemented
27C3×#3746C2211yescharacteristic, complemented
28C3×#3745C2211yescharacteristic, complemented
29C3×C8×C3⋊D3C2211yescharacteristic, complemented
30C32×D24C2211yescharacteristic, complemented
31C32×D3×C8C2211yescharacteristic, complemented
32C32×D3×C8C2211yescharacteristic, complemented
33#88811C2212yescomplemented
34#88797C2212yescomplemented
35#88791C2212yescomplemented
36#88790C2212yescomplemented
37C3×#3716C2212yescomplemented
38C3×#3714C2212yescomplemented
39C3×#3712C2211yescharacteristic, complemented
40C3×#3711C2211yescharacteristic, complemented
41C3×#3711C2211yescharacteristic, complemented
42#64314—32no—
43#64308—32no—
44#64307—32no—
45D8×C3⋊D3—31no—
46#64113—31no—
47C2×#3745—31no—
48C3×#912—31no—
49C3×D3×D8—31no—
50C3×#904—31no—
51C2×C3×D24—31no—
52C3×#901—31no—
53C3×#901—31no—
54#63937—32no—
55#63934—32no—
56#63925—32no—
57#63830—32no—
58#63825—32no—
59#63810—31no—
60#63808—31no—
61#63808—31no—
62#63808—31no—
63#63808—61no—
64#63807—31no—
65#63807D311yescharacteristic, complemented
66#63803D311yescharacteristic, complemented
67#63795—32no—
68#63795—32no—
69#63794—32no—
70#63794—32no—
71D3×D24—31no—
72D3×D24—31no—
73D3×D24—31no—
74D3×D24—31no—
75D3×D24—61no—
76D3×D24—61no—
77D3×D24D311yescharacteristic, complemented
78C2×D3×C3⋊D3—22no—
79C2×D3×C3⋊D3—22no—
80C2×C3×D32—22no—
81C4⋊(C3⋊(C3⋊D3))C2312yes—
82C3×C4⋊(C3⋊D3)C2312yes—
83C3×C4×C3⋊D3C2311yescharacteristic
84C3×#634C2312yes—
85C32×D12C2312yes—
86C32×C4×D3C2311yescharacteristic
87C32×C4×D3C2311yescharacteristic
88#6295—22no—
89#6294—22no—
90#6292—22no—
91#6291—22no—
92#6291—22no—
93#6289—22no—
94C3×#627D411yescharacteristic
95C3×#626—22no—
96C3×#626D411yescharacteristic
97C3×#626D411yescharacteristic
98C3×#625—22no—
99C3×#625D411yescharacteristic
100C3×D3×Dic3—22no—
101C33×C8C2311yescharacteristic
102C3×C3⋊(C3⋊C8)C2311yescharacteristic
103C32×C3⋊C8C2311yescharacteristic
104C32×C3⋊C8C2311yescharacteristic
105#5769—91no—
106#5757—91no—
107#5752—91no—
108D4×C3⋊D3—32no—
109#3828—32no—
110C2×C4⋊(C3⋊D3)—32no—
111C3×#237—32no—
112C3×D3×D4—32no—
113C3×#235—31no—
114C3×#235—31no—
115C3×#235—32no—
116C2×C3×D12—32no—
117#3811—62no—
118#3811—62no—
119#3811—62no—
120D3×#67—62no—
121D3×#67—62no—
122D3×#67—62no—
123C2×#626—62no—
124#3804—62no—
125#3802—62no—
126D3×D12—32no—
127D3×D12—32no—
128D3×D12—32no—
129D3×D12—32no—
130D3×D12—62no—
131D3×D12—62no—
132D3×D12—62no—
133D3×D12C2×D312yescomplemented
134#3799—32no—
135#3799—32no—
136#3799—32no—
137#3799—62no—
138#3799—62no—
139#3798C2×D311yescharacteristic
140#3796—32no—
141#3796—62no—
142#3795—32no—
143#3795C2×D312yescomplemented
144C32×D8—31no—
145C2×C32×C8—31no—
146C2×C32×C8—31no—
147#3753—32no—
148#3746C2×D311yescharacteristic, complemented
149#3745—32no—
150#3745—31no—
151#3745—31no—
152#3745—31no—
153#3745—61no—
154#3745—61no—
155#3745—61no—
156#3745—121no—
157#3745C2×D311yescharacteristic, complemented
158#3744—32no—
159C8×C3⋊D3C2×D311yescharacteristic, complemented
160C3×#214—32no—
161C3×#213—32no—
162C3×#208—31no—
163C3×#208—31no—
164C3×Dic12—31no—
165C3×Dic12—31no—
166C3×Dic12—61no—
167C3×D24—21no—
168C3×D24—32no—
169C3×D24—31no—
170C3×D24—31no—
171C3×D24—61no—
172C3×D24C2×D311yescharacteristic, complemented
173C3×D24C2×D311yescharacteristic, complemented
174C3×#204—32no—
175C3×ΓL(1,𝔽25)—31no—
176C3×ΓL(1,𝔽25)—31no—
177C3×ΓL(1,𝔽25)—31no—
178C3×ΓL(1,𝔽25)—31no—
179C3×D3×C8—21no—
180C3×D3×C8—21no—
181C3×D3×C8—31no—
182C3×D3×C8—31no—
183C3×D3×C8—61no—
184C3×D3×C8C2×D311yescharacteristic, complemented
185C3×D3×C8C2×D311yescharacteristic, complemented
186C3×D3×C8C2×D311yescharacteristic, complemented
187C3×D3×C8C2×D311yescharacteristic, complemented
188#3717—32no—
189#3717—32no—
190#3717—32no—
191#3717—62no—
192#3716—32no—
193#3716C2×D312yescomplemented
194#3715—32no—
195#3714—32no—
196#3714—32no—
197#3714—32no—
198#3714—32no—
199#3714—62no—
200#3714—62no—
201#3714C2×D312yescomplemented
202#3712C2×D311yescharacteristic, complemented
203#3711C2×D311yescharacteristic, complemented
204#3711C2×D311yescharacteristic, complemented
205C2×C3⋊(C3⋊D3)—22no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3C2×D411yescharacteristic
208C2×C32×D3—22no—
209C2×C32×D3C2×D411yescharacteristic
210C2×C32×D3C2×D411yescharacteristic
211D3×C3⋊D3—82no—
212D3×C3⋊D3—82no—
213C3×D32—82no—
214C33×C4C2411yescharacteristic
215C3×C3⋊Dic3—22no—
216C3×C3⋊Dic3C2×D411yescharacteristic
217C32×Dic3C2×D411yescharacteristic
218C32×Dic3C2×D411yescharacteristic
219#1009—92no—
220#1009—92no—
221#1004—92no—
222C3×#135—91no—
223C2×C3×D8—91no—
224C3×#131—91no—
225#949—92no—
226#932—92no—
227#919—91no—
228#919—91no—
229#914—92no—
230#914—92no—
231#912—31no—
232#912—91no—
233#911—92no—
234#911—92no—
235D3×D8—31no—
236D3×D8—91no—
237D3×D8—91no—
238D3×D8—91no—
239D3×D8—181no—
240#908—92no—
241#908—92no—
242#908—92no—
243#904—31no—
244#904—91no—
245#904—91no—
246#904—91no—
247#904—181no—
248C2×D24—31no—
249C2×D24—91no—
250C2×D24—91no—
251C2×D24—91no—
252C2×D24—181no—
253#901—31no—
254#901—31no—
255C22×C3⋊D3—62no—
256C22×C3⋊D3—62no—
257C22×C3×D3—62no—
258C22×C3×D3—62no—
259C2×D32—22no—
260C2×D32—62no—
261C2×D32—62no—
262C2×D32—62no—
263C2×D32—62no—
264C2×D32—122no—
265C2×D32—122no—
266C32×D4—32no—
267C2×C32×C4—31no—
268C2×C32×C4—31no—
269#638—62no—
270#638—62no—
271C4⋊(C3⋊D3)—32no—
272C4⋊(C3⋊D3)—32no—
273C4⋊(C3⋊D3)—32no—
274C4⋊(C3⋊D3)—62no—
275C4⋊(C3⋊D3)—62no—
276C4⋊(C3⋊D3)—62no—
277C4⋊(C3⋊D3)—62no—
278C4⋊(C3⋊D3)—122no—
279C4⋊(C3⋊D3)C22×D312yes—
280C4×C3⋊D3—62no—
281C4×C3⋊D3C22×D311yescharacteristic
282#634C22×D312yes—
283C3×#67—31no—
284C3×#67—31no—
285C3×#67—31no—
286C3×#67—31no—
287C3×#67—62no—
288C3×#67—62no—
289C3×#67—62no—
290C2×C3×Dic3—62no—
291C3×D12—22no—
292C3×D12—31no—
293C3×D12—31no—
294C3×D12—32no—
295C3×D12—32no—
296C3×D12—62no—
297C3×D12—62no—
298C3×D12C22×D312yes—
299C3×D12C22×D312yes—
300C3×C4×D3—21no—
301C3×C4×D3—21no—
302C3×C4×D3—31no—
303C3×C4×D3—31no—
304C3×C4×D3—61no—
305C3×C4×D3—62no—
306C3×C4×D3C22×D311yescharacteristic
307C3×C4×D3C22×D311yescharacteristic
308C3×C4×D3C22×D311yescharacteristic
309C3×C4×D3C22×D311yescharacteristic
310C3×Dic6—31no—
311C3×Dic6—31no—
312C3×Dic6—32no—
313C3×Dic6—32no—
314C3×Dic6—62no—
315#627D1211yescharacteristic
316#626—22no—
317#626—62no—
318#626—62no—
319#626—62no—
320#626—62no—
321#626—62no—
322#626—62no—
323#626—62no—
324#626—62no—
325#626—122no—
326#626—122no—
327#626—122no—
328#626D1211yescharacteristic
329#626D1211yescharacteristic
330#625—22no—
331#625—62no—
332#625D1211yescharacteristic
333#624—62no—
334#624—62no—
335#624—62no—
336#624—122no—
337D3×Dic3—22no—
338D3×Dic3—62no—
339D3×Dic3—62no—
340C32×C8—21no—
341C32×C8—21no—
342C32×C8—21no—
343C32×C8—31no—
344C32×C8—31no—
345C32×C8—41no—
346C32×C8C22×D311yescharacteristic
347C32×C8C22×D311yescharacteristic
348C32×C8C22×D311yescharacteristic
349C3⋊(C3⋊C8)C22×D311yescharacteristic
350C3×C3⋊C8—21no—
351C3×C3⋊C8—21no—
352C3×C3⋊C8—31no—
353C3×C3⋊C8—31no—
354C3×C3⋊C8—61no—
355C3×C3⋊C8C22×D311yescharacteristic
356C3×C3⋊C8C22×D311yescharacteristic
357C3×C3⋊C8C22×D311yescharacteristic
358C3×C3⋊C8C22×D311yescharacteristic
359#576—271noSylow
360C2×C33C22×D411yescharacteristic
361C3⋊(C3⋊D3)—42no—
362C3×C3⋊D3—21no—
363C3×C3⋊D3—42no—
364C32×D3—21no—
365C32×D3—21no—
366C32×D3—42no—
367C3×#41—91no—
368C3×#41—92no—
369C2×C3×D4—92no—
370C2×#67—182no—
371C2×#67—182no—
372#239—92no—
373#239—92no—
374#239—182no—
375#237—32no—
376#237—92no—
377#237—182no—
378D3×D4—32no—
379D3×D4—92no—
380D3×D4—92no—
381D3×D4—92no—
382D3×D4—182no—
383D3×D4—182no—
384D3×D4—182no—
385D3×D4—182no—
386D3×D4—182no—
387D3×D4—182no—
388D3×D4—182no—
389#235—31no—
390#235—31no—
391#235—32no—
392#235—92no—
393#235—92no—
394#235—92no—
395#235—182no—
396#235—182no—
397C2×D12—32no—
398C2×D12—92no—
399C2×D12—92no—
400C2×D12—92no—
401C2×D12—182no—
402C2×D12—182no—
403C3×Q16—91no—
404C3×SD16—92no—
405C3×D8—31no—
406C3×D8—31no—
407C3×D8—61no—
408C3×D8—92no—
409C3×D8—91no—
410C3×M16—91no—
411C3×M16—91no—
412C3×M16—91no—
413C2×C3×C8—31no—
414C2×C3×C8—31no—
415C2×C3×C8—31no—
416C2×C3×C8—31no—
417C2×C3×C8—61no—
418C2×C3×C8—61no—
419C2×C3×C8—91no—
420#215—92no—
421#215—92no—
422#214—32no—
423#214—92no—
424#213—32no—
425#213—92no—
426#213—92no—
427#213—92no—
428#213—182no—
429#208—31no—
430#208—31no—
431Dic12—31no—
432Dic12—31no—
433Dic12—61no—
434D24—32no—
435D24—31no—
436D24—31no—
437D24—61no—
438D24—92no—
439D24—92no—
440D24—92no—
441D24—91no—
442D24—91no—
443D24—91no—
444D24—181no—
445D24—181no—
446D24—181no—
447D24—182no—
448D24—361no—
449D24D3211yescharacteristic, complemented
450#204—32no—
451#204—92no—
452#204—92no—
453#204—92no—
454#204—182no—
455ΓL(1,𝔽25)—31no—
456ΓL(1,𝔽25)—31no—
457ΓL(1,𝔽25)—31no—
458ΓL(1,𝔽25)—31no—
459D3×C8—31no—
460D3×C8—31no—
461D3×C8—61no—
462D3×C8D3211yescharacteristic, complemented
463D3×C8D3211yescharacteristic, complemented
464C22×C32—31no—
465C22×C32—31no—
466C22×C32—62no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—62no—
469C2×C3⋊D3—62no—
470C2×C3⋊D3—62no—
471C2×C3⋊D3—122no—
472C2×C3⋊D3—122no—
473C2×C3⋊D3—122no—
474C2×C3⋊D3—242no—
475C2×C3⋊D3—242no—
476C2×C3⋊D3—242no—
477C2×C3⋊D3C2×D1211yescharacteristic
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—31no—
483C2×C3×D3—31no—
484C2×C3×D3—42no—
485C2×C3×D3—61no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—122no—
489C2×C3×D3—242no—
490C2×C3×D3—242no—
491C2×C3×D3C2×D1211yescharacteristic
492C2×C3×D3C2×D1211yescharacteristic
493C2×C3×D3D3×D411yescharacteristic
494C2×C3×D3D3×D411yescharacteristic
495D32—82no—
496D32—242no—
497D32—242no—
498D32—244no—
499D32—242no—
500D32—242no—
501D32—244no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—31no—
506C32×C4—31no—
507C32×C4—41no—
508C32×C4C23×D311yescharacteristic
509C32×C4C23×D311yescharacteristic
510C32×C4C23×D311yescharacteristic
511C3⋊Dic3—22no—
512C3⋊Dic3C2×D1211yescharacteristic
513C3×Dic3—21no—
514C3×Dic3—21no—
515C3×Dic3—31no—
516C3×Dic3—31no—
517C3×Dic3—61no—
518C3×Dic3—62no—
519C3×Dic3—62no—
520C3×Dic3—122no—
521C3×Dic3C2×D1211yescharacteristic
522C3×Dic3C2×D1211yescharacteristic
523C3×Dic3D3×D411yescharacteristic
524C3×Dic3D3×D411yescharacteristic
525H(5,𝔽2)—272no—
526AGL(1,ℤ/8)—272no—
527AGL(1,ℤ/8)—272no—
528AGL(1,ℤ/8)—272no—
529#135—91no—
530#135—271no—
531#135—271no—
532C2×D8—91no—
533C2×D8—271no—
534C2×D8—271no—
535#131—91no—
536C33#57611yescharacteristic, complemented, Sylow
537C23×C3—182no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—182no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3—182no—
544C22×D3—182no—
545C22×D3—182no—
546C22×D3—362no—
547C22×D3—362no—
548C3×Q8—91no—
549C3×Q8—92no—
550C3×D4—32no—
551C3×D4—32no—
552C3×D4—62no—
553C3×D4—91no—
554C3×D4—91no—
555C3×D4—91no—
556C3×D4—92no—
557C3×D4—182no—
558C3×D4—182no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—91no—
566C2×C3×C4—182no—
567#67—31no—
568#67—31no—
569#67—31no—
570#67—31no—
571#67—62no—
572#67—62no—
573#67—62no—
574#67—182no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—362no—
582#67—362no—
583C2×Dic3—62no—
584C2×Dic3—182no—
585D12—31no—
586D12—31no—
587D12—32no—
588D12—32no—
589D12—62no—
590D12—62no—
591D12—92no—
592D12—92no—
593D12—92no—
594D12—182no—
595D12—182no—
596D12—182no—
597D12—182no—
598D12—182no—
599D12—182no—
600D12—182no—
601D12—182no—
602D12—362no—
603D12—362no—
604D12C2×D3212yes—
605C4×D3—31no—
606C4×D3—31no—
607C4×D3—61no—
608C4×D3—62no—
609C4×D3—182no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—362no—
615C4×D3C2×D3211yescharacteristic
616C4×D3C2×D3211yescharacteristic
617Dic6—31no—
618Dic6—31no—
619Dic6—32no—
620Dic6—32no—
621Dic6—62no—
622C3×C8—21no—
623C3×C8—21no—
624C3×C8—21no—
625C3×C8—31no—
626C3×C8—31no—
627C3×C8—31no—
628C3×C8—31no—
629C3×C8—41no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—91no—
633C3×C8C2×D3211yescharacteristic
634C3×C8C2×D3211yescharacteristic
635C3×C8C2×D3211yescharacteristic
636C3⋊C8—31no—
637C3⋊C8—31no—
638C3⋊C8—61no—
639C3⋊C8C2×D3211yescharacteristic
640C3⋊C8C2×D3211yescharacteristic
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—41no—
645C2×C32—61no—
646C2×C32—61no—
647C2×C32—122no—
648C2×C32C22×D1211yescharacteristic
649C2×C32C2×D3×D411yescharacteristic
650C2×C32C2×D3×D411yescharacteristic
651C3⋊D3—21no—
652C3⋊D3—42no—
653C3⋊D3—122no—
654C3⋊D3—122no—
655C3⋊D3—122no—
656C3⋊D3—242no—
657C3⋊D3—242no—
658C3⋊D3—242no—
659C3⋊D3—482no—
660C3×D3—22no—
661C3×D3—21no—
662C3×D3—21no—
663C3×D3—21no—
664C3×D3—21no—
665C3×D3—41no—
666C3×D3—42no—
667C3×D3—42no—
668C3×D3—62no—
669C3×D3—61no—
670C3×D3—61no—
671C3×D3—82no—
672C3×D3—122no—
673C3×D3—122no—
674C3×D3—242no—
675#41—91no—
676#41—92no—
677#41—272no—
678#41—272no—
679#41—542no—
680C2×D4—92no—
681C2×D4—272no—
682C2×D4—272no—
683C2×D4—542no—
684C2×D4—542no—
685C2×D4—542no—
686Q16—91no—
687SD16—92no—
688SD16—272no—
689SD16—272no—
690D8—31no—
691D8—92no—
692D8—91no—
693D8—272no—
694D8—272no—
695D8—271no—
696M16—91no—
697M16—91no—
698M16—91no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—91no—
702C22×C3—31no—
703C22×C3—31no—
704C22×C3—31no—
705C22×C3—31no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—91no—
711C22×C3—122no—
712C22×C3—182no—
713C22×C3—722no—
714C2×D3—22no—
715C2×D3—31no—
716C2×D3—31no—
717C2×D3—61no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—122no—
721C2×D3—182no—
722C2×D3—182no—
723C2×D3—182no—
724C2×D3—242no—
725C2×D3—242no—
726C2×D3—362no—
727C2×D3—362no—
728C2×D3—362no—
729C2×D3—722no—
730C2×D3—722no—
731C2×D3—722no—
732C2×D3—722no—
733C2×D3—722no—
734C2×D3—724no—
735C2×D3—722no—
736C2×D3—722no—
737C2×D3—724no—
738C2×D3D3×D1211yescharacteristic
739C2×D3D3×D1211yescharacteristic
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—31no—
744C3×C4—31no—
745C3×C4—31no—
746C3×C4—31no—
747C3×C4—41no—
748C3×C4—61no—
749C3×C4—61no—
750C3×C4—91no—
751C3×C4—182no—
752C3×C4C22×D3211yescharacteristic
753C3×C4C22×D3211yescharacteristic
754C3×C4C22×D3211yescharacteristic
755Dic3—31no—
756Dic3—31no—
757Dic3—61no—
758Dic3—62no—
759Dic3—62no—
760Dic3—122no—
761Dic3D3×D1211yescharacteristic
762Dic3D3×D1211yescharacteristic
763C32—21no—
764C32—21no—
765C32—21no—
766C32—41no—
767C32#575211yescharacteristic, complemented
768C32#575711yescharacteristic, complemented
769C32#576911yescharacteristic, complemented
770C23—182no—
771C23—542no—
772C23—542no—
773Q8—91no—
774Q8—92no—
775D4—32no—
776D4—91no—
777D4—91no—
778D4—91no—
779D4—92no—
780D4—182no—
781D4—182no—
782D4—272no—
783D4—542no—
784D4—542no—
785D4—542no—
786D4—542no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—91no—
790C2×C4—182no—
791C2×C4—542no—
792C2×C4—542no—
793C8—31no—
794C8—31no—
795C8—91no—
796C8D3311yescharacteristic
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—41no—
801C2×C3—62no—
802C2×C3—61no—
803C2×C3—61no—
804C2×C3—61no—
805C2×C3—61no—
806C2×C3—121no—
807C2×C3—122no—
808C2×C3—122no—
809C2×C3—181no—
810C2×C3—242no—
811C2×C3—362no—
812C2×C3C2×D3×D1211yescharacteristic
813C2×C3C2×D3×D1211yescharacteristic
814C2×C3D32×D411yescharacteristic
815D3—21no—
816D3—21no—
817D3—42no—
818D3—62no—
819D3—61no—
820D3—61no—
821D3—122no—
822D3—122no—
823D3—242no—
824D3—362no—
825D3—362no—
826D3—362no—
827D3—722no—
828D3—722no—
829D3—722no—
830D3—1442no—
831C22—31no—
832C22—31no—
833C22—62no—
834C22—91no—
835C22—182no—
836C22—542no—
837C22—722no—
838C22—2162no—
839C22—2162no—
840C4—31no—
841C4—31no—
842C4—91no—
843C4—182no—
844C4C2×D3311yescharacteristic
845C3—21no—
846C3—21no—
847C3—21no—
848C3—41no—
849C3#1059467811yescharacteristic, complemented
850C3#1059468011yescharacteristic, complemented
851C3#1059473411yescharacteristic, complemented
852C2—61no—
853C2—61no—
854C2—122no—
855C2—181no—
856C2—362no—
857C2—1082no—
858C2D32×D1211yescharacteristic
subgroupG/H
centerC2D32×D12
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC33×C8C23
socleC2×C33C22×D4
hypercenterC8D33
hypocenterC33#576
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. #11724384C2semidirect
2. #11723654C2semidirect
3. #11723337C2semidirect
4. C3⋊D3×D24C2semidirect
5. D3×#3745C2semidirect
6. C3×#63807C2semidirect
7. C3×#63803C2semidirect
8. C3×D3×D24C2semidirect
9. #11722879C2semidirect
10. #11722870C2semidirect
11. #11722868C2semidirect
15. #89041C22semidirect
16. C3⋊D3×D12C22semidirect
17. D3×C4⋊(C3⋊D3)C22semidirect
18. #89022C22semidirect
19. C3×D3×D12C22semidirect
21. C3×#3795C22semidirect
26. #88852C22semidirect
27. C3×#3746C22semidirect
28. C3×#3745C22semidirect
29. C3×C8×C3⋊D3C22semidirect
30. C32×D24C22semidirect
31. C32×D3×C8C22semidirect
32. C32×D3×C8C22semidirect
33. #88811C22semidirect
34. #88797C22semidirect
35. #88791C22semidirect
36. #88790C22semidirect
37. C3×#3716C22semidirect
38. C3×#3714C22semidirect
39. C3×#3712C22semidirect
40. C3×#3711C22semidirect
41. C3×#3711C22semidirect
65. #63807D3semidirect
66. #63803D3semidirect
77. D3×D24D3semidirect
133. D3×D12C2×D3semidirect
143. #3795C2×D3semidirect
148. #3746C2×D3semidirect
157. #3745C2×D3semidirect
159. C8×C3⋊D3C2×D3semidirect
172. C3×D24C2×D3semidirect
173. C3×D24C2×D3semidirect
184. C3×D3×C8C2×D3semidirect
185. C3×D3×C8C2×D3semidirect
186. C3×D3×C8C2×D3semidirect
187. C3×D3×C8C2×D3semidirect
193. #3716C2×D3semidirect
201. #3714C2×D3semidirect
202. #3712C2×D3semidirect
203. #3711C2×D3semidirect
204. #3711C2×D3semidirect
449. D24D32semidirect
462. D3×C8D32semidirect
463. D3×C8D32semidirect
536. C33#576semidirect
767. C32#5752semidirect
768. C32#5757semidirect
769. C32#5769semidirect
849. C3#10594678semidirect
850. C3#10594680semidirect
851. C3#10594734semidirect

Maximal subgroups

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

subgroupindex
#117243842
#117236542
#117233372
C3⋊D3×D242
D3×#37452
C3×#638072
C3×#638032
C3×D3×D242
#117228792
#117228702
#117228682
#105947343
#105946803
#105946783