Finite Group Databasebeta

← C3⋊D3×#932 #13177536

Subgroups — C3⋊D3×#932 #13177536

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3⋊D3×#235C211yesmaximal, characteristic, complemented
3#11723973C211yesmaximal, characteristic, complemented
4C32×#932C211yesmaximal, characteristic, complemented
5#11723562C212yesmaximal, complemented
6#11723560C212yesmaximal, complemented
7C3⋊D3×#214C212yesmaximal, complemented
8C3⋊D3×#213C212yesmaximal, complemented
9#11723370C211yesmaximal, characteristic, complemented
10#11723365C211yesmaximal, characteristic, complemented
11C3⋊D3×#208C211yesmaximal, characteristic, complemented
12C3⋊D3×AGL(1,ℤ/8)—31nomaximal
13D3×#932—34nomaximal
14C23×C3×C3⋊D3—21no—
15C2×C33×D4C2211yescharacteristic, complemented
16#89076C2211yescharacteristic, complemented
17C2×C3×#638—21no—
18C3×D4×C3⋊D3—21no—
19C3×D4×C3⋊D3—21no—
20C3×D4×C3⋊D3C2212yes—
21C3×D4×C3⋊D3C2212yescomplemented
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C32×#235C2211yescharacteristic, complemented
25C3⋊D3×#67—21no—
26#89028—21no—
27C3⋊D3×D12C2211yescharacteristic, complemented
28C4×D3×C3⋊D3—21no—
29#89020—21no—
30#89018C2211yescharacteristic, complemented
31C3⋊D3×Dic6C2211yescharacteristic, complemented
32#89014C2211yescharacteristic, complemented
33#88861C2212yescomplemented
34#88860C2212yescomplemented
35#88855C2211yescharacteristic, complemented
36C32×#214C2212yescomplemented
37C32×#213C2212yescomplemented
38C32×#208C2211yescharacteristic, complemented
39#88796C2212yescomplemented
40#88793C2212yescomplemented
41#88791C2212yescomplemented
42#88789C2212yescomplemented
43#88787C2212yescomplemented
44C3⋊D3×C3⋊C8C2212yescomplemented
45#41×C3⋊D3—31no—
46C2×D4×C3⋊D3D311yescharacteristic, complemented
47C2×C3×D3×D4—34no—
48D3×#235—34no—
49C32×AGL(1,ℤ/8)—31no—
50#64158—31no—
51#64141—31no—
52#64141—34no—
53#64141—64no—
54#64123—32no—
55SD16×C3⋊D3—32no—
56#64120—32no—
57D8×C3⋊D3—32no—
58#64117—31no—
59M16×C3⋊D3—31no—
60C3×#932D314yescomplemented
61#63934—38no—
62#63932—38no—
63D3×#214—38no—
64D3×#213—38no—
65#63830—34no—
66#63823—34no—
67D3×#208—34no—
68C23×C33—21no—
69C22×C3×C3⋊D3—21no—
70C22×C3×C3⋊D3—22no—
71C22×C3×C3⋊D3—22no—
72C22×C3×C3⋊D3—44no—
73C22×C3×C3⋊D3D411yescharacteristic
74C2×D3×C3⋊D3—21no—
75C33×D4—21no—
76C33×D4C2312yes—
77C2×C33×C4C2311yescharacteristic
78#6312—21no—
79C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic, complemented
80C4×C3⋊(C3⋊D3)—21no—
81#6308C2311yescharacteristic, complemented
82C3×#638—22no—
83C3×#638—22no—
84C2×C3×C3⋊Dic3D411yescharacteristic
85C3×C4⋊(C3⋊D3)—21no—
86C3×C4⋊(C3⋊D3)C2312yes—
87C3×C4×C3⋊D3D411yescharacteristic
88C3×C4×C3⋊D3D411yescharacteristic
89C3×C4×C3⋊D3C2311yescharacteristic
90C3×C4×C3⋊D3C2311yescharacteristic
91C32×#67—21no—
92C32×D12C2311yescharacteristic, complemented
93C32×C4×D3—21no—
94C32×Dic6C2311yescharacteristic, complemented
95#6293—21no—
96#6292—21no—
97#6291—21no—
98#6290—21no—
99#6289—21no—
100Dic3×C3⋊D3—21no—
101D3×C3⋊Dic3—21no—
102C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
103C32×C3⋊C8C2312yescomplemented
104C2×#932—91no—
105D3×AGL(1,ℤ/8)—94no—
106C23×C3⋊D3—21no—
107C23×C3×D3—64no—
108C32×#41—31no—
109C2×C32×D4—24no—
110C2×C32×D4C2×D314yescomplemented
111C2×C32×D4C2×D311yescharacteristic, complemented
112C2×#638—21no—
113#3832—31no—
114Q8×C3⋊D3—31no—
115#3830—31no—
116#3830—61no—
117D4×C3⋊D3—21no—
118D4×C3⋊D3—21no—
119D4×C3⋊D3—31no—
120D4×C3⋊D3—61no—
121D4×C3⋊D3C2×D312yes—
122D4×C3⋊D3C2×D312yescomplemented
123#3828—31no—
124#3828—34no—
125#3828—61no—
126#3828—64no—
127C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
128C2×C4×C3⋊D3—61no—
129C2×C4×C3⋊D3C2×D311yescharacteristic
130C2×C3×#67—64no—
131C3×D3×D4—38no—
132C3×D3×D4—38no—
133C3×D3×D4—64no—
134C3×D3×D4—64no—
135C3×#235C2×D314yescomplemented
136C2×C3×D12—34no—
137C2×C3×C4×D3—34no—
138D3×#67—64no—
139#3804—64no—
140D3×D12—34no—
141C4×D32—64no—
142#3799—34no—
143#3798—64no—
144#3795—34no—
145D3×Dic6—34no—
146C32×SD16—32no—
147C32×D8—32no—
148C32×M16—31no—
149#3755—32no—
150#3754—32no—
151#3754—38no—
152#3754—68no—
153#3753—32no—
154#3753—38no—
155#3753—32no—
156#3753—68no—
157#3748—31no—
158#3748—34no—
159#3748—64no—
160#3745—32no—
161#3744—32no—
162#3743—32no—
163C8×C3⋊D3—32no—
164C3×#214C2×D318yescomplemented
165C3×#213C2×D318yescomplemented
166C3×#208C2×D314yescomplemented
167#3716—38no—
168#3715—38no—
169#3714—38no—
170#3713—38no—
171#3711—38no—
172D3×C3⋊C8—38no—
173C22×C33—22no—
174C22×C33—42no—
175C22×C33C2×D411yescharacteristic
176C2×C3⋊(C3⋊D3)—21no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—44no—
180C2×C3×C3⋊D3—42no—
181C2×C3×C3⋊D3—44no—
182C2×C3×C3⋊D3C2×D411yescharacteristic
183C2×C3×C3⋊D3C2×D411yescharacteristic
184C2×C32×D3—21no—
185D3×C3⋊D3—42no—
186C33×C4C2×D411yescharacteristic
187C33×C4C2411yescharacteristic
188C3⋊(C3⋊Dic3)—21no—
189C3×C3⋊Dic3C2×D411yescharacteristic
190C3×C3⋊Dic3C2×D411yescharacteristic
191C32×Dic3—21no—
192C22×C3×D4—91no—
193D3×#41—94no—
194C2×D3×D4—34no—
195C2×#235—91no—
196C3×AGL(1,ℤ/8)—34no—
197#949—94no—
198C2×#214—92no—
199#932—94no—
200#932—91no—
201#932—91no—
202#932—92no—
203#932—92no—
204#932—91no—
205#932—184no—
206#932C3⋊D311yescharacteristic, direct product factor
207C2×#213—92no—
208C2×#208—91no—
209#914—98no—
210D3×SD16—98no—
211#911—98no—
212D3×D8—98no—
213#908—94no—
214D3×M16—94no—
215C23×C32—21no—
216C23×C32—24no—
217C23×C32—44no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—22no—
220C22×C3⋊D3—22no—
221C22×C3⋊D3—44no—
222C22×C3⋊D3—61no—
223C22×C3⋊D3#6711yescharacteristic
224C22×C3×D3—34no—
225C22×C3×D3—68no—
226C22×C3×D3—68no—
227C22×C3×D3—64no—
228C22×C3×D3—1216no—
229C2×D32—64no—
230C32×Q8—31no—
231C32×D4—21no—
232C32×D4—28no—
233C32×D4—24no—
234C32×D4—31no—
235C32×D4—44no—
236C32×D4—61no—
237C32×D4C22×D318yes—
238C32×D4C22×D312yes—
239C2×C32×C4—24no—
240C2×C32×C4—61no—
241C2×C32×C4C22×D314yes—
242C2×C32×C4C22×D311yescharacteristic
243#638—22no—
244#638—22no—
245#638—61no—
246#638—61no—
247#638—61no—
248#638—64no—
249#638—124no—
250C2×C3⋊Dic3—61no—
251C2×C3⋊Dic3#6711yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—31no—
254C4⋊(C3⋊D3)—34no—
255C4⋊(C3⋊D3)—64no—
256C4⋊(C3⋊D3)—61no—
257C4⋊(C3⋊D3)C22×D312yes—
258C4×C3⋊D3—61no—
259C4×C3⋊D3—61no—
260C4×C3⋊D3—61no—
261C4×C3⋊D3—64no—
262C4×C3⋊D3—124no—
263C4×C3⋊D3#6711yescharacteristic
264C4×C3⋊D3#6711yescharacteristic
265C4×C3⋊D3C22×D311yescharacteristic
266C4×C3⋊D3C22×D311yescharacteristic
267#634—31no—
268#634—34no—
269#634—64no—
270#634—61no—
271C3×#67—24no—
272C3×#67—68no—
273C3×#67—68no—
274C2×C3×Dic3—34no—
275C3×D12—38no—
276C3×D12—64no—
277C3×D12C22×D314yescomplemented
278C3×C4×D3—24no—
279C3×C4×D3—34no—
280C3×C4×D3—34no—
281C3×C4×D3—34no—
282C3×C4×D3—34no—
283C3×Dic6C22×D314yescomplemented
284#627—64no—
285#626—64no—
286#626—64no—
287#625—64no—
288#624—64no—
289D3×Dic3—64no—
290D3×Dic3—64no—
291C32×C8—32no—
292C3⋊(C3⋊C8)—32no—
293C3⋊(C3⋊C8)—38no—
294C3⋊(C3⋊C8)—68no—
295C3×C3⋊C8C22×D318yescomplemented
296C2×AGL(1,ℤ/8)—271noSylow
297C2×C33—21no—
298C2×C33—42no—
299C2×C33C22×D411yescharacteristic
300C3⋊(C3⋊D3)—41no—
301C3×C3⋊D3—21no—
302C3×C3⋊D3—42no—
303C3×C3⋊D3AGL(1,ℤ/8)12yescomplemented
304C32×D3—41no—
305C24×C3—181no—
306C23×D3—64no—
307C3×#41—34no—
308C2×C3×D4—24no—
309C2×C3×D4—92no—
310C2×C3×D4—92no—
311C2×C3×D4—91no—
312C2×C3×D4—181no—
313C2×C3×D4—181no—
314C2×C3×D4—181no—
315C2×C3×D4D3214yescomplemented
316C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
317C22×C3×C4—91no—
318C2×#67—64no—
319C2×#67—181no—
320#239—94no—
321D3×Q8—94no—
322#237—94no—
323#237—184no—
324D3×D4—38no—
325D3×D4—38no—
326D3×D4—64no—
327D3×D4—64no—
328D3×D4—94no—
329D3×D4—184no—
330#235—94no—
331#235—91no—
332#235—91no—
333#235—91no—
334#235—184no—
335#235—181no—
336#235—184no—
337#235—181no—
338#235C2×C3⋊D311yescharacteristic, complemented
339C2×D12—34no—
340C2×D12—91no—
341C2×C4×D3—34no—
342C2×C4×D3—181no—
343C2×C4×D3—184no—
344C2×Dic6—91no—
345C3×SD16—38no—
346C3×D8—38no—
347C3×M16—34no—
348#215—98no—
349#214—98no—
350#214—92no—
351#214—92no—
352#214—92no—
353#214—188no—
354#214C2×C3⋊D312yescomplemented
355#213—98no—
356#213—98no—
357#213—92no—
358#213—92no—
359#213—92no—
360#213—188no—
361#213C2×C3⋊D312yescomplemented
362#208—94no—
363#208—91no—
364#208—92no—
365#208—184no—
366#208C2×C3⋊D311yescharacteristic, complemented
367C2×C3⋊C8—92no—
368D24—98no—
369#204—98no—
370ΓL(1,𝔽25)—98no—
371D3×C8—98no—
372C22×C32—22no—
373C22×C32—24no—
374C22×C32—28no—
375C22×C32—48no—
376C22×C32—42no—
377C22×C32—48no—
378C22×C32—61no—
379C22×C32—88no—
380C22×C32D3×D414yes—
381C22×C32C2×#6711yescharacteristic
382C2×C3⋊D3—22no—
383C2×C3⋊D3—22no—
384C2×C3⋊D3—44no—
385C2×C3⋊D3—42no—
386C2×C3⋊D3—44no—
387C2×C3⋊D3—61no—
388C2×C3⋊D3—64no—
389C2×C3⋊D3—124no—
390C2×C3⋊D3—122no—
391C2×C3⋊D3C2×#6711yescharacteristic
392C2×C3⋊D3C2×#6711yescharacteristic
393C2×C3×D3—24no—
394C2×C3×D3—34no—
395C2×C3×D3—34no—
396C2×C3×D3—68no—
397C2×C3×D3—68no—
398C2×C3×D3—1216no—
399C2×C3×D3—1216no—
400C2×C3×D3—128no—
401D32—128no—
402C32×C4—24no—
403C32×C4—24no—
404C32×C4—61no—
405C32×C4D3×D414yes—
406C32×C4C2×#6711yescharacteristic
407C32×C4C23×D314yes—
408C32×C4C23×D311yescharacteristic
409C3⋊Dic3—61no—
410C3⋊Dic3—64no—
411C3⋊Dic3—124no—
412C3⋊Dic3C2×#6711yescharacteristic
413C3⋊Dic3C2×#6711yescharacteristic
414C3×Dic3—24no—
415C3×Dic3—34no—
416C3×Dic3—34no—
417C2×#41—271no—
418C22×D4—91no—
419AGL(1,ℤ/8)—31no—
420AGL(1,ℤ/8)—271no—
421AGL(1,ℤ/8)—272no—
422AGL(1,ℤ/8)—272no—
423AGL(1,ℤ/8)—271no—
424AGL(1,ℤ/8)—271no—
425C2×SD16—272no—
426C2×D8—272no—
427C2×M16—271no—
428C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
429C23×C3—24no—
430C23×C3—21no—
431C23×C3—44no—
432C23×C3—91no—
433C23×C3—182no—
434C23×C3—182no—
435C23×C3—181no—
436C23×C3—364no—
437C22×D3—34no—
438C22×D3—68no—
439C22×D3—68no—
440C22×D3—64no—
441C22×D3—1216no—
442C22×D3—181no—
443C22×D3—184no—
444C3×Q8—34no—
445C3×D4—24no—
446C3×D4—21no—
447C3×D4—28no—
448C3×D4—34no—
449C3×D4—44no—
450C3×D4—64no—
451C3×D4—92no—
452C3×D4—182no—
453C3×D4—182no—
454C3×D4—181no—
455C3×D4C2×D3218yes—
456C3×D4C22×C3⋊D312yes—
457C2×C3×C4—24no—
458C2×C3×C4—64no—
459C2×C3×C4—91no—
460C2×C3×C4—91no—
461C2×C3×C4—91no—
462C2×C3×C4—91no—
463C2×C3×C4—91no—
464C2×C3×C4C2×D3214yes—
465C2×C3×C4C22×C3⋊D311yescharacteristic
466#67—21no—
467#67—68no—
468#67—68no—
469#67—181no—
470#67—184no—
471#67—181no—
472#67—184no—
473#67—184no—
474#67—181no—
475#67—364no—
476C2×Dic3—34no—
477C2×Dic3—181no—
478C2×Dic3—184no—
479D12—38no—
480D12—64no—
481D12—94no—
482D12—91no—
483D12—184no—
484D12—184no—
485D12—181no—
486D12C22×C3⋊D311yescharacteristic, complemented
487C4×D3—21no—
488C4×D3—34no—
489C4×D3—34no—
490C4×D3—34no—
491C4×D3—34no—
492C4×D3—181no—
493C4×D3—184no—
494C4×D3—184no—
495C4×D3—181no—
496C4×D3—184no—
497C4×D3—181no—
498C4×D3—364no—
499Dic6—94no—
500Dic6—91no—
501Dic6—184no—
502Dic6—181no—
503Dic6—184no—
504Dic6C22×C3⋊D311yescharacteristic, complemented
505C3×C8—38no—
506C3⋊C8—98no—
507C3⋊C8—92no—
508C3⋊C8—188no—
509C3⋊C8C22×C3⋊D312yescomplemented
510C2×C32—21no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—44no—
514C2×C32—42no—
515C2×C32—48no—
516C2×C32—88no—
517C2×C32—121no—
518C2×C32C2×D3×D414yes—
519C2×C32C22×#6711yescharacteristic
520C3⋊D3—21no—
521C3⋊D3—42no—
522C3⋊D3—121no—
523C3⋊D3—124no—
524C3⋊D3—244no—
525C3⋊D3#93212yesdirect product factor
526C3×D3—38no—
527C3×D3—44no—
528C3×D3—64no—
529C3×D3—128no—
530C24—181no—
531#41—31no—
532#41—271no—
533#41—271no—
534#41—271no—
535#41—541no—
536#41—541no—
537C2×Q8—271no—
538C2×D4—92no—
539C2×D4—92no—
540C2×D4—91no—
541C2×D4—181no—
542C2×D4—181no—
543C2×D4—181no—
544C2×D4—271no—
545C2×D4—541no—
546C2×D4D3×C3⋊D311yescharacteristic, complemented
547C22×C4—91no—
548C22×C4—541no—
549SD16—32no—
550SD16—272no—
551SD16—272no—
552SD16—272no—
553D8—32no—
554D8—272no—
555D8—272no—
556D8—272no—
557M16—31no—
558M16—272no—
559M16—271no—
560C2×C8—272no—
561C22×C3—28no—
562C22×C3—22no—
563C22×C3—24no—
564C22×C3—48no—
565C22×C3—48no—
566C22×C3—42no—
567C22×C3—64no—
568C22×C3—88no—
569C22×C3—91no—
570C22×C3—91no—
571C22×C3—182no—
572C22×C3—182no—
573C22×C3—362no—
574C22×C3—364no—
575C22×C3—364no—
576C22×C3D3×#6714yes—
577C22×C3D4×C3⋊D311yescharacteristic
578C2×D3—21no—
579C2×D3—34no—
580C2×D3—34no—
581C2×D3—68no—
582C2×D3—68no—
583C2×D3—1216no—
584C2×D3—1216no—
585C2×D3—128no—
586C2×D3—184no—
587C2×D3—181no—
588C2×D3—364no—
589C2×D3—368no—
590C2×D3—362no—
591C3×C4—24no—
592C3×C4—24no—
593C3×C4—64no—
594C3×C4—91no—
595C3×C4—91no—
596C3×C4D3×#6714yes—
597C3×C4D4×C3⋊D311yescharacteristic
598C3×C4C22×D3214yes—
599C3×C4C23×C3⋊D311yescharacteristic
600Dic3—21no—
601Dic3—34no—
602Dic3—34no—
603Dic3—184no—
604Dic3—181no—
605Dic3—364no—
606C32—24no—
607C32D3×AGL(1,ℤ/8)14yescomplemented
608C32C2×#93211yescharacteristic, complemented
609C23—21no—
610C23—91no—
611C23—182no—
612C23—182no—
613C23—181no—
614C23—364no—
615C23—541no—
616Q8—31no—
617Q8—271no—
618Q8—541no—
619D4—21no—
620D4—31no—
621D4—61no—
622D4—92no—
623D4—182no—
624D4—182no—
625D4—181no—
626D4—271no—
627D4—541no—
628D4—541no—
629D4—541no—
630D4—541no—
631D4C2×D3×C3⋊D312yes—
632C2×C4—61no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—91no—
636C2×C4—91no—
637C2×C4—91no—
638C2×C4—541no—
639C2×C4—541no—
640C2×C4—541no—
641C2×C4—541no—
642C2×C4C2×D3×C3⋊D311yescharacteristic
643C8—32no—
644C8—272no—
645C2×C3—24no—
646C2×C3—21no—
647C2×C3—24no—
648C2×C3—44no—
649C2×C3—48no—
650C2×C3—42no—
651C2×C3—88no—
652C2×C3—92no—
653C2×C3—124no—
654C2×C3—181no—
655C2×C3—362no—
656C2×C3C2×D3×#6714yes—
657C2×C3C2×D4×C3⋊D311yescharacteristic
658D3—38no—
659D3—41no—
660D3—64no—
661D3—128no—
662D3—364no—
663D3—361no—
664D3—724no—
665C22—22no—
666C22—42no—
667C22—61no—
668C22—91no—
669C22—91no—
670C22—182no—
671C22—182no—
672C22—362no—
673C22—364no—
674C22—364no—
675C22—541no—
676C22—1082no—
677C22C3⋊D3×#6711yescharacteristic
678C4—61no—
679C4—91no—
680C4—91no—
681C4—541no—
682C4C3⋊D3×#6711yescharacteristic
683C4C22×D3×C3⋊D311yescharacteristic
684C3—24no—
685C3D3×#93214yescomplemented
686C3C3⋊D3×AGL(1,ℤ/8)11yescharacteristic, complemented
687C2—21no—
688C2—42no—
689C2—92no—
690C2—121no—
691C2—181no—
692C2—362no—
693C2—1081no—
694C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
centerC2C2×C3⋊D3×#67
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC2×C33×D4C22
socleC2×C33C22×D4
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C3⋊D3×#235C2semidirect
3. #11723973C2semidirect
4. C32×#932C2semidirect
5. #11723562C2semidirect
6. #11723560C2semidirect
7. C3⋊D3×#214C2semidirect
8. C3⋊D3×#213C2semidirect
9. #11723370C2semidirect
10. #11723365C2semidirect
11. C3⋊D3×#208C2semidirect
15. C2×C33×D4C22semidirect
16. #89076C22semidirect
21. C3×D4×C3⋊D3C22semidirect
22. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C32×#235C22semidirect
27. C3⋊D3×D12C22semidirect
30. #89018C22semidirect
31. C3⋊D3×Dic6C22semidirect
32. #89014C22semidirect
33. #88861C22semidirect
34. #88860C22semidirect
35. #88855C22semidirect
36. C32×#214C22semidirect
37. C32×#213C22semidirect
38. C32×#208C22semidirect
39. #88796C22semidirect
40. #88793C22semidirect
41. #88791C22semidirect
42. #88789C22semidirect
43. #88787C22semidirect
44. C3⋊D3×C3⋊C8C22semidirect
46. C2×D4×C3⋊D3D3semidirect
60. C3×#932D3semidirect
79. C4⋊(C3⋊(C3⋊D3))C23semidirect
81. #6308C23semidirect
92. C32×D12C23semidirect
94. C32×Dic6C23semidirect
102. C3⋊(C3⋊(C3⋊C8))C23semidirect
103. C32×C3⋊C8C23semidirect
110. C2×C32×D4C2×D3semidirect
111. C2×C32×D4C2×D3semidirect
122. D4×C3⋊D3C2×D3semidirect
127. C2×C4⋊(C3⋊D3)C2×D3semidirect
135. C3×#235C2×D3semidirect
164. C3×#214C2×D3semidirect
165. C3×#213C2×D3semidirect
166. C3×#208C2×D3semidirect
206. #932C3⋊D3direct (N × H)
277. C3×D12C22×D3semidirect
283. C3×Dic6C22×D3semidirect
295. C3×C3⋊C8C22×D3semidirect
303. C3×C3⋊D3AGL(1,ℤ/8)semidirect
315. C2×C3×D4D32semidirect
316. C2×C3×D4C2×C3⋊D3semidirect
338. #235C2×C3⋊D3semidirect
354. #214C2×C3⋊D3semidirect
361. #213C2×C3⋊D3semidirect
366. #208C2×C3⋊D3semidirect
428. C33C2×AGL(1,ℤ/8)semidirect
486. D12C22×C3⋊D3semidirect
504. Dic6C22×C3⋊D3semidirect
509. C3⋊C8C22×C3⋊D3semidirect
525. C3⋊D3#932direct (N × H)
546. C2×D4D3×C3⋊D3semidirect
607. C32D3×AGL(1,ℤ/8)semidirect
608. C32C2×#932semidirect
685. C3D3×#932semidirect
686. C3C3⋊D3×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
C2×C3×D4×C3⋊D32
C3⋊D3×#2352
#117239732
C32×#9322
#117235622
#117235602
C3⋊D3×#2142
C3⋊D3×#2132
#117233702
#117233652
C3⋊D3×#2082
C3⋊D3×AGL(1,ℤ/8)3
D3×#9323