Finite Group Databasebeta

← C3⋊D3×#908 #13176686

Subgroups — C3⋊D3×#908 #13176686

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
1C3⋊D3×#235C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
3#11723949C211yesmaximal, characteristic, complemented
4C3×M16×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×#908C211yesmaximal, characteristic, complemented
6#11723378C211yesmaximal, characteristic, complemented
7#11723367C211yesmaximal, characteristic, complemented
8#11723320C212yesmaximal, complemented
9#11723319C212yesmaximal, complemented
10C3⋊D3×D24C212yesmaximal, complemented
11C3⋊D3×#204C212yesmaximal, complemented
12C3⋊D3×AGL(1,ℤ/8)—31nomaximal
13D3×#908—34nomaximal
14C22×D3×C3⋊D3—21no—
15#89076C2211yescharacteristic, complemented
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C32×#235C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic, complemented
20C3⋊D3×#67—21no—
21C2×#6291—21no—
22#89028—21no—
23C3⋊D3×D12—21no—
24C3⋊D3×D12—21no—
25C3⋊D3×D12C2212yes—
26C3⋊D3×D12C2212yescomplemented
27C3⋊D3×D12C2211yescharacteristic, complemented
28C4×D3×C3⋊D3—21no—
29#89020—21no—
30#89018C2211yescharacteristic, complemented
31C3⋊D3×Dic6C2211yescharacteristic, complemented
32#89014C2211yescharacteristic, complemented
33C33×M16C2211yescharacteristic, complemented
34#88852C2212yescomplemented
35#88851C2212yescomplemented
36C3×#3748C2211yescharacteristic, complemented
37C3×#3743C2212yescomplemented
38C3×C8×C3⋊D3C2212yescomplemented
39C32×D24C2212yescomplemented
40C32×#204C2212yescomplemented
41#88795C2212yescomplemented
42#88794C2212yescomplemented
43#88790C2212yescomplemented
44#88790C2212yescomplemented
45#41×C3⋊D3—31no—
46C2×D4×C3⋊D3—31no—
47D3×#235—34no—
48C2×D3×D12—34no—
49C32×AGL(1,ℤ/8)—31no—
50#64158—31no—
51#64141—31no—
52#64123—32no—
53SD16×C3⋊D3—32no—
54#64120—32no—
55D8×C3⋊D3—32no—
56#64117—31no—
57#64117—34no—
58#64117—64no—
59M16×C3⋊D3D311yescharacteristic, complemented
60C3×#908D314yescomplemented
61C3×D3×M16—34no—
62#63830—34no—
63#63825—34no—
64#63795—38no—
65#63794—38no—
66D3×D24—38no—
67D3×#204—38no—
68C22×C3⋊(C3⋊D3)—21no—
69C22×C3×C3⋊D3D411yescharacteristic
70C22×C32×D3—21no—
71C2×D3×C3⋊D3—22no—
72C2×D3×C3⋊D3—22no—
73C2×D3×C3⋊D3—21no—
74C2×D3×C3⋊D3—44no—
75C2×C33×C4C2311yescharacteristic
76#6312—21no—
77C4⋊(C3⋊(C3⋊D3))—21no—
78C4⋊(C3⋊(C3⋊D3))C2312yes—
79C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic, complemented
80C4×C3⋊(C3⋊D3)—21no—
81#6308C2311yescharacteristic, complemented
82C2×C3×C3⋊Dic3D411yescharacteristic
83C3×C4×C3⋊D3D411yescharacteristic
84C3×C4×C3⋊D3D411yescharacteristic
85C3×C4×C3⋊D3C2311yescharacteristic
86C3×C4×C3⋊D3C2311yescharacteristic
87C32×#67—21no—
88C32×D12—21no—
89C32×D12C2312yes—
90C32×D12C2311yescharacteristic, complemented
91C32×C4×D3—21no—
92C32×Dic6C2311yescharacteristic, complemented
93#6293—21no—
94#6292—21no—
95#6291—21no—
96#6291—22no—
97#6291—22no—
98#6290—21no—
99#6289—21no—
100Dic3×C3⋊D3—21no—
101D3×C3⋊Dic3—21no—
102C33×C8C2312yescomplemented
103C3×C3⋊(C3⋊C8)C2312yescomplemented
104D3×AGL(1,ℤ/8)—94no—
105C2×#908—91no—
106C23×C3⋊D3—61no—
107C22×D32—64no—
108C32×#41—31no—
109C2×C32×D4—31no—
110C2×#638—61no—
111#3832—31no—
112Q8×C3⋊D3—31no—
113#3830—31no—
114#3830—61no—
115D4×C3⋊D3—32no—
116D4×C3⋊D3—32no—
117D4×C3⋊D3—31no—
118D4×C3⋊D3—61no—
119D4×C3⋊D3—61no—
120D4×C3⋊D3—61no—
121#3828—31no—
122#3828—34no—
123#3828—61no—
124#3828—64no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C4⋊(C3⋊D3)—34no—
127C2×C4⋊(C3⋊D3)—64no—
128C2×C4×C3⋊D3—61no—
129C2×C4×C3⋊D3C2×D311yescharacteristic
130C3×#235C2×D314yescomplemented
131C2×C3×D12C2×D314yescomplemented
132C2×C3×C4×D3—34no—
133D3×#67—64no—
134C2×#626—64no—
135#3804—64no—
136D3×D12—38no—
137D3×D12—38no—
138D3×D12—34no—
139D3×D12—64no—
140D3×D12—64no—
141C4×D32—64no—
142#3799—34no—
143#3798—64no—
144#3795—34no—
145D3×Dic6—34no—
146C32×SD16—32no—
147C32×D8—32no—
148C32×M16—24no—
149C32×M16C2×D314yescomplemented
150C32×M16C2×D311yescharacteristic, complemented
151#3755—32no—
152#3754—32no—
153#3753—32no—
154#3753—32no—
155#3748C2×D311yescharacteristic, complemented
156#3745—32no—
157#3745—38no—
158#3745—68no—
159#3744—32no—
160#3744—38no—
161#3744—68no—
162#3743C2×D312yescomplemented
163C8×C3⋊D3C2×D312yescomplemented
164C3×#208—34no—
165C3×D24C2×D318yescomplemented
166C3×#204C2×D318yescomplemented
167C3×ΓL(1,𝔽25)—38no—
168C3×D3×C8—38no—
169#3717—38no—
170#3716—38no—
171#3714—38no—
172#3714—38no—
173C22×C33C2×D411yescharacteristic
174C2×C3⋊(C3⋊D3)—21no—
175C2×C3⋊(C3⋊D3)—22no—
176C2×C3⋊(C3⋊D3)—42no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3C2×D411yescharacteristic
179C2×C3×C3⋊D3C2×D411yescharacteristic
180C2×C32×D3—21no—
181C2×C32×D3—22no—
182C2×C32×D3—42no—
183D3×C3⋊D3—44no—
184D3×C3⋊D3—42no—
185D3×C3⋊D3—44no—
186C33×C4C2×D411yescharacteristic
187C33×C4C2411yescharacteristic
188C3⋊(C3⋊Dic3)—21no—
189C3×C3⋊Dic3C2×D411yescharacteristic
190C3×C3⋊Dic3C2×D411yescharacteristic
191C32×Dic3—21no—
192D3×#41—94no—
193C2×D3×D4—94no—
194C2×#235—91no—
195C22×D12—91no—
196C3×AGL(1,ℤ/8)—34no—
197C2×C3×M16—91no—
198#949—94no—
199#932—94no—
200#914—98no—
201D3×SD16—98no—
202#911—98no—
203D3×D8—98no—
204#908—91no—
205#908—91no—
206#908—94no—
207#908—91no—
208#908—92no—
209#908—92no—
210#908—184no—
211#908C3⋊D311yescharacteristic, direct product factor
212D3×M16—34no—
213C2×D24—92no—
214C2×#204—92no—
215C23×C32—61no—
216C22×C3⋊D3—61no—
217C22×C3⋊D3—62no—
218C22×C3⋊D3—62no—
219C22×C3⋊D3—61no—
220C22×C3⋊D3—64no—
221C22×C3⋊D3—124no—
222C22×C3⋊D3—124no—
223C22×C3⋊D3D1211yescharacteristic
224C22×C3×D3—24no—
225C22×C3×D3—34no—
226C2×D32—68no—
227C2×D32—68no—
228C2×D32—64no—
229C2×D32—1216no—
230C32×Q8—31no—
231C32×D4—32no—
232C32×D4—31no—
233C32×D4—61no—
234C32×D4—61no—
235C2×C32×C4—24no—
236C2×C32×C4—61no—
237C2×C32×C4C22×D314yes—
238C2×C32×C4C22×D311yescharacteristic
239#638—61no—
240#638—61no—
241#638—61no—
242#638—62no—
243#638—62no—
244#638—64no—
245#638—124no—
246C2×C3⋊Dic3—61no—
247C2×C3⋊Dic3D1211yescharacteristic
248C4⋊(C3⋊D3)—32no—
249C4⋊(C3⋊D3)—31no—
250C4⋊(C3⋊D3)—34no—
251C4⋊(C3⋊D3)—38no—
252C4⋊(C3⋊D3)—68no—
253C4⋊(C3⋊D3)—64no—
254C4⋊(C3⋊D3)—61no—
255C4⋊(C3⋊D3)—61no—
256C4⋊(C3⋊D3)—64no—
257C4⋊(C3⋊D3)—124no—
258C4×C3⋊D3—61no—
259C4×C3⋊D3—61no—
260C4×C3⋊D3—61no—
261C4×C3⋊D3—64no—
262C4×C3⋊D3—124no—
263C4×C3⋊D3D1211yescharacteristic
264C4×C3⋊D3D1211yescharacteristic
265C4×C3⋊D3C22×D311yescharacteristic
266C4×C3⋊D3C22×D311yescharacteristic
267#634—31no—
268#634—34no—
269#634—64no—
270#634—61no—
271C3×#67—24no—
272C2×C3×Dic3—34no—
273C3×D12—24no—
274C3×D12C22×D318yes—
275C3×D12C22×D314yescomplemented
276C3×C4×D3—24no—
277C3×C4×D3—34no—
278C3×C4×D3—34no—
279C3×C4×D3—34no—
280C3×C4×D3—34no—
281C3×Dic6C22×D314yescomplemented
282#627—64no—
283#626—64no—
284#626—64no—
285#626—68no—
286#626—68no—
287#625—64no—
288#624—64no—
289D3×Dic3—64no—
290D3×Dic3—64no—
291C32×C8—28no—
292C32×C8C22×D318yescomplemented
293C32×C8C22×D312yescomplemented
294C3⋊(C3⋊C8)C22×D312yescomplemented
295C3×C3⋊C8—38no—
296C2×AGL(1,ℤ/8)—271noSylow
297C2×C33—21no—
298C2×C33C22×D411yescharacteristic
299C3⋊(C3⋊D3)—42no—
300C3⋊(C3⋊D3)—41no—
301C3×C3⋊D3—21no—
302C3×C3⋊D3AGL(1,ℤ/8)12yescomplemented
303C32×D3—42no—
304C32×D3—41no—
305C23×D3—181no—
306C23×D3—184no—
307C3×#41—34no—
308C2×C3×D4—34no—
309C22×C3×C4—91no—
310C2×#67—184no—
311C2×#67—181no—
312#239—94no—
313D3×Q8—94no—
314#237—94no—
315#237—184no—
316D3×D4—94no—
317D3×D4—98no—
318D3×D4—98no—
319D3×D4—184no—
320D3×D4—184no—
321D3×D4—184no—
322#235—94no—
323#235—91no—
324#235—91no—
325#235—91no—
326#235—184no—
327#235—181no—
328#235—184no—
329#235—181no—
330#235C2×C3⋊D311yescharacteristic, complemented
331C2×D12—94no—
332C2×D12—91no—
333C2×D12—92no—
334C2×D12—92no—
335C2×D12—91no—
336C2×D12—184no—
337C2×D12—181no—
338C2×D12—181no—
339C2×D12—181no—
340C2×D12C2×C3⋊D311yescharacteristic, complemented
341C2×C4×D3—34no—
342C2×C4×D3—181no—
343C2×C4×D3—184no—
344C2×Dic6—91no—
345C3×SD16—38no—
346C3×D8—38no—
347C3×M16—24no—
348C3×M16—91no—
349C3×M16—92no—
350C3×M16D3214yescomplemented
351C3×M16C2×C3⋊D311yescharacteristic, complemented
352C2×C3×C8—92no—
353#215—98no—
354#214—98no—
355#213—98no—
356#213—98no—
357#208—34no—
358D24—92no—
359D24—92no—
360D24—98no—
361D24—92no—
362D24—188no—
363D24C2×C3⋊D312yescomplemented
364#204—92no—
365#204—92no—
366#204—98no—
367#204—92no—
368#204—188no—
369#204C2×C3⋊D312yescomplemented
370ΓL(1,𝔽25)—38no—
371D3×C8—38no—
372C22×C32—24no—
373C22×C32—61no—
374C22×C32—62no—
375C22×C32—122no—
376C22×C32C2×D1211yescharacteristic
377C22×C32D3×D414yes—
378C2×C3⋊D3—22no—
379C2×C3⋊D3—61no—
380C2×C3⋊D3—62no—
381C2×C3⋊D3—64no—
382C2×C3⋊D3—68no—
383C2×C3⋊D3—124no—
384C2×C3⋊D3—128no—
385C2×C3⋊D3—124no—
386C2×C3⋊D3—122no—
387C2×C3⋊D3—122no—
388C2×C3⋊D3—124no—
389C2×C3⋊D3—128no—
390C2×C3⋊D3—248no—
391C2×C3⋊D3C2×D1211yescharacteristic
392C2×C3⋊D3C2×D1211yescharacteristic
393C2×C3×D3—24no—
394C2×C3×D3—28no—
395C2×C3×D3—34no—
396C2×C3×D3—34no—
397C2×C3×D3—48no—
398C2×C3×D3—68no—
399D32—128no—
400D32—1216no—
401D32—1216no—
402C32×C4—24no—
403C32×C4—24no—
404C32×C4—61no—
405C32×C4C2×D1211yescharacteristic
406C32×C4D3×D414yes—
407C32×C4C23×D314yes—
408C32×C4C23×D311yescharacteristic
409C3⋊Dic3—61no—
410C3⋊Dic3—64no—
411C3⋊Dic3—124no—
412C3⋊Dic3C2×D1211yescharacteristic
413C3⋊Dic3C2×D1211yescharacteristic
414C3×Dic3—24no—
415C3×Dic3—34no—
416C3×Dic3—34no—
417C2×#41—271no—
418C22×D4—271no—
419AGL(1,ℤ/8)—31no—
420AGL(1,ℤ/8)—272no—
421AGL(1,ℤ/8)—272no—
422AGL(1,ℤ/8)—271no—
423AGL(1,ℤ/8)—271no—
424AGL(1,ℤ/8)—271no—
425C2×SD16—272no—
426C2×D8—272no—
427C2×M16—91no—
428C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
429C23×C3—64no—
430C23×C3—91no—
431C22×D3—21no—
432C22×D3—34no—
433C22×D3—181no—
434C22×D3—182no—
435C22×D3—182no—
436C22×D3—184no—
437C22×D3—188no—
438C22×D3—188no—
439C22×D3—184no—
440C22×D3—181no—
441C22×D3—364no—
442C22×D3—364no—
443C22×D3—3616no—
444C3×Q8—34no—
445C3×D4—38no—
446C3×D4—34no—
447C3×D4—64no—
448C3×D4—64no—
449C2×C3×C4—24no—
450C2×C3×C4—64no—
451C2×C3×C4—91no—
452C2×C3×C4—91no—
453C2×C3×C4—91no—
454C2×C3×C4—91no—
455C2×C3×C4—91no—
456C2×C3×C4C2×D3214yes—
457C2×C3×C4C22×C3⋊D311yescharacteristic
458#67—21no—
459#67—181no—
460#67—184no—
461#67—188no—
462#67—188no—
463#67—181no—
464#67—184no—
465#67—184no—
466#67—181no—
467#67—364no—
468C2×Dic3—34no—
469C2×Dic3—181no—
470C2×Dic3—184no—
471D12—21no—
472D12—98no—
473D12—94no—
474D12—92no—
475D12—91no—
476D12—188no—
477D12—184no—
478D12—184no—
479D12—182no—
480D12—182no—
481D12—181no—
482D12—184no—
483D12—181no—
484D12—364no—
485D12C22×C3⋊D312yes—
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—28no—
506C3×C8—92no—
507C3×C8C2×D3218yescomplemented
508C3×C8C22×C3⋊D312yescomplemented
509C3⋊C8—38no—
510C2×C32—21no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—44no—
514C2×C32—122no—
515C2×C32—121no—
516C2×C32C22×D1211yescharacteristic
517C2×C32C2×D3×D414yes—
518C3⋊D3—21no—
519C3⋊D3—121no—
520C3⋊D3—122no—
521C3⋊D3—128no—
522C3⋊D3—124no—
523C3⋊D3—244no—
524C3⋊D3—248no—
525C3⋊D3#90812yesdirect product factor
526C3×D3—38no—
527C3×D3—48no—
528C3×D3—44no—
529C3×D3—64no—
530C24—541no—
531#41—31no—
532#41—271no—
533#41—271no—
534#41—271no—
535#41—541no—
536#41—541no—
537C2×Q8—271no—
538C2×D4—31no—
539C2×D4—271no—
540C2×D4—272no—
541C2×D4—272no—
542C2×D4—271no—
543C2×D4—541no—
544C2×D4—541no—
545C2×D4—541no—
546C2×D4—541no—
547C22×C4—91no—
548C22×C4—541no—
549SD16—32no—
550SD16—272no—
551SD16—272no—
552SD16—272no—
553D8—32no—
554D8—272no—
555D8—272no—
556D8—272no—
557M16—91no—
558M16—92no—
559M16D3×C3⋊D311yescharacteristic, complemented
560C2×C8—92no—
561C22×C3—24no—
562C22×C3—64no—
563C22×C3—68no—
564C22×C3—91no—
565C22×C3—91no—
566C22×C3—128no—
567C22×C3—182no—
568C22×C3D3×D1214yes—
569C22×C3D4×C3⋊D311yescharacteristic
570C2×D3—21no—
571C2×D3—22no—
572C2×D3—34no—
573C2×D3—34no—
574C2×D3—42no—
575C2×D3—68no—
576C2×D3—184no—
577C2×D3—188no—
578C2×D3—181no—
579C2×D3—182no—
580C2×D3—364no—
581C2×D3—368no—
582C2×D3—3616no—
583C2×D3—368no—
584C2×D3—364no—
585C2×D3—362no—
586C2×D3—364no—
587C2×D3—3616no—
588C2×D3—362no—
589C2×D3—368no—
590C2×D3—728no—
591C3×C4—24no—
592C3×C4—24no—
593C3×C4—64no—
594C3×C4—91no—
595C3×C4—91no—
596C3×C4D3×D1214yes—
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—
607C32C2×#90811yescharacteristic, complemented
608C32D3×AGL(1,ℤ/8)14yescomplemented
609C23—61no—
610C23—91no—
611C23—541no—
612C23—542no—
613C23—542no—
614C23—541no—
615C23—1084no—
616Q8—31no—
617Q8—271no—
618Q8—541no—
619D4—31no—
620D4—32no—
621D4—61no—
622D4—61no—
623D4—271no—
624D4—272no—
625D4—541no—
626D4—542no—
627D4—542no—
628D4—541no—
629D4—541no—
630D4—541no—
631D4—541no—
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—92no—
644C8C2×D3×C3⋊D312yescomplemented
645C2×C3—21no—
646C2×C3—24no—
647C2×C3—24no—
648C2×C3—44no—
649C2×C3—92no—
650C2×C3—128no—
651C2×C3—124no—
652C2×C3—181no—
653C2×C3C2×D3×D1214yes—
654C2×C3C2×D4×C3⋊D311yescharacteristic
655D3—38no—
656D3—42no—
657D3—41no—
658D3—64no—
659D3—362no—
660D3—361no—
661D3—368no—
662D3—364no—
663D3—728no—
664D3—724no—
665C22—61no—
666C22—62no—
667C22—91no—
668C22—91no—
669C22—122no—
670C22—182no—
671C22—541no—
672C22—542no—
673C22—1082no—
674C22—1084no—
675C22—1082no—
676C22—1084no—
677C22C3⋊D3×D1211yescharacteristic
678C4—61no—
679C4—91no—
680C4—91no—
681C4—541no—
682C4C3⋊D3×D1211yescharacteristic
683C4C22×D3×C3⋊D311yescharacteristic
684C3—24no—
685C3D3×#90814yescomplemented
686C3C3⋊D3×AGL(1,ℤ/8)11yescharacteristic, complemented
687C2—21no—
688C2—92no—
689C2—122no—
690C2—121no—
691C2—181no—
692C2—1082no—
693C2—1081no—
694C2C2×C3⋊D3×D1211yescharacteristic
subgroupG/H
centerC2C2×C3⋊D3×D12
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×M16C22
socleC2×C33C22×D4
hypercenterM16D3×C3⋊D3
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#235C2semidirect
2. C2×C3⋊D3×D12C2semidirect
3. #11723949C2semidirect
4. C3×M16×C3⋊D3C2semidirect
5. C32×#908C2semidirect
6. #11723378C2semidirect
7. #11723367C2semidirect
8. #11723320C2semidirect
9. #11723319C2semidirect
10. C3⋊D3×D24C2semidirect
11. C3⋊D3×#204C2semidirect
15. #89076C22semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
18. C32×#235C22semidirect
19. C2×C32×D12C22semidirect
26. C3⋊D3×D12C22semidirect
27. C3⋊D3×D12C22semidirect
30. #89018C22semidirect
31. C3⋊D3×Dic6C22semidirect
32. #89014C22semidirect
33. C33×M16C22semidirect
34. #88852C22semidirect
35. #88851C22semidirect
36. C3×#3748C22semidirect
37. C3×#3743C22semidirect
38. C3×C8×C3⋊D3C22semidirect
39. C32×D24C22semidirect
40. C32×#204C22semidirect
41. #88795C22semidirect
42. #88794C22semidirect
43. #88790C22semidirect
44. #88790C22semidirect
59. M16×C3⋊D3D3semidirect
60. C3×#908D3semidirect
79. C4⋊(C3⋊(C3⋊D3))C23semidirect
81. #6308C23semidirect
90. C32×D12C23semidirect
92. C32×Dic6C23semidirect
102. C33×C8C23semidirect
103. C3×C3⋊(C3⋊C8)C23semidirect
130. C3×#235C2×D3semidirect
131. C2×C3×D12C2×D3semidirect
149. C32×M16C2×D3semidirect
150. C32×M16C2×D3semidirect
155. #3748C2×D3semidirect
162. #3743C2×D3semidirect
163. C8×C3⋊D3C2×D3semidirect
165. C3×D24C2×D3semidirect
166. C3×#204C2×D3semidirect
211. #908C3⋊D3direct (N × H)
275. C3×D12C22×D3semidirect
281. C3×Dic6C22×D3semidirect
292. C32×C8C22×D3semidirect
293. C32×C8C22×D3semidirect
294. C3⋊(C3⋊C8)C22×D3semidirect
302. C3×C3⋊D3AGL(1,ℤ/8)semidirect
330. #235C2×C3⋊D3semidirect
340. C2×D12C2×C3⋊D3semidirect
350. C3×M16D32semidirect
351. C3×M16C2×C3⋊D3semidirect
363. D24C2×C3⋊D3semidirect
369. #204C2×C3⋊D3semidirect
428. C33C2×AGL(1,ℤ/8)semidirect
486. D12C22×C3⋊D3semidirect
504. Dic6C22×C3⋊D3semidirect
507. C3×C8C2×D32semidirect
508. C3×C8C22×C3⋊D3semidirect
525. C3⋊D3#908direct (N × H)
559. M16D3×C3⋊D3semidirect
607. C32C2×#908semidirect
608. C32D3×AGL(1,ℤ/8)semidirect
644. C8C2×D3×C3⋊D3semidirect
685. C3D3×#908semidirect
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
C3⋊D3×#2352
C2×C3⋊D3×D122
#117239492
C3×M16×C3⋊D32
C32×#9082
#117233782
#117233672
#117233202
#117233192
C3⋊D3×D242
C3⋊D3×#2042
C3⋊D3×AGL(1,ℤ/8)3
D3×#9083