Finite Group Databasebeta

← D3×#64117 #13176693

Subgroups — D3×#64117 #13176693

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
1D3×#3828C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723949C211yesmaximal, characteristic, complemented
4C3×#64117C211yesmaximal, characteristic, complemented
5C32×D3×M16C211yesmaximal, characteristic, complemented
6#11723371C211yesmaximal, characteristic, complemented
7#11723370C211yesmaximal, characteristic, complemented
8#11723316C212yesmaximal, complemented
9#11723315C212yesmaximal, complemented
10D3×#3745C212yesmaximal, complemented
11D3×#3744C212yesmaximal, complemented
12C2×#64117—31nomaximal
13D3×#908—34nomaximal
14C22×D3×C3⋊D3—21no—
15#89076C2211yescharacteristic, complemented
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C3×#3828C2211yescharacteristic, complemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C32×C4×D3C2211yescharacteristic
20D3×#638—21no—
21C2×#6292—21no—
22#89031—21no—
23D3×C4⋊(C3⋊D3)—21no—
24D3×C4⋊(C3⋊D3)—21no—
25D3×C4⋊(C3⋊D3)C2212yes—
26D3×C4⋊(C3⋊D3)C2212yescomplemented
27D3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C4×D3×C3⋊D3—21no—
29#89022C2211yescharacteristic, complemented
30#89021C2211yescharacteristic, complemented
31#89020—21no—
32D3×#634C2211yescharacteristic, complemented
33C33×M16C2211yescharacteristic, complemented
34#88852C2212yescomplemented
35#88851C2212yescomplemented
36C3×#3745C2212yescomplemented
37C3×#3744C2212yescomplemented
38C32×#208C2211yescharacteristic, complemented
39C32×ΓL(1,𝔽25)C2212yescomplemented
40C32×D3×C8C2212yescomplemented
41#88797C2212yescomplemented
42#88796C2212yescomplemented
43#88791C2212yescomplemented
44#88791C2212yescomplemented
45C2×#3828—31no—
46C22×C4⋊(C3⋊D3)—31no—
47D3×#235—34no—
48C2×D3×D12—34no—
49C2×C32×M16—31no—
50#64117—31no—
51#64117—31no—
52#64117—31no—
53#64117—32no—
54#64117—32no—
55#64117—34no—
56#64117—64no—
57#64117D311yescharacteristic, direct product factor
58C2×#3745—32no—
59C2×#3744—32no—
60C3×#908—34no—
61C3×D3×M16D314yescomplemented
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⋊D3—21no—
70C22×C32×D3D411yescharacteristic
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
82C3×#638—21no—
83C3×C4⋊(C3⋊D3)—21no—
84C3×C4⋊(C3⋊D3)C2312yes—
85C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
86C3×C4×C3⋊D3—21no—
87C3×#634C2311yescharacteristic, complemented
88C2×C32×Dic3D411yescharacteristic
89C32×C4×D3D411yescharacteristic
90C32×C4×D3D411yescharacteristic
91C32×C4×D3C2311yescharacteristic
92C32×C4×D3C2311yescharacteristic
93#6293—21no—
94#6292—21no—
95#6292—22no—
96#6292—22no—
97#6291—21no—
98#6290—21no—
99#6289—21no—
100Dic3×C3⋊D3—21no—
101D3×C3⋊Dic3—21no—
102C33×C8C2312yescomplemented
103C32×C3⋊C8C2312yescomplemented
104D3×AGL(1,ℤ/8)—91no—
105C2×#908—94no—
106C23×C3⋊D3—61no—
107C22×D32—64no—
108C22×C32×C4—31no—
109C2×#638—61no—
110#3828—31no—
111#3828—34no—
112#3828—31no—
113#3828—31no—
114#3828—61no—
115#3828—61no—
116#3828—64no—
117#3828C2×D311yescharacteristic, complemented
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—34no—
120C2×C4⋊(C3⋊D3)—32no—
121C2×C4⋊(C3⋊D3)—32no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C4⋊(C3⋊D3)—61no—
124C2×C4⋊(C3⋊D3)—61no—
125C2×C4⋊(C3⋊D3)—61no—
126C2×C4⋊(C3⋊D3)—64no—
127C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
128C2×C4×C3⋊D3—61no—
129C2×#634—31no—
130C3×#235—34no—
131C2×C3×D12—34no—
132C2×C3×C4×D3C2×D314yes—
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×M16—24no—
147C32×M16—31no—
148C32×M16—32no—
149C32×M16C2×D314yescomplemented
150C32×M16C2×D311yescharacteristic, complemented
151C2×C32×C8—32no—
152#3745—32no—
153#3745—32no—
154#3745—32no—
155#3745—38no—
156#3745—68no—
157#3745C2×D312yescomplemented
158#3744—32no—
159#3744—32no—
160#3744—32no—
161#3744—38no—
162#3744—68no—
163#3744C2×D312yescomplemented
164C3×#208C2×D314yescomplemented
165C3×D24—38no—
166C3×#204—38no—
167C3×ΓL(1,𝔽25)C2×D318yescomplemented
168C3×D3×C8C2×D318yescomplemented
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—21no—
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—42no—
180C2×C32×D3—22no—
181C2×C32×D3C2×D411yescharacteristic
182C2×C32×D3C2×D411yescharacteristic
183D3×C3⋊D3—44no—
184D3×C3⋊D3—42no—
185D3×C3⋊D3—44no—
186C33×C4C2×D411yescharacteristic
187C33×C4C2411yescharacteristic
188C3⋊(C3⋊Dic3)—21no—
189C3×C3⋊Dic3—21no—
190C32×Dic3C2×D411yescharacteristic
191C32×Dic3C2×D411yescharacteristic
192D3×#41—91no—
193C2×D3×D4—91no—
194C2×#235—94no—
195C22×D12—94no—
196C3×AGL(1,ℤ/8)—91no—
197C2×C3×M16—34no—
198#949—91no—
199#932—91no—
200#914—92no—
201D3×SD16—92no—
202#911—92no—
203D3×D8—92no—
204#908—34no—
205#908—98no—
206#908—98no—
207#908—94no—
208#908—94no—
209#908—94no—
210#908—91no—
211#908—184no—
212D3×M16C3⋊D311yescharacteristic, complemented
213C2×D24—98no—
214C2×#204—98no—
215C23×C32—31no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—62no—
218C22×C3⋊D3—62no—
219C22×C3⋊D3—61no—
220C22×C3⋊D3—61no—
221C22×C3⋊D3—64no—
222C22×C3⋊D3—124no—
223C22×C3⋊D3—124no—
224C22×C3×D3—64no—
225C22×C3×D3D1214yes—
226C2×D32—68no—
227C2×D32—68no—
228C2×D32—64no—
229C2×D32—1216no—
230C2×C32×C4—24no—
231C2×C32×C4—31no—
232C2×C32×C4—31no—
233C2×C32×C4—31no—
234C2×C32×C4—31no—
235C2×C32×C4—31no—
236C2×C32×C4C22×D314yes—
237C2×C32×C4C22×D311yescharacteristic
238#638—21no—
239#638—61no—
240#638—61no—
241#638—61no—
242#638—64no—
243#638—124no—
244C2×C3⋊Dic3—61no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—32no—
247C4⋊(C3⋊D3)—31no—
248C4⋊(C3⋊D3)—34no—
249C4⋊(C3⋊D3)—38no—
250C4⋊(C3⋊D3)—68no—
251C4⋊(C3⋊D3)—64no—
252C4⋊(C3⋊D3)—62no—
253C4⋊(C3⋊D3)—62no—
254C4⋊(C3⋊D3)—61no—
255C4⋊(C3⋊D3)—61no—
256C4⋊(C3⋊D3)—64no—
257C4⋊(C3⋊D3)—124no—
258C4⋊(C3⋊D3)C22×D312yes—
259C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
260C4×C3⋊D3—21no—
261C4×C3⋊D3—61no—
262C4×C3⋊D3—61no—
263C4×C3⋊D3—61no—
264C4×C3⋊D3—64no—
265C4×C3⋊D3—124no—
266#634—31no—
267#634—34no—
268#634—64no—
269#634—61no—
270#634C22×D311yescharacteristic, complemented
271C3×#67—64no—
272C2×C3×Dic3D1214yes—
273C3×D12—34no—
274C3×D12—38no—
275C3×D12—64no—
276C3×C4×D3—64no—
277C3×C4×D3D1214yes—
278C3×C4×D3D1214yes—
279C3×C4×D3C22×D314yes—
280C3×C4×D3C22×D314yes—
281C3×Dic6—34no—
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×C8—32no—
293C32×C8C22×D318yescomplemented
294C32×C8C22×D312yescomplemented
295C3×C3⋊C8C22×D318yescomplemented
296C2×AGL(1,ℤ/8)—271noSylow
297C2×C33—21no—
298C2×C33C22×D411yescharacteristic
299C3⋊(C3⋊D3)—42no—
300C3⋊(C3⋊D3)—41no—
301C3×C3⋊D3—42no—
302C3×C3⋊D3—41no—
303C32×D3—21no—
304C32×D3AGL(1,ℤ/8)12yescomplemented
305C23×D3—184no—
306C23×D3—181no—
307C3×#41—91no—
308C2×C3×D4—91no—
309C22×C3×C4—34no—
310C2×#67—184no—
311C2×#67—181no—
312#239—91no—
313D3×Q8—91no—
314#237—91no—
315#237—181no—
316D3×D4—91no—
317D3×D4—92no—
318D3×D4—92no—
319D3×D4—181no—
320D3×D4—181no—
321D3×D4—181no—
322#235—34no—
323#235—94no—
324#235—94no—
325#235—94no—
326#235—91no—
327#235—184no—
328#235—184no—
329#235—184no—
330#235—181no—
331C2×D12—34no—
332C2×D12—98no—
333C2×D12—94no—
334C2×D12—98no—
335C2×D12—94no—
336C2×D12—91no—
337C2×D12—184no—
338C2×D12—184no—
339C2×D12—184no—
340C2×D12—184no—
341C2×C4×D3—184no—
342C2×C4×D3—181no—
343C2×C4×D3C2×C3⋊D311yescharacteristic
344C2×Dic6—94no—
345C3×SD16—92no—
346C3×D8—92no—
347C3×M16—24no—
348C3×M16—34no—
349C3×M16—38no—
350C3×M16D3214yescomplemented
351C3×M16C2×C3⋊D311yescharacteristic, complemented
352C2×C3×C8—38no—
353#215—92no—
354#214—92no—
355#213—92no—
356#213—92no—
357#208C2×C3⋊D311yescharacteristic, complemented
358D24—38no—
359D24—98no—
360D24—98no—
361D24—98no—
362D24—92no—
363D24—188no—
364#204—38no—
365#204—98no—
366#204—98no—
367#204—98no—
368#204—92no—
369#204—188no—
370ΓL(1,𝔽25)C2×C3⋊D312yescomplemented
371D3×C8C2×C3⋊D312yescomplemented
372C22×C32—24no—
373C22×C32—31no—
374C22×C32—31no—
375C22×C32—62no—
376C22×C32C2×D1214yes—
377C22×C32D3×D411yescharacteristic
378C2×C3⋊D3—21no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—42no—
381C2×C3⋊D3—61no—
382C2×C3⋊D3—62no—
383C2×C3⋊D3—64no—
384C2×C3⋊D3—68no—
385C2×C3⋊D3—124no—
386C2×C3⋊D3—128no—
387C2×C3⋊D3—122no—
388C2×C3⋊D3—124no—
389C2×C3⋊D3—124no—
390C2×C3⋊D3—122no—
391C2×C3⋊D3—128no—
392C2×C3⋊D3—248no—
393C2×C3×D3—28no—
394C2×C3×D3—64no—
395C2×C3×D3—68no—
396C2×C3×D3—128no—
397C2×C3×D3C2×D1214yes—
398C2×C3×D3C2×D1214yes—
399D32—1216no—
400D32—128no—
401D32—1216no—
402C32×C4—24no—
403C32×C4—24no—
404C32×C4—31no—
405C32×C4—31no—
406C32×C4C2×D1214yes—
407C32×C4D3×D411yescharacteristic
408C32×C4C23×D314yes—
409C32×C4C23×D311yescharacteristic
410C3⋊Dic3—21no—
411C3⋊Dic3—61no—
412C3⋊Dic3—64no—
413C3⋊Dic3—124no—
414C3×Dic3—64no—
415C3×Dic3C2×D1214yes—
416C3×Dic3C2×D1214yes—
417C2×#41—271no—
418C22×D4—271no—
419AGL(1,ℤ/8)—91no—
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—31no—
428C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
429C23×C3—34no—
430C23×C3—181no—
431C22×D3—64no—
432C22×D3—184no—
433C22×D3—188no—
434C22×D3—188no—
435C22×D3—184no—
436C22×D3—181no—
437C22×D3—181no—
438C22×D3—182no—
439C22×D3—182no—
440C22×D3—364no—
441C22×D3—364no—
442C22×D3—3616no—
443C22×D3C4⋊(C3⋊D3)11yescharacteristic
444C3×Q8—91no—
445C3×D4—91no—
446C3×D4—92no—
447C3×D4—181no—
448C3×D4—181no—
449C2×C3×C4—24no—
450C2×C3×C4—34no—
451C2×C3×C4—34no—
452C2×C3×C4—34no—
453C2×C3×C4—34no—
454C2×C3×C4—34no—
455C2×C3×C4—181no—
456C2×C3×C4C2×D3214yes—
457C2×C3×C4C22×C3⋊D311yescharacteristic
458#67—64no—
459#67—184no—
460#67—184no—
461#67—184no—
462#67—181no—
463#67—181no—
464#67—181no—
465#67—182no—
466#67—182no—
467#67—364no—
468C2×Dic3—184no—
469C2×Dic3—181no—
470C2×Dic3C4⋊(C3⋊D3)11yescharacteristic
471D12—38no—
472D12—34no—
473D12—64no—
474D12—98no—
475D12—94no—
476D12—92no—
477D12—91no—
478D12—188no—
479D12—184no—
480D12—188no—
481D12—188no—
482D12—184no—
483D12—181no—
484D12—184no—
485D12—181no—
486D12—364no—
487C4×D3—64no—
488C4×D3—184no—
489C4×D3—184no—
490C4×D3—181no—
491C4×D3—184no—
492C4×D3—181no—
493C4×D3—181no—
494C4×D3—364no—
495C4×D3C4⋊(C3⋊D3)11yescharacteristic
496C4×D3C4⋊(C3⋊D3)11yescharacteristic
497C4×D3C22×C3⋊D311yescharacteristic
498C4×D3C22×C3⋊D311yescharacteristic
499Dic6—34no—
500Dic6—94no—
501Dic6—91no—
502Dic6—184no—
503Dic6—184no—
504Dic6—181no—
505C3×C8—28no—
506C3×C8—38no—
507C3×C8C2×D3218yescomplemented
508C3×C8C22×C3⋊D312yescomplemented
509C3⋊C8C22×C3⋊D312yescomplemented
510C2×C32—21no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—32no—
514C2×C32—44no—
515C2×C32—61no—
516C2×C32C22×D1214yes—
517C2×C32C2×D3×D411yescharacteristic
518C3⋊D3—42no—
519C3⋊D3—41no—
520C3⋊D3—121no—
521C3⋊D3—122no—
522C3⋊D3—128no—
523C3⋊D3—124no—
524C3⋊D3—244no—
525C3⋊D3—248no—
526C3×D3—24no—
527C3×D3—128no—
528C3×D3—124no—
529C3×D3#90818yescomplemented
530C24—541no—
531#41—91no—
532#41—271no—
533#41—271no—
534#41—271no—
535#41—541no—
536#41—541no—
537C2×Q8—271no—
538C2×D4—91no—
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—31no—
548C22×C4—541no—
549SD16—92no—
550SD16—272no—
551SD16—272no—
552SD16—272no—
553D8—92no—
554D8—272no—
555D8—272no—
556D8—272no—
557M16—31no—
558M16—32no—
559M16D3×C3⋊D311yescharacteristic, complemented
560C2×C8—32no—
561C22×C3—24no—
562C22×C3—34no—
563C22×C3—34no—
564C22×C3—68no—
565C22×C3—181no—
566C22×C3—182no—
567C22×C3—362no—
568C22×C3D3×D1214yes—
569C22×C3C2×C4⋊(C3⋊D3)11yescharacteristic
570C2×D3—22no—
571C2×D3—64no—
572C2×D3—68no—
573C2×D3—128no—
574C2×D3—184no—
575C2×D3—188no—
576C2×D3—181no—
577C2×D3—182no—
578C2×D3—364no—
579C2×D3—368no—
580C2×D3—364no—
581C2×D3—3616no—
582C2×D3—368no—
583C2×D3—3616no—
584C2×D3—362no—
585C2×D3—368no—
586C2×D3—364no—
587C2×D3—362no—
588C2×D3—728no—
589C2×D3C2×C4⋊(C3⋊D3)11yescharacteristic
590C2×D3C2×C4⋊(C3⋊D3)11yescharacteristic
591C3×C4—24no—
592C3×C4—24no—
593C3×C4—34no—
594C3×C4—34no—
595C3×C4—181no—
596C3×C4D3×D1214yes—
597C3×C4C2×C4⋊(C3⋊D3)11yescharacteristic
598C3×C4C22×D3214yes—
599C3×C4C23×C3⋊D311yescharacteristic
600Dic3—64no—
601Dic3—184no—
602Dic3—181no—
603Dic3—364no—
604Dic3C2×C4⋊(C3⋊D3)11yescharacteristic
605Dic3C2×C4⋊(C3⋊D3)11yescharacteristic
606C32—24no—
607C32C2×#90814yescomplemented
608C32D3×AGL(1,ℤ/8)11yescharacteristic, complemented
609C23—31no—
610C23—181no—
611C23—541no—
612C23—542no—
613C23—542no—
614C23—541no—
615C23—1084no—
616Q8—91no—
617Q8—271no—
618Q8—541no—
619D4—91no—
620D4—92no—
621D4—181no—
622D4—181no—
623D4—271no—
624D4—272no—
625D4—542no—
626D4—542no—
627D4—541no—
628D4—541no—
629D4—541no—
630D4—541no—
631D4—541no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—181no—
638C2×C4—541no—
639C2×C4—541no—
640C2×C4—541no—
641C2×C4—541no—
642C2×C4C2×D3×C3⋊D311yescharacteristic
643C8—32no—
644C8C2×D3×C3⋊D312yescomplemented
645C2×C3—21no—
646C2×C3—24no—
647C2×C3—24no—
648C2×C3—38no—
649C2×C3—44no—
650C2×C3—64no—
651C2×C3—362no—
652C2×C3—361no—
653C2×C3C2×D3×D1214yes—
654C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
655D3—21no—
656D3—128no—
657D3—124no—
658D3—362no—
659D3—361no—
660D3—368no—
661D3—364no—
662D3—728no—
663D3—724no—
664D3#6411712yesdirect product factor
665C22—31no—
666C22—31no—
667C22—62no—
668C22—181no—
669C22—182no—
670C22—362no—
671C22—541no—
672C22—542no—
673C22—1082no—
674C22—1084no—
675C22—1082no—
676C22—1084no—
677C22D3×C4⋊(C3⋊D3)11yescharacteristic
678C4—31no—
679C4—31no—
680C4—181no—
681C4—541no—
682C4D3×C4⋊(C3⋊D3)11yescharacteristic
683C4C22×D3×C3⋊D311yescharacteristic
684C3—24no—
685C3D3×#90814yescomplemented
686C3C2×#6411711yescharacteristic, complemented
687C2—21no—
688C2—32no—
689C2—61no—
690C2—362no—
691C2—361no—
692C2—1082no—
693C2—1081no—
694C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
subgroupG/H
centerC2C2×D3×C4⋊(C3⋊D3)
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. D3×#3828C2semidirect
2. C2×D3×C4⋊(C3⋊D3)C2semidirect
3. #11723949C2semidirect
4. C3×#64117C2semidirect
5. C32×D3×M16C2semidirect
6. #11723371C2semidirect
7. #11723370C2semidirect
8. #11723316C2semidirect
9. #11723315C2semidirect
10. D3×#3745C2semidirect
11. D3×#3744C2semidirect
15. #89076C22semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C3×#3828C22semidirect
18. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. D3×C4⋊(C3⋊D3)C22semidirect
27. D3×C4⋊(C3⋊D3)C22semidirect
29. #89022C22semidirect
30. #89021C22semidirect
32. D3×#634C22semidirect
33. C33×M16C22semidirect
34. #88852C22semidirect
35. #88851C22semidirect
36. C3×#3745C22semidirect
37. C3×#3744C22semidirect
38. C32×#208C22semidirect
39. C32×ΓL(1,𝔽25)C22semidirect
40. C32×D3×C8C22semidirect
41. #88797C22semidirect
42. #88796C22semidirect
43. #88791C22semidirect
44. #88791C22semidirect
57. #64117D3direct (N × H)
61. C3×D3×M16D3semidirect
79. C4⋊(C3⋊(C3⋊D3))C23semidirect
81. #6308C23semidirect
85. C3×C4⋊(C3⋊D3)C23semidirect
87. C3×#634C23semidirect
102. C33×C8C23semidirect
103. C32×C3⋊C8C23semidirect
117. #3828C2×D3semidirect
127. C2×C4⋊(C3⋊D3)C2×D3semidirect
149. C32×M16C2×D3semidirect
150. C32×M16C2×D3semidirect
157. #3745C2×D3semidirect
163. #3744C2×D3semidirect
164. C3×#208C2×D3semidirect
167. C3×ΓL(1,𝔽25)C2×D3semidirect
168. C3×D3×C8C2×D3semidirect
212. D3×M16C3⋊D3semidirect
259. C4⋊(C3⋊D3)C22×D3semidirect
270. #634C22×D3semidirect
293. C32×C8C22×D3semidirect
294. C32×C8C22×D3semidirect
295. C3×C3⋊C8C22×D3semidirect
304. C32×D3AGL(1,ℤ/8)semidirect
350. C3×M16D32semidirect
351. C3×M16C2×C3⋊D3semidirect
357. #208C2×C3⋊D3semidirect
370. ΓL(1,𝔽25)C2×C3⋊D3semidirect
371. D3×C8C2×C3⋊D3semidirect
428. C33C2×AGL(1,ℤ/8)semidirect
507. C3×C8C2×D32semidirect
508. C3×C8C22×C3⋊D3semidirect
509. C3⋊C8C22×C3⋊D3semidirect
529. C3×D3#908semidirect
559. M16D3×C3⋊D3semidirect
607. C32C2×#908semidirect
608. C32D3×AGL(1,ℤ/8)semidirect
644. C8C2×D3×C3⋊D3semidirect
664. D3#64117direct (N × H)
685. C3D3×#908semidirect
686. C3C2×#64117semidirect

Maximal subgroups

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

subgroupindex
D3×#38282
C2×D3×C4⋊(C3⋊D3)2
#117239492
C3×#641172
C32×D3×M162
#117233712
#117233702
#117233162
#117233152
D3×#37452
D3×#37442
C2×#641173
D3×#9083