Finite Group Databasebeta

← C3⋊D3×#949 #13177980

Subgroups — C3⋊D3×#949 #13177980

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×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
3#11723990C211yesmaximal, characteristic, complemented
4C32×#949C211yesmaximal, characteristic, complemented
5#11723570C212yesmaximal, complemented
6C3⋊D3×#215C212yesmaximal, complemented
7#11723546C212yesmaximal, complemented
8C3⋊D3×#213C212yesmaximal, complemented
9#11723371C211yesmaximal, characteristic, complemented
10#11723364C211yesmaximal, characteristic, complemented
11C3⋊D3×#208C211yesmaximal, characteristic, complemented
12C3⋊D3×AGL(1,ℤ/8)—31nomaximal
13D3×#949—34nomaximal
14C22×D3×C3⋊D3—21no—
15C33×#41C2211yescharacteristic, complemented
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C3×#3832C2211yescharacteristic, complemented
18C3×Q8×C3⋊D3C2211yescharacteristic, complemented
19C3×#3830—21no—
20C3×#3830C2211yescharacteristic, complemented
21C3×D4×C3⋊D3—21no—
22C3×D4×C3⋊D3C2211yescharacteristic, complemented
23C3×#3828—21no—
24C3×#3828C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3—21no—
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C32×D12C2211yescharacteristic, complemented
28C2×#6291—21no—
29C3⋊D3×D12—21no—
30C3⋊D3×D12—21no—
31C3⋊D3×D12C2212yes—
32C3⋊D3×D12C2212yescomplemented
33#88862C2212yescomplemented
34#88860C2212yescomplemented
35#88855C2211yescharacteristic, complemented
36C32×#215C2212yescomplemented
37C32×#213C2212yescomplemented
38C32×#208C2211yescharacteristic, complemented
39#88797C2212yescomplemented
40#88792C2212yescomplemented
41#88791C2212yescomplemented
42#88789C2212yescomplemented
43#88787C2212yescomplemented
44C3⋊D3×C3⋊C8C2212yescomplemented
45#41×C3⋊D3D311yescharacteristic, complemented
46C2×D4×C3⋊D3—31no—
47C3×D3×#41—34no—
48C2×D3×D12—34no—
49C32×AGL(1,ℤ/8)—31no—
50#64158—31no—
51#64158—34no—
52#64158—64no—
53#64141—31no—
54#64123—32no—
55SD16×C3⋊D3—32no—
56#64120—32no—
57D8×C3⋊D3—32no—
58#64117—31no—
59M16×C3⋊D3—31no—
60C3×#949D314yescomplemented
61#63939—38no—
62D3×#215—38no—
63#63925—38no—
64D3×#213—38no—
65#63825—34no—
66#63823—34no—
67D3×#208—34no—
68C22×C3⋊(C3⋊D3)—21no—
69C22×C3×C3⋊D3—21no—
70C22×C3×C3⋊D3D411yescharacteristic
71C22×C32×D3—21no—
72C2×D3×C3⋊D3—22no—
73C2×D3×C3⋊D3—22no—
74C2×D3×C3⋊D3—44no—
75C33×Q8C2311yescharacteristic, complemented
76C33×D4—21no—
77C33×D4C2311yescharacteristic, complemented
78C2×C33×C4—21no—
79C2×C33×C4C2311yescharacteristic
80C4⋊(C3⋊(C3⋊D3))—21no—
81C4⋊(C3⋊(C3⋊D3))C2312yes—
82C3×#638—21no—
83C3×#638—21no—
84C3×#638—21no—
85C2×C3×C3⋊Dic3—21no—
86C2×C3×C3⋊Dic3D411yescharacteristic
87C3×C4⋊(C3⋊D3)—21no—
88C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
89C3×C4×C3⋊D3—21no—
90C3×C4×C3⋊D3—21no—
91C3×C4×C3⋊D3—21no—
92C3×C4×C3⋊D3D411yescharacteristic
93C3×C4×C3⋊D3D411yescharacteristic
94C3×C4×C3⋊D3C2311yescharacteristic
95C3×C4×C3⋊D3C2311yescharacteristic
96C3×#634—21no—
97C3×#634C2311yescharacteristic, complemented
98C32×D12—21no—
99C32×D12C2312yes—
100#6291—22no—
101#6291—22no—
102C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
103C32×C3⋊C8C2312yescomplemented
104C2×#949—91no—
105D3×AGL(1,ℤ/8)—94no—
106C23×C3⋊D3—61no—
107C22×D32—64no—
108C32×#41—24no—
109C32×#41C2×D314yescomplemented
110C32×#41C2×D311yescharacteristic, complemented
111C2×C32×D4—31no—
112C2×#638—61no—
113#3832C2×D311yescharacteristic, complemented
114Q8×C3⋊D3C2×D311yescharacteristic, complemented
115#3830—21no—
116#3830C2×D311yescharacteristic, complemented
117D4×C3⋊D3—21no—
118D4×C3⋊D3—32no—
119D4×C3⋊D3—32no—
120D4×C3⋊D3—61no—
121D4×C3⋊D3—61no—
122D4×C3⋊D3C2×D311yescharacteristic, complemented
123#3828—21no—
124#3828C2×D311yescharacteristic, complemented
125C2×C4⋊(C3⋊D3)—31no—
126C2×C4⋊(C3⋊D3)—34no—
127C2×C4⋊(C3⋊D3)—64no—
128C2×C4×C3⋊D3—21no—
129C2×C4×C3⋊D3C2×D311yescharacteristic
130C3×#239—34no—
131C3×D3×Q8—34no—
132C3×#237—34no—
133C3×#237—64no—
134C3×D3×D4—34no—
135C3×D3×D4—64no—
136C3×#235—34no—
137C3×#235—64no—
138C2×C3×D12C2×D314yescomplemented
139C2×C3×C4×D3—34no—
140C2×C3×C4×D3—64no—
141C2×#626—64no—
142D3×D12—38no—
143D3×D12—38no—
144D3×D12—64no—
145D3×D12—64no—
146C32×SD16—32no—
147C32×D8—32no—
148C32×M16—31no—
149#3755—32no—
150#3755—38no—
151#3755—68no—
152#3754—32no—
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×#215C2×D318yescomplemented
165C3×#213C2×D318yescomplemented
166C3×#208C2×D314yescomplemented
167#3717—38no—
168#3715—38no—
169#3714—38no—
170#3713—38no—
171#3711—38no—
172D3×C3⋊C8—38no—
173C22×C33—21no—
174C22×C33C2×D411yescharacteristic
175C2×C3⋊(C3⋊D3)—22no—
176C2×C3⋊(C3⋊D3)—42no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3—21no—
179C2×C3×C3⋊D3—42no—
180C2×C3×C3⋊D3C2×D411yescharacteristic
181C2×C3×C3⋊D3C2×D411yescharacteristic
182C2×C32×D3—22no—
183C2×C32×D3—42no—
184D3×C3⋊D3—44no—
185D3×C3⋊D3—44no—
186C33×C4—21no—
187C33×C4C2×D411yescharacteristic
188C33×C4C2411yescharacteristic
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3C2×D411yescharacteristic
191C3×C3⋊Dic3C2×D411yescharacteristic
192C2×C3×#41—91no—
193D3×#41—34no—
194C2×D3×D4—94no—
195C22×D12—91no—
196C3×AGL(1,ℤ/8)—34no—
197#949—94no—
198#949—91no—
199#949—91no—
200#949—92no—
201#949—92no—
202#949—91no—
203#949—184no—
204#949C3⋊D311yescharacteristic, direct product factor
205C2×#215—92no—
206#932—94no—
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—61no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—61no—
218C22×C3⋊D3—62no—
219C22×C3⋊D3—62no—
220C22×C3⋊D3—64no—
221C22×C3⋊D3—124no—
222C22×C3⋊D3—124no—
223C22×C3⋊D3#6711yescharacteristic
224C22×C3×D3—24no—
225C22×C3×D3—34no—
226C22×C3×D3—64no—
227C2×D32—68no—
228C2×D32—68no—
229C2×D32—1216no—
230C32×Q8—24no—
231C32×Q8C22×D314yescomplemented
232C32×Q8C22×D311yescharacteristic, complemented
233C32×D4—21no—
234C32×D4—24no—
235C32×D4—24no—
236C32×D4—32no—
237C32×D4—44no—
238C32×D4—61no—
239C32×D4C22×D314yescomplemented
240C32×D4C22×D311yescharacteristic, complemented
241C2×C32×C4—21no—
242C2×C32×C4—24no—
243C2×C32×C4—24no—
244C2×C32×C4—44no—
245C2×C32×C4C22×D314yes—
246C2×C32×C4C22×D311yescharacteristic
247#638—21no—
248#638—21no—
249#638—21no—
250#638—62no—
251#638—62no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3#6711yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—32no—
256C4⋊(C3⋊D3)—38no—
257C4⋊(C3⋊D3)—68no—
258C4⋊(C3⋊D3)—61no—
259C4⋊(C3⋊D3)—64no—
260C4⋊(C3⋊D3)—124no—
261C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—21no—
265C4×C3⋊D3#6711yescharacteristic
266C4×C3⋊D3#6711yescharacteristic
267C4×C3⋊D3C22×D311yescharacteristic
268C4×C3⋊D3C22×D311yescharacteristic
269#634—21no—
270#634C22×D311yescharacteristic, complemented
271C3×#67—64no—
272C3×#67—64no—
273C3×#67—64no—
274C2×C3×Dic3—34no—
275C2×C3×Dic3—64no—
276C3×D12—24no—
277C3×D12—34no—
278C3×D12—64no—
279C3×D12C22×D318yes—
280C3×C4×D3—34no—
281C3×C4×D3—34no—
282C3×C4×D3—34no—
283C3×C4×D3—34no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287C3×Dic6—34no—
288C3×Dic6—64no—
289#626—68no—
290#626—68no—
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—41no—
299C2×C33C22×D411yescharacteristic
300C3⋊(C3⋊D3)—42no—
301C3×C3⋊D3—21no—
302C3×C3⋊D3—41no—
303C3×C3⋊D3AGL(1,ℤ/8)12yescomplemented
304C32×D3—42no—
305C23×D3—181no—
306C23×D3—184no—
307C3×#41—24no—
308C3×#41—91no—
309C3×#41—91no—
310C3×#41—91no—
311C3×#41—181no—
312C3×#41—181no—
313C3×#41D3214yescomplemented
314C3×#41C2×C3⋊D311yescharacteristic, complemented
315C2×C3×Q8—91no—
316C2×C3×D4—34no—
317C2×C3×D4—91no—
318C2×C3×D4—181no—
319C22×C3×C4—91no—
320C22×C3×C4—181no—
321C2×#67—184no—
322#239—34no—
323D3×Q8—34no—
324#237—34no—
325#237—64no—
326D3×D4—34no—
327D3×D4—64no—
328D3×D4—98no—
329D3×D4—98no—
330D3×D4—184no—
331D3×D4—184no—
332#235—34no—
333#235—64no—
334C2×D12—94no—
335C2×D12—91no—
336C2×D12—92no—
337C2×D12—92no—
338C2×D12—184no—
339C2×D12—181no—
340C2×D12—181no—
341C2×D12—181no—
342C2×D12C2×C3⋊D311yescharacteristic, complemented
343C2×C4×D3—34no—
344C2×C4×D3—64no—
345C3×SD16—38no—
346C3×D8—38no—
347C3×M16—34no—
348#215—98no—
349#215—92no—
350#215—92no—
351#215—92no—
352#215—188no—
353#215C2×C3⋊D312yescomplemented
354#214—98no—
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—21no—
373C22×C32—24no—
374C22×C32—24no—
375C22×C32—44no—
376C22×C32—62no—
377C22×C32—122no—
378C22×C32D3×D414yes—
379C22×C32C2×#6711yescharacteristic
380C2×C3⋊D3—22no—
381C2×C3⋊D3—21no—
382C2×C3⋊D3—42no—
383C2×C3⋊D3—62no—
384C2×C3⋊D3—68no—
385C2×C3⋊D3—128no—
386C2×C3⋊D3—124no—
387C2×C3⋊D3—122no—
388C2×C3⋊D3—124no—
389C2×C3⋊D3—128no—
390C2×C3⋊D3—248no—
391C2×C3⋊D3C2×#6711yescharacteristic
392C2×C3⋊D3C2×#6711yescharacteristic
393C2×C3×D3—28no—
394C2×C3×D3—34no—
395C2×C3×D3—34no—
396C2×C3×D3—48no—
397C2×C3×D3—68no—
398C2×C3×D3—64no—
399C2×C3×D3—128no—
400D32—1216no—
401D32—1216no—
402C32×C4—21no—
403C32×C4—24no—
404C32×C4—24no—
405C32×C4—24no—
406C32×C4—44no—
407C32×C4D3×D414yes—
408C32×C4C2×#6711yescharacteristic
409C32×C4C23×D314yes—
410C32×C4C23×D311yescharacteristic
411C3⋊Dic3—21no—
412C3⋊Dic3C2×#6711yescharacteristic
413C3⋊Dic3C2×#6711yescharacteristic
414C3×Dic3—34no—
415C3×Dic3—34no—
416C3×Dic3—64no—
417C2×#41—91no—
418C22×D4—271no—
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—64no—
430C23×C3—91no—
431C23×C3—181no—
432C22×D3—21no—
433C22×D3—34no—
434C22×D3—64no—
435C22×D3—182no—
436C22×D3—182no—
437C22×D3—188no—
438C22×D3—188no—
439C22×D3—184no—
440C22×D3—181no—
441C22×D3—364no—
442C22×D3—364no—
443C22×D3—3616no—
444C3×Q8—24no—
445C3×Q8—91no—
446C3×Q8—181no—
447C3×Q8C2×D3214yescomplemented
448C3×Q8C22×C3⋊D311yescharacteristic, complemented
449C3×D4—24no—
450C3×D4—21no—
451C3×D4—24no—
452C3×D4—38no—
453C3×D4—44no—
454C3×D4—64no—
455C3×D4—91no—
456C3×D4—181no—
457C3×D4—181no—
458C3×D4—181no—
459C3×D4—181no—
460C3×D4C2×D3214yescomplemented
461C3×D4C22×C3⋊D311yescharacteristic, complemented
462C2×C3×C4—24no—
463C2×C3×C4—21no—
464C2×C3×C4—24no—
465C2×C3×C4—44no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—91no—
470C2×C3×C4—91no—
471C2×C3×C4—181no—
472C2×C3×C4—181no—
473C2×C3×C4—181no—
474C2×C3×C4—181no—
475C2×C3×C4C2×D3214yes—
476C2×C3×C4C22×C3⋊D311yescharacteristic
477#67—64no—
478#67—64no—
479#67—64no—
480#67—188no—
481#67—188no—
482C2×Dic3—34no—
483C2×Dic3—64no—
484D12—21no—
485D12—34no—
486D12—64no—
487D12—98no—
488D12—92no—
489D12—188no—
490D12—182no—
491D12—182no—
492D12—184no—
493D12—181no—
494D12—364no—
495D12C22×C3⋊D312yes—
496C4×D3—34no—
497C4×D3—34no—
498C4×D3—34no—
499C4×D3—34no—
500C4×D3—64no—
501C4×D3—64no—
502C4×D3—64no—
503Dic6—34no—
504Dic6—64no—
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—41no—
515C2×C32—44no—
516C2×C32—84no—
517C2×C32—122no—
518C2×C32C2×D3×D414yes—
519C2×C32C22×#6711yescharacteristic
520C3⋊D3—21no—
521C3⋊D3—41no—
522C3⋊D3—122no—
523C3⋊D3—128no—
524C3⋊D3—248no—
525C3⋊D3#94912yesdirect product factor
526C3×D3—38no—
527C3×D3—48no—
528C3×D3—64no—
529C3×D3—124no—
530C24—541no—
531#41—91no—
532#41—91no—
533#41—91no—
534#41—181no—
535#41—181no—
536#41D3×C3⋊D311yescharacteristic, complemented
537C2×Q8—91no—
538C2×D4—31no—
539C2×D4—91no—
540C2×D4—181no—
541C2×D4—272no—
542C2×D4—272no—
543C2×D4—271no—
544C2×D4—541no—
545C2×D4—541no—
546C2×D4—541no—
547C22×C4—91no—
548C22×C4—181no—
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—24no—
562C22×C3—21no—
563C22×C3—24no—
564C22×C3—44no—
565C22×C3—68no—
566C22×C3—91no—
567C22×C3—91no—
568C22×C3—128no—
569C22×C3—182no—
570C22×C3—181no—
571C22×C3—362no—
572C22×C3D3×#6714yes—
573C22×C3D4×C3⋊D311yescharacteristic
574C2×D3—22no—
575C2×D3—34no—
576C2×D3—34no—
577C2×D3—42no—
578C2×D3—68no—
579C2×D3—64no—
580C2×D3—128no—
581C2×D3—188no—
582C2×D3—182no—
583C2×D3—368no—
584C2×D3—3616no—
585C2×D3—364no—
586C2×D3—364no—
587C2×D3—3616no—
588C2×D3—362no—
589C2×D3—368no—
590C2×D3—728no—
591C3×C4—24no—
592C3×C4—21no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—44no—
596C3×C4—91no—
597C3×C4—91no—
598C3×C4—181no—
599C3×C4D3×#6714yes—
600C3×C4D4×C3⋊D311yescharacteristic
601C3×C4C22×D3214yes—
602C3×C4C23×C3⋊D311yescharacteristic
603Dic3—34no—
604Dic3—34no—
605Dic3—64no—
606C32—24no—
607C32D3×AGL(1,ℤ/8)14yescomplemented
608C32C2×#94911yescharacteristic, complemented
609C23—61no—
610C23—91no—
611C23—181no—
612C23—542no—
613C23—542no—
614C23—541no—
615C23—1084no—
616Q8—91no—
617Q8—181no—
618Q8C2×D3×C3⋊D311yescharacteristic, complemented
619D4—21no—
620D4—32no—
621D4—61no—
622D4—91no—
623D4—181no—
624D4—181no—
625D4—181no—
626D4—181no—
627D4—272no—
628D4—542no—
629D4—542no—
630D4—541no—
631D4C2×D3×C3⋊D311yescharacteristic, complemented
632C2×C4—21no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—91no—
636C2×C4—91no—
637C2×C4—91no—
638C2×C4—181no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4C2×D3×C3⋊D311yescharacteristic
643C8—32no—
644C8—272no—
645C2×C3—24no—
646C2×C3—21no—
647C2×C3—24no—
648C2×C3—44no—
649C2×C3—44no—
650C2×C3—41no—
651C2×C3—84no—
652C2×C3—92no—
653C2×C3—128no—
654C2×C3—181no—
655C2×C3—361no—
656C2×C3C2×D3×#6714yes—
657C2×C3C2×D4×C3⋊D311yescharacteristic
658D3—38no—
659D3—42no—
660D3—64no—
661D3—124no—
662D3—368no—
663D3—362no—
664D3—728no—
665C22—21no—
666C22—62no—
667C22—91no—
668C22—91no—
669C22—122no—
670C22—182no—
671C22—181no—
672C22—362no—
673C22—542no—
674C22—1082no—
675C22—1084no—
676C22—1084no—
677C22C3⋊D3×#6711yescharacteristic
678C4—21no—
679C4—91no—
680C4—91no—
681C4—181no—
682C4C3⋊D3×#6711yescharacteristic
683C4C22×D3×C3⋊D311yescharacteristic
684C3—24no—
685C3D3×#94914yescomplemented
686C3C3⋊D3×AGL(1,ℤ/8)11yescharacteristic, complemented
687C2—21no—
688C2—41no—
689C2—92no—
690C2—122no—
691C2—181no—
692C2—361no—
693C2—1082no—
694C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
centerC2C2×C3⋊D3×#67
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×#41C22
socleC2×C33C22×D4
hypercenter#41D3×C3⋊D3
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×#41×C3⋊D3C2semidirect
2. C2×C3⋊D3×D12C2semidirect
3. #11723990C2semidirect
4. C32×#949C2semidirect
5. #11723570C2semidirect
6. C3⋊D3×#215C2semidirect
7. #11723546C2semidirect
8. C3⋊D3×#213C2semidirect
9. #11723371C2semidirect
10. #11723364C2semidirect
11. C3⋊D3×#208C2semidirect
15. C33×#41C22semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C3×#3832C22semidirect
18. C3×Q8×C3⋊D3C22semidirect
20. C3×#3830C22semidirect
22. C3×D4×C3⋊D3C22semidirect
24. C3×#3828C22semidirect
27. C2×C32×D12C22semidirect
32. C3⋊D3×D12C22semidirect
33. #88862C22semidirect
34. #88860C22semidirect
35. #88855C22semidirect
36. C32×#215C22semidirect
37. C32×#213C22semidirect
38. C32×#208C22semidirect
39. #88797C22semidirect
40. #88792C22semidirect
41. #88791C22semidirect
42. #88789C22semidirect
43. #88787C22semidirect
44. C3⋊D3×C3⋊C8C22semidirect
45. #41×C3⋊D3D3semidirect
60. C3×#949D3semidirect
75. C33×Q8C23semidirect
77. C33×D4C23semidirect
88. C3×C4⋊(C3⋊D3)C23semidirect
97. C3×#634C23semidirect
102. C3⋊(C3⋊(C3⋊C8))C23semidirect
103. C32×C3⋊C8C23semidirect
109. C32×#41C2×D3semidirect
110. C32×#41C2×D3semidirect
113. #3832C2×D3semidirect
114. Q8×C3⋊D3C2×D3semidirect
116. #3830C2×D3semidirect
122. D4×C3⋊D3C2×D3semidirect
124. #3828C2×D3semidirect
138. C2×C3×D12C2×D3semidirect
164. C3×#215C2×D3semidirect
165. C3×#213C2×D3semidirect
166. C3×#208C2×D3semidirect
204. #949C3⋊D3direct (N × H)
231. C32×Q8C22×D3semidirect
232. C32×Q8C22×D3semidirect
239. C32×D4C22×D3semidirect
240. C32×D4C22×D3semidirect
261. C4⋊(C3⋊D3)C22×D3semidirect
270. #634C22×D3semidirect
295. C3×C3⋊C8C22×D3semidirect
303. C3×C3⋊D3AGL(1,ℤ/8)semidirect
313. C3×#41D32semidirect
314. C3×#41C2×C3⋊D3semidirect
342. C2×D12C2×C3⋊D3semidirect
353. #215C2×C3⋊D3semidirect
361. #213C2×C3⋊D3semidirect
366. #208C2×C3⋊D3semidirect
428. C33C2×AGL(1,ℤ/8)semidirect
447. C3×Q8C2×D32semidirect
448. C3×Q8C22×C3⋊D3semidirect
460. C3×D4C2×D32semidirect
461. C3×D4C22×C3⋊D3semidirect
509. C3⋊C8C22×C3⋊D3semidirect
525. C3⋊D3#949direct (N × H)
536. #41D3×C3⋊D3semidirect
607. C32D3×AGL(1,ℤ/8)semidirect
608. C32C2×#949semidirect
618. Q8C2×D3×C3⋊D3semidirect
631. D4C2×D3×C3⋊D3semidirect
685. C3D3×#949semidirect
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×#41×C3⋊D32
C2×C3⋊D3×D122
#117239902
C32×#9492
#117235702
C3⋊D3×#2152
#117235462
C3⋊D3×#2132
#117233712
#117233642
C3⋊D3×#2082
C3⋊D3×AGL(1,ℤ/8)3
D3×#9493