Finite Group Databasebeta

← D3×#64158 #13177987

Subgroups — D3×#64158 #13177987

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
1C32×D3×#41C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723990C211yesmaximal, characteristic, complemented
4C3×#64158C211yesmaximal, characteristic, complemented
5#11723568C212yesmaximal, complemented
6D3×#3755C212yesmaximal, complemented
7#11723544C212yesmaximal, complemented
8D3×#3753C212yesmaximal, complemented
9#11723367C211yesmaximal, characteristic, complemented
10#11723365C211yesmaximal, characteristic, complemented
11D3×#3748C211yesmaximal, characteristic, complemented
12C2×#64158—31nomaximal
13D3×#949—34nomaximal
14C22×D3×C3⋊D3—21no—
15C33×#41C2211yescharacteristic, complemented
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C32×#239C2211yescharacteristic, complemented
19C32×D3×Q8C2211yescharacteristic, complemented
20C32×#237—21no—
21C32×#237C2211yescharacteristic, complemented
22C32×D3×D4—21no—
23C32×D3×D4C2211yescharacteristic, complemented
24C32×#235—21no—
25C32×#235C2211yescharacteristic, complemented
26C2×C32×C4×D3—21no—
27C2×C32×C4×D3C2211yescharacteristic
28C2×#6292—21no—
29D3×C4⋊(C3⋊D3)—21no—
30D3×C4⋊(C3⋊D3)—21no—
31D3×C4⋊(C3⋊D3)C2212yes—
32D3×C4⋊(C3⋊D3)C2212yescomplemented
33#88862C2212yescomplemented
34#88860C2212yescomplemented
35#88855C2211yescharacteristic, complemented
36C3×#3755C2212yescomplemented
37C3×#3753C2212yescomplemented
38C3×#3748C2211yescharacteristic, complemented
39#88795C2212yescomplemented
40#88793C2212yescomplemented
41#88790C2212yescomplemented
42#88789C2212yescomplemented
43#88786C2212yescomplemented
44D3×C3⋊(C3⋊C8)C2212yescomplemented
45C2×C32×#41—31no—
46C22×C4⋊(C3⋊D3)—31no—
47C3×D3×#41D314yescomplemented
48C2×D3×D12—34no—
49#64158—31no—
50#64158—31no—
51#64158—34no—
52#64158—32no—
53#64158—32no—
54#64158—31no—
55#64158—64no—
56#64158D311yescharacteristic, direct product factor
57C2×#3755—32no—
58C2×#3753—32no—
59C2×#3748—31no—
60C3×#949—34no—
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×C32×D3—21no—
71C22×C32×D3D411yescharacteristic
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×C4⋊(C3⋊D3)—21no—
83C3×C4⋊(C3⋊D3)C2312yes—
84C32×#67—21no—
85C32×#67—21no—
86C32×#67—21no—
87C2×C32×Dic3—21no—
88C2×C32×Dic3D411yescharacteristic
89C32×D12—21no—
90C32×D12C2311yescharacteristic, complemented
91C32×C4×D3—21no—
92C32×C4×D3—21no—
93C32×C4×D3—21no—
94C32×C4×D3D411yescharacteristic
95C32×C4×D3D411yescharacteristic
96C32×C4×D3C2311yescharacteristic
97C32×C4×D3C2311yescharacteristic
98C32×Dic6—21no—
99C32×Dic6C2311yescharacteristic, complemented
100#6292—22no—
101#6292—22no—
102C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
103C3×C3⋊(C3⋊C8)C2312yescomplemented
104C2×#949—94no—
105D3×AGL(1,ℤ/8)—91no—
106C23×C3⋊D3—61no—
107C22×D32—64no—
108C32×#41—24no—
109C32×#41—31no—
110C32×#41—31no—
111C32×#41—31no—
112C32×#41—61no—
113C32×#41—61no—
114C32×#41C2×D314yescomplemented
115C32×#41C2×D311yescharacteristic, complemented
116C2×C32×Q8—31no—
117C2×C32×D4—31no—
118C2×C32×D4—61no—
119C22×C32×C4—31no—
120C22×C32×C4—61no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)—34no—
123C2×C4⋊(C3⋊D3)—32no—
124C2×C4⋊(C3⋊D3)—32no—
125C2×C4⋊(C3⋊D3)—61no—
126C2×C4⋊(C3⋊D3)—61no—
127C2×C4⋊(C3⋊D3)—61no—
128C2×C4⋊(C3⋊D3)—64no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
130C3×#239C2×D314yescomplemented
131C3×D3×Q8C2×D314yescomplemented
132C3×#237—24no—
133C3×#237C2×D314yescomplemented
134C3×D3×D4—24no—
135C3×D3×D4C2×D314yescomplemented
136C3×#235—24no—
137C3×#235C2×D314yescomplemented
138C2×C3×D12—34no—
139C2×C3×C4×D3—24no—
140C2×C3×C4×D3C2×D314yes—
141C2×#626—64no—
142D3×D12—38no—
143D3×D12—38no—
144D3×D12—64no—
145D3×D12—64no—
146#3755—32no—
147#3755—38no—
148#3755—32no—
149#3755—32no—
150#3755—68no—
151#3755C2×D312yescomplemented
152#3753—32no—
153#3753—38no—
154#3753—32no—
155#3753—32no—
156#3753—68no—
157#3753C2×D312yescomplemented
158#3748—31no—
159#3748—34no—
160#3748—32no—
161#3748—64no—
162#3748C2×D311yescharacteristic, complemented
163C2×C3⋊(C3⋊C8)—32no—
164C3×#215—38no—
165C3×#213—38no—
166C3×#208—34no—
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—42no—
179C2×C32×D3—22no—
180C2×C32×D3—21no—
181C2×C32×D3—42no—
182C2×C32×D3C2×D411yescharacteristic
183C2×C32×D3C2×D411yescharacteristic
184D3×C3⋊D3—44no—
185D3×C3⋊D3—44no—
186C33×C4—21no—
187C33×C4C2×D411yescharacteristic
188C33×C4C2411yescharacteristic
189C32×Dic3—21no—
190C32×Dic3C2×D411yescharacteristic
191C32×Dic3C2×D411yescharacteristic
192C2×C3×#41—34no—
193D3×#41C3⋊D311yescharacteristic, complemented
194C2×D3×D4—91no—
195C22×D12—94no—
196C3×AGL(1,ℤ/8)—91no—
197#949—34no—
198#949—94no—
199#949—98no—
200#949—98no—
201#949—94no—
202#949—94no—
203#949—91no—
204#949—184no—
205C2×#215—98no—
206#932—91no—
207C2×#213—98no—
208C2×#208—94no—
209#914—92no—
210D3×SD16—92no—
211#911—92no—
212D3×D8—92no—
213#908—91no—
214D3×M16—91no—
215C23×C32—31no—
216C23×C32—61no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—62no—
219C22×C3⋊D3—62no—
220C22×C3⋊D3—61no—
221C22×C3⋊D3—64no—
222C22×C3⋊D3—124no—
223C22×C3⋊D3—124no—
224C22×C3×D3—24no—
225C22×C3×D3—64no—
226C22×C3×D3#6714yes—
227C2×D32—68no—
228C2×D32—68no—
229C2×D32—1216no—
230C32×Q8—24no—
231C32×Q8—31no—
232C32×Q8—61no—
233C32×Q8C22×D314yescomplemented
234C32×Q8C22×D311yescharacteristic, complemented
235C32×D4—21no—
236C32×D4—24no—
237C32×D4—24no—
238C32×D4—31no—
239C32×D4—44no—
240C32×D4—61no—
241C32×D4—61no—
242C32×D4—61no—
243C32×D4—61no—
244C32×D4C22×D314yescomplemented
245C32×D4C22×D311yescharacteristic, complemented
246C2×C32×C4—21no—
247C2×C32×C4—24no—
248C2×C32×C4—24no—
249C2×C32×C4—31no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—44no—
255C2×C32×C4—61no—
256C2×C32×C4—61no—
257C2×C32×C4—61no—
258C2×C32×C4—61no—
259C2×C32×C4C22×D314yes—
260C2×C32×C4C22×D311yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—32no—
263C4⋊(C3⋊D3)—38no—
264C4⋊(C3⋊D3)—68no—
265C4⋊(C3⋊D3)—62no—
266C4⋊(C3⋊D3)—62no—
267C4⋊(C3⋊D3)—61no—
268C4⋊(C3⋊D3)—64no—
269C4⋊(C3⋊D3)—124no—
270C4⋊(C3⋊D3)C22×D312yes—
271C3×#67—24no—
272C3×#67—24no—
273C3×#67—24no—
274C2×C3×Dic3—24no—
275C2×C3×Dic3#6714yes—
276C3×D12—24no—
277C3×D12—38no—
278C3×D12—64no—
279C3×D12C22×D314yescomplemented
280C3×C4×D3—24no—
281C3×C4×D3—24no—
282C3×C4×D3—24no—
283C3×C4×D3#6714yes—
284C3×C4×D3#6714yes—
285C3×C4×D3C22×D314yes—
286C3×C4×D3C22×D314yes—
287C3×Dic6—24no—
288C3×Dic6C22×D314yescomplemented
289#626—68no—
290#626—68no—
291C3⋊(C3⋊C8)—32no—
292C3⋊(C3⋊C8)—38no—
293C3⋊(C3⋊C8)—68no—
294C3⋊(C3⋊C8)C22×D312yescomplemented
295C3×C3⋊C8—38no—
296C2×AGL(1,ℤ/8)—271noSylow
297C2×C33—21no—
298C2×C33—41no—
299C2×C33C22×D411yescharacteristic
300C3⋊(C3⋊D3)—42no—
301C3×C3⋊D3—42no—
302C32×D3—21no—
303C32×D3—41no—
304C32×D3AGL(1,ℤ/8)12yescomplemented
305C23×D3—184no—
306C23×D3—181no—
307C3×#41—24no—
308C3×#41—34no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—64no—
312C3×#41—64no—
313C3×#41D3214yescomplemented
314C3×#41C2×C3⋊D311yescharacteristic, complemented
315C2×C3×Q8—34no—
316C2×C3×D4—34no—
317C2×C3×D4—64no—
318C2×C3×D4—91no—
319C22×C3×C4—34no—
320C22×C3×C4—64no—
321C2×#67—181no—
322#239C2×C3⋊D311yescharacteristic, complemented
323D3×Q8C2×C3⋊D311yescharacteristic, complemented
324#237—21no—
325#237C2×C3⋊D311yescharacteristic, complemented
326D3×D4—21no—
327D3×D4—92no—
328D3×D4—92no—
329D3×D4—181no—
330D3×D4—181no—
331D3×D4C2×C3⋊D311yescharacteristic, complemented
332#235—21no—
333#235C2×C3⋊D311yescharacteristic, complemented
334C2×D12—34no—
335C2×D12—98no—
336C2×D12—98no—
337C2×D12—94no—
338C2×D12—91no—
339C2×D12—184no—
340C2×D12—184no—
341C2×D12—184no—
342C2×D12—184no—
343C2×C4×D3—21no—
344C2×C4×D3C2×C3⋊D311yescharacteristic
345C3×SD16—92no—
346C3×D8—92no—
347C3×M16—91no—
348#215—38no—
349#215—98no—
350#215—98no—
351#215—98no—
352#215—92no—
353#215—188no—
354#214—92no—
355#213—38no—
356#213—98no—
357#213—98no—
358#213—98no—
359#213—92no—
360#213—92no—
361#213—188no—
362#208—34no—
363#208—98no—
364#208—94no—
365#208—91no—
366#208—184no—
367C2×C3⋊C8—98no—
368D24—92no—
369#204—92no—
370ΓL(1,𝔽25)—92no—
371D3×C8—92no—
372C22×C32—21no—
373C22×C32—24no—
374C22×C32—24no—
375C22×C32—31no—
376C22×C32—31no—
377C22×C32—44no—
378C22×C32—62no—
379C22×C32—61no—
380C22×C32—122no—
381C22×C32D3×D411yescharacteristic
382C22×C32C2×#6714yes—
383C2×C3⋊D3—22no—
384C2×C3⋊D3—42no—
385C2×C3⋊D3—62no—
386C2×C3⋊D3—68no—
387C2×C3⋊D3—128no—
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—24no—
395C2×C3×D3—48no—
396C2×C3×D3—68no—
397C2×C3×D3—128no—
398C2×C3×D3C2×#6714yes—
399C2×C3×D3C2×#6714yes—
400D32—1216no—
401D32—1216no—
402C32×C4—21no—
403C32×C4—24no—
404C32×C4—24no—
405C32×C4—24no—
406C32×C4—31no—
407C32×C4—31no—
408C32×C4—44no—
409C32×C4—61no—
410C32×C4D3×D411yescharacteristic
411C32×C4C2×#6714yes—
412C32×C4C23×D314yes—
413C32×C4C23×D311yescharacteristic
414C3×Dic3—24no—
415C3×Dic3C2×#6714yes—
416C3×Dic3C2×#6714yes—
417C2×#41—31no—
418C22×D4—271no—
419AGL(1,ℤ/8)—91no—
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—34no—
430C23×C3—64no—
431C23×C3—181no—
432C22×D3—21no—
433C22×D3—64no—
434C22×D3—188no—
435C22×D3—188no—
436C22×D3—184no—
437C22×D3—181no—
438C22×D3—182no—
439C22×D3—182no—
440C22×D3—364no—
441C22×D3—364no—
442C22×D3—3616no—
443C22×D3#63811yescharacteristic
444C3×Q8—24no—
445C3×Q8—34no—
446C3×Q8—64no—
447C3×Q8C2×D3214yescomplemented
448C3×Q8C22×C3⋊D311yescharacteristic, complemented
449C3×D4—24no—
450C3×D4—21no—
451C3×D4—24no—
452C3×D4—34no—
453C3×D4—44no—
454C3×D4—64no—
455C3×D4—64no—
456C3×D4—64no—
457C3×D4—64no—
458C3×D4—92no—
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—34no—
466C2×C3×C4—34no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—44no—
471C2×C3×C4—64no—
472C2×C3×C4—64no—
473C2×C3×C4—64no—
474C2×C3×C4—64no—
475C2×C3×C4C2×D3214yes—
476C2×C3×C4C22×C3⋊D311yescharacteristic
477#67—21no—
478#67—21no—
479#67—21no—
480#67—182no—
481#67—182no—
482C2×Dic3—21no—
483C2×Dic3#63811yescharacteristic
484D12—21no—
485D12—38no—
486D12—64no—
487D12—98no—
488D12—92no—
489D12—188no—
490D12—188no—
491D12—188no—
492D12—184no—
493D12—181no—
494D12—364no—
495D12C22×C3⋊D311yescharacteristic, complemented
496C4×D3—21no—
497C4×D3—21no—
498C4×D3—21no—
499C4×D3#63811yescharacteristic
500C4×D3#63811yescharacteristic
501C4×D3C22×C3⋊D311yescharacteristic
502C4×D3C22×C3⋊D311yescharacteristic
503Dic6—21no—
504Dic6C22×C3⋊D311yescharacteristic, complemented
505C3×C8—92no—
506C3⋊C8—38no—
507C3⋊C8—98no—
508C3⋊C8—92no—
509C3⋊C8—188no—
510C2×C32—21no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—32no—
514C2×C32—44no—
515C2×C32—41no—
516C2×C32—44no—
517C2×C32—61no—
518C2×C32—84no—
519C2×C32—121no—
520C2×C32C2×D3×D411yescharacteristic
521C2×C32C22×#6714yes—
522C3⋊D3—42no—
523C3⋊D3—122no—
524C3⋊D3—128no—
525C3⋊D3—248no—
526C3×D3—24no—
527C3×D3—44no—
528C3×D3—128no—
529C3×D3#94918yescomplemented
530C24—541no—
531#41—31no—
532#41—31no—
533#41—31no—
534#41—61no—
535#41—61no—
536#41D3×C3⋊D311yescharacteristic, complemented
537C2×Q8—31no—
538C2×D4—31no—
539C2×D4—61no—
540C2×D4—91no—
541C2×D4—272no—
542C2×D4—272no—
543C2×D4—271no—
544C2×D4—541no—
545C2×D4—541no—
546C2×D4—541no—
547C22×C4—31no—
548C22×C4—61no—
549SD16—92no—
550SD16—272no—
551SD16—272no—
552SD16—272no—
553D8—92no—
554D8—272no—
555D8—272no—
556D8—272no—
557M16—91no—
558M16—272no—
559M16—271no—
560C2×C8—272no—
561C22×C3—24no—
562C22×C3—21no—
563C22×C3—24no—
564C22×C3—34no—
565C22×C3—34no—
566C22×C3—44no—
567C22×C3—68no—
568C22×C3—64no—
569C22×C3—128no—
570C22×C3—182no—
571C22×C3—362no—
572C22×C3D3×#6714yes—
573C22×C3C2×#63811yescharacteristic
574C2×D3—22no—
575C2×D3—21no—
576C2×D3—42no—
577C2×D3—68no—
578C2×D3—128no—
579C2×D3—188no—
580C2×D3—182no—
581C2×D3—368no—
582C2×D3—364no—
583C2×D3—3616no—
584C2×D3—3616no—
585C2×D3—362no—
586C2×D3—368no—
587C2×D3—364no—
588C2×D3—728no—
589C2×D3C2×#63811yescharacteristic
590C2×D3C2×#63811yescharacteristic
591C3×C4—24no—
592C3×C4—21no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—34no—
596C3×C4—34no—
597C3×C4—44no—
598C3×C4—64no—
599C3×C4D3×#6714yes—
600C3×C4C2×#63811yescharacteristic
601C3×C4C22×D3214yes—
602C3×C4C23×C3⋊D311yescharacteristic
603Dic3—21no—
604Dic3C2×#63811yescharacteristic
605Dic3C2×#63811yescharacteristic
606C32—24no—
607C32D3×AGL(1,ℤ/8)11yescharacteristic, complemented
608C32C2×#94914yescomplemented
609C23—31no—
610C23—61no—
611C23—181no—
612C23—542no—
613C23—542no—
614C23—541no—
615C23—1084no—
616Q8—31no—
617Q8—61no—
618Q8C2×D3×C3⋊D311yescharacteristic, complemented
619D4—21no—
620D4—31no—
621D4—61no—
622D4—61no—
623D4—61no—
624D4—61no—
625D4—92no—
626D4—181no—
627D4—272no—
628D4—542no—
629D4—542no—
630D4—541no—
631D4C2×D3×C3⋊D311yescharacteristic, complemented
632C2×C4—21no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4C2×D3×C3⋊D311yescharacteristic
643C8—92no—
644C8—272no—
645C2×C3—24no—
646C2×C3—21no—
647C2×C3—24no—
648C2×C3—38no—
649C2×C3—44no—
650C2×C3—44no—
651C2×C3—41no—
652C2×C3—64no—
653C2×C3—84no—
654C2×C3—124no—
655C2×C3—362no—
656C2×C3C2×D3×#6714yes—
657C2×C3C22×#63811yescharacteristic
658D3—21no—
659D3—41no—
660D3—128no—
661D3—368no—
662D3—362no—
663D3—728no—
664D3#6415812yesdirect product factor
665C22—21no—
666C22—31no—
667C22—31no—
668C22—62no—
669C22—61no—
670C22—122no—
671C22—182no—
672C22—362no—
673C22—542no—
674C22—1082no—
675C22—1084no—
676C22—1084no—
677C22D3×#63811yescharacteristic
678C4—21no—
679C4—31no—
680C4—31no—
681C4—61no—
682C4D3×#63811yescharacteristic
683C4C22×D3×C3⋊D311yescharacteristic
684C3—24no—
685C3D3×#94914yescomplemented
686C3C2×#6415811yescharacteristic, complemented
687C2—21no—
688C2—32no—
689C2—41no—
690C2—61no—
691C2—121no—
692C2—362no—
693C2—1082no—
694C2C2×D3×#63811yescharacteristic
subgroupG/H
centerC2C2×D3×#638
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. C32×D3×#41C2semidirect
2. C2×D3×C4⋊(C3⋊D3)C2semidirect
3. #11723990C2semidirect
4. C3×#64158C2semidirect
5. #11723568C2semidirect
6. D3×#3755C2semidirect
7. #11723544C2semidirect
8. D3×#3753C2semidirect
9. #11723367C2semidirect
10. #11723365C2semidirect
11. D3×#3748C2semidirect
15. C33×#41C22semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C32×#239C22semidirect
19. C32×D3×Q8C22semidirect
21. C32×#237C22semidirect
23. C32×D3×D4C22semidirect
25. C32×#235C22semidirect
32. D3×C4⋊(C3⋊D3)C22semidirect
33. #88862C22semidirect
34. #88860C22semidirect
35. #88855C22semidirect
36. C3×#3755C22semidirect
37. C3×#3753C22semidirect
38. C3×#3748C22semidirect
39. #88795C22semidirect
40. #88793C22semidirect
41. #88790C22semidirect
42. #88789C22semidirect
43. #88786C22semidirect
44. D3×C3⋊(C3⋊C8)C22semidirect
47. C3×D3×#41D3semidirect
56. #64158D3direct (N × H)
75. C33×Q8C23semidirect
77. C33×D4C23semidirect
90. C32×D12C23semidirect
99. C32×Dic6C23semidirect
102. C3⋊(C3⋊(C3⋊C8))C23semidirect
103. C3×C3⋊(C3⋊C8)C23semidirect
114. C32×#41C2×D3semidirect
115. C32×#41C2×D3semidirect
129. C2×C4⋊(C3⋊D3)C2×D3semidirect
130. C3×#239C2×D3semidirect
131. C3×D3×Q8C2×D3semidirect
133. C3×#237C2×D3semidirect
135. C3×D3×D4C2×D3semidirect
137. C3×#235C2×D3semidirect
151. #3755C2×D3semidirect
157. #3753C2×D3semidirect
162. #3748C2×D3semidirect
193. D3×#41C3⋊D3semidirect
233. C32×Q8C22×D3semidirect
234. C32×Q8C22×D3semidirect
244. C32×D4C22×D3semidirect
245. C32×D4C22×D3semidirect
279. C3×D12C22×D3semidirect
288. C3×Dic6C22×D3semidirect
294. C3⋊(C3⋊C8)C22×D3semidirect
304. C32×D3AGL(1,ℤ/8)semidirect
313. C3×#41D32semidirect
314. C3×#41C2×C3⋊D3semidirect
322. #239C2×C3⋊D3semidirect
323. D3×Q8C2×C3⋊D3semidirect
325. #237C2×C3⋊D3semidirect
331. D3×D4C2×C3⋊D3semidirect
333. #235C2×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
495. D12C22×C3⋊D3semidirect
504. Dic6C22×C3⋊D3semidirect
529. C3×D3#949semidirect
536. #41D3×C3⋊D3semidirect
607. C32D3×AGL(1,ℤ/8)semidirect
608. C32C2×#949semidirect
618. Q8C2×D3×C3⋊D3semidirect
631. D4C2×D3×C3⋊D3semidirect
664. D3#64158direct (N × H)
685. C3D3×#949semidirect
686. C3C2×#64158semidirect

Maximal subgroups

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

subgroupindex
C32×D3×#412
C2×D3×C4⋊(C3⋊D3)2
#117239902
C3×#641582
#117235682
D3×#37552
#117235442
D3×#37532
#117233672
#117233652
D3×#37482
C2×#641583
D3×#9493