Finite Group Databasebeta

← #13176700

Subgroups — #13176700

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724578C211yesmaximal, characteristic, complemented
2C2×#89026C211yesmaximal, characteristic, complemented
3M16×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#64117C211yesmaximal, characteristic, complemented
5C32×#908C211yesmaximal, characteristic, complemented
6#11723365C211yesmaximal, characteristic, complemented
7#11723364C211yesmaximal, characteristic, complemented
8#11723324C212yesmaximal, complemented
9#11723323C212yesmaximal, complemented
10#11723322C212yesmaximal, complemented
11#11723321C212yesmaximal, complemented
12C3⋊D3×AGL(1,ℤ/8)—31nomaximal
13#10594716—34nomaximal
14C22×D3×C3⋊D3—21no—
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C3×#3828C2211yescharacteristic, complemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C32×#235C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic, complemented
20#89039—21no—
21C2×#6290—21no—
22#89029—21no—
23#89026—21no—
24#89026—21no—
25#89026C2212yes—
26#89026C2212yescomplemented
27#89026C2211yescharacteristic, complemented
28C4×D3×C3⋊D3—21no—
29#89020—21no—
30#89019C2211yescharacteristic, complemented
31#89017C2211yescharacteristic, complemented
32#89015C2211yescharacteristic, complemented
33C33×M16C2211yescharacteristic, complemented
34#88855C2211yescharacteristic, complemented
35#88850C2212yescomplemented
36C8×C3⋊(C3⋊D3)C2212yescomplemented
37C3×#3745C2212yescomplemented
38C3×#3744C2212yescomplemented
39C32×D24C2212yescomplemented
40C32×#204C2212yescomplemented
41#88793C2212yescomplemented
42#88792C2212yescomplemented
43#88789C2212yescomplemented
44#88789C2212yescomplemented
45#41×C3⋊D3—31no—
46C2×D4×C3⋊D3—31no—
47#64306—34no—
48C2×#3802—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#64117D311yescharacteristic, complemented
57M16×C3⋊D3—31no—
58M16×C3⋊D3—34no—
59M16×C3⋊D3—64no—
60C3×#908—34no—
61C3×#908D314yescomplemented
62#63823—34no—
63#63823—34no—
64#63798—38no—
65#63798—38no—
66#63797—38no—
67#63796—38no—
68C22×C3⋊(C3⋊D3)D411yescharacteristic
69C22×C3×C3⋊D3—21no—
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
76C2×C3⋊(C3⋊Dic3)D411yescharacteristic
77C4×C3⋊(C3⋊D3)D411yescharacteristic
78C4×C3⋊(C3⋊D3)D411yescharacteristic
79C4×C3⋊(C3⋊D3)C2311yescharacteristic
80C4×C3⋊(C3⋊D3)C2311yescharacteristic
81C3×#638—21no—
82C3×C4⋊(C3⋊D3)—21no—
83C3×C4⋊(C3⋊D3)C2312yes—
84C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
85C3×C4×C3⋊D3—21no—
86C3×#634C2311yescharacteristic, complemented
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#6290—21no—
97#6290—22no—
98#6290—22no—
99#6289—21no—
100Dic3×C3⋊D3—21no—
101D3×C3⋊Dic3—21no—
102C33×C8C2312yescomplemented
103C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
104D3×AGL(1,ℤ/8)—94no—
105D3×AGL(1,ℤ/8)—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—61no—
122#3828C2×D311yescharacteristic, complemented
123C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—34no—
126C2×C4×C3⋊D3—61no—
127C2×C4×C3⋊D3—64no—
128C3×#235—34no—
129C3×#235C2×D314yescomplemented
130C2×C3×D12—34no—
131C2×C3×D12C2×D314yescomplemented
132#3811—64no—
133C2×#625—64no—
134#3805—64no—
135#3802—38no—
136#3802—38no—
137#3802—34no—
138#3802—64no—
139#3802—64no—
140C4×D32—64no—
141#3798—64no—
142#3797—34no—
143#3796—34no—
144#3796—34no—
145C32×SD16—32no—
146C32×D8—32no—
147C32×M16—24no—
148C32×M16C2×D314yescomplemented
149C32×M16C2×D311yescharacteristic, complemented
150#3755—32no—
151#3754—32no—
152#3753—32no—
153#3753—32no—
154#3748—31no—
155#3748—34no—
156#3748—64no—
157#3745C2×D312yescomplemented
158#3744C2×D312yescomplemented
159#3743—32no—
160#3743—38no—
161#3743—68no—
162C8×C3⋊D3—32no—
163C8×C3⋊D3—38no—
164C8×C3⋊D3—68no—
165C3×D24—38no—
166C3×D24C2×D318yescomplemented
167C3×#204—38no—
168C3×#204C2×D318yescomplemented
169#3715—38no—
170#3715—38no—
171#3713—38no—
172#3713—38no—
173C22×C33C2×D411yescharacteristic
174C2×C3⋊(C3⋊D3)—22no—
175C2×C3⋊(C3⋊D3)C2×D411yescharacteristic
176C2×C3⋊(C3⋊D3)C2×D411yescharacteristic
177C2×C3×C3⋊D3—21no—
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—42no—
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)C2×D411yescharacteristic
189C3⋊(C3⋊Dic3)C2×D411yescharacteristic
190C3×C3⋊Dic3—21no—
191C32×Dic3—21no—
192D3×#41—94no—
193D3×#41—91no—
194C2×D3×D4—94no—
195C2×D3×D4—91no—
196C3×AGL(1,ℤ/8)—34no—
197C3×AGL(1,ℤ/8)—91no—
198#949—94no—
199#949—91no—
200#932—94no—
201#932—91no—
202#914—98no—
203#914—92no—
204D3×SD16—98no—
205D3×SD16—92no—
206#911—98no—
207#911—92no—
208D3×D8—98no—
209D3×D8—92no—
210#908—34no—
211#908C3⋊D311yescharacteristic, complemented
212D3×M16—94no—
213D3×M16—91no—
214D3×M16—184no—
215C23×C32—61no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—31no—
218C22×C3⋊D3—34no—
219C22×C3⋊D3—64no—
220C22×C3⋊D3—62no—
221C22×C3⋊D3—62no—
222C22×C3⋊D3—61no—
223C22×C3⋊D3—124no—
224C22×C3×D3—24no—
225C22×C3×D3—64no—
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—21no—
240#638—61no—
241#638—61no—
242#638—62no—
243#638—62no—
244C2×C3⋊Dic3—31no—
245C2×C3⋊Dic3—34no—
246C2×C3⋊Dic3—64no—
247C2×C3⋊Dic3—61no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—61no—
250C4⋊(C3⋊D3)C22×D312yes—
251C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
252C4×C3⋊D3—21no—
253C4×C3⋊D3—31no—
254C4×C3⋊D3—31no—
255C4×C3⋊D3—31no—
256C4×C3⋊D3—31no—
257C4×C3⋊D3—34no—
258C4×C3⋊D3—34no—
259C4×C3⋊D3—34no—
260C4×C3⋊D3—34no—
261C4×C3⋊D3—64no—
262C4×C3⋊D3—64no—
263C4×C3⋊D3—64no—
264C4×C3⋊D3—64no—
265C4×C3⋊D3—61no—
266C4×C3⋊D3—61no—
267#634—61no—
268#634C22×D311yescharacteristic, complemented
269C3×#67—24no—
270C3×#67—64no—
271C3×D12—24no—
272C3×D12—34no—
273C3×D12—38no—
274C3×D12—64no—
275C3×D12C22×D318yes—
276C3×D12C22×D314yescomplemented
277C3×C4×D3—24no—
278C3×C4×D3—64no—
279C3×Dic6—34no—
280C3×Dic6C22×D314yescomplemented
281#627—64no—
282#626—64no—
283#626—64no—
284#625—64no—
285#625—68no—
286#625—68no—
287#624—64no—
288D3×Dic3—64no—
289D3×Dic3—64no—
290C32×C8—28no—
291C32×C8C22×D318yescomplemented
292C32×C8C22×D312yescomplemented
293C3⋊(C3⋊C8)—32no—
294C3⋊(C3⋊C8)—38no—
295C3⋊(C3⋊C8)—68no—
296C2×AGL(1,ℤ/8)—271noSylow
297C2×C33—21no—
298C2×C33C22×D411yescharacteristic
299C3⋊(C3⋊D3)—21no—
300C3⋊(C3⋊D3)AGL(1,ℤ/8)12yescomplemented
301C3×C3⋊D3—42no—
302C3×C3⋊D3—41no—
303C32×D3—42no—
304C32×D3—41no—
305C23×D3—181no—
306C23×D3—184no—
307C3×#41—34no—
308C3×#41—91no—
309C2×C3×D4—34no—
310C2×C3×D4—91no—
311C2×#67—181no—
312C2×#67—184no—
313#239—94no—
314#239—91no—
315D3×Q8—94no—
316D3×Q8—91no—
317#237—94no—
318#237—91no—
319#237—181no—
320#237—184no—
321D3×D4—94no—
322D3×D4—98no—
323D3×D4—98no—
324D3×D4—92no—
325D3×D4—92no—
326D3×D4—91no—
327D3×D4—181no—
328D3×D4—181no—
329D3×D4—184no—
330D3×D4—184no—
331D3×D4—181no—
332D3×D4—184no—
333#235—34no—
334#235—181no—
335#235—184no—
336#235C2×C3⋊D311yescharacteristic, complemented
337C2×D12—34no—
338C2×D12C2×C3⋊D311yescharacteristic, complemented
339C2×C4×D3—94no—
340C2×C4×D3—91no—
341C2×C4×D3—184no—
342C2×C4×D3—181no—
343C2×C4×D3—184no—
344C3×SD16—38no—
345C3×SD16—92no—
346C3×D8—38no—
347C3×D8—92no—
348C3×M16—24no—
349C3×M16D3214yescomplemented
350C3×M16C2×C3⋊D311yescharacteristic, complemented
351#215—98no—
352#215—92no—
353#214—98no—
354#214—92no—
355#213—98no—
356#213—98no—
357#213—92no—
358#213—92no—
359#208—94no—
360#208—91no—
361#208—184no—
362D24—38no—
363D24C2×C3⋊D312yescomplemented
364#204—38no—
365#204C2×C3⋊D312yescomplemented
366ΓL(1,𝔽25)—98no—
367ΓL(1,𝔽25)—92no—
368ΓL(1,𝔽25)—188no—
369D3×C8—98no—
370D3×C8—92no—
371D3×C8—188no—
372C22×C32—24no—
373C22×C32—61no—
374C22×C32—62no—
375C22×C32—122no—
376C22×C32D3×D414yes—
377C22×C32D3×D411yescharacteristic
378C2×C3⋊D3—21no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—31no—
381C2×C3⋊D3—31no—
382C2×C3⋊D3—34no—
383C2×C3⋊D3—34no—
384C2×C3⋊D3—42no—
385C2×C3⋊D3—64no—
386C2×C3⋊D3—64no—
387C2×C3⋊D3—62no—
388C2×C3⋊D3—68no—
389C2×C3⋊D3—128no—
390C2×C3⋊D3—122no—
391C2×C3⋊D3—124no—
392C2×C3⋊D3—124no—
393C2×C3×D3—24no—
394C2×C3×D3—28no—
395C2×C3×D3—48no—
396C2×C3×D3—64no—
397C2×C3×D3—68no—
398C2×C3×D3—128no—
399D32—128no—
400D32—1216no—
401D32—1216no—
402C32×C4—24no—
403C32×C4—24no—
404C32×C4—61no—
405C32×C4D3×D414yes—
406C32×C4D3×D411yescharacteristic
407C32×C4C23×D314yes—
408C32×C4C23×D311yescharacteristic
409C3⋊Dic3—21no—
410C3⋊Dic3—31no—
411C3⋊Dic3—31no—
412C3⋊Dic3—34no—
413C3⋊Dic3—34no—
414C3⋊Dic3—64no—
415C3⋊Dic3—64no—
416C3×Dic3—24no—
417C3×Dic3—64no—
418C2×#41—271no—
419C22×D4—271no—
420AGL(1,ℤ/8)—31no—
421AGL(1,ℤ/8)—91no—
422AGL(1,ℤ/8)—272no—
423AGL(1,ℤ/8)—272no—
424AGL(1,ℤ/8)—271no—
425AGL(1,ℤ/8)—271no—
426C2×SD16—272no—
427C2×D8—272no—
428C2×M16—271no—
429C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
430C23×C3—64no—
431C23×C3—181no—
432C22×D3—21no—
433C22×D3—64no—
434C22×D3—94no—
435C22×D3—91no—
436C22×D3—184no—
437C22×D3—181no—
438C22×D3—182no—
439C22×D3—182no—
440C22×D3—184no—
441C22×D3—188no—
442C22×D3—188no—
443C22×D3—364no—
444C22×D3—3616no—
445C3×Q8—34no—
446C3×Q8—91no—
447C3×D4—38no—
448C3×D4—34no—
449C3×D4—64no—
450C3×D4—64no—
451C3×D4—91no—
452C3×D4—92no—
453C3×D4—181no—
454C3×D4—181no—
455C2×C3×C4—24no—
456C2×C3×C4—64no—
457C2×C3×C4—181no—
458C2×C3×C4C2×D3214yes—
459C2×C3×C4C22×C3⋊D311yescharacteristic
460#67—21no—
461#67—64no—
462#67—181no—
463#67—184no—
464#67—181no—
465#67—182no—
466#67—182no—
467#67—184no—
468#67—188no—
469#67—188no—
470C2×Dic3—94no—
471C2×Dic3—91no—
472C2×Dic3—184no—
473C2×Dic3—181no—
474C2×Dic3—184no—
475D12—21no—
476D12—38no—
477D12—34no—
478D12—64no—
479D12—184no—
480D12—181no—
481D12C22×C3⋊D312yes—
482D12C22×C3⋊D311yescharacteristic, complemented
483C4×D3—21no—
484C4×D3—64no—
485C4×D3—94no—
486C4×D3—94no—
487C4×D3—91no—
488C4×D3—91no—
489C4×D3—94no—
490C4×D3—94no—
491C4×D3—91no—
492C4×D3—91no—
493C4×D3—184no—
494C4×D3—184no—
495C4×D3—184no—
496C4×D3—184no—
497C4×D3—181no—
498C4×D3—184no—
499C4×D3—184no—
500C4×D3—181no—
501Dic6—34no—
502Dic6—181no—
503Dic6—184no—
504Dic6C22×C3⋊D311yescharacteristic, complemented
505C3×C8—28no—
506C3×C8C2×D3218yescomplemented
507C3×C8C22×C3⋊D312yescomplemented
508C3⋊C8—98no—
509C3⋊C8—92no—
510C3⋊C8—188no—
511C2×C32—21no—
512C2×C32—24no—
513C2×C32—24no—
514C2×C32—44no—
515C2×C32—122no—
516C2×C32—121no—
517C2×C32C2×D3×D414yes—
518C2×C32C2×D3×D411yescharacteristic
519C3⋊D3—32no—
520C3⋊D3—38no—
521C3⋊D3—42no—
522C3⋊D3—41no—
523C3⋊D3—68no—
524C3⋊D3—61no—
525C3⋊D3—64no—
526C3⋊D3—124no—
527C3×D3—48no—
528C3×D3—44no—
529C3×D3—128no—
530C3×D3—124no—
531C24—541no—
532#41—31no—
533#41—91no—
534#41—271no—
535#41—271no—
536#41—541no—
537#41—541no—
538C2×Q8—271no—
539C2×D4—31no—
540C2×D4—91no—
541C2×D4—271no—
542C2×D4—272no—
543C2×D4—272no—
544C2×D4—541no—
545C2×D4—541no—
546C2×D4—541no—
547C2×D4—541no—
548C22×C4—271no—
549C22×C4—541no—
550SD16—32no—
551SD16—92no—
552SD16—272no—
553SD16—272no—
554D8—32no—
555D8—92no—
556D8—272no—
557D8—272no—
558M16—271no—
559M16—272no—
560M16D3×C3⋊D311yescharacteristic, complemented
561C2×C8—272no—
562C22×C3—24no—
563C22×C3—64no—
564C22×C3—68no—
565C22×C3—128no—
566C22×C3—181no—
567C22×C3—182no—
568C22×C3—362no—
569C22×C3#380214yes—
570C22×C3D4×C3⋊D311yescharacteristic
571C2×D3—21no—
572C2×D3—22no—
573C2×D3—42no—
574C2×D3—64no—
575C2×D3—68no—
576C2×D3—94no—
577C2×D3—91no—
578C2×D3—94no—
579C2×D3—91no—
580C2×D3—128no—
581C2×D3—184no—
582C2×D3—184no—
583C2×D3—182no—
584C2×D3—188no—
585C2×D3—368no—
586C2×D3—364no—
587C2×D3—362no—
588C2×D3—364no—
589C2×D3—3616no—
590C2×D3—368no—
591C2×D3—3616no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—64no—
595C3×C4—181no—
596C3×C4#380214yes—
597C3×C4D4×C3⋊D311yescharacteristic
598C3×C4C22×D3214yes—
599C3×C4C23×C3⋊D311yescharacteristic
600Dic3—21no—
601Dic3—64no—
602Dic3—94no—
603Dic3—94no—
604Dic3—91no—
605Dic3—91no—
606Dic3—184no—
607Dic3—184no—
608C32—24no—
609C32D3×AGL(1,ℤ/8)14yescomplemented
610C32D3×AGL(1,ℤ/8)11yescharacteristic, complemented
611C23—61no—
612C23—181no—
613C23—271no—
614C23—541no—
615C23—542no—
616C23—542no—
617C23—1084no—
618Q8—31no—
619Q8—91no—
620Q8—541no—
621D4—31no—
622D4—32no—
623D4—61no—
624D4—61no—
625D4—91no—
626D4—92no—
627D4—181no—
628D4—181no—
629D4—541no—
630D4—541no—
631D4—542no—
632D4—542no—
633D4—541no—
634C2×C4—61no—
635C2×C4—181no—
636C2×C4—271no—
637C2×C4—271no—
638C2×C4—271no—
639C2×C4—271no—
640C2×C4—271no—
641C2×C4—541no—
642C2×C4—541no—
643C2×C4—541no—
644C2×C4C2×D3×C3⋊D311yescharacteristic
645C8—272no—
646C8C2×D3×C3⋊D312yescomplemented
647C2×C3—21no—
648C2×C3—24no—
649C2×C3—24no—
650C2×C3—44no—
651C2×C3—128no—
652C2×C3—124no—
653C2×C3—362no—
654C2×C3—361no—
655C2×C3C2×#380214yes—
656C2×C3C2×D4×C3⋊D311yescharacteristic
657D3—42no—
658D3—41no—
659D3—92no—
660D3—98no—
661D3—128no—
662D3—124no—
663D3—188no—
664D3—181no—
665D3—184no—
666D3—364no—
667C22—61no—
668C22—62no—
669C22—122no—
670C22—181no—
671C22—182no—
672C22—271no—
673C22—271no—
674C22—362no—
675C22—542no—
676C22—1084no—
677C22—1082no—
678C22—1084no—
679C22#8902611yescharacteristic
680C4—61no—
681C4—181no—
682C4—271no—
683C4—271no—
684C4#8902611yescharacteristic
685C4C22×D3×C3⋊D311yescharacteristic
686C3—24no—
687C3#1059471614yescomplemented
688C3C3⋊D3×AGL(1,ℤ/8)11yescharacteristic, complemented
689C2—21no—
690C2—122no—
691C2—121no—
692C2—272no—
693C2—362no—
694C2—361no—
695C2—541no—
696C2C2×#8902611yescharacteristic
subgroupG/H
centerC2C2×#89026
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. #11724578C2semidirect
2. C2×#89026C2semidirect
3. M16×C3⋊(C3⋊D3)C2semidirect
4. C3×#64117C2semidirect
5. C32×#908C2semidirect
6. #11723365C2semidirect
7. #11723364C2semidirect
8. #11723324C2semidirect
9. #11723323C2semidirect
10. #11723322C2semidirect
11. #11723321C2semidirect
16. C3×#3828C22semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C32×#235C22semidirect
19. C2×C32×D12C22semidirect
26. #89026C22semidirect
27. #89026C22semidirect
30. #89019C22semidirect
31. #89017C22semidirect
32. #89015C22semidirect
33. C33×M16C22semidirect
34. #88855C22semidirect
35. #88850C22semidirect
36. C8×C3⋊(C3⋊D3)C22semidirect
37. C3×#3745C22semidirect
38. C3×#3744C22semidirect
39. C32×D24C22semidirect
40. C32×#204C22semidirect
41. #88793C22semidirect
42. #88792C22semidirect
43. #88789C22semidirect
44. #88789C22semidirect
56. #64117D3semidirect
61. C3×#908D3semidirect
84. C3×C4⋊(C3⋊D3)C23semidirect
86. C3×#634C23semidirect
90. C32×D12C23semidirect
92. C32×Dic6C23semidirect
102. C33×C8C23semidirect
103. C3⋊(C3⋊(C3⋊C8))C23semidirect
122. #3828C2×D3semidirect
123. C2×C4⋊(C3⋊D3)C2×D3semidirect
129. C3×#235C2×D3semidirect
131. C2×C3×D12C2×D3semidirect
148. C32×M16C2×D3semidirect
149. C32×M16C2×D3semidirect
157. #3745C2×D3semidirect
158. #3744C2×D3semidirect
166. C3×D24C2×D3semidirect
168. C3×#204C2×D3semidirect
211. #908C3⋊D3semidirect
251. C4⋊(C3⋊D3)C22×D3semidirect
268. #634C22×D3semidirect
276. C3×D12C22×D3semidirect
280. C3×Dic6C22×D3semidirect
291. C32×C8C22×D3semidirect
292. C32×C8C22×D3semidirect
300. C3⋊(C3⋊D3)AGL(1,ℤ/8)semidirect
336. #235C2×C3⋊D3semidirect
338. C2×D12C2×C3⋊D3semidirect
349. C3×M16D32semidirect
350. C3×M16C2×C3⋊D3semidirect
363. D24C2×C3⋊D3semidirect
365. #204C2×C3⋊D3semidirect
429. C33C2×AGL(1,ℤ/8)semidirect
482. D12C22×C3⋊D3semidirect
504. Dic6C22×C3⋊D3semidirect
506. C3×C8C2×D32semidirect
507. C3×C8C22×C3⋊D3semidirect
560. M16D3×C3⋊D3semidirect
609. C32D3×AGL(1,ℤ/8)semidirect
610. C32D3×AGL(1,ℤ/8)semidirect
646. C8C2×D3×C3⋊D3semidirect
687. C3#10594716semidirect
688. 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
#117245782
C2×#890262
M16×C3⋊(C3⋊D3)2
C3×#641172
C32×#9082
#117233652
#117233642
#117233242
#117233232
#117233222
#117233212
C3⋊D3×AGL(1,ℤ/8)3
#105947163