Finite Group Databasebeta

← #11860317

Subgroups — #11860317

Order 1152.

1251 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5#10591572C212yesmaximal, complemented
6#10591571C212yesmaximal, complemented
7#10591436C212yesmaximal, complemented
8#10591435C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10#10591086C211yesmaximal, characteristic, complemented
11#10591060C211yesmaximal, characteristic, complemented
12Dic3×AGL(1,ℤ/8)—31nomaximal
13#78866—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17Q8×C3⋊Dic3C2211yescharacteristic, complemented
18Q8×C3⋊Dic3C2211yescharacteristic, complemented
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3—21no—
21D4×C3⋊Dic3C2211yescharacteristic, complemented
22D4×C3⋊Dic3C2211yescharacteristic, complemented
23#64135—21no—
24#64135C2211yescharacteristic
25C2×C4×C3⋊Dic3—21no—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C3×#949C418yescomplemented
28C2×C3×#215C2212yes—
29C2×C3×#213C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C2×C3×#208C2211yescharacteristic
33C2×(C2×D3)⋊Dic3—21no—
34#63898—21no—
35#63898—21no—
36#63898C2212yes—
37#63898C2212yes—
38C3×#835C2212yescomplemented
39C3×#832C2212yescomplemented
40#63575C2212yescomplemented
41#63573C2212yescomplemented
42#63563C2212yes—
43#63563C2212yes—
44#63555C2212yescomplemented
45#63553C2212yescomplemented
46C2×C3×AGL(1,ℤ/8)—31no—
47Dic3×#41—31no—
48Dic3×#41—31no—
49Dic3×#41—61no—
50C2×#949D311yescharacteristic
51C2×D4×Dic3—31no—
52C2×#893—31no—
53C3×#417—31no—
54#5232D311yescharacteristic, complemented
55#5215—31no—
56#5164—32no—
57Dic3×SD16—32no—
58#5152—32no—
59Dic3×D8—32no—
60#5131—31no—
61#5121—31no—
62Dic3×M16—31no—
63Dic3×M16—31no—
64#4964—31no—
65#4817—32no—
66#4788—32no—
67#4785—32no—
68#4756—32no—
69C23×C3×D3—21no—
70C32×#41—22no—
71C32×#41C2×C414yescomplemented
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4—21no—
74C2×C32×D4C2311yescharacteristic
75C22×C32×C4—21no—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3—21no—
79C22×C3⋊Dic3D411yescharacteristic
80C22×C3⋊Dic3D411yescharacteristic
81C22×C3×Dic3—21no—
82C2×C3×D12—21no—
83C2×C3×D12—22no—
84C2×C3×D12C2×C414yescomplemented
85C2×C3×D12C2312yes—
86C2×D3×Dic3—22no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—44no—
89#3757—21no—
90#3757—21no—
91#3757—21no—
92C4⋊(C3⋊Dic3)—21no—
93C4⋊(C3⋊Dic3)—21no—
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95C4⋊(C3⋊Dic3)C2311yescharacteristic
96C4×C3⋊Dic3—21no—
97C4×C3⋊Dic3—21no—
98C4×C3⋊Dic3—21no—
99C4×C3⋊Dic3D411yescharacteristic
100C4×C3⋊Dic3D411yescharacteristic
101C4×C3⋊Dic3C2311yescharacteristic
102C4×C3⋊Dic3C2311yescharacteristic
103C3×#215C2×C418yescomplemented
104C3×#213C2×C418yescomplemented
105C3×C4⋊Dic3—21no—
106C3×C4⋊Dic3C2312yes—
107C3×#208—22no—
108C3×#208C2×C414yescomplemented
109C2×C3×C3⋊C8C2312yes—
110C2×C3×C3⋊C8C2312yes—
111(C2×D3)⋊Dic3—22no—
112(C2×D3)⋊Dic3—22no—
113C4×AGL(1,ℤ/8)—91noSylow
114C2×C3×#41—21no—
115C2×C3×#41C2×D311yescharacteristic
116C2×C3×#41C2×D311yescharacteristic
117C22×C3×D4—31no—
118C23×Dic3—61no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—61no—
121C3×AGL(1,ℤ/8)—38no—
122C2×C3×SD16—32no—
123C2×C3×D8—32no—
124C2×C3×M16—31no—
125C2×C3×M16—31no—
126C2×C3×C4⋊C4—31no—
127C2×#217—61no—
128#949Dic318yescomplemented
129Q8×Dic3—31no—
130Q8×Dic3—31no—
131Q8×Dic3—31no—
132Q8×Dic3—31no—
133Q8×Dic3—61no—
134Q8×Dic3—61no—
135C2×#215C2×D312yes—
136D4×Dic3—31no—
137D4×Dic3—31no—
138D4×Dic3—31no—
139D4×Dic3—31no—
140D4×Dic3—32no—
141D4×Dic3—32no—
142D4×Dic3—61no—
143D4×Dic3—61no—
144D4×Dic3—61no—
145D4×Dic3—61no—
146D4×Dic3—61no—
147D4×Dic3—61no—
148D4×Dic3—61no—
149D4×Dic3—61no—
150D4×Dic3—62no—
151D4×Dic3—62no—
152C2×#213C2×D312yes—
153C2×(C2×D3)⋊C4—61no—
154#926—31no—
155#926—31no—
156#926—61no—
157#926—61no—
158#926—61no—
159#926—62no—
160C2×C4⋊Dic3C2×D311yescharacteristic
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—61no—
164C2×C4×Dic3—61no—
165C2×C4×Dic3—61no—
166C2×C4×Dic3—62no—
167C2×#208C2×D311yescharacteristic
168C2×#208C2×D311yescharacteristic
169#893—32no—
170#893—32no—
171#893—61no—
172#893—61no—
173C3×#103—32no—
174C3×#102—32no—
175#835C2×D312yescomplemented
176#832—32no—
177#832—32no—
178#832C2×D312yescomplemented
179#821—32no—
180#821—32no—
181#818—32no—
182#817—32no—
183#815—32no—
184#815—32no—
185C8×Dic3—32no—
186C8×Dic3—32no—
187#808—32no—
188#807—32no—
189C23×C32—21no—
190C23×C32C2×D411yescharacteristic
191C22×C3×D3—24no—
192C22×C3×D3—22no—
193C22×C3×D3—42no—
194C22×C3×D3—42no—
195C32×Q8—21no—
196C32×Q8C22×C412yescomplemented
197C32×D4—24no—
198C32×D4—21no—
199C32×D4C22×C412yescomplemented
200C2×C32×C4—21no—
201C2×C32×C4—24no—
202C2×C32×C4C22×C412yes—
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4#4112yes—
205C2×C32×C4C2411yescharacteristic
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—41no—
210C2×C3⋊Dic3—42no—
211C2×C3⋊Dic3—42no—
212C2×C3⋊Dic3C2×D411yescharacteristic
213C2×C3⋊Dic3C2×D411yescharacteristic
214C2×C3⋊Dic3C2×D411yescharacteristic
215C2×C3⋊Dic3C2×D411yescharacteristic
216C2×C3×Dic3—22no—
217C2×C3×Dic3—42no—
218C3×D12—24no—
219C3×D12—22no—
220C3×D12C22×C414yes—
221D3×Dic3—44no—
222D3×Dic3—44no—
223C3×C3⋊C8—22no—
224C3×C3⋊C8C22×C414yescomplemented
225C2×AGL(1,ℤ/8)—31no—
226C4×#41—91no—
227C2×C4×D4—91no—
228#442—92no—
229#440—92no—
230C4×SD16—92no—
231C4×D8—92no—
232#428—91no—
233#418—91no—
234#417—31no—
235C4×M16—91no—
236C24×C3—61no—
237C23×D3—21no—
238C3×#41—24no—
239C3×#41—22no—
240C3×#41—22no—
241C3×#41—24no—
242C3×#41C4×D314yescomplemented
243C3×#41C2×Dic314yescomplemented
244C2×C3×Q8—21no—
245C2×C3×Q8C22×D311yescharacteristic
246C2×C3×Q8C22×D311yescharacteristic
247C2×C3×D4—22no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—34no—
252C2×C3×D4—32no—
253C2×C3×D4—61no—
254C2×C3×D4—62no—
255C2×C3×D4C22×D311yescharacteristic
256C2×C3×D4C22×D311yescharacteristic
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—61no—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C22×Dic3—21no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—61no—
270C22×Dic3—61no—
271C22×Dic3—62no—
272C22×Dic3—62no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3—61no—
276C22×Dic3—61no—
277C22×Dic3—62no—
278C22×Dic3—62no—
279C22×Dic3—124no—
280C2×D12—21no—
281C2×D12—22no—
282C2×D12C2×Dic314yescomplemented
283C2×D12C22×D312yes—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—124no—
287C3×SD16—38no—
288C3×D8—38no—
289C3×M16—34no—
290C3×M16—62no—
291C2×C3×C8—32no—
292C2×C3×C8—32no—
293C3×C4⋊C4—32no—
294C3×C4⋊C4—61no—
295#217—62no—
296#217—62no—
297#217—61no—
298#217—61no—
299#217—61no—
300#217—61no—
301#217—62no—
302#217—62no—
303#217—62no—
304#217—61no—
305#217—61no—
306#215C2×Dic318yescomplemented
307#213C2×Dic318yescomplemented
308(C2×D3)⋊C4—62no—
309(C2×D3)⋊C4—62no—
310C4⋊Dic3—21no—
311C4⋊Dic3—31no—
312C4⋊Dic3—31no—
313C4⋊Dic3—31no—
314C4⋊Dic3—31no—
315C4⋊Dic3—61no—
316C4⋊Dic3—61no—
317C4⋊Dic3—61no—
318C4⋊Dic3—61no—
319C4⋊Dic3—61no—
320C4⋊Dic3—61no—
321C4⋊Dic3—62no—
322C4⋊Dic3—62no—
323C4⋊Dic3C22×D312yes—
324C4×Dic3—31no—
325C4×Dic3—31no—
326C4×Dic3—31no—
327C4×Dic3—31no—
328C4×Dic3—31no—
329C4×Dic3—31no—
330C4×Dic3—31no—
331C4×Dic3—31no—
332C4×Dic3—61no—
333C4×Dic3—61no—
334C4×Dic3—61no—
335C4×Dic3—61no—
336C4×Dic3—61no—
337C4×Dic3—61no—
338C4×Dic3—61no—
339C4×Dic3—61no—
340C4×Dic3—62no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—61no—
344C4×Dic3—61no—
345#208—22no—
346#208C2×Dic314yescomplemented
347C2×C3⋊C8C22×D312yes—
348C2×C3⋊C8C22×D312yes—
349C22×C32—22no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32C4×D412yes—
355C22×C32C22×D411yescharacteristic
356C2×C3×D3—24no—
357C2×C3×D3—48no—
358C2×C3×D3—42no—
359C2×C3×D3—42no—
360C32×C4—22no—
361C32×C4C4×D412yes—
362C32×C4C23×C411yescharacteristic
363C32×C4C2×#4111yescharacteristic
364C3⋊Dic3—21no—
365C3⋊Dic3—21no—
366C3⋊Dic3—21no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
370C3×Dic3—42no—
371C2×#41D3211yescharacteristic
372C22×D4—31no—
373C23×C4—181no—
374AGL(1,ℤ/8)—38no—
375C2×SD16—32no—
376C2×D8—32no—
377C2×M16—31no—
378C2×M16—31no—
379C4×Q8—91no—
380C4×Q8—91no—
381C4×D4—92no—
382C4×D4—92no—
383C4×D4—91no—
384C4×D4—91no—
385C4×D4—181no—
386C4×D4—181no—
387C4×D4—181no—
388C4×D4—181no—
389#117—91no—
390#117—181no—
391C2×C4⋊C4—31no—
392C2×C22⋊C4—181no—
393C2×C42—91no—
394C2×C42—181no—
395#107—92no—
396#106—92no—
397#103—32no—
398#102—32no—
399#102—92no—
400#102—92no—
401#97—92no—
402C4×C8—92no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—64no—
408C23×C3—62no—
409C23×C3—122no—
410C23×C3—122no—
411C23×C3D3×D411yescharacteristic
412C23×C3D3×D411yescharacteristic
413C22×D3—24no—
414C22×D3—22no—
415C22×D3—42no—
416C22×D3—42no—
417C3×Q8—22no—
418C3×Q8—21no—
419C3×Q8—21no—
420C3×Q8—22no—
421C3×Q8C2×C4×D312yescomplemented
422C3×Q8C22×Dic312yescomplemented
423C3×D4—28no—
424C3×D4—22no—
425C3×D4—24no—
426C3×D4—24no—
427C3×D4—21no—
428C3×D4—21no—
429C3×D4—22no—
430C3×D4—34no—
431C3×D4—64no—
432C3×D4—62no—
433C3×D4C2×C4×D312yescomplemented
434C3×D4C22×Dic312yescomplemented
435C2×C3×C4—22no—
436C2×C3×C4—28no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—62no—
446C2×C3×C4—122no—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4D3×D411yescharacteristic
449C2×C3×C4D3×D411yescharacteristic
450C2×C3×C4#23712yes—
451C2×C3×C4#23712yes—
452C2×C3×C4C22×Dic312yes—
453C2×C3×C4C23×D311yescharacteristic
454C2×C3×C4C23×D311yescharacteristic
455C2×Dic3—22no—
456C2×Dic3—31no—
457C2×Dic3—31no—
458C2×Dic3—31no—
459C2×Dic3—31no—
460C2×Dic3—31no—
461C2×Dic3—31no—
462C2×Dic3—31no—
463C2×Dic3—31no—
464C2×Dic3—42no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—122no—
478C2×Dic3—124no—
479C2×Dic3—122no—
480C2×Dic3—122no—
481C2×Dic3—124no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—124no—
485C2×Dic3—122no—
486C2×Dic3—124no—
487C2×Dic3—122no—
488C2×Dic3—122no—
489D12—24no—
490D12—22no—
491D12C22×Dic314yes—
492C4×D3—124no—
493C4×D3—124no—
494C3×C8—34no—
495C3×C8—62no—
496C3⋊C8—22no—
497C3⋊C8C22×Dic314yescomplemented
498C2×C32—22no—
499C2×C32—42no—
500C2×C32C2×C4×D411yescharacteristic
501C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
502C2×C32#57511yescharacteristic
503C3×D3—44no—
504C24—61no—
505#41—22no—
506#41D3×Dic314yescomplemented
507C2×Q8C2×D3211yescharacteristic
508C2×D4—21no—
509C2×D4—32no—
510C2×D4—34no—
511C2×D4—62no—
512C2×D4—61no—
513C2×D4C2×D3211yescharacteristic
514C22×C4—21no—
515C22×C4—61no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4—182no—
519C22×C4—182no—
520C22×C4—181no—
521C22×C4—181no—
522C22×C4—364no—
523C22×C4C2×D3211yescharacteristic
524SD16—38no—
525D8—38no—
526M16—34no—
527M16—62no—
528C2×C8—32no—
529C2×C8—32no—
530C4⋊C4—32no—
531C4⋊C4—61no—
532C4⋊C4—91no—
533C4⋊C4—91no—
534C4⋊C4—181no—
535C4⋊C4—181no—
536C22⋊C4—182no—
537C22⋊C4—182no—
538C22⋊C4—181no—
539C22⋊C4—181no—
540C22⋊C4—181no—
541C42—91no—
542C42—91no—
543C42—91no—
544C42—91no—
545C42—181no—
546C42—181no—
547C42—181no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—24no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—21no—
556C22×C3—22no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—64no—
566C22×C3—128no—
567C22×C3—122no—
568C22×C3—122no—
569C22×C3#67⋊C412yes—
570C22×C3D4×Dic312yes—
571C22×C3C2×D3×D411yescharacteristic
572C22×C3C2×D3×D411yescharacteristic
573C2×D3—24no—
574C2×D3—48no—
575C2×D3—42no—
576C2×D3—42no—
577C3×C4—24no—
578C3×C4—22no—
579C3×C4—22no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—22no—
583C3×C4—122no—
584C3×C4#67⋊C412yes—
585C3×C4D4×Dic312yes—
586C3×C4C22×C4×D311yescharacteristic
587C3×C4C2×#23711yescharacteristic
588C3×C4C2×#23711yescharacteristic
589C3×C4C23×Dic311yescharacteristic
590Dic3—32no—
591Dic3—32no—
592Dic3—42no—
593Dic3—62no—
594Dic3—62no—
595Dic3—61no—
596Dic3—61no—
597Dic3—61no—
598Dic3—61no—
599Dic3—61no—
600Dic3—61no—
601Dic3—121no—
602Dic3—121no—
603Dic3—122no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—121no—
609C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
610C23—21no—
611C23—62no—
612C23—64no—
613C23—122no—
614C23—122no—
615C23#381111yescharacteristic
616Q8—21no—
617Q8C2×D3×Dic312yescomplemented
618D4—24no—
619D4—21no—
620D4—34no—
621D4—62no—
622D4—64no—
623D4C2×D3×Dic312yescomplemented
624C2×C4—21no—
625C2×C4—24no—
626C2×C4—62no—
627C2×C4—91no—
628C2×C4—91no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—122no—
632C2×C4—182no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4—364no—
636C2×C4—362no—
637C2×C4—364no—
638C2×C4—361no—
639C2×C4—362no—
640C2×C4C2×D3×Dic312yes—
641C2×C4#380512yes—
642C2×C4#381111yescharacteristic
643C2×C4C22×D3211yescharacteristic
644C8—34no—
645C8—62no—
646C2×C3—22no—
647C2×C3—22no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—42no—
652C2×C3—44no—
653C2×C3—42no—
654C2×C3—42no—
655C2×C3—124no—
656C2×C3C2×#67⋊C411yescharacteristic
657C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
658C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
659C2×C3#577311yescharacteristic
660C2×C3#577711yescharacteristic
661C2×C3C2×D4×Dic311yescharacteristic
662D3—44no—
663C22—21no—
664C22—21no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—64no—
669C22—128no—
670C22—122no—
671C22—122no—
672C22#67⋊Dic312yes—
673C22C2×#381111yescharacteristic
674C4—22no—
675C4—92no—
676C4—122no—
677C4—181no—
678C4—181no—
679C4—181no—
680C4—361no—
681C4—361no—
682C4#67⋊Dic312yes—
683C4C22×D3×Dic311yescharacteristic
684C4C2×#380511yescharacteristic
685C3—21no—
686C3#7886611yescharacteristic, complemented
687C3Dic3×AGL(1,ℤ/8)11yescharacteristic, complemented
688C2—22no—
689C2—42no—
690C2—124no—
691C2#1059545811yescharacteristic
692C2#1059547111yescharacteristic
693C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#949C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
3. C2×#63898C2semidirect
4. C3×#5232C2semidirect
5. #10591572C2semidirect
6. #10591571C2semidirect
7. #10591436C2semidirect
8. #10591435C2semidirect
9. #10591130C2semidirect
10. #10591086C2semidirect
11. #10591060C2semidirect
17. Q8×C3⋊Dic3C22semidirect
18. Q8×C3⋊Dic3C22semidirect
21. D4×C3⋊Dic3C22semidirect
22. D4×C3⋊Dic3C22semidirect
27. C3×#949C4semidirect
38. C3×#835C22semidirect
39. C3×#832C22semidirect
40. #63575C22semidirect
41. #63573C22semidirect
44. #63555C22semidirect
45. #63553C22semidirect
54. #5232D3semidirect
71. C32×#41C2×C4semidirect
84. C2×C3×D12C2×C4semidirect
103. C3×#215C2×C4semidirect
104. C3×#213C2×C4semidirect
108. C3×#208C2×C4semidirect
128. #949Dic3semidirect
175. #835C2×D3semidirect
178. #832C2×D3semidirect
196. C32×Q8C22×C4semidirect
199. C32×D4C22×C4semidirect
224. C3×C3⋊C8C22×C4semidirect
242. C3×#41C4×D3semidirect
243. C3×#41C2×Dic3semidirect
282. C2×D12C2×Dic3semidirect
306. #215C2×Dic3semidirect
307. #213C2×Dic3semidirect
346. #208C2×Dic3semidirect
369. C3⋊Dic3AGL(1,ℤ/8)semidirect
421. C3×Q8C2×C4×D3semidirect
422. C3×Q8C22×Dic3semidirect
433. C3×D4C2×C4×D3semidirect
434. C3×D4C22×Dic3semidirect
497. C3⋊C8C22×Dic3semidirect
506. #41D3×Dic3semidirect
609. C32C4×AGL(1,ℤ/8)semidirect
617. Q8C2×D3×Dic3semidirect
623. D4C2×D3×Dic3semidirect
686. C3#78866semidirect
687. C3Dic3×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
#41×C3⋊Dic32
C2×C3×#9492
C2×#638982
C3×#52322
#105915722
#105915712
#105914362
#105914352
#105911302
#105910862
#105910602
Dic3×AGL(1,ℤ/8)3
#788663