Finite Group Databasebeta

← C3×#83963 #11868075

Subgroups — C3×#83963 #11868075

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3C2×C3×#932C211yesmaximal, characteristic, complemented
4C3×#5745C211yesmaximal, characteristic, complemented
5C3×#5237C211yesmaximal, characteristic, complemented
6C2×C3×#833C211yesmaximal, characteristic, complemented
7C3×#5177C214yesmaximal, complemented
8C3×#5160C214yesmaximal, complemented
9C3×#5125C211yesmaximal, characteristic, complemented
10C3×#3068—31nomaximal
11#83963C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C32×AGL(1,ℤ/8)—22no—
16C32×AGL(1,ℤ/8)—22no—
17C2×C32×SD16C2212yescomplemented
18C2×C32×D8C2212yescomplemented
19C2×C32×M16C2211yescharacteristic
20C3×#951—21no—
21C3×#950—22no—
22C3×#949—21no—
23C3×#942C2212yescomplemented
24C2×C3×#214—21no—
25C3×#932—22no—
26C3×#932C2214yes—
27C3×#932C2212yescomplemented
28C2×C3×#213—21no—
29C2×C3×#208C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C3×#907—22no—
33C3×D3×M16—22no—
34C3×#901C2214yescomplemented
35C3×#836C2212yescomplemented
36C3×#833C2212yescomplemented
37C3×#833C2214yescomplemented
38C3×#819C2214yescomplemented
39C3×#575—31no—
40C2×C3×AGL(1,ℤ/8)—21no—
41C2×C3×AGL(1,ℤ/8)—31no—
42C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
43C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
44C3×#568—31no—
45#5822C2×C311yescharacteristic, complemented
46C2×#932C2×C311yescharacteristic, complemented
47#5745C2×C311yescharacteristic, complemented
48C3×#472—34no—
49C3×#471—34no—
50C3×#430—31no—
51C3×#413—31no—
52C2×C3×#100—31no—
53#5237C2×C311yescharacteristic, complemented
54C2×#833C2×C311yescharacteristic, complemented
55#5177C2×C314yescomplemented
56#5160C2×C314yescomplemented
57#5125C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41—21no—
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4—21no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2312yes—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235D412yes—
78C3×#235C2312yes—
79C2×C3×D12D411yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6D411yescharacteristic
82C32×SD16—24no—
83C32×D8—24no—
84C32×M16D412yes—
85C32×M16D412yes—
86C2×C32×C8C2312yes—
87C3×#216—22no—
88C3×#215—22no—
89C3×#214—24no—
90C3×#214—22no—
91C3×#213—24no—
92C3×#213—22no—
93C3×#208—21no—
94C3×#208—21no—
95C3×#208—21no—
96C3×#208C2312yes—
97C3×#208C2312yes—
98C3×#208C2312yes—
99C2×C3×C3⋊C8—21no—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8—21no—
102C3×ΓL(1,𝔽25)—24no—
103C3×D3×C8—24no—
104#3068—31noSylow
105C2×C3×#41—21no—
106C2×C3×#41—31no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C22×C311yescharacteristic
109C22×C3×D4—21no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C22×C311yescharacteristic
112C2×#235C22×C311yescharacteristic
113C3×#137—32no—
114C3×#137—61no—
115C3×AGL(1,ℤ/8)—24no—
116C3×AGL(1,ℤ/8)—24no—
117C3×AGL(1,ℤ/8)—22no—
118C3×AGL(1,ℤ/8)—22no—
119C3×AGL(1,ℤ/8)—22no—
120C3×AGL(1,ℤ/8)—22no—
121C3×AGL(1,ℤ/8)—34no—
122C3×AGL(1,ℤ/8)—32no—
123C3×AGL(1,ℤ/8)—62no—
124C3×AGL(1,ℤ/8)—61no—
125C3×#135—62no—
126C2×C3×SD16—22no—
127C2×C3×SD16—61no—
128C2×C3×SD16C2×D312yescomplemented
129C2×C3×SD16C22×C312yescomplemented
130C2×C3×D8—22no—
131C2×C3×D8—61no—
132C2×C3×D8C2×D312yescomplemented
133C2×C3×D8C22×C312yescomplemented
134C3×#131—34no—
135C3×#131—62no—
136C2×C3×M16—21no—
137C2×C3×M16—31no—
138C2×C3×M16—31no—
139C2×C3×M16—31no—
140C2×C3×M16—62no—
141C2×C3×M16C2×D311yescharacteristic
142C2×C3×M16C22×C311yescharacteristic
143#951—21no—
144#950—22no—
145#949—21no—
146#942C22×C312yescomplemented
147C2×#214—21no—
148#932—22no—
149#932C22×C314yes—
150#932C22×C312yescomplemented
151C2×#213—21no—
152C2×#208C22×C311yescharacteristic
153C2×#208C22×C311yescharacteristic
154C2×#208C22×C311yescharacteristic
155#907—22no—
156D3×M16—22no—
157#901C22×C314yescomplemented
158C3×#108—34no—
159C3×#101—32no—
160C3×#100—34no—
161C3×#100—32no—
162#836C22×C312yescomplemented
163#833C22×C312yescomplemented
164#833C22×C314yescomplemented
165#819C22×C314yescomplemented
166C23×C32—22no—
167C23×C32—21no—
168C23×C32—41no—
169C23×C32—41no—
170C23×C32—82no—
171C23×C32#4111yescharacteristic
172C22×C3×D3—21no—
173C32×Q8—21no—
174C32×Q8—21no—
175C32×D4—21no—
176C32×D4—22no—
177C32×D4—22no—
178C32×D4—21no—
179C32×D4—41no—
180C32×D4—41no—
181C32×D4—41no—
182C32×D4—41no—
183C2×C32×C4—21no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4#4111yescharacteristic
191C2×C32×C4C2411yescharacteristic
192C3×#67—22no—
193C3×#67—22no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12C2×D412yes—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×Dic6—21no—
200C3×Dic6C2×D412yes—
201C32×C8C2×D414yes—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205#575—31no—
206C2×AGL(1,ℤ/8)—31no—
207C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
208#568—31no—
209#472—34no—
210#471—34no—
211#430—31no—
212#413—31no—
213C2×#100—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—41no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—21no—
225C3×#41—21no—
226C3×#41—21no—
227C3×#41—32no—
228C3×#41—32no—
229C3×#41—41no—
230C3×#41—41no—
231C3×#41—61no—
232C3×#41—61no—
233C2×C3×Q8—21no—
234C2×C3×Q8—31no—
235C2×C3×Q8C22×D311yescharacteristic
236C2×C3×Q8C23×C311yescharacteristic
237C2×C3×D4—22no—
238C2×C3×D4—22no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—22no—
253C2×C3×D4—31no—
254C2×C3×D4—41no—
255C2×C3×D4—41no—
256C2×C3×D4—41no—
257C2×C3×D4—41no—
258C2×C3×D4—61no—
259C2×C3×D4C22×D311yescharacteristic
260C2×C3×D4C22×D312yes—
261C2×C3×D4C23×C312yes—
262C2×C3×D4C23×C311yescharacteristic
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—41no—
267C22×C3×C4—61no—
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C23×C311yescharacteristic
270C2×#67—21no—
271#235—21no—
272#235—21no—
273#235C3×D412yes—
274#235C23×C312yes—
275C2×D12C3×D411yescharacteristic
276C2×C4×D3—21no—
277C2×Dic6C3×D411yescharacteristic
278C3×Q16—62no—
279C3×SD16—28no—
280C3×SD16—24no—
281C3×SD16—24no—
282C3×SD16—64no—
283C3×SD16—62no—
284C3×SD16—62no—
285C3×D8—28no—
286C3×D8—24no—
287C3×D8—24no—
288C3×D8—64no—
289C3×D8—62no—
290C3×M16—22no—
291C3×M16—22no—
292C3×M16—32no—
293C3×M16—32no—
294C3×M16—32no—
295C3×M16—61no—
296C3×M16—61no—
297C3×M16—61no—
298C3×M16—64no—
299C3×M16#6712yes—
300C3×M16#6712yes—
301C3×M16C3×D412yes—
302C3×M16C3×D412yes—
303C2×C3×C8—22no—
304C2×C3×C8—61no—
305C2×C3×C8—61no—
306C2×C3×C8—61no—
307C2×C3×C8—64no—
308C2×C3×C8C22×D312yes—
309C2×C3×C8C23×C312yes—
310#216—22no—
311#215—22no—
312#214—24no—
313#214—22no—
314#213—24no—
315#213—22no—
316#208—21no—
317#208—21no—
318#208—21no—
319#208C23×C312yes—
320#208C23×C312yes—
321#208C23×C312yes—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325ΓL(1,𝔽25)—24no—
326D3×C8—24no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—42no—
330C22×C32—81no—
331C22×C32—82no—
332C22×C32—82no—
333C22×C32—82no—
334C22×C32#12111yescharacteristic
335C22×C32#12111yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C2×C3×D3—22no—
338C2×C3×D3—81no—
339C32×C4—41no—
340C32×C4#12111yescharacteristic
341C32×C4#12111yescharacteristic
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—22no—
345C2×#41—31no—
346C2×#41C2×C3×D311yescharacteristic
347C22×D4C2×C3×D311yescharacteristic
348#137—32no—
349#137—61no—
350AGL(1,ℤ/8)—22no—
351AGL(1,ℤ/8)—22no—
352AGL(1,ℤ/8)—34no—
353AGL(1,ℤ/8)—32no—
354AGL(1,ℤ/8)—62no—
355AGL(1,ℤ/8)—61no—
356#135—62no—
357C2×SD16—61no—
358C2×SD16C2×C3×D312yescomplemented
359C2×D8—61no—
360C2×D8C2×C3×D312yescomplemented
361#131—34no—
362#131—62no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—62no—
367C2×M16C2×C3×D311yescharacteristic
368#108—34no—
369#101—32no—
370#100—34no—
371#100—32no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—21no—
375C23×C3—22no—
376C23×C3—21no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—61no—
386C23×C3—82no—
387C23×C3—82no—
388C23×C3—84no—
389C23×C3#23711yescharacteristic
390C23×C3C3×#4111yescharacteristic
391C22×D3—21no—
392C3×Q8—22no—
393C3×Q8—21no—
394C3×Q8—21no—
395C3×Q8—21no—
396C3×Q8—21no—
397C3×Q8—32no—
398C3×Q8—41no—
399C3×Q8—61no—
400C3×D4—22no—
401C3×D4—24no—
402C3×D4—22no—
403C3×D4—21no—
404C3×D4—21no—
405C3×D4—22no—
406C3×D4—22no—
407C3×D4—21no—
408C3×D4—21no—
409C3×D4—22no—
410C3×D4—32no—
411C3×D4—42no—
412C3×D4—41no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—42no—
417C3×D4—41no—
418C3×D4—41no—
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—41no—
423C3×D4—41no—
424C3×D4—41no—
425C3×D4—62no—
426C3×D4—62no—
427C3×D4—61no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—61no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4D3×D411yescharacteristic
447C2×C3×C4D3×D411yescharacteristic
448C2×C3×C4#23711yescharacteristic
449C2×C3×C4C2×#6711yescharacteristic
450C2×C3×C4C2×#6711yescharacteristic
451C2×C3×C4C2×C3×D411yescharacteristic
452C2×C3×C4C2×C3×D411yescharacteristic
453C2×C3×C4C2×C3×D411yescharacteristic
454C2×C3×C4C2×C3×D411yescharacteristic
455C2×C3×C4C3×#4111yescharacteristic
456C2×C3×C4C23×D311yescharacteristic
457C2×C3×C4C24×C311yescharacteristic
458#67—22no—
459#67—22no—
460C2×Dic3—21no—
461D12—21no—
462D12C2×C3×D412yes—
463C4×D3—22no—
464C4×D3—22no—
465Dic6—21no—
466Dic6C2×C3×D412yes—
467C3×C8—24no—
468C3×C8—62no—
469C3×C8—62no—
470C3×C8—62no—
471C3×C8C2×#6714yes—
472C3×C8C2×C3×D414yes—
473C3⋊C8—22no—
474C3⋊C8—22no—
475C3⋊C8—22no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—81no—
480C2×C32—82no—
481C2×C32C2×#12111yescharacteristic
482C3×D3—42no—
483C24—21no—
484#41—21no—
485#41—21no—
486#41—21no—
487#41—21no—
488#41—32no—
489#41—32no—
490#41—61no—
491#41—61no—
492C2×Q8—31no—
493C2×Q8C22×C3×D311yescharacteristic
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—31no—
501C2×D4—61no—
502C2×D4C22×C3×D311yescharacteristic
503C2×D4C22×C3×D312yes—
504C22×C4—21no—
505C22×C4—61no—
506C22×C4C22×C3×D311yescharacteristic
507Q16—62no—
508SD16—24no—
509SD16—64no—
510SD16—62no—
511SD16—62no—
512D8—24no—
513D8—64no—
514D8—62no—
515M16—32no—
516M16—32no—
517M16—32no—
518M16—61no—
519M16—61no—
520M16—61no—
521M16—64no—
522M16C3×#6712yes—
523M16C3×#6712yes—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—64no—
528C2×C8C22×C3×D312yes—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—44no—
537C22×C3—41no—
538C22×C3—42no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—62no—
542C22×C3—82no—
543C22×C3—82no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—84no—
547C22×C3—82no—
548C22×C3—82no—
549C22×C3—82no—
550C22×C3—82no—
551C22×C3—82no—
552C22×C3—84no—
553C22×C3—84no—
554C22×C3—241no—
555C22×C3#93811yescharacteristic
556C22×C3#93811yescharacteristic
557C22×C3C3×#12111yescharacteristic
558C22×C3C3×#12111yescharacteristic
559C22×C3C2×#23711yescharacteristic
560C22×C3C2×C3×#4111yescharacteristic
561C2×D3—22no—
562C2×D3—81no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—42no—
568C3×C4—41no—
569C3×C4—41no—
570C3×C4—62no—
571C3×C4#93811yescharacteristic
572C3×C4#93811yescharacteristic
573C3×C4C3×#12111yescharacteristic
574C3×C4C3×#12111yescharacteristic
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C22×#6711yescharacteristic
577C3×C4C22×C3×D411yescharacteristic
578C3×C4C22×C3×D411yescharacteristic
579Dic3—22no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—21no—
582C23—22no—
583C23—41no—
584C23—41no—
585C23—61no—
586C23—82no—
587C23C3×#23711yescharacteristic
588Q8—21no—
589Q8—21no—
590Q8—32no—
591Q8—61no—
592D4—22no—
593D4—21no—
594D4—21no—
595D4—22no—
596D4—32no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—62no—
602D4—62no—
603D4—61no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—61no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4C3×D3×D411yescharacteristic
611C2×C4C3×D3×D411yescharacteristic
612C2×C4C3×#23711yescharacteristic
613C2×C4C2×C3×#6711yescharacteristic
614C2×C4C2×C3×#6711yescharacteristic
615C2×C4C23×C3×D311yescharacteristic
616C8—62no—
617C8—62no—
618C8—62no—
619C8C2×C3×#6714yes—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—41no—
629C2×C3—41no—
630C2×C3—84no—
631C2×C3—82no—
632C2×C3—82no—
633C2×C3—81no—
634C2×C3—82no—
635C2×C3—81no—
636C2×C3—122no—
637C2×C3C2×#93811yescharacteristic
638C2×C3C2×C3×#12111yescharacteristic
639D3—42no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—62no—
644C22—82no—
645C22—81no—
646C22—82no—
647C22—82no—
648C22—241no—
649C22C3×#93811yescharacteristic
650C22C3×#93811yescharacteristic
651C22C2×C3×#23711yescharacteristic
652C4—41no—
653C4—62no—
654C4C3×#93811yescharacteristic
655C4C3×#93811yescharacteristic
656C4C2×C3×D3×D411yescharacteristic
657C4C22×C3×#6711yescharacteristic
658C3—21no—
659C3#8396311yescharacteristic, direct product factor
660C3C3×#306811yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—82no—
665C2—81no—
666C2—122no—
667C2C2×C3×#93811yescharacteristic
subgroupG/H
centerC2×C3C2×#938
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC2×C32C2×#121
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#3068
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. C3×#5822C2semidirect
3. C2×C3×#932C2semidirect
4. C3×#5745C2semidirect
5. C3×#5237C2semidirect
6. C2×C3×#833C2semidirect
7. C3×#5177C2semidirect
8. C3×#5160C2semidirect
9. C3×#5125C2semidirect
11. #83963C3direct (N × H)
17. C2×C32×SD16C22semidirect
18. C2×C32×D8C22semidirect
23. C3×#942C22semidirect
27. C3×#932C22semidirect
34. C3×#901C22semidirect
35. C3×#836C22semidirect
36. C3×#833C22semidirect
37. C3×#833C22semidirect
38. C3×#819C22semidirect
42. C2×C3×AGL(1,ℤ/8)D3semidirect
43. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
45. #5822C2×C3semidirect
46. C2×#932C2×C3semidirect
47. #5745C2×C3semidirect
53. #5237C2×C3semidirect
54. C2×#833C2×C3semidirect
55. #5177C2×C3semidirect
56. #5160C2×C3semidirect
57. #5125C2×C3semidirect
128. C2×C3×SD16C2×D3semidirect
129. C2×C3×SD16C22×C3semidirect
132. C2×C3×D8C2×D3semidirect
133. C2×C3×D8C22×C3semidirect
146. #942C22×C3semidirect
150. #932C22×C3semidirect
157. #901C22×C3semidirect
162. #836C22×C3semidirect
163. #833C22×C3semidirect
164. #833C22×C3semidirect
165. #819C22×C3semidirect
207. C2×AGL(1,ℤ/8)C3×D3semidirect
358. C2×SD16C2×C3×D3semidirect
360. C2×D8C2×C3×D3semidirect
580. C32#3068semidirect
659. C3#83963direct (N × H)
660. C3C3×#3068semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C3×#58222
C2×C3×#9322
C3×#57452
C3×#52372
C2×C3×#8332
C3×#51772
C3×#51602
C3×#51252
C3×#30683
#839633