Finite Group Databasebeta

← C2×C3×#5238 #11863696

Subgroups — C2×C3×#5238 #11863696

Order 1152.

2069 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C3×#5238C218yesmaximal, direct product factor
6C2×C3×#835C211yesmaximal, characteristic, complemented
7C2×C3×#832C211yesmaximal, characteristic, complemented
8C2×C3×#830C211yesmaximal, characteristic, complemented
9C2×C3×#449—31nomaximal
10C2×#5238C311yesmaximal, characteristic, direct product factor
11C2×C32×#41—24no—
12C2×C32×#41—24no—
13C2×C32×#41—22no—
14C2×C32×#41C2214yescomplemented
15C22×C32×Q8C2211yescharacteristic
16C22×C32×D4—21no—
17C22×C32×D4C2211yescharacteristic
18C23×C32×C4—21no—
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67—21no—
21C22×C3×D12C2211yescharacteristic
22C2×C3×#215—24no—
23C2×C3×#215C2214yescomplemented
24C2×C3×#213—24no—
25C2×C3×#213C2214yescomplemented
26C3×#930—22no—
27C3×#930C2214yescomplemented
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C3×#835C2214yescomplemented
33C3×#832C2214yescomplemented
34C3×#830C2214yescomplemented
35C22×C3×#41—21no—
36C22×C3×#41D311yescharacteristic, complemented
37C22×C3×#41C2×C311yescharacteristic, complemented
38C22×C3×SD16—31no—
39C22×C3×D8—31no—
40C2×C3×#121—31no—
41C22×#215C2×C311yescharacteristic, complemented
42C22×#213C2×C311yescharacteristic, complemented
43C2×#930C2×C311yescharacteristic, complemented
44C3×#449—38no—
45C2×C3×#103—31no—
46C2×C3×#102—31no—
47C2×C3×C22⋊C8—31no—
48#5238C2×C318yesdirect product factor
49C2×#835C2×C311yescharacteristic, complemented
50C2×#832C2×C311yescharacteristic, complemented
51C2×#830C2×C311yescharacteristic, complemented
52C24×C32—21no—
53C24×C32D411yescharacteristic
54C23×C3×D3—21no—
55C32×#41—216no—
56C32×#41—28no—
57C32×#41—28no—
58C2×C32×Q8—22no—
59C2×C32×Q8—21no—
60C2×C32×Q8D414yescomplemented
61C2×C32×Q8C2312yes—
62C2×C32×D4—28no—
63C2×C32×D4—24no—
64C2×C32×D4—21no—
65C2×C32×D4—22no—
66C2×C32×D4D414yescomplemented
67C2×C32×D4C2312yes—
68C22×C32×C4—28no—
69C22×C32×C4—21no—
70C22×C32×C4—24no—
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4D411yescharacteristic
74C22×C32×C4D412yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—24no—
78C2×C3×#67—44no—
79C22×C3×Dic3—21no—
80C2×C3×D12—22no—
81C2×C3×D12—22no—
82C2×C3×D12—21no—
83C2×C3×D12C2312yes—
84C3×#215—28no—
85C3×#213—28no—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C2×#449—31noSylow
94C2×C3×#41—28no—
95C2×C3×#41—28no—
96C2×C3×#41—24no—
97C2×C3×#41—24no—
98C2×C3×#41—24no—
99C2×C3×#41—24no—
100C2×C3×#41—24no—
101C2×C3×#41—22no—
102C2×C3×#41—22no—
103C2×C3×#41—24no—
104C2×C3×#41C2×D314yescomplemented
105C2×C3×#41C22×C314yescomplemented
106C22×C3×Q8—21no—
107C22×C3×Q8C2×D311yescharacteristic
108C22×C3×Q8C22×C311yescharacteristic
109C22×C3×D4—22no—
110C22×C3×D4—21no—
111C22×C3×D4—21no—
112C22×C3×D4—21no—
113C22×C3×D4—31no—
114C22×C3×D4—61no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C22×C311yescharacteristic
117C23×C3×C4—22no—
118C23×C3×C4—21no—
119C23×C3×C4—21no—
120C23×C3×C4—21no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C22×#67—21no—
124C22×D12C22×C311yescharacteristic
125C2×C3×SD16—34no—
126C2×C3×SD16—64no—
127C2×C3×D8—34no—
128C2×C3×D8—64no—
129C22×C3×C8—31no—
130C22×C3×C8—31no—
131C3×#121—34no—
132C3×#121—62no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—61no—
135C2×#215—24no—
136C2×#215C22×C314yescomplemented
137C2×#213—24no—
138C2×#213C22×C314yescomplemented
139#930—22no—
140#930C22×C314yescomplemented
141C2×(C2×D3)⋊C4—21no—
142C2×C4⋊Dic3C22×C311yescharacteristic
143C22×C3⋊C8C22×C311yescharacteristic
144C22×C3⋊C8C22×C311yescharacteristic
145C3×#103—34no—
146C3×#102—34no—
147C3×C22⋊C8—34no—
148#835C22×C314yescomplemented
149#832C22×C314yescomplemented
150#830C22×C314yescomplemented
151C23×C32—24no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—42no—
157C23×C32—42no—
158C23×C32C2×D412yes—
159C23×C32C2×D411yescharacteristic
160C22×C3×D3—22no—
161C22×C3×D3—42no—
162C22×C3×D3—42no—
163C22×C3×D3—42no—
164C32×Q8—24no—
165C32×Q8—22no—
166C32×Q8C2×D414yescomplemented
167C32×D4—216no—
168C32×D4—24no—
169C32×D4—22no—
170C32×D4C2×D414yescomplemented
171C2×C32×C4—216no—
172C2×C32×C4—22no—
173C2×C32×C4—24no—
174C2×C32×C4—22no—
175C2×C32×C4—24no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2411yescharacteristic
183C3×#67—48no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—42no—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—42no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—22no—
191C22×#41C3×D311yescharacteristic, complemented
192C22×SD16—31no—
193C22×D8—31no—
194C2×#121—31no—
195#449—38no—
196C2×#103—31no—
197C2×#102—31no—
198C2×C22⋊C8—31no—
199C24×C3—22no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—61no—
204C24×C3#6711yescharacteristic
205C24×C3C3×D411yescharacteristic
206C23×D3—21no—
207C3×#41—232no—
208C3×#41—216no—
209C3×#41—216no—
210C3×#41—216no—
211C3×#41—216no—
212C3×#41—28no—
213C3×#41—28no—
214C3×#41—28no—
215C3×#41—28no—
216C2×C3×Q8—24no—
217C2×C3×Q8—22no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—21no—
222C2×C3×Q8—24no—
223C2×C3×Q8—22no—
224C2×C3×Q8#6714yescomplemented
225C2×C3×Q8C3×D414yescomplemented
226C2×C3×Q8C22×D312yes—
227C2×C3×Q8C23×C312yes—
228C2×C3×D4—216no—
229C2×C3×D4—28no—
230C2×C3×D4—28no—
231C2×C3×D4—28no—
232C2×C3×D4—22no—
233C2×C3×D4—24no—
234C2×C3×D4—24no—
235C2×C3×D4—24no—
236C2×C3×D4—21no—
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—22no—
240C2×C3×D4—24no—
241C2×C3×D4—22no—
242C2×C3×D4—32no—
243C2×C3×D4—64no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—61no—
247C2×C3×D4—124no—
248C2×C3×D4#6714yescomplemented
249C2×C3×D4C3×D414yescomplemented
250C2×C3×D4C22×D312yes—
251C2×C3×D4C23×C312yes—
252C22×C3×C4—22no—
253C22×C3×C4—216no—
254C22×C3×C4—28no—
255C22×C3×C4—28no—
256C22×C3×C4—28no—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—24no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—24no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—21no—
268C22×C3×C4—22no—
269C22×C3×C4—21no—
270C22×C3×C4—22no—
271C22×C3×C4—61no—
272C22×C3×C4#6712yes—
273C22×C3×C4#6711yescharacteristic
274C22×C3×C4C3×D411yescharacteristic
275C22×C3×C4C3×D412yes—
276C22×C3×C4C22×D312yes—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C23×C312yes—
279C22×C3×C4C23×C311yescharacteristic
280C2×#67—24no—
281C2×#67—44no—
282C22×Dic3—21no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—21no—
286C2×D12C23×C312yes—
287C3×SD16—68no—
288C3×D8—68no—
289C2×C3×C8—32no—
290C2×C3×C8—32no—
291C2×C3×C8—62no—
292C2×C3×C8—62no—
293C3×C4⋊C4—32no—
294C3×C4⋊C4—61no—
295C3×C22⋊C4—64no—
296#215—28no—
297#213—28no—
298(C2×D3)⋊C4—24no—
299C4⋊Dic3—21no—
300C4⋊Dic3C23×C312yes—
301C2×C3⋊C8—22no—
302C2×C3⋊C8—22no—
303C2×C3⋊C8C23×C312yes—
304C2×C3⋊C8C23×C312yes—
305C22×C32—22no—
306C22×C32—24no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32—44no—
312C22×C32—48no—
313C22×C32#12012yes—
314C22×C32#13512yes—
315C22×C32AGL(1,ℤ/8)12yes—
316C22×C32C22×D411yescharacteristic
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—84no—
321C32×C4—22no—
322C32×C4—24no—
323C32×C4#12012yes—
324C32×C4C22×D411yescharacteristic
325C32×C4C22×D411yescharacteristic
326C3×Dic3—42no—
327C2×#41—24no—
328C2×#41—24no—
329C2×#41—22no—
330C2×#41C2×C3×D314yescomplemented
331C22×Q8C2×C3×D311yescharacteristic
332C22×D4—21no—
333C22×D4—31no—
334C22×D4—61no—
335C22×D4C2×C3×D311yescharacteristic
336C23×C4—21no—
337C23×C4C2×C3×D311yescharacteristic
338C2×SD16—34no—
339C2×SD16—64no—
340C2×D8—34no—
341C2×D8—64no—
342C22×C8—31no—
343C22×C8—31no—
344#121—34no—
345#121—62no—
346C2×C4⋊C4—31no—
347C2×C22⋊C4—61no—
348#103—34no—
349#102—34no—
350C22⋊C8—34no—
351C23×C3—24no—
352C23×C3—28no—
353C23×C3—24no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—22no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—44no—
369C23×C3—44no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—62no—
375C23×C3—122no—
376C23×C3—122no—
377C23×C3—122no—
378C23×C3C2×#6712yes—
379C23×C3C2×#6711yescharacteristic
380C23×C3C2×C3×D412yes—
381C23×C3C2×C3×D411yescharacteristic
382C22×D3—22no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C3×Q8—28no—
387C3×Q8—24no—
388C3×Q8—24no—
389C3×Q8—24no—
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—24no—
393C3×Q8C2×#6714yescomplemented
394C3×Q8C2×C3×D414yescomplemented
395C3×D4—232no—
396C3×D4—216no—
397C3×D4—216no—
398C3×D4—28no—
399C3×D4—24no—
400C3×D4—24no—
401C3×D4—24no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—24no—
405C3×D4—62no—
406C3×D4—62no—
407C3×D4—128no—
408C3×D4—122no—
409C3×D4C2×#6714yescomplemented
410C3×D4C2×C3×D414yescomplemented
411C2×C3×C4—24no—
412C2×C3×C4—28no—
413C2×C3×C4—24no—
414C2×C3×C4—232no—
415C2×C3×C4—216no—
416C2×C3×C4—216no—
417C2×C3×C4—28no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—62no—
438C2×C3×C4—122no—
439C2×C3×C4C2×#6712yes—
440C2×C3×C4C2×#6711yescharacteristic
441C2×C3×C4C2×#6712yes—
442C2×C3×C4C2×#6712yes—
443C2×C3×C4C2×C3×D412yes—
444C2×C3×C4C2×C3×D411yescharacteristic
445C2×C3×C4C2×C3×D412yes—
446C2×C3×C4C2×C3×D412yes—
447C2×C3×C4C23×D311yescharacteristic
448C2×C3×C4C24×C311yescharacteristic
449#67—48no—
450C2×Dic3—22no—
451C2×Dic3—42no—
452D12—22no—
453D12—22no—
454D12—42no—
455C3×C8—62no—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—22no—
459C2×C32—42no—
460C2×C32—44no—
461C2×C32#44914yescomplemented
462C2×C32C2×#12011yescharacteristic
463C2×C32C2×#13511yescharacteristic
464C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
465C3×D3—82no—
466C24—21no—
467C24—61no—
468C24C3×#6711yescharacteristic
469#41—216no—
470#41—28no—
471#41—28no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8C3×#6714yescomplemented
475C2×Q8C22×C3×D312yes—
476C2×D4—28no—
477C2×D4—24no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—32no—
481C2×D4—64no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—61no—
485C2×D4—124no—
486C2×D4C3×#6714yescomplemented
487C2×D4C22×C3×D312yes—
488C22×C4—28no—
489C22×C4—21no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—61no—
494C22×C4C3×#6711yescharacteristic
495C22×C4C3×#6712yes—
496C22×C4C22×C3×D312yes—
497C22×C4C22×C3×D311yescharacteristic
498SD16—68no—
499D8—68no—
500C2×C8—32no—
501C2×C8—32no—
502C2×C8—62no—
503C2×C8—62no—
504C4⋊C4—32no—
505C4⋊C4—61no—
506C22⋊C4—64no—
507C22×C3—24no—
508C22×C3—28no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—24no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—21no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—48no—
526C22×C3—416no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—44no—
530C22×C3—48no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—44no—
534C22×C3—48no—
535C22×C3—122no—
536C22×C3—122no—
537C22×C3—122no—
538C22×C3—244no—
539C22×C3#94912yes—
540C22×C3#95012yes—
541C22×C3#95312yes—
542C22×C3C3×#12012yes—
543C22×C3C3×#13512yes—
544C22×C3C3×AGL(1,ℤ/8)12yes—
545C22×C3C22×#6711yescharacteristic
546C22×C3C22×C3×D411yescharacteristic
547C2×D3—42no—
548C2×D3—42no—
549C2×D3—42no—
550C2×D3—84no—
551C3×C4—24no—
552C3×C4—28no—
553C3×C4—22no—
554C3×C4—24no—
555C3×C4—22no—
556C3×C4—24no—
557C3×C4—22no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—122no—
561C3×C4#95312yes—
562C3×C4C3×#12012yes—
563C3×C4C22×#6711yescharacteristic
564C3×C4C22×#6711yescharacteristic
565C3×C4C22×C3×D411yescharacteristic
566C3×C4C22×C3×D411yescharacteristic
567Dic3—42no—
568C32C2×#44911yescharacteristic, complemented, Sylow
569C23—22no—
570C23—22no—
571C23—22no—
572C23—24no—
573C23—22no—
574C23—42no—
575C23—42no—
576C23—62no—
577C23—122no—
578C23—122no—
579C23—122no—
580C23C2×C3×#6712yes—
581C23C2×C3×#6711yescharacteristic
582Q8—24no—
583Q8—22no—
584Q8C2×C3×#6714yescomplemented
585D4—216no—
586D4—24no—
587D4—22no—
588D4—62no—
589D4—62no—
590D4—128no—
591D4—122no—
592D4C2×C3×#6714yescomplemented
593C2×C4—216no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—62no—
601C2×C4—122no—
602C2×C4C2×C3×#6712yes—
603C2×C4C2×C3×#6711yescharacteristic
604C2×C4C2×C3×#6712yes—
605C2×C4C2×C3×#6712yes—
606C2×C4C23×C3×D311yescharacteristic
607C8—62no—
608C8—62no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—24no—
612C2×C3—21no—
613C2×C3—44no—
614C2×C3—48no—
615C2×C3—42no—
616C2×C3—44no—
617C2×C3—42no—
618C2×C3—44no—
619C2×C3—242no—
620C2×C3#523814yesdirect product factor
621C2×C3C3×#44914yescomplemented
622C2×C3C2×#94911yescharacteristic
623C2×C3C2×#95011yescharacteristic
624C2×C3C2×#95311yescharacteristic
625C2×C3C2×C3×#12011yescharacteristic
626C2×C3C2×C3×#13511yescharacteristic
627C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
628D3—82no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—24no—
633C22—42no—
634C22—42no—
635C22—44no—
636C22—48no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22—244no—
641C22C3×#94912yes—
642C22C3×#95012yes—
643C22C3×#95312yes—
644C22C22×C3×#6711yescharacteristic
645C4—22no—
646C4—24no—
647C4—122no—
648C4C3×#95312yes—
649C4C22×C3×#6711yescharacteristic
650C4C22×C3×#6711yescharacteristic
651C3—21no—
652C3C2×#523811yescharacteristic, direct product factor
653C3C2×C3×#44911yescharacteristic, complemented
654C2—42no—
655C2—44no—
656C2—242no—
657C2C3×#523814yesdirect product factor
658C2C2×C3×#94911yescharacteristic
659C2C2×C3×#95011yescharacteristic
660C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×#41C2
socleC23×C32C2×D4
hypercenterC22×C3×#41D3
hypocenterC3C2×C3×#449
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C32×#41C2semidirect
2. C22×C3×#215C2semidirect
3. C22×C3×#213C2semidirect
4. C2×C3×#930C2semidirect
5. C3×#5238C2direct (N × H)
6. C2×C3×#835C2semidirect
7. C2×C3×#832C2semidirect
8. C2×C3×#830C2semidirect
10. C2×#5238C3direct (N × H)
14. C2×C32×#41C22semidirect
23. C2×C3×#215C22semidirect
25. C2×C3×#213C22semidirect
27. C3×#930C22semidirect
32. C3×#835C22semidirect
33. C3×#832C22semidirect
34. C3×#830C22semidirect
36. C22×C3×#41D3semidirect
37. C22×C3×#41C2×C3semidirect
41. C22×#215C2×C3semidirect
42. C22×#213C2×C3semidirect
43. C2×#930C2×C3semidirect
48. #5238C2×C3direct (N × H)
49. C2×#835C2×C3semidirect
50. C2×#832C2×C3semidirect
51. C2×#830C2×C3semidirect
60. C2×C32×Q8D4semidirect
66. C2×C32×D4D4semidirect
104. C2×C3×#41C2×D3semidirect
105. C2×C3×#41C22×C3semidirect
136. C2×#215C22×C3semidirect
138. C2×#213C22×C3semidirect
140. #930C22×C3semidirect
148. #835C22×C3semidirect
149. #832C22×C3semidirect
150. #830C22×C3semidirect
166. C32×Q8C2×D4semidirect
170. C32×D4C2×D4semidirect
191. C22×#41C3×D3semidirect
224. C2×C3×Q8#67semidirect
225. C2×C3×Q8C3×D4semidirect
248. C2×C3×D4#67semidirect
249. C2×C3×D4C3×D4semidirect
330. C2×#41C2×C3×D3semidirect
393. C3×Q8C2×#67semidirect
394. C3×Q8C2×C3×D4semidirect
409. C3×D4C2×#67semidirect
410. C3×D4C2×C3×D4semidirect
461. C2×C32#449semidirect
474. C2×Q8C3×#67semidirect
486. C2×D4C3×#67semidirect
568. C32C2×#449semidirect
584. Q8C2×C3×#67semidirect
592. D4C2×C3×#67semidirect
620. C2×C3#5238direct (N × H)
621. C2×C3C3×#449semidirect
652. C3C2×#5238direct (N × H)
653. C3C2×C3×#449semidirect
657. C2C3×#5238direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×#412
C22×C3×#2152
C22×C3×#2132
C2×C3×#9302
C3×#52382
C2×C3×#8352
C2×C3×#8322
C2×C3×#8302
C2×C3×#4493
C2×#52383