Finite Group Databasebeta

← C3×Dic3×#137 #11860374

Subgroups — C3×Dic3×#137 #11860374

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic
2C3×Dic3×#41C211yesmaximal, characteristic
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic
5C3×#5225C211yesmaximal, characteristic, complemented
6C3×#5184C212yesmaximal, complemented
7C3×Dic3×Q16C212yesmaximal, complemented
8C3×#5164C212yesmaximal, complemented
9C3×Dic3×SD16C212yesmaximal, complemented
10C3×#5121C211yesmaximal, characteristic, complemented
11C3×Dic3×M16C211yesmaximal, characteristic, complemented
12C3×C4×#137—31nomaximal
13Dic3×#137C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×Q8C2211yescharacteristic
16C32×#137C418yescomplemented
17C2×C32×Q16C2212yes—
18C2×C32×SD16C2212yes—
19C2×C32×M16C2211yescharacteristic
20C3×Q8×Dic3—21no—
21C3×Q8×Dic3—21no—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2212yes—
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×D4×Dic3—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×#926—21no—
31C3×#926C2211yescharacteristic
32C2×C3×C4⋊Dic3—21no—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4×Dic3—21no—
35C2×C3×C4×Dic3—21no—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C3×#835C2212yes—
39C3×#835C2212yes—
40C3×#835C2212yes—
41C3×#832C2212yes—
42C3×#818C2212yes—
43C3×#817C2212yes—
44C3×#815C2212yes—
45C3×C8×Dic3C2212yes—
46C2×C3×#137—21no—
47C2×C3×#137D311yescharacteristic
48C2×C3×#137C2×C311yescharacteristic
49C3×C4×#41—31no—
50C2×C3×C4×Q8—31no—
51Dic3×#41C2×C311yescharacteristic
52C2×Q8×Dic3C2×C311yescharacteristic, complemented
53C3×#441—32no—
54C3×#440—32no—
55C3×C4×Q16—32no—
56C3×C4×SD16—32no—
57C3×#428—31no—
58C3×#419—31no—
59C3×#417—31no—
60C3×C4×M16—31no—
61#5232C2×C311yescharacteristic
62#5225C2×C311yescharacteristic, complemented
63#5184C2×C312yescomplemented
64Dic3×Q16C2×C312yescomplemented
65#5164C2×C312yescomplemented
66Dic3×SD16C2×C312yescomplemented
67#5121C2×C311yescharacteristic, complemented
68Dic3×M16C2×C311yescharacteristic, complemented
69C32×#41—22no—
70C32×#41C2×C414yes—
71C2×C32×Q8—21no—
72C2×C32×Q8—22no—
73C2×C32×Q8C2×C414yescomplemented
74C2×C32×Q8C2312yes—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3D411yescharacteristic
85C22×C3×Dic3D411yescharacteristic
86C32×Q16C2×C418yescomplemented
87C32×SD16C2×C418yescomplemented
88C32×M16C2×C414yescomplemented
89C2×C32×C8C2312yes—
90C3×#217—21no—
91C3×#217—21no—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4×Dic3—21no—
102C3×C4×Dic3—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3—22no—
105C3×C4×Dic3—22no—
106C3×C4×Dic3D411yescharacteristic
107C3×C4×Dic3D411yescharacteristic
108C3×C4×Dic3C2311yescharacteristic
109C3×C4×Dic3C2311yescharacteristic
110C3×#208—22no—
111C2×C3×C3⋊C8C2312yes—
112C4×#137—31noSylow
113C2×C3×#41—21no—
114C2×C3×#41C2×D311yescharacteristic
115C2×C3×#41C22×C311yescharacteristic
116C22×C3×Q8—21no—
117C22×C3×Q8C2×D311yescharacteristic
118C22×C3×Q8C22×C311yescharacteristic
119C3×#137—28no—
120C3×#137Dic318yesdirect product factor
121C3×#137C3×C418yescomplemented
122C2×C3×Q16—22no—
123C2×C3×Q16C2×D312yes—
124C2×C3×Q16C22×C312yes—
125C2×C3×SD16—22no—
126C2×C3×SD16C2×D312yes—
127C2×C3×SD16C22×C312yes—
128C2×C3×M16—21no—
129C2×C3×M16—31no—
130C2×C3×M16C2×D311yescharacteristic
131C2×C3×M16C22×C311yescharacteristic
132C3×C4×Q8—32no—
133C3×C4×Q8—31no—
134C3×C4×Q8—32no—
135C3×C4×Q8—31no—
136C3×C4×Q8—61no—
137C3×C4×Q8—61no—
138C3×C4×D4—31no—
139C3×C4×D4—31no—
140C3×C4×D4—61no—
141C3×C4×D4—61no—
142C3×#117—31no—
143C3×#117—61no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—61no—
146C2×C3×C42—31no—
147C2×C3×C42—61no—
148C2×C3×C42—61no—
149Q8×Dic3—21no—
150Q8×Dic3—21no—
151Q8×Dic3C22×C312yes—
152Q8×Dic3C22×C312yes—
153Q8×Dic3C22×C311yescharacteristic
154Q8×Dic3C22×C311yescharacteristic
155D4×Dic3—21no—
156D4×Dic3—21no—
157D4×Dic3C22×C311yescharacteristic
158D4×Dic3C22×C311yescharacteristic
159#926—21no—
160#926C22×C311yescharacteristic
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3C22×C311yescharacteristic
163C2×C4×Dic3—21no—
164C2×C4×Dic3—21no—
165C2×C4×Dic3C22×C311yescharacteristic
166C2×#208C22×C311yescharacteristic
167C3×#107—32no—
168C3×#106—32no—
169C3×#103—32no—
170C3×#103—32no—
171C3×#103—32no—
172C3×#102—32no—
173C3×#97—32no—
174C3×C4×C8—32no—
175#835C22×C312yes—
176#835C22×C312yes—
177#835C22×C312yes—
178#832C22×C312yes—
179#818C22×C312yes—
180#817C22×C312yes—
181#815C22×C312yes—
182C8×Dic3C22×C312yes—
183C23×C32—21no—
184C23×C32C2×D411yescharacteristic
185C32×Q8—24no—
186C32×Q8—22no—
187C32×Q8—21no—
188C32×Q8C22×C414yes—
189C32×Q8C22×C412yes—
190C32×D4—24no—
191C32×D4—21no—
192C32×D4C22×C412yes—
193C2×C32×C4—24no—
194C2×C32×C4—21no—
195C2×C32×C4—22no—
196C2×C32×C4—24no—
197C2×C32×C4C22×C412yes—
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4#4112yes—
200C2×C32×C4C2411yescharacteristic
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3—42no—
207C2×C3×Dic3—42no—
208C2×C3×Dic3—42no—
209C2×C3×Dic3C2×D411yescharacteristic
210C2×C3×Dic3C2×D411yescharacteristic
211C2×C3×Dic3C2×D411yescharacteristic
212C2×C3×Dic3C2×D411yescharacteristic
213C32×C8C22×C414yes—
214C3×C3⋊C8—22no—
215C2×#137C3×D311yescharacteristic
216C4×#41—31no—
217C2×C4×Q8—31no—
218#441—32no—
219#440—32no—
220C4×Q16—32no—
221C4×SD16—32no—
222#428—31no—
223#419—31no—
224#417—31no—
225C4×M16—31no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—24no—
229C3×#41—42no—
230C3×#41C2×Dic314yes—
231C3×#41C2×C3×C414yes—
232C2×C3×Q8—21no—
233C2×C3×Q8—22no—
234C2×C3×Q8—21no—
235C2×C3×Q8—22no—
236C2×C3×Q8—24no—
237C2×C3×Q8—22no—
238C2×C3×Q8—21no—
239C2×C3×Q8—41no—
240C2×C3×Q8—42no—
241C2×C3×Q8C2×Dic314yescomplemented
242C2×C3×Q8C2×C3×C414yescomplemented
243C2×C3×Q8C22×D312yes—
244C2×C3×Q8C22×D311yescharacteristic
245C2×C3×Q8C23×C312yes—
246C2×C3×Q8C23×C311yescharacteristic
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—41no—
251C2×C3×D4C22×D311yescharacteristic
252C2×C3×D4C23×C311yescharacteristic
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—41no—
261C22×C3×C4—41no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—61no—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C23×C311yescharacteristic
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3C3×D411yescharacteristic
271C22×Dic3C3×D411yescharacteristic
272C3×Q16—28no—
273C3×Q16C2×Dic318yescomplemented
274C3×Q16C2×C3×C418yescomplemented
275C3×SD16—28no—
276C3×SD16C2×Dic318yescomplemented
277C3×SD16C2×C3×C418yescomplemented
278C3×M16—24no—
279C3×M16—62no—
280C3×M16C2×Dic314yescomplemented
281C3×M16C2×C3×C414yescomplemented
282C2×C3×C8—22no—
283C2×C3×C8—32no—
284C2×C3×C8C22×D312yes—
285C2×C3×C8C23×C312yes—
286C3×C4⋊C4—32no—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—31no—
289C3×C4⋊C4—62no—
290C3×C4⋊C4—62no—
291C3×C4⋊C4—61no—
292C3×C4⋊C4—61no—
293C3×C4⋊C4—61no—
294C3×C22⋊C4—61no—
295C3×C22⋊C4—61no—
296C3×C22⋊C4—61no—
297C3×C42—31no—
298C3×C42—31no—
299C3×C42—31no—
300C3×C42—31no—
301C3×C42—61no—
302C3×C42—61no—
303C3×C42—62no—
304C3×C42—62no—
305C3×C42—61no—
306#217—21no—
307#217—21no—
308#217—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—22no—
311C4⋊Dic3—22no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C23×C311yescharacteristic
315C4⋊Dic3C23×C312yes—
316C4⋊Dic3C23×C311yescharacteristic
317C4×Dic3—21no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C4×Dic3—22no—
321C4×Dic3—22no—
322C4×Dic3C3×D411yescharacteristic
323C4×Dic3C3×D411yescharacteristic
324C4×Dic3C23×C311yescharacteristic
325C4×Dic3C23×C311yescharacteristic
326#208—22no—
327C2×C3⋊C8C23×C312yes—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—22no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32C4×D412yes—
334C22×C32C22×D411yescharacteristic
335C32×C4—22no—
336C32×C4—24no—
337C32×C4C4×D412yes—
338C32×C4C23×C411yescharacteristic
339C32×C4C2×#4111yescharacteristic
340C3×Dic3—21no—
341C3×Dic3—21no—
342C3×Dic3—21no—
343C3×Dic3—41no—
344C3×Dic3—42no—
345C3×Dic3—41no—
346C3×Dic3#13712yesdirect product factor
347C2×#41C2×C3×D311yescharacteristic
348C22×Q8C2×C3×D311yescharacteristic
349#137C3×Dic318yesdirect product factor
350C2×Q16C2×C3×D312yes—
351C2×SD16C2×C3×D312yes—
352C2×M16—31no—
353C2×M16C2×C3×D311yescharacteristic
354C4×Q8—32no—
355C4×Q8—32no—
356C4×Q8—31no—
357C4×Q8—31no—
358C4×Q8—61no—
359C4×Q8—61no—
360C4×D4—31no—
361C4×D4—31no—
362C4×D4—61no—
363C4×D4—61no—
364#117—31no—
365#117—61no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—61no—
368C2×C42—31no—
369C2×C42—61no—
370C2×C42—61no—
371#107—32no—
372#106—32no—
373#103—32no—
374#103—32no—
375#103—32no—
376#102—32no—
377#97—32no—
378C4×C8—32no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—41no—
383C23×C3D3×D411yescharacteristic
384C23×C3C2×C3×D411yescharacteristic
385C3×Q8—24no—
386C3×Q8—24no—
387C3×Q8—22no—
388C3×Q8—21no—
389C3×Q8—22no—
390C3×Q8—21no—
391C3×Q8—24no—
392C3×Q8—22no—
393C3×Q8—44no—
394C3×Q8—42no—
395C3×Q8—41no—
396C3×Q8C22×Dic314yes—
397C3×Q8C22×Dic312yes—
398C3×Q8C22×C3×C414yes—
399C3×Q8C22×C3×C412yes—
400C3×D4—24no—
401C3×D4—24no—
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—22no—
405C3×D4—41no—
406C3×D4—44no—
407C3×D4C22×Dic312yes—
408C3×D4C22×C3×C412yes—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—31no—
422C2×C3×C4—31no—
423C2×C3×C4—31no—
424C2×C3×C4—31no—
425C2×C3×C4—44no—
426C2×C3×C4—41no—
427C2×C3×C4—44no—
428C2×C3×C4—42no—
429C2×C3×C4—62no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—62no—
433C2×C3×C4—122no—
434C2×C3×C4—121no—
435C2×C3×C4—122no—
436C2×C3×C4—122no—
437C2×C3×C4D3×D411yescharacteristic
438C2×C3×C4#23712yes—
439C2×C3×C4C22×Dic312yes—
440C2×C3×C4C22×C3×C412yes—
441C2×C3×C4C2×C3×D411yescharacteristic
442C2×C3×C4C3×#4112yes—
443C2×C3×C4C23×D311yescharacteristic
444C2×C3×C4C24×C311yescharacteristic
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—41no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3C2×C3×D411yescharacteristic
454C2×Dic3C2×C3×D411yescharacteristic
455C2×Dic3C2×C3×D411yescharacteristic
456C2×Dic3C2×C3×D411yescharacteristic
457C3×C8—24no—
458C3×C8—62no—
459C3×C8C22×Dic314yes—
460C3×C8C22×C3×C414yes—
461C3⋊C8—22no—
462C2×C32—22no—
463C2×C32—42no—
464C2×C32C2×C4×D411yescharacteristic
465C2×C32C2×#13711yescharacteristic
466C2×C32#57511yescharacteristic
467#41—22no—
468#41C2×C3×Dic314yes—
469C2×Q8—21no—
470C2×Q8—22no—
471C2×Q8C2×C3×Dic314yescomplemented
472C2×Q8C22×C3×D312yes—
473C2×Q8C22×C3×D311yescharacteristic
474C2×D4—21no—
475C2×D4C22×C3×D311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4C22×C3×D311yescharacteristic
484Q16C2×C3×Dic318yescomplemented
485SD16C2×C3×Dic318yescomplemented
486M16—62no—
487M16C2×C3×Dic314yescomplemented
488C2×C8—32no—
489C2×C8C22×C3×D312yes—
490C4⋊C4—32no—
491C4⋊C4—31no—
492C4⋊C4—31no—
493C4⋊C4—62no—
494C4⋊C4—62no—
495C4⋊C4—61no—
496C4⋊C4—61no—
497C4⋊C4—61no—
498C22⋊C4—61no—
499C22⋊C4—61no—
500C22⋊C4—61no—
501C42—31no—
502C42—31no—
503C42—31no—
504C42—31no—
505C42—61no—
506C42—61no—
507C42—62no—
508C42—62no—
509C42—61no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—42no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3D4×Dic312yes—
528C22×C3C3×C4×D412yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×C3×D411yescharacteristic
531C3×C4—22no—
532C3×C4—24no—
533C3×C4—22no—
534C3×C4—24no—
535C3×C4—22no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—32no—
539C3×C4—42no—
540C3×C4—44no—
541C3×C4—61no—
542C3×C4—61no—
543C3×C4—61no—
544C3×C4—121no—
545C3×C4—121no—
546C3×C4—122no—
547C3×C4D4×Dic312yes—
548C3×C4C3×C4×D412yes—
549C3×C4C2×#23711yescharacteristic
550C3×C4C23×Dic311yescharacteristic
551C3×C4C23×C3×C411yescharacteristic
552C3×C4C2×C3×#4111yescharacteristic
553Dic3—21no—
554Dic3—21no—
555Dic3—21no—
556Dic3—41no—
557Dic3—42no—
558Dic3—41no—
559Dic3C3×#13712yesdirect product factor
560C32C4×#13711yescharacteristic, complemented, Sylow
561C23—21no—
562C23C3×D3×D411yescharacteristic
563Q8—24no—
564Q8—22no—
565Q8—21no—
566Q8C22×C3×Dic314yes—
567Q8C22×C3×Dic312yes—
568D4—24no—
569D4—21no—
570D4C22×C3×Dic312yes—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—31no—
578C2×C4—31no—
579C2×C4—62no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—122no—
584C2×C4—121no—
585C2×C4—122no—
586C2×C4—122no—
587C2×C4C3×D3×D411yescharacteristic
588C2×C4C3×#23712yes—
589C2×C4C22×C3×Dic312yes—
590C2×C4C23×C3×D311yescharacteristic
591C8—62no—
592C8C22×C3×Dic314yes—
593C2×C3—22no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—42no—
599C2×C3—42no—
600C2×C3—42no—
601C2×C3—82no—
602C2×C3D3×#13711yescharacteristic
603C2×C3#577711yescharacteristic
604C2×C3C2×D4×Dic311yescharacteristic
605C2×C3C2×C3×C4×D411yescharacteristic
606C2×C3C2×C3×#13711yescharacteristic
607C2×C3C3×#57511yescharacteristic
608C22—21no—
609C22—21no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22C3×D4×Dic312yes—
614C22C2×C3×D3×D411yescharacteristic
615C4—22no—
616C4—24no—
617C4—32no—
618C4—61no—
619C4—61no—
620C4—61no—
621C4—121no—
622C4—121no—
623C4—122no—
624C4C3×D4×Dic312yes—
625C4C2×C3×#23711yescharacteristic
626C4C23×C3×Dic311yescharacteristic
627C3—21no—
628C3Dic3×#13711yescharacteristic, direct product factor
629C3C3×C4×#13711yescharacteristic, complemented
630C2—22no—
631C2—42no—
632C2C3×D3×#13711yescharacteristic
633C2C3×#577711yescharacteristic
634C2C2×C3×D4×Dic311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#137D3
hypocenterC3C3×C4×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
3. C2×C3×Q8×Dic3C2semidirect
5. C3×#5225C2semidirect
6. C3×#5184C2semidirect
7. C3×Dic3×Q16C2semidirect
8. C3×#5164C2semidirect
9. C3×Dic3×SD16C2semidirect
10. C3×#5121C2semidirect
11. C3×Dic3×M16C2semidirect
13. Dic3×#137C3direct (N × H)
16. C32×#137C4semidirect
52. C2×Q8×Dic3C2×C3semidirect
62. #5225C2×C3semidirect
63. #5184C2×C3semidirect
64. Dic3×Q16C2×C3semidirect
65. #5164C2×C3semidirect
66. Dic3×SD16C2×C3semidirect
67. #5121C2×C3semidirect
68. Dic3×M16C2×C3semidirect
73. C2×C32×Q8C2×C4semidirect
86. C32×Q16C2×C4semidirect
87. C32×SD16C2×C4semidirect
88. C32×M16C2×C4semidirect
120. C3×#137Dic3direct (N × H)
121. C3×#137C3×C4semidirect
241. C2×C3×Q8C2×Dic3semidirect
242. C2×C3×Q8C2×C3×C4semidirect
273. C3×Q16C2×Dic3semidirect
274. C3×Q16C2×C3×C4semidirect
276. C3×SD16C2×Dic3semidirect
277. C3×SD16C2×C3×C4semidirect
280. C3×M16C2×Dic3semidirect
281. C3×M16C2×C3×C4semidirect
346. C3×Dic3#137direct (N × H)
349. #137C3×Dic3direct (N × H)
471. C2×Q8C2×C3×Dic3semidirect
484. Q16C2×C3×Dic3semidirect
485. SD16C2×C3×Dic3semidirect
487. M16C2×C3×Dic3semidirect
559. Dic3C3×#137direct (N × H)
560. C32C4×#137semidirect
628. C3Dic3×#137direct (N × H)
629. C3C3×C4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×Dic3×#412
C2×C3×Q8×Dic32
C3×#52322
C3×#52252
C3×#51842
C3×Dic3×Q162
C3×#51642
C3×Dic3×SD162
C3×#51212
C3×Dic3×M162
C3×C4×#1373
Dic3×#1373