Finite Group Databasebeta

← Dic3×#1004 #11900180

Subgroups — Dic3×#1004 #11900180

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2#10596269C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4#10595506C214yesmaximal, complemented
5C2×Dic3×#67C214yesmaximal, complemented
6#10595222C214yesmaximal, complemented
7#10595215C214yesmaximal, complemented
8Dic3×#237C214yesmaximal, complemented
9D3×D4×Dic3C214yesmaximal, complemented
10#10594986C212yesmaximal, complemented
11Dic3×#235C212yesmaximal, complemented
12Dic3×H(5,𝔽2)—31nomaximal
13C4×#1004—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2214yes—
16C23×C3×Dic3C2212yescomplemented
17C3×#1004C4116yescomplemented
18C2×C3×#237C2214yes—
19C2×C3×D3×D4C2214yes—
20C2×C3×#235C2212yes—
21C22×D3×Dic3C2214yescomplemented
22C2×#3757C2214yescomplemented
23D4×C3⋊Dic3C2214yescomplemented
24D4×C3⋊Dic3C2214yescomplemented
25#64135C2212yescomplemented
26C2×C3×#217C2212yescomplemented
27C3×D4×Dic3C2214yescomplemented
28C3×D4×Dic3C2214yescomplemented
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C3×C4×Dic3C2211yescharacteristic, complemented
31#67⋊Dic3C2218yescomplemented
32#67⋊Dic3C2218yescomplemented
33Dic3×#67C2218yescomplemented
34Dic3×#67C2214yescomplemented
35Dic3×#67C2214yescomplemented
36Dic3×#67C2218yescomplemented
37Dic3×#67C2218yescomplemented
38D3×#217C2218yescomplemented
39C2×Dic3⋊Dic3C2214yescomplemented
40C2×(C2×D3)⋊Dic3C2214yescomplemented
41#63955C2218yescomplemented
42C2×Dic32C2214yescomplemented
43#63898C2214yescomplemented
44Dic3×D12C2212yescomplemented
45Dic3×D12C2212yescomplemented
46D3×C4⋊Dic3C2214yescomplemented
47C4×D3×Dic3C2214yescomplemented
48#63855C2214yescomplemented
49#63843C2214yescomplemented
50Dic3×Dic6C2212yescomplemented
51Dic3×Dic6C2212yescomplemented
52#63841C2214yescomplemented
53C2×C3×H(5,𝔽2)—31no—
54C2×#1004D311yescharacteristic
55C2×C3×C4×D4—31no—
56#5827—34no—
57#5827—32no—
58Dic3×#41—34no—
59Dic3×#41—32no—
60#5798—31no—
61#5798—31no—
62#5798—34no—
63#5798—34no—
64#5798—61no—
65C2×D4×Dic3—34no—
66C2×D4×Dic3—34no—
67C2×D4×Dic3D311yescharacteristic, complemented
68C2×C4×#67—34no—
69#5546—34no—
70#5545—34no—
71C4×D3×D4—34no—
72C4×#237—34no—
73#5504—32no—
74#5486—34no—
75C4×#235—32no—
76C24×C32C2312yes—
77C23×C3×D3C2314yes—
78C2×C32×D4C2×C418yescomplemented
79C2×C32×D4C2314yes—
80C22×C32×C4C2311yescharacteristic
81C22×C3⋊Dic3C2314yes—
82C22×C3⋊Dic3C2314yes—
83C2×C3×#67C2×C4132yescomplemented
84C2×C3×#67C2314yes—
85C2×C3×#67C2318yes—
86C22×C3×Dic3—44no—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2314yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2314yes—
92C22×C3×Dic3C2314yes—
93C3×#237C2×C4132yescomplemented
94C3×D3×D4C2×C4132yescomplemented
95C3×#235C2×C4116yescomplemented
96C2×C3×D12C2312yes—
97C2×C3×C4×D3C2314yes—
98C2×C3×Dic6C2312yes—
99C2×D3×Dic3—48no—
100C2×D3×Dic3C2314yes—
101C2×D3×Dic3C2318yes—
102C2×D3×Dic3C2314yes—
103#3757C2314yes—
104#3757C2318yes—
105C4⋊(C3⋊Dic3)C2312yes—
106C4⋊(C3⋊Dic3)C2312yes—
107C4×C3⋊Dic3C2314yes—
108C3×#217C2318yes—
109C3×C4⋊Dic3C2314yes—
110C3×C4×Dic3C2312yes—
111C3×C4×Dic3C2312yes—
112Dic3⋊Dic3C2314yes—
113Dic3⋊Dic3C2314yes—
114Dic3⋊Dic3C2318yes—
115(C2×D3)⋊Dic3C2318yes—
116(C2×D3)⋊Dic3C2314yes—
117(C2×D3)⋊Dic3C2314yes—
118Dic32C2318yes—
119Dic32C2314yes—
120Dic32C2314yes—
121C4×H(5,𝔽2)—91noSylow
122C3×H(5,𝔽2)—316no—
123C2×C3×#41—34no—
124C2×C3×#41—32no—
125C22×C3×D4—21no—
126C22×C3×D4—34no—
127C22×C3×D4—34no—
128C22×C3×D4C2×D311yescharacteristic
129C22×C3×D4C2×D311yescharacteristic
130C23×C3×C4—32no—
131C22×#67C2×D314yes—
132C23×Dic3—34no—
133C23×Dic3C2×D312yescomplemented
134#1004Dic3116yesdirect product factor
135C2×#237C2×D314yes—
136C2×D3×D4C2×D314yes—
137C2×#235C2×D312yes—
138C22×C4×D3—34no—
139C3×C4×D4—34no—
140C3×C4×D4—34no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—32no—
143C2×C3×C42—31no—
144C2×#217—34no—
145C2×#217—34no—
146C2×#217—34no—
147C2×#217—38no—
148C2×#217—64no—
149C2×#217C2×D312yescomplemented
150Q8×Dic3—34no—
151Q8×Dic3—32no—
152Q8×Dic3—32no—
153D4×Dic3—34no—
154D4×Dic3—34no—
155D4×Dic3—34no—
156D4×Dic3—34no—
157D4×Dic3—38no—
158D4×Dic3—34no—
159D4×Dic3—38no—
160D4×Dic3—38no—
161D4×Dic3—34no—
162D4×Dic3—38no—
163D4×Dic3—38no—
164D4×Dic3—34no—
165D4×Dic3—32no—
166D4×Dic3—32no—
167D4×Dic3—64no—
168D4×Dic3—64no—
169D4×Dic3C2×D314yescomplemented
170D4×Dic3C2×D314yescomplemented
171C4×#67—34no—
172C4×#67—34no—
173C4×#67—38no—
174C4×#67—38no—
175C4×#67—38no—
176C2×(C2×D3)⋊C4—34no—
177#926—32no—
178#926—32no—
179#926—38no—
180#926—34no—
181#926—34no—
182#926—62no—
183C2×C4⋊Dic3—34no—
184C2×C4⋊Dic3—34no—
185C2×C4⋊Dic3C2×D311yescharacteristic, complemented
186C2×Dic3⋊C4—34no—
187C2×C4×Dic3—34no—
188C2×C4×Dic3—34no—
189C2×C4×Dic3—34no—
190C2×C4×Dic3C2×D311yescharacteristic, complemented
191#893—34no—
192#892—34no—
193D3×C4⋊C4—34no—
194#887—34no—
195#67⋊C4—38no—
196#67⋊C4—38no—
197D3×C22⋊C4—38no—
198#877—38no—
199C4×D12—32no—
200C4×D12—32no—
201#872—34no—
202C42×D3—34no—
203C4×Dic6—32no—
204C4×Dic6—32no—
205C23×C32—42no—
206C23×C32—42no—
207C23×C32C22×C418yescomplemented
208C23×C32C2414yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—44no—
211C22×C3×D3—44no—
212C22×C3×D3C22×C4116yescomplemented
213C22×C3×D3C2414yes—
214C32×D4C22×C4116yescomplemented
215C2×C32×C4C22×C414yescomplemented
216C2×C32×C4C2412yes—
217C2×C3⋊Dic3—44no—
218C2×C3⋊Dic3—44no—
219C2×C3⋊Dic3C2414yes—
220C2×C3⋊Dic3C2414yes—
221C3×#67C22×C4116yescomplemented
222C3×#67C22×C4132yescomplemented
223C2×C3×Dic3—28no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—42no—
226C2×C3×Dic3—44no—
227C2×C3×Dic3—41no—
228C2×C3×Dic3C22×C4116yescomplemented
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2411yescharacteristic
232C2×C3×Dic3C2414yes—
233C2×C3×Dic3C2411yescharacteristic
234C3×D12C22×C418yescomplemented
235C3×C4×D3C22×C4116yescomplemented
236C3×Dic6C22×C418yescomplemented
237D3×Dic3—28no—
238D3×Dic3—48no—
239D3×Dic3—44no—
240C2×H(5,𝔽2)—31no—
241#520—92no—
242#520—94no—
243#518—94no—
244#518—94no—
245#518—91no—
246C4×#41—92no—
247C4×#41—94no—
248C2×C4×D4—31no—
249C2×C4×D4—94no—
250C2×C4×D4—94no—
251C24×C3—22no—
252C24×C3—34no—
253C24×C3C22×D312yes—
254C24×C3C22×D312yes—
255C23×D3C22×D314yes—
256C3×#41—332no—
257C3×#41—316no—
258C2×C3×Q8—32no—
259C2×C3×D4—28no—
260C2×C3×D4—24no—
261C2×C3×D4—332no—
262C2×C3×D4—34no—
263C2×C3×D4—38no—
264C2×C3×D4—332no—
265C2×C3×D4—32no—
266C2×C3×D4C4×D318yescomplemented
267C2×C3×D4C2×Dic318yescomplemented
268C2×C3×D4C22×D314yes—
269C2×C3×D4C22×D314yes—
270C22×C3×C4—21no—
271C22×C3×C4—34no—
272C22×C3×C4—34no—
273C22×C3×C4—34no—
274C22×C3×C4—31no—
275C22×C3×C4—34no—
276C22×C3×C4—31no—
277C22×C3×C4—32no—
278C22×C3×C4—124no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C2×#67C2×Dic3132yescomplemented
282C2×#67C22×D318yes—
283C2×#67C22×D314yes—
284C22×Dic3—34no—
285C22×Dic3—34no—
286C22×Dic3—34no—
287C22×Dic3—34no—
288C22×Dic3—34no—
289C22×Dic3—34no—
290C22×Dic3—38no—
291C22×Dic3—44no—
292C22×Dic3—64no—
293C22×Dic3—64no—
294C22×Dic3—128no—
295C22×Dic3C22×D314yes—
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D314yes—
299C22×Dic3C22×D312yes—
300C22×Dic3C22×D314yes—
301#237C2×Dic3132yescomplemented
302D3×D4C2×Dic3132yescomplemented
303#235C2×Dic3116yescomplemented
304C2×D12C22×D312yes—
305C2×C4×D3—34no—
306C2×C4×D3—34no—
307C2×C4×D3—38no—
308C2×C4×D3—128no—
309C2×C4×D3C22×D314yes—
310C2×Dic6C22×D312yes—
311C3×C4⋊C4—34no—
312C3×C22⋊C4—38no—
313C3×C42—32no—
314C3×C42—32no—
315#217—38no—
316#217—34no—
317#217—34no—
318#217—38no—
319#217—38no—
320#217—34no—
321#217—34no—
322#217—64no—
323#217—68no—
324#217C22×D318yes—
325(C2×D3)⋊C4—34no—
326(C2×D3)⋊C4—34no—
327(C2×D3)⋊C4—38no—
328C4⋊Dic3—32no—
329C4⋊Dic3—32no—
330C4⋊Dic3—32no—
331C4⋊Dic3—32no—
332C4⋊Dic3—38no—
333C4⋊Dic3—34no—
334C4⋊Dic3—34no—
335C4⋊Dic3—62no—
336C4⋊Dic3—62no—
337C4⋊Dic3C22×D314yes—
338Dic3⋊C4—34no—
339Dic3⋊C4—34no—
340Dic3⋊C4—38no—
341C4×Dic3—34no—
342C4×Dic3—34no—
343C4×Dic3—34no—
344C4×Dic3—34no—
345C4×Dic3—38no—
346C4×Dic3—34no—
347C4×Dic3—38no—
348C4×Dic3—34no—
349C4×Dic3—64no—
350C4×Dic3C22×D312yes—
351C4×Dic3C22×D312yes—
352C22×C32—21no—
353C22×C32—24no—
354C22×C32—21no—
355C22×C32—24no—
356C22×C32—48no—
357C22×C32C23×C418yes—
358C22×C32C23×C412yes—
359C22×C32C2511yescharacteristic
360C2×C3×D3—24no—
361C2×C3×D3—24no—
362C2×C3×D3—416no—
363C2×C3×D3C23×C418yes—
364C32×C4C23×C414yes—
365C3⋊Dic3—24no—
366C3⋊Dic3—24no—
367C3×Dic3—24no—
368C3×Dic3—21no—
369C3×Dic3—22no—
370C3×Dic3C23×C418yes—
371C3×Dic3H(5,𝔽2)12yescomplemented
372H(5,𝔽2)—316no—
373C2×#41—34no—
374C2×#41—32no—
375C22×D4—34no—
376C22×D4—34no—
377C22×D4D3211yescharacteristic
378C23×C4—32no—
379C23×C4—94no—
380C4×Q8—92no—
381C4×Q8—92no—
382C4×Q8—94no—
383C4×D4—34no—
384C4×D4—34no—
385C4×D4—92no—
386C4×D4—92no—
387C4×D4—98no—
388C4×D4—98no—
389C4×D4—94no—
390C4×D4—94no—
391C4×D4—98no—
392C4×D4—98no—
393C4×D4—98no—
394C4×D4—94no—
395C4×D4—94no—
396C4×D4—94no—
397#117—94no—
398#117—98no—
399#117—94no—
400#117—92no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—94no—
403C2×C4⋊C4—94no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—98no—
406C2×C22⋊C4—94no—
407C2×C22⋊C4—94no—
408C2×C42—31no—
409C2×C42—94no—
410C2×C42—94no—
411C23×C3—21no—
412C23×C3—24no—
413C23×C3—28no—
414C23×C3—34no—
415C23×C3—316no—
416C23×C3—42no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—82no—
421C23×C3—82no—
422C23×C3—124no—
423C23×C3—124no—
424C23×C3C2×C4×D318yescomplemented
425C23×C3C22×Dic318yescomplemented
426C23×C3C23×D311yescharacteristic
427C23×C3C23×D314yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D314yes—
430C22×D3—44no—
431C22×D3—44no—
432C22×D3C22×Dic3116yescomplemented
433C22×D3C23×D314yes—
434C3×Q8—38no—
435C3×D4—216no—
436C3×D4—332no—
437C3×D4—316no—
438C3×D4—38no—
439C3×D4C2×C4×D3116yescomplemented
440C3×D4C22×Dic3116yescomplemented
441C2×C3×C4—22no—
442C2×C3×C4—24no—
443C2×C3×C4—316no—
444C2×C3×C4—34no—
445C2×C3×C4—31no—
446C2×C3×C4—316no—
447C2×C3×C4—32no—
448C2×C3×C4—34no—
449C2×C3×C4—31no—
450C2×C3×C4—68no—
451C2×C3×C4—62no—
452C2×C3×C4—121no—
453C2×C3×C4—122no—
454C2×C3×C4—124no—
455C2×C3×C4C2×C4×D314yescomplemented
456C2×C3×C4C22×Dic314yescomplemented
457C2×C3×C4C23×D312yes—
458C2×C3×C4C23×D312yes—
459#67C22×Dic3116yescomplemented
460#67C22×Dic3132yescomplemented
461C2×Dic3—22no—
462C2×Dic3—28no—
463C2×Dic3—34no—
464C2×Dic3—34no—
465C2×Dic3—34no—
466C2×Dic3—34no—
467C2×Dic3—44no—
468C2×Dic3—42no—
469C2×Dic3—41no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—68no—
473C2×Dic3—124no—
474C2×Dic3—128no—
475C2×Dic3—124no—
476C2×Dic3—124no—
477C2×Dic3—124no—
478C2×Dic3—124no—
479C2×Dic3—244no—
480C2×Dic3—244no—
481C2×Dic3C22×Dic3116yescomplemented
482C2×Dic3C23×D312yes—
483C2×Dic3C23×D314yes—
484C2×Dic3C23×D311yescharacteristic
485C2×Dic3C23×D311yescharacteristic
486C2×Dic3C23×D314yes—
487D12C22×Dic318yescomplemented
488C4×D3—68no—
489C4×D3—124no—
490C4×D3—128no—
491C4×D3C22×Dic3116yescomplemented
492Dic6C22×Dic318yescomplemented
493C2×C32—28no—
494C2×C32—22no—
495C2×C32C24×C411yescharacteristic
496C2×C32C2×H(5,𝔽2)11yescharacteristic
497C2×C32#58511yescharacteristic
498C3×D3—28no—
499C24—34no—
500C24C2×D3212yes—
501#41—332no—
502#41—316no—
503C2×Q8—32no—
504C2×D4—38no—
505C2×D4—34no—
506C2×D4—332no—
507C2×D4—332no—
508C2×D4—32no—
509C2×D4D3×Dic318yescomplemented
510C2×D4C2×D3214yes—
511C22×C4—34no—
512C22×C4—34no—
513C22×C4—31no—
514C22×C4—34no—
515C22×C4—31no—
516C22×C4—32no—
517C22×C4—34no—
518C22×C4—94no—
519C22×C4—94no—
520C22×C4—98no—
521C22×C4—94no—
522C22×C4—94no—
523C22×C4—124no—
524C22×C4—368no—
525C22×C4C2×D3211yescharacteristic
526C4⋊C4—34no—
527C4⋊C4—94no—
528C4⋊C4—98no—
529C4⋊C4—94no—
530C4⋊C4—92no—
531C4⋊C4—92no—
532C22⋊C4—38no—
533C22⋊C4—94no—
534C22⋊C4—94no—
535C22⋊C4—98no—
536C22⋊C4—98no—
537C22⋊C4—94no—
538C42—32no—
539C42—32no—
540C42—94no—
541C42—94no—
542C42—98no—
543C42—94no—
544C22×C3—21no—
545C22×C3—24no—
546C22×C3—21no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—21no—
550C22×C3—24no—
551C22×C3—21no—
552C22×C3—22no—
553C22×C3—28no—
554C22×C3—21no—
555C22×C3—38no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—48no—
561C22×C3—48no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—88no—
565C22×C3—1216no—
566C22×C3C22×C4×D318yes—
567C22×C3C22×C4×D312yes—
568C22×C3C23×Dic318yes—
569C22×C3C23×Dic312yes—
570C22×C3C24×D311yescharacteristic
571C22×C3C24×D311yescharacteristic
572C2×D3—24no—
573C2×D3—24no—
574C2×D3—416no—
575C2×D3C23×Dic318yes—
576C3×C4—24no—
577C3×C4—38no—
578C3×C4—32no—
579C3×C4—64no—
580C3×C4—61no—
581C3×C4—62no—
582C3×C4C22×C4×D314yes—
583C3×C4C23×Dic314yes—
584Dic3—21no—
585Dic3—24no—
586Dic3—22no—
587Dic3—64no—
588Dic3—64no—
589Dic3—64no—
590Dic3—64no—
591Dic3—124no—
592Dic3—124no—
593Dic3#100412yesdirect product factor
594Dic3C23×Dic318yes—
595C32C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
596C23—34no—
597C23—316no—
598C23—42no—
599C23—42no—
600C23—124no—
601C23—124no—
602C23C2×D3×Dic318yescomplemented
603C23C22×D3214yes—
604C23C22×D3211yescharacteristic
605Q8—38no—
606D4—332no—
607D4—316no—
608D4—38no—
609D4C2×D3×Dic3116yescomplemented
610C2×C4—316no—
611C2×C4—31no—
612C2×C4—34no—
613C2×C4—316no—
614C2×C4—32no—
615C2×C4—31no—
616C2×C4—34no—
617C2×C4—62no—
618C2×C4—68no—
619C2×C4—94no—
620C2×C4—94no—
621C2×C4—124no—
622C2×C4—122no—
623C2×C4—121no—
624C2×C4—188no—
625C2×C4—368no—
626C2×C4—364no—
627C2×C4—364no—
628C2×C4—364no—
629C2×C4C2×D3×Dic314yescomplemented
630C2×C4C22×D3212yes—
631C2×C3—28no—
632C2×C3—22no—
633C2×C3—22no—
634C2×C3—28no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—42no—
639C2×C3—48no—
640C2×C3—68no—
641C2×C3C23×C4×D311yescharacteristic
642C2×C3C2×#100411yescharacteristic
643C2×C3#596411yescharacteristic
644C2×C3D3×H(5,𝔽2)11yescharacteristic
645C2×C3#596611yescharacteristic
646C2×C3C24×Dic311yescharacteristic
647D3—28no—
648C22—21no—
649C22—24no—
650C22—21no—
651C22—24no—
652C22—38no—
653C22—48no—
654C22—64no—
655C22—64no—
656C22—1216no—
657C22C22×D3×Dic318yes—
658C22C22×D3×Dic312yes—
659C22C23×D3211yescharacteristic
660C4—32no—
661C4—38no—
662C4—61no—
663C4—64no—
664C4—62no—
665C4—184no—
666C4—184no—
667C4C22×D3×Dic314yes—
668C3—21no—
669C3C4×#100411yescharacteristic, complemented
670C3Dic3×H(5,𝔽2)11yescharacteristic, complemented
671C2—22no—
672C2—28no—
673C2—68no—
674C2D3×#100411yescharacteristic
675C2#1059667811yescharacteristic
676C2C23×D3×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC22×C32×D4C22
socle, cosocleC22×C32C25
prime radicalC2×C3×#1004C2
hypercenterC22×D4D32
hypocenterC32C4×H(5,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10596269C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. #10595506C2semidirect
5. C2×Dic3×#67C2semidirect
6. #10595222C2semidirect
7. #10595215C2semidirect
8. Dic3×#237C2semidirect
9. D3×D4×Dic3C2semidirect
10. #10594986C2semidirect
11. Dic3×#235C2semidirect
16. C23×C3×Dic3C22semidirect
17. C3×#1004C4semidirect
21. C22×D3×Dic3C22semidirect
22. C2×#3757C22semidirect
23. D4×C3⋊Dic3C22semidirect
24. D4×C3⋊Dic3C22semidirect
25. #64135C22semidirect
26. C2×C3×#217C22semidirect
27. C3×D4×Dic3C22semidirect
28. C3×D4×Dic3C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #67⋊Dic3C22semidirect
32. #67⋊Dic3C22semidirect
33. Dic3×#67C22semidirect
34. Dic3×#67C22semidirect
35. Dic3×#67C22semidirect
36. Dic3×#67C22semidirect
37. Dic3×#67C22semidirect
38. D3×#217C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. #63955C22semidirect
42. C2×Dic32C22semidirect
43. #63898C22semidirect
44. Dic3×D12C22semidirect
45. Dic3×D12C22semidirect
46. D3×C4⋊Dic3C22semidirect
47. C4×D3×Dic3C22semidirect
48. #63855C22semidirect
49. #63843C22semidirect
50. Dic3×Dic6C22semidirect
51. Dic3×Dic6C22semidirect
52. #63841C22semidirect
67. C2×D4×Dic3D3semidirect
78. C2×C32×D4C2×C4semidirect
83. C2×C3×#67C2×C4semidirect
93. C3×#237C2×C4semidirect
94. C3×D3×D4C2×C4semidirect
95. C3×#235C2×C4semidirect
133. C23×Dic3C2×D3semidirect
134. #1004Dic3direct (N × H)
149. C2×#217C2×D3semidirect
169. D4×Dic3C2×D3semidirect
170. D4×Dic3C2×D3semidirect
185. C2×C4⋊Dic3C2×D3semidirect
190. C2×C4×Dic3C2×D3semidirect
207. C23×C32C22×C4semidirect
212. C22×C3×D3C22×C4semidirect
214. C32×D4C22×C4semidirect
215. C2×C32×C4C22×C4semidirect
221. C3×#67C22×C4semidirect
222. C3×#67C22×C4semidirect
228. C2×C3×Dic3C22×C4semidirect
234. C3×D12C22×C4semidirect
235. C3×C4×D3C22×C4semidirect
236. C3×Dic6C22×C4semidirect
266. C2×C3×D4C4×D3semidirect
267. C2×C3×D4C2×Dic3semidirect
281. C2×#67C2×Dic3semidirect
301. #237C2×Dic3semidirect
302. D3×D4C2×Dic3semidirect
303. #235C2×Dic3semidirect
371. C3×Dic3H(5,𝔽2)semidirect
424. C23×C3C2×C4×D3semidirect
425. C23×C3C22×Dic3semidirect
432. C22×D3C22×Dic3semidirect
439. C3×D4C2×C4×D3semidirect
440. C3×D4C22×Dic3semidirect
455. C2×C3×C4C2×C4×D3semidirect
456. C2×C3×C4C22×Dic3semidirect
459. #67C22×Dic3semidirect
460. #67C22×Dic3semidirect
481. C2×Dic3C22×Dic3semidirect
487. D12C22×Dic3semidirect
491. C4×D3C22×Dic3semidirect
492. Dic6C22×Dic3semidirect
509. C2×D4D3×Dic3semidirect
593. Dic3#1004direct (N × H)
595. C32C4×H(5,𝔽2)semidirect
602. C23C2×D3×Dic3semidirect
609. D4C2×D3×Dic3semidirect
629. C2×C4C2×D3×Dic3semidirect
669. C3C4×#1004semidirect
670. C3Dic3×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
#105962692
C2×C3×D4×Dic32
#105955062
C2×Dic3×#672
#105952222
#105952152
Dic3×#2372
D3×D4×Dic32
#105949862
Dic3×#2352
Dic3×H(5,𝔽2)3
C4×#10043