Finite Group Databasebeta

← C2×#11723727 #13178797

Subgroups — C2×#11723727 #13178797

Order 1728.

3898 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×#638C211yesmaximal, characteristic, complemented
3C22×#6295C212yesmaximal, complemented
4C2×C3×#3757C211yesmaximal, characteristic, complemented
5#11723727C218yesmaximal, direct product factor
6C2×#88814C212yesmaximal, complemented
7C2×#63981—31nomaximal
8C2×#63977—31nomaximal
9C2×#63976—31nomaximal
10C24×C33C2211yescharacteristic
11C23×C3×C3⋊D3—24no—
12C23×C3×C3⋊D3—28no—
13C23×C3×C3⋊D3C2212yes—
14C23×C3×C3⋊D3C2214yescomplemented
15C23×C3×C3⋊D3C2211yescharacteristic, complemented
16C2×C3×#638—24no—
17C2×C3×#638C2214yescomplemented
18C22×C3×C3⋊Dic3C2212yescomplemented
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×#6295—28no—
21C2×#6295C2218yescomplemented
22C3×#3757C2214yescomplemented
23#88814C2218yescomplemented
24C24×C3⋊D3D311yescharacteristic, complemented
25C24×C3×D3—31no—
26C24×C3×D3—31no—
27C24×C3×D3—61no—
28C22×#638D311yescharacteristic, complemented
29C22×C3×#67—31no—
30C22×C3×#67—31no—
31C22×C3×#67—61no—
32C22×#626—32no—
33C22×#626—32no—
34C22×#625—32no—
35C2×#3757D311yescharacteristic, complemented
36C2×C3×#217—31no—
37C2×C3×#217—31no—
38C2×C3×#217—61no—
39#63981—38no—
40#63977—38no—
41#63976—38no—
42C2×#3722—32no—
43C2×(C2×D3)⋊Dic3—32no—
44C2×(C2×D3)⋊Dic3—32no—
45C23×C33—24no—
46C23×C33D414yescomplemented
47C23×C33C2312yes—
48C23×C33C2311yescharacteristic
49C22×C3×C3⋊D3—232no—
50C22×C3×C3⋊D3—24no—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—28no—
53C22×C3×C3⋊D3—216no—
54C22×C3×C3⋊D3—22no—
55C22×C3×C3⋊D3—24no—
56C22×C3×C3⋊D3D418yescomplemented
57C22×C3×C3⋊D3C2314yes—
58C22×C3×C3⋊D3C2312yescomplemented
59C3×#638—28no—
60C2×C3×C3⋊Dic3—22no—
61C2×C3×C3⋊Dic3—24no—
62C2×C3×C3⋊Dic3C2314yescomplemented
63C2×C3×C3⋊Dic3C2312yescomplemented
64#6295—216no—
65C2×#953—91no—
66C2×#937—91no—
67C2×#882—91no—
68C24×C32—21no—
69C24×C32—21no—
70C24×C32—21no—
71C24×C32—41no—
72C24×C32C2×D311yescharacteristic
73C24×C32C2×D311yescharacteristic
74C24×C32C2×D311yescharacteristic
75C23×C3⋊D3—24no—
76C23×C3⋊D3—28no—
77C23×C3⋊D3C2×D312yes—
78C23×C3⋊D3C2×D314yescomplemented
79C23×C3⋊D3C2×D311yescharacteristic, complemented
80C23×C3×D3—32no—
81C23×C3×D3—32no—
82C23×C3×D3—31no—
83C23×C3×D3—31no—
84C23×C3×D3—34no—
85C23×C3×D3—34no—
86C23×C3×D3—68no—
87C23×C3×D3—68no—
88C23×C3×D3—62no—
89C23×C3×D3—64no—
90C23×C3×D3—616no—
91C23×C3×D3—68no—
92C23×C3×D3—64no—
93C23×C3×D3—64no—
94C23×C3×D3—61no—
95C2×#638—24no—
96C2×#638C2×D314yescomplemented
97C22×C3⋊Dic3C2×D312yescomplemented
98C22×C3⋊Dic3C2×D311yescharacteristic, complemented
99C2×C3×#67—34no—
100C2×C3×#67—34no—
101C2×C3×#67—64no—
102C2×C3×#67—68no—
103C2×C3×#67—64no—
104C2×C3×#67—64no—
105C22×C3×Dic3—32no—
106C22×C3×Dic3—32no—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—61no—
110C22×C3×Dic3—62no—
111C2×#626—38no—
112C2×#626—38no—
113C2×#626—68no—
114C2×#626—68no—
115C2×#625—38no—
116C2×#625—68no—
117#3757C2×D314yescomplemented
118C3×#217—34no—
119C3×#217—34no—
120C3×#217—64no—
121#3722—38no—
122(C2×D3)⋊Dic3—38no—
123(C2×D3)⋊Dic3—38no—
124C22×C33—28no—
125C22×C33—24no—
126C22×C33C2×D412yes—
127C22×C33C2×D414yes—
128C22×C33C2×D414yescomplemented
129C22×C33C2411yescharacteristic
130C2×C3×C3⋊D3—232no—
131C2×C3×C3⋊D3—216no—
132C2×C3×C3⋊D3—24no—
133C2×C3×C3⋊D3—24no—
134C2×C3×C3⋊D3—22no—
135C2×C3×C3⋊D3—24no—
136C2×C3×C3⋊D3—44no—
137C2×C3×C3⋊D3C2×D418yescomplemented
138C3×C3⋊Dic3—22no—
139C3×C3⋊Dic3—24no—
140C25×C3—91no—
141C24×D3—31no—
142C24×D3—31no—
143C24×D3—61no—
144C22×C3×D4—91no—
145C22×#67—31no—
146C22×#67—31no—
147C22×#67—61no—
148C22×#67—92no—
149C22×#67—92no—
150C22×D12—92no—
151C2×C3×C22⋊C4—91no—
152#953—98no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—61no—
156C2×#217—92no—
157#937—98no—
158C2×(C2×D3)⋊C4—92no—
159C2×(C2×D3)⋊C4—92no—
160#882—98no—
161C23×C32—24no—
162C23×C32—28no—
163C23×C32—24no—
164C23×C32—24no—
165C23×C32—24no—
166C23×C32—24no—
167C23×C32—24no—
168C23×C32—22no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32—44no—
175C23×C32—42no—
176C23×C32—41no—
177C23×C32—44no—
178C23×C32—44no—
179C23×C32—48no—
180C23×C32D1214yescomplemented
181C23×C32#6714yescomplemented
182C23×C32#6714yescomplemented
183C23×C32C22×D312yes—
184C23×C32C22×D312yes—
185C23×C32C22×D312yes—
186C23×C32C22×D311yescharacteristic
187C23×C32C22×D311yescharacteristic
188C23×C32C22×D311yescharacteristic
189C22×C3⋊D3—232no—
190C22×C3⋊D3—24no—
191C22×C3⋊D3—24no—
192C22×C3⋊D3—28no—
193C22×C3⋊D3—216no—
194C22×C3⋊D3—22no—
195C22×C3⋊D3—24no—
196C22×C3⋊D3#6718yescomplemented
197C22×C3⋊D3C22×D314yes—
198C22×C3⋊D3C22×D312yescomplemented
199C22×C3×D3—38no—
200C22×C3×D3—38no—
201C22×C3×D3—34no—
202C22×C3×D3—34no—
203C22×C3×D3—32no—
204C22×C3×D3—32no—
205C22×C3×D3—68no—
206C22×C3×D3—64no—
207C22×C3×D3—62no—
208C22×C3×D3—616no—
209C22×C3×D3—616no—
210C22×C3×D3—632no—
211C22×C3×D3—664no—
212C22×C3×D3—632no—
213C22×C3×D3—632no—
214C22×C3×D3—68no—
215C22×C3×D3—616no—
216C22×C3×D3—68no—
217C22×C3×D3—64no—
218C22×C3×D3—68no—
219C22×C3×D3—64no—
220C22×C3×D3—64no—
221C22×C3×D3—64no—
222C22×C3×D3—68no—
223C22×C3×D3—64no—
224C22×C3×D3—62no—
225C22×C3×D3—64no—
226C22×C3×D3—64no—
227C22×C3×D3—62no—
228C22×C3×D3—124no—
229#638—28no—
230C2×C3⋊Dic3—22no—
231C2×C3⋊Dic3—24no—
232C2×C3⋊Dic3C22×D312yescomplemented
233C2×C3⋊Dic3C22×D314yescomplemented
234C3×#67—616no—
235C3×#67—68no—
236C3×#67—68no—
237C2×C3×Dic3—32no—
238C2×C3×Dic3—34no—
239C2×C3×Dic3—32no—
240C2×C3×Dic3—34no—
241C2×C3×Dic3—62no—
242C2×C3×Dic3—64no—
243C2×C3×Dic3—64no—
244C2×C3×Dic3—62no—
245C2×C3×Dic3—64no—
246C2×C3×Dic3—64no—
247C2×C3×Dic3—62no—
248C2×C3×Dic3—124no—
249#626—616no—
250#626—616no—
251#625—616no—
252C2×#120—271noSylow
253C2×C33—24no—
254C2×C33#12014yescomplemented
255C2×C33C22×D411yescharacteristic
256C2×C33C22×D412yes—
257C3×C3⋊D3—28no—
258C3×C3⋊D3—42no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—41no—
263C24×C3—92no—
264C24×C3—94no—
265C24×C3—91no—
266C24×C3—188no—
267C24×C3—184no—
268C24×C3D3211yescharacteristic
269C24×C3D3211yescharacteristic
270C24×C3D3211yescharacteristic
271C23×D3—32no—
272C23×D3—32no—
273C23×D3—34no—
274C23×D3—34no—
275C23×D3—31no—
276C23×D3—31no—
277C23×D3—62no—
278C23×D3—64no—
279C23×D3—61no—
280C23×D3—68no—
281C23×D3—68no—
282C23×D3—616no—
283C23×D3—68no—
284C23×D3—64no—
285C23×D3—64no—
286C2×C3×D4—94no—
287C2×C3×D4—184no—
288C22×C3×C4—91no—
289C22×C3×C4—92no—
290C2×#67—34no—
291C2×#67—34no—
292C2×#67—64no—
293C2×#67—68no—
294C2×#67—64no—
295C2×#67—64no—
296C2×#67—98no—
297C2×#67—98no—
298C2×#67—188no—
299C2×#67—188no—
300C22×Dic3—31no—
301C22×Dic3—32no—
302C22×Dic3—32no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—62no—
306C2×D12—98no—
307C2×D12—188no—
308C3×C22⋊C4—94no—
309#217—34no—
310#217—34no—
311#217—64no—
312#217—98no—
313(C2×D3)⋊C4—98no—
314(C2×D3)⋊C4—98no—
315C22×C32—28no—
316C22×C32—24no—
317C22×C32—28no—
318C22×C32—216no—
319C22×C32—28no—
320C22×C32—28no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—24no—
334C22×C32—24no—
335C22×C32—42no—
336C22×C32—44no—
337C22×C32—44no—
338C22×C32—41no—
339C22×C32—44no—
340C22×C32—44no—
341C22×C32—48no—
342C22×C32—48no—
343C22×C32—416no—
344C22×C32—48no—
345C22×C32C2×D1212yes—
346C22×C32C2×D1214yescomplemented
347C22×C32D3×D414yes—
348C22×C32D3×D414yes—
349C22×C32C2×#6712yes—
350C22×C32C2×#6712yes—
351C22×C32C2×#6714yes—
352C22×C32C2×#6714yescomplemented
353C22×C32C2×#6714yescomplemented
354C22×C32C23×D311yescharacteristic
355C22×C32C23×D311yescharacteristic
356C22×C32C23×D311yescharacteristic
357C2×C3⋊D3—232no—
358C2×C3⋊D3—216no—
359C2×C3⋊D3—24no—
360C2×C3⋊D3—24no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—24no—
363C2×C3⋊D3—44no—
364C2×C3⋊D3C2×#6718yescomplemented
365C2×C3×D3—38no—
366C2×C3×D3—38no—
367C2×C3×D3—68no—
368C2×C3×D3—664no—
369C2×C3×D3—632no—
370C2×C3×D3—632no—
371C2×C3×D3—68no—
372C2×C3×D3—68no—
373C2×C3×D3—632no—
374C2×C3×D3—616no—
375C2×C3×D3—616no—
376C2×C3×D3—64no—
377C2×C3×D3—64no—
378C2×C3×D3—64no—
379C2×C3×D3—64no—
380C2×C3×D3—64no—
381C2×C3×D3—62no—
382C2×C3×D3—64no—
383C2×C3×D3—64no—
384C2×C3×D3—62no—
385C2×C3×D3—124no—
386C2×C3×D3—128no—
387C2×C3×D3—124no—
388C2×C3×D3—124no—
389C3⋊Dic3—22no—
390C3⋊Dic3—24no—
391C3×Dic3—64no—
392C3×Dic3—62no—
393C3×Dic3—64no—
394C3×Dic3—64no—
395C3×Dic3—62no—
396C3×Dic3—124no—
397C25—91no—
398C22×D4—91no—
399C22×D4—272no—
400#120—278no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4—272no—
403C33C2×#12011yescharacteristic, complemented, Sylow
404C23×C3—28no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—44no—
418C23×C3—44no—
419C23×C3—48no—
420C23×C3—44no—
421C23×C3—42no—
422C23×C3—41no—
423C23×C3—94no—
424C23×C3—98no—
425C23×C3—92no—
426C23×C3—1816no—
427C23×C3—1832no—
428C23×C3—184no—
429C23×C3—188no—
430C23×C3—184no—
431C23×C3—182no—
432C23×C3—184no—
433C23×C3#62514yescomplemented
434C23×C3#62614yescomplemented
435C23×C3#62614yescomplemented
436C23×C3C2×D3212yes—
437C23×C3C2×D3212yes—
438C23×C3C2×D3212yes—
439C23×C3C2×D3211yescharacteristic
440C23×C3C2×D3211yescharacteristic
441C23×C3C2×D3211yescharacteristic
442C22×D3—34no—
443C22×D3—34no—
444C22×D3—38no—
445C22×D3—38no—
446C22×D3—32no—
447C22×D3—32no—
448C22×D3—68no—
449C22×D3—64no—
450C22×D3—62no—
451C22×D3—616no—
452C22×D3—616no—
453C22×D3—632no—
454C22×D3—664no—
455C22×D3—632no—
456C22×D3—632no—
457C22×D3—68no—
458C22×D3—616no—
459C22×D3—68no—
460C22×D3—64no—
461C22×D3—68no—
462C22×D3—64no—
463C22×D3—68no—
464C22×D3—64no—
465C22×D3—64no—
466C22×D3—64no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—124no—
472C3×D4—188no—
473C2×C3×C4—92no—
474C2×C3×C4—94no—
475C2×C3×C4—182no—
476C2×C3×C4—184no—
477#67—616no—
478#67—68no—
479#67—68no—
480#67—1816no—
481#67—1816no—
482C2×Dic3—32no—
483C2×Dic3—34no—
484C2×Dic3—34no—
485C2×Dic3—32no—
486C2×Dic3—62no—
487C2×Dic3—64no—
488C2×Dic3—64no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—64no—
492C2×Dic3—64no—
493C2×Dic3—124no—
494D12—1816no—
495C2×C32—24no—
496C2×C32—28no—
497C2×C32—24no—
498C2×C32—24no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—22no—
503C2×C32—22no—
504C2×C32—22no—
505C2×C32—24no—
506C2×C32—24no—
507C2×C32—24no—
508C2×C32—44no—
509C2×C32—41no—
510C2×C32—42no—
511C2×C32—44no—
512C2×C32—44no—
513C2×C32—48no—
514C2×C32#88214yescomplemented
515C2×C32#93714yescomplemented
516C2×C32#95314yescomplemented
517C2×C32C22×D1211yescharacteristic
518C2×C32C2×D3×D412yes—
519C2×C32C2×D3×D412yes—
520C2×C32C22×#6711yescharacteristic
521C2×C32C22×#6711yescharacteristic
522C2×C32C22×#6712yes—
523C3⋊D3—28no—
524C3⋊D3—42no—
525C3×D3—616no—
526C3×D3—68no—
527C3×D3—68no—
528C3×D3—124no—
529C3×D3—122no—
530C3×D3—122no—
531C24—92no—
532C24—94no—
533C24—91no—
534C24—188no—
535C24—184no—
536C24#111311yescharacteristic
537C2×D4—94no—
538C2×D4—184no—
539C2×D4—278no—
540C2×D4—548no—
541C22×C4—92no—
542C22×C4—91no—
543C22⋊C4—94no—
544C22⋊C4—278no—
545C22×C3—28no—
546C22×C3—216no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—28no—
551C22×C3—28no—
552C22×C3—28no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—48no—
568C22×C3—48no—
569C22×C3—48no—
570C22×C3—416no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—98no—
576C22×C3—1832no—
577C22×C3—184no—
578C22×C3—184no—
579C22×C3—1816no—
580C22×C3—182no—
581C22×C3—184no—
582C22×C3—364no—
583C22×C3C2×#62512yes—
584C22×C3C2×#62514yescomplemented
585C22×C3C2×#62612yes—
586C22×C3C2×#62612yes—
587C22×C3C2×#62614yescomplemented
588C22×C3C2×#62614yescomplemented
589C22×C3D3×#6714yes—
590C22×C3D3×#6714yes—
591C22×C3#381114yes—
592C22×C3C22×D3211yescharacteristic
593C22×C3C22×D3211yescharacteristic
594C22×C3C22×D3211yescharacteristic
595C2×D3—38no—
596C2×D3—38no—
597C2×D3—68no—
598C2×D3—664no—
599C2×D3—632no—
600C2×D3—632no—
601C2×D3—68no—
602C2×D3—68no—
603C2×D3—632no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—616no—
609C2×D3—616no—
610C2×D3—64no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—64no—
614C2×D3—64no—
615C2×D3—124no—
616C2×D3—128no—
617C2×D3—124no—
618C2×D3—124no—
619C3×C4—182no—
620C3×C4—184no—
621Dic3—64no—
622Dic3—62no—
623Dic3—62no—
624Dic3—64no—
625Dic3—64no—
626Dic3—124no—
627C32—21no—
628C32—21no—
629C32—21no—
630C32—41no—
631C32C2×#88211yescharacteristic, complemented
632C32C2×#93711yescharacteristic, complemented
633C32C2×#95311yescharacteristic, complemented
634C23—24no—
635C23—94no—
636C23—98no—
637C23—92no—
638C23—1816no—
639C23—1832no—
640C23—184no—
641C23—188no—
642C23—184no—
643C23—182no—
644C23—184no—
645C23#629514yescomplemented
646C23C2×#111312yes—
647C23C2×#111311yescharacteristic
648D4—188no—
649D4—5416no—
650C2×C4—94no—
651C2×C4—92no—
652C2×C4—182no—
653C2×C4—184no—
654C2×C3—28no—
655C2×C3—24no—
656C2×C3—24no—
657C2×C3—24no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—22no—
664C2×C3—24no—
665C2×C3—24no—
666C2×C3—24no—
667C2×C3—44no—
668C2×C3—44no—
669C2×C3—48no—
670C2×C3—41no—
671C2×C3—42no—
672C2×C3—44no—
673C2×C3—188no—
674C2×C3—362no—
675C2×C3#6397614yescomplemented
676C2×C3#6397714yescomplemented
677C2×C3#6398114yescomplemented
678C2×C3C22×#62511yescharacteristic
679C2×C3C22×#62611yescharacteristic
680C2×C3C22×#62611yescharacteristic
681C2×C3C2×D3×#6712yes—
682C2×C3C2×D3×#6712yes—
683C2×C3C2×#381112yes—
684D3—616no—
685D3—68no—
686D3—68no—
687D3—124no—
688D3—122no—
689D3—122no—
690C22—24no—
691C22—28no—
692C22—98no—
693C22—1832no—
694C22—184no—
695C22—184no—
696C22—1816no—
697C22—182no—
698C22—184no—
699C22—364no—
700C22C2×#629512yes—
701C22C2×#629514yescomplemented
702C22#8904914yes—
703C22C22×#111311yescharacteristic
704C4—182no—
705C4—184no—
706C3—21no—
707C3—21no—
708C3—21no—
709C3—41no—
710C3C2×#6397611yescharacteristic, complemented
711C3C2×#6397711yescharacteristic, complemented
712C3C2×#6398111yescharacteristic, complemented
713C2—24no—
714C2—188no—
715C2—362no—
716C2#1172372714yesdirect product factor
717C2C22×#629511yescharacteristic
718C2C2×#8904912yes—
subgroupG/H
centerC23C2×#1113
commutator, cosocleC22×C33C24
FrattiniC22C22×#1113
FittingC24×C33C22
socleC23×C33C23
hypercenterC24#1113
hypocenterC33C2×#120
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C24×C3×C3⋊D3C2semidirect
2. C22×C3×#638C2semidirect
3. C22×#6295C2semidirect
4. C2×C3×#3757C2semidirect
5. #11723727C2direct (N × H)
6. C2×#88814C2semidirect
14. C23×C3×C3⋊D3C22semidirect
15. C23×C3×C3⋊D3C22semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
21. C2×#6295C22semidirect
22. C3×#3757C22semidirect
23. #88814C22semidirect
24. C24×C3⋊D3D3semidirect
28. C22×#638D3semidirect
35. C2×#3757D3semidirect
46. C23×C33D4semidirect
56. C22×C3×C3⋊D3D4semidirect
58. C22×C3×C3⋊D3C23semidirect
62. C2×C3×C3⋊Dic3C23semidirect
63. C2×C3×C3⋊Dic3C23semidirect
78. C23×C3⋊D3C2×D3semidirect
79. C23×C3⋊D3C2×D3semidirect
96. C2×#638C2×D3semidirect
97. C22×C3⋊Dic3C2×D3semidirect
98. C22×C3⋊Dic3C2×D3semidirect
117. #3757C2×D3semidirect
128. C22×C33C2×D4semidirect
137. C2×C3×C3⋊D3C2×D4semidirect
180. C23×C32D12semidirect
181. C23×C32#67semidirect
182. C23×C32#67semidirect
196. C22×C3⋊D3#67semidirect
198. C22×C3⋊D3C22×D3semidirect
232. C2×C3⋊Dic3C22×D3semidirect
233. C2×C3⋊Dic3C22×D3semidirect
254. C2×C33#120semidirect
346. C22×C32C2×D12semidirect
352. C22×C32C2×#67semidirect
353. C22×C32C2×#67semidirect
364. C2×C3⋊D3C2×#67semidirect
403. C33C2×#120semidirect
433. C23×C3#625semidirect
434. C23×C3#626semidirect
435. C23×C3#626semidirect
514. C2×C32#882semidirect
515. C2×C32#937semidirect
516. C2×C32#953semidirect
584. C22×C3C2×#625semidirect
587. C22×C3C2×#626semidirect
588. C22×C3C2×#626semidirect
631. C32C2×#882semidirect
632. C32C2×#937semidirect
633. C32C2×#953semidirect
645. C23#6295semidirect
675. C2×C3#63976semidirect
676. C2×C3#63977semidirect
677. C2×C3#63981semidirect
701. C22C2×#6295semidirect
710. C3C2×#63976semidirect
711. C3C2×#63977semidirect
712. C3C2×#63981semidirect
716. C2#11723727direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C3⋊D32
C22×C3×#6382
C22×#62952
C2×C3×#37572
#117237272
C2×#888142
C2×#639813
C2×#639773
C2×#639763