Finite Group Databasebeta

← C4×#88677 #13150870

Subgroups — C4×#88677 #13150870

Order 1728.

1727 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#272C211yesmaximal, characteristic, complemented
2C2×#88677C211yesmaximal, characteristic
3C2×C4×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
4C4×#638⋊C3C212yesmaximal, complemented
5#11721320C211yesmaximal, characteristic, complemented
6#11721315C212yesmaximal, complemented
7#11721161C211yesmaximal, characteristic, complemented
8C4×#6200C212yesmaximal, complemented
9#11721147C211yesmaximal, characteristic, complemented
10C4×#6199C211yesmaximal, characteristic, complemented
11#11721124C212yesmaximal, complemented
12C4×D3×#67—32nomaximal
13C23×#272C2211yescharacteristic
14C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
16C22×#1084C2211yescharacteristic, complemented
17C2×C4×#272—24no—
18C2×C4×#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic, complemented
21C2×C4×#272C2211yescharacteristic, complemented
22C2×#638⋊C3C2212yes—
23C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
24#88677C418yesdirect product factor
25C2×#6200C2212yes—
26C2×#6199C2211yescharacteristic
27C2×#6199C2211yescharacteristic
28C2×#6199C2211yescharacteristic
29C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
30C4×((C3⋊D3)⋊C3)⋊C2—24no—
31#3757⋊C3C2212yescomplemented
32#3752⋊C3C2212yescomplemented
33#3750⋊C3C2212yescomplemented
34C4×(C3⋊Dic3)⋊C3C2212yescomplemented
35#88451C2212yescomplemented
36#88450C2212yescomplemented
37#88448C2212yescomplemented
38#88447C2212yescomplemented
39C22×C3×C4×D3—32no—
40C22×C3×C4×D3—61no—
41C2×D3×#67—32no—
42C2×C4×D32—32no—
43C4×#638D312yescomplemented
44C3×C4×#67—32no—
45Dic3×#67—32no—
46D3×#217—32no—
47#63952—32no—
48D3×(C2×D3)⋊C4—32no—
49#63904—32no—
50C4×#626—32no—
51C4×#625—32no—
52#63879—32no—
53D3×Dic3⋊C4—32no—
54C4×D3×Dic3—32no—
55C23×H(3,𝔽3)C2311yescharacteristic
56C22×#272—22no—
57C22×#272—22no—
58C22×#272C2×C414yescomplemented
59C22×#272C2311yescharacteristic
60C22×#272C2311yescharacteristic
61C22×(C3⋊D3)⋊C3C2312yes—
62C2×((C3⋊D3)⋊C3)⋊C2—22no—
63C2×((C3⋊D3)⋊C3)⋊C2—22no—
64C2×((C3⋊D3)⋊C3)⋊C2C2×C414yescomplemented
65C2×C4×H(3,𝔽3)—22no—
66C2×C4×H(3,𝔽3)C2311yescharacteristic
67C2×C4×H(3,𝔽3)C2311yescharacteristic
68C2×#1084—22no—
69C2×#1084C2311yescharacteristic
70C2×#1084C2311yescharacteristic
71C4×#272—22no—
72C4×#272—22no—
73C4×#272—22no—
74C4×#272D414yescomplemented
75#638⋊C3C2×C418yescomplemented
76C2×(C3⋊Dic3)⋊C3C2312yes—
77C2×(C3⋊Dic3)⋊C3C2312yes—
78C2×(C3⋊Dic3)⋊C3C2312yes—
79C4×(C3⋊D3)⋊C3—24no—
80#6200C2×C418yescomplemented
81#6199—22no—
82#6199—22no—
83#6199C2×C414yescomplemented
84((C3⋊D3)⋊C3)⋊C4—24no—
85C2×C4×#67—91no—
86C4×D3×D4—92no—
87C23×C3×D3—32no—
88C23×C3×D3—61no—
89C22×D32—32no—
90C22×C32×C4—21no—
91C22×C32×C4C2×D312yescomplemented
92C2×#638C2×D312yes—
93C2×C4×C3⋊D3C2×D312yescomplemented
94C2×C3×#67—32no—
95C22×C3×Dic3—32no—
96C22×C3×Dic3—61no—
97C2×C3×C4×D3—32no—
98C2×C3×C4×D3—32no—
99C2×C3×C4×D3—32no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—68no—
103C2×C3×C4×D3—61no—
104C2×C3×C4×D3—61no—
105C2×C3×C4×D3—61no—
106C2×C3×C4×D3—61no—
107C2×C3×C4×D3—68no—
108D3×#67—316no—
109C2×#626—32no—
110C2×#625—32no—
111C2×#624—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114C2×D3×Dic3—32no—
115C2×D3×Dic3—32no—
116C4×D32—68no—
117#3757C2×D312yescomplemented
118#3752C2×D312yescomplemented
119#3750C2×D312yescomplemented
120C4×C3⋊Dic3C2×D312yescomplemented
121C3×#217—32no—
122C3×(C2×D3)⋊C4—32no—
123C3×Dic3⋊C4—32no—
124C3×C4×Dic3—32no—
125#3724—32no—
126Dic3⋊Dic3—32no—
127#3722—32no—
128(C2×D3)⋊Dic3—32no—
129(C2×D3)⋊Dic3—32no—
130(C2×D3)⋊Dic3—32no—
131Dic32—32no—
132Dic32—32no—
133C22×H(3,𝔽3)—21no—
134C22×H(3,𝔽3)—21no—
135C22×H(3,𝔽3)C22×C412yescomplemented
136C22×H(3,𝔽3)C2411yescharacteristic
137C2×#272—21no—
138C2×#272—21no—
139C2×#272—28no—
140C2×#272C22×C412yes—
141C2×#272C22×C412yescomplemented
142C2×#272C2×D412yes—
143C2×#272#4112yes—
144C2×(C3⋊D3)⋊C3—22no—
145C2×(C3⋊D3)⋊C3—22no—
146C2×(C3⋊D3)⋊C3C22×C414yescomplemented
147((C3⋊D3)⋊C3)⋊C2—28no—
148C4×H(3,𝔽3)—21no—
149C4×H(3,𝔽3)C2×D412yescomplemented
150#1084—21no—
151#1084C2×D412yescomplemented
152(C3⋊Dic3)⋊C3—22no—
153(C3⋊Dic3)⋊C3—22no—
154(C3⋊Dic3)⋊C3C22×C414yescomplemented
155C23×C3×C4—91no—
156C22×#67—91no—
157C2×D3×D4—92no—
158C22×C4×D3—32no—
159C22×C4×D3—61no—
160C22×C4×D3—91no—
161C22×C4×D3—92no—
162C3×C4×D4—92no—
163C2×#217—91no—
164D4×Dic3—92no—
165C4×#67—32no—
166C4×#67—92no—
167C4×#67—92no—
168C4×#67—92no—
169C4×#67—92no—
170C4×#67—92no—
171C2×(C2×D3)⋊C4—91no—
172C2×Dic3⋊C4—91no—
173C2×C4×Dic3—91no—
174#893—92no—
175D3×C4⋊C4—92no—
176#67⋊C4—92no—
177#67⋊C4—92no—
178D3×C22⋊C4—92no—
179D3×C22⋊C4—92no—
180C4×D12—92no—
181C42×D3—92no—
182C23×C32—21no—
183C23×C32C22×D312yes—
184C22×C3⋊D3C22×D312yes—
185C22×C3×D3—32no—
186C22×C3×D3—38no—
187C22×C3×D3—32no—
188C22×C3×D3—32no—
189C22×C3×D3—64no—
190C22×C3×D3—61no—
191C22×C3×D3—61no—
192C22×C3×D3—64no—
193C22×C3×D3—64no—
194C22×C3×D3—64no—
195C22×C3×D3—64no—
196C2×D32—38no—
197C2×D32—64no—
198C2×D32—64no—
199C2×C32×C4—24no—
200C2×C32×C4—24no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4C22×D312yes—
204C2×C32×C4C22×D312yes—
205#638C4×D318yescomplemented
206C2×C3⋊Dic3C22×D312yes—
207C2×C3⋊Dic3C22×D312yes—
208C2×C3⋊Dic3C22×D312yes—
209C4×C3⋊D3—24no—
210C3×#67—38no—
211C2×C3×Dic3—32no—
212C2×C3×Dic3—32no—
213C2×C3×Dic3—32no—
214C2×C3×Dic3—32no—
215C2×C3×Dic3—32no—
216C2×C3×Dic3—61no—
217C2×C3×Dic3—61no—
218C2×C3×Dic3—64no—
219C2×C3×Dic3—64no—
220C3×C4×D3—38no—
221C3×C4×D3—64no—
222C3×C4×D3—64no—
223C3×C4×D3—64no—
224C3×C4×D3—64no—
225C3×C4×D3—64no—
226C3×C4×D3—64no—
227C3×C4×D3—64no—
228C3×C4×D3—64no—
229#626—38no—
230#625—38no—
231#624—64no—
232D3×Dic3—38no—
233D3×Dic3—64no—
234D3×Dic3—64no—
235D3×Dic3—64no—
236C2×C4×D4—271noSylow
237C2×H(3,𝔽3)—22no—
238C2×H(3,𝔽3)C23×C411yescharacteristic
239C2×H(3,𝔽3)C22×D411yescharacteristic
240C2×H(3,𝔽3)C2×#4111yescharacteristic
241#272—22no—
242#272C4×D414yescomplemented
243(C3⋊D3)⋊C3—24no—
244C24×C3—91no—
245C23×D3—32no—
246C23×D3—61no—
247C23×D3—91no—
248C23×D3—92no—
249C2×C3×D4—92no—
250C22×C3×C4—32no—
251C22×C3×C4—61no—
252C22×C3×C4—92no—
253C22×C3×C4—91no—
254C22×C3×C4—91no—
255C22×C3×C4—91no—
256C22×C3×C4—91no—
257C22×C3×C4—91no—
258C22×C3×C4—184no—
259C22×C3×C4D3211yescharacteristic
260C2×#67—32no—
261C2×#67—92no—
262C2×#67—92no—
263C2×#67—98no—
264C2×#67—92no—
265C22×Dic3—32no—
266C22×Dic3—61no—
267C22×Dic3—91no—
268C22×Dic3—91no—
269C22×Dic3—91no—
270C22×Dic3—92no—
271D3×D4—916no—
272C2×D12—92no—
273C2×C4×D3—32no—
274C2×C4×D3—32no—
275C2×C4×D3—32no—
276C2×C4×D3—32no—
277C2×C4×D3—32no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×C4×D3—61no—
281C2×C4×D3—61no—
282C2×C4×D3—68no—
283C2×C4×D3—68no—
284C2×C4×D3—92no—
285C2×C4×D3—92no—
286C2×C4×D3—92no—
287C2×C4×D3—92no—
288C2×C4×D3—92no—
289C2×C4×D3—92no—
290C2×C4×D3—188no—
291C2×C4×D3—184no—
292C3×C4⋊C4—92no—
293C3×C22⋊C4—92no—
294C3×C22⋊C4—92no—
295C3×C42—92no—
296#217—32no—
297#217—92no—
298#217—92no—
299#217—92no—
300(C2×D3)⋊C4—32no—
301(C2×D3)⋊C4—92no—
302(C2×D3)⋊C4—92no—
303(C2×D3)⋊C4—92no—
304(C2×D3)⋊C4—92no—
305(C2×D3)⋊C4—92no—
306C4⋊Dic3—92no—
307Dic3⋊C4—32no—
308Dic3⋊C4—92no—
309Dic3⋊C4—92no—
310Dic3⋊C4—92no—
311C4×Dic3—32no—
312C4×Dic3—92no—
313C4×Dic3—92no—
314C4×Dic3—92no—
315C4×Dic3—92no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—21no—
321C22×C32—22no—
322C22×C32C2×C4×D314yescomplemented
323C22×C32C23×D312yes—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3C2×C4×D314yescomplemented
327C2×C3×D3—34no—
328C2×C3×D3—34no—
329C2×C3×D3—34no—
330C2×C3×D3—34no—
331C2×C3×D3—34no—
332C2×C3×D3—62no—
333C2×C3×D3—62no—
334C2×C3×D3—62no—
335C2×C3×D3—62no—
336C2×C3×D3—616no—
337C2×C3×D3—62no—
338C2×C3×D3—616no—
339C2×C3×D3—62no—
340C2×C3×D3—62no—
341C2×C3×D3—62no—
342C2×C3×D3—62no—
343C2×C3×D3—62no—
344D32—616no—
345C32×C4—22no—
346C32×C4—22no—
347C32×C4—22no—
348C32×C4D3×D414yescomplemented
349C3⋊Dic3—22no—
350C3⋊Dic3—22no—
351C3⋊Dic3C2×C4×D314yescomplemented
352C3×Dic3—34no—
353C3×Dic3—34no—
354C3×Dic3—62no—
355C3×Dic3—62no—
356C3×Dic3—62no—
357C3×Dic3—62no—
358C3×Dic3—62no—
359C22×D4—271no—
360C23×C4—91no—
361C23×C4—271no—
362C4×D4—92no—
363C4×D4—272no—
364C4×D4—272no—
365C4×D4—272no—
366C2×C4⋊C4—271no—
367C2×C22⋊C4—271no—
368C2×C22⋊C4—271no—
369C2×C42—271no—
370H(3,𝔽3)C2×C4×D411yescharacteristic, complemented, Sylow
371C23×C3—32no—
372C23×C3—61no—
373C23×C3—92no—
374C23×C3—91no—
375C23×C3—91no—
376C23×C3—94no—
377C23×C3—182no—
378C23×C3—182no—
379C23×C3C2×D3211yescharacteristic
380C22×D3—32no—
381C22×D3—32no—
382C22×D3—38no—
383C22×D3—32no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—64no—
391C22×D3—92no—
392C22×D3—94no—
393C22×D3—98no—
394C22×D3—184no—
395C22×D3—184no—
396C22×D3—182no—
397C22×D3—182no—
398C3×D4—98no—
399C2×C3×C4—22no—
400C2×C3×C4—32no—
401C2×C3×C4—32no—
402C2×C3×C4—64no—
403C2×C3×C4—64no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—92no—
407C2×C3×C4—91no—
408C2×C3×C4—94no—
409C2×C3×C4—92no—
410C2×C3×C4—92no—
411C2×C3×C4—91no—
412C2×C3×C4—182no—
413C2×C3×C4—182no—
414C2×C3×C4—184no—
415C2×C3×C4—182no—
416C2×C3×C4—182no—
417C2×C3×C4C2×D3211yescharacteristic
418C2×C3×C4C2×D3211yescharacteristic
419#67—38no—
420#67—98no—
421#67—98no—
422#67—98no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—92no—
433C2×Dic3—92no—
434C2×Dic3—92no—
435C2×Dic3—94no—
436C2×Dic3—184no—
437C2×Dic3—182no—
438C2×Dic3—182no—
439D12—98no—
440C4×D3—38no—
441C4×D3—64no—
442C4×D3—64no—
443C4×D3—64no—
444C4×D3—64no—
445C4×D3—64no—
446C4×D3—64no—
447C4×D3—64no—
448C4×D3—64no—
449C4×D3—98no—
450C4×D3—184no—
451C4×D3—184no—
452C4×D3—184no—
453C4×D3—184no—
454C4×D3—184no—
455C2×C32—24no—
456C2×C32—24no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32C22×C4×D312yes—
461C2×C32C2×D3×D412yes—
462C2×C32D3×#4112yes—
463C3⋊D3—24no—
464C3×D3—38no—
465C3×D3—64no—
466C3×D3—64no—
467C3×D3—64no—
468C3×D3—64no—
469C24—91no—
470C24—271no—
471C2×D4—92no—
472C2×D4—272no—
473C2×D4—278no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—91no—
478C22×C4—92no—
479C22×C4—91no—
480C22×C4—184no—
481C22×C4—271no—
482C22×C4—271no—
483C22×C4—271no—
484C22×C4—272no—
485C22×C4—544no—
486C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
487C4⋊C4—92no—
488C4⋊C4—272no—
489C22⋊C4—92no—
490C22⋊C4—92no—
491C22⋊C4—272no—
492C22⋊C4—272no—
493C42—92no—
494C42—272no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—32no—
498C22×C3—34no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—62no—
502C22×C3—62no—
503C22×C3—61no—
504C22×C3—62no—
505C22×C3—94no—
506C22×C3—92no—
507C22×C3—92no—
508C22×C3—92no—
509C22×C3—92no—
510C22×C3—188no—
511C22×C3—182no—
512C22×C3—182no—
513C22×C3—181no—
514C22×C3—181no—
515C22×C3C4×D3212yes—
516C22×C3C22×D3211yescharacteristic
517C2×D3—34no—
518C2×D3—34no—
519C2×D3—34no—
520C2×D3—34no—
521C2×D3—34no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—616no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—616no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—94no—
535C2×D3—182no—
536C2×D3—182no—
537C2×D3—1816no—
538C2×D3—188no—
539C3×C4—21no—
540C3×C4—34no—
541C3×C4—62no—
542C3×C4—62no—
543C3×C4—62no—
544C3×C4—94no—
545C3×C4—92no—
546C3×C4—182no—
547C3×C4—182no—
548C3×C4—181no—
549C3×C4#381112yes—
550Dic3—34no—
551Dic3—34no—
552Dic3—62no—
553Dic3—62no—
554Dic3—62no—
555Dic3—62no—
556Dic3—62no—
557Dic3—94no—
558Dic3—182no—
559Dic3—182no—
560C32—21no—
561C32C4×D3×D412yescomplemented
562C23—91no—
563C23—92no—
564C23—91no—
565C23—94no—
566C23—182no—
567C23—182no—
568C23—274no—
569C23—542no—
570C23—542no—
571C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
572D4—98no—
573D4—278no—
574C2×C4—22no—
575C2×C4—92no—
576C2×C4—91no—
577C2×C4—94no—
578C2×C4—92no—
579C2×C4—92no—
580C2×C4—91no—
581C2×C4—182no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—184no—
586C2×C4—274no—
587C2×C4—544no—
588C2×C4—542no—
589C2×C4—542no—
590C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
591C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
592C2×C3—22no—
593C2×C3—32no—
594C2×C3—32no—
595C2×C3—32no—
596C2×C3—64no—
597C2×C3—64no—
598C2×C3—61no—
599C2×C3—61no—
600C2×C3—61no—
601C2×C3—94no—
602C2×C3—184no—
603C2×C3—182no—
604C2×C3C2×C4×D3211yescharacteristic
605C2×C3#6430611yescharacteristic
606C2×C3C2×#381111yescharacteristic
607D3—38no—
608D3—64no—
609D3—64no—
610D3—64no—
611D3—64no—
612D3—184no—
613C22—21no—
614C22—21no—
615C22—92no—
616C22—92no—
617C22—92no—
618C22—94no—
619C22—92no—
620C22—188no—
621C22—181no—
622C22—182no—
623C22—181no—
624C22—182no—
625C22—548no—
626C22C4×((C3⋊D3)⋊C3)⋊C212yescomplemented
627C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
628C4—21no—
629C4—92no—
630C4—94no—
631C4—181no—
632C4—182no—
633C4—182no—
634C4#8867712yesdirect product factor
635C3—32no—
636C3—61no—
637C3C4×#381111yescharacteristic
638C2—22no—
639C2—94no—
640C2—182no—
641C2—184no—
642C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
643C2#1172249111yescharacteristic
644C2C2×#8867711yescharacteristic
subgroupG/H
centerC2×C4C2×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC2×#88677C2
cosocleC22×H(3,𝔽3)C24
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C4×D4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×#272C2semidirect
3. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
4. C4×#638⋊C3C2semidirect
5. #11721320C2semidirect
6. #11721315C2semidirect
7. #11721161C2semidirect
8. C4×#6200C2semidirect
9. #11721147C2semidirect
10. C4×#6199C2semidirect
11. #11721124C2semidirect
15. C22×C4×H(3,𝔽3)C22semidirect
16. C22×#1084C22semidirect
20. C2×C4×#272C22semidirect
21. C2×C4×#272C22semidirect
23. C2×C4×(C3⋊D3)⋊C3C22semidirect
24. #88677C4direct (N × H)
29. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
31. #3757⋊C3C22semidirect
32. #3752⋊C3C22semidirect
33. #3750⋊C3C22semidirect
34. C4×(C3⋊Dic3)⋊C3C22semidirect
35. #88451C22semidirect
36. #88450C22semidirect
37. #88448C22semidirect
38. #88447C22semidirect
43. C4×#638D3semidirect
58. C22×#272C2×C4semidirect
64. C2×((C3⋊D3)⋊C3)⋊C2C2×C4semidirect
74. C4×#272D4semidirect
75. #638⋊C3C2×C4semidirect
80. #6200C2×C4semidirect
83. #6199C2×C4semidirect
91. C22×C32×C4C2×D3semidirect
93. C2×C4×C3⋊D3C2×D3semidirect
117. #3757C2×D3semidirect
118. #3752C2×D3semidirect
119. #3750C2×D3semidirect
120. C4×C3⋊Dic3C2×D3semidirect
135. C22×H(3,𝔽3)C22×C4semidirect
141. C2×#272C22×C4semidirect
146. C2×(C3⋊D3)⋊C3C22×C4semidirect
149. C4×H(3,𝔽3)C2×D4semidirect
151. #1084C2×D4semidirect
154. (C3⋊Dic3)⋊C3C22×C4semidirect
205. #638C4×D3semidirect
242. #272C4×D4semidirect
322. C22×C32C2×C4×D3semidirect
326. C2×C3⋊D3C2×C4×D3semidirect
348. C32×C4D3×D4semidirect
351. C3⋊Dic3C2×C4×D3semidirect
370. H(3,𝔽3)C2×C4×D4semidirect
486. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
561. C32C4×D3×D4semidirect
626. C22C4×((C3⋊D3)⋊C3)⋊C2semidirect
634. C4#88677direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#2722
C2×#886772
C2×C4×((C3⋊D3)⋊C3)⋊C22
C4×#638⋊C32
#117213202
#117213152
#117211612
C4×#62002
#117211472
C4×#61992
#117211242
C4×D3×#673