Finite Group Databasebeta

← C3×#638⋊A4 #72220528

Subgroups — C3×#638⋊A4 #72220528

Order 2592.

1060 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×C3×(C3⋊D3)⋊A4C211yesmaximal, characteristic, complemented
3C3×(C3⋊Dic3)⋊A4C211yesmaximal, characteristic, complemented
4C22×C3×#638C311yesmaximal, characteristic, complemented
5C3×A4×#67—31nomaximal
6#638⋊A4C313yesmaximal, direct product factor
7C2×C3×C22⋊H(3,𝔽3)—21no—
8C2×C3×C22⋊H(3,𝔽3)C2211yescharacteristic
9C3×(C3⋊D3)⋊A4—21no—
10C3×#638⋊C3—41nomaximal
11C24×C33C2×C311yescharacteristic, complemented
12C23×C3×C3⋊D3C2×C311yescharacteristic, complemented
13C22×C32×A4—21no—
14C22×C32×A4D311yescharacteristic, complemented
15C2×C3×D3×A4—31no—
16C2×C3×#638—31no—
17C2×C3×#638—31no—
18C2×C3×#638—31no—
19C2×C3×#638—31no—
20C22×C3×C3⋊Dic3C2×C311yescharacteristic, complemented
21C3×Dic3×A4—31no—
22C22×C22⋊H(3,𝔽3)—23no—
23C22×C22⋊H(3,𝔽3)C2×C313yescomplemented
24C2×(C3⋊D3)⋊A4C2×C313yescomplemented
25(C3⋊Dic3)⋊A4C2×C313yescomplemented
26C22×C3×H(3,𝔽3)—41no—
27C2×C3×(C3⋊D3)⋊C3—41no—
28C3×C22⋊H(3,𝔽3)D411yescharacteristic, complemented
29C3×(C3⋊Dic3)⋊C3—41no—
30C22×#638C3211yescharacteristic, complemented
31C22×C3×#67—31no—
32C22×C3×#67—91no—
33C3×D4×A4—91no—
34A4×#67—33no—
35C23×C33—21no—
36C23×C33—31no—
37C23×C33—31no—
38C23×C33—61no—
39C23×C33C22×C311yescharacteristic
40C22×C3×C3⋊D3—21no—
41C22×C3×C3⋊D3—31no—
42C22×C3×C3⋊D3—31no—
43C22×C3×C3⋊D3—61no—
44C2×C32×A4—22no—
45C2×C32×A4—21no—
46C2×C32×A4—21no—
47C2×C32×A4C2×D311yescharacteristic
48C3×D3×A4—61no—
49C3×#638—32no—
50C3×#638—31no—
51C3×#638—31no—
52C3×#638—31no—
53C3×#638A411yescharacteristic, complemented
54C2×C3×C3⋊Dic3—31no—
55C2×C3×C3⋊Dic3—31no—
56C32×#67—121no—
57C2×C22⋊H(3,𝔽3)—26no—
58C2×C22⋊H(3,𝔽3)—23no—
59C2×C22⋊H(3,𝔽3)—23no—
60C2×C22⋊H(3,𝔽3)C22×C313yes—
61(C3⋊D3)⋊A4—23no—
62#638⋊C3—43no—
63C2×C3×H(3,𝔽3)—41no—
64C2×C3×H(3,𝔽3)—81no—
65C3×(C3⋊D3)⋊C3—81no—
66C24×C32—21no—
67C24×C32—31no—
68C24×C32—61no—
69C24×C32C3×D311yescharacteristic
70C24×C32C2×C3211yescharacteristic, complemented
71C23×C3⋊D3C2×C3211yescharacteristic, complemented
72C23×C3×D3—31no—
73C23×C3×D3—91no—
74C22×C3×A4—23no—
75C22×C3×A4—31no—
76C22×C3×A4—61no—
77C22×C3×A4—62no—
78C22×C3×A4—61no—
79C22×C3×A4—91no—
80C22×C3×A4C3×D313yescomplemented
81C2×D3×A4—33no—
82C2×#638—31no—
83C2×#638—31no—
84C2×#638—31no—
85C2×#638—31no—
86C22×C3⋊Dic3C2×C3211yescharacteristic, complemented
87C2×C3×#67—91no—
88C2×C3×#67—93no—
89C2×C3×#67—93no—
90C2×C3×#67—93no—
91C2×C3×#67—93no—
92C2×C3×#67—91no—
93C2×C3×#67—91no—
94C2×C3×#67—91no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—91no—
97C3×C4×A4—91no—
98Dic3×A4—33no—
99C22×C33—31no—
100C22×C33—31no—
101C22×C33—31no—
102C22×C33—41no—
103C22×C33—61no—
104C22×C33—61no—
105C22×C33—61no—
106C22×C33—61no—
107C22×C33—81no—
108C22×C33C3×D411yescharacteristic, complemented
109C22×C33C2×A411yescharacteristic, complemented
110C2×C3×C3⋊D3—31no—
111C2×C3×C3⋊D3—61no—
112C2×C3×C3⋊D3—61no—
113C2×C3×C3⋊D3—61no—
114C2×C3×C3⋊D3—61no—
115C2×C3×C3⋊D3C2×A411yescharacteristic, complemented
116C2×C32×D3—121no—
117C32×A4—21no—
118C32×A4#6711yescharacteristic, complemented
119C3×C3⋊Dic3—31no—
120C3×C3⋊Dic3C2×A411yescharacteristic, complemented
121C32×Dic3—121no—
122C22×H(3,𝔽3)—43no—
123C22×H(3,𝔽3)—83no—
124C2×(C3⋊D3)⋊C3—43no—
125C22⋊H(3,𝔽3)—23no—
126C22⋊H(3,𝔽3)C3×D413yescomplemented
127(C3⋊Dic3)⋊C3—43no—
128C22×C3×D4—91no—
129C22×#67—31no—
130C22×#67—91no—
131D4×A4—93no—
132C3×H(3,𝔽3)—41noSylow
133C23×C32—21no—
134C23×C32—22no—
135C23×C32—21no—
136C23×C32—21no—
137C23×C32—31no—
138C23×C32—31no—
139C23×C32—33no—
140C23×C32—33no—
141C23×C32—31no—
142C23×C32—31no—
143C23×C32—31no—
144C23×C32—61no—
145C23×C32—61no—
146C23×C32—62no—
147C23×C32—61no—
148C23×C32—61no—
149C23×C32—63no—
150C23×C32—63no—
151C23×C32—61no—
152C23×C32—61no—
153C23×C32—63no—
154C23×C32—62no—
155C23×C32—66no—
156C23×C32C2×C3×D311yescharacteristic
157C23×C32C22×C3211yescharacteristic
158C22×C3⋊D3—21no—
159C22×C3⋊D3—31no—
160C22×C3⋊D3—31no—
161C22×C3⋊D3—61no—
162C22×C3×D3—61no—
163C22×C3×D3—91no—
164C22×C3×D3—93no—
165C22×C3×D3—93no—
166C22×C3×D3—91no—
167C22×C3×D3—181no—
168C22×C3×D3—183no—
169C22×C3×D3—181no—
170C2×C3×A4—26no—
171C2×C3×A4—23no—
172C2×C3×A4—23no—
173C2×C3×A4—31no—
174C2×C3×A4—61no—
175C2×C3×A4—61no—
176C2×C3×A4—62no—
177C2×C3×A4—64no—
178C2×C3×A4—62no—
179C2×C3×A4—62no—
180C2×C3×A4—61no—
181C2×C3×A4—181no—
182C2×C3×A4C2×C3×D313yes—
183D3×A4—63no—
184C32×D4—361no—
185#638—32no—
186#638—31no—
187#638—31no—
188#638—31no—
189#638C3×A411yescharacteristic, complemented
190C2×C3⋊Dic3—31no—
191C2×C3⋊Dic3—31no—
192C3×#67—31no—
193C3×#67—91no—
194C3×#67—91no—
195C3×#67—91no—
196C3×#67—93no—
197C3×#67—93no—
198C3×#67—96no—
199C3×#67—92no—
200C3×#67—93no—
201C3×#67—91no—
202C3×#67—123no—
203C2×C3×Dic3—91no—
204C2×C3×Dic3—93no—
205C2×C3×Dic3—93no—
206C2×C3×Dic3—91no—
207C2×C33—21no—
208C2×C33—31no—
209C2×C33—31no—
210C2×C33—41no—
211C2×C33—61no—
212C2×C33—81no—
213C2×C33—82no—
214C2×C33—81no—
215C2×C33C22×A411yescharacteristic
216C3×C3⋊D3—21no—
217C3×C3⋊D3—61no—
218C32×D3—241no—
219C2×H(3,𝔽3)—43no—
220C2×H(3,𝔽3)—83no—
221C2×H(3,𝔽3)—83no—
222C2×H(3,𝔽3)—86no—
223(C3⋊D3)⋊C3—83no—
224C24×C3—21no—
225C24×C3—31no—
226C24×C3—61no—
227C24×C3—91no—
228C24×C3(C3⋊D3)⋊C311yescharacteristic, complemented
229C24×C3C32×D311yescharacteristic
230C23×D3—31no—
231C23×D3—91no—
232C22×A4—33no—
233C22×A4—63no—
234C22×A4—93no—
235C2×C3×D4—271no—
236C2×C3×D4—271no—
237C2×C3×D4—271no—
238C2×C3×D4—271no—
239C22×C3×C4—91no—
240C2×#67—91no—
241C2×#67—93no—
242C2×#67—93no—
243C2×#67—93no—
244C2×#67—93no—
245C2×#67—91no—
246C2×#67—91no—
247C2×#67—91no—
248C22×Dic3—31no—
249C22×Dic3—91no—
250C4×A4—93no—
251C22×C32—21no—
252C22×C32—21no—
253C22×C32—31no—
254C22×C32—31no—
255C22×C32—31no—
256C22×C32—31no—
257C22×C32—33no—
258C22×C32—33no—
259C22×C32—31no—
260C22×C32—33no—
261C22×C32—31no—
262C22×C32—31no—
263C22×C32—31no—
264C22×C32—43no—
265C22×C32—61no—
266C22×C32—61no—
267C22×C32—61no—
268C22×C32—61no—
269C22×C32—61no—
270C22×C32—63no—
271C22×C32—63no—
272C22×C32—63no—
273C22×C32—61no—
274C22×C32—61no—
275C22×C32—61no—
276C22×C32—61no—
277C22×C32—62no—
278C22×C32—62no—
279C22×C32—61no—
280C22×C32—61no—
281C22×C32—61no—
282C22×C32—61no—
283C22×C32—63no—
284C22×C32—63no—
285C22×C32—63no—
286C22×C32—63no—
287C22×C32—62no—
288C22×C32—66no—
289C22×C32—66no—
290C22×C32—62no—
291C22×C32—66no—
292C22×C32—66no—
293C22×C32—83no—
294C22×C32—121no—
295C22×C32—241no—
296C22×C32—242no—
297C22×C32—241no—
298C22×C32—361no—
299C22×C32C3×#6711yescharacteristic
300C22×C32C32×D411yescharacteristic, complemented
301C22×C32D3×A411yescharacteristic
302C22×C32C2×C3×A411yescharacteristic, complemented
303C2×C3⋊D3—31no—
304C2×C3⋊D3—61no—
305C2×C3⋊D3—61no—
306C2×C3⋊D3—61no—
307C2×C3⋊D3—61no—
308C2×C3⋊D3C2×C3×A411yescharacteristic, complemented
309C2×C3×D3—31no—
310C2×C3×D3—91no—
311C2×C3×D3—93no—
312C2×C3×D3—91no—
313C2×C3×D3—123no—
314C2×C3×D3—181no—
315C2×C3×D3—181no—
316C2×C3×D3—183no—
317C2×C3×D3—183no—
318C2×C3×D3—183no—
319C2×C3×D3—183no—
320C2×C3×D3—181no—
321C2×C3×D3—181no—
322C3×A4—23no—
323C3×A4—31no—
324C3×A4—61no—
325C3×A4—62no—
326C3×A4—61no—
327C3×A4C3×#6713yescomplemented
328C32×C4—361no—
329C3⋊Dic3—31no—
330C3⋊Dic3C2×C3×A411yescharacteristic, complemented
331C3×Dic3—31no—
332C3×Dic3—91no—
333C3×Dic3—93no—
334C3×Dic3—91no—
335C3×Dic3—123no—
336C22×D4—91noSylow
337C33—41no—
338C33—81no—
339C33D4×A411yescharacteristic, complemented
340H(3,𝔽3)—43no—
341H(3,𝔽3)—83no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—33no—
347C23×C3—33no—
348C23×C3—31no—
349C23×C3—31no—
350C23×C3—31no—
351C23×C3—31no—
352C23×C3—31no—
353C23×C3—61no—
354C23×C3—62no—
355C23×C3—61no—
356C23×C3—61no—
357C23×C3—63no—
358C23×C3—63no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—63no—
362C23×C3—62no—
363C23×C3—66no—
364C23×C3—61no—
365C23×C3—181no—
366C23×C3—271no—
367C23×C3—271no—
368C23×C3—541no—
369C23×C3C2×(C3⋊D3)⋊C311yescharacteristic
370C23×C3C2×C32×D311yescharacteristic
371C22×D3—61no—
372C22×D3—91no—
373C22×D3—93no—
374C22×D3—93no—
375C22×D3—91no—
376C22×D3—181no—
377C22×D3—183no—
378C22×D3—181no—
379C2×A4—33no—
380C2×A4—63no—
381C2×A4—66no—
382C2×A4—63no—
383C2×A4—183no—
384C3×D4—91no—
385C3×D4—271no—
386C3×D4—271no—
387C3×D4—272no—
388C3×D4—271no—
389C3×D4—363no—
390C2×C3×C4—271no—
391C2×C3×C4—271no—
392#67—31no—
393#67—91no—
394#67—91no—
395#67—91no—
396#67—93no—
397#67—93no—
398#67—96no—
399#67—92no—
400#67—93no—
401#67—91no—
402C2×Dic3—91no—
403C2×Dic3—93no—
404C2×Dic3—93no—
405C2×Dic3—91no—
406C2×C32—21no—
407C2×C32—22no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—31no—
411C2×C32—31no—
412C2×C32—33no—
413C2×C32—33no—
414C2×C32—31no—
415C2×C32—31no—
416C2×C32—31no—
417C2×C32—43no—
418C2×C32—61no—
419C2×C32—61no—
420C2×C32—62no—
421C2×C32—61no—
422C2×C32—61no—
423C2×C32—63no—
424C2×C32—63no—
425C2×C32—62no—
426C2×C32—63no—
427C2×C32—66no—
428C2×C32—61no—
429C2×C32—61no—
430C2×C32—83no—
431C2×C32—86no—
432C2×C32—83no—
433C2×C32—121no—
434C2×C32—241no—
435C2×C32—241no—
436C2×C32—242no—
437C2×C32—244no—
438C2×C32—242no—
439C2×C32—242no—
440C2×C32—241no—
441C2×C32—721no—
442C2×C32C2×D3×A411yescharacteristic
443C2×C32C22×C3×A411yescharacteristic
444C3⋊D3—21no—
445C3⋊D3—61no—
446C3×D3—61no—
447C3×D3—181no—
448C3×D3—183no—
449C3×D3—181no—
450C3×D3—243no—
451C24—91no—
452C24C3×(C3⋊D3)⋊C311yescharacteristic, complemented
453C2×D4—271no—
454C2×D4—271no—
455C2×D4—271no—
456C2×D4—271no—
457C22×C4—91no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—31no—
461C22×C3—31no—
462C22×C3—33no—
463C22×C3—33no—
464C22×C3—31no—
465C22×C3—31no—
466C22×C3—33no—
467C22×C3—31no—
468C22×C3—31no—
469C22×C3—31no—
470C22×C3—31no—
471C22×C3—61no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—63no—
475C22×C3—63no—
476C22×C3—63no—
477C22×C3—61no—
478C22×C3—61no—
479C22×C3—61no—
480C22×C3—61no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—61no—
484C22×C3—61no—
485C22×C3—61no—
486C22×C3—61no—
487C22×C3—63no—
488C22×C3—63no—
489C22×C3—63no—
490C22×C3—63no—
491C22×C3—62no—
492C22×C3—66no—
493C22×C3—66no—
494C22×C3—66no—
495C22×C3—62no—
496C22×C3—66no—
497C22×C3—61no—
498C22×C3—61no—
499C22×C3—91no—
500C22×C3—123no—
501C22×C3—243no—
502C22×C3—271no—
503C22×C3—363no—
504C22×C3—541no—
505C22×C3—541no—
506C22×C3—541no—
507C22×C3—541no—
508C22×C3#638⋊C311yescharacteristic, complemented
509C22×C3(C3⋊D3)⋊A411yescharacteristic, complemented
510C22×C3C32×#6711yescharacteristic
511C22×C3C3×D3×A411yescharacteristic
512C2×D3—31no—
513C2×D3—91no—
514C2×D3—93no—
515C2×D3—91no—
516C2×D3—181no—
517C2×D3—181no—
518C2×D3—183no—
519C2×D3—183no—
520C2×D3—183no—
521C2×D3—183no—
522C2×D3—181no—
523C2×D3—181no—
524A4—33no—
525A4—63no—
526C3×C4—91no—
527C3×C4—271no—
528C3×C4—363no—
529Dic3—31no—
530Dic3—91no—
531Dic3—93no—
532Dic3—91no—
533C32—21no—
534C32—31no—
535C32—43no—
536C32—61no—
537C32—83no—
538C32—121no—
539C32—241no—
540C32—242no—
541C32—241no—
542C32A4×#6711yescharacteristic
543C32C3×D4×A411yescharacteristic, complemented
544C23—21no—
545C23—31no—
546C23—31no—
547C23—61no—
548C23—181no—
549C23—271no—
550C23—271no—
551C23—541no—
552C23C2×C3×(C3⋊D3)⋊C311yescharacteristic
553D4—91no—
554D4—271no—
555D4—271no—
556D4—272no—
557D4—271no—
558C2×C4—271no—
559C2×C4—271no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—33no—
565C2×C3—33no—
566C2×C3—31no—
567C2×C3—31no—
568C2×C3—31no—
569C2×C3—31no—
570C2×C3—31no—
571C2×C3—61no—
572C2×C3—62no—
573C2×C3—61no—
574C2×C3—61no—
575C2×C3—63no—
576C2×C3—63no—
577C2×C3—62no—
578C2×C3—63no—
579C2×C3—66no—
580C2×C3—61no—
581C2×C3—61no—
582C2×C3—61no—
583C2×C3—123no—
584C2×C3—181no—
585C2×C3—243no—
586C2×C3—246no—
587C2×C3—243no—
588C2×C3—541no—
589C2×C3—723no—
590C2×C3C2×(C3⋊D3)⋊A411yescharacteristic
591C2×C3C2×C3×D3×A411yescharacteristic
592D3—61no—
593D3—181no—
594D3—183no—
595D3—181no—
596C22—31no—
597C22—31no—
598C22—31no—
599C22—61no—
600C22—61no—
601C22—61no—
602C22—61no—
603C22—91no—
604C22—271no—
605C22—541no—
606C22—541no—
607C22—541no—
608C22—541no—
609C22C3×#638⋊C311yescharacteristic, complemented
610C22C3×(C3⋊D3)⋊A411yescharacteristic, complemented
611C4—91no—
612C4—271no—
613C3—21no—
614C3—31no—
615C3—61no—
616C3—123no—
617C3—243no—
618C3#638⋊A411yescharacteristic, direct product factor
619C3C3×A4×#6711yescharacteristic
620C2—21no—
621C2—31no—
622C2—31no—
623C2—61no—
624C2—181no—
625C2—541no—
626C2C2×C3×(C3⋊D3)⋊A411yescharacteristic
subgroupG/H
centerC2×C3C2×(C3⋊D3)⋊A4
commutator, cosocleC23×C32C22×C32
FrattiniC2×C3C2×C3×D3×A4
FittingC24×C33C2×C3
socleC23×C32C2×C3×D3
hypercenterC22×C3(C3⋊D3)⋊A4
hypocenterC22×C32C32×D4
LCSG ▷ C23×C32 ▷ C22×C32
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊H(3,𝔽3)C2semidirect
2. C2×C3×(C3⋊D3)⋊A4C2semidirect
3. C3×(C3⋊Dic3)⋊A4C2semidirect
4. C22×C3×#638C3semidirect
6. #638⋊A4C3direct (N × H)
11. C24×C33C2×C3semidirect
12. C23×C3×C3⋊D3C2×C3semidirect
14. C22×C32×A4D3semidirect
20. C22×C3×C3⋊Dic3C2×C3semidirect
23. C22×C22⋊H(3,𝔽3)C2×C3semidirect
24. C2×(C3⋊D3)⋊A4C2×C3semidirect
25. (C3⋊Dic3)⋊A4C2×C3semidirect
28. C3×C22⋊H(3,𝔽3)D4semidirect
30. C22×#638C32semidirect
53. C3×#638A4semidirect
70. C24×C32C2×C32semidirect
71. C23×C3⋊D3C2×C32semidirect
80. C22×C3×A4C3×D3semidirect
86. C22×C3⋊Dic3C2×C32semidirect
108. C22×C33C3×D4semidirect
109. C22×C33C2×A4semidirect
115. C2×C3×C3⋊D3C2×A4semidirect
118. C32×A4#67semidirect
120. C3×C3⋊Dic3C2×A4semidirect
126. C22⋊H(3,𝔽3)C3×D4semidirect
189. #638C3×A4semidirect
228. C24×C3(C3⋊D3)⋊C3semidirect
300. C22×C32C32×D4semidirect
302. C22×C32C2×C3×A4semidirect
308. C2×C3⋊D3C2×C3×A4semidirect
327. C3×A4C3×#67semidirect
330. C3⋊Dic3C2×C3×A4semidirect
339. C33D4×A4semidirect
452. C24C3×(C3⋊D3)⋊C3semidirect
508. C22×C3#638⋊C3semidirect
509. C22×C3(C3⋊D3)⋊A4semidirect
543. C32C3×D4×A4semidirect
609. C22C3×#638⋊C3semidirect
610. C22C3×(C3⋊D3)⋊A4semidirect
618. C3#638⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊H(3,𝔽3)2
C2×C3×(C3⋊D3)⋊A42
C3×(C3⋊Dic3)⋊A42
C22×C3×#6383
C3×A4×#673
#638⋊A43
C3×#638⋊C34