Finite Group Databasebeta

← C3×#11714175 #72275049

Subgroups — C3×#11714175 #72275049

Order 2304.

1206 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×#87522C211yesmaximal, characteristic, complemented
2C3×#87521C211yesmaximal, characteristic, complemented
3C3×#73032C212yesmaximal, complemented
4C3×#73026C212yesmaximal, complemented
5C3×#3025⋊C3C211yesmaximal, characteristic, complemented
6#11714175C311yesmaximal, characteristic, direct product factor
7C3×#33553—31nomaximal
8C3×#5950C2211yescharacteristic, complemented
9C3×#5935C2212yescomplemented
10C3×#5934C2212yescomplemented
11C2×C3×C4⋊S4—41nomaximal
12C3×#458⋊C3C2211yescharacteristic, complemented
13C3×B(4,𝔽2)⋊C3C2211yescharacteristic, complemented
14#87522C2×C311yescharacteristic, complemented
15#87521C2×C311yescharacteristic, complemented
16C3×#3537—31no—
17C3×#3027—31no—
18C3×#3025D311yescharacteristic, complemented
19C3×#3021—31no—
20#3025⋊C3—21no—
21#3025⋊C3C2×C311yescharacteristic, complemented
22#73032C2×C312yescomplemented
23#73026C2×C312yescomplemented
24C3×#2200—32no—
25C3×#2200—32no—
26C3×#2196—32no—
27C3×#2196—32no—
28C3×#2128—31no—
29C3×#2122—31no—
30C3×#2120—31no—
31C22×C3×S4—42no—
32C3×#997C2311yescharacteristic
33C2×C3×C4×A4—41no—
34C3×#986—81no—
35C3×C4⋊S4—41no—
36C3×C4⋊S4—41no—
37C3×C4⋊S4—42no—
38C3×C4⋊S4—81no—
39#33553—31noSylow
40C3×#585C2×D311yescharacteristic, complemented
41#5950—21no—
42#5950C22×C311yescharacteristic, complemented
43#5935C22×C312yescomplemented
44#5934C22×C312yescomplemented
45C2×C4⋊S4—41no—
46C2×C3×AGL(1,ℤ/8)—61no—
47C3×#560—32no—
48C3×#560—61no—
49C3×#553—61no—
50C3×#553—61no—
51C3×D42—32no—
52C3×D42—61no—
53C3×D42—61no—
54C3×D42—61no—
55C3×#540—61no—
56C3×#538—62no—
57C3×#535—31no—
58C3×#535—31no—
59C3×#535—61no—
60C3×#534—62no—
61C3×#525—31no—
62C2×C3×#121—61no—
63C3×#458—31no—
64C3×#458C2×D311yescharacteristic, complemented
65C3×B(4,𝔽2)—31no—
66C3×B(4,𝔽2)—32no—
67C3×B(4,𝔽2)—32no—
68C3×B(4,𝔽2)—62no—
69C3×B(4,𝔽2)C2×D311yescharacteristic
70C3×#454—62no—
71C3×#453—32no—
72C3×#453—32no—
73C3×#421—61no—
74C3×#413—31no—
75C3×#410—31no—
76C3×#410—31no—
77C3×#410—61no—
78#458⋊C3—21no—
79#458⋊C3C22×C311yescharacteristic, complemented
80B(4,𝔽2)⋊C3—21no—
81B(4,𝔽2)⋊C3C22×C311yescharacteristic, complemented
82C3×#353—32no—
83C3×#353—32no—
84C3×#352—32no—
85C3×AΣL(1,𝔽16)—32no—
86C3×AΣL(1,𝔽16)—32no—
87C3×AΣL(1,𝔽16)—32no—
88C22×C3×A4—41no—
89C2×C3×S4—42no—
90C2×C3×S4—42no—
91C2×C3×S4—84no—
92C2×C3×S4—82no—
93C2×C3×D12—161no—
94C3×#41⋊C3—81no—
95C3×C4×A4—41no—
96C3×C4×A4—41no—
97C3×C4×A4—81no—
98C3×GL(2,𝔽3)—82no—
99#3537—31no—
100#3027—31no—
101#3025C3×D311yescharacteristic, complemented
102#3021—31no—
103#2200—32no—
104#2200—32no—
105#2196—32no—
106#2196—32no—
107#2128—31no—
108#2122—31no—
109#2120—31no—
110C22×S4—42no—
111C3×2−1+4—61no—
112C3×H(5,𝔽2)—31no—
113C3×H(5,𝔽2)—61no—
114C3×H(5,𝔽2)C22×D311yescharacteristic
115C2×C3×#41—31no—
116C2×C3×#41—61no—
117C2×C3×#41—61no—
118C22×C3×D4—31no—
119C22×C3×D4—31no—
120C22×C3×D4—62no—
121C22×C3×D4—61no—
122C22×C3×D4—62no—
123C22×C3×D4—62no—
124C23×C3×C4S411yescharacteristic, complemented
125#997—21no—
126#997C23×C311yescharacteristic
127C2×C4×A4—41no—
128C2×C4×A4—81no—
129#986—81no—
130C4⋊S4—42no—
131C4⋊S4—41no—
132C4⋊S4—41no—
133C4⋊S4—81no—
134C3×AGL(1,ℤ/8)—62no—
135C3×AGL(1,ℤ/8)—62no—
136C3×AGL(1,ℤ/8)—121no—
137C3×AGL(1,ℤ/8)—121no—
138C2×C3×SD16—121no—
139C2×C3×D8—121no—
140C2×C3×M16—61no—
141C3×#127—32no—
142C3×#127—61no—
143C3×#127—61no—
144C3×#127—121no—
145C3×#126—62no—
146C3×#126—62no—
147C3×#125—61no—
148C3×#124—32no—
149C3×#124—61no—
150C3×#124—121no—
151C3×#123—31no—
152C3×#123—31no—
153C3×#123—62no—
154C3×#123—62no—
155C3×#123—62no—
156C3×#123—62no—
157C3×C22⋊Q8—61no—
158C3×#121—62no—
159C3×#121—62no—
160C3×#121—62no—
161C3×#121—61no—
162C3×#121—61no—
163C3×#121—62no—
164C3×#121—61no—
165C3×#121—62no—
166C3×#121—62no—
167C3×#121—61no—
168C3×#121—61no—
169C3×#121—62no—
170C3×#121—62no—
171C3×#121—61no—
172C3×#121—61no—
173C3×#121—121no—
174C3×#121—121no—
175C3×#120—32no—
176C3×#120—32no—
177C3×#120—31no—
178C3×#120—31no—
179C3×#120—61no—
180C3×#120—61no—
181C3×#120—62no—
182C3×#120—62no—
183C3×#120—62no—
184C3×#120—62no—
185C3×#120—62no—
186C3×#120—62no—
187C3×C4×D4—62no—
188C3×C4×D4—61no—
189C3×C4×D4—61no—
190C3×C4×D4—62no—
191C3×C4×D4—61no—
192C3×C4×D4—61no—
193C3×#117—31no—
194C3×#117—31no—
195C3×#117—31no—
196C3×#117—61no—
197C2×C3×C4⋊C4—61no—
198C2×C3×C22⋊C4—62no—
199C3×#104—62no—
200C3×#104—62no—
201C3×#101—61no—
202C3×#100—32no—
203C3×#99—31no—
204C3×#99—31no—
205C3×#99—32no—
206C3×#99—61no—
207C3×#99—62no—
208C3×#99—62no—
209C3×#99—61no—
210C22×C3×D3—162no—
211C2×C3×A4—42no—
212C2×C3×A4—41no—
213C2×C3×A4—81no—
214C3×S4—82no—
215C3×S4—82no—
216C3×S4—162no—
217C2×C32×C4—161no—
218C3×D12—161no—
219C3×D12—161no—
220C3×D12—162no—
221C3×SL(2,𝔽3)—81no—
222#585C2×C3×D311yescharacteristic, complemented
223C2×AGL(1,ℤ/8)—61no—
224#560—32no—
225#560—61no—
226#553—61no—
227#553—61no—
228D42—32no—
229D42—61no—
230D42—61no—
231D42—61no—
232#540—61no—
233#538—62no—
234#535—31no—
235#535—31no—
236#535—61no—
237#534—62no—
238#525—31no—
239C2×#121—61no—
240#458—31no—
241#458C2×C3×D311yescharacteristic, complemented
242B(4,𝔽2)—31no—
243B(4,𝔽2)—32no—
244B(4,𝔽2)—32no—
245B(4,𝔽2)—62no—
246B(4,𝔽2)C2×C3×D311yescharacteristic
247#454—62no—
248#453—32no—
249#453—32no—
250#421—61no—
251#413—31no—
252#410—31no—
253#410—31no—
254#410—61no—
255#353—32no—
256#353—32no—
257#352—32no—
258AΣL(1,𝔽16)—32no—
259AΣL(1,𝔽16)—32no—
260AΣL(1,𝔽16)—32no—
261C24×C3—32no—
262C24×C3—61no—
263C24×C3—62no—
264C24×C3C2×S411yescharacteristic
265C22×A4—41no—
266C22×A4—81no—
267C2×S4—42no—
268C2×S4—42no—
269C2×S4—82no—
270C2×S4—84no—
271C3×#41—21no—
272C3×#41—61no—
273C3×#41—61no—
274C3×#41—61no—
275C3×#41—121no—
276C3×#41—121no—
277C3×#41—121no—
278C3×#41—121no—
279C3×#41—121no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—61no—
283C2×C3×D4—31no—
284C2×C3×D4—31no—
285C2×C3×D4—31no—
286C2×C3×D4—32no—
287C2×C3×D4—61no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4—61no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—62no—
305C2×C3×D4—121no—
306C2×C3×D4—121no—
307C2×C3×D4—121no—
308C2×C3×D4—121no—
309C2×C3×D4—121no—
310C2×C3×D4—122no—
311C2×C3×D4—122no—
312C2×C3×D4—241no—
313C2×C3×D4—241no—
314C2×C3×D4—244no—
315C2×C3×D4—244no—
316C2×C3×D4—244no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—62no—
326C22×C3×C4C2×S411yescharacteristic
327C22×C3×C4C2×S411yescharacteristic
328C2×D12—161no—
329#41⋊C3—81no—
330#41⋊C3—161no—
331C4×A4—41no—
332C4×A4—41no—
333C4×A4—81no—
334C4×A4—81no—
335C4×A4—81no—
336C4×A4—161no—
337GL(2,𝔽3)—82no—
338C3×SD16—122no—
339C3×SD16—122no—
340C3×D8—122no—
341C3×D8—122no—
342C3×M16—62no—
343C3×M16—121no—
344C2×C3×C8—121no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—62no—
351C3×C4⋊C4—62no—
352C3×C4⋊C4—62no—
353C3×C4⋊C4—121no—
354C3×C22⋊C4—32no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—62no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—62no—
362C3×C22⋊C4—62no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—62no—
367C3×C22⋊C4—62no—
368C3×C22⋊C4—62no—
369C3×C22⋊C4—62no—
370C3×C22⋊C4—62no—
371C3×C22⋊C4—122no—
372C3×C22⋊C4—122no—
373C3×C42—32no—
374C3×C42—61no—
375C3×C42—61no—
376C3×C42—121no—
377C22×C32—161no—
378C2×C3×D3—162no—
379C2×C3×D3—162no—
380C2×C3×D3—324no—
381C3×A4—41no—
382C3×A4—81no—
383C32×C4—161no—
384C32×C4—161no—
3852−1+4—61no—
386H(5,𝔽2)—31no—
387H(5,𝔽2)—61no—
388H(5,𝔽2)C22×C3×D311yescharacteristic
389C2×#41—31no—
390C2×#41—61no—
391C2×#41—61no—
392C22×D4—31no—
393C22×D4—31no—
394C22×D4—62no—
395C22×D4—61no—
396C22×D4—62no—
397C22×D4—62no—
398C23×C4C3×S411yescharacteristic, complemented
399AGL(1,ℤ/8)—62no—
400AGL(1,ℤ/8)—62no—
401AGL(1,ℤ/8)—121no—
402AGL(1,ℤ/8)—121no—
403C2×SD16—121no—
404C2×D8—121no—
405C2×M16—61no—
406#127—32no—
407#127—61no—
408#127—61no—
409#127—121no—
410#126—62no—
411#126—62no—
412#125—61no—
413#124—32no—
414#124—61no—
415#124—121no—
416#123—31no—
417#123—31no—
418#123—62no—
419#123—62no—
420#123—62no—
421#123—62no—
422C22⋊Q8—61no—
423#121—62no—
424#121—62no—
425#121—62no—
426#121—61no—
427#121—61no—
428#121—61no—
429#121—62no—
430#121—62no—
431#121—61no—
432#121—61no—
433#121—62no—
434#121—62no—
435#121—61no—
436#121—61no—
437#121—62no—
438#121—121no—
439#121—121no—
440#120—32no—
441#120—32no—
442#120—31no—
443#120—31no—
444#120—61no—
445#120—61no—
446#120—62no—
447#120—62no—
448#120—62no—
449#120—62no—
450#120—62no—
451#120—62no—
452C4×D4—62no—
453C4×D4—61no—
454C4×D4—61no—
455C4×D4—62no—
456C4×D4—61no—
457C4×D4—61no—
458#117—31no—
459#117—31no—
460#117—31no—
461#117—61no—
462C2×C4⋊C4—61no—
463C2×C22⋊C4—62no—
464#104—62no—
465#104—62no—
466#101—61no—
467#100—32no—
468#99—31no—
469#99—31no—
470#99—32no—
471#99—61no—
472#99—62no—
473#99—62no—
474#99—61no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3—31no—
478C23×C3—42no—
479C23×C3—61no—
480C23×C3—62no—
481C23×C3—62no—
482C23×C3—61no—
483C23×C3—124no—
484C23×C3—122no—
485C23×C3—242no—
486C23×C3—241no—
487C23×C3—242no—
488C23×C3—242no—
489C23×C3—242no—
490C23×C3C22×S411yescharacteristic
491C22×D3—162no—
492C2×A4—42no—
493C2×A4—41no—
494C2×A4—81no—
495C2×A4—82no—
496C2×A4—81no—
497C2×A4—161no—
498S4—82no—
499S4—82no—
500S4—162no—
501C3×Q8—21no—
502C3×Q8—61no—
503C3×Q8—121no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—121no—
507C3×D4—121no—
508C3×D4—121no—
509C3×D4—121no—
510C3×D4—121no—
511C3×D4—121no—
512C3×D4—122no—
513C3×D4—122no—
514C3×D4—122no—
515C3×D4—124no—
516C3×D4—124no—
517C3×D4—121no—
518C3×D4—121no—
519C3×D4—242no—
520C3×D4—241no—
521C3×D4—242no—
522C3×D4—242no—
523C3×D4—242no—
524C3×D4—242no—
525C3×D4—242no—
526C3×D4—242no—
527C3×D4—482no—
528C3×D4—482no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—62no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—62no—
545C2×C3×C4—121no—
546C2×C3×C4—121no—
547C2×C3×C4—122no—
548C2×C3×C4—161no—
549C2×C3×C4—242no—
550C2×C3×C4—242no—
551C2×C3×C4—242no—
552C2×C3×C4—321no—
553D12—161no—
554D12—161no—
555D12—162no—
556SL(2,𝔽3)—81no—
557SL(2,𝔽3)—161no—
558C3×C8—122no—
559C2×C32—162no—
560C2×C32—161no—
561C3×D3—322no—
562C3×D3—322no—
563C24—32no—
564C24—61no—
565C24—62no—
566C24C2×C3×S411yescharacteristic
567#41—21no—
568#41—61no—
569#41—61no—
570#41—61no—
571#41—121no—
572#41—121no—
573#41—121no—
574#41—121no—
575#41—121no—
576C2×Q8—31no—
577C2×Q8—61no—
578C2×Q8—61no—
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—32no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—62no—
593C2×D4—62no—
594C2×D4—62no—
595C2×D4—62no—
596C2×D4—62no—
597C2×D4—62no—
598C2×D4—62no—
599C2×D4—62no—
600C2×D4—62no—
601C2×D4—121no—
602C2×D4—121no—
603C2×D4—121no—
604C2×D4—121no—
605C2×D4—121no—
606C2×D4—122no—
607C2×D4—122no—
608C2×D4—241no—
609C2×D4—241no—
610C2×D4—244no—
611C2×D4—244no—
612C2×D4—244no—
613C22×C4—21no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4C2×C3×S411yescharacteristic
623C22×C4C2×C3×S411yescharacteristic
624SD16—122no—
625SD16—122no—
626D8—122no—
627D8—122no—
628M16—62no—
629M16—121no—
630C2×C8—121no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4—62no—
637C4⋊C4—62no—
638C4⋊C4—62no—
639C4⋊C4—121no—
640C22⋊C4—32no—
641C22⋊C4—31no—
642C22⋊C4—31no—
643C22⋊C4—62no—
644C22⋊C4—62no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—62no—
653C22⋊C4—62no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C22⋊C4—122no—
658C22⋊C4—122no—
659C42—32no—
660C42—61no—
661C42—61no—
662C42—121no—
663C22×C3—31no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—62no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—122no—
674C22×C3—122no—
675C22×C3—122no—
676C22×C3—122no—
677C22×C3—122no—
678C22×C3—122no—
679C22×C3—161no—
680C22×C3—241no—
681C22×C3—242no—
682C22×C3—242no—
683C22×C3—321no—
684C22×C3—484no—
685C22×C3—482no—
686C2×D3—162no—
687C2×D3—162no—
688C2×D3—324no—
689A4—41no—
690A4—81no—
691A4—81no—
692A4—161no—
693C3×C4—31no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—122no—
698C3×C4—122no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—161no—
702C3×C4—161no—
703C3×C4—242no—
704C3×C4—321no—
705C3×C4—321no—
706C3×C4#1020⋊C211yescharacteristic
707C32—161noSylow
708C23—21no—
709C23—31no—
710C23—31no—
711C23—42no—
712C23—61no—
713C23—62no—
714C23—62no—
715C23—61no—
716C23—124no—
717C23—122no—
718C23—242no—
719C23—241no—
720C23—242no—
721C23—242no—
722C23—242no—
723C23C22×C3×S411yescharacteristic
724Q8—21no—
725Q8—61no—
726Q8—121no—
727D4—61no—
728D4—61no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—121no—
733D4—121no—
734D4—121no—
735D4—122no—
736D4—122no—
737D4—122no—
738D4—124no—
739D4—124no—
740D4—121no—
741D4—121no—
742D4—242no—
743D4—241no—
744D4—242no—
745D4—242no—
746D4—242no—
747D4—242no—
748D4—242no—
749D4—242no—
750D4—482no—
751D4—482no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—41no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—62no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—122no—
771C2×C4—242no—
772C2×C4—242no—
773C2×C4—242no—
774C8—122no—
775C2×C3—42no—
776C2×C3—61no—
777C2×C3—121no—
778C2×C3—121no—
779C2×C3—162no—
780C2×C3—161no—
781C2×C3—242no—
782C2×C3—242no—
783C2×C3—322no—
784C2×C3—321no—
785C2×C3C2×#1020⋊C211yescharacteristic
786D3—322no—
787D3—322no—
788C22—31no—
789C22—41no—
790C22—41no—
791C22—62no—
792C22—61no—
793C22—61no—
794C22—81no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22—241no—
805C22—242no—
806C22—242no—
807C22—484no—
808C22—482no—
809C4—31no—
810C4—41no—
811C4—61no—
812C4—61no—
813C4—122no—
814C4—122no—
815C4—121no—
816C4—121no—
817C4—242no—
818C4C3×#1020⋊C211yescharacteristic
819C3—161no—
820C3—321no—
821C3#1171417511yescharacteristic, direct product factor
822C2—42no—
823C2—61no—
824C2—121no—
825C2—121no—
826C2—242no—
827C2—242no—
828C2C2×C3×#1020⋊C211yescharacteristic
subgroupG/H
center, socleC2×C3C2×#1020⋊C2
commutator, cosocle, hypocenter#997C23×C3
FrattiniC23C22×C3×S4
FittingC3×#3025D3
hypercenterC3×C4#1020⋊C2
LCSG ▷ #997
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#87522C2semidirect
2. C3×#87521C2semidirect
3. C3×#73032C2semidirect
4. C3×#73026C2semidirect
5. C3×#3025⋊C3C2semidirect
6. #11714175C3direct (N × H)
8. C3×#5950C22semidirect
9. C3×#5935C22semidirect
10. C3×#5934C22semidirect
12. C3×#458⋊C3C22semidirect
13. C3×B(4,𝔽2)⋊C3C22semidirect
14. #87522C2×C3semidirect
15. #87521C2×C3semidirect
18. C3×#3025D3semidirect
21. #3025⋊C3C2×C3semidirect
22. #73032C2×C3semidirect
23. #73026C2×C3semidirect
40. C3×#585C2×D3semidirect
42. #5950C22×C3semidirect
43. #5935C22×C3semidirect
44. #5934C22×C3semidirect
64. C3×#458C2×D3semidirect
79. #458⋊C3C22×C3semidirect
81. B(4,𝔽2)⋊C3C22×C3semidirect
101. #3025C3×D3semidirect
124. C23×C3×C4S4semidirect
222. #585C2×C3×D3semidirect
241. #458C2×C3×D3semidirect
398. C23×C4C3×S4semidirect
821. C3#11714175direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#875222
C3×#875212
C3×#730322
C3×#730262
C3×#3025⋊C32
#117141753
C3×#335533
C2×C3×C4⋊S44