Finite Group Databasebeta

← C3×#11714174 #72275010

Subgroups — C3×#11714174 #72275010

Order 2304.

1204 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 1204 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×#87519C211yesmaximal, characteristic, complemented
3C3×#73028C212yesmaximal, complemented
4C3×#73026C212yesmaximal, complemented
5C3×#3027⋊C3C211yesmaximal, characteristic, complemented
6#11714174C311yesmaximal, characteristic, direct product factor
7C3×#33553—31nomaximal
8C3×#5950C2211yescharacteristic, complemented
9C3×#5935C2212yescomplemented
10C3×#5934C2211yescharacteristic, complemented
11C3×#5932C2211yescharacteristic, complemented
12C3×D4×S4—41nomaximal
13C3×B(4,𝔽2)⋊C3C2212yescomplemented
14#87522C2×C311yescharacteristic, complemented
15#87519C2×C311yescharacteristic, complemented
16C3×#3537—31no—
17C3×#3027D311yescharacteristic, complemented
18C3×#3025—31no—
19C3×#3021—31no—
20#3027⋊C3—21no—
21#3027⋊C3C2×C311yescharacteristic, complemented
22#73028C2×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
33C3×D4×A4—41no—
34C3×GL(2,ℤ/4)—42no—
35C3×#986—81no—
36C3×C4⋊S4—41no—
37C3×C4×S4—41no—
38C3×C4×S4—81no—
39#33553—31noSylow
40C3×#585C2×D311yescharacteristic, complemented
41#5950—21no—
42#5950C22×C311yescharacteristic, complemented
43#5935C22×C312yescomplemented
44#5934C22×C311yescharacteristic, complemented
45#5932C22×C311yescharacteristic, complemented
46D4×S4—41no—
47C2×C3×AGL(1,ℤ/8)—61no—
48C3×#560—32no—
49C3×#560—61no—
50C3×#553—61no—
51C3×#553—61no—
52C3×D42—32no—
53C3×D42—61no—
54C3×D42—61no—
55C3×D42—61no—
56C3×#540—61no—
57C3×#538—62no—
58C3×#535—31no—
59C3×#535—31no—
60C3×#534—62no—
61C3×#525—31no—
62C3×#525—61no—
63C2×C3×#121—61no—
64C3×#458—31no—
65C3×#458—31no—
66C3×#458—61no—
67C3×B(4,𝔽2)—32no—
68C3×B(4,𝔽2)—31no—
69C3×B(4,𝔽2)—31no—
70C3×B(4,𝔽2)—61no—
71C3×B(4,𝔽2)C2×D312yescomplemented
72C3×#454—62no—
73C3×#453—32no—
74C3×#453—32no—
75C3×#421—61no—
76C3×#413—31no—
77C3×#410—31no—
78C3×#410—31no—
79C3×#410—61no—
80B(4,𝔽2)⋊C3—22no—
81B(4,𝔽2)⋊C3C22×C312yescomplemented
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—42no—
89C2×C3×S4—41no—
90C2×C3×S4—42no—
91C2×C3×S4—84no—
92C2×C3×S4—81no—
93C3×D3×D4—161no—
94C3×#41⋊C3—81no—
95C3×C4×A4—41no—
96C3×C4×A4—81no—
97C3×SL(2,ℤ/4)—41no—
98C3×SL(2,ℤ/4)—81no—
99C3×GL(2,𝔽3)—82no—
100#3537—31no—
101#3027C3×D311yescharacteristic, complemented
102#3025—31no—
103#3021—31no—
104#2200—32no—
105#2200—32no—
106#2196—32no—
107#2196—32no—
108#2128—31no—
109#2122—31no—
110#2120—31no—
111C22×S4—42no—
112C3×2−1+4—61no—
113C3×H(5,𝔽2)—31no—
114C3×H(5,𝔽2)—61no—
115C3×H(5,𝔽2)C22×D311yescharacteristic
116C2×C3×#41—31no—
117C2×C3×#41—61no—
118C2×C3×#41—61no—
119C22×C3×D4—31no—
120C22×C3×D4—62no—
121C22×C3×D4—61no—
122C22×C3×D4—62no—
123C22×C3×D4—62no—
124C22×C3×D4S411yescharacteristic, complemented
125C23×C3×C4—31no—
126#997—21no—
127#997C23×C311yescharacteristic
128D4×A4—41no—
129D4×A4—81no—
130GL(2,ℤ/4)—42no—
131#986—81no—
132C4⋊S4—41no—
133C4×S4—41no—
134C4×S4—81no—
135C3×AGL(1,ℤ/8)—62no—
136C3×AGL(1,ℤ/8)—62no—
137C3×AGL(1,ℤ/8)—121no—
138C3×AGL(1,ℤ/8)—121no—
139C2×C3×SD16—121no—
140C2×C3×D8—121no—
141C2×C3×M16—61no—
142C3×#127—32no—
143C3×#127—61no—
144C3×#127—61no—
145C3×#126—62no—
146C3×#126—62no—
147C3×#125—61no—
148C3×#124—32no—
149C3×#124—61no—
150C3×#123—31no—
151C3×#123—31no—
152C3×#123—62no—
153C3×#123—62no—
154C3×#123—62no—
155C3×#123—62no—
156C3×#123—61no—
157C3×#123—61no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—121no—
160C3×#121—62no—
161C3×#121—62no—
162C3×#121—62no—
163C3×#121—62no—
164C3×#121—61no—
165C3×#121—61no—
166C3×#121—61no—
167C3×#121—62no—
168C3×#121—61no—
169C3×#121—62no—
170C3×#121—62no—
171C3×#121—61no—
172C3×#121—61no—
173C3×#121—62no—
174C3×#121—61no—
175C3×#121—121no—
176C3×#120—31no—
177C3×#120—31no—
178C3×#120—32no—
179C3×#120—32no—
180C3×#120—61no—
181C3×#120—61no—
182C3×#120—62no—
183C3×#120—62no—
184C3×#120—62no—
185C3×#120—62no—
186C3×#120—61no—
187C3×#120—61no—
188C3×C4×D4—62no—
189C3×C4×D4—61no—
190C3×C4×D4—62no—
191C3×C4×D4—61no—
192C3×C4×D4—61no—
193C3×C4×D4—61no—
194C3×C4×D4—121no—
195C3×C4×D4—121no—
196C3×#117—31no—
197C3×#117—31no—
198C3×#117—31no—
199C3×#117—61no—
200C2×C3×C4⋊C4—61no—
201C2×C3×C22⋊C4—62no—
202C3×#104—62no—
203C3×#104—62no—
204C3×#101—61no—
205C3×#100—32no—
206C3×#99—32no—
207C3×#99—31no—
208C3×#99—31no—
209C3×#99—61no—
210C3×#99—61no—
211C3×#99—61no—
212C3×#99—61no—
213C3×#99—61no—
214C3×#99—61no—
215C22×C3×D3—162no—
216C2×C3×A4—41no—
217C2×C3×A4—81no—
218C2×C3×A4—82no—
219C3×S4—42no—
220C3×S4—82no—
221C3×S4—82no—
222C32×D4—161no—
223C3×#67—162no—
224C3×D12—161no—
225C3×C4×D3—161no—
226C3×SL(2,𝔽3)—81no—
227#585C2×C3×D311yescharacteristic, complemented
228C2×AGL(1,ℤ/8)—61no—
229#560—32no—
230#560—61no—
231#553—61no—
232#553—61no—
233D42—32no—
234D42—61no—
235D42—61no—
236D42—61no—
237#540—61no—
238#538—62no—
239#535—31no—
240#535—31no—
241#534—62no—
242#525—31no—
243#525—61no—
244C2×#121—61no—
245#458—31no—
246#458—31no—
247#458—61no—
248B(4,𝔽2)—32no—
249B(4,𝔽2)—31no—
250B(4,𝔽2)—31no—
251B(4,𝔽2)—61no—
252B(4,𝔽2)C2×C3×D312yescomplemented
253#454—62no—
254#453—32no—
255#453—32no—
256#421—61no—
257#413—31no—
258#410—31no—
259#410—31no—
260#410—61no—
261#353—32no—
262#353—32no—
263#352—32no—
264AΣL(1,𝔽16)—32no—
265AΣL(1,𝔽16)—32no—
266AΣL(1,𝔽16)—32no—
267C24×C3—31no—
268C24×C3—61no—
269C24×C3—62no—
270C24×C3C2×S412yes—
271C22×A4—42no—
272C22×A4—82no—
273C2×S4—41no—
274C2×S4—42no—
275C2×S4—81no—
276C2×S4—84no—
277C3×#41—21no—
278C3×#41—61no—
279C3×#41—61no—
280C3×#41—61no—
281C3×#41—121no—
282C3×#41—121no—
283C3×#41—121no—
284C3×#41—121no—
285C3×#41—121no—
286C2×C3×Q8—31no—
287C2×C3×Q8—61no—
288C2×C3×Q8—61no—
289C2×C3×D4—31no—
290C2×C3×D4—31no—
291C2×C3×D4—31no—
292C2×C3×D4—32no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—62no—
305C2×C3×D4—62no—
306C2×C3×D4—62no—
307C2×C3×D4—62no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C2×C3×D4—121no—
312C2×C3×D4—121no—
313C2×C3×D4—121no—
314C2×C3×D4—121no—
315C2×C3×D4—121no—
316C2×C3×D4—241no—
317C2×C3×D4—241no—
318C2×C3×D4—244no—
319C2×C3×D4—244no—
320C2×C3×D4—244no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—121no—
332C22×C3×C4—121no—
333C22×C3×C4C2×S411yescharacteristic
334D3×D4—161no—
335#41⋊C3—81no—
336#41⋊C3—161no—
337C4×A4—41no—
338C4×A4—81no—
339C4×A4—81no—
340C4×A4—161no—
341SL(2,ℤ/4)—41no—
342SL(2,ℤ/4)—81no—
343GL(2,𝔽3)—82no—
344C3×SD16—122no—
345C3×SD16—122no—
346C3×D8—122no—
347C3×D8—122no—
348C3×M16—62no—
349C3×M16—121no—
350C2×C3×C8—121no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—62no—
357C3×C4⋊C4—62no—
358C3×C4⋊C4—62no—
359C3×C4⋊C4—121no—
360C3×C4⋊C4—121no—
361C3×C4⋊C4—121no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—32no—
365C3×C22⋊C4—62no—
366C3×C22⋊C4—62no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—62no—
370C3×C22⋊C4—62no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—62no—
374C3×C22⋊C4—62no—
375C3×C22⋊C4—62no—
376C3×C22⋊C4—62no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—121no—
381C3×C22⋊C4—121no—
382C3×C22⋊C4—121no—
383C3×C22⋊C4—121no—
384C3×C42—32no—
385C3×C42—61no—
386C3×C42—61no—
387C3×C42—121no—
388C22×C32—162no—
389C2×C3×D3—161no—
390C2×C3×D3—162no—
391C2×C3×D3—324no—
392C3×A4—41no—
393C3×A4—81no—
394C32×C4—161no—
395C3×Dic3—161no—
3962−1+4—61no—
397H(5,𝔽2)—31no—
398H(5,𝔽2)—61no—
399H(5,𝔽2)C22×C3×D311yescharacteristic
400C2×#41—31no—
401C2×#41—61no—
402C2×#41—61no—
403C22×D4—31no—
404C22×D4—62no—
405C22×D4—61no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4C3×S411yescharacteristic, complemented
409C23×C4—31no—
410AGL(1,ℤ/8)—62no—
411AGL(1,ℤ/8)—62no—
412AGL(1,ℤ/8)—121no—
413AGL(1,ℤ/8)—121no—
414C2×SD16—121no—
415C2×D8—121no—
416C2×M16—61no—
417#127—32no—
418#127—61no—
419#127—61no—
420#126—62no—
421#126—62no—
422#125—61no—
423#124—32no—
424#124—61no—
425#123—31no—
426#123—31no—
427#123—62no—
428#123—62no—
429#123—62no—
430#123—62no—
431#123—61no—
432#123—61no—
433C22⋊Q8—61no—
434C22⋊Q8—121no—
435#121—62no—
436#121—62no—
437#121—62no—
438#121—61no—
439#121—61no—
440#121—62no—
441#121—61no—
442#121—61no—
443#121—62no—
444#121—62no—
445#121—61no—
446#121—61no—
447#121—62no—
448#121—62no—
449#121—61no—
450#121—121no—
451#120—31no—
452#120—31no—
453#120—32no—
454#120—32no—
455#120—61no—
456#120—61no—
457#120—62no—
458#120—62no—
459#120—62no—
460#120—62no—
461#120—61no—
462#120—61no—
463C4×D4—62no—
464C4×D4—61no—
465C4×D4—62no—
466C4×D4—61no—
467C4×D4—61no—
468C4×D4—61no—
469C4×D4—121no—
470C4×D4—121no—
471#117—31no—
472#117—31no—
473#117—31no—
474#117—61no—
475C2×C4⋊C4—61no—
476C2×C22⋊C4—62no—
477#104—62no—
478#104—62no—
479#101—61no—
480#100—32no—
481#99—32no—
482#99—31no—
483#99—31no—
484#99—61no—
485#99—61no—
486#99—61no—
487#99—61no—
488#99—61no—
489#99—61no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—62no—
494C23×C3—61no—
495C23×C3—62no—
496C23×C3—61no—
497C23×C3—82no—
498C23×C3—121no—
499C23×C3—122no—
500C23×C3—124no—
501C23×C3—242no—
502C23×C3—241no—
503C23×C3—242no—
504C23×C3—242no—
505C23×C3C22×S411yescharacteristic
506C22×D3—162no—
507C2×A4—41no—
508C2×A4—81no—
509C2×A4—82no—
510C2×A4—81no—
511C2×A4—161no—
512C2×A4—162no—
513S4—42no—
514S4—82no—
515S4—82no—
516C3×Q8—21no—
517C3×Q8—61no—
518C3×Q8—121no—
519C3×D4—41no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—121no—
523C3×D4—121no—
524C3×D4—121no—
525C3×D4—121no—
526C3×D4—121no—
527C3×D4—121no—
528C3×D4—122no—
529C3×D4—122no—
530C3×D4—124no—
531C3×D4—122no—
532C3×D4—124no—
533C3×D4—121no—
534C3×D4—161no—
535C3×D4—242no—
536C3×D4—242no—
537C3×D4—242no—
538C3×D4—242no—
539C3×D4—242no—
540C3×D4—242no—
541C3×D4—242no—
542C3×D4—242no—
543C3×D4—242no—
544C3×D4—321no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—62no—
559C2×C3×C4—61no—
560C2×C3×C4—121no—
561C2×C3×C4—121no—
562C2×C3×C4—121no—
563C2×C3×C4—121no—
564C2×C3×C4—121no—
565C2×C3×C4—121no—
566C2×C3×C4—241no—
567C2×C3×C4—242no—
568C2×C3×C4—242no—
569C2×C3×C4—242no—
570#67—162no—
571D12—161no—
572C4×D3—161no—
573SL(2,𝔽3)—81no—
574SL(2,𝔽3)—161no—
575C3×C8—122no—
576C2×C32—161no—
577C2×C32—322no—
578C3×D3—162no—
579C3×D3—322no—
580C24—31no—
581C24—61no—
582C24—62no—
583C24C2×C3×S412yes—
584#41—21no—
585#41—61no—
586#41—61no—
587#41—61no—
588#41—121no—
589#41—121no—
590#41—121no—
591#41—121no—
592#41—121no—
593C2×Q8—31no—
594C2×Q8—61no—
595C2×Q8—61no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—32no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4—62no—
612C2×D4—62no—
613C2×D4—62no—
614C2×D4—62no—
615C2×D4—62no—
616C2×D4—62no—
617C2×D4—62no—
618C2×D4—121no—
619C2×D4—121no—
620C2×D4—121no—
621C2×D4—121no—
622C2×D4—121no—
623C2×D4—241no—
624C2×D4—241no—
625C2×D4—244no—
626C2×D4—244no—
627C2×D4—244no—
628C22×C4—21no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—121no—
639C22×C4—121no—
640C22×C4C2×C3×S411yescharacteristic
641SD16—122no—
642SD16—122no—
643D8—122no—
644D8—122no—
645M16—62no—
646M16—121no—
647C2×C8—121no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—62no—
654C4⋊C4—62no—
655C4⋊C4—62no—
656C4⋊C4—121no—
657C4⋊C4—121no—
658C4⋊C4—121no—
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—32no—
662C22⋊C4—62no—
663C22⋊C4—62no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—62no—
667C22⋊C4—62no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—62no—
671C22⋊C4—62no—
672C22⋊C4—62no—
673C22⋊C4—62no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—121no—
678C22⋊C4—121no—
679C22⋊C4—121no—
680C22⋊C4—121no—
681C42—32no—
682C42—61no—
683C42—61no—
684C42—121no—
685C22×C3—31no—
686C22×C3—41no—
687C22×C3—42no—
688C22×C3—62no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—81no—
692C22×C3—122no—
693C22×C3—122no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—122no—
698C22×C3—122no—
699C22×C3—122no—
700C22×C3—121no—
701C22×C3—122no—
702C22×C3—162no—
703C22×C3—241no—
704C22×C3—241no—
705C22×C3—322no—
706C22×C3—484no—
707C22×C3—482no—
708C2×D3—161no—
709C2×D3—162no—
710C2×D3—324no—
711A4—41no—
712A4—81no—
713A4—81no—
714A4—161no—
715C3×C4—31no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—122no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4—122no—
722C3×C4—121no—
723C3×C4—161no—
724C3×C4—241no—
725C3×C4—241no—
726C3×C4—321no—
727C3×C4#1020⋊C211yescharacteristic
728Dic3—161no—
729C32—161noSylow
730C23—21no—
731C23—31no—
732C23—31no—
733C23—62no—
734C23—61no—
735C23—62no—
736C23—61no—
737C23—82no—
738C23—121no—
739C23—122no—
740C23—124no—
741C23—242no—
742C23—241no—
743C23—242no—
744C23—242no—
745C23C22×C3×S411yescharacteristic
746Q8—21no—
747Q8—61no—
748Q8—121no—
749D4—41no—
750D4—61no—
751D4—61no—
752D4—121no—
753D4—121no—
754D4—121no—
755D4—121no—
756D4—121no—
757D4—121no—
758D4—122no—
759D4—122no—
760D4—124no—
761D4—122no—
762D4—124no—
763D4—121no—
764D4—242no—
765D4—242no—
766D4—242no—
767D4—242no—
768D4—242no—
769D4—242no—
770D4—242no—
771D4—242no—
772D4—242no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4—61no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—241no—
795C2×C4—242no—
796C2×C4—242no—
797C2×C4—242no—
798C8—122no—
799C2×C3—61no—
800C2×C3—82no—
801C2×C3—121no—
802C2×C3—122no—
803C2×C3—121no—
804C2×C3—161no—
805C2×C3—242no—
806C2×C3—322no—
807C2×C3—321no—
808C2×C3—642no—
809C2×C3C2×#1020⋊C211yescharacteristic
810D3—162no—
811D3—322no—
812C22—31no—
813C22—41no—
814C22—42no—
815C22—62no—
816C22—61no—
817C22—61no—
818C22—81no—
819C22—122no—
820C22—122no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—122no—
825C22—122no—
826C22—122no—
827C22—121no—
828C22—122no—
829C22—241no—
830C22—241no—
831C22—484no—
832C22—482no—
833C4—31no—
834C4—61no—
835C4—61no—
836C4—122no—
837C4—121no—
838C4—121no—
839C4—122no—
840C4—121no—
841C4—241no—
842C4—241no—
843C4C3×#1020⋊C211yescharacteristic
844C3—161no—
845C3—321no—
846C3#1171417411yescharacteristic, direct product factor
847C2—61no—
848C2—82no—
849C2—121no—
850C2—122no—
851C2—121no—
852C2—242no—
853C2C2×C3×#1020⋊C211yescharacteristic
subgroupG/H
center, socleC2×C3C2×#1020⋊C2
commutator, cosocle, hypocenter#997C23×C3
FrattiniC23C22×C3×S4
FittingC3×#3027D3
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×#87519C2semidirect
3. C3×#73028C2semidirect
4. C3×#73026C2semidirect
5. C3×#3027⋊C3C2semidirect
6. #11714174C3direct (N × H)
8. C3×#5950C22semidirect
9. C3×#5935C22semidirect
10. C3×#5934C22semidirect
11. C3×#5932C22semidirect
13. C3×B(4,𝔽2)⋊C3C22semidirect
14. #87522C2×C3semidirect
15. #87519C2×C3semidirect
17. C3×#3027D3semidirect
21. #3027⋊C3C2×C3semidirect
22. #73028C2×C3semidirect
23. #73026C2×C3semidirect
40. C3×#585C2×D3semidirect
42. #5950C22×C3semidirect
43. #5935C22×C3semidirect
44. #5934C22×C3semidirect
45. #5932C22×C3semidirect
71. C3×B(4,𝔽2)C2×D3semidirect
81. B(4,𝔽2)⋊C3C22×C3semidirect
101. #3027C3×D3semidirect
124. C22×C3×D4S4semidirect
227. #585C2×C3×D3semidirect
252. B(4,𝔽2)C2×C3×D3semidirect
408. C22×D4C3×S4semidirect
846. C3#11714174direct (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×#875192
C3×#730282
C3×#730262
C3×#3027⋊C32
#117141743
C3×#335533
C3×D4×S44