Finite Group Databasebeta

← C3×#71671 #11792787

Subgroups — C3×#71671 #11792787

Order 1152.

1607 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#120C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic, complemented
3C3×#5804C211yesmaximal, characteristic, complemented
4C3×#5247C211yesmaximal, characteristic, complemented
5C2×C3×#834C211yesmaximal, characteristic, complemented
6C2×C3×#806C211yesmaximal, characteristic, complemented
7C3×#4527C211yesmaximal, characteristic, complemented
8C3×#2021—31nomaximal
9#71671C311yesmaximal, characteristic, direct product factor
10C25×C32C2211yescharacteristic
11C22×C32×D4—21no—
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×#67C2211yescharacteristic
15C32×#120—22no—
16C32×#120—22no—
17C2×C32×C22⋊C4—21no—
18C2×C32×C22⋊C4C2211yescharacteristic
19C3×#953—22no—
20C3×#953—21no—
21C3×#953—22no—
22C2×C3×#217—21no—
23C2×C3×#217—22no—
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C3×#939—22no—
28C3×#937—21no—
29C3×#935—21no—
30C3×#929—21no—
31C3×#834—22no—
32C3×#806—22no—
33C3×#534—31no—
34C2×C3×#120—21no—
35C2×C3×#120—31no—
36C2×C3×#120D311yescharacteristic, complemented
37C2×C3×#120C2×C311yescharacteristic, complemented
38C2×#953C2×C311yescharacteristic, complemented
39#5804C2×C311yescharacteristic, complemented
40C2×C3×#99—31no—
41C2×C3×#99—31no—
42C3×#379—31no—
43#5247C2×C311yescharacteristic, complemented
44C2×#834C2×C311yescharacteristic, complemented
45C2×#806C2×C311yescharacteristic, complemented
46C3×#342—31no—
47#4527C2×C311yescharacteristic, complemented
48C24×C32—21no—
49C24×C32—21no—
50C24×C32—21no—
51C24×C32—21no—
52C24×C32—21no—
53C24×C32—21no—
54C24×C32—44no—
55C24×C32D411yescharacteristic, complemented
56C24×C32D412yescomplemented
57C24×C32C2311yescharacteristic
58C23×C3×D3D411yescharacteristic, complemented
59C2×C32×D4—24no—
60C2×C32×D4—21no—
61C2×C32×D4—21no—
62C2×C32×D4—21no—
63C2×C32×D4—21no—
64C2×C32×D4—21no—
65C2×C32×D4—21no—
66C2×C32×D4—44no—
67C22×C32×C4—21no—
68C22×C32×C4D411yescharacteristic, complemented
69C2×C3×#67—24no—
70C2×C3×#67—21no—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C2×C3×#67—22no—
77C2×C3×#67—44no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3D411yescharacteristic, complemented
81C22×C3×Dic3D412yescomplemented
82C32×C22⋊C4—24no—
83C32×C22⋊C4—21no—
84C32×C22⋊C4D412yescomplemented
85C3×#217—22no—
86C3×#217—24no—
87C3×#217—21no—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—21no—
91C3×#217—21no—
92C3×#217—44no—
93C3×#217D412yescomplemented
94C3×(C2×D3)⋊C4—22no—
95C3×Dic3⋊C4—22no—
96#2021—31noSylow
97C25×C3—21no—
98C25×C3C2×D311yescharacteristic
99C25×C3C22×C311yescharacteristic
100C22×C3×D4—22no—
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4—21no—
104C22×C3×D4—31no—
105C22×C3×D4—61no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C22×C311yescharacteristic
108C22×#67—21no—
109C22×#67C22×C311yescharacteristic
110C3×#123—61no—
111C3×#123—61no—
112C3×#121—62no—
113C3×#120—24no—
114C3×#120—24no—
115C3×#120—22no—
116C3×#120—22no—
117C3×#120—22no—
118C3×#120—22no—
119C3×#120—62no—
120C3×#120—61no—
121C3×#120—62no—
122C3×#120—61no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—31no—
130C2×C3×C22⋊C4—61no—
131C2×C3×C22⋊C4—62no—
132C2×C3×C22⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4C22×C311yescharacteristic
134#953—21no—
135#953—22no—
136#953—22no—
137C2×#217—21no—
138C2×#217—22no—
139C2×#217C22×C311yescharacteristic
140C2×#217C22×C311yescharacteristic
141C2×#217C22×C311yescharacteristic
142#939—22no—
143#937—21no—
144#935—21no—
145#929—21no—
146C3×#99—62no—
147C3×#99—62no—
148#834—22no—
149#806—22no—
150C23×C32—24no—
151C23×C32—22no—
152C23×C32—21no—
153C23×C32—24no—
154C23×C32—24no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32—21no—
158C23×C32—21no—
159C23×C32—44no—
160C23×C32—42no—
161C23×C32—42no—
162C23×C32—44no—
163C23×C32—42no—
164C23×C32—42no—
165C23×C32—44no—
166C23×C32—44no—
167C23×C32—42no—
168C23×C32—41no—
169C23×C32—41no—
170C23×C32—41no—
171C23×C32—41no—
172C23×C32C2×D411yescharacteristic
173C23×C32C2×D411yescharacteristic
174C23×C32C2×D411yescharacteristic
175C23×C32C2×D411yescharacteristic
176C23×C32C2×D411yescharacteristic
177C23×C32C2×D411yescharacteristic
178C23×C32#4111yescharacteristic
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—42no—
183C32×D4—48no—
184C32×D4—41no—
185C32×D4—41no—
186C32×D4—41no—
187C32×D4—41no—
188C2×C32×C4—21no—
189C2×C32×C4—22no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—42no—
193C3×#67—48no—
194C3×#67—41no—
195C3×#67—41no—
196C3×#67—41no—
197C3×#67—41no—
198C3×#67—82no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—42no—
205C2×C3×Dic3—42no—
206C2×C3×Dic3—42no—
207C2×C3×Dic3—41no—
208#534—31no—
209C2×#120—31no—
210C2×#120C3×D311yescharacteristic, complemented
211C2×#99—31no—
212C2×#99—31no—
213#379—31no—
214#342—31no—
215C24×C3—22no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—22no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—22no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—31no—
233C24×C3—41no—
234C24×C3—41no—
235C24×C3—41no—
236C24×C3—41no—
237C24×C3—44no—
238C24×C3—44no—
239C24×C3—48no—
240C24×C3#6712yescomplemented
241C24×C3#6711yescharacteristic, complemented
242C24×C3C3×D412yescomplemented
243C24×C3C3×D411yescharacteristic, complemented
244C24×C3C22×D311yescharacteristic
245C24×C3C23×C311yescharacteristic
246C23×D3C3×D411yescharacteristic, complemented
247C2×C3×D4—28no—
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4—22no—
251C2×C3×D4—22no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—41no—
265C2×C3×D4—41no—
266C2×C3×D4—41no—
267C2×C3×D4—41no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—48no—
271C2×C3×D4—64no—
272C2×C3×D4—61no—
273C2×C3×D4—61no—
274C2×C3×D4—61no—
275C2×C3×D4—61no—
276C2×C3×D4—61no—
277C2×C3×D4—61no—
278C2×C3×D4—62no—
279C2×C3×D4—124no—
280C22×C3×C4—22no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—32no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288C22×C3×C4#6711yescharacteristic, complemented
289C22×C3×C4C3×D411yescharacteristic, complemented
290C2×#67—24no—
291C2×#67—21no—
292C2×#67—21no—
293C2×#67—21no—
294C2×#67—21no—
295C2×#67—21no—
296C2×#67—21no—
297C2×#67—22no—
298C2×#67—44no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3C3×D411yescharacteristic, complemented
302C22×Dic3C3×D412yescomplemented
303C3×C4⋊C4—62no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—32no—
312C3×C22⋊C4—62no—
313C3×C22⋊C4—64no—
314C3×C22⋊C4—62no—
315C3×C22⋊C4—61no—
316C3×C22⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—124no—
321C3×C22⋊C4#6712yescomplemented
322C3×C22⋊C4C3×D412yescomplemented
323#217—22no—
324#217—24no—
325#217—21no—
326#217—21no—
327#217—21no—
328#217—21no—
329#217—21no—
330#217—44no—
331#217C3×D412yescomplemented
332(C2×D3)⋊C4—22no—
333Dic3⋊C4—22no—
334C22×C32—22no—
335C22×C32—24no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—24no—
339C22×C32—24no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—42no—
345C22×C32—44no—
346C22×C32—42no—
347C22×C32—44no—
348C22×C32—44no—
349C22×C32—42no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—44no—
353C22×C32—41no—
354C22×C32—42no—
355C22×C32—81no—
356C22×C32#12011yescharacteristic
357C22×C32#12011yescharacteristic
358C22×C32#12011yescharacteristic
359C22×C32#12111yescharacteristic
360C22×C32#12111yescharacteristic
361C22×C32#12111yescharacteristic
362C22×C32#12711yescharacteristic
363C2×C3×D3—42no—
364C2×C3×D3—41no—
365C2×C3×D3—42no—
366C2×C3×D3—81no—
367C32×C4—42no—
368C32×C4—41no—
369C3×Dic3—42no—
370C3×Dic3—41no—
371C3×Dic3—42no—
372C3×Dic3—81no—
373C25C2×C3×D311yescharacteristic
374C22×D4—21no—
375C22×D4—31no—
376C22×D4—61no—
377C22×D4C2×C3×D311yescharacteristic
378#123—61no—
379#123—61no—
380#121—62no—
381#120—22no—
382#120—22no—
383#120—62no—
384#120—61no—
385#120—62no—
386#120—61no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—31no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4C2×C3×D311yescharacteristic
394#99—62no—
395#99—62no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—28no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—48no—
435C23×C3—44no—
436C23×C3—44no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—44no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3—48no—
447C23×C3—44no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3—42no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—48no—
460C23×C3—48no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—122no—
473C23×C3D3×D411yescharacteristic
474C23×C3D3×D411yescharacteristic
475C23×C3D3×D411yescharacteristic
476C23×C3#23711yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C23×C3C2×#6711yescharacteristic
480C23×C3C2×C3×D411yescharacteristic
481C23×C3C2×C3×D411yescharacteristic
482C23×C3C2×C3×D411yescharacteristic
483C23×C3C2×C3×D411yescharacteristic
484C23×C3C2×C3×D411yescharacteristic
485C23×C3C2×C3×D411yescharacteristic
486C23×C3C3×#4111yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—42no—
491C3×D4—416no—
492C3×D4—48no—
493C3×D4—48no—
494C3×D4—42no—
495C3×D4—42no—
496C3×D4—42no—
497C3×D4—42no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—128no—
507C3×D4—121no—
508C3×D4—121no—
509C3×D4—121no—
510C3×D4—121no—
511C3×D4—242no—
512C2×C3×C4—22no—
513C2×C3×C4—24no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—44no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—62no—
528C2×C3×C4—61no—
529C2×C3×C4—62no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—121no—
536#67—48no—
537#67—41no—
538#67—41no—
539#67—41no—
540#67—41no—
541#67—82no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544C2×Dic3—21no—
545C2×Dic3—22no—
546C2×Dic3—21no—
547C2×Dic3—42no—
548C2×Dic3—42no—
549C2×Dic3—42no—
550C2×Dic3—41no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—44no—
558C2×C32—81no—
559C2×C32#39211yescharacteristic
560C2×C32B(4,𝔽2)12yes—
561C3×D3—81no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—31no—
569C24—44no—
570C24C3×#6712yescomplemented
571C24C3×#6711yescharacteristic, complemented
572C24C22×C3×D311yescharacteristic
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—44no—
581C2×D4—64no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—62no—
589C2×D4—124no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—32no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4C3×#6711yescharacteristic, complemented
596C4⋊C4—62no—
597C22⋊C4—24no—
598C22⋊C4—21no—
599C22⋊C4—32no—
600C22⋊C4—62no—
601C22⋊C4—64no—
602C22⋊C4—62no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—124no—
609C22⋊C4C3×#6712yescomplemented
610C22×C3—24no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—24no—
618C22×C3—28no—
619C22×C3—24no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—44no—
648C22×C3—48no—
649C22×C3—42no—
650C22×C3—44no—
651C22×C3—42no—
652C22×C3—44no—
653C22×C3—42no—
654C22×C3—44no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—44no—
658C22×C3—42no—
659C22×C3—44no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—48no—
663C22×C3—44no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—48no—
670C22×C3—48no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—82no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—82no—
683C22×C3—122no—
684C22×C3—121no—
685C22×C3—122no—
686C22×C3—241no—
687C22×C3#93711yescharacteristic
688C22×C3#93711yescharacteristic
689C22×C3#93811yescharacteristic
690C22×C3#93911yescharacteristic
691C22×C3#93911yescharacteristic
692C22×C3#94011yescharacteristic
693C22×C3#95311yescharacteristic
694C22×C3C3×#12011yescharacteristic
695C22×C3C3×#12011yescharacteristic
696C22×C3C3×#12011yescharacteristic
697C22×C3C3×#12111yescharacteristic
698C22×C3C3×#12111yescharacteristic
699C22×C3C3×#12111yescharacteristic
700C22×C3C3×#12711yescharacteristic
701C2×D3—42no—
702C2×D3—41no—
703C2×D3—42no—
704C2×D3—81no—
705C3×C4—44no—
706C3×C4—42no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—122no—
712C3×C4—121no—
713C3×C4—122no—
714C3×C4—241no—
715Dic3—42no—
716Dic3—41no—
717Dic3—42no—
718Dic3—81no—
719C32#202111yescharacteristic, complemented, Sylow
720C23—24no—
721C23—24no—
722C23—24no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—44no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—122no—
746C23C3×D3×D411yescharacteristic
747C23C3×D3×D411yescharacteristic
748C23C3×D3×D411yescharacteristic
749C23C3×#23711yescharacteristic
750C23C2×C3×#6711yescharacteristic
751C23C2×C3×#6711yescharacteristic
752C23C2×C3×#6711yescharacteristic
753D4—48no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—128no—
759D4—121no—
760D4—121no—
761D4—121no—
762D4—121no—
763D4—242no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—42no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—121no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—22no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—41no—
798C2×C3—48no—
799C2×C3—44no—
800C2×C3—44no—
801C2×C3—82no—
802C2×C3—81no—
803C2×C3—81no—
804C2×C3—241no—
805C2×C3#503212yes—
806C2×C3#522311yescharacteristic
807C2×C3C3×#39211yescharacteristic
808C2×C3C3×B(4,𝔽2)12yes—
809D3—81no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—81no—
832C22—122no—
833C22—121no—
834C22—122no—
835C22—241no—
836C22C3×#93711yescharacteristic
837C22C3×#93711yescharacteristic
838C22C3×#93811yescharacteristic
839C22C3×#93911yescharacteristic
840C22C3×#93911yescharacteristic
841C22C3×#94011yescharacteristic
842C22C3×#95311yescharacteristic
843C4—42no—
844C4—41no—
845C4—122no—
846C4—121no—
847C4—122no—
848C4—241no—
849C3—21no—
850C3#7167111yescharacteristic, direct product factor
851C3C3×#202111yescharacteristic, complemented
852C2—21no—
853C2—21no—
854C2—21no—
855C2—21no—
856C2—21no—
857C2—21no—
858C2—44no—
859C2—81no—
860C2—241no—
861C2C3×#503212yes—
862C2C3×#522311yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC2×C32×#120C2
socleC22×C32#120
hypercenterC2×C3×#120D3
hypocenterC3C3×#2021
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C2×C32×#120C2semidirect
2. C2×C3×#953C2semidirect
3. C3×#5804C2semidirect
4. C3×#5247C2semidirect
5. C2×C3×#834C2semidirect
6. C2×C3×#806C2semidirect
7. C3×#4527C2semidirect
9. #71671C3direct (N × H)
36. C2×C3×#120D3semidirect
37. C2×C3×#120C2×C3semidirect
38. C2×#953C2×C3semidirect
39. #5804C2×C3semidirect
43. #5247C2×C3semidirect
44. C2×#834C2×C3semidirect
45. C2×#806C2×C3semidirect
47. #4527C2×C3semidirect
55. C24×C32D4semidirect
56. C24×C32D4semidirect
58. C23×C3×D3D4semidirect
68. C22×C32×C4D4semidirect
80. C22×C3×Dic3D4semidirect
81. C22×C3×Dic3D4semidirect
84. C32×C22⋊C4D4semidirect
93. C3×#217D4semidirect
210. C2×#120C3×D3semidirect
240. C24×C3#67semidirect
241. C24×C3#67semidirect
242. C24×C3C3×D4semidirect
243. C24×C3C3×D4semidirect
246. C23×D3C3×D4semidirect
288. C22×C3×C4#67semidirect
289. C22×C3×C4C3×D4semidirect
301. C22×Dic3C3×D4semidirect
302. C22×Dic3C3×D4semidirect
321. C3×C22⋊C4#67semidirect
322. C3×C22⋊C4C3×D4semidirect
331. #217C3×D4semidirect
570. C24C3×#67semidirect
571. C24C3×#67semidirect
595. C22×C4C3×#67semidirect
609. C22⋊C4C3×#67semidirect
719. C32#2021semidirect
850. C3#71671direct (N × H)
851. C3C3×#2021semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C2×C3×#9532
C3×#58042
C3×#52472
C2×C3×#8342
C2×C3×#8062
C3×#45272
C3×#20213
#716713