Finite Group Databasebeta

← C3×#359558 #72270199

Subgroups — C3×#359558 #72270199

Order 1536.

9432 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3484C211yesmaximal, characteristic
2C3×#34171C211yesmaximal, characteristic, complemented
3C2×C3×#1911C212yesmaximal, complemented
4C3×#20953C212yesmaximal, complemented
5C3×#20616C212yesmaximal, complemented
6C2×C3×#1783C211yesmaximal, characteristic, complemented
7C3×#10994C214yesmaximal, complemented
8C3×#10740C212yesmaximal, complemented
9#359558C311yesmaximal, characteristic, direct product factor, Sylow
10C22×C3×H(5,𝔽2)C2211yescharacteristic
11C24×C3×D4C2211yescharacteristic
12C3×#3484—28no—
13C3×#3484—24no—
14C3×#3484C418yescomplemented
15C2×C3×#546—24no—
16C2×C3×D42—24no—
17C2×C3×#535C2212yes—
18C2×C3×#534—22no—
19C2×C3×#525C2212yes—
20C22×C3×#120—22no—
21C2×C3×#518C2211yescharacteristic
22C2×C3×#518C2211yescharacteristic, complemented
23C2×C3×#518C2211yescharacteristic, complemented
24C2×C3×#421C2214yescomplemented
25C3×#2896C2214yescomplemented
26C22×C3×#100C2212yes—
27C22×C3×#100C2212yescomplemented
28C2×C3×#407C2212yescomplemented
29C3×D4×C22⋊C4—28no—
30C3×#2309C2212yes—
31C3×#2308—22no—
32C3×#2280C2212yescomplemented
33C2×C3×#379—22no—
34C3×#1911—28no—
35C3×#1887—24no—
36C3×#1885—24no—
37C3×#1792—28no—
38C3×#1783—24no—
39C3×#1733C2214yescomplemented
40C2×C3×H(3,ℤ/4)C2214yescomplemented
41C2×#3484C2×C311yescharacteristic
42#34171C2×C311yescharacteristic, complemented
43C2×#1911C2×C312yescomplemented
44#20953C2×C312yescomplemented
45#20616C2×C312yescomplemented
46C2×#1783C2×C311yescharacteristic, complemented
47#10994C2×C314yescomplemented
48#10740C2×C312yescomplemented
49C26×C3D412yes—
50C2×C3×H(5,𝔽2)—24no—
51C2×C3×H(5,𝔽2)—22no—
52C2×C3×H(5,𝔽2)—24no—
53C2×C3×H(5,𝔽2)—24no—
54C2×C3×H(5,𝔽2)—42no—
55C2×C3×H(5,𝔽2)—42no—
56C2×C3×H(5,𝔽2)C2×C414yescomplemented
57C22×C3×#41—22no—
58C22×C3×#41C2312yes—
59C23×C3×D4—24no—
60C23×C3×D4—24no—
61C23×C3×D4—24no—
62C23×C3×D4—24no—
63C23×C3×D4—22no—
64C23×C3×D4—24no—
65C23×C3×D4—22no—
66C23×C3×D4—42no—
67C23×C3×D4—42no—
68C23×C3×D4C2×C414yes—
69C23×C3×D4D414yes—
70C23×C3×D4D412yes—
71C23×C3×D4C2311yescharacteristic
72C23×C3×D4C2311yescharacteristic
73C24×C3×C4C2311yescharacteristic
74C22×C3×M16C2314yes—
75C3×#546—232no—
76C3×#546—232no—
77C3×D42—232no—
78C3×D42—232no—
79C3×#535—24no—
80C3×#535—24no—
81C3×#535C2×C418yes—
82C3×#535D418yes—
83C3×#534—216no—
84C3×#534—216no—
85C2×C3×#127D414yes—
86C2×C3×#124D414yes—
87C3×#525—24no—
88C3×#525—24no—
89C3×#525—24no—
90C3×#525C2×C418yescomplemented
91C2×C3×#123—24no—
92C2×C3×#123—22no—
93C2×C3×C22⋊Q8—22no—
94C2×C3×#121—28no—
95C2×C3×#121—22no—
96C2×C3×#121—24no—
97C2×C3×#120—28no—
98C2×C3×#120—216no—
99C2×C3×#120—24no—
100C2×C3×#120—216no—
101C2×C3×#120—22no—
102C2×C3×#120—24no—
103C3×#518—22no—
104C3×#518—24no—
105C3×#518—24no—
106C3×#518—24no—
107C3×#518—42no—
108C3×#518—42no—
109C3×#518C2×C414yescomplemented
110C2×C3×C4×D4—24no—
111C2×C3×C4×D4—24no—
112C2×C3×C4×D4—24no—
113C2×C3×C4×D4—24no—
114C2×C3×#117C2312yes—
115C2×C3×#117C2312yes—
116C2×C3×#117C2312yes—
117C22×C3×C22⋊C4—24no—
118C22×C3×C22⋊C4—28no—
119C22×C3×C22⋊C4—22no—
120C22×C3×C22⋊C4—22no—
121C22×C3×C22⋊C4—22no—
122C3×#421—28no—
123C3×#421—44no—
124C2×C3×#104—28no—
125C3×#419—24no—
126C3×#418—24no—
127C3×#417—28no—
128C3×#416—44no—
129C2×C3×#100—24no—
130C2×C3×#100—24no—
131C2×C3×#100—24no—
132C2×C3×#100—24no—
133C2×C3×#100—24no—
134C2×C3×#100—24no—
135C3×#407—24no—
136C3×#407—42no—
137C2×C3×C22⋊C8—42no—
138C3×#390—24no—
139C3×#390D418yescomplemented
140C3×#386—28no—
141C3×#386—28no—
142C3×#381—22no—
143C3×#380—24no—
144C3×#379—28no—
145C3×#379—22no—
146C3×#379—24no—
147C3×C4×C22⋊C4—24no—
148C3×#339—28no—
149C3×H(3,ℤ/4)—28no—
150C22×H(5,𝔽2)C22×C311yescharacteristic
151C24×D4C22×C311yescharacteristic
152#3484—24no—
153#3484—28no—
154#3484C3×C418yescomplemented
155C2×#546—24no—
156C2×D42—24no—
157C2×#535C22×C312yes—
158C2×#534—22no—
159C2×#525C22×C312yes—
160C22×#120—22no—
161C2×#518C22×C311yescharacteristic
162C2×#518C22×C311yescharacteristic, complemented
163C2×#518C22×C311yescharacteristic, complemented
164C2×#421C22×C314yescomplemented
165#2896C22×C314yescomplemented
166C22×#100C22×C312yes—
167C22×#100C22×C312yescomplemented
168C2×#407C22×C312yescomplemented
169D4×C22⋊C4—28no—
170#2309C22×C312yes—
171#2308—22no—
172#2280C22×C312yescomplemented
173C2×#379—22no—
174#1911—28no—
175#1887—24no—
176#1885—24no—
177#1792—28no—
178#1783—24no—
179#1733C22×C314yescomplemented
180C2×H(3,ℤ/4)C22×C314yescomplemented
181C25×C3—22no—
182C25×C3—24no—
183C25×C3—24no—
184C25×C3—24no—
185C25×C3—24no—
186C25×C3—42no—
187C25×C3—42no—
188C25×C3—88no—
189C25×C3C22⋊C418yes—
190C25×C3C2×D411yescharacteristic
191C25×C3C2×D412yes—
192C25×C3C2×D412yes—
193C3×H(5,𝔽2)—216no—
194C3×H(5,𝔽2)—48no—
195C3×H(5,𝔽2)—416no—
196C3×H(5,𝔽2)—416no—
197C3×H(5,𝔽2)—48no—
198C3×H(5,𝔽2)—48no—
199C2×C3×#41—28no—
200C2×C3×#41—28no—
201C2×C3×#41—22no—
202C2×C3×#41—22no—
203C2×C3×#41—24no—
204C2×C3×#41—24no—
205C2×C3×#41—24no—
206C2×C3×#41—24no—
207C2×C3×#41—48no—
208C2×C3×#41—48no—
209C2×C3×#41C22×C414yes—
210C2×C3×#41C2×D414yes—
211C22×C3×Q8C2×D412yes—
212C22×C3×D4—24no—
213C22×C3×D4—24no—
214C22×C3×D4—28no—
215C22×C3×D4—28no—
216C22×C3×D4—28no—
217C22×C3×D4—24no—
218C22×C3×D4—24no—
219C22×C3×D4—24no—
220C22×C3×D4—24no—
221C22×C3×D4—22no—
222C22×C3×D4—232no—
223C22×C3×D4—28no—
224C22×C3×D4—216no—
225C22×C3×D4—28no—
226C22×C3×D4—216no—
227C22×C3×D4—216no—
228C22×C3×D4—216no—
229C22×C3×D4—22no—
230C22×C3×D4—22no—
231C22×C3×D4—22no—
232C22×C3×D4—22no—
233C22×C3×D4—22no—
234C22×C3×D4—22no—
235C22×C3×D4—22no—
236C22×C3×D4—22no—
237C22×C3×D4—48no—
238C22×C3×D4—48no—
239C22×C3×D4—42no—
240C22×C3×D4—42no—
241C22×C3×D4—416no—
242C22×C3×D4—416no—
243C22×C3×D4—416no—
244C22×C3×D4—416no—
245C22×C3×D4—48no—
246C22×C3×D4—48no—
247C22×C3×D4—44no—
248C22×C3×D4—44no—
249C22×C3×D4—44no—
250C22×C3×D4—44no—
251C22×C3×D4—816no—
252C22×C3×D4C22⋊C418yes—
253C22×C3×D4C22×C412yes—
254C22×C3×D4C22×C412yes—
255C22×C3×D4C2×D412yes—
256C22×C3×D4C2×D414yes—
257C22×C3×D4C2×D414yes—
258C22×C3×D4C2×D414yes—
259C22×C3×D4C2×D412yes—
260C22×C3×D4C2×D412yes—
261C22×C3×D4#4114yes—
262C23×C3×C4—22no—
263C23×C3×C4—24no—
264C23×C3×C4—22no—
265C23×C3×C4—22no—
266C23×C3×C4—22no—
267C23×C3×C4—22no—
268C23×C3×C4—22no—
269C23×C3×C4—22no—
270C23×C3×C4—22no—
271C23×C3×C4—24no—
272C23×C3×C4—24no—
273C23×C3×C4C22×C412yes—
274C23×C3×C4C2×D411yescharacteristic
275C23×C3×C4C2×D412yes—
276C23×C3×C4C2411yescharacteristic
277C2×C3×M16—24no—
278C2×C3×M16—24no—
279C2×C3×M16—24no—
280C2×C3×M16—24no—
281C2×C3×M16—24no—
282C2×C3×M16—24no—
283C22×C3×C8—24no—
284C3×#127—28no—
285C3×#127C22⋊C4116yescomplemented
286C3×#124—28no—
287C3×#124C22⋊C4116yescomplemented
288C3×#123—28no—
289C3×#123—232no—
290C3×#123—28no—
291C3×C22⋊Q8—28no—
292C3×C22⋊Q8—28no—
293C3×#121—28no—
294C3×#121—264no—
295C3×#121—216no—
296C3×#121—28no—
297C3×#121—216no—
298C3×#120—28no—
299C3×#120—264no—
300C3×#120—232no—
301C3×#120—28no—
302C3×#120—216no—
303C3×#120—216no—
304C3×C4×D4—216no—
305C3×C4×D4—216no—
306C3×C4×D4—216no—
307C3×C4×D4—216no—
308C3×C4×D4—416no—
309C3×C4×D4—416no—
310C3×#117—22no—
311C3×#117—22no—
312C3×#117—24no—
313C3×#117—24no—
314C3×#117—24no—
315C3×#117—24no—
316C3×#117C22×C414yes—
317C3×#117C2×D414yes—
318C2×C3×C4⋊C4—24no—
319C2×C3×C4⋊C4—22no—
320C2×C3×C4⋊C4—22no—
321C2×C3×C4⋊C4C2×D414yescomplemented
322C2×C3×C22⋊C4—24no—
323C2×C3×C22⋊C4—24no—
324C2×C3×C22⋊C4—28no—
325C2×C3×C22⋊C4—232no—
326C2×C3×C22⋊C4—24no—
327C2×C3×C22⋊C4—28no—
328C2×C3×C22⋊C4—28no—
329C2×C3×C22⋊C4—22no—
330C2×C3×C22⋊C4—28no—
331C2×C3×C22⋊C4—24no—
332C2×C3×C22⋊C4—24no—
333C2×C3×C22⋊C4—22no—
334C2×C3×C22⋊C4—22no—
335C2×C3×C22⋊C4—216no—
336C2×C3×C22⋊C4—44no—
337C2×C3×C22⋊C4—44no—
338C2×C3×C22⋊C4—44no—
339C2×C3×C22⋊C4—44no—
340C2×C3×C22⋊C4—816no—
341C2×C3×C42—22no—
342C2×C3×C42C2×D414yes—
343C2×C3×C42C2×D414yescomplemented
344C3×#104—416no—
345C3×#103—48no—
346C3×#102—48no—
347C3×#100—48no—
348C3×#100—48no—
349C3×C22⋊C8—48no—
350C3×#95—28no—
351C26C3×D412yes—
352C2×H(5,𝔽2)—24no—
353C2×H(5,𝔽2)—22no—
354C2×H(5,𝔽2)—24no—
355C2×H(5,𝔽2)—24no—
356C2×H(5,𝔽2)—42no—
357C2×H(5,𝔽2)—42no—
358C2×H(5,𝔽2)C2×C3×C414yescomplemented
359C22×#41—22no—
360C22×#41C23×C312yes—
361C23×D4—22no—
362C23×D4—24no—
363C23×D4—24no—
364C23×D4—24no—
365C23×D4—24no—
366C23×D4—22no—
367C23×D4—24no—
368C23×D4—42no—
369C23×D4—42no—
370C23×D4C2×C3×C414yes—
371C23×D4C3×D412yes—
372C23×D4C3×D414yes—
373C23×D4C23×C311yescharacteristic
374C23×D4C23×C311yescharacteristic
375C24×C4C23×C311yescharacteristic
376C22×M16C23×C314yes—
377#546—232no—
378#546—232no—
379D42—232no—
380D42—232no—
381#535—24no—
382#535—24no—
383#535C2×C3×C418yes—
384#535C3×D418yes—
385#534—216no—
386#534—216no—
387C2×#127C3×D414yes—
388C2×#124C3×D414yes—
389#525—24no—
390#525—24no—
391#525—24no—
392#525C2×C3×C418yescomplemented
393C2×#123—24no—
394C2×#123—22no—
395C2×C22⋊Q8—22no—
396C2×#121—28no—
397C2×#121—22no—
398C2×#121—24no—
399C2×#120—28no—
400C2×#120—216no—
401C2×#120—24no—
402C2×#120—216no—
403C2×#120—22no—
404C2×#120—24no—
405#518—22no—
406#518—24no—
407#518—24no—
408#518—24no—
409#518—42no—
410#518—42no—
411#518C2×C3×C414yescomplemented
412C2×C4×D4—24no—
413C2×C4×D4—24no—
414C2×C4×D4—24no—
415C2×C4×D4—24no—
416C2×#117C23×C312yes—
417C2×#117C23×C312yes—
418C2×#117C23×C312yes—
419C22×C22⋊C4—24no—
420C22×C22⋊C4—22no—
421C22×C22⋊C4—22no—
422C22×C22⋊C4—22no—
423C22×C22⋊C4—28no—
424#421—28no—
425#421—44no—
426C2×#104—28no—
427#419—24no—
428#418—24no—
429#417—28no—
430#416—44no—
431C2×#100—24no—
432C2×#100—24no—
433C2×#100—24no—
434C2×#100—24no—
435C2×#100—24no—
436C2×#100—24no—
437#407—24no—
438#407—42no—
439C2×C22⋊C8—42no—
440#390—24no—
441#390C3×D418yescomplemented
442#386—28no—
443#386—28no—
444#381—22no—
445#380—24no—
446#379—28no—
447#379—24no—
448#379—22no—
449C4×C22⋊C4—24no—
450#339—28no—
451H(3,ℤ/4)—28no—
452C24×C3—21no—
453C24×C3—21no—
454C24×C3—22no—
455C24×C3—22no—
456C24×C3—21no—
457C24×C3—22no—
458C24×C3—22no—
459C24×C3—22no—
460C24×C3—22no—
461C24×C3—22no—
462C24×C3—22no—
463C24×C3—28no—
464C24×C3—21no—
465C24×C3—22no—
466C24×C3—21no—
467C24×C3—21no—
468C24×C3—216no—
469C24×C3—216no—
470C24×C3—44no—
471C24×C3—48no—
472C24×C3—48no—
473C24×C3—48no—
474C24×C3—48no—
475C24×C3—48no—
476C24×C3—416no—
477C24×C3—416no—
478C24×C3—44no—
479C24×C3—44no—
480C24×C3—88no—
481C24×C3—816no—
482C24×C3—84no—
483C24×C3—84no—
484C24×C3—88no—
485C24×C3—88no—
486C24×C3—816no—
487C24×C3—816no—
488C24×C3—88no—
489C24×C3—88no—
490C24×C3—816no—
491C24×C3C2×C22⋊C412yes—
492C24×C3C2×C22⋊C414yes—
493C24×C3C2×C22⋊C414yes—
494C24×C3#12014yes—
495C24×C3#12014yes—
496C24×C3#12014yes—
497C24×C3#12314yes—
498C24×C3C22×D411yescharacteristic
499C3×#41—28no—
500C3×#41—28no—
501C3×#41—28no—
502C3×#41—28no—
503C3×#41—432no—
504C3×#41—432no—
505C3×#41—44no—
506C3×#41—44no—
507C3×#41—44no—
508C3×#41—44no—
509C2×C3×Q8—22no—
510C2×C3×Q8—24no—
511C2×C3×Q8—24no—
512C2×C3×Q8C2×C22⋊C414yescomplemented
513C2×C3×D4—216no—
514C2×C3×D4—216no—
515C2×C3×D4—24no—
516C2×C3×D4—24no—
517C2×C3×D4—216no—
518C2×C3×D4—216no—
519C2×C3×D4—232no—
520C2×C3×D4—24no—
521C2×C3×D4—24no—
522C2×C3×D4—24no—
523C2×C3×D4—24no—
524C2×C3×D4—24no—
525C2×C3×D4—22no—
526C2×C3×D4—24no—
527C2×C3×D4—24no—
528C2×C3×D4—24no—
529C2×C3×D4—28no—
530C2×C3×D4—28no—
531C2×C3×D4—28no—
532C2×C3×D4—28no—
533C2×C3×D4—24no—
534C2×C3×D4—28no—
535C2×C3×D4—28no—
536C2×C3×D4—28no—
537C2×C3×D4—28no—
538C2×C3×D4—24no—
539C2×C3×D4—48no—
540C2×C3×D4—464no—
541C2×C3×D4—464no—
542C2×C3×D4—432no—
543C2×C3×D4—432no—
544C2×C3×D4—48no—
545C2×C3×D4—48no—
546C2×C3×D4—48no—
547C2×C3×D4—48no—
548C2×C3×D4—48no—
549C2×C3×D4—48no—
550C2×C3×D4—416no—
551C2×C3×D4—416no—
552C2×C3×D4—416no—
553C2×C3×D4—416no—
554C2×C3×D4—42no—
555C2×C3×D4—42no—
556C2×C3×D4—42no—
557C2×C3×D4—42no—
558C2×C3×D4—416no—
559C2×C3×D4—816no—
560C2×C3×D4—864no—
561C2×C3×D4C2×C22⋊C418yes—
562C2×C3×D4C2×C22⋊C414yescomplemented
563C2×C3×D4C4×D418yes—
564C2×C3×D4#12018yes—
565C2×C3×D4#12118yes—
566C22×C3×C4—28no—
567C22×C3×C4—21no—
568C22×C3×C4—24no—
569C22×C3×C4—22no—
570C22×C3×C4—21no—
571C22×C3×C4—21no—
572C22×C3×C4—21no—
573C22×C3×C4—21no—
574C22×C3×C4—21no—
575C22×C3×C4—216no—
576C22×C3×C4—24no—
577C22×C3×C4—24no—
578C22×C3×C4—24no—
579C22×C3×C4—24no—
580C22×C3×C4—24no—
581C22×C3×C4—24no—
582C22×C3×C4—24no—
583C22×C3×C4—24no—
584C22×C3×C4—24no—
585C22×C3×C4—24no—
586C22×C3×C4—44no—
587C22×C3×C4—44no—
588C22×C3×C4—44no—
589C22×C3×C4—44no—
590C22×C3×C4—44no—
591C22×C3×C4—44no—
592C22×C3×C4—44no—
593C22×C3×C4—44no—
594C22×C3×C4—48no—
595C22×C3×C4—48no—
596C22×C3×C4—88no—
597C22×C3×C4—88no—
598C22×C3×C4—88no—
599C22×C3×C4C2×C22⋊C412yes—
600C22×C3×C4C23×C411yescharacteristic
601C22×C3×C4C22×D412yes—
602C22×C3×C4C22×D412yes—
603C22×C3×C4C22×D412yes—
604C22×C3×C4C22×D411yescharacteristic
605C22×C3×C4C2×#4112yes—
606C22×C3×C4H(5,𝔽2)12yes—
607C22×C3×C4H(5,𝔽2)12yes—
608C3×M16—44no—
609C3×M16—44no—
610C3×M16—44no—
611C3×M16—44no—
612C2×C3×C8—44no—
613C2×C3×C8—44no—
614C2×C3×C8—44no—
615C3×C4⋊C4—216no—
616C3×C4⋊C4—24no—
617C3×C4⋊C4—24no—
618C3×C4⋊C4—28no—
619C3×C4⋊C4—44no—
620C3×C22⋊C4—216no—
621C3×C22⋊C4—216no—
622C3×C22⋊C4—216no—
623C3×C22⋊C4—24no—
624C3×C22⋊C4—24no—
625C3×C22⋊C4—232no—
626C3×C22⋊C4—48no—
627C3×C22⋊C4—48no—
628C3×C22⋊C4—416no—
629C3×C22⋊C4—42no—
630C3×C22⋊C4—42no—
631C3×C22⋊C4—42no—
632C3×C22⋊C4—42no—
633C3×C22⋊C4—816no—
634C3×C42—24no—
635C3×C42—28no—
636C3×C42—44no—
637C3×C42C2×C22⋊C418yescomplemented
638C25—22no—
639C25—24no—
640C25—24no—
641C25—24no—
642C25—24no—
643C25—42no—
644C25—42no—
645C25—88no—
646C25C3×C22⋊C418yes—
647C25C2×C3×D411yescharacteristic
648C25C2×C3×D412yes—
649C25C2×C3×D412yes—
650H(5,𝔽2)—216no—
651H(5,𝔽2)—48no—
652H(5,𝔽2)—416no—
653H(5,𝔽2)—416no—
654H(5,𝔽2)—48no—
655H(5,𝔽2)—48no—
656C2×#41—28no—
657C2×#41—28no—
658C2×#41—22no—
659C2×#41—22no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—24no—
664C2×#41—48no—
665C2×#41—48no—
666C2×#41C22×C3×C414yes—
667C2×#41C2×C3×D414yes—
668C22×Q8C2×C3×D412yes—
669C22×D4—24no—
670C22×D4—24no—
671C22×D4—28no—
672C22×D4—28no—
673C22×D4—28no—
674C22×D4—24no—
675C22×D4—24no—
676C22×D4—24no—
677C22×D4—24no—
678C22×D4—22no—
679C22×D4—232no—
680C22×D4—28no—
681C22×D4—216no—
682C22×D4—28no—
683C22×D4—216no—
684C22×D4—216no—
685C22×D4—216no—
686C22×D4—22no—
687C22×D4—22no—
688C22×D4—22no—
689C22×D4—22no—
690C22×D4—22no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—22no—
694C22×D4—48no—
695C22×D4—48no—
696C22×D4—42no—
697C22×D4—42no—
698C22×D4—416no—
699C22×D4—416no—
700C22×D4—416no—
701C22×D4—416no—
702C22×D4—48no—
703C22×D4—48no—
704C22×D4—44no—
705C22×D4—44no—
706C22×D4—44no—
707C22×D4—44no—
708C22×D4—816no—
709C22×D4C3×C22⋊C418yes—
710C22×D4C22×C3×C412yes—
711C22×D4C22×C3×C412yes—
712C22×D4C2×C3×D412yes—
713C22×D4C2×C3×D414yes—
714C22×D4C2×C3×D414yes—
715C22×D4C2×C3×D414yes—
716C22×D4C2×C3×D412yes—
717C22×D4C2×C3×D412yes—
718C22×D4C3×#4114yes—
719C23×C4—22no—
720C23×C4—24no—
721C23×C4—22no—
722C23×C4—22no—
723C23×C4—22no—
724C23×C4—22no—
725C23×C4—22no—
726C23×C4—22no—
727C23×C4—22no—
728C23×C4—24no—
729C23×C4—24no—
730C23×C4C22×C3×C412yes—
731C23×C4C2×C3×D411yescharacteristic
732C23×C4C2×C3×D412yes—
733C23×C4C24×C311yescharacteristic
734C2×M16—24no—
735C2×M16—24no—
736C2×M16—24no—
737C2×M16—24no—
738C2×M16—24no—
739C2×M16—24no—
740C22×C8—24no—
741#127—28no—
742#127C3×C22⋊C4116yescomplemented
743#124—28no—
744#124C3×C22⋊C4116yescomplemented
745#123—28no—
746#123—232no—
747#123—28no—
748C22⋊Q8—28no—
749C22⋊Q8—28no—
750#121—28no—
751#121—264no—
752#121—216no—
753#121—28no—
754#121—216no—
755#120—28no—
756#120—264no—
757#120—232no—
758#120—28no—
759#120—216no—
760#120—216no—
761C4×D4—216no—
762C4×D4—216no—
763C4×D4—216no—
764C4×D4—216no—
765C4×D4—416no—
766C4×D4—416no—
767#117—22no—
768#117—22no—
769#117—24no—
770#117—24no—
771#117—24no—
772#117—24no—
773#117C22×C3×C414yes—
774#117C2×C3×D414yes—
775C2×C4⋊C4—24no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4C2×C3×D414yescomplemented
779C2×C22⋊C4—24no—
780C2×C22⋊C4—24no—
781C2×C22⋊C4—28no—
782C2×C22⋊C4—232no—
783C2×C22⋊C4—24no—
784C2×C22⋊C4—28no—
785C2×C22⋊C4—28no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—28no—
788C2×C22⋊C4—24no—
789C2×C22⋊C4—24no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—216no—
793C2×C22⋊C4—44no—
794C2×C22⋊C4—44no—
795C2×C22⋊C4—44no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—816no—
798C2×C42—22no—
799C2×C42C2×C3×D414yes—
800C2×C42C2×C3×D414yescomplemented
801#104—416no—
802#103—48no—
803#102—48no—
804#100—48no—
805#100—48no—
806C22⋊C8—48no—
807#95—28no—
808C23×C3—24no—
809C23×C3—24no—
810C23×C3—24no—
811C23×C3—22no—
812C23×C3—24no—
813C23×C3—24no—
814C23×C3—24no—
815C23×C3—24no—
816C23×C3—22no—
817C23×C3—24no—
818C23×C3—22no—
819C23×C3—24no—
820C23×C3—24no—
821C23×C3—24no—
822C23×C3—24no—
823C23×C3—24no—
824C23×C3—24no—
825C23×C3—24no—
826C23×C3—24no—
827C23×C3—44no—
828C23×C3—42no—
829C23×C3—432no—
830C23×C3—48no—
831C23×C3—48no—
832C23×C3—42no—
833C23×C3—42no—
834C23×C3—42no—
835C23×C3—44no—
836C23×C3—44no—
837C23×C3—44no—
838C23×C3—48no—
839C23×C3—48no—
840C23×C3—48no—
841C23×C3—432no—
842C23×C3—432no—
843C23×C3—416no—
844C23×C3—41no—
845C23×C3—41no—
846C23×C3—41no—
847C23×C3—41no—
848C23×C3—42no—
849C23×C3—42no—
850C23×C3—84no—
851C23×C3—84no—
852C23×C3—816no—
853C23×C3—84no—
854C23×C3—84no—
855C23×C3—84no—
856C23×C3—84no—
857C23×C3—84no—
858C23×C3—84no—
859C23×C3—84no—
860C23×C3—84no—
861C23×C3—816no—
862C23×C3—816no—
863C23×C3—832no—
864C23×C3—816no—
865C23×C3—832no—
866C23×C3—832no—
867C23×C3—816no—
868C23×C3—832no—
869C23×C3—168no—
870C23×C3—168no—
871C23×C3#37918yes—
872C23×C3#38618yes—
873C23×C3C22×C22⋊C411yescharacteristic
874C23×C3C2×#12011yescharacteristic
875C23×C3C2×#12011yescharacteristic
876C23×C3C2×#12011yescharacteristic
877C23×C3C2×#12311yescharacteristic
878C23×C3#53411yescharacteristic
879C23×C3#53411yescharacteristic
880C3×Q8—28no—
881C3×Q8—44no—
882C3×D4—216no—
883C3×D4—216no—
884C3×D4—28no—
885C3×D4—216no—
886C3×D4—216no—
887C3×D4—432no—
888C3×D4—432no—
889C3×D4—432no—
890C3×D4—44no—
891C3×D4—44no—
892C3×D4—44no—
893C3×D4—44no—
894C3×D4—44no—
895C3×D4—832no—
896C2×C3×C4—22no—
897C2×C3×C4—28no—
898C2×C3×C4—24no—
899C2×C3×C4—22no—
900C2×C3×C4—22no—
901C2×C3×C4—416no—
902C2×C3×C4—48no—
903C2×C3×C4—41no—
904C2×C3×C4—41no—
905C2×C3×C4—42no—
906C2×C3×C4—41no—
907C2×C3×C4—41no—
908C2×C3×C4—42no—
909C2×C3×C4—48no—
910C2×C3×C4—48no—
911C2×C3×C4—48no—
912C2×C3×C4—48no—
913C2×C3×C4—48no—
914C2×C3×C4—48no—
915C2×C3×C4—44no—
916C2×C3×C4—44no—
917C2×C3×C4—816no—
918C2×C3×C4—168no—
919C2×C3×C4—168no—
920C2×C3×C4C22×C22⋊C412yes—
921C2×C3×C4C2×C4×D412yes—
922C2×C3×C4#51812yes—
923C2×C3×C4C2×#12012yes—
924C2×C3×C4C2×#12112yes—
925C2×C3×C4#53412yes—
926C2×C3×C4D4214yes—
927C2×C3×C4D4214yes—
928C2×C3×C4#54614yes—
929C2×C3×C4#54614yes—
930C3×C8—84no—
931C24—21no—
932C24—22no—
933C24—21no—
934C24—22no—
935C24—21no—
936C24—22no—
937C24—22no—
938C24—22no—
939C24—22no—
940C24—22no—
941C24—22no—
942C24—28no—
943C24—22no—
944C24—21no—
945C24—21no—
946C24—21no—
947C24—216no—
948C24—216no—
949C24—44no—
950C24—48no—
951C24—48no—
952C24—48no—
953C24—48no—
954C24—48no—
955C24—416no—
956C24—416no—
957C24—44no—
958C24—44no—
959C24—88no—
960C24—816no—
961C24—84no—
962C24—84no—
963C24—88no—
964C24—88no—
965C24—816no—
966C24—816no—
967C24—88no—
968C24—88no—
969C24—816no—
970C24C2×C3×C22⋊C412yes—
971C24C2×C3×C22⋊C414yes—
972C24C2×C3×C22⋊C414yes—
973C24C3×#12014yes—
974C24C3×#12014yes—
975C24C3×#12014yes—
976C24C3×#12314yes—
977C24C22×C3×D411yescharacteristic
978#41—28no—
979#41—28no—
980#41—28no—
981#41—28no—
982#41—432no—
983#41—432no—
984#41—44no—
985#41—44no—
986#41—44no—
987#41—44no—
988C2×Q8—22no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8C2×C3×C22⋊C414yescomplemented
992C2×D4—216no—
993C2×D4—216no—
994C2×D4—216no—
995C2×D4—216no—
996C2×D4—24no—
997C2×D4—24no—
998C2×D4—232no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—22no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—24no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—28no—
1011C2×D4—28no—
1012C2×D4—24no—
1013C2×D4—28no—
1014C2×D4—28no—
1015C2×D4—28no—
1016C2×D4—28no—
1017C2×D4—24no—
1018C2×D4—48no—
1019C2×D4—464no—
1020C2×D4—464no—
1021C2×D4—432no—
1022C2×D4—432no—
1023C2×D4—48no—
1024C2×D4—48no—
1025C2×D4—48no—
1026C2×D4—48no—
1027C2×D4—48no—
1028C2×D4—48no—
1029C2×D4—416no—
1030C2×D4—416no—
1031C2×D4—416no—
1032C2×D4—416no—
1033C2×D4—416no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—42no—
1037C2×D4—42no—
1038C2×D4—816no—
1039C2×D4—864no—
1040C2×D4C2×C3×C22⋊C418yes—
1041C2×D4C2×C3×C22⋊C414yescomplemented
1042C2×D4C3×C4×D418yes—
1043C2×D4C3×#12018yes—
1044C2×D4C3×#12118yes—
1045C22×C4—28no—
1046C22×C4—21no—
1047C22×C4—24no—
1048C22×C4—22no—
1049C22×C4—21no—
1050C22×C4—21no—
1051C22×C4—21no—
1052C22×C4—21no—
1053C22×C4—21no—
1054C22×C4—216no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—48no—
1074C22×C4—48no—
1075C22×C4—88no—
1076C22×C4—88no—
1077C22×C4—88no—
1078C22×C4C2×C3×C22⋊C412yes—
1079C22×C4C23×C3×C411yescharacteristic
1080C22×C4C22×C3×D412yes—
1081C22×C4C22×C3×D412yes—
1082C22×C4C22×C3×D412yes—
1083C22×C4C22×C3×D411yescharacteristic
1084C22×C4C2×C3×#4112yes—
1085C22×C4C3×H(5,𝔽2)12yes—
1086C22×C4C3×H(5,𝔽2)12yes—
1087M16—44no—
1088M16—44no—
1089M16—44no—
1090M16—44no—
1091C2×C8—44no—
1092C2×C8—44no—
1093C2×C8—44no—
1094C4⋊C4—216no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—44no—
1099C22⋊C4—216no—
1100C22⋊C4—216no—
1101C22⋊C4—216no—
1102C22⋊C4—232no—
1103C22⋊C4—24no—
1104C22⋊C4—24no—
1105C22⋊C4—48no—
1106C22⋊C4—48no—
1107C22⋊C4—416no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—816no—
1113C42—24no—
1114C42—28no—
1115C42—44no—
1116C42C2×C3×C22⋊C418yescomplemented
1117C22×C3—22no—
1118C22×C3—22no—
1119C22×C3—22no—
1120C22×C3—24no—
1121C22×C3—24no—
1122C22×C3—24no—
1123C22×C3—28no—
1124C22×C3—28no—
1125C22×C3—41no—
1126C22×C3—41no—
1127C22×C3—41no—
1128C22×C3—41no—
1129C22×C3—48no—
1130C22×C3—48no—
1131C22×C3—48no—
1132C22×C3—48no—
1133C22×C3—48no—
1134C22×C3—42no—
1135C22×C3—44no—
1136C22×C3—42no—
1137C22×C3—42no—
1138C22×C3—44no—
1139C22×C3—44no—
1140C22×C3—48no—
1141C22×C3—48no—
1142C22×C3—42no—
1143C22×C3—48no—
1144C22×C3—44no—
1145C22×C3—48no—
1146C22×C3—44no—
1147C22×C3—84no—
1148C22×C3—84no—
1149C22×C3—84no—
1150C22×C3—84no—
1151C22×C3—84no—
1152C22×C3—84no—
1153C22×C3—84no—
1154C22×C3—864no—
1155C22×C3—84no—
1156C22×C3—1616no—
1157C22×C3C2×#37911yescharacteristic
1158C22×C3C2×#38611yescharacteristic
1159C22×C3#230811yescharacteristic
1160C22×C3#240311yescharacteristic
1161C22×C3#240311yescharacteristic
1162C22×C3#240511yescharacteristic
1163C22×C3#240511yescharacteristic
1164C3×C4—48no—
1165C3×C4—42no—
1166C3×C4—44no—
1167C3×C4—84no—
1168C3×C4—84no—
1169C3×C4D4×C22⋊C414yes—
1170C3×C4#241014yes—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—22no—
1181C23—24no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—44no—
1191C23—42no—
1192C23—432no—
1193C23—48no—
1194C23—48no—
1195C23—42no—
1196C23—42no—
1197C23—42no—
1198C23—44no—
1199C23—44no—
1200C23—44no—
1201C23—48no—
1202C23—48no—
1203C23—48no—
1204C23—432no—
1205C23—432no—
1206C23—416no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—42no—
1212C23—42no—
1213C23—84no—
1214C23—84no—
1215C23—816no—
1216C23—84no—
1217C23—84no—
1218C23—84no—
1219C23—84no—
1220C23—84no—
1221C23—84no—
1222C23—84no—
1223C23—84no—
1224C23—816no—
1225C23—816no—
1226C23—832no—
1227C23—816no—
1228C23—832no—
1229C23—832no—
1230C23—816no—
1231C23—832no—
1232C23—168no—
1233C23—168no—
1234C23C3×#37918yes—
1235C23C3×#38618yes—
1236C23C22×C3×C22⋊C411yescharacteristic
1237C23C2×C3×#12011yescharacteristic
1238C23C2×C3×#12011yescharacteristic
1239C23C2×C3×#12011yescharacteristic
1240C23C2×C3×#12311yescharacteristic
1241C23C3×#53411yescharacteristic
1242C23C3×#53411yescharacteristic
1243Q8—28no—
1244Q8—44no—
1245D4—216no—
1246D4—216no—
1247D4—216no—
1248D4—216no—
1249D4—28no—
1250D4—432no—
1251D4—432no—
1252D4—432no—
1253D4—44no—
1254D4—44no—
1255D4—44no—
1256D4—44no—
1257D4—44no—
1258D4—832no—
1259C2×C4—28no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—416no—
1265C2×C4—48no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—42no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—42no—
1272C2×C4—48no—
1273C2×C4—48no—
1274C2×C4—48no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4—48no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—816no—
1281C2×C4—168no—
1282C2×C4—168no—
1283C2×C4C22×C3×C22⋊C412yes—
1284C2×C4C2×C3×C4×D412yes—
1285C2×C4C3×#51812yes—
1286C2×C4C2×C3×#12012yes—
1287C2×C4C2×C3×#12112yes—
1288C2×C4C3×#53412yes—
1289C2×C4C3×D4214yes—
1290C2×C4C3×D4214yes—
1291C2×C4C3×#54614yes—
1292C2×C4C3×#54614yes—
1293C8—84no—
1294C2×C3—21no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—21no—
1299C2×C3—21no—
1300C2×C3—44no—
1301C2×C3—48no—
1302C2×C3—48no—
1303C2×C3—84no—
1304C2×C3#1386711yescharacteristic
1305C2×C3#2389712yes—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—24no—
1310C22—24no—
1311C22—24no—
1312C22—28no—
1313C22—28no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—48no—
1319C22—48no—
1320C22—48no—
1321C22—48no—
1322C22—42no—
1323C22—44no—
1324C22—42no—
1325C22—42no—
1326C22—44no—
1327C22—44no—
1328C22—48no—
1329C22—48no—
1330C22—48no—
1331C22—42no—
1332C22—48no—
1333C22—44no—
1334C22—48no—
1335C22—44no—
1336C22—84no—
1337C22—84no—
1338C22—84no—
1339C22—84no—
1340C22—84no—
1341C22—84no—
1342C22—84no—
1343C22—864no—
1344C22—84no—
1345C22—1616no—
1346C22C2×C3×#37911yescharacteristic
1347C22C2×C3×#38611yescharacteristic
1348C22C3×#230811yescharacteristic
1349C22C3×#240311yescharacteristic
1350C22C3×#240311yescharacteristic
1351C22C3×#240511yescharacteristic
1352C22C3×#240511yescharacteristic
1353C4—48no—
1354C4—42no—
1355C4—44no—
1356C4—84no—
1357C4—84no—
1358C4C3×D4×C22⋊C414yes—
1359C4C3×#241014yes—
1360C3#35955811yescharacteristic, direct product factor, Sylow
1361C2—21no—
1362C2—21no—
1363C2—21no—
1364C2—21no—
1365C2—21no—
1366C2—21no—
1367C2—44no—
1368C2—48no—
1369C2—48no—
1370C2—84no—
1371C2C3×#1386711yescharacteristic
1372C2C3×#2389712yes—
subgroupG/H
center, socleC22×C3#2403
commutatorC22×C4C23×C3×C4
Frattini, cosocleC23×C4C24×C3
prime radicalC2×C3×#3484C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#34171C2semidirect
3. C2×C3×#1911C2semidirect
4. C3×#20953C2semidirect
5. C3×#20616C2semidirect
6. C2×C3×#1783C2semidirect
7. C3×#10994C2semidirect
8. C3×#10740C2semidirect
9. #359558C3direct (N × H)
14. C3×#3484C4semidirect
22. C2×C3×#518C22semidirect
23. C2×C3×#518C22semidirect
24. C2×C3×#421C22semidirect
25. C3×#2896C22semidirect
27. C22×C3×#100C22semidirect
28. C2×C3×#407C22semidirect
32. C3×#2280C22semidirect
39. C3×#1733C22semidirect
40. C2×C3×H(3,ℤ/4)C22semidirect
42. #34171C2×C3semidirect
43. C2×#1911C2×C3semidirect
44. #20953C2×C3semidirect
45. #20616C2×C3semidirect
46. C2×#1783C2×C3semidirect
47. #10994C2×C3semidirect
48. #10740C2×C3semidirect
56. C2×C3×H(5,𝔽2)C2×C4semidirect
90. C3×#525C2×C4semidirect
109. C3×#518C2×C4semidirect
139. C3×#390D4semidirect
154. #3484C3×C4semidirect
162. C2×#518C22×C3semidirect
163. C2×#518C22×C3semidirect
164. C2×#421C22×C3semidirect
165. #2896C22×C3semidirect
167. C22×#100C22×C3semidirect
168. C2×#407C22×C3semidirect
172. #2280C22×C3semidirect
179. #1733C22×C3semidirect
180. C2×H(3,ℤ/4)C22×C3semidirect
285. C3×#127C22⋊C4semidirect
287. C3×#124C22⋊C4semidirect
321. C2×C3×C4⋊C4C2×D4semidirect
343. C2×C3×C42C2×D4semidirect
358. C2×H(5,𝔽2)C2×C3×C4semidirect
392. #525C2×C3×C4semidirect
411. #518C2×C3×C4semidirect
441. #390C3×D4semidirect
512. C2×C3×Q8C2×C22⋊C4semidirect
562. C2×C3×D4C2×C22⋊C4semidirect
637. C3×C42C2×C22⋊C4semidirect
742. #127C3×C22⋊C4semidirect
744. #124C3×C22⋊C4semidirect
778. C2×C4⋊C4C2×C3×D4semidirect
800. C2×C42C2×C3×D4semidirect
991. C2×Q8C2×C3×C22⋊C4semidirect
1041. C2×D4C2×C3×C22⋊C4semidirect
1116. C42C2×C3×C22⋊C4semidirect
1360. C3#359558direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#34842
C3×#341712
C2×C3×#19112
C3×#209532
C3×#206162
C2×C3×#17832
C3×#109942
C3×#107402
#3595583