Finite Group Databasebeta

← C3×#84005 #11865020

Subgroups — C3×#84005 #11865020

Order 1152.

1655 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C32×#575C211yesmaximal, characteristic, complemented
3C3×#5830C211yesmaximal, characteristic, complemented
4C3×#5822C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6C3×#5202C214yesmaximal, complemented
7C3×#5198C214yesmaximal, complemented
8C3×#5139C211yesmaximal, characteristic, complemented
9C2×C3×#823C211yesmaximal, characteristic, complemented
10C3×#3019—31nomaximal
11#84005C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C2×C32×#41C2211yescharacteristic, complemented
14C3×#1009—22no—
15C3×#1009—22no—
16C3×#1009—22no—
17C3×#1009C2214yes—
18C2×C3×#239—21no—
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4—22no—
21C2×C3×#235—21no—
22C2×C3×#235C2211yescharacteristic
23C22×C3×D12—21no—
24C22×C3×D12C2211yescharacteristic
25C32×#137—21no—
26C32×#137C2212yescomplemented
27C32×AGL(1,ℤ/8)—21no—
28C32×AGL(1,ℤ/8)C2212yescomplemented
29C32×#135—22no—
30C2×C32×M16C2211yescharacteristic, complemented
31C3×#951—21no—
32C3×#950—22no—
33C3×#949—21no—
34C3×#947C2212yescomplemented
35C3×#942C2212yescomplemented
36C3×#940C2212yescomplemented
37C3×#937—22no—
38C3×#932C2212yescomplemented
39C3×#930—22no—
40C3×#926C2211yescharacteristic, complemented
41C2×C3×#208C2211yescharacteristic, complemented
42C3×#837C2214yescomplemented
43C3×#825C2214yescomplemented
44C3×#823C2214yescomplemented
45C2×C3×H(5,𝔽2)—31no—
46C2×#1009C2×C311yescharacteristic, complemented
47C3×#575—21no—
48C3×#575—31no—
49C3×#575D311yescharacteristic, complemented
50C3×#575C2×C311yescharacteristic, complemented
51C3×#535—31no—
52#5830C2×C311yescharacteristic, complemented
53#5822C2×C311yescharacteristic, complemented
54C3×#455—34no—
55C3×#453—34no—
56C3×#421—31no—
57C3×#421—31no—
58C2×C3×#100—31no—
59#5236C2×C311yescharacteristic, complemented
60#5202C2×C314yescomplemented
61#5198C2×C314yescomplemented
62#5139C2×C311yescharacteristic, complemented
63C2×#823C2×C311yescharacteristic, complemented
64C23×C3×D3—22no—
65C23×C3×D3D412yes—
66C32×#41—21no—
67C32×#41—21no—
68C32×#41—21no—
69C32×#41—21no—
70C32×#41—21no—
71C32×#41—21no—
72C32×#41D412yescomplemented
73C32×#41C2312yes—
74C2×C32×Q8D411yescharacteristic, complemented
75C2×C32×Q8C2311yescharacteristic, complemented
76C2×C32×D4—21no—
77C2×C32×D4—21no—
78C2×C32×D4D411yescharacteristic, complemented
79C2×C32×D4C2311yescharacteristic, complemented
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—22no—
84C2×C3×#67—21no—
85C2×C3×#67—24no—
86C3×#239—24no—
87C3×#239—24no—
88C3×D3×D4—28no—
89C3×D3×D4—24no—
90C3×D3×D4—28no—
91C3×D3×D4—24no—
92C3×#235—24no—
93C3×#235—21no—
94C3×#235—21no—
95C3×#235—24no—
96C3×#235D412yescomplemented
97C3×#235C2312yes—
98C2×C3×D12—22no—
99C2×C3×D12—24no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—24no—
105C2×C3×D12D412yes—
106C2×C3×D12D411yescharacteristic, complemented
107C2×C3×D12C2312yes—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—21no—
110C2×C3×Dic6D411yescharacteristic, complemented
111C32×Q16—22no—
112C32×SD16—22no—
113C32×SD16—22no—
114C32×D8—22no—
115C32×M16—21no—
116C32×M16C2312yescomplemented
117C2×C32×C8—21no—
118C3×#217—21no—
119C3×#216—22no—
120C3×#215—22no—
121C3×#214—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—24no—
124C3×C4⋊Dic3—21no—
125C3×C4×Dic3C2312yescomplemented
126C3×#208—21no—
127C3×#208C2312yescomplemented
128C2×C3×C3⋊C8—21no—
129#3019—31noSylow
130C3×H(5,𝔽2)—34no—
131C3×H(5,𝔽2)—62no—
132C3×H(5,𝔽2)—62no—
133C3×H(5,𝔽2)—62no—
134C2×C3×#41—21no—
135C2×C3×#41—21no—
136C2×C3×#41—31no—
137C2×C3×#41—61no—
138C2×C3×#41—61no—
139C2×C3×#41C2×D311yescharacteristic
140C2×C3×#41C2×D311yescharacteristic, complemented
141C2×C3×#41C22×C311yescharacteristic
142C2×C3×#41C22×C311yescharacteristic, complemented
143C22×C3×D4—31no—
144C22×C3×D4—61no—
145C22×C3×D4—62no—
146C22×C3×D4—61no—
147#1009—22no—
148#1009—22no—
149#1009—22no—
150#1009C22×C314yes—
151C2×#239—21no—
152C2×D3×D4—22no—
153C2×D3×D4—21no—
154C2×#235—21no—
155C2×#235C22×C311yescharacteristic
156C22×D12—21no—
157C22×D12C22×C311yescharacteristic
158C3×#137—22no—
159C3×#137—21no—
160C3×#137—21no—
161C3×#137—22no—
162C3×#137—32no—
163C3×#137—61no—
164C3×#137C2×D312yescomplemented
165C3×#137C22×C312yescomplemented
166C3×AGL(1,ℤ/8)—22no—
167C3×AGL(1,ℤ/8)—21no—
168C3×AGL(1,ℤ/8)—21no—
169C3×AGL(1,ℤ/8)—22no—
170C3×AGL(1,ℤ/8)—32no—
171C3×AGL(1,ℤ/8)—61no—
172C3×AGL(1,ℤ/8)C2×D312yescomplemented
173C3×AGL(1,ℤ/8)C22×C312yescomplemented
174C3×#135—24no—
175C3×#135—22no—
176C3×#135—22no—
177C3×#135—62no—
178C2×C3×M16—21no—
179C2×C3×M16—31no—
180C2×C3×M16C2×D311yescharacteristic, complemented
181C2×C3×M16C22×C311yescharacteristic, complemented
182C3×#127—32no—
183C3×#124—32no—
184C3×#121—62no—
185C3×#120—62no—
186C3×#117—31no—
187#951—21no—
188#950—22no—
189#949—21no—
190#947C22×C312yescomplemented
191#942C22×C312yescomplemented
192#940C22×C312yescomplemented
193#937—22no—
194#932C22×C312yescomplemented
195#930—22no—
196#926C22×C311yescharacteristic, complemented
197C2×#208C22×C311yescharacteristic, complemented
198C3×#104—34no—
199C3×#104—34no—
200C3×#100—34no—
201#837C22×C314yescomplemented
202#825C22×C314yescomplemented
203#823C22×C314yescomplemented
204C23×C32—21no—
205C23×C32—21no—
206C23×C32C2×D411yescharacteristic
207C22×C3×D3—21no—
208C22×C3×D3—22no—
209C22×C3×D3—28no—
210C22×C3×D3—22no—
211C22×C3×D3—82no—
212C22×C3×D3—84no—
213C22×C3×D3C2×D414yes—
214C32×Q8—21no—
215C32×Q8—21no—
216C32×Q8—21no—
217C32×Q8C2×D412yes—
218C32×D4—21no—
219C32×D4—22no—
220C32×D4—22no—
221C32×D4—21no—
222C32×D4—21no—
223C32×D4—41no—
224C32×D4—41no—
225C32×D4C2×D412yes—
226C2×C32×C4—21no—
227C2×C32×C4—22no—
228C2×C32×C4—22no—
229C2×C32×C4—21no—
230C2×C32×C4—41no—
231C2×C32×C4—41no—
232C2×C32×C4C2×D411yescharacteristic
233C2×C32×C4C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2411yescharacteristic
238C3×#67—28no—
239C3×#67—22no—
240C3×#67—22no—
241C3×#67—84no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—22no—
244C3×D12—28no—
245C3×D12—22no—
246C3×D12—21no—
247C3×D12—22no—
248C3×D12—22no—
249C3×D12—22no—
250C3×D12C2×D412yes—
251C3×C4×D3—28no—
252C3×C4×D3—22no—
253C3×C4×D3—22no—
254C3×Dic6—21no—
255C3×Dic6C2×D412yes—
256C32×C8—22no—
257C3×C3⋊C8—22no—
258C2×H(5,𝔽2)—31no—
259#575—31no—
260#575C3×D311yescharacteristic, complemented
261#535—31no—
262#455—34no—
263#453—34no—
264#421—31no—
265#421—31no—
266C2×#100—31no—
267C24×C3—32no—
268C24×C3—62no—
269C23×D3—22no—
270C23×D3C3×D412yes—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—22no—
276C3×#41—22no—
277C3×#41—21no—
278C3×#41—21no—
279C3×#41—21no—
280C3×#41—21no—
281C3×#41—21no—
282C3×#41—21no—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—32no—
288C3×#41—32no—
289C3×#41—41no—
290C3×#41—41no—
291C3×#41—41no—
292C3×#41—41no—
293C3×#41—64no—
294C3×#41—64no—
295C3×#41—64no—
296C3×#41—64no—
297C3×#41—61no—
298C3×#41—61no—
299C3×#41#6712yescomplemented
300C3×#41C3×D412yescomplemented
301C3×#41C22×D312yes—
302C3×#41C23×C312yes—
303C2×C3×Q8—21no—
304C2×C3×Q8—21no—
305C2×C3×Q8—31no—
306C2×C3×Q8#6711yescharacteristic, complemented
307C2×C3×Q8C3×D411yescharacteristic, complemented
308C2×C3×Q8C22×D311yescharacteristic, complemented
309C2×C3×Q8C23×C311yescharacteristic, complemented
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—31no—
317C2×C3×D4—32no—
318C2×C3×D4—32no—
319C2×C3×D4—41no—
320C2×C3×D4—41no—
321C2×C3×D4—64no—
322C2×C3×D4—62no—
323C2×C3×D4—64no—
324C2×C3×D4—68no—
325C2×C3×D4—68no—
326C2×C3×D4—64no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—64no—
330C2×C3×D4—64no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4#6711yescharacteristic, complemented
336C2×C3×D4C3×D411yescharacteristic, complemented
337C2×C3×D4C22×D311yescharacteristic, complemented
338C2×C3×D4C23×C311yescharacteristic, complemented
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—41no—
345C22×C3×C4—41no—
346C22×C3×C4—62no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C23×C311yescharacteristic
350C2×#67—22no—
351C2×#67—21no—
352C2×#67—24no—
353#239—24no—
354#239—24no—
355D3×D4—28no—
356D3×D4—24no—
357D3×D4—28no—
358D3×D4—24no—
359#235—24no—
360#235—21no—
361#235—21no—
362#235—24no—
363#235C3×D412yescomplemented
364#235C23×C312yes—
365C2×D12—22no—
366C2×D12—24no—
367C2×D12—21no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—21no—
371C2×D12—24no—
372C2×D12C3×D412yes—
373C2×D12C3×D411yescharacteristic, complemented
374C2×D12C23×C312yes—
375C2×C4×D3—22no—
376C2×C4×D3—21no—
377C2×Dic6C3×D411yescharacteristic, complemented
378C3×Q16—24no—
379C3×Q16—22no—
380C3×Q16—22no—
381C3×Q16—62no—
382C3×SD16—24no—
383C3×SD16—24no—
384C3×SD16—22no—
385C3×SD16—22no—
386C3×SD16—22no—
387C3×SD16—22no—
388C3×SD16—62no—
389C3×SD16—62no—
390C3×D8—24no—
391C3×D8—22no—
392C3×D8—22no—
393C3×D8—62no—
394C3×M16—22no—
395C3×M16—21no—
396C3×M16—21no—
397C3×M16—22no—
398C3×M16—32no—
399C3×M16—61no—
400C3×M16C22×D312yescomplemented
401C3×M16C23×C312yescomplemented
402C2×C3×C8—22no—
403C2×C3×C8—21no—
404C2×C3×C8—21no—
405C2×C3×C8—61no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—64no—
408C3×C22⋊C4—61no—
409C3×C42—32no—
410#217—21no—
411#216—22no—
412#215—22no—
413#214—22no—
414#213—22no—
415(C2×D3)⋊C4—24no—
416C4⋊Dic3—21no—
417C4×Dic3C23×C312yescomplemented
418#208—21no—
419#208C23×C312yescomplemented
420C2×C3⋊C8—21no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—42no—
425C22×C32—42no—
426C22×C32#12011yescharacteristic
427C22×C32#12011yescharacteristic
428C22×C32C22×D411yescharacteristic
429C2×C3×D3—24no—
430C2×C3×D3—22no—
431C2×C3×D3—44no—
432C2×C3×D3—42no—
433C2×C3×D3—44no—
434C2×C3×D3—82no—
435C2×C3×D3—88no—
436C32×C4—22no—
437C32×C4—41no—
438C32×C4#12011yescharacteristic
439C32×C4#12011yescharacteristic
440C32×C4C22×D411yescharacteristic
441C32×C4C22×D411yescharacteristic
442C3×Dic3—22no—
443C3×Dic3—42no—
444H(5,𝔽2)—34no—
445H(5,𝔽2)—62no—
446H(5,𝔽2)—62no—
447H(5,𝔽2)—62no—
448C2×#41—31no—
449C2×#41—61no—
450C2×#41—61no—
451C2×#41C2×C3×D311yescharacteristic
452C2×#41C2×C3×D311yescharacteristic, complemented
453C22×D4—31no—
454C22×D4—61no—
455C22×D4—62no—
456C22×D4—61no—
457#137—21no—
458#137—32no—
459#137—61no—
460#137C2×C3×D312yescomplemented
461AGL(1,ℤ/8)—21no—
462AGL(1,ℤ/8)—32no—
463AGL(1,ℤ/8)—61no—
464AGL(1,ℤ/8)C2×C3×D312yescomplemented
465#135—22no—
466#135—62no—
467C2×M16—31no—
468C2×M16C2×C3×D311yescharacteristic, complemented
469#127—32no—
470#124—32no—
471#121—62no—
472#120—62no—
473#117—31no—
474#104—34no—
475#104—34no—
476#100—34no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—34no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—68no—
486C23×C3—61no—
487C23×C3—62no—
488C23×C3—62no—
489C23×C3—242no—
490C23×C3—244no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×C3×D411yescharacteristic
493C22×D3—22no—
494C22×D3—21no—
495C22×D3—28no—
496C22×D3—22no—
497C22×D3—82no—
498C22×D3—84no—
499C22×D3C2×C3×D414yes—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—22no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—22no—
508C3×Q8—32no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—61no—
512C3×Q8C2×#6712yes—
513C3×Q8C2×C3×D412yes—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—22no—
518C3×D4—22no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—22no—
526C3×D4—32no—
527C3×D4—41no—
528C3×D4—41no—
529C3×D4—42no—
530C3×D4—42no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—41no—
537C3×D4—68no—
538C3×D4—68no—
539C3×D4—62no—
540C3×D4—62no—
541C3×D4—61no—
542C3×D4—62no—
543C3×D4—62no—
544C3×D4—62no—
545C3×D4—62no—
546C3×D4—244no—
547C3×D4C2×#6712yes—
548C3×D4C2×C3×D412yes—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—42no—
564C2×C3×C4—42no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—42no—
568C2×C3×C4—42no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—68no—
574C2×C3×C4—61no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4D3×D411yescharacteristic
579C2×C3×C4D3×D411yescharacteristic
580C2×C3×C4D3×D411yescharacteristic
581C2×C3×C4C2×#6711yescharacteristic
582C2×C3×C4C2×#6711yescharacteristic
583C2×C3×C4C2×C3×D411yescharacteristic
584C2×C3×C4C2×C3×D411yescharacteristic
585C2×C3×C4C2×C3×D411yescharacteristic
586C2×C3×C4C2×C3×D411yescharacteristic
587C2×C3×C4C2×C3×D411yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C24×C311yescharacteristic
590#67—28no—
591#67—22no—
592#67—22no—
593#67—84no—
594C2×Dic3—21no—
595C2×Dic3—22no—
596D12—28no—
597D12—22no—
598D12—21no—
599D12—22no—
600D12—22no—
601D12—22no—
602D12C2×C3×D412yes—
603C4×D3—28no—
604C4×D3—22no—
605C4×D3—22no—
606Dic6—21no—
607Dic6C2×C3×D412yes—
608C3×C8—24no—
609C3×C8—22no—
610C3×C8—22no—
611C3×C8—62no—
612C3⋊C8—22no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—42no—
617C2×C32—81no—
618C2×C32C2×#12011yescharacteristic
619C3×D3—44no—
620C3×D3—42no—
621C24—32no—
622C24—62no—
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—32no—
630#41—32no—
631#41—64no—
632#41—64no—
633#41—64no—
634#41—64no—
635#41—61no—
636#41—61no—
637#41C3×#6712yescomplemented
638#41C22×C3×D312yes—
639C2×Q8—31no—
640C2×Q8C3×#6711yescharacteristic, complemented
641C2×Q8C22×C3×D311yescharacteristic, complemented
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—32no—
645C2×D4—31no—
646C2×D4—32no—
647C2×D4—64no—
648C2×D4—62no—
649C2×D4—64no—
650C2×D4—68no—
651C2×D4—68no—
652C2×D4—64no—
653C2×D4—62no—
654C2×D4—61no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4C3×#6711yescharacteristic, complemented
662C2×D4C22×C3×D311yescharacteristic, complemented
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—62no—
666C22×C4—61no—
667C22×C4C22×C3×D311yescharacteristic
668Q16—22no—
669Q16—62no—
670SD16—22no—
671SD16—22no—
672SD16—62no—
673SD16—62no—
674D8—22no—
675D8—62no—
676M16—21no—
677M16—32no—
678M16—61no—
679M16C22×C3×D312yescomplemented
680C2×C8—21no—
681C2×C8—61no—
682C4⋊C4—61no—
683C22⋊C4—64no—
684C22⋊C4—61no—
685C42—32no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—62no—
702C22×C3—64no—
703C22×C3—81no—
704C22×C3—82no—
705C22×C3—82no—
706C22×C3—124no—
707C22×C3—124no—
708C22×C3—122no—
709C22×C3—242no—
710C22×C3—248no—
711C22×C3#93711yescharacteristic
712C22×C3#93711yescharacteristic
713C22×C3C3×#12011yescharacteristic
714C22×C3C3×#12011yescharacteristic
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C22×C3×D411yescharacteristic
717C2×D3—24no—
718C2×D3—22no—
719C2×D3—44no—
720C2×D3—42no—
721C2×D3—44no—
722C2×D3—82no—
723C2×D3—88no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—62no—
735C3×C4—122no—
736C3×C4#93711yescharacteristic
737C3×C4#93711yescharacteristic
738C3×C4C3×#12011yescharacteristic
739C3×C4C3×#12011yescharacteristic
740C3×C4C2×D3×D411yescharacteristic
741C3×C4C22×#6711yescharacteristic
742C3×C4C22×C3×D411yescharacteristic
743C3×C4C22×C3×D411yescharacteristic
744Dic3—22no—
745Dic3—42no—
746C32#301911yescharacteristic, complemented, Sylow
747C23—21no—
748C23—21no—
749C23—34no—
750C23—68no—
751C23—61no—
752C23—62no—
753C23—62no—
754C23—242no—
755C23—244no—
756C23C3×D3×D411yescharacteristic
757Q8—21no—
758Q8—21no—
759Q8—21no—
760Q8—32no—
761Q8—61no—
762Q8C2×C3×#6712yes—
763D4—22no—
764D4—22no—
765D4—21no—
766D4—21no—
767D4—21no—
768D4—32no—
769D4—41no—
770D4—41no—
771D4—68no—
772D4—68no—
773D4—62no—
774D4—62no—
775D4—61no—
776D4—62no—
777D4—62no—
778D4—62no—
779D4—62no—
780D4—244no—
781D4C2×C3×#6712yes—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—68no—
789C2×C4—61no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4C3×D3×D411yescharacteristic
794C2×C4C3×D3×D411yescharacteristic
795C2×C4C3×D3×D411yescharacteristic
796C2×C4C2×C3×#6711yescharacteristic
797C2×C4C2×C3×#6711yescharacteristic
798C2×C4C23×C3×D311yescharacteristic
799C8—22no—
800C8—62no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—41no—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—42no—
812C2×C3—42no—
813C2×C3—82no—
814C2×C3—82no—
815C2×C3—81no—
816C2×C3—81no—
817C2×C3—124no—
818C2×C3—122no—
819C2×C3C2×#93711yescharacteristic
820C2×C3C2×C3×#12011yescharacteristic
821D3—44no—
822D3—42no—
823C22—22no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—41no—
828C22—62no—
829C22—64no—
830C22—124no—
831C22—124no—
832C22—122no—
833C22—242no—
834C22—248no—
835C22C3×#93711yescharacteristic
836C22C3×#93711yescharacteristic
837C22C2×C3×D3×D411yescharacteristic
838C4—22no—
839C4—41no—
840C4—62no—
841C4—122no—
842C4C3×#93711yescharacteristic
843C4C3×#93711yescharacteristic
844C4C2×C3×D3×D411yescharacteristic
845C4C22×C3×#6711yescharacteristic
846C3—21no—
847C3#8400511yescharacteristic, direct product factor
848C3C3×#301911yescharacteristic, complemented
849C2—21no—
850C2—21no—
851C2—21no—
852C2—42no—
853C2—81no—
854C2—124no—
855C2—122no—
856C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC2×C3C2×#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#575C2
socleC2×C32C2×#120
hypercenterC3×#575D3
hypocenterC3C3×#3019
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#575

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C32×#575C2semidirect
3. C3×#5830C2semidirect
4. C3×#5822C2semidirect
5. C3×#5236C2semidirect
6. C3×#5202C2semidirect
7. C3×#5198C2semidirect
8. C3×#5139C2semidirect
9. C2×C3×#823C2semidirect
11. #84005C3direct (N × H)
13. C2×C32×#41C22semidirect
26. C32×#137C22semidirect
28. C32×AGL(1,ℤ/8)C22semidirect
30. C2×C32×M16C22semidirect
34. C3×#947C22semidirect
35. C3×#942C22semidirect
36. C3×#940C22semidirect
38. C3×#932C22semidirect
40. C3×#926C22semidirect
41. C2×C3×#208C22semidirect
42. C3×#837C22semidirect
43. C3×#825C22semidirect
44. C3×#823C22semidirect
46. C2×#1009C2×C3semidirect
49. C3×#575D3semidirect
50. C3×#575C2×C3semidirect
52. #5830C2×C3semidirect
53. #5822C2×C3semidirect
59. #5236C2×C3semidirect
60. #5202C2×C3semidirect
61. #5198C2×C3semidirect
62. #5139C2×C3semidirect
63. C2×#823C2×C3semidirect
72. C32×#41D4semidirect
74. C2×C32×Q8D4semidirect
75. C2×C32×Q8C23semidirect
78. C2×C32×D4D4semidirect
79. C2×C32×D4C23semidirect
96. C3×#235D4semidirect
106. C2×C3×D12D4semidirect
110. C2×C3×Dic6D4semidirect
116. C32×M16C23semidirect
125. C3×C4×Dic3C23semidirect
127. C3×#208C23semidirect
140. C2×C3×#41C2×D3semidirect
142. C2×C3×#41C22×C3semidirect
164. C3×#137C2×D3semidirect
165. C3×#137C22×C3semidirect
172. C3×AGL(1,ℤ/8)C2×D3semidirect
173. C3×AGL(1,ℤ/8)C22×C3semidirect
180. C2×C3×M16C2×D3semidirect
181. C2×C3×M16C22×C3semidirect
190. #947C22×C3semidirect
191. #942C22×C3semidirect
192. #940C22×C3semidirect
194. #932C22×C3semidirect
196. #926C22×C3semidirect
197. C2×#208C22×C3semidirect
201. #837C22×C3semidirect
202. #825C22×C3semidirect
203. #823C22×C3semidirect
260. #575C3×D3semidirect
299. C3×#41#67semidirect
300. C3×#41C3×D4semidirect
306. C2×C3×Q8#67semidirect
307. C2×C3×Q8C3×D4semidirect
308. C2×C3×Q8C22×D3semidirect
309. C2×C3×Q8C23×C3semidirect
335. C2×C3×D4#67semidirect
336. C2×C3×D4C3×D4semidirect
337. C2×C3×D4C22×D3semidirect
338. C2×C3×D4C23×C3semidirect
363. #235C3×D4semidirect
373. C2×D12C3×D4semidirect
377. C2×Dic6C3×D4semidirect
400. C3×M16C22×D3semidirect
401. C3×M16C23×C3semidirect
417. C4×Dic3C23×C3semidirect
419. #208C23×C3semidirect
452. C2×#41C2×C3×D3semidirect
460. #137C2×C3×D3semidirect
464. AGL(1,ℤ/8)C2×C3×D3semidirect
468. C2×M16C2×C3×D3semidirect
637. #41C3×#67semidirect
640. C2×Q8C3×#67semidirect
641. C2×Q8C22×C3×D3semidirect
661. C2×D4C3×#67semidirect
662. C2×D4C22×C3×D3semidirect
679. M16C22×C3×D3semidirect
746. C32#3019semidirect
847. C3#84005direct (N × H)
848. C3C3×#3019semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C32×#5752
C3×#58302
C3×#58222
C3×#52362
C3×#52022
C3×#51982
C3×#51392
C2×C3×#8232
C3×#30193
#840053