Finite Group Databasebeta

← C3×#84006 #11865076

Subgroups — C3×#84006 #11865076

Order 1152.

1527 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C32×#575C211yesmaximal, characteristic, complemented
3C3×#5825C211yesmaximal, characteristic, complemented
4C3×#5822C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6C3×#5205C214yesmaximal, complemented
7C3×#5201C214yesmaximal, complemented
8C3×#5139C211yesmaximal, characteristic, complemented
9C2×C3×#824C211yesmaximal, characteristic, complemented
10C3×#3020—31nomaximal
11#84006C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C2×C32×#41C2211yescharacteristic
14C3×#1010—22no—
15C3×#1010—22no—
16C3×#1010—22no—
17C3×#1010C2214yes—
18C2×C3×D3×Q8—21no—
19C2×C3×#237—21no—
20C2×C3×#237—22no—
21C2×C3×#235—21no—
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6—21no—
24C22×C3×Dic6C2211yescharacteristic
25C32×#137—21no—
26C32×#137C2212yescomplemented
27C32×AGL(1,ℤ/8)—21no—
28C32×AGL(1,ℤ/8)C2212yescomplemented
29C32×#135—22no—
30C2×C32×M16C2211yescharacteristic
31C3×#951—21no—
32C3×#950—22no—
33C3×#949—21no—
34C3×#944C2212yescomplemented
35C3×#942C2212yescomplemented
36C3×#936C2212yescomplemented
37C3×#935—22no—
38C3×#932C2212yescomplemented
39C3×#926C2211yescharacteristic
40C3×#924—22no—
41C2×C3×#208C2211yescharacteristic
42C3×#837C2214yescomplemented
43C3×#825C2214yescomplemented
44C3×#824C2214yescomplemented
45C2×C3×2−1+4—31no—
46C2×#1010C2×C311yescharacteristic, complemented
47C3×#575—21no—
48C3×#575—31no—
49C3×#575D311yescharacteristic, complemented
50C3×#575C2×C311yescharacteristic, complemented
51C3×#536—31no—
52#5825C2×C311yescharacteristic, complemented
53#5822C2×C311yescharacteristic, complemented
54C3×#456—34no—
55C3×#454—34no—
56C3×#421—31no—
57C3×#421—31no—
58C2×C3×#101—31no—
59#5236C2×C311yescharacteristic, complemented
60#5205C2×C314yescomplemented
61#5201C2×C314yescomplemented
62#5139C2×C311yescharacteristic, complemented
63C2×#824C2×C311yescharacteristic, complemented
64C32×#41—21no—
65C32×#41—21no—
66C32×#41—21no—
67C32×#41—21no—
68C32×#41—21no—
69C32×#41—21no—
70C32×#41D412yes—
71C32×#41C2312yes—
72C2×C32×Q8D411yescharacteristic
73C2×C32×Q8C2311yescharacteristic
74C2×C32×D4—21no—
75C2×C32×D4—21no—
76C2×C32×D4D411yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C2×C3×#67—22no—
82C2×C3×#67—21no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3D412yes—
85C3×D3×Q8—24no—
86C3×D3×Q8—24no—
87C3×#237—28no—
88C3×#237—24no—
89C3×#237—24no—
90C3×#237—28no—
91C3×#235—24no—
92C3×#235—21no—
93C3×#235—21no—
94C3×#235—24no—
95C3×#235D412yes—
96C3×#235C2312yes—
97C2×C3×D12D411yescharacteristic
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—21no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—24no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—24no—
107C2×C3×Dic6D412yes—
108C2×C3×Dic6D411yescharacteristic
109C2×C3×Dic6C2312yes—
110C32×Q16—22no—
111C32×SD16—22no—
112C32×SD16—22no—
113C32×D8—22no—
114C32×M16—21no—
115C32×M16C2312yes—
116C2×C32×C8—21no—
117C3×#217—21no—
118C3×#217—24no—
119C3×#216—22no—
120C3×#215—22no—
121C3×#214—22no—
122C3×#213—22no—
123C3×C4⋊Dic3—21no—
124C3×Dic3⋊C4—24no—
125C3×C4×Dic3C2312yes—
126C3×#208—21no—
127C3×#208C2312yes—
128C2×C3×C3⋊C8—21no—
129#3020—31noSylow
130C3×2−1+4—34no—
131C3×2−1+4—62no—
132C3×2−1+4—62no—
133C3×2−1+4—62no—
134C2×C3×#41—21no—
135C2×C3×#41—21no—
136C2×C3×#41—31no—
137C2×C3×#41—61no—
138C2×C3×#41—62no—
139C2×C3×#41—61no—
140C2×C3×#41C2×D311yescharacteristic
141C2×C3×#41C2×D311yescharacteristic
142C2×C3×#41C22×C311yescharacteristic
143C2×C3×#41C22×C311yescharacteristic
144C22×C3×Q8—31no—
145C22×C3×Q8—61no—
146C22×C3×Q8—61no—
147#1010—22no—
148#1010—22no—
149#1010—22no—
150#1010C22×C314yes—
151C2×D3×Q8—21no—
152C2×#237—21no—
153C2×#237—22no—
154C2×#235—21no—
155C2×#235C22×C311yescharacteristic
156C22×Dic6—21no—
157C22×Dic6C22×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
181C2×C3×M16C22×C311yescharacteristic
182C3×C4⋊Q8—32no—
183C3×#124—32no—
184C3×#123—62no—
185C3×C22⋊Q8—62no—
186C3×#117—31no—
187#951—21no—
188#950—22no—
189#949—21no—
190#944C22×C312yescomplemented
191#942C22×C312yescomplemented
192#936C22×C312yescomplemented
193#935—22no—
194#932C22×C312yescomplemented
195#926C22×C311yescharacteristic
196#924—22no—
197C2×#208C22×C311yescharacteristic
198C3×#104—34no—
199C3×#104—34no—
200C3×#101—34no—
201#837C22×C314yescomplemented
202#825C22×C314yescomplemented
203#824C22×C314yescomplemented
204C23×C32—21no—
205C23×C32—21no—
206C23×C32C2×D411yescharacteristic
207C22×C3×D3—21no—
208C32×Q8—21no—
209C32×Q8—21no—
210C32×Q8—21no—
211C32×Q8C2×D412yes—
212C32×D4—21no—
213C32×D4—22no—
214C32×D4—22no—
215C32×D4—21no—
216C32×D4—21no—
217C32×D4—41no—
218C32×D4—41no—
219C32×D4C2×D412yes—
220C2×C32×C4—21no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—21no—
224C2×C32×C4—41no—
225C2×C32×C4—41no—
226C2×C32×C4C2×D411yescharacteristic
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D411yescharacteristic
229C2×C32×C4C2×D411yescharacteristic
230C2×C32×C4C2×D411yescharacteristic
231C2×C32×C4C2411yescharacteristic
232C3×#67—28no—
233C3×#67—22no—
234C3×#67—22no—
235C2×C3×Dic3—28no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3C2×D414yes—
241C3×D12—21no—
242C3×D12C2×D412yes—
243C3×C4×D3—28no—
244C3×C4×D3—22no—
245C3×C4×D3—22no—
246C3×Dic6—28no—
247C3×Dic6—22no—
248C3×Dic6—21no—
249C3×Dic6—22no—
250C3×Dic6—22no—
251C3×Dic6—22no—
252C3×Dic6C2×D412yes—
253C32×C8—22no—
254C3×C3⋊C8—22no—
255C2×2−1+4—31no—
256#575—31no—
257#575C3×D311yescharacteristic, complemented
258#536—31no—
259#456—34no—
260#454—34no—
261#421—31no—
262#421—31no—
263C2×#101—31no—
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—22no—
269C3×#41—22no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—21no—
276C3×#41—21no—
277C3×#41—21no—
278C3×#41—22no—
279C3×#41—22no—
280C3×#41—32no—
281C3×#41—32no—
282C3×#41—41no—
283C3×#41—41no—
284C3×#41—41no—
285C3×#41—41no—
286C3×#41—64no—
287C3×#41—64no—
288C3×#41—68no—
289C3×#41—68no—
290C3×#41—64no—
291C3×#41—64no—
292C3×#41—61no—
293C3×#41—61no—
294C3×#41#6712yes—
295C3×#41C3×D412yes—
296C3×#41C22×D312yes—
297C3×#41C23×C312yes—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8—32no—
301C2×C3×Q8—32no—
302C2×C3×Q8—31no—
303C2×C3×Q8—64no—
304C2×C3×Q8—62no—
305C2×C3×Q8—64no—
306C2×C3×Q8—64no—
307C2×C3×Q8—64no—
308C2×C3×Q8—61no—
309C2×C3×Q8—61no—
310C2×C3×Q8—61no—
311C2×C3×Q8—61no—
312C2×C3×Q8#6711yescharacteristic
313C2×C3×Q8C3×D411yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C23×C311yescharacteristic
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—31no—
323C2×C3×D4—41no—
324C2×C3×D4—41no—
325C2×C3×D4—62no—
326C2×C3×D4—61no—
327C2×C3×D4#6711yescharacteristic
328C2×C3×D4C3×D411yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C23×C311yescharacteristic
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—32no—
337C22×C3×C4—41no—
338C22×C3×C4—41no—
339C22×C3×C4—62no—
340C22×C3×C4—62no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C23×C311yescharacteristic
344C2×#67—22no—
345C2×#67—21no—
346C22×Dic3—22no—
347C22×Dic3C3×D412yes—
348D3×Q8—24no—
349D3×Q8—24no—
350#237—28no—
351#237—24no—
352#237—24no—
353#237—28no—
354#235—24no—
355#235—21no—
356#235—21no—
357#235—24no—
358#235C3×D412yes—
359#235C23×C312yes—
360C2×D12C3×D411yescharacteristic
361C2×C4×D3—22no—
362C2×C4×D3—21no—
363C2×Dic6—22no—
364C2×Dic6—24no—
365C2×Dic6—21no—
366C2×Dic6—21no—
367C2×Dic6—21no—
368C2×Dic6—21no—
369C2×Dic6—24no—
370C2×Dic6C3×D412yes—
371C2×Dic6C3×D411yescharacteristic
372C2×Dic6C23×C312yes—
373C3×Q16—24no—
374C3×Q16—22no—
375C3×Q16—22no—
376C3×Q16—62no—
377C3×SD16—24no—
378C3×SD16—24no—
379C3×SD16—22no—
380C3×SD16—22no—
381C3×SD16—22no—
382C3×SD16—22no—
383C3×SD16—62no—
384C3×SD16—62no—
385C3×D8—24no—
386C3×D8—22no—
387C3×D8—22no—
388C3×D8—62no—
389C3×M16—22no—
390C3×M16—21no—
391C3×M16—21no—
392C3×M16—22no—
393C3×M16—32no—
394C3×M16—61no—
395C3×M16C22×D312yes—
396C3×M16C23×C312yes—
397C2×C3×C8—22no—
398C2×C3×C8—21no—
399C2×C3×C8—21no—
400C2×C3×C8—61no—
401C3×C4⋊C4—64no—
402C3×C4⋊C4—61no—
403C3×C22⋊C4—64no—
404C3×C22⋊C4—61no—
405C3×C42—32no—
406#217—21no—
407#217—24no—
408#216—22no—
409#215—22no—
410#214—22no—
411#213—22no—
412C4⋊Dic3—21no—
413Dic3⋊C4—24no—
414C4×Dic3C23×C312yes—
415#208—21no—
416#208C23×C312yes—
417C2×C3⋊C8—21no—
418C22×C32—22no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32#12011yescharacteristic
424C22×C32#12011yescharacteristic
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—22no—
427C2×C3×D3—42no—
428C32×C4—22no—
429C32×C4—41no—
430C32×C4#12011yescharacteristic
431C32×C4#12011yescharacteristic
432C32×C4C22×D411yescharacteristic
433C32×C4C22×D411yescharacteristic
434C3×Dic3—24no—
435C3×Dic3—22no—
436C3×Dic3—42no—
4372−1+4—34no—
4382−1+4—62no—
4392−1+4—62no—
4402−1+4—62no—
441C2×#41—31no—
442C2×#41—61no—
443C2×#41—62no—
444C2×#41—61no—
445C2×#41C2×C3×D311yescharacteristic
446C2×#41C2×C3×D311yescharacteristic
447C22×Q8—31no—
448C22×Q8—61no—
449C22×Q8—61no—
450#137—21no—
451#137—32no—
452#137—61no—
453#137C2×C3×D312yescomplemented
454AGL(1,ℤ/8)—21no—
455AGL(1,ℤ/8)—32no—
456AGL(1,ℤ/8)—61no—
457AGL(1,ℤ/8)C2×C3×D312yescomplemented
458#135—22no—
459#135—62no—
460C2×M16—31no—
461C2×M16C2×C3×D311yescharacteristic
462C4⋊Q8—32no—
463#124—32no—
464#123—62no—
465C22⋊Q8—62no—
466#117—31no—
467#104—34no—
468#104—34no—
469#101—34no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—61no—
478C23×C3D3×D411yescharacteristic
479C23×C3C2×C3×D411yescharacteristic
480C22×D3—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—22no—
489C3×Q8—32no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—68no—
493C3×Q8—62no—
494C3×Q8—62no—
495C3×Q8—61no—
496C3×Q8—62no—
497C3×Q8—62no—
498C3×Q8C2×#6712yes—
499C3×Q8C2×C3×D412yes—
500C3×D4—22no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—22no—
512C3×D4—32no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—42no—
516C3×D4—42no—
517C3×D4—42no—
518C3×D4—42no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—68no—
524C3×D4—62no—
525C3×D4—62no—
526C3×D4—61no—
527C3×D4C2×#6712yes—
528C3×D4C2×C3×D412yes—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—34no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—42no—
549C2×C3×C4—42no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—68no—
555C2×C3×C4—68no—
556C2×C3×C4—62no—
557C2×C3×C4—62no—
558C2×C3×C4—61no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C2×#6711yescharacteristic
567C2×C3×C4C2×C3×D411yescharacteristic
568C2×C3×C4C2×C3×D411yescharacteristic
569C2×C3×C4C2×C3×D411yescharacteristic
570C2×C3×C4C2×C3×D411yescharacteristic
571C2×C3×C4C2×C3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C24×C311yescharacteristic
574#67—28no—
575#67—22no—
576#67—22no—
577C2×Dic3—28no—
578C2×Dic3—22no—
579C2×Dic3—21no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3C2×C3×D414yes—
583D12—21no—
584D12C2×C3×D412yes—
585C4×D3—28no—
586C4×D3—22no—
587C4×D3—22no—
588Dic6—28no—
589Dic6—22no—
590Dic6—21no—
591Dic6—22no—
592Dic6—22no—
593Dic6—22no—
594Dic6C2×C3×D412yes—
595C3×C8—24no—
596C3×C8—22no—
597C3×C8—22no—
598C3×C8—62no—
599C3⋊C8—22no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—42no—
604C2×C32—81no—
605C2×C32C2×#12011yescharacteristic
606C3×D3—42no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—32no—
614#41—32no—
615#41—64no—
616#41—64no—
617#41—68no—
618#41—68no—
619#41—64no—
620#41—64no—
621#41—61no—
622#41—61no—
623#41C3×#6712yes—
624#41C22×C3×D312yes—
625C2×Q8—32no—
626C2×Q8—32no—
627C2×Q8—31no—
628C2×Q8—64no—
629C2×Q8—62no—
630C2×Q8—64no—
631C2×Q8—64no—
632C2×Q8—64no—
633C2×Q8—61no—
634C2×Q8—61no—
635C2×Q8—61no—
636C2×Q8—61no—
637C2×Q8C3×#6711yescharacteristic
638C2×Q8C22×C3×D311yescharacteristic
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—31no—
642C2×D4—62no—
643C2×D4—61no—
644C2×D4C3×#6711yescharacteristic
645C2×D4C22×C3×D311yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—32no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—61no—
652C22×C4C22×C3×D311yescharacteristic
653Q16—22no—
654Q16—62no—
655SD16—22no—
656SD16—22no—
657SD16—62no—
658SD16—62no—
659D8—22no—
660D8—62no—
661M16—21no—
662M16—32no—
663M16—61no—
664M16C22×C3×D312yes—
665C2×C8—21no—
666C2×C8—61no—
667C4⋊C4—64no—
668C4⋊C4—61no—
669C22⋊C4—64no—
670C22⋊C4—61no—
671C42—32no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—62no—
688C22×C3—81no—
689C22×C3—82no—
690C22×C3—82no—
691C22×C3—122no—
692C22×C3#93711yescharacteristic
693C22×C3#93711yescharacteristic
694C22×C3C3×#12011yescharacteristic
695C22×C3C3×#12011yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C22×C3C22×C3×D411yescharacteristic
698C2×D3—22no—
699C2×D3—42no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—42no—
707C3×C4—42no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—64no—
711C3×C4—62no—
712C3×C4—122no—
713C3×C4#93711yescharacteristic
714C3×C4#93711yescharacteristic
715C3×C4C3×#12011yescharacteristic
716C3×C4C3×#12011yescharacteristic
717C3×C4C2×D3×D411yescharacteristic
718C3×C4C22×#6711yescharacteristic
719C3×C4C22×C3×D411yescharacteristic
720C3×C4C22×C3×D411yescharacteristic
721Dic3—24no—
722Dic3—22no—
723Dic3—42no—
724C32#302011yescharacteristic, complemented, Sylow
725C23—21no—
726C23—21no—
727C23—61no—
728C23C3×D3×D411yescharacteristic
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—32no—
733Q8—68no—
734Q8—62no—
735Q8—62no—
736Q8—61no—
737Q8—62no—
738Q8—62no—
739Q8C2×C3×#6712yes—
740D4—22no—
741D4—22no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—32no—
746D4—41no—
747D4—41no—
748D4—68no—
749D4—62no—
750D4—62no—
751D4—61no—
752D4C2×C3×#6712yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—34no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—68no—
761C2×C4—68no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—61no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4C3×D3×D411yescharacteristic
769C2×C4C3×D3×D411yescharacteristic
770C2×C4C3×D3×D411yescharacteristic
771C2×C4C2×C3×#6711yescharacteristic
772C2×C4C2×C3×#6711yescharacteristic
773C2×C4C23×C3×D311yescharacteristic
774C8—22no—
775C8—62no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—41no—
784C2×C3—41no—
785C2×C3—41no—
786C2×C3—42no—
787C2×C3—42no—
788C2×C3—82no—
789C2×C3—82no—
790C2×C3—81no—
791C2×C3—81no—
792C2×C3—122no—
793C2×C3C2×#93711yescharacteristic
794C2×C3C2×C3×#12011yescharacteristic
795D3—42no—
796C22—22no—
797C22—41no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—62no—
802C22—122no—
803C22C3×#93711yescharacteristic
804C22C3×#93711yescharacteristic
805C22C2×C3×D3×D411yescharacteristic
806C4—22no—
807C4—41no—
808C4—64no—
809C4—62no—
810C4—122no—
811C4C3×#93711yescharacteristic
812C4C3×#93711yescharacteristic
813C4C2×C3×D3×D411yescharacteristic
814C4C22×C3×#6711yescharacteristic
815C3—21no—
816C3#8400611yescharacteristic, direct product factor
817C3C3×#302011yescharacteristic, complemented
818C2—21no—
819C2—21no—
820C2—21no—
821C2—42no—
822C2—81no—
823C2—122no—
824C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC2×C3C2×#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#575C2
socleC2×C32C2×#120
hypercenterC3×#575D3
hypocenterC3C3×#3020
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×#1010C2semidirect
2. C32×#575C2semidirect
3. C3×#5825C2semidirect
4. C3×#5822C2semidirect
5. C3×#5236C2semidirect
6. C3×#5205C2semidirect
7. C3×#5201C2semidirect
8. C3×#5139C2semidirect
9. C2×C3×#824C2semidirect
11. #84006C3direct (N × H)
26. C32×#137C22semidirect
28. C32×AGL(1,ℤ/8)C22semidirect
34. C3×#944C22semidirect
35. C3×#942C22semidirect
36. C3×#936C22semidirect
38. C3×#932C22semidirect
42. C3×#837C22semidirect
43. C3×#825C22semidirect
44. C3×#824C22semidirect
46. C2×#1010C2×C3semidirect
49. C3×#575D3semidirect
50. C3×#575C2×C3semidirect
52. #5825C2×C3semidirect
53. #5822C2×C3semidirect
59. #5236C2×C3semidirect
60. #5205C2×C3semidirect
61. #5201C2×C3semidirect
62. #5139C2×C3semidirect
63. C2×#824C2×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
190. #944C22×C3semidirect
191. #942C22×C3semidirect
192. #936C22×C3semidirect
194. #932C22×C3semidirect
201. #837C22×C3semidirect
202. #825C22×C3semidirect
203. #824C22×C3semidirect
257. #575C3×D3semidirect
453. #137C2×C3×D3semidirect
457. AGL(1,ℤ/8)C2×C3×D3semidirect
724. C32#3020semidirect
816. C3#84006direct (N × H)
817. C3C3×#3020semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C32×#5752
C3×#58252
C3×#58222
C3×#52362
C3×#52052
C3×#52012
C3×#51392
C2×C3×#8242
C3×#30203
#840063