Finite Group Databasebeta

← C3×D3×#936 #13174707

Subgroups — C3×D3×#936 #13174707

Order 1728.

1762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64145C211yesmaximal, characteristic, complemented
4C32×#936C211yesmaximal, characteristic, complemented
5C3×D3×#217C214yesmaximal, complemented
6C3×#63959C214yesmaximal, complemented
7C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
8C3×#63863C211yesmaximal, characteristic, complemented
9C3×#63860C211yesmaximal, characteristic, complemented
10C2×C3×#936—31nomaximal
11C3×D3×#124—31nomaximal
12D3×#936C311yesmaximal, characteristic, direct product factor
13C23×C32×D3C2212yes—
14C2×C33×D4C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×#67C2212yes—
17C32×D3×D4—24no—
18C2×C32×D12C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic, complemented
21C2×C3×#627C2212yescomplemented
22C2×C3×D3×Dic3C2212yes—
23C2×C3×D3×Dic3C2212yes—
24C3×D3×Dic6—24no—
25C3×#3757C2214yescomplemented
26C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C32×#217C2214yescomplemented
28C32×C4×Dic3C2211yescharacteristic, complemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C3×(C2×D3)⋊Dic3C2214yescomplemented
31C3×Dic32C2212yescomplemented
32C22×C32×D4—31no—
33C2×C3×D3×Q8—31no—
34C2×C3×D3×D4—21no—
35C2×C3×D3×D4D311yescharacteristic
36C2×C3×D3×D4C2×C311yescharacteristic
37C22×C3×Dic6—31no—
38C2×D3×Dic6C2×C311yescharacteristic, complemented
39C32×#124—31no—
40#64145C2×C311yescharacteristic, complemented
41C2×C3×#217—34no—
42C3×#947—31no—
43C3×#936—21no—
44C3×#936—31no—
45C3×#936—31no—
46C3×#936—31no—
47C3×#936—34no—
48C3×#936—31no—
49C3×#936—61no—
50C3×#936D311yescharacteristic, direct product factor
51C3×#936C2×C311yescharacteristic, complemented
52C2×C3×C4×Dic3—31no—
53C3×#885—34no—
54C3×D3×C22⋊C4—34no—
55C3×#875—31no—
56C3×C42×D3—31no—
57D3×#217C2×C314yescomplemented
58#63959C2×C314yescomplemented
59C4×D3×Dic3C2×C311yescharacteristic, complemented
60#63863C2×C311yescharacteristic, complemented
61#63860C2×C311yescharacteristic, complemented
62C23×C33C2312yes—
63C22×C32×D3—24no—
64C22×C32×D3—28no—
65C22×C32×D3C2312yes—
66C22×C32×D3C2311yescharacteristic
67C33×D4—22no—
68C2×C33×C4C2311yescharacteristic
69C2×C3×C3⋊Dic3C2312yes—
70C2×C3×C3⋊Dic3C2312yes—
71C3×#634—22no—
72C32×#67—24no—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2311yescharacteristic
76C32×D12—22no—
77C32×C4×D3D414yes—
78C32×Dic6—22no—
79C3×#627—24no—
80C3×D3×Dic3—24no—
81C3×D3×Dic3—24no—
82C2×C3×#124—91no—
83C2×#936—31no—
84D3×#124—31no—
85C24×C32—32no—
86C23×C3×D3—22no—
87C23×C3×D3C2×D312yes—
88C23×C3×D3C22×C312yes—
89C2×C32×Q8—31no—
90C2×C32×D4—21no—
91C2×C32×D4—21no—
92C2×C32×D4—21no—
93C2×C32×D4—32no—
94C2×C32×D4—31no—
95C2×C32×D4—41no—
96C2×C32×D4—64no—
97C2×C32×D4C2×D311yescharacteristic
98C2×C32×D4C2×D311yescharacteristic
99C2×C32×D4C22×C311yescharacteristic
100C22×C32×C4—31no—
101C2×#634C22×C311yescharacteristic, complemented
102C2×C3×#67—22no—
103C2×C3×#67C2×D312yes—
104C2×C3×#67C22×C312yes—
105C22×C3×Dic3—32no—
106C22×C3×Dic3—32no—
107C3×D3×Q8—64no—
108C3×D3×D4—28no—
109C3×D3×D4—24no—
110C3×D3×D4—24no—
111C2×C3×D12—21no—
112C2×C3×D12C2×D311yescharacteristic
113C2×C3×D12C22×C311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3C2×D311yescharacteristic
118C2×C3×C4×D3C22×C311yescharacteristic
119C2×C3×Dic6—21no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—31no—
122C2×C3×Dic6—32no—
123C2×C3×Dic6—32no—
124C2×C3×Dic6—64no—
125C2×C3×Dic6—61no—
126C2×C3×Dic6C2×D311yescharacteristic, complemented
127C2×C3×Dic6C22×C311yescharacteristic, complemented
128C2×#627C22×C312yescomplemented
129C2×D3×Dic3C22×C312yes—
130C2×D3×Dic3C22×C312yes—
131D3×Dic6—24no—
132C32×C22⋊C4—34no—
133C32×C42—31no—
134#3757C22×C314yescomplemented
135C4×C3⋊Dic3C22×C311yescharacteristic, complemented
136C3×#217—24no—
137C3×#217—34no—
138C3×#217—34no—
139C3×#217—34no—
140C3×#217—34no—
141C3×#217—64no—
142C3×#217C2×D314yescomplemented
143C3×#217C22×C314yescomplemented
144C3×(C2×D3)⋊C4—34no—
145C3×(C2×D3)⋊C4—34no—
146C3×C4×Dic3—21no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—32no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—61no—
152C3×C4×Dic3C2×D311yescharacteristic, complemented
153C3×C4×Dic3C22×C311yescharacteristic, complemented
154(C2×D3)⋊Dic3C22×C314yescomplemented
155(C2×D3)⋊Dic3C22×C314yescomplemented
156Dic32C22×C312yescomplemented
157C22×C33—22no—
158C22×C33—24no—
159C22×C33C2411yescharacteristic
160C2×C32×D3—22no—
161C2×C32×D3—24no—
162C2×C32×D3—48no—
163C2×C32×D3C2×D412yes—
164C2×C32×D3#4114yes—
165C33×C4C2×D412yes—
166C3×C3⋊Dic3—22no—
167C3×C3⋊Dic3—22no—
168C32×Dic3—22no—
169C32×Dic3—22no—
170C32×Dic3C2×D412yes—
171C22×C3×Q8—91no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4—61no—
175C2×D3×Q8—31no—
176C2×D3×D4C3×D311yescharacteristic
177C22×Dic6—31no—
178C3×#124—31no—
179C3×#124—31no—
180C3×#124—61no—
181C3×#124—91no—
182C3×#124—94no—
183C3×#124—91no—
184C3×#124—91no—
185C2×C3×C22⋊C4—94no—
186C2×C3×C42—91no—
187C2×#217—34no—
188#947—31no—
189#936—31no—
190#936—31no—
191#936—31no—
192#936—34no—
193#936—31no—
194#936—61no—
195#936C3×D311yescharacteristic, direct product factor
196C2×C4×Dic3—31no—
197#885—34no—
198D3×C22⋊C4—34no—
199#875—31no—
200C42×D3—31no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—31no—
205C23×C32—32no—
206C23×C32—42no—
207C23×C32—64no—
208C23×C32—68no—
209C23×C32C22×D312yes—
210C23×C32C22×D312yes—
211C23×C32C23×C312yes—
212C22×C3×D3—28no—
213C22×C3×D3—28no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3—28no—
217C22×C3×D3—21no—
218C22×C3×D3—22no—
219C22×C3×D3—48no—
220C22×C3×D3C22×D312yes—
221C22×C3×D3C22×D311yescharacteristic
222C22×C3×D3C23×C312yes—
223C22×C3×D3C23×C311yescharacteristic
224C32×Q8—62no—
225C32×D4—22no—
226C32×D4—24no—
227C32×D4—22no—
228C32×D4—22no—
229C32×D4—42no—
230C32×D4—42no—
231C32×D4—44no—
232C32×D4—64no—
233C32×D4—62no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—31no—
238C2×C32×C4—34no—
239C2×C32×C4—32no—
240C2×C32×C4—32no—
241C2×C32×C4—41no—
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C23×C311yescharacteristic
245C2×C3⋊Dic3C23×C312yes—
246C2×C3⋊Dic3C23×C312yes—
247#634—22no—
248C3×#67—28no—
249C3×#67—24no—
250C3×#67—24no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—32no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—32no—
257C2×C3×Dic3—32no—
258C2×C3×Dic3—62no—
259C2×C3×Dic3—62no—
260C2×C3×Dic3—64no—
261C2×C3×Dic3—64no—
262C2×C3×Dic3C22×D312yes—
263C2×C3×Dic3C22×D312yes—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C23×C312yes—
266C2×C3×Dic3C23×C312yes—
267C2×C3×Dic3C23×C311yescharacteristic
268C3×D12—24no—
269C3×D12—22no—
270C3×D12—22no—
271C3×C4×D3—24no—
272C3×C4×D3—64no—
273C3×C4×D3—64no—
274C3×C4×D3#6714yes—
275C3×C4×D3C3×D414yes—
276C3×Dic6—22no—
277C3×Dic6—22no—
278C3×Dic6—42no—
279C3×Dic6—64no—
280C3×Dic6—62no—
281C3×Dic6—62no—
282C3×Dic6—64no—
283C3×Dic6—122no—
284#627—24no—
285D3×Dic3—24no—
286D3×Dic3—24no—
287C2×#124—91noSylow
288C2×C33—42no—
289C2×C33C22×D411yescharacteristic
290C2×C33C2×#4112yes—
291C32×D3—42no—
292C32×D3#12414yescomplemented
293C24×C3—32no—
294C24×C3—32no—
295C24×C3—62no—
296C23×D3C2×C3×D312yes—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—92no—
301C2×C3×Q8—91no—
302C2×C3×Q8—184no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—32no—
307C2×C3×D4—32no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—41no—
311C2×C3×D4—61no—
312C2×C3×D4—62no—
313C2×C3×D4—64no—
314C2×C3×D4—64no—
315C2×C3×D4—68no—
316C2×C3×D4D3211yescharacteristic
317C2×C3×D4C2×C3×D311yescharacteristic
318C2×C3×D4C2×C3×D311yescharacteristic
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—92no—
323C22×C3×C4—92no—
324C2×#67C2×C3×D312yes—
325C22×Dic3—32no—
326C22×Dic3—32no—
327D3×Q8—64no—
328D3×D4—24no—
329C2×D12C2×C3×D311yescharacteristic
330C2×C4×D3—32no—
331C2×C4×D3—32no—
332C2×C4×D3C2×C3×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—32no—
336C2×Dic6—32no—
337C2×Dic6—61no—
338C2×Dic6—64no—
339C2×Dic6C2×C3×D311yescharacteristic, complemented
340C3×C22⋊C4—34no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—64no—
343C3×C22⋊C4—94no—
344C3×C22⋊C4—94no—
345C3×C22⋊C4—94no—
346C3×C42—31no—
347C3×C42—31no—
348C3×C42—61no—
349C3×C42—92no—
350C3×C42—91no—
351#217—34no—
352#217—34no—
353#217—34no—
354#217—34no—
355#217—64no—
356#217C2×C3×D314yescomplemented
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—34no—
359C4×Dic3—31no—
360C4×Dic3—31no—
361C4×Dic3—32no—
362C4×Dic3—32no—
363C4×Dic3—61no—
364C4×Dic3C2×C3×D311yescharacteristic, complemented
365C22×C32—22no—
366C22×C32—24no—
367C22×C32—24no—
368C22×C32—24no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—24no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—32no—
376C22×C32—34no—
377C22×C32—41no—
378C22×C32—42no—
379C22×C32—42no—
380C22×C32—44no—
381C22×C32—44no—
382C22×C32—44no—
383C22×C32—44no—
384C22×C32—62no—
385C22×C32—64no—
386C22×C32—84no—
387C22×C32—128no—
388C22×C32C23×D311yescharacteristic
389C22×C32C23×D311yescharacteristic
390C22×C32C24×C311yescharacteristic
391C2×C3×D3—24no—
392C2×C3×D3—24no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—22no—
398C2×C3×D3—44no—
399C2×C3×D3—416no—
400C2×C3×D3—48no—
401C2×C3×D3—48no—
402C2×C3×D3#23714yes—
403C2×C3×D3C2×#6712yes—
404C2×C3×D3C2×C3×D412yes—
405C2×C3×D3C3×#4114yes—
406C32×C4—22no—
407C32×C4—22no—
408C32×C4—22no—
409C32×C4—32no—
410C32×C4—42no—
411C32×C4—62no—
412C32×C4—62no—
413C32×C4D3×D412yes—
414C32×C4C2×#6712yes—
415C32×C4C2×C3×D412yes—
416C3⋊Dic3—22no—
417C3⋊Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—42no—
424C3×Dic3—42no—
425C3×Dic3—62no—
426C3×Dic3—62no—
427C3×Dic3—62no—
428C3×Dic3—62no—
429C3×Dic3—122no—
430C3×Dic3—122no—
431C3×Dic3C2×#6712yes—
432C3×Dic3C2×C3×D412yes—
433C22×Q8—91no—
434C22×D4—31no—
435#124—31no—
436#124—91no—
437#124—94no—
438#124—91no—
439#124—91no—
440C2×C22⋊C4—94no—
441C2×C42—91no—
442C33C2×#12411yescharacteristic, complemented, Sylow
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—31no—
447C23×C3—31no—
448C23×C3—32no—
449C23×C3—32no—
450C23×C3—42no—
451C23×C3—61no—
452C23×C3—62no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3—68no—
456C23×C3—68no—
457C23×C3—68no—
458C23×C3—128no—
459C23×C3C2×D3212yes—
460C23×C3C22×C3×D312yes—
461C23×C3C22×C3×D312yes—
462C22×D3—28no—
463C22×D3—24no—
464C22×D3C22×C3×D312yes—
465C22×D3C22×C3×D311yescharacteristic
466C3×Q8—62no—
467C3×Q8—62no—
468C3×Q8—122no—
469C3×Q8—184no—
470C3×Q8—182no—
471C3×D4—24no—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—22no—
475C3×D4—42no—
476C3×D4—42no—
477C3×D4—44no—
478C3×D4—64no—
479C3×D4—64no—
480C3×D4—64no—
481C3×D4—68no—
482C3×D4—62no—
483C3×D4—62no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—41no—
496C2×C3×C4—64no—
497C2×C3×C4—61no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—92no—
501C2×C3×C4—92no—
502C2×C3×C4—184no—
503C2×C3×C4—184no—
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507#67—24no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—64no—
515C2×Dic3—64no—
516C2×Dic3C22×C3×D312yes—
517C2×Dic3C22×C3×D312yes—
518C2×Dic3C22×C3×D311yescharacteristic
519D12—22no—
520C4×D3—64no—
521C4×D3—64no—
522C4×D3C3×#6714yes—
523Dic6—22no—
524Dic6—64no—
525Dic6—62no—
526Dic6—62no—
527Dic6—64no—
528Dic6—122no—
529C2×C32—22no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—22no—
533C2×C32—22no—
534C2×C32—21no—
535C2×C32—34no—
536C2×C32—41no—
537C2×C32—42no—
538C2×C32—42no—
539C2×C32—44no—
540C2×C32—42no—
541C2×C32—42no—
542C2×C32—82no—
543C2×C32—82no—
544C2×C32—84no—
545C2×C32—122no—
546C2×C32C2×D3×D411yescharacteristic
547C2×C32C2×#23712yes—
548C2×C32D3×#4112yes—
549C2×C32C22×#6711yescharacteristic
550C2×C32C22×C3×D411yescharacteristic
551C2×C32C2×C3×#4112yes—
552C3×D3—24no—
553C3×D3—44no—
554C3×D3—42no—
555C3×D3—42no—
556C3×D3#93614yesdirect product factor
557C3×D3C3×#12414yescomplemented
558C24—32no—
559C2×Q8—31no—
560C2×Q8—92no—
561C2×Q8—91no—
562C2×Q8—184no—
563C2×D4—32no—
564C2×D4—31no—
565C2×D4—64no—
566C2×D4C3×D3211yescharacteristic
567C22×C4—31no—
568C22×C4—92no—
569C22×C4—92no—
570C22⋊C4—34no—
571C22⋊C4—94no—
572C22⋊C4—94no—
573C22⋊C4—94no—
574C42—31no—
575C42—92no—
576C42—91no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—22no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—34no—
588C22×C3—32no—
589C22×C3—32no—
590C22×C3—34no—
591C22×C3—44no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—41no—
598C22×C3—62no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—62no—
603C22×C3—62no—
604C22×C3—64no—
605C22×C3—84no—
606C22×C3—124no—
607C22×C3—128no—
608C22×C3—128no—
609C22×C3—1216no—
610C22×C3C22×D3211yescharacteristic
611C22×C3C23×C3×D311yescharacteristic
612C22×C3C23×C3×D311yescharacteristic
613C2×D3—24no—
614C2×D3—22no—
615C2×D3—48no—
616C2×D3C3×#23714yes—
617C2×D3C2×C3×#6712yes—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—32no—
622C3×C4—32no—
623C3×C4—42no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—122no—
630C3×C4—122no—
631C3×C4—182no—
632C3×C4—182no—
633C3×C4D3×#6712yes—
634C3×C4C3×D3×D412yes—
635C3×C4C2×C3×#6712yes—
636Dic3—22no—
637Dic3—22no—
638Dic3—62no—
639Dic3—62no—
640Dic3—62no—
641Dic3—62no—
642Dic3—122no—
643Dic3—122no—
644Dic3C2×C3×#6712yes—
645C32—21no—
646C32—21no—
647C32—21no—
648C32—41no—
649C32D3×#12411yescharacteristic, complemented
650C32C2×#93611yescharacteristic, complemented
651C32C2×C3×#12411yescharacteristic, complemented
652C23—31no—
653C23—32no—
654C23—64no—
655C23—68no—
656C23C2×C3×D3212yes—
657Q8—62no—
658Q8—184no—
659Q8—182no—
660D4—22no—
661D4—64no—
662D4—62no—
663C2×C4—31no—
664C2×C4—34no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—92no—
668C2×C4—92no—
669C2×C4—184no—
670C2×C4—184no—
671C2×C4C2×C3×D3211yescharacteristic
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—22no—
676C2×C3—22no—
677C2×C3—22no—
678C2×C3—34no—
679C2×C3—34no—
680C2×C3—44no—
681C2×C3—42no—
682C2×C3—42no—
683C2×C3—42no—
684C2×C3—41no—
685C2×C3—42no—
686C2×C3—64no—
687C2×C3—82no—
688C2×C3—82no—
689C2×C3—84no—
690C2×C3—124no—
691C2×C3—122no—
692C2×C3—122no—
693C2×C3D3×#23712yes—
694C2×C3C2×D3×#6711yescharacteristic
695C2×C3C2×C3×D3×D411yescharacteristic
696C2×C3C2×C3×#23712yes—
697C2×C3C3×D3×#4112yes—
698C2×C3C22×C3×#6711yescharacteristic
699D3—42no—
700D3C3×#93614yesdirect product factor
701C22—22no—
702C22—24no—
703C22—32no—
704C22—34no—
705C22—62no—
706C22—64no—
707C22—128no—
708C22C22×C3×D3211yescharacteristic
709C4—32no—
710C4—62no—
711C4—62no—
712C4—182no—
713C4—182no—
714C4C3×D3×#6712yes—
715C3—21no—
716C3—21no—
717C3—21no—
718C3—41no—
719C3D3×#93611yescharacteristic, direct product factor
720C3C3×D3×#12411yescharacteristic, complemented
721C3C2×C3×#93611yescharacteristic, complemented
722C2—34no—
723C2—42no—
724C2—122no—
725C2C3×D3×#23712yes—
726C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC2×C32×D3×D4C2
hypercenterC2×C3×D4D32
hypocenterC32C2×C3×#124
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64145C2semidirect
4. C32×#936C2semidirect
5. C3×D3×#217C2semidirect
6. C3×#63959C2semidirect
7. C3×C4×D3×Dic3C2semidirect
8. C3×#63863C2semidirect
9. C3×#63860C2semidirect
12. D3×#936C3direct (N × H)
15. C2×C3×#634C22semidirect
20. C2×C32×Dic6C22semidirect
21. C2×C3×#627C22semidirect
25. C3×#3757C22semidirect
26. C3×C4×C3⋊Dic3C22semidirect
27. C32×#217C22semidirect
28. C32×C4×Dic3C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
30. C3×(C2×D3)⋊Dic3C22semidirect
31. C3×Dic32C22semidirect
38. C2×D3×Dic6C2×C3semidirect
40. #64145C2×C3semidirect
50. C3×#936D3direct (N × H)
51. C3×#936C2×C3semidirect
57. D3×#217C2×C3semidirect
58. #63959C2×C3semidirect
59. C4×D3×Dic3C2×C3semidirect
60. #63863C2×C3semidirect
61. #63860C2×C3semidirect
101. C2×#634C22×C3semidirect
126. C2×C3×Dic6C2×D3semidirect
127. C2×C3×Dic6C22×C3semidirect
128. C2×#627C22×C3semidirect
134. #3757C22×C3semidirect
135. C4×C3⋊Dic3C22×C3semidirect
142. C3×#217C2×D3semidirect
143. C3×#217C22×C3semidirect
152. C3×C4×Dic3C2×D3semidirect
153. C3×C4×Dic3C22×C3semidirect
154. (C2×D3)⋊Dic3C22×C3semidirect
155. (C2×D3)⋊Dic3C22×C3semidirect
156. Dic32C22×C3semidirect
195. #936C3×D3direct (N × H)
292. C32×D3#124semidirect
339. C2×Dic6C2×C3×D3semidirect
356. #217C2×C3×D3semidirect
364. C4×Dic3C2×C3×D3semidirect
442. C33C2×#124semidirect
556. C3×D3#936direct (N × H)
557. C3×D3C3×#124semidirect
649. C32D3×#124semidirect
650. C32C2×#936semidirect
651. C32C2×C3×#124semidirect
700. D3C3×#936direct (N × H)
719. C3D3×#936direct (N × H)
720. C3C3×D3×#124semidirect
721. C3C2×C3×#936semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3×D3×Dic62
C3×#641452
C32×#9362
C3×D3×#2172
C3×#639592
C3×C4×D3×Dic32
C3×#638632
C3×#638602
C2×C3×#9363
C3×D3×#1243
D3×#9363