Finite Group Databasebeta

← C3×#83427 #11864659

Subgroups — C3×#83427 #11864659

Order 1152.

1571 conjugacy classes of subgroups.

The subgroup lattice has 755 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C32×#537C211yesmaximal, characteristic, complemented
3C2×C3×#951C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6C3×#5050C212yesmaximal, complemented
7C3×#5047C212yesmaximal, complemented
8C3×#5040C212yesmaximal, complemented
9C3×#5037C212yesmaximal, complemented
10C2×C3×#810C211yesmaximal, characteristic, complemented
11C3×#4966C211yesmaximal, characteristic, complemented
12C3×#3013—31nomaximal
13#83427C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C32×#41C2211yescharacteristic
16C3×#1010—24no—
17C3×#1010—24no—
18C2×C3×D3×Q8—21no—
19C2×C3×#237—22no—
20C2×C3×#237—21no—
21C2×C3×#235C2212yes—
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6C2212yes—
24C22×C3×Dic6C2211yescharacteristic
25C32×C22⋊Q8—21no—
26C32×C22⋊Q8C2212yes—
27C32×#121—21no—
28C32×#121—22no—
29C32×#121C2212yes—
30C2×C32×C4⋊C4C2211yescharacteristic
31C3×#951—24no—
32C3×#950—24no—
33C2×C3×#216C2211yescharacteristic
34C2×C3×#216C2212yes—
35C2×C3×#215C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#214C2212yes—
38C2×C3×#213C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic
40C22×C3×C3⋊C8C2211yescharacteristic
41C3×#830C2212yes—
42C3×#830C2212yes—
43C3×#810C2212yes—
44C3×#810C2212yes—
45C3×#810C2212yes—
46C3×#809C2212yes—
47C2×C3×2−1+4—31no—
48C2×#1010C2×C311yescharacteristic, complemented
49C2×C3×#137—31no—
50C2×C3×#135—31no—
51C3×#537—21no—
52C3×#537D311yescharacteristic, complemented
53C3×#537C2×C311yescharacteristic, complemented
54C2×#951C2×C311yescharacteristic, complemented
55C2×#950C2×C311yescharacteristic, complemented
56C3×#452—32no—
57C3×#451—32no—
58C3×#449—32no—
59C3×#448—32no—
60C3×#417—31no—
61C2×C3×#103—31no—
62C3×#408—31no—
63#5234C2×C311yescharacteristic, complemented
64#5050C2×C312yescomplemented
65#5047C2×C312yescomplemented
66#5040C2×C312yescomplemented
67#5037C2×C312yescomplemented
68C2×#810C2×C311yescharacteristic, complemented
69#4966C2×C311yescharacteristic, complemented
70C32×#41—22no—
71C32×#41—22no—
72C32×#41—22no—
73C32×#41—22no—
74C2×C32×Q8D411yescharacteristic
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4—22no—
78C2×C32×D4D412yes—
79C2×C32×D4D411yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4C2312yes—
84C22×C32×C4C2311yescharacteristic
85C2×C3×#67—22no—
86C2×C3×#67—21no—
87C22×C3×Dic3—22no—
88C22×C3×Dic3—21no—
89C3×D3×Q8—28no—
90C3×#237—216no—
91C3×#237—28no—
92C3×#235—22no—
93C3×#235—24no—
94C3×#235—24no—
95C3×#235D414yescomplemented
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—22no—
102C2×C3×Dic6—24no—
103C2×C3×Dic6—24no—
104C2×C3×Dic6D414yescomplemented
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2312yes—
107C32×C4⋊C4—21no—
108C32×C4⋊C4—22no—
109C32×C4⋊C4C2312yes—
110C32×C22⋊C4—22no—
111C32×C22⋊C4—22no—
112C3×#216—22no—
113C3×#216—24no—
114C3×#215—22no—
115C3×#214—22no—
116C3×#214—24no—
117C3×#213—22no—
118C3×#208—22no—
119C2×C3×C3⋊C8—22no—
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2312yes—
123#3013—31noSylow
124C3×2−1+4—64no—
125C3×2−1+4—64no—
126C2×C3×#41—21no—
127C2×C3×#41—21no—
128C2×C3×#41—31no—
129C2×C3×#41—32no—
130C2×C3×#41—61no—
131C2×C3×#41—62no—
132C2×C3×#41C2×D311yescharacteristic
133C2×C3×#41C2×D311yescharacteristic
134C2×C3×#41C22×C311yescharacteristic
135C2×C3×#41C22×C311yescharacteristic
136C22×C3×Q8—31no—
137C22×C3×Q8—32no—
138C22×C3×Q8—61no—
139#1010—24no—
140#1010—24no—
141C2×D3×Q8—21no—
142C2×#237—22no—
143C2×#237—21no—
144C2×#235C22×C312yes—
145C2×#235C22×C311yescharacteristic
146C22×Dic6C22×C312yes—
147C22×Dic6C22×C311yescharacteristic
148C3×#137—64no—
149C3×#135—64no—
150C2×C3×Q16—31no—
151C2×C3×Q16—32no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16—32no—
155C2×C3×D8—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C22⋊Q8—22no—
159C3×C22⋊Q8—21no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—22no—
162C3×C22⋊Q8C2×D312yes—
163C3×C22⋊Q8C22×C312yes—
164C3×#121—22no—
165C3×#121—24no—
166C3×#121—21no—
167C3×#121—22no—
168C3×#121—21no—
169C3×#121—22no—
170C3×#121—22no—
171C3×#121C2×D312yes—
172C3×#121C22×C312yes—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4C2×D311yescharacteristic
175C2×C3×C4⋊C4C22×C311yescharacteristic
176#951—24no—
177#950—24no—
178C2×#216C22×C312yes—
179C2×#216C22×C311yescharacteristic
180C2×#215C22×C311yescharacteristic
181C2×#214C22×C312yes—
182C2×#214C22×C311yescharacteristic
183C2×#213C22×C311yescharacteristic
184C2×#208C22×C311yescharacteristic
185C22×C3⋊C8C22×C311yescharacteristic
186C3×#103—32no—
187C3×#103—32no—
188C3×#103—32no—
189C3×#102—32no—
190C3×C22⋊C8—32no—
191C3×C22⋊C8—32no—
192#830C22×C312yes—
193#830C22×C312yes—
194#810C22×C312yes—
195#810C22×C312yes—
196#810C22×C312yes—
197#809C22×C312yes—
198C23×C32—21no—
199C23×C32C2×D412yes—
200C23×C32C2×D411yescharacteristic
201C22×C3×D3—21no—
202C32×Q8—22no—
203C32×Q8—21no—
204C32×Q8—21no—
205C32×D4—24no—
206C32×D4—22no—
207C32×D4—21no—
208C32×D4—21no—
209C32×D4—42no—
210C32×D4—82no—
211C2×C32×C4—22no—
212C2×C32×C4—21no—
213C2×C32×C4—22no—
214C2×C32×C4—22no—
215C2×C32×C4—42no—
216C2×C32×C4—81no—
217C2×C32×C4C2×D412yes—
218C2×C32×C4C2×D412yes—
219C2×C32×C4C2×D412yes—
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2411yescharacteristic
222C3×#67—28no—
223C3×#67—24no—
224C2×C3×Dic3—28no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—22no—
228C3×D12—21no—
229C3×D12C2×D412yes—
230C3×C4×D3—28no—
231C3×C4×D3—24no—
232C3×Dic6—28no—
233C3×Dic6—24no—
234C3×Dic6—22no—
235C3×Dic6—21no—
236C3×Dic6C2×D412yes—
237C3×Dic6C2×D414yes—
238C3×C3⋊C8—21no—
239C3×C3⋊C8—21no—
240C3×C3⋊C8—22no—
241C2×2−1+4—31no—
242C2×#137—31no—
243C2×#135—31no—
244#537C3×D311yescharacteristic, complemented
245#452—32no—
246#451—32no—
247#449—32no—
248#448—32no—
249#417—31no—
250C2×#103—31no—
251#408—31no—
252C3×#41—22no—
253C3×#41—22no—
254C3×#41—22no—
255C3×#41—22no—
256C3×#41—22no—
257C3×#41—22no—
258C3×#41—22no—
259C3×#41—22no—
260C3×#41—34no—
261C3×#41—42no—
262C3×#41—42no—
263C3×#41—42no—
264C3×#41—42no—
265C3×#41—64no—
266C3×#41—64no—
267C3×#41—616no—
268C3×#41—68no—
269C3×#41—62no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—34no—
273C2×C3×Q8—32no—
274C2×C3×Q8—31no—
275C2×C3×Q8—64no—
276C2×C3×Q8—64no—
277C2×C3×Q8—68no—
278C2×C3×Q8—62no—
279C2×C3×Q8—62no—
280C2×C3×Q8—61no—
281C2×C3×Q8#6711yescharacteristic
282C2×C3×Q8C3×D411yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C23×C311yescharacteristic
285C2×C3×D4—22no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—24no—
289C2×C3×D4—22no—
290C2×C3×D4—22no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—62no—
296C2×C3×D4—61no—
297C2×C3×D4#6712yes—
298C2×C3×D4#6711yescharacteristic
299C2×C3×D4C3×D412yes—
300C2×C3×D4C3×D411yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C23×C311yescharacteristic
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—22no—
311C22×C3×C4—62no—
312C22×C3×C4—61no—
313C22×C3×C4—62no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D312yes—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C23×C312yes—
318C22×C3×C4C23×C311yescharacteristic
319C2×#67—22no—
320C2×#67—21no—
321C22×Dic3—22no—
322C22×Dic3—21no—
323D3×Q8—28no—
324#237—216no—
325#237—28no—
326#235—22no—
327#235—24no—
328#235—24no—
329#235C3×D414yescomplemented
330C2×D12C23×C311yescharacteristic
331C2×C4×D3—22no—
332C2×C4×D3—21no—
333C2×Dic6—22no—
334C2×Dic6—21no—
335C2×Dic6—22no—
336C2×Dic6—24no—
337C2×Dic6—24no—
338C2×Dic6C3×D414yescomplemented
339C2×Dic6C23×C311yescharacteristic
340C2×Dic6C23×C312yes—
341C3×Q16—62no—
342C3×Q16—64no—
343C3×SD16—62no—
344C3×SD16—64no—
345C3×SD16—62no—
346C3×D8—62no—
347C3×M16—62no—
348C2×C3×C8—32no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—62no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—24no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—22no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—22no—
358C3×C4⋊C4—22no—
359C3×C4⋊C4C22×D312yes—
360C3×C4⋊C4C23×C312yes—
361C3×C22⋊C4—24no—
362C3×C22⋊C4—24no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—22no—
366C3×C22⋊C4—22no—
367#216—22no—
368#216—24no—
369#215—22no—
370#214—22no—
371#214—24no—
372#213—22no—
373#208—22no—
374C2×C3⋊C8—22no—
375C2×C3⋊C8C23×C312yes—
376C2×C3⋊C8C23×C311yescharacteristic
377C2×C3⋊C8C23×C311yescharacteristic
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32#12012yes—
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—22no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—22no—
392C32×C4—41no—
393C32×C4—42no—
394C32×C4#12012yes—
395C32×C4C22×D411yescharacteristic
396C32×C4C22×D411yescharacteristic
397C3×Dic3—22no—
398C3×Dic3—24no—
3992−1+4—64no—
4002−1+4—64no—
401C2×#41—31no—
402C2×#41—32no—
403C2×#41—61no—
404C2×#41—62no—
405C2×#41C2×C3×D311yescharacteristic
406C2×#41C2×C3×D311yescharacteristic
407C22×Q8—31no—
408C22×Q8—32no—
409C22×Q8—61no—
410#137—64no—
411#135—64no—
412C2×Q16—31no—
413C2×Q16—32no—
414C2×SD16—31no—
415C2×SD16—31no—
416C2×SD16—32no—
417C2×D8—31no—
418C2×M16—31no—
419C22×C8—31no—
420C22⋊Q8—21no—
421C22⋊Q8C2×C3×D312yes—
422#121—21no—
423#121—22no—
424#121C2×C3×D312yes—
425C2×C4⋊C4C2×C3×D311yescharacteristic
426#103—32no—
427#103—32no—
428#103—32no—
429#102—32no—
430C22⋊C8—32no—
431C22⋊C8—32no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—61no—
438C23×C3C2×#6712yes—
439C23×C3C2×#6711yescharacteristic
440C23×C3C2×C3×D412yes—
441C23×C3C2×C3×D411yescharacteristic
442C22×D3—21no—
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—21no—
446C3×Q8—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—34no—
450C3×Q8—32no—
451C3×Q8—42no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—68no—
455C3×Q8—64no—
456C3×Q8—62no—
457C3×Q8—61no—
458C3×D4—24no—
459C3×D4—24no—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—32no—
467C3×D4—42no—
468C3×D4—41no—
469C3×D4—41no—
470C3×D4—44no—
471C3×D4—44no—
472C3×D4—42no—
473C3×D4—42no—
474C3×D4—68no—
475C3×D4—64no—
476C3×D4—61no—
477C3×D4—82no—
478C3×D4—82no—
479C3×D4—84no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—44no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—68no—
501C2×C3×C4—68no—
502C2×C3×C4—64no—
503C2×C3×C4—62no—
504C2×C3×C4—61no—
505C2×C3×C4—64no—
506C2×C3×C4—81no—
507C2×C3×C4—81no—
508C2×C3×C4—82no—
509C2×C3×C4D3×D412yes—
510C2×C3×C4D3×D412yes—
511C2×C3×C4C2×#6712yes—
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×C3×D412yes—
514C2×C3×C4C2×C3×D412yes—
515C2×C3×C4C2×C3×D412yes—
516C2×C3×C4C2×C3×D411yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C24×C311yescharacteristic
519#67—28no—
520#67—24no—
521C2×Dic3—28no—
522C2×Dic3—24no—
523C2×Dic3—21no—
524C2×Dic3—22no—
525D12—21no—
526D12C2×C3×D412yes—
527C4×D3—28no—
528C4×D3—24no—
529Dic6—28no—
530Dic6—24no—
531Dic6—22no—
532Dic6—21no—
533Dic6C2×C3×D412yes—
534Dic6C2×C3×D414yes—
535C3×C8—61no—
536C3×C8—61no—
537C3×C8—62no—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C3⋊C8—22no—
541C2×C32—22no—
542C2×C32—42no—
543C2×C32—81no—
544C2×C32C2×#12011yescharacteristic
545C2×C32#57711yescharacteristic
546C2×C32#57811yescharacteristic
547C3×D3—42no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—34no—
553#41—64no—
554#41—64no—
555#41—616no—
556#41—68no—
557#41—62no—
558C2×Q8—32no—
559C2×Q8—31no—
560C2×Q8—34no—
561C2×Q8—64no—
562C2×Q8—64no—
563C2×Q8—68no—
564C2×Q8—62no—
565C2×Q8—62no—
566C2×Q8—61no—
567C2×Q8C3×#6711yescharacteristic
568C2×Q8C22×C3×D311yescharacteristic
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—31no—
572C2×D4—62no—
573C2×D4—61no—
574C2×D4C3×#6712yes—
575C2×D4C3×#6711yescharacteristic
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—62no—
580C22×C4—61no—
581C22×C4—62no—
582C22×C4—61no—
583C22×C4C22×C3×D312yes—
584C22×C4C22×C3×D311yescharacteristic
585Q16—62no—
586Q16—64no—
587SD16—62no—
588SD16—64no—
589SD16—62no—
590D8—62no—
591M16—62no—
592C2×C8—32no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—62no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4C22×C3×D312yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3#93712yes—
631C22×C3C3×#12012yes—
632C22×C3C22×#6711yescharacteristic
633C22×C3C22×C3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—64no—
650C3×C4—62no—
651C3×C4#93712yes—
652C3×C4C3×#12012yes—
653C3×C4C2×D3×D411yescharacteristic
654C3×C4C2×D3×D411yescharacteristic
655C3×C4C22×C3×D411yescharacteristic
656C3×C4C22×C3×D411yescharacteristic
657Dic3—22no—
658Dic3—24no—
659C32#301311yescharacteristic, complemented, Sylow
660C23—21no—
661C23—61no—
662C23C2×C3×#6712yes—
663C23C2×C3×#6711yescharacteristic
664Q8—22no—
665Q8—21no—
666Q8—21no—
667Q8—34no—
668Q8—32no—
669Q8—68no—
670Q8—64no—
671Q8—62no—
672Q8—61no—
673D4—24no—
674D4—22no—
675D4—21no—
676D4—21no—
677D4—32no—
678D4—42no—
679D4—68no—
680D4—64no—
681D4—61no—
682D4—82no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—42no—
688C2×C4—68no—
689C2×C4—68no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—61no—
693C2×C4—64no—
694C2×C4—81no—
695C2×C4C3×D3×D412yes—
696C2×C4C3×D3×D412yes—
697C2×C4C2×C3×#6712yes—
698C2×C4C2×C3×#6711yescharacteristic
699C2×C4C23×C3×D311yescharacteristic
700C8—61no—
701C8—61no—
702C8—62no—
703C2×C3—22no—
704C2×C3—22no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—42no—
709C2×C3—42no—
710C2×C3—42no—
711C2×C3—82no—
712C2×C3—82no—
713C2×C3—81no—
714C2×C3—81no—
715C2×C3—122no—
716C2×C3C2×#93711yescharacteristic
717C2×C3#583611yescharacteristic
718C2×C3#583811yescharacteristic
719C2×C3C2×C3×#12011yescharacteristic
720C2×C3C3×#57711yescharacteristic
721C2×C3C3×#57811yescharacteristic
722D3—42no—
723C22—21no—
724C22—21no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22C3×#93712yes—
735C22C22×C3×#6711yescharacteristic
736C4—22no—
737C4—41no—
738C4—42no—
739C4—64no—
740C4—62no—
741C4C3×#93712yes—
742C4C2×C3×D3×D411yescharacteristic
743C4C2×C3×D3×D411yescharacteristic
744C3—21no—
745C3#8342711yescharacteristic, direct product factor
746C3C3×#301311yescharacteristic, complemented
747C2—22no—
748C2—42no—
749C2—81no—
750C2—122no—
751C2C2×C3×#93711yescharacteristic
752C2C3×#583611yescharacteristic
753C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#537C2
socleC22×C32C22×D4
hypercenterC3×#537D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C32×#537C2semidirect
3. C2×C3×#951C2semidirect
4. C2×C3×#950C2semidirect
5. C3×#5234C2semidirect
6. C3×#5050C2semidirect
7. C3×#5047C2semidirect
8. C3×#5040C2semidirect
9. C3×#5037C2semidirect
10. C2×C3×#810C2semidirect
11. C3×#4966C2semidirect
13. #83427C3direct (N × H)
48. C2×#1010C2×C3semidirect
52. C3×#537D3semidirect
53. C3×#537C2×C3semidirect
54. C2×#951C2×C3semidirect
55. C2×#950C2×C3semidirect
63. #5234C2×C3semidirect
64. #5050C2×C3semidirect
65. #5047C2×C3semidirect
66. #5040C2×C3semidirect
67. #5037C2×C3semidirect
68. C2×#810C2×C3semidirect
69. #4966C2×C3semidirect
95. C3×#235D4semidirect
104. C2×C3×Dic6D4semidirect
244. #537C3×D3semidirect
329. #235C3×D4semidirect
338. C2×Dic6C3×D4semidirect
659. C32#3013semidirect
745. C3#83427direct (N × H)
746. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C32×#5372
C2×C3×#9512
C2×C3×#9502
C3×#52342
C3×#50502
C3×#50472
C3×#50402
C3×#50372
C2×C3×#8102
C3×#49662
C3×#30133
#834273