Finite Group Databasebeta

← D3×#5240 #11857523

Subgroups — D3×#5240 #11857523

Order 1152.

1655 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2D3×#926C212yesmaximal, complemented
3#10592939C211yesmaximal, characteristic, complemented
4C3×#5240C211yesmaximal, characteristic, complemented
5#10591528C214yesmaximal, complemented
6D3×#834C214yesmaximal, complemented
7#10591231C212yesmaximal, complemented
8C2×#5240—31nomaximal
9D3×#410—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×D3×#41—22no—
12C3×D3×#41—22no—
13C3×D3×#41—22no—
14C3×D3×#41—22no—
15C2×C3×#239C411yescharacteristic, complemented
16C2×C3×D3×Q8C411yescharacteristic, complemented
17C2×C3×#237C411yescharacteristic, complemented
18C2×C3×#237C2212yes—
19C2×C3×D3×D4C411yescharacteristic, complemented
20C2×C3×D3×D4C2212yes—
21C2×C3×#235C412yescomplemented
22C2×C3×#235C2211yescharacteristic
23C22×C3×C4×D3C412yescomplemented
24C22×C3×C4×D3C2211yescharacteristic
25#64135C2212yescomplemented
26C3×#926C2212yescomplemented
27D3×#217C2214yes—
28#63955C2214yescomplemented
29D3×C4⋊Dic3—22no—
30C4×D3×Dic3—22no—
31#63855—22no—
32#63841—22no—
33#63661C2214yescomplemented
34C3×#834C2214yescomplemented
35#63580C2218yescomplemented
36C22×C3×#41—31no—
37C2×D3×#41D311yescharacteristic
38C2×#926—32no—
39D3×#117—32no—
40C3×#410—31no—
41#5240—31no—
42#5240—31no—
43#5240—32no—
44#5240—34no—
45#5240—61no—
46#5240D311yescharacteristic, direct product factor
47C2×#834—34no—
48#5006—32no—
49D3×#99—34no—
50#4740—34no—
51C23×C3×D3C2×C412yes—
52C23×C3×D3C2311yescharacteristic
53C32×#41—22no—
54C32×#41—22no—
55C2×C32×Q8C2×C411yescharacteristic, complemented
56C2×C32×D4C2×C411yescharacteristic, complemented
57C2×C32×D4C2312yes—
58C22×C32×C4C2×C412yescomplemented
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67C2×C412yes—
61C2×C3×#67C2×C412yescomplemented
62C2×C3×#67C2312yes—
63C22×C3×Dic3C2×C412yescomplemented
64C22×C3×Dic3C2311yescharacteristic
65C3×#239—22no—
66C3×#239—22no—
67C3×D3×Q8—22no—
68C3×D3×Q8—22no—
69C3×#237—24no—
70C3×#237—24no—
71C3×#237—22no—
72C3×#237—22no—
73C3×D3×D4—24no—
74C3×D3×D4—24no—
75C3×D3×D4—22no—
76C3×D3×D4—22no—
77C3×#235—22no—
78C3×#235—22no—
79C3×#235—24no—
80C3×#235—24no—
81C2×C3×D12C2×C412yes—
82C2×C3×D12C2×C411yescharacteristic, complemented
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3C2×C412yes—
88C2×C3×C4×D3C2×C411yescharacteristic
89C2×C3×C4×D3C2×C411yescharacteristic
90C2×C3×C4×D3C2×C411yescharacteristic
91C2×C3×C4×D3C2×C411yescharacteristic
92C2×C3×C4×D3C2×C412yescomplemented
93C2×C3×C4×D3C2×C412yescomplemented
94C2×C3×C4×D3D412yes—
95C2×C3×C4×D3D412yes—
96C2×C3×C4×D3D412yes—
97C2×C3×C4×D3D412yes—
98C2×C3×Dic6C2×C412yescomplemented
99C2×C3×Dic6C2×C411yescharacteristic, complemented
100C2×D3×Dic3—24no—
101#3757C2314yes—
102C4⋊(C3⋊Dic3)—22no—
103C4×C3⋊Dic3—22no—
104C3×#217C2314yes—
105C3×C4⋊Dic3—22no—
106C3×C4×Dic3—22no—
107Dic3⋊Dic3—24no—
108(C2×D3)⋊Dic3—24no—
109Dic32—24no—
110C2×#410—91noSylow
111C2×C3×#41—21no—
112C2×C3×#41—31no—
113C2×C3×#41—31no—
114C2×C3×#41—32no—
115C2×C3×#41—32no—
116C2×C3×#41—31no—
117C2×C3×#41—62no—
118C2×C3×#41—62no—
119C2×C3×#41—62no—
120C2×C3×#41—62no—
121C2×C3×#41C2×D311yescharacteristic
122C2×C3×#41C2×D311yescharacteristic
123C22×C3×Q8—31no—
124C22×C3×D4—31no—
125C22×C3×D4—32no—
126C23×C3×C4—31no—
127C23×C3×C4—32no—
128D3×#41—22no—
129D3×#41—22no—
130D3×#41—22no—
131D3×#41—22no—
132C2×#239Dic311yescharacteristic, complemented
133C2×D3×Q8Dic311yescharacteristic, complemented
134C2×#237Dic311yescharacteristic, complemented
135C2×#237C2×D312yes—
136C2×D3×D4Dic311yescharacteristic, complemented
137C2×D3×D4C2×D312yes—
138C2×#235Dic312yescomplemented
139C2×#235C2×D311yescharacteristic
140C22×C4×D3Dic312yescomplemented
141C22×C4×D3C2×D311yescharacteristic
142C3×#117—32no—
143C2×#217—34no—
144#926—32no—
145#926—32no—
146#926—34no—
147#926—62no—
148#926—62no—
149#926—62no—
150#926C2×D312yescomplemented
151C2×C4⋊Dic3—62no—
152C2×C4×Dic3—62no—
153#892—62no—
154D3×C4⋊C4—62no—
155D3×C22⋊C4—34no—
156#877—34no—
157#872—62no—
158C42×D3—62no—
159C3×#99—34no—
160#834—34no—
161#834—34no—
162#834—38no—
163#834—64no—
164#834C2×D314yescomplemented
165#806—38no—
166C23×C32C22×C412yes—
167C23×C32C2411yescharacteristic
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3—44no—
172C22×C3×D3C22×C411yescharacteristic
173C22×C3×D3C22×C412yes—
174C22×C3×D3C22×C411yescharacteristic
175C22×C3×D3C2×D412yes—
176C22×C3×D3C2×D412yes—
177C32×Q8—22no—
178C32×D4—24no—
179C32×D4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C22×C412yes—
183C2×C32×C4C22×C411yescharacteristic
184C2×C32×C4C22×C411yescharacteristic
185C2×C32×C4C2×D412yes—
186C2×C32×C4C2×D412yes—
187C2×C3⋊Dic3—24no—
188C3×#67—24no—
189C3×#67—24no—
190C3×#67—24no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—24no—
194C2×C3×Dic3C22×C412yes—
195C2×C3×Dic3C22×C411yescharacteristic
196C2×C3×Dic3C22×C411yescharacteristic
197C2×C3×Dic3C2×D412yes—
198C2×C3×Dic3C2×D412yes—
199C3×D12—24no—
200C3×D12—22no—
201C3×C4×D3—22no—
202C3×C4×D3—22no—
203C3×C4×D3—22no—
204C3×C4×D3—22no—
205C3×C4×D3—22no—
206C3×C4×D3—22no—
207C3×C4×D3C22⋊C411yescharacteristic
208C3×C4×D3C22⋊C411yescharacteristic
209C3×C4×D3C22⋊C411yescharacteristic
210C3×C4×D3C22⋊C411yescharacteristic
211C3×C4×D3C22⋊C412yes—
212C3×C4×D3C22⋊C412yes—
213C3×C4×D3C22⋊C412yes—
214C3×C4×D3C22⋊C412yes—
215C3×C4×D3C22⋊C412yes—
216C3×C4×D3C22⋊C412yes—
217C3×Dic6—22no—
218C3×Dic6—24no—
219D3×Dic3—48no—
220C22×#41—31no—
221C2×#117—92no—
222#410—31no—
223#410—94no—
224#410—92no—
225#410—91no—
226C2×#99—94no—
227C24×C3—31no—
228C24×C3—32no—
229C23×D3C2×Dic312yes—
230C23×D3C22×D311yescharacteristic
231C3×#41—22no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—22no—
235C3×#41—42no—
236C3×#41—42no—
237C3×#41—64no—
238C3×#41—64no—
239C3×#41—64no—
240C3×#41—64no—
241C3×#41—62no—
242C3×#41—62no—
243C3×#41—62no—
244C3×#41—62no—
245C3×#41—62no—
246C3×#41—62no—
247C2×C3×Q8—21no—
248C2×C3×Q8—32no—
249C2×C3×Q8—31no—
250C2×C3×Q8—62no—
251C2×C3×Q8—62no—
252C2×C3×Q8C4×D311yescharacteristic, complemented
253C2×C3×Q8C2×Dic311yescharacteristic, complemented
254C2×C3×D4—21no—
255C2×C3×D4—22no—
256C2×C3×D4—32no—
257C2×C3×D4—32no—
258C2×C3×D4—32no—
259C2×C3×D4—32no—
260C2×C3×D4—31no—
261C2×C3×D4—62no—
262C2×C3×D4—62no—
263C2×C3×D4—64no—
264C2×C3×D4—64no—
265C2×C3×D4C4×D311yescharacteristic, complemented
266C2×C3×D4C2×Dic311yescharacteristic, complemented
267C2×C3×D4C22×D312yes—
268C2×C3×D4C22×D312yes—
269C22×C3×C4—22no—
270C22×C3×C4—21no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—32no—
277C22×C3×C4—32no—
278C22×C3×C4—32no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—32no—
282C22×C3×C4—32no—
283C22×C3×C4—32no—
284C22×C3×C4—62no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4—62no—
288C22×C3×C4C4×D312yescomplemented
289C22×C3×C4C2×Dic312yescomplemented
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C2×#67C2×Dic312yes—
293C2×#67C2×Dic312yescomplemented
294C2×#67C22×D312yes—
295C22×Dic3—64no—
296C22×Dic3C2×Dic312yescomplemented
297C22×Dic3C22×D311yescharacteristic
298#239—22no—
299#239—22no—
300D3×Q8—22no—
301D3×Q8—22no—
302#237—24no—
303#237—24no—
304#237—22no—
305#237—22no—
306D3×D4—24no—
307D3×D4—24no—
308D3×D4—22no—
309D3×D4—22no—
310#235—22no—
311#235—22no—
312#235—24no—
313#235—24no—
314C2×D12C2×Dic312yes—
315C2×D12C2×Dic311yescharacteristic, complemented
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—22no—
320C2×C4×D3—64no—
321C2×C4×D3C2×Dic312yes—
322C2×C4×D3C2×Dic311yescharacteristic
323C2×C4×D3C2×Dic311yescharacteristic
324C2×C4×D3C2×Dic311yescharacteristic
325C2×C4×D3C2×Dic311yescharacteristic
326C2×C4×D3C2×Dic312yescomplemented
327C2×C4×D3C2×Dic312yescomplemented
328C2×C4×D3#6712yes—
329C2×C4×D3#6712yes—
330C2×C4×D3#6712yes—
331C2×C4×D3#6712yes—
332C2×Dic6C2×Dic312yescomplemented
333C2×Dic6C2×Dic311yescharacteristic, complemented
334C3×C4⋊C4—62no—
335C3×C22⋊C4—34no—
336C3×C42—62no—
337#217—34no—
338#217—34no—
339#217—64no—
340#217—64no—
341#217C22×D314yes—
342(C2×D3)⋊C4—64no—
343C4⋊Dic3—22no—
344C4⋊Dic3—64no—
345C4⋊Dic3—62no—
346C4⋊Dic3—62no—
347C4⋊Dic3—122no—
348Dic3⋊C4—64no—
349C4×Dic3—22no—
350C4×Dic3—64no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353C4×Dic3—64no—
354C4×Dic3—122no—
355C22×C32—22no—
356C22×C32—41no—
357C22×C32—42no—
358C22×C32C23×C411yescharacteristic
359C22×C32C22×D412yes—
360C2×C3×D3—24no—
361C2×C3×D3—22no—
362C2×C3×D3—22no—
363C2×C3×D3—41no—
364C2×C3×D3—42no—
365C2×C3×D3—44no—
366C2×C3×D3—44no—
367C2×C3×D3—42no—
368C2×C3×D3C2×C22⋊C411yescharacteristic
369C2×C3×D3C2×C22⋊C412yes—
370C2×C3×D3C2×C22⋊C411yescharacteristic
371C32×C4—22no—
372C32×C4C2×C22⋊C412yes—
373C32×C4C2×C22⋊C411yescharacteristic
374C32×C4C2×C22⋊C411yescharacteristic
375C3⋊Dic3—44no—
376C3×Dic3—22no—
377C3×Dic3—44no—
378C3×Dic3C2×C22⋊C412yes—
379C3×Dic3C2×C22⋊C411yescharacteristic
380C3×Dic3C2×C22⋊C411yescharacteristic
381C2×#41—31no—
382C2×#41—31no—
383C2×#41—32no—
384C2×#41—32no—
385C2×#41—31no—
386C2×#41—62no—
387C2×#41—62no—
388C2×#41—62no—
389C2×#41—62no—
390C2×#41D3211yescharacteristic
391C22×Q8—31no—
392C22×D4—31no—
393C22×D4—32no—
394C23×C4—31no—
395C23×C4—32no—
396#117—32no—
397#117—94no—
398#117—92no—
399#117—182no—
400#117—182no—
401C2×C4⋊C4—182no—
402C2×C22⋊C4—94no—
403C2×C42—182no—
404#99—34no—
405#99—98no—
406#99—94no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—31no—
410C23×C3—32no—
411C23×C3—31no—
412C23×C3—32no—
413C23×C3—32no—
414C23×C3—62no—
415C23×C3—62no—
416C23×C3—122no—
417C23×C3—124no—
418C23×C3C2×C4×D312yes—
419C23×C3C22×Dic312yes—
420C23×C3C23×D311yescharacteristic
421C23×C3C23×D311yescharacteristic
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—42no—
425C22×D3—44no—
426C22×D3C22×Dic311yescharacteristic
427C22×D3C22×Dic312yes—
428C22×D3C22×Dic311yescharacteristic
429C22×D3C2×#6712yes—
430C22×D3C2×#6712yes—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—42no—
434C3×Q8—64no—
435C3×Q8—62no—
436C3×D4—24no—
437C3×D4—24no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—42no—
441C3×D4—44no—
442C3×D4—64no—
443C3×D4—64no—
444C3×D4—64no—
445C3×D4—64no—
446C3×D4—62no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—64no—
482C2×C3×C4C2×C4×D312yes—
483C2×C3×C4C2×C4×D311yescharacteristic
484C2×C3×C4C2×C4×D311yescharacteristic
485C2×C3×C4D3×D412yes—
486C2×C3×C4D3×D412yes—
487C2×C3×C4C22×Dic312yes—
488C2×C3×C4C22×Dic311yescharacteristic
489C2×C3×C4C22×Dic311yescharacteristic
490C2×C3×C4C2×#6712yes—
491C2×C3×C4C2×#6712yes—
492#67—24no—
493#67—24no—
494#67—24no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—64no—
499C2×Dic3—64no—
500C2×Dic3—124no—
501C2×Dic3—128no—
502C2×Dic3C22×Dic312yes—
503C2×Dic3C22×Dic311yescharacteristic
504C2×Dic3C22×Dic311yescharacteristic
505C2×Dic3C2×#6712yes—
506C2×Dic3C2×#6712yes—
507D12—24no—
508D12—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—128no—
516C4×D3#21711yescharacteristic
517C4×D3#21711yescharacteristic
518C4×D3#21711yescharacteristic
519C4×D3#21711yescharacteristic
520C4×D3#21712yes—
521C4×D3#21712yes—
522C4×D3#21712yes—
523C4×D3#21712yes—
524C4×D3#21712yes—
525C4×D3#21712yes—
526Dic6—22no—
527Dic6—24no—
528C2×C32—22no—
529C2×C32—21no—
530C2×C32—42no—
531C2×C32C22×C22⋊C411yescharacteristic
532C3×D3—21no—
533C3×D3—22no—
534C3×D3—42no—
535C3×D3#41012yescomplemented
536C24—31no—
537C24—32no—
538#41—22no—
539#41—22no—
540#41—64no—
541#41—64no—
542#41—64no—
543#41—64no—
544#41—62no—
545#41—62no—
546#41—62no—
547#41—62no—
548#41—62no—
549#41—62no—
550C2×Q8—32no—
551C2×Q8—31no—
552C2×Q8—62no—
553C2×Q8—62no—
554C2×Q8D3×Dic311yescharacteristic, complemented
555C2×D4—32no—
556C2×D4—32no—
557C2×D4—32no—
558C2×D4—32no—
559C2×D4—31no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—64no—
563C2×D4—64no—
564C2×D4D3×Dic311yescharacteristic, complemented
565C2×D4C2×D3212yes—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—184no—
584C22×C4D3×Dic312yescomplemented
585C22×C4C2×D3211yescharacteristic
586C4⋊C4—62no—
587C4⋊C4—184no—
588C4⋊C4—182no—
589C22⋊C4—34no—
590C22⋊C4—94no—
591C22⋊C4—184no—
592C42—62no—
593C42—184no—
594C42—182no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—21no—
598C22×C3—22no—
599C22×C3—31no—
600C22×C3—31no—
601C22×C3—32no—
602C22×C3—42no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—64no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—81no—
611C22×C3—82no—
612C22×C3—122no—
613C22×C3—121no—
614C22×C3—122no—
615C22×C3—124no—
616C22×C3—124no—
617C22×C3C22×C4×D311yescharacteristic
618C22×C3C2×D3×D412yes—
619C22×C3C23×Dic311yescharacteristic
620C22×C3C22×#6712yes—
621C2×D3—24no—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—42no—
629C2×D3C2×#21711yescharacteristic
630C2×D3C2×#21712yes—
631C2×D3C2×#21711yescharacteristic
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—21no—
635C3×C4—22no—
636C3×C4—21no—
637C3×C4—31no—
638C3×C4—31no—
639C3×C4—32no—
640C3×C4—42no—
641C3×C4—62no—
642C3×C4—124no—
643C3×C4D3×C22⋊C411yescharacteristic
644C3×C4D3×C22⋊C412yes—
645C3×C4D3×C22⋊C411yescharacteristic
646C3×C4C2×#21712yes—
647C3×C4C2×#21711yescharacteristic
648C3×C4C2×#21711yescharacteristic
649Dic3—22no—
650Dic3—44no—
651Dic3—124no—
652Dic3—124no—
653Dic3—244no—
654Dic3C2×#21712yes—
655Dic3C2×#21711yescharacteristic
656Dic3C2×#21711yescharacteristic
657C32C2×#41011yescharacteristic, complemented, Sylow
658C23—31no—
659C23—32no—
660C23—31no—
661C23—32no—
662C23—32no—
663C23—62no—
664C23—62no—
665C23—122no—
666C23—124no—
667C23C2×D3×Dic312yes—
668C23C22×D3211yescharacteristic
669Q8—22no—
670Q8—64no—
671Q8—62no—
672D4—24no—
673D4—22no—
674D4—64no—
675D4—64no—
676D4—64no—
677D4—64no—
678D4—62no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—184no—
706C2×C4—368no—
707C2×C4C2×D3×Dic312yes—
708C2×C4C2×D3×Dic311yescharacteristic
709C2×C4C2×D3×Dic311yescharacteristic
710C2×C4D3×#6712yes—
711C2×C4D3×#6712yes—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—32no—
718C2×C3—42no—
719C2×C3—41no—
720C2×C3—42no—
721C2×C3—42no—
722C2×C3—61no—
723C2×C3—62no—
724C2×C3—82no—
725C2×C3—122no—
726C2×C3C2×D3×C22⋊C411yescharacteristic
727C2×C3C22×#21711yescharacteristic
728D3—21no—
729D3—22no—
730D3—42no—
731D3#524012yesdirect product factor
732C22—22no—
733C22—31no—
734C22—31no—
735C22—32no—
736C22—41no—
737C22—42no—
738C22—64no—
739C22—62no—
740C22—62no—
741C22—122no—
742C22—121no—
743C22—122no—
744C22—124no—
745C22—124no—
746C22C22×D3×Dic311yescharacteristic
747C22C2×D3×#6712yes—
748C4—22no—
749C4—31no—
750C4—31no—
751C4—32no—
752C4—62no—
753C4—124no—
754C4—364no—
755C4D3×#21711yescharacteristic
756C4D3×#21712yes—
757C4D3×#21711yescharacteristic
758C3—21no—
759C3D3×#41011yescharacteristic, complemented
760C3C2×#524011yescharacteristic, complemented
761C2—22no—
762C2—21no—
763C2—32no—
764C2—42no—
765C2—61no—
766C2—62no—
767C2—122no—
768C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC4D3×#217
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×#41C22
socleC2×C32C22×C22⋊C4
prime radicalC2×C3×D3×#41C2
cosocleC23×C32C24
hypercenterC2×#41D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. #10592939C2semidirect
4. C3×#5240C2semidirect
5. #10591528C2semidirect
6. D3×#834C2semidirect
7. #10591231C2semidirect
15. C2×C3×#239C4semidirect
16. C2×C3×D3×Q8C4semidirect
17. C2×C3×#237C4semidirect
19. C2×C3×D3×D4C4semidirect
21. C2×C3×#235C4semidirect
23. C22×C3×C4×D3C4semidirect
25. #64135C22semidirect
26. C3×#926C22semidirect
28. #63955C22semidirect
33. #63661C22semidirect
34. C3×#834C22semidirect
35. #63580C22semidirect
46. #5240D3direct (N × H)
55. C2×C32×Q8C2×C4semidirect
56. C2×C32×D4C2×C4semidirect
58. C22×C32×C4C2×C4semidirect
61. C2×C3×#67C2×C4semidirect
63. C22×C3×Dic3C2×C4semidirect
82. C2×C3×D12C2×C4semidirect
92. C2×C3×C4×D3C2×C4semidirect
93. C2×C3×C4×D3C2×C4semidirect
98. C2×C3×Dic6C2×C4semidirect
99. C2×C3×Dic6C2×C4semidirect
132. C2×#239Dic3semidirect
133. C2×D3×Q8Dic3semidirect
134. C2×#237Dic3semidirect
136. C2×D3×D4Dic3semidirect
138. C2×#235Dic3semidirect
140. C22×C4×D3Dic3semidirect
150. #926C2×D3semidirect
164. #834C2×D3semidirect
252. C2×C3×Q8C4×D3semidirect
253. C2×C3×Q8C2×Dic3semidirect
265. C2×C3×D4C4×D3semidirect
266. C2×C3×D4C2×Dic3semidirect
288. C22×C3×C4C4×D3semidirect
289. C22×C3×C4C2×Dic3semidirect
293. C2×#67C2×Dic3semidirect
296. C22×Dic3C2×Dic3semidirect
315. C2×D12C2×Dic3semidirect
326. C2×C4×D3C2×Dic3semidirect
327. C2×C4×D3C2×Dic3semidirect
332. C2×Dic6C2×Dic3semidirect
333. C2×Dic6C2×Dic3semidirect
535. C3×D3#410semidirect
554. C2×Q8D3×Dic3semidirect
564. C2×D4D3×Dic3semidirect
584. C22×C4D3×Dic3semidirect
657. C32C2×#410semidirect
731. D3#5240direct (N × H)
759. C3D3×#410semidirect
760. C3C2×#5240semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
D3×#9262
#105929392
C3×#52402
#105915282
D3×#8342
#105912312
C2×#52403
D3×#4103