Finite Group Databasebeta

← C2×D3×#3716 #13170552

Subgroups — C2×D3×#3716 #13170552

Order 1728.

1522 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#634C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88796C211yesmaximal, characteristic, complemented
5C2×#88794C211yesmaximal, characteristic, complemented
6C2×C3×#3716C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8D3×#3716C218yesmaximal, direct product factor
9C2×D3×#214—31nomaximal
10C22×#3716—31nomaximal
11C2×D3×#204—31nomaximal
12C22×C3×D32—21no—
13C2×#6308C2211yescharacteristic, complemented
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6293—21no—
19C2×D3×C3⋊Dic3—21no—
20D3×#634—22no—
21D3×#634C2214yescomplemented
22C2×C3×#626—21no—
23C3×D3×D12—22no—
24C3×D3×D12C2214yes—
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88811C2214yescomplemented
28#88796C2214yescomplemented
29#88794C2214yescomplemented
30C3×#3716C2214yescomplemented
31C3×D3×C3⋊C8C2214yescomplemented
32C22×#634—31no—
33C2×C3×D3×D4—31no—
34C22×C3×D12—31no—
35C2×D3×D12D311yescharacteristic
36C2×D3×Dic6—31no—
37C2×D3×Dic6—31no—
38C2×D3×Dic6—61no—
39C2×#3754—31no—
40C2×#3744—31no—
41C2×C3×#214—31no—
42C22×C3×C3⋊C8—31no—
43C2×C3×#204—31no—
44C2×C3×D3×C8—31no—
45D3×#214—38no—
46C2×#3717—31no—
47C2×#3716—31no—
48C2×#3716—31no—
49C2×#3716—31no—
50C2×#3716—31no—
51C2×#3716—31no—
52C2×#3716—38no—
53C2×#3716—61no—
54C2×#3716—61no—
55C2×#3716D311yescharacteristic, direct product factor
56C2×#3715—31no—
57C2×D3×C3⋊C8D311yescharacteristic, complemented
58D3×#204—38no—
59C22×C3×C3⋊D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3D411yescharacteristic
62C2×C3×D32—24no—
63C2×C3×D32—44no—
64C2×C33×C4C2311yescharacteristic
65C2×C3⋊(C3⋊Dic3)—21no—
66#6308—21no—
67#6308C2312yescomplemented
68C2×C3×C3⋊Dic3—21no—
69C3×C4⋊(C3⋊D3)—21no—
70C3×C4⋊(C3⋊D3)C2312yes—
71C3×#634—21no—
72C3×#634C2312yescomplemented
73C2×C32×Dic3D411yescharacteristic
74C32×D12—21no—
75C32×D12C2312yes—
76C32×C4×D3D412yes—
77C32×C4×D3C2312yes—
78#6293—24no—
79D3×C3⋊Dic3—24no—
80C3×#626—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C22×#214—91no—
84C2×D3×SD16—91no—
85C22×#204—91no—
86C23×C3×D3—61no—
87C23×C3×D3—61no—
88C22×D32—21no—
89C2×C32×D4—31no—
90C22×C32×C4—31no—
91C22×C3⋊Dic3—61no—
92C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
93C2×#634—31no—
94C2×#634—31no—
95C2×#634—31no—
96C2×#634—34no—
97C2×#634—62no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—61no—
102C2×#634—121no—
103C2×#634C2×D311yescharacteristic, complemented
104C2×C3×#67—61no—
105C3×D3×D4—34no—
106C3×D3×D4—62no—
107C2×C3×D12—21no—
108C2×C3×D12—31no—
109C2×C3×D12—31no—
110C2×C3×D12—34no—
111C2×C3×D12—62no—
112C2×C3×D12—61no—
113C2×C3×D12—61no—
114C2×C3×D12C2×D311yescharacteristic
115C2×C3×D12C2×D311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2×D311yescharacteristic
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×C3×Dic6—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—61no—
122C2×#627—62no—
123C2×#627—61no—
124C2×#627—61no—
125C2×#626—21no—
126C2×D3×Dic3—62no—
127C2×D3×Dic3—61no—
128C2×D3×Dic3—61no—
129D3×D12—22no—
130D3×D12C2×D314yes—
131D3×Dic6—34no—
132D3×Dic6—34no—
133D3×Dic6—64no—
134D3×Dic6—64no—
135D3×Dic6—62no—
136D3×Dic6—62no—
137C2×C32×C8—31no—
138#3754—34no—
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140#3744—34no—
141C3×#214—34no—
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8—31no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—34no—
146C2×C3×C3⋊C8—61no—
147C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
148C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
149C3×#204—34no—
150C3×D3×C8—34no—
151#3717—34no—
152#3716—34no—
153#3716—34no—
154#3716—34no—
155#3716—34no—
156#3716—34no—
157#3716—64no—
158#3716—64no—
159#3716C2×D314yesdirect product factor
160#3715—34no—
161D3×C3⋊C8C2×D314yescomplemented
162C22×C33C2×D411yescharacteristic
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—42no—
165C2×C32×D3—22no—
166C2×C32×D3—42no—
167C2×C32×D3SD1614yescomplemented
168C2×C32×D3C2×D412yes—
169C3×D32—48no—
170C33×C4C2×D411yescharacteristic
171C33×C4C2411yescharacteristic
172C3⋊(C3⋊Dic3)—22no—
173C3×C3⋊Dic3—22no—
174C32×Dic3C2×D412yes—
175C22×C3×D4—91no—
176C2×D3×Q8—91no—
177C2×D3×D4—31no—
178C22×D12—31no—
179C22×Dic6—91no—
180C22×Dic6—91no—
181C22×Dic6—181no—
182C2×C3×SD16—91no—
183C22×C3×C8—91no—
184C2×#215—91no—
185C2×#214—31no—
186C2×#214—98no—
187C2×#214—91no—
188C2×#214—91no—
189C2×#214—91no—
190C2×#214—91no—
191C2×#214—181no—
192C22×C3⋊C8—31no—
193D3×SD16—98no—
194C2×#204—31no—
195C2×#204—98no—
196C2×#204—91no—
197C2×#204—91no—
198C2×#204—91no—
199C2×#204—91no—
200C2×#204—181no—
201C2×D3×C8—31no—
202C23×C32—31no—
203C23×C32—61no—
204C22×C3⋊D3—21no—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—41no—
209C22×C3×D3—64no—
210C22×C3×D3—61no—
211C22×C3×D3—61no—
212C22×C3×D3—64no—
213C22×C3×D3—121no—
214C22×C3×D3—124no—
215C22×C3×D3—124no—
216C22×C3×D3D1211yescharacteristic
217C22×C3×D3#6711yescharacteristic
218C2×D32—24no—
219C2×D32—44no—
220C32×D4—32no—
221C32×D4—61no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—31no—
226C2×C32×C4—32no—
227C2×C32×C4—32no—
228C2×C32×C4—41no—
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C22×D311yescharacteristic
231C2×C32×C4C22×D311yescharacteristic
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—64no—
234C2×C3⋊Dic3—61no—
235C2×C3⋊Dic3—62no—
236C2×C3⋊Dic3—61no—
237C2×C3⋊Dic3—61no—
238C2×C3⋊Dic3—121no—
239C2×C3⋊Dic3—121no—
240C2×C3⋊Dic3—122no—
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)C22×D312yes—
243#634—21no—
244#634—32no—
245#634—32no—
246#634—32no—
247#634—62no—
248#634—62no—
249#634—62no—
250#634—64no—
251#634—61no—
252#634—62no—
253#634—61no—
254#634—61no—
255#634—122no—
256#634—121no—
257#634—121no—
258#634—122no—
259#634C22×D312yescomplemented
260C3×#67—64no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3D1211yescharacteristic
266C2×C3×Dic3#6711yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—22no—
270C3×D12—32no—
271C3×D12—32no—
272C3×D12—41no—
273C3×D12—62no—
274C3×D12—64no—
275C3×D12—61no—
276C3×D12—61no—
277C3×D12—121no—
278C3×D12C22×D312yes—
279C3×D12C22×D312yes—
280C3×C4×D3—22no—
281C3×C4×D3—22no—
282C3×C4×D3D1212yes—
283C3×C4×D3#6712yes—
284C3×C4×D3C22×D312yes—
285C3×C4×D3C22×D312yes—
286C3×Dic6—32no—
287C3×Dic6—32no—
288C3×Dic6—62no—
289C3×Dic6—62no—
290C3×Dic6—61no—
291C3×Dic6—61no—
292#627—68no—
293#627—64no—
294#627—64no—
295#626—24no—
296D3×Dic3—68no—
297D3×Dic3—64no—
298D3×Dic3—64no—
299C32×C8—32no—
300C3⋊(C3⋊C8)C22×D312yescomplemented
301C3×C3⋊C8—22no—
302C3×C3⋊C8—32no—
303C3×C3⋊C8—32no—
304C3×C3⋊C8—62no—
305C3×C3⋊C8C22×D312yescomplemented
306C3×C3⋊C8C22×D312yescomplemented
307C22×SD16—271noSylow
308C2×C33C2×SD1612yescomplemented
309C2×C33C22×D411yescharacteristic
310C3×C3⋊D3—42no—
311C32×D3—42no—
312C32×D3C2×SD1614yescomplemented
313C24×C3—181no—
314C23×D3—61no—
315C23×D3—61no—
316C2×C3×Q8—91no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—94no—
321C2×C3×D4—91no—
322C2×C3×D4—182no—
323C2×C3×D4—181no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C2×#67—61no—
328C22×Dic3—181no—
329C22×Dic3—181no—
330C22×Dic3—182no—
331D3×Q8—94no—
332D3×Q8—182no—
333D3×D4—34no—
334D3×D4—62no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—34no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—61no—
341C2×D12D3211yescharacteristic
342C2×C4×D3—181no—
343C2×C4×D3D3211yescharacteristic
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×Dic6—94no—
348C2×Dic6—94no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C2×Dic6—184no—
353C2×Dic6—181no—
354C2×Dic6—181no—
355C2×Dic6—181no—
356C2×Dic6—182no—
357C2×Dic6—182no—
358C2×Dic6—184no—
359C2×Dic6—181no—
360C2×Dic6—181no—
361C2×Dic6—182no—
362C2×Dic6—181no—
363C2×Dic6—361no—
364C3×SD16—94no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—61no—
368C2×C3×C8—94no—
369C2×C3×C8—91no—
370#215—94no—
371#214—34no—
372#214—94no—
373#214—94no—
374#214—94no—
375#214—94no—
376#214—184no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—34no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8D3211yescharacteristic, complemented
382#204—34no—
383#204—94no—
384#204—94no—
385#204—94no—
386#204—94no—
387#204—184no—
388D3×C8—34no—
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—34no—
393C22×C32—32no—
394C22×C32—41no—
395C22×C32—62no—
396C22×C32—122no—
397C22×C32C2×D1211yescharacteristic
398C22×C32D3×D411yescharacteristic
399C22×C32C2×#6711yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—42no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—24no—
405C2×C3×D3—22no—
406C2×C3×D3—42no—
407C2×C3×D3—42no—
408C2×C3×D3—42no—
409C2×C3×D3—62no—
410C2×C3×D3—62no—
411C2×C3×D3—82no—
412C2×C3×D3—122no—
413C2×C3×D3—128no—
414C2×C3×D3—122no—
415C2×C3×D3—122no—
416C2×C3×D3—128no—
417C2×C3×D3—242no—
418C2×C3×D3#20414yescomplemented
419C2×C3×D3#21414yescomplemented
420C2×C3×D3C2×D1212yes—
421C2×C3×D3C2×#6712yes—
422D32—48no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—32no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4C2×D1211yescharacteristic
433C32×C4D3×D411yescharacteristic
434C32×C4C2×#6711yescharacteristic
435C32×C4C23×D311yescharacteristic
436C32×C4C23×D311yescharacteristic
437C32×C4C23×D311yescharacteristic
438C3⋊Dic3—22no—
439C3⋊Dic3—62no—
440C3⋊Dic3—64no—
441C3⋊Dic3—62no—
442C3⋊Dic3—62no—
443C3⋊Dic3—122no—
444C3⋊Dic3—122no—
445C3⋊Dic3—124no—
446C3×Dic3—22no—
447C3×Dic3—64no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3C2×D1212yes—
451C3×Dic3C2×#6712yes—
452C22×Q8—271no—
453C22×D4—91no—
454C2×SD16—91no—
455C2×SD16—271no—
456C2×SD16—278no—
457C2×SD16—271no—
458C2×SD16—271no—
459C22×C8—91no—
460C33C22×SD1611yescharacteristic, complemented, Sylow
461C23×C3—31no—
462C23×C3—31no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—121no—
467C23×C3—184no—
468C23×C3—181no—
469C23×C3—364no—
470C22×D3—21no—
471C22×D3—64no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—64no—
475C22×D3—121no—
476C22×D3—124no—
477C22×D3—124no—
478C22×D3#62611yescharacteristic
479C3×Q8—92no—
480C3×Q8—181no—
481C3×D4—32no—
482C3×D4—32no—
483C3×D4—62no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—92no—
487C3×D4—121no—
488C3×D4—184no—
489C3×D4—181no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—41no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—181no—
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507#67—64no—
508C2×Dic3—62no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—184no—
512C2×Dic3—184no—
513C2×Dic3—188no—
514C2×Dic3—182no—
515C2×Dic3—181no—
516C2×Dic3—181no—
517C2×Dic3—181no—
518C2×Dic3—361no—
519C2×Dic3—361no—
520C2×Dic3—362no—
521C2×Dic3#62611yescharacteristic
522D12—21no—
523D12—32no—
524D12—32no—
525D12—62no—
526D12—64no—
527D12—61no—
528D12—61no—
529D12—121no—
530D12C2×D3212yes—
531C4×D3—184no—
532C4×D3#62612yes—
533C4×D3C2×D3212yes—
534Dic6—32no—
535Dic6—32no—
536Dic6—62no—
537Dic6—62no—
538Dic6—61no—
539Dic6—61no—
540Dic6—92no—
541Dic6—92no—
542Dic6—92no—
543Dic6—182no—
544Dic6—182no—
545Dic6—182no—
546Dic6—184no—
547Dic6—184no—
548Dic6—188no—
549Dic6—182no—
550Dic6—181no—
551Dic6—181no—
552Dic6—181no—
553Dic6—184no—
554Dic6—362no—
555Dic6—361no—
556Dic6—361no—
557Dic6—362no—
558C3×C8—32no—
559C3×C8—32no—
560C3×C8—62no—
561C3×C8—92no—
562C3⋊C8—32no—
563C3⋊C8—32no—
564C3⋊C8—62no—
565C3⋊C8C2×D3212yescomplemented
566C2×C32—21no—
567C2×C32—22no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—22no—
571C2×C32—22no—
572C2×C32—34no—
573C2×C32—42no—
574C2×C32—41no—
575C2×C32—122no—
576C2×C32C2×#20412yescomplemented
577C2×C32D3×SD1612yescomplemented
578C2×C32C2×#21412yescomplemented
579C2×C32C22×D1211yescharacteristic
580C2×C32C2×D3×D411yescharacteristic
581C2×C32C22×#6711yescharacteristic
582C3⋊D3—42no—
583C3×D3—24no—
584C3×D3—42no—
585C3×D3—42no—
586C3×D3—82no—
587C3×D3—122no—
588C3×D3—122no—
589C3×D3—242no—
590C3×D3C2×#20414yescomplemented
591C3×D3C2×#21414yescomplemented
592C24—181no—
593C2×Q8—91no—
594C2×Q8—274no—
595C2×Q8—271no—
596C2×Q8—541no—
597C2×Q8—542no—
598C2×D4—31no—
599C2×D4—94no—
600C2×D4—91no—
601C2×D4—182no—
602C2×D4—181no—
603C22×C4—31no—
604C22×C4—541no—
605SD16—94no—
606SD16—274no—
607SD16—274no—
608SD16—274no—
609C2×C8—31no—
610C2×C8—94no—
611C2×C8—91no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—34no—
617C22×C3—32no—
618C22×C3—34no—
619C22×C3—41no—
620C22×C3—62no—
621C22×C3—64no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—122no—
625C22×C3—122no—
626C22×C3—122no—
627C22×C3—182no—
628C22×C3—242no—
629C22×C3—368no—
630C22×C3—362no—
631C22×C3D3×D1211yescharacteristic
632C22×C3C2×#62611yescharacteristic
633C22×C3D3×#6711yescharacteristic
634C2×D3—22no—
635C2×D3—42no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—122no—
639C2×D3—128no—
640C2×D3—122no—
641C2×D3—122no—
642C2×D3—128no—
643C2×D3—242no—
644C2×D3#371614yesdirect product factor
645C2×D3C2×#62612yes—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—62no—
657C3×C4—182no—
658C3×C4D3×D1211yescharacteristic
659C3×C4C2×#62611yescharacteristic
660C3×C4D3×#6711yescharacteristic
661C3×C4C22×D3211yescharacteristic
662C3×C4C22×D3211yescharacteristic
663C3×C4C22×D3211yescharacteristic
664Dic3—64no—
665Dic3—62no—
666Dic3—62no—
667Dic3—184no—
668Dic3—182no—
669Dic3—182no—
670Dic3—182no—
671Dic3—362no—
672Dic3—362no—
673Dic3—364no—
674Dic3C2×#62612yes—
675C32—21no—
676C32—21no—
677C32—21no—
678C32—41no—
679C32C22×#20411yescharacteristic, complemented
680C32C2×D3×SD1611yescharacteristic, complemented
681C32C22×#21411yescharacteristic, complemented
682C23—31no—
683C23—61no—
684C23—184no—
685C23—181no—
686C23—364no—
687Q8—92no—
688Q8—181no—
689Q8—272no—
690Q8—544no—
691Q8—541no—
692D4—32no—
693D4—61no—
694D4—92no—
695D4—184no—
696D4—181no—
697C2×C4—31no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—181no—
701C2×C4—544no—
702C2×C4—541no—
703C2×C4D3311yescharacteristic
704C8—32no—
705C8—92no—
706C2×C3—22no—
707C2×C3—22no—
708C2×C3—22no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—34no—
713C2×C3—34no—
714C2×C3—42no—
715C2×C3—41no—
716C2×C3—64no—
717C2×C3—122no—
718C2×C3—122no—
719C2×C3—242no—
720C2×C3—362no—
721C2×C3D3×#20412yescomplemented
722C2×C3C2×#371612yescomplemented
723C2×C3D3×#21412yescomplemented
724C2×C3C2×D3×D1211yescharacteristic
725C2×C3C22×#62611yescharacteristic
726C2×C3C2×D3×#6711yescharacteristic
727D3—42no—
728D3—122no—
729D3—122no—
730D3—242no—
731D3C2×#371614yesdirect product factor
732C22—34no—
733C22—32no—
734C22—62no—
735C22—122no—
736C22—182no—
737C22—368no—
738C22—362no—
739C22D3×#62611yescharacteristic
740C4—32no—
741C4—182no—
742C4—542no—
743C4D3×#62611yescharacteristic
744C4C2×D3311yescharacteristic
745C3—21no—
746C3—21no—
747C3—21no—
748C3—41no—
749C3C2×D3×#20411yescharacteristic, complemented
750C3C22×#371611yescharacteristic, complemented
751C3C2×D3×#21411yescharacteristic, complemented
752C2—34no—
753C2—122no—
754C2—362no—
755C2D3×#371612yesdirect product factor
756C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×C3×D3×D12C2
hypercenterC2×C4D33
hypocenterC33C22×SD16
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#634C2semidirect
3. C2×#88811C2semidirect
4. C2×#88796C2semidirect
5. C2×#88794C2semidirect
6. C2×C3×#3716C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. D3×#3716C2direct (N × H)
13. C2×#6308C22semidirect
15. C2×C3×#634C22semidirect
21. D3×#634C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88811C22semidirect
28. #88796C22semidirect
29. #88794C22semidirect
30. C3×#3716C22semidirect
31. C3×D3×C3⋊C8C22semidirect
55. C2×#3716D3direct (N × H)
57. C2×D3×C3⋊C8D3semidirect
67. #6308C23semidirect
72. C3×#634C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
103. C2×#634C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
147. C2×C3×C3⋊C8C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
159. #3716C2×D3direct (N × H)
161. D3×C3⋊C8C2×D3semidirect
167. C2×C32×D3SD16semidirect
259. #634C22×D3semidirect
300. C3⋊(C3⋊C8)C22×D3semidirect
305. C3×C3⋊C8C22×D3semidirect
306. C3×C3⋊C8C22×D3semidirect
308. C2×C33C2×SD16semidirect
312. C32×D3C2×SD16semidirect
381. C2×C3⋊C8D32semidirect
418. C2×C3×D3#204semidirect
419. C2×C3×D3#214semidirect
460. C33C22×SD16semidirect
565. C3⋊C8C2×D32semidirect
576. C2×C32C2×#204semidirect
577. C2×C32D3×SD16semidirect
578. C2×C32C2×#214semidirect
590. C3×D3C2×#204semidirect
591. C3×D3C2×#214semidirect
644. C2×D3#3716direct (N × H)
679. C32C22×#204semidirect
680. C32C2×D3×SD16semidirect
681. C32C22×#214semidirect
721. C2×C3D3×#204semidirect
722. C2×C3C2×#3716semidirect
723. C2×C3D3×#214semidirect
731. D3C2×#3716direct (N × H)
749. C3C2×D3×#204semidirect
750. C3C22×#3716semidirect
751. C3C2×D3×#214semidirect
755. C2D3×#3716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#6342
C2×C3×D3×D122
C2×#888112
C2×#887962
C2×#887942
C2×C3×#37162
C2×C3×D3×C3⋊C82
D3×#37162
C2×D3×#2143
C22×#37163
C2×D3×#2043