Finite Group Databasebeta

← #13161952

Subgroups — #13161952

Order 1728.

1160 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#3754C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4C2×#88811C211yesmaximal, characteristic, complemented
5C3×#63659C211yesmaximal, characteristic, complemented
6#11722075C211yesmaximal, characteristic, complemented
7#11722072C211yesmaximal, characteristic, complemented
8#10591467—31nomaximal
9#10591459—31nomaximal
10#10591458—31nomaximal
11C23×C3×C3⋊D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638—21no—
14C3×D4×C3⋊D3—22no—
15C3×D4×C3⋊D3—22no—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic, complemented
19C3×#3754—22no—
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23#88815—21no—
24#88814—21no—
25#88811—22no—
26C2×D4×C3⋊D3D311yescharacteristic
27C2×C3×D3×D4—31no—
28C2×C3×D3×D4—31no—
29C2×C3×D3×D4—61no—
30C2×#3754D311yescharacteristic, complemented
31C2×C3×#214—31no—
32C2×C3×#214—31no—
33C2×C3×#214—61no—
34#63871—31no—
35#63857—31no—
36#63856—31no—
37C2×#3717—31no—
38C2×#3716—31no—
39C2×#3715—31no—
40#63659D311yescharacteristic, complemented
41C3×#832—31no—
42C3×#832—31no—
43C3×#832—61no—
44#63564—31no—
45#63563—31no—
46#63562—31no—
47#63557—31no—
48(C2×D3)⋊(C3⋊C8)—31no—
49(C2×D3)⋊(C3⋊C8)—31no—
50C23×C33—21no—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—42no—
54C22×C3×C3⋊D3—42no—
55C22×C3×C3⋊D3D411yescharacteristic
56C33×D4—21no—
57C33×D4D412yes—
58C2×C33×C4C2311yescharacteristic
59C3×#638—24no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3D411yescharacteristic
63C3×C4⋊(C3⋊D3)—21no—
64C3×C4⋊(C3⋊D3)D412yes—
65C3×C4×C3⋊D3—21no—
66C3×C4×C3⋊D3—21no—
67C3×#634—21no—
68C3×#634—21no—
69C3×C3⋊(C3⋊C8)—21no—
70C3×C3⋊(C3⋊C8)—21no—
71#5218—91no—
72#5169—91no—
73#4776—91no—
74C23×C3⋊D3—21no—
75C23×C3×D3—61no—
76C23×C3×D3—61no—
77C23×C3×D3—62no—
78C2×C32×D4—21no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—41no—
82C2×C32×D4C2×D311yescharacteristic
83C2×C32×D4C2×D311yescharacteristic
84C2×C32×D4C2×D311yescharacteristic
85C2×#638—21no—
86D4×C3⋊D3—22no—
87D4×C3⋊D3—22no—
88C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
89C2×C4×C3⋊D3C2×D311yescharacteristic
90C2×#634C2×D311yescharacteristic, complemented
91C2×C3×#67—61no—
92C2×C3×#67—61no—
93C2×C3×#67—62no—
94C3×D3×D4—62no—
95C3×D3×D4—62no—
96C3×D3×D4—64no—
97C3×D3×D4—64no—
98C3×D3×D4—62no—
99C3×D3×D4—62no—
100C2×C3×D12—31no—
101C2×C3×D12—31no—
102C2×C3×D12—61no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—61no—
109#3754—22no—
110C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
111C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
112C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
113C3×#214—64no—
114C3×#214—62no—
115C3×#214—62no—
116C3×C4⋊Dic3—31no—
117C3×C4⋊Dic3—31no—
118C3×C4⋊Dic3—61no—
119C2×C3×C3⋊C8—31no—
120C2×C3×C3⋊C8—31no—
121C2×C3×C3⋊C8—31no—
122C2×C3×C3⋊C8—31no—
123C2×C3×C3⋊C8—61no—
124C2×C3×C3⋊C8—61no—
125#3724—61no—
126Dic3⋊Dic3—61no—
127Dic3⋊Dic3—61no—
128#3722—61no—
129(C2×D3)⋊Dic3—61no—
130(C2×D3)⋊Dic3—61no—
131#3717—62no—
132#3716—62no—
133#3715—62no—
134C22×C33—22no—
135C22×C33—41no—
136C22×C33—41no—
137C22×C33C2×D411yescharacteristic
138C2×C3×C3⋊D3—21no—
139C2×C3×C3⋊D3—21no—
140C2×C3×C3⋊D3—22no—
141C2×C3×C3⋊D3—48no—
142C2×C3×C3⋊D3—41no—
143C2×C3×C3⋊D3—41no—
144C2×C3×C3⋊D3SD1612yescomplemented
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C3×C3⋊Dic3—21no—
148C3×C3⋊Dic3—41no—
149C3×C3⋊Dic3—41no—
150C22×C3×D4—91no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C2×D3×D4—61no—
154C2×C3×SD16—91no—
155#946—91no—
156C2×#215—91no—
157C2×#214—31no—
158C2×#214—31no—
159C2×#214—61no—
160C2×#214—91no—
161#924—91no—
162C2×#204—91no—
163#897—91no—
164C3×#102—91no—
165#832—31no—
166#832—31no—
167#832—61no—
168#832—91no—
169#830—91no—
170#821—91no—
171(C2×D3)⋊C8—91no—
172(C2×D3)⋊C8—91no—
173#809—91no—
174C23×C32—21no—
175C23×C32—22no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—41no—
179C23×C32—41no—
180C23×C32—42no—
181C22×C3⋊D3—24no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—42no—
184C22×C3⋊D3—42no—
185C22×C3⋊D3#6711yescharacteristic
186C22×C3×D3—31no—
187C22×C3×D3—31no—
188C22×C3×D3—61no—
189C22×C3×D3—62no—
190C22×C3×D3—68no—
191C22×C3×D3—64no—
192C22×C3×D3—64no—
193C22×C3×D3—61no—
194C22×C3×D3—61no—
195C22×C3×D3—122no—
196C22×C3×D3—122no—
197C22×C3×D3—124no—
198C22×C3×D3—124no—
199C22×C3×D3—122no—
200C22×C3×D3—122no—
201C32×D4—21no—
202C32×D4—22no—
203C32×D4—21no—
204C32×D4—21no—
205C32×D4—22no—
206C32×D4—22no—
207C32×D4—22no—
208C32×D4—42no—
209C32×D4—41no—
210C32×D4—41no—
211C32×D4—42no—
212C32×D4D1212yes—
213C32×D4#6712yes—
214C32×D4#6712yes—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—41no—
219C2×C32×C4C22×D311yescharacteristic
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222#638—24no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3#6711yescharacteristic
226C4⋊(C3⋊D3)—21no—
227C4⋊(C3⋊D3)#6712yes—
228C4×C3⋊D3—21no—
229C4×C3⋊D3—21no—
230#634—21no—
231#634—21no—
232C3×#67—68no—
233C3×#67—64no—
234C3×#67—64no—
235C2×C3×Dic3—31no—
236C2×C3×Dic3—31no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—121no—
243C2×C3×Dic3—121no—
244C3×D12—32no—
245C3×D12—32no—
246C3×D12—62no—
247C3×D12—62no—
248C3×D12—61no—
249C3×D12—61no—
250C3×C4×D3—62no—
251C3×C4×D3—62no—
252C3×C4×D3—61no—
253C3×C4×D3—61no—
254C3×C4×D3—61no—
255C3×C4×D3—61no—
256C3×Dic6—62no—
257C3×Dic6—61no—
258C3×Dic6—61no—
259C3×Dic6—61no—
260C3×Dic6—61no—
261C3×Dic6—121no—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—62no—
265C3×C3⋊C8—61no—
266C3×C3⋊C8—61no—
267C3×C3⋊C8—61no—
268C3×C3⋊C8—61no—
269C3×C3⋊C8—121no—
270#450—271noSylow
271C2×C33—42no—
272C2×C33#12011yescharacteristic
273C2×C33C2×SD1611yescharacteristic
274C2×C33AGL(1,ℤ/8)11yescharacteristic
275C3×C3⋊D3—22no—
276C3×C3⋊D3—42no—
277C24×C3—181no—
278C23×D3—61no—
279C23×D3—61no—
280C23×D3—62no—
281C2×C3×Q8—91no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—41no—
286C2×C3×D4—91no—
287C2×C3×D4—181no—
288C2×C3×D4—182no—
289C2×C3×D4—182no—
290C2×C3×D4D3211yescharacteristic
291C2×C3×D4D3211yescharacteristic
292C2×C3×D4D3211yescharacteristic
293C22×C3×C4—91no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—62no—
297D3×D4—62no—
298D3×D4—62no—
299D3×D4—64no—
300D3×D4—64no—
301D3×D4—62no—
302D3×D4—62no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—61no—
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—61no—
312C3×SD16—182no—
313C2×C3×C8—91no—
314C2×C3×C8—91no—
315C3×C4⋊C4—91no—
316#217—181no—
317#215—182no—
318#214—64no—
319#214—62no—
320#214—62no—
321#214—182no—
322(C2×D3)⋊C4—181no—
323(C2×D3)⋊C4—181no—
324C4⋊Dic3—31no—
325C4⋊Dic3—31no—
326C4⋊Dic3—61no—
327C4⋊Dic3—181no—
328Dic3⋊C4—181no—
329Dic3⋊C4—181no—
330C2×C3⋊C8—31no—
331C2×C3⋊C8—31no—
332C2×C3⋊C8—31no—
333C2×C3⋊C8—31no—
334C2×C3⋊C8—61no—
335C2×C3⋊C8—61no—
336#204—182no—
337C22×C32—22no—
338C22×C32—24no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—41no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—44no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—81no—
357C22×C32—81no—
358C22×C32—81no—
359C22×C32—81no—
360C22×C32—82no—
361C22×C32—82no—
362C22×C32D3×D411yescharacteristic
363C22×C32D3×D411yescharacteristic
364C22×C32C2×#6711yescharacteristic
365C2×C3⋊D3—21no—
366C2×C3⋊D3—21no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—48no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3#21412yescomplemented
372C2×C3×D3—32no—
373C2×C3×D3—32no—
374C2×C3×D3—62no—
375C2×C3×D3—62no—
376C2×C3×D3—62no—
377C2×C3×D3—61no—
378C2×C3×D3—61no—
379C2×C3×D3—61no—
380C2×C3×D3—61no—
381C2×C3×D3—64no—
382C2×C3×D3—62no—
383C2×C3×D3—62no—
384C2×C3×D3—1216no—
385C2×C3×D3—128no—
386C2×C3×D3—128no—
387C2×C3×D3—122no—
388C2×C3×D3—122no—
389C2×C3×D3—121no—
390C2×C3×D3—121no—
391C2×C3×D3—121no—
392C2×C3×D3—121no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×D1211yescharacteristic
402C32×C4D3×D411yescharacteristic
403C32×C4D3×D411yescharacteristic
404C32×C4C2×#6711yescharacteristic
405C32×C4C2×#6711yescharacteristic
406C32×C4C2×#6711yescharacteristic
407C3⋊Dic3—21no—
408C3⋊Dic3—41no—
409C3⋊Dic3—41no—
410C3×Dic3—62no—
411C3×Dic3—61no—
412C3×Dic3—61no—
413C3×Dic3—122no—
414C3×Dic3—121no—
415C3×Dic3—121no—
416C3×Dic3—121no—
417C3×Dic3—121no—
418C3×Dic3—241no—
419C22×D4—91no—
420C2×SD16—91no—
421C2×SD16—271no—
422C22⋊Q8—271no—
423#102—91no—
424#102—271no—
425C22⋊C8—271no—
426C33#45011yescharacteristic, complemented, Sylow
427C23×C3—22no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—42no—
434C23×C3—91no—
435C23×C3—184no—
436C23×C3—181no—
437C23×C3—362no—
438C23×C3—362no—
439C22×D3—31no—
440C22×D3—31no—
441C22×D3—61no—
442C22×D3—62no—
443C22×D3—68no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—122no—
449C22×D3—122no—
450C22×D3—124no—
451C22×D3—124no—
452C22×D3—122no—
453C22×D3—122no—
454C3×Q8—181no—
455C3×Q8—181no—
456C3×D4—22no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—22no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—42no—
466C3×D4—42no—
467C3×D4—92no—
468C3×D4—184no—
469C3×D4—181no—
470C3×D4#62512yes—
471C3×D4#62612yes—
472C3×D4#62612yes—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—41no—
477C2×C3×C4—91no—
478C2×C3×C4—181no—
479C2×C3×C4—181no—
480C2×C3×C4—181no—
481C2×C3×C4—181no—
482C2×C3×C4C2×D3211yescharacteristic
483C2×C3×C4C2×D3211yescharacteristic
484C2×C3×C4C2×D3211yescharacteristic
485#67—68no—
486#67—64no—
487#67—64no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497D12—32no—
498D12—32no—
499D12—62no—
500D12—62no—
501D12—61no—
502D12—61no—
503C4×D3—62no—
504C4×D3—62no—
505C4×D3—61no—
506C4×D3—61no—
507C4×D3—61no—
508C4×D3—61no—
509Dic6—62no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—121no—
515C3×C8—181no—
516C3×C8—181no—
517C3⋊C8—62no—
518C3⋊C8—61no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—121no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32—42no—
536C2×C32—44no—
537C2×C32—42no—
538C2×C32—42no—
539C2×C32—82no—
540C2×C32—82no—
541C2×C32—84no—
542C2×C32#88211yescharacteristic
543C2×C32#91111yescharacteristic
544C2×C32D3×SD1611yescharacteristic
545C2×C32D3×SD1611yescharacteristic
546C2×C32#91411yescharacteristic
547C2×C32#93211yescharacteristic
548C2×C32C2×#21411yescharacteristic
549C2×C32#93711yescharacteristic
550C2×C32#95311yescharacteristic
551C3⋊D3—22no—
552C3⋊D3—42no—
553C3×D3—64no—
554C3×D3—62no—
555C3×D3—62no—
556C3×D3—124no—
557C3×D3—122no—
558C3×D3—122no—
559C24—181no—
560C2×Q8—91no—
561C2×D4—91no—
562C2×D4—181no—
563C2×D4—182no—
564C2×D4—182no—
565C2×D4#111311yescharacteristic
566C22×C4—91no—
567SD16—182no—
568SD16—542no—
569C2×C8—91no—
570C2×C8—91no—
571C4⋊C4—91no—
572C4⋊C4—541no—
573C22⋊C4—541no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—44no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—92no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3—182no—
603C22×C3—368no—
604C22×C3—361no—
605C22×C3—361no—
606C22×C3D3×#6711yescharacteristic
607C22×C3D3×#6711yescharacteristic
608C22×C3#381111yescharacteristic
609C2×D3—32no—
610C2×D3—32no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—64no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—1216no—
622C2×D3—128no—
623C2×D3—128no—
624C2×D3—122no—
625C2×D3—122no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—181no—
639C3×C4—361no—
640C3×C4—361no—
641C3×C4C2×#62511yescharacteristic
642C3×C4C2×#62611yescharacteristic
643C3×C4C2×#62611yescharacteristic
644C3×C4D3×#6711yescharacteristic
645C3×C4D3×#6711yescharacteristic
646C3×C4#381111yescharacteristic
647Dic3—62no—
648Dic3—61no—
649Dic3—61no—
650Dic3—122no—
651Dic3—121no—
652Dic3—121no—
653Dic3—121no—
654Dic3—121no—
655Dic3—241no—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32#477611yescharacteristic, complemented
661C32#516911yescharacteristic, complemented
662C32#521811yescharacteristic, complemented
663C23—21no—
664C23—91no—
665C23—184no—
666C23—181no—
667C23—362no—
668C23—362no—
669Q8—181no—
670Q8—181no—
671D4—21no—
672D4—92no—
673D4—184no—
674D4—181no—
675D4#629512yes—
676C2×C4—91no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4C2×#111311yescharacteristic
682C8—181no—
683C8—181no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—44no—
694C2×C3—42no—
695C2×C3—42no—
696C2×C3—42no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3—82no—
701C2×C3—82no—
702C2×C3—84no—
703C2×C3—182no—
704C2×C3—362no—
705C2×C3D3×#21411yescharacteristic
706C2×C3D3×#21411yescharacteristic
707C2×C3#6393011yescharacteristic
708C2×C3#6393211yescharacteristic
709C2×C3#6393411yescharacteristic
710C2×C3#6393711yescharacteristic
711C2×C3#6397611yescharacteristic
712C2×C3#6397711yescharacteristic
713C2×C3#6398111yescharacteristic
714D3—64no—
715D3—62no—
716D3—62no—
717D3—124no—
718D3—122no—
719D3—122no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—92no—
724C22—181no—
725C22—181no—
726C22—182no—
727C22—368no—
728C22—361no—
729C22—361no—
730C22#8904911yescharacteristic
731C4—181no—
732C4—361no—
733C4—361no—
734C4C2×#629511yescharacteristic
735C4#8904911yescharacteristic
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059145811yescharacteristic, complemented
741C3#1059145911yescharacteristic, complemented
742C3#1059146711yescharacteristic, complemented
743C2—42no—
744C2—182no—
745C2—362no—
746C2#1172370411yescharacteristic
747C2#1172370611yescharacteristic
748C2#1172372711yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC2×C33×C4C23
FrattiniC2×C4C2×#1113
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC2×C3×D4×C3⋊D3C2
hypercenterC2×D4#1113
hypocenterC33#450
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3754C2semidirect
3. #11723674C2semidirect
4. C2×#88811C2semidirect
5. C3×#63659C2semidirect
6. #11722075C2semidirect
7. #11722072C2semidirect
18. C2×C3×#634C22semidirect
20. C3×C4⋊(C3⋊Dic3)C22semidirect
21. C2×C3×C3⋊(C3⋊C8)C22semidirect
22. C2×C3×C3⋊(C3⋊C8)C22semidirect
30. C2×#3754D3semidirect
40. #63659D3semidirect
90. C2×#634C2×D3semidirect
110. C4⋊(C3⋊Dic3)C2×D3semidirect
111. C2×C3⋊(C3⋊C8)C2×D3semidirect
112. C2×C3⋊(C3⋊C8)C2×D3semidirect
144. C2×C3×C3⋊D3SD16semidirect
371. C2×C3⋊D3#214semidirect
426. C33#450semidirect
660. C32#4776semidirect
661. C32#5169semidirect
662. C32#5218semidirect
740. C3#10591458semidirect
741. C3#10591459semidirect
742. C3#10591467semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C3×#37542
#117236742
C2×#888112
C3×#636592
#117220752
#117220722
#105914673
#105914593
#105914583