Finite Group Databasebeta

← #10718913

Subgroups — #10718913

Order 768.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C4⋊C4C211yesmaximal, characteristic
2C2×#4928C211yesmaximal, characteristic
3C2×#4928C211yesmaximal, characteristic
4C2×#4928C211yesmaximal, characteristic
5C2×C4×C4⋊Dic3C211yesmaximal, characteristic
6#71568C212yesmaximal
7#71564C212yesmaximal
8#71535C211yesmaximal, characteristic
9#71535C211yesmaximal, characteristic
10#69409C212yesmaximal
11Dic3⋊#95C212yesmaximal
12#14045—31nomaximal, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×C4⋊Dic3C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×Dic3⋊C4C2212yes—
23C22×Dic3⋊C4C2212yes—
24C22×Dic3⋊C4C2212yes—
25C22×C4×Dic3C2212yes—
26C3×C4×C4⋊C4—24no—
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C4×C4⋊Dic3—24no—
38#4928—24no—
39#4928—24no—
40#4928C418yescomplemented
41C2×#389—31no—
42C2×#389—31no—
43C2×#389—31no—
44C2×C4×C4⋊C4—31no—
45C2×C4×C4⋊C4D311yescharacteristic
46#1444—32no—
47#1441—32no—
48#1436—32no—
49C4⋊#95—31no—
50C4⋊#95—31no—
51C4⋊#95—32no—
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2311yescharacteristic
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3C2312yes—
60C23×Dic3C2312yes—
61C23×Dic3C2312yes—
62C23×Dic3C2312yes—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—22no—
68C2×C3×C4⋊C4Q814yes—
69C2×C3×C42—22no—
70C2×C3×C42—22no—
71C2×C3×C42—22no—
72C2×C3×C42—22no—
73C2×C3×C42—22no—
74C2×C3×C42—22no—
75C2×C3×C42—22no—
76C2×C3×C42C2×C414yes—
77C2×C3×C42D414yes—
78C2×C4⋊Dic3—22no—
79C2×C4⋊Dic3—22no—
80C2×C4⋊Dic3—22no—
81C2×C4⋊Dic3—22no—
82C2×C4⋊Dic3—22no—
83C2×C4⋊Dic3—22no—
84C2×C4⋊Dic3—22no—
85C2×C4⋊Dic3C2×C414yes—
86C2×C4⋊Dic3C2×C414yes—
87C2×C4⋊Dic3D414yes—
88C2×C4⋊Dic3Q814yes—
89C2×C4⋊Dic3Q814yes—
90C2×Dic3⋊C4—24no—
91C2×Dic3⋊C4—24no—
92C2×Dic3⋊C4—24no—
93C2×Dic3⋊C4—42no—
94C2×Dic3⋊C4—42no—
95C2×Dic3⋊C4—42no—
96C2×Dic3⋊C4—42no—
97C2×Dic3⋊C4—42no—
98C2×Dic3⋊C4C2×C418yes—
99C2×C4×Dic3—24no—
100C2×C4×Dic3—24no—
101C2×C4×Dic3—42no—
102C3×#95—22no—
103C3×#95—22no—
104C3⋊#95—24no—
105C3⋊#95—24no—
106C3⋊#95—24no—
107C3⋊#95—24no—
108C3⋊#95—42no—
109C3⋊#95—42no—
110C3⋊#95—42no—
111C3⋊#95C2×C418yes—
112C22×C4⋊C4—31no—
113C22×C4⋊C4—31no—
114C22×C4⋊C4—31no—
115C22×C4⋊C4—32no—
116C22×C4⋊C4—31no—
117C22×C4⋊C4—32no—
118C22×C4⋊C4—32no—
119C22×C4⋊C4C2×D311yescharacteristic
120C22×C4⋊C4C2×D311yescharacteristic
121C22×C42—32no—
122C22×C42C2×D311yescharacteristic
123C22×C42C2×D311yescharacteristic
124C22×C42C2×D311yescharacteristic
125#389—38no—
126#389—64no—
127#389—64no—
128C4×C4⋊C4—24no—
129C4×C4⋊C4—64no—
130C2×#95—32no—
131C2×#95—32no—
132C2×#95—32no—
133C2×#95—32no—
134C2×#95—32no—
135C2×#95—32no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95C2×D311yescharacteristic
139C2×#95C2×D311yescharacteristic
140C24×C3C2411yescharacteristic
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4C22×C412yes—
174C22×C3×C4C22×C412yes—
175C22×C3×C4C22×C412yes—
176C22×C3×C4C2×D412yes—
177C22×C3×C4C2×D412yes—
178C22×C3×C4C2×D412yes—
179C22×C3×C4C2×D412yes—
180C22×C3×C4C2×Q812yes—
181C22×C3×C4C2×Q812yes—
182C22×C3×C4C2×Q812yes—
183C22×C3×C4C2×Q812yes—
184C22×C3×C4C2×Q812yes—
185C22×C3×C4#4112yes—
186C22×C3×C4#4112yes—
187C22×C3×C4#4112yes—
188C22×C3×C4#4112yes—
189C22×C3×C4#4112yes—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—22no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3C22×C414yes—
214C22×Dic3C22×C414yes—
215C22×Dic3C2×D414yes—
216C22×Dic3C2×Q814yes—
217C22×Dic3C2×Q814yes—
218C3×C4⋊C4—28no—
219C3×C4⋊C4—28no—
220C3×C42—28no—
221C3×C42—28no—
222C3×C42—44no—
223C4⋊Dic3—28no—
224C4⋊Dic3—28no—
225C4⋊Dic3—44no—
226C4⋊Dic3C4⋊C4116yescomplemented
227Dic3⋊C4—48no—
228Dic3⋊C4—48no—
229Dic3⋊C4—48no—
230C4×Dic3—48no—
231C23×C4—32no—
232C23×C4—32no—
233C23×C4—32no—
234C23×C4—32no—
235C23×C4C22×D311yescharacteristic
236C23×C4C22×D311yescharacteristic
237C23×C4C22×D311yescharacteristic
238C23×C4C22×D311yescharacteristic
239C23×C4C22×D311yescharacteristic
240C23×C4C22×D311yescharacteristic
241C23×C4C22×D311yescharacteristic
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—34no—
248C2×C4⋊C4—34no—
249C2×C4⋊C4—34no—
250C2×C4⋊C4—34no—
251C2×C4⋊C4—34no—
252C2×C4⋊C4—38no—
253C2×C4⋊C4—62no—
254C2×C4⋊C4—62no—
255C2×C4⋊C4—62no—
256C2×C4⋊C4—62no—
257C2×C4⋊C4—64no—
258C2×C4⋊C4—64no—
259C2×C4⋊C4—62no—
260C2×C4⋊C4—62no—
261C2×C4⋊C4—64no—
262C2×C4⋊C4—62no—
263C2×C4⋊C4—122no—
264C2×C4⋊C4—122no—
265C2×C4⋊C4—122no—
266C2×C4⋊C4—122no—
267C2×C4⋊C4—122no—
268C2×C4⋊C4Dic614yes—
269C2×C42—22no—
270C2×C42—22no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—64no—
277C2×C42—64no—
278C2×C42—122no—
279C2×C42C4×D314yes—
280C2×C42#6714yes—
281#95—22no—
282#95—22no—
283#95—38no—
284#95—64no—
285#95—64no—
286#95—64no—
287#95—64no—
288#95—122no—
289#95—122no—
290#95—122no—
291C23×C3C23×C411yescharacteristic
292C23×C3C22×D411yescharacteristic
293C23×C3C22×D411yescharacteristic
294C23×C3C22×Q811yescharacteristic
295C23×C3C22×Q811yescharacteristic
296C23×C3C22×Q811yescharacteristic
297C23×C3C2×#4111yescharacteristic
298C23×C3C2×#4111yescharacteristic
299C23×C3C2×#4111yescharacteristic
300C23×C3C2×#4111yescharacteristic
301C23×C3C2×#4111yescharacteristic
302C23×C3H(5,𝔽2)11yescharacteristic
303C23×C3H(5,𝔽2)11yescharacteristic
304C23×C3H(5,𝔽2)11yescharacteristic
305C23×C32−1+411yescharacteristic
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4C2×C4⋊C414yes—
347C2×C3×C4C4×D414yes—
348C2×C3×C4C4×Q814yes—
349C2×C3×C4C4×Q814yes—
350C2×C3×C4#12114yes—
351C2×C3×C4C22⋊Q814yes—
352C2×C3×C4C22⋊Q814yes—
353C2×C3×C4#12514yes—
354C2×C3×C4C4⋊Q814yes—
355C2×Dic3—24no—
356C2×Dic3—24no—
357C2×Dic3—24no—
358C2×Dic3—24no—
359C2×Dic3—24no—
360C2×Dic3—24no—
361C2×Dic3—24no—
362C2×Dic3—24no—
363C2×Dic3—24no—
364C2×Dic3—24no—
365C2×Dic3—24no—
366C2×Dic3—24no—
367C2×Dic3—42no—
368C2×Dic3—42no—
369C2×Dic3—42no—
370C2×Dic3—42no—
371C2×Dic3—42no—
372C2×Dic3—42no—
373C2×Dic3—42no—
374C2×Dic3—42no—
375C2×Dic3—42no—
376C2×Dic3—42no—
377C2×Dic3—42no—
378C2×Dic3—42no—
379C2×Dic3—42no—
380C2×Dic3—42no—
381C2×Dic3—42no—
382C2×Dic3C2×C4⋊C418yes—
383C24C23×D311yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—34no—
417C22×C4—34no—
418C22×C4—34no—
419C22×C4—34no—
420C22×C4—34no—
421C22×C4—62no—
422C22×C4—62no—
423C22×C4—62no—
424C22×C4—62no—
425C22×C4—62no—
426C22×C4—62no—
427C22×C4—62no—
428C22×C4—62no—
429C22×C4—62no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—62no—
437C22×C4—62no—
438C22×C4—62no—
439C22×C4—62no—
440C22×C4—62no—
441C22×C4—62no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4C2×Dic612yes—
445C22×C4C2×Dic612yes—
446C22×C4C2×Dic612yes—
447C22×C4C2×C4×D312yes—
448C22×C4C2×C4×D312yes—
449C22×C4C2×C4×D312yes—
450C22×C4#23512yes—
451C22×C4#23512yes—
452C22×C4#23512yes—
453C22×C4#23512yes—
454C22×C4D3×D412yes—
455C22×C4#23712yes—
456C22×C4D3×Q812yes—
457C22×C4D3×Q812yes—
458C22×C4C2×#6712yes—
459C22×C4C2×#6712yes—
460C22×C4C2×#6712yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—316no—
464C4⋊C4—68no—
465C4⋊C4—68no—
466C4⋊C4—128no—
467C4⋊C4—128no—
468C4⋊C4—128no—
469C4⋊C4—124no—
470C42—28no—
471C42—28no—
472C42—44no—
473C42—128no—
474C22×C3C22×C4⋊C411yescharacteristic
475C22×C3C2×C4×D411yescharacteristic
476C22×C3C2×C4×Q811yescharacteristic
477C22×C3C2×C4×Q811yescharacteristic
478C22×C3C4×#4111yescharacteristic
479C22×C3#51811yescharacteristic
480C22×C3#52011yescharacteristic
481C22×C3C2×#12111yescharacteristic
482C22×C3C2×C22⋊Q811yescharacteristic
483C22×C3C2×C22⋊Q811yescharacteristic
484C22×C3#52511yescharacteristic
485C22×C3C2×#12511yescharacteristic
486C22×C3#52911yescharacteristic
487C22×C3C2×C4⋊Q811yescharacteristic
488C22×C3#53311yescharacteristic
489C22×C3#53511yescharacteristic
490C22×C3#53711yescharacteristic
491C22×C3#54011yescharacteristic
492C22×C3#54211yescharacteristic
493C22×C3#54611yescharacteristic
494C22×C3#54611yescharacteristic
495C22×C3D4×Q811yescharacteristic
496C22×C3#55011yescharacteristic
497C22×C3#55211yescharacteristic
498C22×C3#55311yescharacteristic
499C22×C3#55411yescharacteristic
500C22×C3#55411yescharacteristic
501C22×C3#55411yescharacteristic
502C22×C3#55411yescharacteristic
503C22×C3#55411yescharacteristic
504C22×C3#55511yescharacteristic
505C22×C3#55711yescharacteristic
506C22×C3#55711yescharacteristic
507C22×C3Q8211yescharacteristic
508C22×C3Q8211yescharacteristic
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4#38918yes—
516Dic3—28no—
517Dic3—44no—
518Dic3—44no—
519Dic3—82no—
520C23C22×Dic611yescharacteristic
521C23C22×C4×D311yescharacteristic
522C23C2×#23511yescharacteristic
523C23C2×#23511yescharacteristic
524C23C2×#23511yescharacteristic
525C23C2×#23511yescharacteristic
526C23C2×D3×D411yescharacteristic
527C23C2×#23711yescharacteristic
528C23C2×D3×Q811yescharacteristic
529C23C2×D3×Q811yescharacteristic
530C23#100911yescharacteristic
531C23#100911yescharacteristic
532C23#100911yescharacteristic
533C23#101011yescharacteristic
534C23C22×#6711yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—38no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—64no—
577C2×C4—64no—
578C2×C4—64no—
579C2×C4—64no—
580C2×C4—64no—
581C2×C4—64no—
582C2×C4—64no—
583C2×C4—64no—
584C2×C4—64no—
585C2×C4—64no—
586C2×C4—64no—
587C2×C4—64no—
588C2×C4—122no—
589C2×C4—122no—
590C2×C4—122no—
591C2×C4—122no—
592C2×C4—122no—
593C2×C4—122no—
594C2×C4—122no—
595C2×C4—122no—
596C2×C4—122no—
597C2×C4—122no—
598C2×C4—122no—
599C2×C4—122no—
600C2×C4—122no—
601C2×C4—122no—
602C2×C4—122no—
603C2×C4C4×Dic614yes—
604C2×C4#88714yes—
605C2×C4#88914yes—
606C2×C4D3×C4⋊C414yes—
607C2×C4#89614yes—
608C2×C4#92414yes—
609C2×C4C4×#6714yes—
610C2×C4#93914yes—
611C2×C4#94414yes—
612C2×C3C2×#38911yescharacteristic
613C2×C3C4×C22⋊Q811yescharacteristic
614C2×C3#232411yescharacteristic
615C2×C3#234911yescharacteristic
616C2×C3Q8×C4⋊C411yescharacteristic
617C2×C3#236911yescharacteristic
618C2×C3#237011yescharacteristic
619C2×C3#241411yescharacteristic
620C2×C3#241711yescharacteristic
621C2×C3#245111yescharacteristic
622C2×C3#245411yescharacteristic
623C2×C3#250711yescharacteristic
624C2×C3#250811yescharacteristic
625C2×C3#256711yescharacteristic
626C2×C3#258411yescharacteristic
627C22C2×C4×Dic611yescharacteristic
628C22#547011yescharacteristic
629C22C4×#23511yescharacteristic
630C22#547911yescharacteristic
631C22C2×#88711yescharacteristic
632C22C2×#88911yescharacteristic
633C22C2×D3×C4⋊C411yescharacteristic
634C22C2×#89611yescharacteristic
635C22#552111yescharacteristic
636C22#552311yescharacteristic
637C22#553411yescharacteristic
638C22#553511yescharacteristic
639C22D4×Dic611yescharacteristic
640C22#554111yescharacteristic
641C22#554311yescharacteristic
642C22#555011yescharacteristic
643C22#555011yescharacteristic
644C22#555311yescharacteristic
645C22#556311yescharacteristic
646C22#556511yescharacteristic
647C22Q8×Dic611yescharacteristic
648C22Q8×Dic611yescharacteristic
649C22#556711yescharacteristic
650C22#556711yescharacteristic
651C22#557911yescharacteristic
652C22#557911yescharacteristic
653C22#557911yescharacteristic
654C22#557911yescharacteristic
655C22C2×#92411yescharacteristic
656C22C2×C4×#6711yescharacteristic
657C22#579111yescharacteristic
658C22C2×#93911yescharacteristic
659C22C2×#94411yescharacteristic
660C22#583011yescharacteristic
661C22#583311yescharacteristic
662C4—24no—
663C4—24no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—68no—
669C4—124no—
670C4—124no—
671C4—242no—
672C4#497618yes—
673C3#1404511yescharacteristic, complemented, Sylow
674C2C4⋊C4×Dic611yescharacteristic
675C2#7365611yescharacteristic
676C2#7365911yescharacteristic
677C2#7367411yescharacteristic
678C2#7367711yescharacteristic
679C2#7368411yescharacteristic
680C2#7368611yescharacteristic
681C2#7377011yescharacteristic
682C2C4×#92411yescharacteristic
683C2C2×#497611yescharacteristic
684C2#8223611yescharacteristic
685C2#8235011yescharacteristic
686C2#8235311yescharacteristic
687C2#8247811yescharacteristic
688C2#8248311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×C4×C4⋊C4C2
socle, prime radical, cosocleC24×C3C24
hypercenterC2×C4×C4⋊C4D3
hypocenterC3#14045
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
40. #4928C4semidirect
226. C4⋊Dic3C4⋊C4semidirect
673. C3#14045semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C4⋊C42
C2×#49282
C2×C4×C4⋊Dic32
#715682
#715642
#715352
#694092
Dic3⋊#952
#140453