Finite Group Databasebeta

← C3×#14025 #10632632

Subgroups — C3×#14025 #10632632

Order 768.

3422 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#127C211yesmaximal, characteristic
2C22×C3×C4×D4C211yesmaximal, characteristic, complemented
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×C3×#390C211yesmaximal, characteristic, complemented
5C2×C3×#390C211yesmaximal, characteristic, complemented
6C2×C3×#386C214yesmaximal, complemented
7C3×#1438C214yesmaximal, complemented
8C3×C4⋊#95C211yesmaximal, characteristic, complemented
9C3×C4×#95C211yesmaximal, characteristic, complemented
10#14025C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×D4C2211yescharacteristic
12C23×C3×D4C2214yes—
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2212yes—
15C2×C3×#127—24no—
16C2×C3×#127—24no—
17C2×C3×#127C418yescomplemented
18C2×C3×C4×D4—24no—
19C2×C3×C4×D4—24no—
20C2×C3×C4×D4—24no—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2214yes—
26C22×C3×C22⋊C4C2214yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C42C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C22×C3×C42C2211yescharacteristic
31C3×#390—24no—
32C3×#390—24no—
33C3×#390—24no—
34C3×#386—216no—
35C2×C3×#95C2214yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C22×#127C2×C311yescharacteristic
39C22×C4×D4C2×C311yescharacteristic, complemented
40C2×#390C2×C311yescharacteristic, complemented
41C2×#390C2×C311yescharacteristic, complemented
42C2×#390C2×C311yescharacteristic, complemented
43C2×#386C2×C314yescomplemented
44#1438C2×C314yescomplemented
45C4⋊#95C2×C311yescharacteristic, complemented
46C4×#95C2×C311yescharacteristic, complemented
47C25×C3C2312yes—
48C25×C3C2312yes—
49C22×C3×D4—28no—
50C22×C3×D4—28no—
51C22×C3×D4—22no—
52C22×C3×D4—22no—
53C22×C3×D4—28no—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—28no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—44no—
64C22×C3×D4—44no—
65C22×C3×D4C2×C414yes—
66C22×C3×D4C2×C414yescomplemented
67C22×C3×D4C2×C4116yescomplemented
68C22×C3×D4D414yes—
69C22×C3×D4D414yes—
70C23×C3×C4—24no—
71C23×C3×C4—24no—
72C23×C3×C4—24no—
73C23×C3×C4—28no—
74C23×C3×C4—44no—
75C23×C3×C4C2312yes—
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2312yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C3×#127—232no—
83C3×C4×D4—232no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4D414yescomplemented
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—28no—
94C2×C3×C22⋊C4—28no—
95C2×C3×C22⋊C4—28no—
96C2×C3×C22⋊C4—28no—
97C2×C3×C22⋊C4—28no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—44no—
101C2×C3×C22⋊C4—44no—
102C2×C3×C22⋊C4—44no—
103C2×C3×C42—22no—
104C2×C3×C42—22no—
105C2×C3×C42—22no—
106C2×C3×C42—22no—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C2×C3×C42—22no—
110C2×C3×C42C2×C414yescomplemented
111C2×C3×C42D414yescomplemented
112C3×#95—28no—
113C3×#95—24no—
114C3×#95D418yescomplemented
115C23×D4C22×C311yescharacteristic
116C23×D4C22×C314yes—
117C23×D4C22×C311yescharacteristic
118C24×C4C22×C312yes—
119C2×#127—24no—
120C2×#127—24no—
121C2×#127C3×C418yescomplemented
122C2×C4×D4—24no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C22×C4⋊C4C22×C311yescharacteristic
126C22×C4⋊C4C22×C311yescharacteristic
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C314yes—
130C22×C22⋊C4C22×C314yes—
131C22×C22⋊C4C22×C312yes—
132C22×C42C22×C311yescharacteristic
133C22×C42C22×C311yescharacteristic
134C22×C42C22×C311yescharacteristic
135#390—24no—
136#390—24no—
137#390—24no—
138#386—216no—
139C2×#95C22×C312yes—
140C2×#95C22×C314yes—
141C2×#95C22×C312yes—
142C24×C3—22no—
143C24×C3—22no—
144C24×C3—24no—
145C24×C3—22no—
146C24×C3—22no—
147C24×C3—24no—
148C24×C3—24no—
149C24×C3—24no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—24no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—24no—
158C24×C3—24no—
159C24×C3—24no—
160C24×C3C22×C414yes—
161C24×C3C22×C414yes—
162C24×C3C2×D414yes—
163C24×C3C2×D414yes—
164C24×C3C2411yescharacteristic
165C2×C3×D4—232no—
166C2×C3×D4—28no—
167C2×C3×D4—28no—
168C2×C3×D4—28no—
169C2×C3×D4—28no—
170C2×C3×D4—28no—
171C2×C3×D4—232no—
172C2×C3×D4—28no—
173C2×C3×D4—28no—
174C2×C3×D4—28no—
175C2×C3×D4—28no—
176C2×C3×D4—416no—
177C2×C3×D4—416no—
178C2×C3×D4—416no—
179C2×C3×D4—416no—
180C2×C3×D4—416no—
181C2×C3×D4—44no—
182C2×C3×D4—44no—
183C2×C3×D4—44no—
184C2×C3×D4—44no—
185C2×C3×D4C22⋊C4116yescomplemented
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—216no—
194C22×C3×C4—24no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—24no—
208C22×C3×C4—24no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—24no—
213C22×C3×C4—416no—
214C22×C3×C4—416no—
215C22×C3×C4—48no—
216C22×C3×C4—48no—
217C22×C3×C4C22×C414yes—
218C22×C3×C4C22×C412yes—
219C22×C3×C4C2×D414yes—
220C22×C3×C4C2×D412yes—
221C22×C3×C4C2×D414yes—
222C22×C3×C4C2×D414yes—
223C22×C3×C4C2×D414yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D412yes—
229C22×C3×C4#4114yes—
230C22×C3×C4#4112yes—
231C22×C3×C4#4112yes—
232C3×C4⋊C4—28no—
233C3×C4⋊C4—44no—
234C3×C22⋊C4—216no—
235C3×C22⋊C4—416no—
236C3×C22⋊C4—416no—
237C3×C22⋊C4—48no—
238C3×C22⋊C4—48no—
239C3×C42—28no—
240C3×C42—28no—
241C3×C42—44no—
242C25C23×C312yes—
243C25C23×C312yes—
244C22×D4—28no—
245C22×D4—28no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—28no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—28no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4C2×C3×C414yes—
261C22×D4C2×C3×C414yescomplemented
262C22×D4C2×C3×C4116yescomplemented
263C22×D4C3×D414yes—
264C22×D4C3×D414yes—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—28no—
269C23×C4—44no—
270C23×C4C23×C312yes—
271C23×C4C23×C311yescharacteristic
272C23×C4C23×C312yes—
273C23×C4C23×C312yes—
274C23×C4C23×C312yes—
275C23×C4C23×C311yescharacteristic
276C23×C4C23×C311yescharacteristic
277#127—232no—
278C4×D4—232no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4C3×D414yescomplemented
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—28no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—28no—
291C2×C22⋊C4—28no—
292C2×C22⋊C4—28no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—44no—
296C2×C22⋊C4—44no—
297C2×C22⋊C4—44no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42C2×C3×C414yescomplemented
306C2×C42C3×D414yescomplemented
307#95—28no—
308#95—24no—
309#95C3×D418yescomplemented
310C23×C3—28no—
311C23×C3—24no—
312C23×C3—24no—
313C23×C3—28no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—28no—
319C23×C3—28no—
320C23×C3—28no—
321C23×C3—28no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—28no—
325C23×C3—24no—
326C23×C3—28no—
327C23×C3—42no—
328C23×C3—44no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—44no—
333C23×C3—44no—
334C23×C3—44no—
335C23×C3—44no—
336C23×C3—44no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—44no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—44no—
347C23×C3—44no—
348C23×C3—44no—
349C23×C3—44no—
350C23×C3—44no—
351C23×C3—44no—
352C23×C3—44no—
353C23×C3—44no—
354C23×C3—44no—
355C23×C3C2×C22⋊C418yes—
356C23×C3C23×C411yescharacteristic
357C23×C3C22×D411yescharacteristic
358C23×C3C22×D411yescharacteristic
359C23×C3C22×D411yescharacteristic
360C23×C3C22×D411yescharacteristic
361C23×C3C22×D412yes—
362C23×C3C2×#4111yescharacteristic
363C23×C3C2×#4111yescharacteristic
364C23×C3C2×#4112yes—
365C23×C3H(5,𝔽2)12yes—
366C23×C3H(5,𝔽2)12yes—
367C3×D4—232no—
368C3×D4—464no—
369C3×D4—416no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—28no—
388C2×C3×C4—432no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—44no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—44no—
402C2×C3×C4—44no—
403C2×C3×C4C2×C22⋊C414yes—
404C2×C3×C4C4×D414yes—
405C2×C3×C4C4×D414yes—
406C2×C3×C4C4×D418yescomplemented
407C2×C3×C4#12014yes—
408C2×C3×C4#12114yes—
409C2×C3×C4#12114yes—
410C2×C3×C4#12314yes—
411C2×C3×C4#12714yescomplemented
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—22no—
421C24—22no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24C22×C3×C414yes—
431C24C22×C3×C414yes—
432C24C2×C3×D414yes—
433C24C2×C3×D414yes—
434C24C24×C311yescharacteristic
435C2×D4—232no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—232no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—416no—
447C2×D4—416no—
448C2×D4—416no—
449C2×D4—416no—
450C2×D4—416no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4C3×C22⋊C4116yescomplemented
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—216no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—416no—
484C22×C4—416no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4C22×C3×C414yes—
488C22×C4C22×C3×C412yes—
489C22×C4C2×C3×D414yes—
490C22×C4C2×C3×D412yes—
491C22×C4C2×C3×D414yes—
492C22×C4C2×C3×D414yes—
493C22×C4C2×C3×D414yes—
494C22×C4C2×C3×D412yes—
495C22×C4C2×C3×D412yes—
496C22×C4C2×C3×D412yes—
497C22×C4C2×C3×D412yes—
498C22×C4C2×C3×D412yes—
499C22×C4C3×#4114yes—
500C22×C4C3×#4112yes—
501C22×C4C3×#4112yes—
502C4⋊C4—28no—
503C4⋊C4—44no—
504C22⋊C4—216no—
505C22⋊C4—416no—
506C22⋊C4—416no—
507C22⋊C4—48no—
508C22⋊C4—48no—
509C42—28no—
510C42—28no—
511C42—44no—
512C22×C3—216no—
513C22×C3—28no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—48no—
517C22×C3—48no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—48no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—48no—
526C22×C3—48no—
527C22×C3—44no—
528C22×C3—84no—
529C22×C3—82no—
530C22×C3—82no—
531C22×C3—84no—
532C22×C3—82no—
533C22×C3—82no—
534C22×C3C22×C22⋊C411yescharacteristic
535C22×C3C2×C4×D411yescharacteristic
536C22×C3C2×C4×D412yes—
537C22×C3C2×C4×D411yescharacteristic
538C22×C3#51812yes—
539C22×C3C2×#12011yescharacteristic
540C22×C3C2×#12111yescharacteristic
541C22×C3C2×#12111yescharacteristic
542C22×C3C2×#12311yescharacteristic
543C22×C3C2×#12711yescharacteristic
544C22×C3#53212yes—
545C22×C3#53211yescharacteristic
546C22×C3#53511yescharacteristic
547C22×C3#53511yescharacteristic
548C22×C3#54012yes—
549C22×C3D4212yes—
550C22×C3D4212yes—
551C22×C3D4212yes—
552C22×C3#54612yes—
553C22×C3#54612yes—
554C22×C3#55012yes—
555C22×C3#55012yes—
556C22×C3#55912yes—
557C3×C4—28no—
558C3×C4—24no—
559C3×C4—44no—
560C3×C4—42no—
561C3×C4—44no—
562C3×C4—82no—
563C3×C4#38618yescomplemented
564C23—24no—
565C23—24no—
566C23—28no—
567C23—28no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—28no—
573C23—28no—
574C23—28no—
575C23—28no—
576C23—24no—
577C23—24no—
578C23—28no—
579C23—24no—
580C23—28no—
581C23—44no—
582C23—42no—
583C23—44no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23—44no—
591C23—44no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—44no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23C2×C3×C22⋊C418yes—
610C23C23×C3×C411yescharacteristic
611C23C22×C3×D411yescharacteristic
612C23C22×C3×D411yescharacteristic
613C23C22×C3×D411yescharacteristic
614C23C22×C3×D411yescharacteristic
615C23C22×C3×D412yes—
616C23C2×C3×#4111yescharacteristic
617C23C2×C3×#4112yes—
618C23C2×C3×#4111yescharacteristic
619C23C3×H(5,𝔽2)12yes—
620C23C3×H(5,𝔽2)12yes—
621D4—232no—
622D4—464no—
623D4—416no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—28no—
642C2×C4—432no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—44no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4C2×C3×C22⋊C414yes—
658C2×C4C3×C4×D414yes—
659C2×C4C3×C4×D414yes—
660C2×C4C3×C4×D418yescomplemented
661C2×C4C3×#12014yes—
662C2×C4C3×#12114yes—
663C2×C4C3×#12114yes—
664C2×C4C3×#12314yes—
665C2×C4C3×#12714yescomplemented
666C2×C3—48no—
667C2×C3—84no—
668C2×C3C2×#38611yescharacteristic
669C2×C3C4×#12711yescharacteristic
670C2×C3#232811yescharacteristic
671C2×C3D4×C22⋊C412yes—
672C2×C3#236612yes—
673C2×C3#242812yes—
674C2×C3#243111yescharacteristic
675C2×C3#243311yescharacteristic
676C2×C3#244512yes—
677C2×C3#254111yescharacteristic
678C2×C3#254411yescharacteristic
679C22—28no—
680C22—216no—
681C22—48no—
682C22—48no—
683C22—44no—
684C22—44no—
685C22—48no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—48no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—48no—
695C22—84no—
696C22—82no—
697C22—82no—
698C22—84no—
699C22—82no—
700C22—82no—
701C22C22×C3×C22⋊C411yescharacteristic
702C22C2×C3×C4×D411yescharacteristic
703C22C2×C3×C4×D412yes—
704C22C2×C3×C4×D411yescharacteristic
705C22C3×#51812yes—
706C22C2×C3×#12011yescharacteristic
707C22C2×C3×#12111yescharacteristic
708C22C2×C3×#12111yescharacteristic
709C22C2×C3×#12311yescharacteristic
710C22C2×C3×#12711yescharacteristic
711C22C3×#53212yes—
712C22C3×#53211yescharacteristic
713C22C3×#53511yescharacteristic
714C22C3×#53511yescharacteristic
715C22C3×#54012yes—
716C22C3×D4212yes—
717C22C3×D4212yes—
718C22C3×D4212yes—
719C22C3×#54612yes—
720C22C3×#54612yes—
721C22C3×#55012yes—
722C22C3×#55012yes—
723C22C3×#55912yes—
724C4—24no—
725C4—28no—
726C4—44no—
727C4—42no—
728C4—44no—
729C4—82no—
730C4C3×#38618yescomplemented
731C3#1402511yescharacteristic, direct product factor, Sylow
732C2—48no—
733C2—84no—
734C2C2×C3×#38611yescharacteristic
735C2C3×C4×#12711yescharacteristic
736C2C3×#232811yescharacteristic
737C2C3×D4×C22⋊C412yes—
738C2C3×#236612yes—
739C2C3×#242812yes—
740C2C3×#243111yescharacteristic
741C2C3×#243311yescharacteristic
742C2C3×#244512yes—
743C2C3×#254111yescharacteristic
744C2C3×#254411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC22×C3×#127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×D4C2semidirect
3. C2×C3×#390C2semidirect
4. C2×C3×#390C2semidirect
5. C2×C3×#390C2semidirect
6. C2×C3×#386C2semidirect
7. C3×#1438C2semidirect
8. C3×C4⋊#95C2semidirect
9. C3×C4×#95C2semidirect
10. #14025C3direct (N × H)
17. C2×C3×#127C4semidirect
39. C22×C4×D4C2×C3semidirect
40. C2×#390C2×C3semidirect
41. C2×#390C2×C3semidirect
42. C2×#390C2×C3semidirect
43. C2×#386C2×C3semidirect
44. #1438C2×C3semidirect
45. C4⋊#95C2×C3semidirect
46. C4×#95C2×C3semidirect
66. C22×C3×D4C2×C4semidirect
67. C22×C3×D4C2×C4semidirect
89. C2×C3×C4⋊C4D4semidirect
110. C2×C3×C42C2×C4semidirect
111. C2×C3×C42D4semidirect
114. C3×#95D4semidirect
121. C2×#127C3×C4semidirect
185. C2×C3×D4C22⋊C4semidirect
261. C22×D4C2×C3×C4semidirect
262. C22×D4C2×C3×C4semidirect
284. C2×C4⋊C4C3×D4semidirect
305. C2×C42C2×C3×C4semidirect
306. C2×C42C3×D4semidirect
309. #95C3×D4semidirect
406. C2×C3×C4C4×D4semidirect
411. C2×C3×C4#127semidirect
455. C2×D4C3×C22⋊C4semidirect
563. C3×C4#386semidirect
660. C2×C4C3×C4×D4semidirect
665. C2×C4C3×#127semidirect
730. C4C3×#386semidirect
731. C3#14025direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1272
C22×C3×C4×D42
C2×C3×#3902
C2×C3×#3862
C3×#14382
C3×C4⋊#952
C3×C4×#952
#140253