Finite Group Databasebeta

← C3×#14189 #10632796

Subgroups — C3×#14189 #10632796

Order 768.

2830 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#392C211yesmaximal, characteristic
3C2×C3×#390C212yesmaximal, complemented
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#386C212yesmaximal, complemented
6C2×C3×#385C212yesmaximal, complemented
7C3×#1444C211yesmaximal, characteristic, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1438C211yesmaximal, characteristic, complemented
10C3×#1437C212yesmaximal, complemented
11C3×C4×#95C211yesmaximal, characteristic, complemented
12#14189C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C24×C3×C4C2212yes—
16C2×C3×C4×D4—28no—
17C2×C3×C4×D4—24no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C42C2212yes—
30C22×C3×C42C2211yescharacteristic
31C3×#392C418yescomplemented
32C3×#390—28no—
33C3×#388—24no—
34C3×#386—28no—
35C3×#385—28no—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2212yes—
43C22×C4×D4C2×C311yescharacteristic, complemented
44C2×#392C2×C311yescharacteristic
45C2×#390C2×C312yescomplemented
46C2×#388C2×C311yescharacteristic, complemented
47C2×#386C2×C312yescomplemented
48C2×#385C2×C312yescomplemented
49#1444C2×C311yescharacteristic, complemented
50#1439C2×C311yescharacteristic, complemented
51#1438C2×C311yescharacteristic, complemented
52#1437C2×C312yescomplemented
53C4×#95C2×C311yescharacteristic, complemented
54C25×C3C2311yescharacteristic
55C25×C3C2312yes—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—22no—
61C22×C3×D4—24no—
62C22×C3×D4—22no—
63C22×C3×D4—24no—
64C22×C3×D4—42no—
65C22×C3×D4—42no—
66C22×C3×D4C2×C414yes—
67C22×C3×D4C2×C418yescomplemented
68C23×C3×C4—24no—
69C23×C3×C4—24no—
70C23×C3×C4—24no—
71C23×C3×C4—24no—
72C23×C3×C4—24no—
73C23×C3×C4—42no—
74C23×C3×C4—42no—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2312yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2312yes—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C3×C4×D4—232no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—42no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—42no—
109C2×C3×C22⋊C4—42no—
110C2×C3×C22⋊C4—42no—
111C2×C3×C22⋊C4C2×C414yescomplemented
112C2×C3×C22⋊C4C2×C418yescomplemented
113C2×C3×C22⋊C4D418yescomplemented
114C2×C3×C42—24no—
115C2×C3×C42—24no—
116C2×C3×C42—24no—
117C2×C3×C42—42no—
118C2×C3×C42D414yescomplemented
119C3×#95—24no—
120C3×#95—24no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95C2×C414yescomplemented
125C3×#95D418yescomplemented
126C23×D4C22×C311yescharacteristic
127C23×D4C22×C312yes—
128C24×C4C22×C312yes—
129C2×C4×D4—28no—
130C2×C4×D4—24no—
131C22×C4⋊C4C22×C311yescharacteristic
132C22×C4⋊C4C22×C311yescharacteristic
133C22×C4⋊C4C22×C312yes—
134C22×C22⋊C4C22×C311yescharacteristic
135C22×C22⋊C4C22×C311yescharacteristic
136C22×C22⋊C4C22×C312yes—
137C22×C22⋊C4C22×C312yes—
138C22×C22⋊C4C22×C312yes—
139C22×C22⋊C4C22×C312yes—
140C22×C22⋊C4C22×C311yescharacteristic
141C22×C22⋊C4C22×C312yes—
142C22×C42C22×C312yes—
143C22×C42C22×C311yescharacteristic
144#392C3×C418yescomplemented
145#390—28no—
146#388—24no—
147#386—28no—
148#385—28no—
149C2×#95C22×C311yescharacteristic
150C2×#95C22×C311yescharacteristic
151C2×#95C22×C312yes—
152C2×#95C22×C312yes—
153C2×#95C22×C311yescharacteristic
154C2×#95C22×C311yescharacteristic
155C2×#95C22×C312yes—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—21no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3C22×C412yes—
179C24×C3C22×C414yes—
180C24×C3C2×D414yes—
181C24×C3#4114yes—
182C24×C3C2411yescharacteristic
183C2×C3×D4—28no—
184C2×C3×D4—28no—
185C2×C3×D4—216no—
186C2×C3×D4—216no—
187C2×C3×D4—216no—
188C2×C3×D4—28no—
189C2×C3×D4—216no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C2×C3×D4—48no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—216no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—48no—
235C22×C3×C4—48no—
236C22×C3×C4—48no—
237C22×C3×C4—48no—
238C22×C3×C4—48no—
239C22×C3×C4—48no—
240C22×C3×C4C22×C412yes—
241C22×C3×C4C22×C412yes—
242C22×C3×C4C22×C414yes—
243C22×C3×C4C2×D414yes—
244C22×C3×C4C2×D414yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D414yes—
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4#4112yes—
252C22×C3×C4#4114yes—
253C3×C4⋊C4—28no—
254C3×C4⋊C4—48no—
255C3×C4⋊C4—44no—
256C3×C22⋊C4—28no—
257C3×C22⋊C4—216no—
258C3×C22⋊C4—216no—
259C3×C22⋊C4—48no—
260C3×C22⋊C4—48no—
261C3×C22⋊C4—48no—
262C3×C22⋊C4—44no—
263C3×C22⋊C4—44no—
264C3×C42—28no—
265C3×C42—48no—
266C25C23×C311yescharacteristic
267C25C23×C312yes—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—22no—
273C22×D4—24no—
274C22×D4—22no—
275C22×D4—24no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4C2×C3×C414yes—
279C22×D4C2×C3×C418yescomplemented
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4C23×C311yescharacteristic
288C23×C4C23×C311yescharacteristic
289C23×C4C23×C311yescharacteristic
290C23×C4C23×C312yes—
291C23×C4C23×C312yes—
292C23×C4C23×C311yescharacteristic
293C23×C4C23×C312yes—
294C23×C4C23×C311yescharacteristic
295C23×C4C23×C311yescharacteristic
296C4×D4—232no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—42no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4C2×C3×C414yescomplemented
324C2×C22⋊C4C2×C3×C418yescomplemented
325C2×C22⋊C4C3×D418yescomplemented
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—42no—
330C2×C42C3×D414yescomplemented
331#95—24no—
332#95—24no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95C2×C3×C414yescomplemented
337#95C3×D418yescomplemented
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—22no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—42no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—42no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3C4×D418yes—
396C23×C3C23×C411yescharacteristic
397C23×C3C22×D411yescharacteristic
398C23×C3C22×D412yes—
399C23×C3C22×D412yes—
400C23×C3C2×#4111yescharacteristic
401C23×C3C2×#4112yes—
402C23×C3C2×#4112yes—
403C23×C3H(5,𝔽2)11yescharacteristic
404C23×C3H(5,𝔽2)11yescharacteristic
405C23×C3H(5,𝔽2)11yescharacteristic
406C23×C32−1+411yescharacteristic
407C3×D4—232no—
408C3×D4—432no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—432no—
436C2×C3×C4—42no—
437C2×C3×C4—41no—
438C2×C3×C4—42no—
439C2×C3×C4—41no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4C4×D414yes—
458C2×C3×C4C4×D418yescomplemented
459C2×C3×C4#12014yes—
460C2×C3×C4#12714yes—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—22no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24C22×C3×C412yes—
484C24C22×C3×C414yes—
485C24C2×C3×D414yes—
486C24C3×#4114yes—
487C24C24×C311yescharacteristic
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4—216no—
493C2×D4—28no—
494C2×D4—216no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—216no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4C22×C3×C412yes—
546C22×C4C22×C3×C412yes—
547C22×C4C22×C3×C414yes—
548C22×C4C2×C3×D414yes—
549C22×C4C2×C3×D414yes—
550C22×C4C2×C3×D412yes—
551C22×C4C2×C3×D414yes—
552C22×C4C2×C3×D412yes—
553C22×C4C2×C3×D414yes—
554C22×C4C2×C3×D414yes—
555C22×C4C2×C3×D412yes—
556C22×C4C3×#4112yes—
557C22×C4C3×#4114yes—
558C4⋊C4—28no—
559C4⋊C4—48no—
560C4⋊C4—44no—
561C22⋊C4—28no—
562C22⋊C4—216no—
563C22⋊C4—216no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C42—28no—
570C42—48no—
571C22×C3—28no—
572C22×C3—28no—
573C22×C3—28no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—42no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—82no—
595C22×C3—82no—
596C22×C3—81no—
597C22×C3C2×C4×D411yescharacteristic
598C22×C3C2×C4×D412yes—
599C22×C3C2×C4×D412yes—
600C22×C3#51811yescharacteristic
601C22×C3#52011yescharacteristic
602C22×C3C2×#12011yescharacteristic
603C22×C3#52511yescharacteristic
604C22×C3#52512yes—
605C22×C3C2×#12711yescharacteristic
606C22×C3#53211yescharacteristic
607C22×C3#53212yes—
608C22×C3#53511yescharacteristic
609C22×C3#53711yescharacteristic
610C22×C3#54011yescharacteristic
611C22×C3#54211yescharacteristic
612C22×C3D4212yes—
613C22×C3D4212yes—
614C22×C3#54612yes—
615C22×C3#54612yes—
616C22×C3#54712yes—
617C22×C3#54812yes—
618C22×C3#55112yes—
619C22×C3#55312yes—
620C3×C4—28no—
621C3×C4—24no—
622C3×C4—24no—
623C3×C4—24no—
624C3×C4—42no—
625C3×C4—44no—
626C3×C4—44no—
627C3×C4—81no—
628C3×C4—81no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23C3×C4×D418yes—
687C23C23×C3×C411yescharacteristic
688C23C22×C3×D411yescharacteristic
689C23C22×C3×D412yes—
690C23C22×C3×D412yes—
691C23C2×C3×#4111yescharacteristic
692C23C2×C3×#4112yes—
693C23C2×C3×#4112yes—
694C23C3×H(5,𝔽2)11yescharacteristic
695C23C3×H(5,𝔽2)11yescharacteristic
696C23C3×H(5,𝔽2)11yescharacteristic
697C23C3×2−1+411yescharacteristic
698D4—232no—
699D4—432no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—432no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4C3×C4×D414yes—
749C2×C4C3×C4×D418yescomplemented
750C2×C4C3×#12014yes—
751C2×C4C3×#12714yes—
752C2×C3—48no—
753C2×C3—82no—
754C2×C3C4×#12011yescharacteristic
755C2×C3C4×#12711yescharacteristic
756C2×C3#232411yescharacteristic
757C2×C3#235812yes—
758C2×C3#236112yes—
759C2×C3#243011yescharacteristic
760C2×C3#243311yescharacteristic
761C2×C3#246112yes—
762C2×C3#246412yes—
763C2×C3#254011yescharacteristic
764C2×C3#260311yescharacteristic
765C22—28no—
766C22—28no—
767C22—28no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—81no—
786C22—81no—
787C22—82no—
788C22—82no—
789C22—81no—
790C22—81no—
791C22C2×C3×C4×D412yes—
792C22C2×C3×C4×D412yes—
793C22C2×C3×C4×D411yescharacteristic
794C22C3×#51811yescharacteristic
795C22C3×#52011yescharacteristic
796C22C2×C3×#12011yescharacteristic
797C22C3×#52512yes—
798C22C3×#52511yescharacteristic
799C22C2×C3×#12711yescharacteristic
800C22C3×#53211yescharacteristic
801C22C3×#53212yes—
802C22C3×#53511yescharacteristic
803C22C3×#53711yescharacteristic
804C22C3×#54011yescharacteristic
805C22C3×#54211yescharacteristic
806C22C3×D4212yes—
807C22C3×D4212yes—
808C22C3×#54612yes—
809C22C3×#54612yes—
810C22C3×#54712yes—
811C22C3×#54812yes—
812C22C3×#55112yes—
813C22C3×#55312yes—
814C4—24no—
815C4—24no—
816C4—24no—
817C4—28no—
818C4—44no—
819C4—44no—
820C4—42no—
821C4—81no—
822C4—81no—
823C3#1418911yescharacteristic, direct product factor, Sylow
824C2—48no—
825C2—82no—
826C2C3×C4×#12011yescharacteristic
827C2C3×C4×#12711yescharacteristic
828C2C3×#232411yescharacteristic
829C2C3×#235812yes—
830C2C3×#236112yes—
831C2C3×#243011yescharacteristic
832C2C3×#243311yescharacteristic
833C2C3×#246112yes—
834C2C3×#246412yes—
835C2C3×#254011yescharacteristic
836C2C3×#260311yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
3. C2×C3×#390C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×#386C2semidirect
6. C2×C3×#385C2semidirect
7. C3×#1444C2semidirect
8. C3×#1439C2semidirect
9. C3×#1438C2semidirect
10. C3×#1437C2semidirect
11. C3×C4×#95C2semidirect
12. #14189C3direct (N × H)
31. C3×#392C4semidirect
43. C22×C4×D4C2×C3semidirect
45. C2×#390C2×C3semidirect
46. C2×#388C2×C3semidirect
47. C2×#386C2×C3semidirect
48. C2×#385C2×C3semidirect
49. #1444C2×C3semidirect
50. #1439C2×C3semidirect
51. #1438C2×C3semidirect
52. #1437C2×C3semidirect
53. C4×#95C2×C3semidirect
67. C22×C3×D4C2×C4semidirect
111. C2×C3×C22⋊C4C2×C4semidirect
112. C2×C3×C22⋊C4C2×C4semidirect
113. C2×C3×C22⋊C4D4semidirect
118. C2×C3×C42D4semidirect
124. C3×#95C2×C4semidirect
125. C3×#95D4semidirect
144. #392C3×C4semidirect
279. C22×D4C2×C3×C4semidirect
323. C2×C22⋊C4C2×C3×C4semidirect
324. C2×C22⋊C4C2×C3×C4semidirect
325. C2×C22⋊C4C3×D4semidirect
330. C2×C42C3×D4semidirect
336. #95C2×C3×C4semidirect
337. #95C3×D4semidirect
458. C2×C3×C4C4×D4semidirect
749. C2×C4C3×C4×D4semidirect
823. C3#14189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3862
C2×C3×#3852
C3×#14442
C3×#14392
C3×#14382
C3×#14372
C3×C4×#952
#141893