Finite Group Databasebeta

← C3×#14176 #10632783

Subgroups — C3×#14176 #10632783

Order 768.

2422 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C2×C3×#394C211yesmaximal, characteristic
3C2×C3×#388C212yesmaximal, complemented
4C2×C3×#385C212yesmaximal, complemented
5C2×C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
6C3×#1444C211yesmaximal, characteristic, complemented
7C3×#1441C211yesmaximal, characteristic, complemented
8C3×#1438C211yesmaximal, characteristic
9C3×#1437C212yesmaximal, complemented
10C3×#1434C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal, complemented
12#14176C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2212yes—
15C2×C3×C4×D4—28no—
16C2×C3×C4×D4—24no—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C42C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C3×#394C418yescomplemented
30C3×#388—28no—
31C3×#385—28no—
32C3×C4×C4⋊C4—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C22×C4×D4C2×C311yescharacteristic
43C2×#394C2×C311yescharacteristic
44C2×#388C2×C312yescomplemented
45C2×#385C2×C312yescomplemented
46C2×C4×C4⋊C4C2×C311yescharacteristic, complemented
47#1444C2×C311yescharacteristic, complemented
48#1441C2×C311yescharacteristic, complemented
49#1438C2×C311yescharacteristic
50#1437C2×C312yescomplemented
51#1434C2×C311yescharacteristic, complemented
52C22⋊#95C2×C312yescomplemented
53C25×C3C2312yes—
54C22×C3×D4—24no—
55C22×C3×D4—24no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4C2×C414yes—
59C23×C3×C4—24no—
60C23×C3×C4—24no—
61C23×C3×C4—24no—
62C23×C3×C4—24no—
63C23×C3×C4—24no—
64C23×C3×C4—42no—
65C23×C3×C4—42no—
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C3×C4×D4—232no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—24no—
85C2×C3×C4⋊C4—42no—
86C2×C3×C4⋊C4C2×C414yescomplemented
87C2×C3×C4⋊C4D414yescomplemented
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4C2×C418yescomplemented
101C2×C3×C22⋊C4C2×C418yescomplemented
102C2×C3×C22⋊C4D418yes—
103C2×C3×C42—22no—
104C2×C3×C42—24no—
105C2×C3×C42—22no—
106C2×C3×C42—22no—
107C2×C3×C42—22no—
108C2×C3×C42—24no—
109C2×C3×C42D414yes—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—24no—
113C3×#95—24no—
114C3×#95—24no—
115C3×#95—24no—
116C3×#95—22no—
117C3×#95—42no—
118C3×#95C2×C414yescomplemented
119C23×D4C22×C311yescharacteristic
120C24×C4C22×C312yes—
121C2×C4×D4—28no—
122C2×C4×D4—24no—
123C22×C4⋊C4C22×C311yescharacteristic
124C22×C4⋊C4C22×C312yes—
125C22×C4⋊C4C22×C311yescharacteristic
126C22×C4⋊C4C22×C311yescharacteristic
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C312yes—
131C22×C22⋊C4C22×C312yes—
132C22×C42C22×C311yescharacteristic
133C22×C42C22×C311yescharacteristic
134C22×C42C22×C311yescharacteristic
135#394C3×C418yescomplemented
136#388—28no—
137#385—28no—
138C4×C4⋊C4—24no—
139C2×#95C22×C311yescharacteristic
140C2×#95C22×C312yes—
141C2×#95C22×C312yes—
142C2×#95C22×C312yes—
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C312yes—
145C2×#95C22×C311yescharacteristic
146C2×#95C22×C312yes—
147C2×#95C22×C311yescharacteristic
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3C22×C414yes—
161C24×C3C2×D414yes—
162C24×C3#4114yes—
163C24×C3C2411yescharacteristic
164C2×C3×D4—28no—
165C2×C3×D4—28no—
166C2×C3×D4—216no—
167C2×C3×D4—216no—
168C2×C3×D4—28no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—216no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
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—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—48no—
213C22×C3×C4—48no—
214C22×C3×C4—48no—
215C22×C3×C4—48no—
216C22×C3×C4—48no—
217C22×C3×C4—48no—
218C22×C3×C4C22×C414yes—
219C22×C3×C4C22×C412yes—
220C22×C3×C4C22×C412yes—
221C22×C3×C4C22×C412yes—
222C22×C3×C4C2×D414yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D414yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2×D412yes—
230C22×C3×C4#4112yes—
231C22×C3×C4#4112yes—
232C22×C3×C4#4112yes—
233C22×C3×C4#4112yes—
234C3×C4⋊C4—28no—
235C3×C4⋊C4—28no—
236C3×C4⋊C4—28no—
237C3×C4⋊C4—48no—
238C3×C22⋊C4—216no—
239C3×C22⋊C4—216no—
240C3×C22⋊C4—216no—
241C3×C22⋊C4—48no—
242C3×C22⋊C4—48no—
243C3×C42—28no—
244C3×C42—28no—
245C3×C42—44no—
246C25C23×C312yes—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4C2×C3×C414yes—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4C23×C312yes—
260C23×C4C23×C312yes—
261C23×C4C23×C311yescharacteristic
262C23×C4C23×C311yescharacteristic
263C23×C4C23×C312yes—
264C23×C4C23×C311yescharacteristic
265C23×C4C23×C311yescharacteristic
266C23×C4C23×C311yescharacteristic
267C23×C4C23×C311yescharacteristic
268C23×C4C23×C311yescharacteristic
269C4×D4—232no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4C2×C3×C414yescomplemented
280C2×C4⋊C4C3×D414yescomplemented
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4C2×C3×C418yescomplemented
294C2×C22⋊C4C2×C3×C418yescomplemented
295C2×C22⋊C4C3×D418yes—
296C2×C42—24no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—24no—
302C2×C42C3×D414yes—
303#95—22no—
304#95—22no—
305#95—24no—
306#95—24no—
307#95—24no—
308#95—24no—
309#95—22no—
310#95—42no—
311#95C2×C3×C414yescomplemented
312C23×C3—24no—
313C23×C3—24no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—24no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3C4×D418yes—
347C23×C3C23×C411yescharacteristic
348C23×C3C22×D411yescharacteristic
349C23×C3C22×D412yes—
350C23×C3C22×D411yescharacteristic
351C23×C3C2×#4111yescharacteristic
352C23×C3C2×#4112yes—
353C23×C3C2×#4111yescharacteristic
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3H(5,𝔽2)12yes—
357C23×C32−1+412yes—
358C3×D4—232no—
359C2×C3×C4—22no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—24no—
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—24no—
388C2×C3×C4—24no—
389C2×C3×C4—432no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4C4×D414yes—
415C2×C3×C4C4×D414yescomplemented
416C2×C3×C4#12014yes—
417C2×C3×C4#12114yes—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24C22×C3×C414yes—
431C24C2×C3×D414yes—
432C24C3×#4114yes—
433C24C24×C311yescharacteristic
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—216no—
437C2×D4—216no—
438C2×D4—28no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—216no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
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—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4C22×C3×C414yes—
489C22×C4C22×C3×C412yes—
490C22×C4C22×C3×C412yes—
491C22×C4C22×C3×C412yes—
492C22×C4C2×C3×D414yes—
493C22×C4C2×C3×D412yes—
494C22×C4C2×C3×D412yes—
495C22×C4C2×C3×D412yes—
496C22×C4C2×C3×D414yes—
497C22×C4C2×C3×D412yes—
498C22×C4C2×C3×D412yes—
499C22×C4C2×C3×D412yes—
500C22×C4C3×#4112yes—
501C22×C4C3×#4112yes—
502C22×C4C3×#4112yes—
503C22×C4C3×#4112yes—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—28no—
507C4⋊C4—48no—
508C22⋊C4—216no—
509C22⋊C4—216no—
510C22⋊C4—216no—
511C22⋊C4—48no—
512C22⋊C4—48no—
513C42—28no—
514C42—28no—
515C42—44no—
516C22×C3—28no—
517C22×C3—28no—
518C22×C3—28no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3C2×C4×D411yescharacteristic
532C22×C3C2×C4×D412yes—
533C22×C3C2×C4×D411yescharacteristic
534C22×C3C4×#4111yescharacteristic
535C22×C3#52012yes—
536C22×C3C2×#12011yescharacteristic
537C22×C3C2×#12111yescharacteristic
538C22×C3#52511yescharacteristic
539C22×C3#52511yescharacteristic
540C22×C3#52512yes—
541C22×C3#52911yescharacteristic
542C22×C3#53211yescharacteristic
543C22×C3#53511yescharacteristic
544C22×C3#53611yescharacteristic
545C22×C3#54212yes—
546C22×C3D4212yes—
547C22×C3#54612yes—
548C22×C3#54712yes—
549C22×C3#54712yes—
550C22×C3#54812yes—
551C22×C3#55112yes—
552C22×C3#55212yes—
553C22×C3#55312yes—
554C3×C4—24no—
555C3×C4—24no—
556C3×C4—24no—
557C3×C4—24no—
558C3×C4—42no—
559C3×C4—44no—
560C3×C4—42no—
561C3×C4—44no—
562C3×C4—42no—
563C3×C4—82no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23C3×C4×D418yes—
599C23C23×C3×C411yescharacteristic
600C23C22×C3×D411yescharacteristic
601C23C22×C3×D412yes—
602C23C22×C3×D411yescharacteristic
603C23C2×C3×#4111yescharacteristic
604C23C2×C3×#4112yes—
605C23C2×C3×#4111yescharacteristic
606C23C2×C3×#4111yescharacteristic
607C23C2×C3×#4111yescharacteristic
608C23C3×H(5,𝔽2)12yes—
609C23C3×2−1+412yes—
610D4—232no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—432no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4C3×C4×D414yes—
667C2×C4C3×C4×D414yescomplemented
668C2×C4C3×#12014yes—
669C2×C4C3×#12114yes—
670C2×C3—48no—
671C2×C3C4×#12011yescharacteristic
672C2×C3C4×#12111yescharacteristic
673C2×C3#232611yescharacteristic
674C2×C3#235912yes—
675C2×C3#236112yes—
676C2×C3#240611yescharacteristic
677C2×C3#240811yescharacteristic
678C2×C3#246112yes—
679C2×C3#246812yes—
680C2×C3#253611yescharacteristic
681C2×C3#259811yescharacteristic
682C22—28no—
683C22—28no—
684C22—28no—
685C22—44no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22C2×C3×C4×D411yescharacteristic
698C22C2×C3×C4×D412yes—
699C22C2×C3×C4×D411yescharacteristic
700C22C3×C4×#4111yescharacteristic
701C22C3×#52012yes—
702C22C2×C3×#12011yescharacteristic
703C22C2×C3×#12111yescharacteristic
704C22C3×#52511yescharacteristic
705C22C3×#52512yes—
706C22C3×#52511yescharacteristic
707C22C3×#52911yescharacteristic
708C22C3×#53211yescharacteristic
709C22C3×#53511yescharacteristic
710C22C3×#53611yescharacteristic
711C22C3×#54212yes—
712C22C3×D4212yes—
713C22C3×#54612yes—
714C22C3×#54712yes—
715C22C3×#54712yes—
716C22C3×#54812yes—
717C22C3×#55112yes—
718C22C3×#55212yes—
719C22C3×#55312yes—
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—44no—
725C4—44no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—82no—
730C3#1417611yescharacteristic, direct product factor, Sylow
731C2—48no—
732C2C3×C4×#12011yescharacteristic
733C2C3×C4×#12111yescharacteristic
734C2C3×#232611yescharacteristic
735C2C3×#235912yes—
736C2C3×#236112yes—
737C2C3×#240611yescharacteristic
738C2C3×#240811yescharacteristic
739C2C3×#246112yes—
740C2C3×#246812yes—
741C2C3×#253611yescharacteristic
742C2C3×#259811yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×#388C2semidirect
4. C2×C3×#385C2semidirect
5. C2×C3×C4×C4⋊C4C2semidirect
6. C3×#1444C2semidirect
7. C3×#1441C2semidirect
9. C3×#1437C2semidirect
10. C3×#1434C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14176C3direct (N × H)
29. C3×#394C4semidirect
44. C2×#388C2×C3semidirect
45. C2×#385C2×C3semidirect
46. C2×C4×C4⋊C4C2×C3semidirect
47. #1444C2×C3semidirect
48. #1441C2×C3semidirect
50. #1437C2×C3semidirect
51. #1434C2×C3semidirect
52. C22⋊#95C2×C3semidirect
86. C2×C3×C4⋊C4C2×C4semidirect
87. C2×C3×C4⋊C4D4semidirect
100. C2×C3×C22⋊C4C2×C4semidirect
101. C2×C3×C22⋊C4C2×C4semidirect
118. C3×#95C2×C4semidirect
135. #394C3×C4semidirect
279. C2×C4⋊C4C2×C3×C4semidirect
280. C2×C4⋊C4C3×D4semidirect
293. C2×C22⋊C4C2×C3×C4semidirect
294. C2×C22⋊C4C2×C3×C4semidirect
311. #95C2×C3×C4semidirect
415. C2×C3×C4C4×D4semidirect
667. C2×C4C3×C4×D4semidirect
730. C3#14176direct (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×#3942
C2×C3×#3882
C2×C3×#3852
C2×C3×C4×C4⋊C42
C3×#14442
C3×#14412
C3×#14382
C3×#14372
C3×#14342
C3×C22⋊#952
#141763