Finite Group Databasebeta

← C3×#14175 #10632782

Subgroups — C3×#14175 #10632782

Order 768.

2854 conjugacy classes of subgroups.

The subgroup lattice has 842 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×#386C212yesmaximal, complemented
4C2×C3×#386C212yesmaximal, complemented
5C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#1442C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8C3×#1438C211yesmaximal, characteristic, complemented
9C3×#1437C212yesmaximal, complemented
10C3×#1434C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal, complemented
12#14175C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C24×C3×C4C2212yes—
16C24×C3×C4C2211yescharacteristic
17C2×C3×C4×D4—28no—
18C2×C3×C4×D4—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C42C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C3×#392C418yescomplemented
30C3×#386—28no—
31C3×#386—28no—
32C3×C4×C22⋊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, complemented
43C2×#392C2×C311yescharacteristic
44C2×#386C2×C312yescomplemented
45C2×#386C2×C312yescomplemented
46C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
47#1442C2×C311yescharacteristic, complemented
48#1439C2×C311yescharacteristic, complemented
49#1438C2×C311yescharacteristic, complemented
50#1437C2×C312yescomplemented
51#1434C2×C311yescharacteristic, complemented
52C22⋊#95C2×C312yescomplemented
53C25×C3C2311yescharacteristic
54C25×C3C2312yes—
55C22×C3×D4—24no—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—42no—
64C22×C3×D4—42no—
65C22×C3×D4C2×C414yescomplemented
66C22×C3×D4C2×C418yescomplemented
67C23×C3×C4—24no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—24no—
71C23×C3×C4—24no—
72C23×C3×C4—22no—
73C23×C3×C4—24no—
74C23×C3×C4—24no—
75C23×C3×C4—24no—
76C23×C3×C4—42no—
77C23×C3×C4—42no—
78C23×C3×C4—42no—
79C23×C3×C4C2312yes—
80C23×C3×C4C2312yes—
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2312yes—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C3×C4×D4—232no—
89C2×C3×C4⋊C4—24no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—22no—
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—42no—
104C2×C3×C22⋊C4—42no—
105C2×C3×C22⋊C4—42no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4C2×C414yescomplemented
109C2×C3×C22⋊C4C2×C418yescomplemented
110C2×C3×C22⋊C4D414yescomplemented
111C2×C3×C22⋊C4D418yescomplemented
112C2×C3×C42—24no—
113C2×C3×C42—22no—
114C2×C3×C42—42no—
115C2×C3×C42D414yescomplemented
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—24no—
119C3×#95—24no—
120C3×#95—24no—
121C3×#95—24no—
122C3×#95—22no—
123C3×#95—42no—
124C3×#95C2×C414yescomplemented
125C23×D4C22×C311yescharacteristic
126C23×D4C22×C312yes—
127C24×C4C22×C312yes—
128C24×C4C22×C311yescharacteristic
129C2×C4×D4—28no—
130C2×C4×D4—24no—
131C22×C4⋊C4C22×C311yescharacteristic
132C22×C22⋊C4C22×C312yes—
133C22×C22⋊C4C22×C312yes—
134C22×C22⋊C4C22×C312yes—
135C22×C22⋊C4C22×C311yescharacteristic
136C22×C22⋊C4C22×C312yes—
137C22×C22⋊C4C22×C311yescharacteristic
138C22×C22⋊C4C22×C312yes—
139C22×C42C22×C311yescharacteristic
140C22×C42C22×C311yescharacteristic
141#392C3×C418yescomplemented
142#386—28no—
143#386—28no—
144C4×C22⋊C4—24no—
145C2×#95C22×C311yescharacteristic
146C2×#95C22×C312yes—
147C2×#95C22×C312yes—
148C2×#95C22×C312yes—
149C2×#95C22×C311yescharacteristic
150C2×#95C22×C312yes—
151C2×#95C22×C311yescharacteristic
152C2×#95C22×C312yes—
153C2×#95C22×C311yescharacteristic
154C24×C3—21no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3C22×C414yes—
175C24×C3C22×C412yes—
176C24×C3C2×D414yes—
177C24×C3C2×D412yes—
178C24×C3#4114yes—
179C24×C3#4112yes—
180C24×C3C2411yescharacteristic
181C2×C3×D4—28no—
182C2×C3×D4—28no—
183C2×C3×D4—216no—
184C2×C3×D4—216no—
185C2×C3×D4—216no—
186C2×C3×D4—216no—
187C2×C3×D4—28no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—216no—
201C22×C3×C4—28no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
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—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—48no—
234C22×C3×C4—48no—
235C22×C3×C4—48no—
236C22×C3×C4—48no—
237C22×C3×C4—48no—
238C22×C3×C4—48no—
239C22×C3×C4—44no—
240C22×C3×C4—48no—
241C22×C3×C4—44no—
242C22×C3×C4—48no—
243C22×C3×C4C22×C414yes—
244C22×C3×C4C22×C412yes—
245C22×C3×C4C22×C412yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D414yes—
248C22×C3×C4C2×D412yes—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4#4112yes—
254C22×C3×C4#4112yes—
255C22×C3×C4#4112yes—
256C3×C4⋊C4—28no—
257C3×C22⋊C4—28no—
258C3×C22⋊C4—216no—
259C3×C22⋊C4—28no—
260C3×C22⋊C4—48no—
261C3×C22⋊C4—48no—
262C3×C22⋊C4—48no—
263C3×C22⋊C4—48no—
264C3×C42—28no—
265C3×C42—44no—
266C25C23×C311yescharacteristic
267C25C23×C312yes—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4C2×C3×C414yescomplemented
279C22×D4C2×C3×C418yescomplemented
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C23×C312yes—
293C23×C4C23×C311yescharacteristic
294C23×C4C23×C312yes—
295C23×C4C23×C311yescharacteristic
296C23×C4C23×C312yes—
297C23×C4C23×C311yescharacteristic
298C23×C4C23×C311yescharacteristic
299C23×C4C23×C311yescharacteristic
300C23×C4C23×C311yescharacteristic
301C4×D4—232no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
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—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4C2×C3×C414yescomplemented
322C2×C22⋊C4C2×C3×C418yescomplemented
323C2×C22⋊C4C3×D418yescomplemented
324C2×C22⋊C4C3×D414yescomplemented
325C2×C42—24no—
326C2×C42—22no—
327C2×C42—42no—
328C2×C42C3×D414yescomplemented
329#95—22no—
330#95—22no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—22no—
336#95—42no—
337#95C2×C3×C414yescomplemented
338C23×C3—22no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—22no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—41no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—41no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3C4×D418yes—
395C23×C3C4×D414yescomplemented
396C23×C3C23×C411yescharacteristic
397C23×C3C22×D411yescharacteristic
398C23×C3C22×D412yes—
399C23×C3C22×D411yescharacteristic
400C23×C3C2×#4111yescharacteristic
401C23×C3C2×#4112yes—
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3H(5,𝔽2)12yes—
406C23×C3H(5,𝔽2)12yes—
407C3×D4—232no—
408C3×D4—432no—
409C2×C3×C4—24no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—22no—
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—22no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—416no—
434C2×C3×C4—432no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4C4×D414yes—
460C2×C3×C4#12014yes—
461C2×C3×C4#12114yes—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24C22×C3×C414yes—
483C24C22×C3×C412yes—
484C24C2×C3×D414yes—
485C24C2×C3×D412yes—
486C24C3×#4114yes—
487C24C3×#4112yes—
488C24C24×C311yescharacteristic
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—216no—
492C2×D4—216no—
493C2×D4—216no—
494C2×D4—216no—
495C2×D4—28no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—216no—
509C22×C4—28no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4C22×C3×C414yes—
552C22×C4C22×C3×C412yes—
553C22×C4C22×C3×C412yes—
554C22×C4C2×C3×D412yes—
555C22×C4C2×C3×D414yes—
556C22×C4C2×C3×D412yes—
557C22×C4C2×C3×D414yes—
558C22×C4C2×C3×D412yes—
559C22×C4C2×C3×D412yes—
560C22×C4C2×C3×D412yes—
561C22×C4C3×#4112yes—
562C22×C4C3×#4112yes—
563C22×C4C3×#4112yes—
564C4⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—216no—
567C22⋊C4—28no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C42—28no—
573C42—44no—
574C22×C3—28no—
575C22×C3—28no—
576C22×C3—28no—
577C22×C3—28no—
578C22×C3—24no—
579C22×C3—42no—
580C22×C3—44no—
581C22×C3—42no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—42no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—42no—
597C22×C3—44no—
598C22×C3—42no—
599C22×C3—44no—
600C22×C3C2×C4×D411yescharacteristic
601C22×C3C2×C4×D411yescharacteristic
602C22×C3C2×C4×D412yes—
603C22×C3C4×#4111yescharacteristic
604C22×C3#51812yes—
605C22×C3C2×#12011yescharacteristic
606C22×C3C2×#12111yescharacteristic
607C22×C3#52511yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#52512yes—
610C22×C3#52911yescharacteristic
611C22×C3#53211yescharacteristic
612C22×C3#53511yescharacteristic
613C22×C3#53511yescharacteristic
614C22×C3#54012yes—
615C22×C3D4212yes—
616C22×C3#54612yes—
617C22×C3#54612yes—
618C22×C3#54612yes—
619C22×C3#54612yes—
620C22×C3#55112yes—
621C22×C3#55312yes—
622C22×C3#55312yes—
623C3×C4—24no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—42no—
627C3×C4—44no—
628C3×C4—42no—
629C3×C4—44no—
630C3×C4—42no—
631C3×C4—82no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23C3×C4×D418yes—
689C23C3×C4×D414yescomplemented
690C23C23×C3×C411yescharacteristic
691C23C22×C3×D411yescharacteristic
692C23C22×C3×D412yes—
693C23C22×C3×D411yescharacteristic
694C23C2×C3×#4111yescharacteristic
695C23C2×C3×#4112yes—
696C23C2×C3×#4111yescharacteristic
697C23C2×C3×#4111yescharacteristic
698C23C2×C3×#4111yescharacteristic
699C23C3×H(5,𝔽2)12yes—
700C23C3×H(5,𝔽2)12yes—
701D4—232no—
702D4—432no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—416no—
728C2×C4—432no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4C3×C4×D414yes—
754C2×C4C3×#12014yes—
755C2×C4C3×#12114yes—
756C2×C3—48no—
757C2×C3—44no—
758C2×C3C4×#12011yescharacteristic
759C2×C3C4×#12111yescharacteristic
760C2×C3#232811yescharacteristic
761C2×C3#235812yes—
762C2×C3#236412yes—
763C2×C3#240411yescharacteristic
764C2×C3#240811yescharacteristic
765C2×C3#245712yes—
766C2×C3#246412yes—
767C2×C3#253511yescharacteristic
768C2×C3#259811yescharacteristic
769C22—28no—
770C22—28no—
771C22—24no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—44no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—44no—
788C22—42no—
789C22—44no—
790C22—42no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22C2×C3×C4×D412yes—
796C22C2×C3×C4×D411yescharacteristic
797C22C2×C3×C4×D411yescharacteristic
798C22C3×C4×#4111yescharacteristic
799C22C3×#51812yes—
800C22C2×C3×#12011yescharacteristic
801C22C2×C3×#12111yescharacteristic
802C22C3×#52511yescharacteristic
803C22C3×#52512yes—
804C22C3×#52511yescharacteristic
805C22C3×#52911yescharacteristic
806C22C3×#53211yescharacteristic
807C22C3×#53511yescharacteristic
808C22C3×#53511yescharacteristic
809C22C3×#54012yes—
810C22C3×D4212yes—
811C22C3×#54612yes—
812C22C3×#54612yes—
813C22C3×#54612yes—
814C22C3×#54612yes—
815C22C3×#55112yes—
816C22C3×#55312yes—
817C22C3×#55312yes—
818C4—24no—
819C4—24no—
820C4—24no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—82no—
827C3#1417511yescharacteristic, direct product factor, Sylow
828C2—48no—
829C2—44no—
830C2C3×C4×#12011yescharacteristic
831C2C3×C4×#12111yescharacteristic
832C2C3×#232811yescharacteristic
833C2C3×#235812yes—
834C2C3×#236412yes—
835C2C3×#240411yescharacteristic
836C2C3×#240811yescharacteristic
837C2C3×#245712yes—
838C2C3×#246412yes—
839C2C3×#253511yescharacteristic
840C2C3×#259811yescharacteristic
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×#386C2semidirect
4. C2×C3×#386C2semidirect
5. C2×C3×C4×C22⋊C4C2semidirect
6. C3×#1442C2semidirect
7. C3×#1439C2semidirect
8. C3×#1438C2semidirect
9. C3×#1437C2semidirect
10. C3×#1434C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14175C3direct (N × H)
29. C3×#392C4semidirect
42. C22×C4×D4C2×C3semidirect
44. C2×#386C2×C3semidirect
45. C2×#386C2×C3semidirect
46. C2×C4×C22⋊C4C2×C3semidirect
47. #1442C2×C3semidirect
48. #1439C2×C3semidirect
49. #1438C2×C3semidirect
50. #1437C2×C3semidirect
51. #1434C2×C3semidirect
52. C22⋊#95C2×C3semidirect
65. C22×C3×D4C2×C4semidirect
66. C22×C3×D4C2×C4semidirect
108. C2×C3×C22⋊C4C2×C4semidirect
109. C2×C3×C22⋊C4C2×C4semidirect
110. C2×C3×C22⋊C4D4semidirect
111. C2×C3×C22⋊C4D4semidirect
115. C2×C3×C42D4semidirect
124. C3×#95C2×C4semidirect
141. #392C3×C4semidirect
278. C22×D4C2×C3×C4semidirect
279. C22×D4C2×C3×C4semidirect
321. C2×C22⋊C4C2×C3×C4semidirect
322. C2×C22⋊C4C2×C3×C4semidirect
323. C2×C22⋊C4C3×D4semidirect
324. C2×C22⋊C4C3×D4semidirect
328. C2×C42C3×D4semidirect
337. #95C2×C3×C4semidirect
395. C23×C3C4×D4semidirect
689. C23C3×C4×D4semidirect
827. C3#14175direct (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×#3862
C2×C3×C4×C22⋊C42
C3×#14422
C3×#14392
C3×#14382
C3×#14372
C3×#14342
C3×C22⋊#952
#141753