Finite Group Databasebeta

← C3×#13968 #10632575

Subgroups — C3×#13968 #10632575

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic
2C22×C3×C4×D4C211yesmaximal, characteristic
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#381C211yesmaximal, characteristic, complemented
5C22×C3×#95C211yesmaximal, characteristic, complemented
6C3×#1441C212yesmaximal, complemented
7C3×#1440C212yesmaximal, complemented
8C3×#1436C212yesmaximal, complemented
9C3×C22⋊#95C212yesmaximal, complemented
10C3×C22⋊#95C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C211yesmaximal, characteristic, complemented
12#13968C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C24×C3×C4C2211yescharacteristic
18C2×C3×#123—24no—
19C2×C3×#123—24no—
20C2×C3×#123C418yescomplemented
21C2×C3×C4×D4—24no—
22C2×C3×C4×D4—24no—
23C2×C3×C4×D4—24no—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2212yes—
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C42C2211yescharacteristic
33C3×#386—24no—
34C3×#381—24no—
35C2×C3×#95—24no—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C2×C3×#95C2212yes—
43C2×C3×#95C2212yes—
44C2×C3×#95C2212yes—
45C22×#123C2×C311yescharacteristic
46C22×C4×D4C2×C311yescharacteristic
47C2×#386C2×C311yescharacteristic
48C2×#381C2×C311yescharacteristic, complemented
49C22×#95C2×C311yescharacteristic, complemented
50#1441C2×C312yescomplemented
51#1440C2×C312yescomplemented
52#1436C2×C312yescomplemented
53C22⋊#95C2×C311yescharacteristic, complemented
54C22⋊#95C2×C312yescomplemented
55C22⋊#95C2×C311yescharacteristic, complemented
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4C2×C414yes—
63C22×C3×D4D414yes—
64C22×C3×D4D414yes—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—24no—
78C23×C3×C4—24no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—24no—
82C23×C3×C4—42no—
83C23×C3×C4—42no—
84C23×C3×C4—42no—
85C23×C3×C4C2×C414yescomplemented
86C23×C3×C4D414yes—
87C23×C3×C4C2312yes—
88C23×C3×C4C2312yes—
89C23×C3×C4C2312yes—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2312yes—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C3×#123—232no—
97C3×C4×D4—232no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—24no—
102C2×C3×C4⋊C4—24no—
103C2×C3×C4⋊C4C2×C418yescomplemented
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—42no—
119C2×C3×C22⋊C4C2×C414yescomplemented
120C2×C3×C22⋊C4C2×C418yescomplemented
121C2×C3×C22⋊C4D414yes—
122C2×C3×C42—22no—
123C2×C3×C42—22no—
124C2×C3×C42—22no—
125C3×#95—24no—
126C3×#95—24no—
127C3×#95—24no—
128C3×#95—24no—
129C3×#95—24no—
130C3×#95—24no—
131C3×#95—24no—
132C3×#95—42no—
133C3×#95—42no—
134C23×D4C22×C311yescharacteristic
135C24×C4C22×C311yescharacteristic
136C24×C4C22×C311yescharacteristic
137C24×C4C22×C311yescharacteristic
138C24×C4C22×C311yescharacteristic
139C2×#123—24no—
140C2×#123—24no—
141C2×#123C3×C418yescomplemented
142C2×C4×D4—24no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C22×C4⋊C4C22×C311yescharacteristic
146C22×C4⋊C4C22×C312yes—
147C22×C22⋊C4C22×C311yescharacteristic
148C22×C22⋊C4C22×C311yescharacteristic
149C22×C22⋊C4C22×C312yes—
150C22×C22⋊C4C22×C311yescharacteristic
151C22×C22⋊C4C22×C312yes—
152C22×C22⋊C4C22×C311yescharacteristic
153C22×C42C22×C311yescharacteristic
154#386—24no—
155#381—24no—
156C2×#95—24no—
157C2×#95C22×C312yes—
158C2×#95C22×C312yes—
159C2×#95C22×C312yes—
160C2×#95C22×C312yes—
161C2×#95C22×C312yes—
162C2×#95C22×C312yes—
163C2×#95C22×C312yes—
164C2×#95C22×C312yes—
165C2×#95C22×C312yes—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3C22×C412yes—
179C24×C3C22×C412yes—
180C24×C3C2×D412yes—
181C24×C3C2×D412yes—
182C24×C3C2×D412yes—
183C24×C3C2×D412yes—
184C24×C3C2×D412yes—
185C24×C3C2×D412yes—
186C24×C3#4112yes—
187C24×C3#4112yes—
188C24×C3C2411yescharacteristic
189C2×C3×D4—28no—
190C2×C3×D4—28no—
191C2×C3×D4—28no—
192C2×C3×D4—28no—
193C2×C3×D4—28no—
194C2×C3×D4—28no—
195C2×C3×D4C22⋊C4116yes—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—28no—
204C22×C3×C4—28no—
205C22×C3×C4—28no—
206C22×C3×C4—28no—
207C22×C3×C4—28no—
208C22×C3×C4—28no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
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—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—28no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—44no—
248C22×C3×C4—48no—
249C22×C3×C4—48no—
250C22×C3×C4—48no—
251C22×C3×C4—48no—
252C22×C3×C4—48no—
253C22×C3×C4—48no—
254C22×C3×C4—44no—
255C22×C3×C4—44no—
256C22×C3×C4—44no—
257C22×C3×C4—44no—
258C22×C3×C4—44no—
259C22×C3×C4—44no—
260C22×C3×C4—44no—
261C22×C3×C4—44no—
262C22×C3×C4C22×C414yes—
263C22×C3×C4C22×C414yes—
264C22×C3×C4C22×C412yes—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×D412yes—
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4#4114yes—
272C22×C3×C4#4114yes—
273C3×C4⋊C4—28no—
274C3×C4⋊C4—216no—
275C3×C22⋊C4—28no—
276C3×C22⋊C4—28no—
277C3×C22⋊C4—216no—
278C3×C22⋊C4—28no—
279C3×C22⋊C4—48no—
280C3×C22⋊C4—44no—
281C3×C42—28no—
282C25C23×C311yescharacteristic
283C25C23×C311yescharacteristic
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4C2×C3×C414yes—
289C22×D4C3×D414yes—
290C22×D4C3×D414yes—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—24no—
304C23×C4—24no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—24no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4C2×C3×C414yescomplemented
312C23×C4C3×D414yes—
313C23×C4C23×C312yes—
314C23×C4C23×C312yes—
315C23×C4C23×C312yes—
316C23×C4C23×C311yescharacteristic
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C312yes—
320C23×C4C23×C311yescharacteristic
321C23×C4C23×C311yescharacteristic
322#123—232no—
323C4×D4—232no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4C2×C3×C418yescomplemented
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4C2×C3×C414yescomplemented
346C2×C22⋊C4C2×C3×C418yescomplemented
347C2×C22⋊C4C3×D414yes—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—42no—
359#95—42no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—42no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3C2×C22⋊C414yes—
399C23×C3C2×C22⋊C414yes—
400C23×C3C4×D414yes—
401C23×C3C4×D414yes—
402C23×C3#12014yes—
403C23×C3#12114yes—
404C23×C3#12114yes—
405C23×C3#12314yes—
406C23×C3C23×C411yescharacteristic
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C22×D411yescharacteristic
410C23×C3C22×D411yescharacteristic
411C23×C3C2×#4111yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4112yes—
414C23×C3C2×#4112yes—
415C23×C3H(5,𝔽2)12yes—
416C23×C32−1+412yes—
417C3×D4—232no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
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—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—24no—
439C2×C3×C4—22no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—416no—
445C2×C3×C4—416no—
446C2×C3×C4—416no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—41no—
452C2×C3×C4—42no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—42no—
456C2×C3×C4—41no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—416no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4C2×C22⋊C414yes—
476C2×C3×C4#12314yescomplemented
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—22no—
489C24C22×C3×C412yes—
490C24C22×C3×C412yes—
491C24C2×C3×D412yes—
492C24C2×C3×D412yes—
493C24C2×C3×D412yes—
494C24C2×C3×D412yes—
495C24C2×C3×D412yes—
496C24C2×C3×D412yes—
497C24C3×#4112yes—
498C24C3×#4112yes—
499C24C24×C311yescharacteristic
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—28no—
506C2×D4C3×C22⋊C4116yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4C22×C3×C414yes—
574C22×C4C22×C3×C414yes—
575C22×C4C22×C3×C412yes—
576C22×C4C2×C3×D412yes—
577C22×C4C2×C3×D412yes—
578C22×C4C2×C3×D412yes—
579C22×C4C2×C3×D412yes—
580C22×C4C2×C3×D412yes—
581C22×C4C2×C3×D412yes—
582C22×C4C3×#4114yes—
583C22×C4C3×#4114yes—
584C4⋊C4—28no—
585C4⋊C4—216no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—216no—
589C22⋊C4—28no—
590C22⋊C4—48no—
591C22⋊C4—44no—
592C42—28no—
593C22×C3—24no—
594C22×C3—28no—
595C22×C3—28no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—28no—
599C22×C3—28no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—28no—
604C22×C3—24no—
605C22×C3—42no—
606C22×C3—44no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3#38618yes—
615C22×C3C22×C22⋊C411yescharacteristic
616C22×C3C2×C4×D411yescharacteristic
617C22×C3C2×C4×D411yescharacteristic
618C22×C3C4×#4112yes—
619C22×C3#52012yes—
620C22×C3C2×#12011yescharacteristic
621C22×C3C2×#12111yescharacteristic
622C22×C3C2×#12111yescharacteristic
623C22×C3C2×#12311yescharacteristic
624C22×C3C2×#12311yescharacteristic
625C22×C3#52511yescharacteristic
626C22×C3#52912yes—
627C22×C3#53411yescharacteristic
628C22×C3#53611yescharacteristic
629C22×C3#53912yes—
630C22×C3#54612yes—
631C22×C3#54612yes—
632C22×C3#54612yes—
633C22×C3#54712yes—
634C22×C3#54712yes—
635C22×C3#54712yes—
636C22×C3#55112yes—
637C22×C3#55212yes—
638C3×C4—24no—
639C3×C4—24no—
640C3×C4—44no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—44no—
646C3×C4—82no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×C3×C22⋊C414yes—
686C23C2×C3×C22⋊C414yes—
687C23C3×C4×D414yes—
688C23C3×C4×D414yes—
689C23C3×#12014yes—
690C23C3×#12114yes—
691C23C3×#12114yes—
692C23C3×#12314yes—
693C23C23×C3×C411yescharacteristic
694C23C22×C3×D411yescharacteristic
695C23C22×C3×D411yescharacteristic
696C23C22×C3×D411yescharacteristic
697C23C22×C3×D411yescharacteristic
698C23C2×C3×#4111yescharacteristic
699C23C2×C3×#4111yescharacteristic
700C23C2×C3×#4112yes—
701C23C2×C3×#4112yes—
702C23C3×H(5,𝔽2)12yes—
703C23C3×2−1+412yes—
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
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×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4C2×C3×C22⋊C414yes—
763C2×C4C3×#12314yescomplemented
764C2×C3—28no—
765C2×C3—44no—
766C2×C3C2×#38611yescharacteristic
767C2×C3C4×#12311yescharacteristic
768C2×C3#232211yescharacteristic
769C2×C3#233912yes—
770C2×C3#235912yes—
771C2×C3#240511yescharacteristic
772C2×C3#240611yescharacteristic
773C2×C3#241912yes—
774C2×C3#242512yes—
775C2×C3#248611yescharacteristic
776C2×C3#253411yescharacteristic
777C22—24no—
778C22—24no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—28no—
789C22—42no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22C3×#38618yes—
799C22C22×C3×C22⋊C411yescharacteristic
800C22C2×C3×C4×D411yescharacteristic
801C22C2×C3×C4×D411yescharacteristic
802C22C3×C4×#4112yes—
803C22C3×#52012yes—
804C22C2×C3×#12011yescharacteristic
805C22C2×C3×#12111yescharacteristic
806C22C2×C3×#12111yescharacteristic
807C22C2×C3×#12311yescharacteristic
808C22C2×C3×#12311yescharacteristic
809C22C3×#52511yescharacteristic
810C22C3×#52912yes—
811C22C3×#53411yescharacteristic
812C22C3×#53611yescharacteristic
813C22C3×#53912yes—
814C22C3×#54612yes—
815C22C3×#54612yes—
816C22C3×#54612yes—
817C22C3×#54712yes—
818C22C3×#54712yes—
819C22C3×#54712yes—
820C22C3×#55112yes—
821C22C3×#55212yes—
822C4—24no—
823C4—24no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—44no—
830C4—82no—
831C3#1396811yescharacteristic, direct product factor, Sylow
832C2—28no—
833C2—44no—
834C2C2×C3×#38611yescharacteristic
835C2C3×C4×#12311yescharacteristic
836C2C3×#232211yescharacteristic
837C2C3×#233912yes—
838C2C3×#235912yes—
839C2C3×#240511yescharacteristic
840C2C3×#240611yescharacteristic
841C2C3×#241912yes—
842C2C3×#242512yes—
843C2C3×#248611yescharacteristic
844C2C3×#253411yescharacteristic
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
4. C2×C3×#381C2semidirect
5. C22×C3×#95C2semidirect
6. C3×#1441C2semidirect
7. C3×#1440C2semidirect
8. C3×#1436C2semidirect
9. C3×C22⋊#95C2semidirect
10. C3×C22⋊#95C2semidirect
11. C3×C22⋊#95C2semidirect
12. #13968C3direct (N × H)
20. C2×C3×#123C4semidirect
48. C2×#381C2×C3semidirect
49. C22×#95C2×C3semidirect
50. #1441C2×C3semidirect
51. #1440C2×C3semidirect
52. #1436C2×C3semidirect
53. C22⋊#95C2×C3semidirect
54. C22⋊#95C2×C3semidirect
55. C22⋊#95C2×C3semidirect
85. C23×C3×C4C2×C4semidirect
103. C2×C3×C4⋊C4C2×C4semidirect
119. C2×C3×C22⋊C4C2×C4semidirect
120. C2×C3×C22⋊C4C2×C4semidirect
141. C2×#123C3×C4semidirect
311. C23×C4C2×C3×C4semidirect
329. C2×C4⋊C4C2×C3×C4semidirect
345. C2×C22⋊C4C2×C3×C4semidirect
346. C2×C22⋊C4C2×C3×C4semidirect
476. C2×C3×C4#123semidirect
763. C2×C4C3×#123semidirect
831. C3#13968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C3×C4×D42
C2×C3×#3862
C2×C3×#3812
C22×C3×#952
C3×#14412
C3×#14402
C3×#14362
C3×C22⋊#952
#139683