Finite Group Databasebeta

← C3×#24140 #10642747

Subgroups — C3×#24140 #10642747

Order 768.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic, complemented
2C3×#2848C211yesmaximal, characteristic, complemented
3C3×#2847C211yesmaximal, characteristic, complemented
4C3×C4×#120C211yesmaximal, characteristic, complemented
5C3×#2044C212yesmaximal, complemented
6C3×#2021C212yesmaximal, complemented
7C3×#1996C211yesmaximal, characteristic, complemented
8C3×#1964C211yesmaximal, characteristic, complemented
9C3×#1889C212yesmaximal, complemented
10C3×#1867C212yesmaximal, complemented
11C3×#1799C211yesmaximal, characteristic, complemented
12#24140C311yesmaximal, characteristic, direct product factor, Sylow
13C24×C3×C4C2211yescharacteristic
14C3×#553—21no—
15C3×#553—22no—
16C3×#552—21no—
17C3×#551—22no—
18C3×#548—21no—
19C3×#546—21no—
20C3×#539—21no—
21C3×#538—21no—
22C3×#534C2212yes—
23C3×#529—21no—
24C3×#525—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#120C2211yescharacteristic
30C2×C3×#120C2212yes—
31C3×#518C2212yes—
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#99C2212yes—
35C2×C3×#99C2212yes—
36C2×C3×#99C2212yes—
37C3×#386—21no—
38C3×#386—22no—
39C3×#386C2211yescharacteristic
40C3×#386C2212yes—
41C3×#385—21no—
42C3×#385—22no—
43C3×#385C2212yes—
44C3×#385C2211yescharacteristic
45C3×#380—21no—
46C3×#380—21no—
47C3×#380C2211yescharacteristic
48C3×#380C2211yescharacteristic
49C3×#379C2212yes—
50C3×#379C2211yescharacteristic
51C3×C4×C22⋊C4—21no—
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#342C2212yes—
54C3×#342C2212yes—
55C3×#342C2212yes—
56#3505C2×C311yescharacteristic, complemented
57#2848C2×C311yescharacteristic, complemented
58#2847C2×C311yescharacteristic, complemented
59C4×#120C2×C311yescharacteristic, complemented
60#2044C2×C312yescomplemented
61#2021C2×C312yescomplemented
62#1996C2×C311yescharacteristic, complemented
63#1964C2×C311yescharacteristic, complemented
64#1889C2×C312yescomplemented
65#1867C2×C312yescomplemented
66#1799C2×C311yescharacteristic, complemented
67C25×C3C2311yescharacteristic
68C2×C3×#41—21no—
69C22×C3×Q8D411yescharacteristic, complemented
70C22×C3×D4—21no—
71C22×C3×D4—22no—
72C22×C3×D4D411yescharacteristic, complemented
73C22×C3×D4C2311yescharacteristic
74C22×C3×D4C2312yes—
75C23×C3×C4—21no—
76C23×C3×C4—21no—
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4—21no—
81C23×C3×C4—44no—
82C23×C3×C4D411yescharacteristic, complemented
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C3×#126—22no—
86C3×#126—22no—
87C3×#126—22no—
88C3×#125—21no—
89C3×#125—22no—
90C3×#124—21no—
91C3×#124—22no—
92C3×#123—22no—
93C3×#123—22no—
94C3×#123—22no—
95C3×#123—22no—
96C3×#123—22no—
97C3×C22⋊Q8—21no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—21no—
100C3×C22⋊Q8—21no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—21no—
103C3×C22⋊Q8—44no—
104C3×#121—21no—
105C3×#121—22no—
106C3×#121—21no—
107C3×#121—21no—
108C3×#121—21no—
109C3×#121—21no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—44no—
113C3×#120—22no—
114C3×#120—22no—
115C3×#120—22no—
116C3×#120—22no—
117C3×#120—24no—
118C3×#120—42no—
119C3×C4×Q8—21no—
120C3×C4×D4—22no—
121C3×C4×D4—21no—
122C3×C4×D4—21no—
123C3×C4×D4—21no—
124C3×C4×D4—21no—
125C3×C4×D4—21no—
126C3×C4×D4—22no—
127C3×C4×D4—22no—
128C3×C4×D4—22no—
129C3×C4×D4—22no—
130C3×C4×D4—44no—
131C3×#117—21no—
132C3×#117—22no—
133C3×#117—22no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—22no—
138C2×C3×C4⋊C4D411yescharacteristic, complemented
139C2×C3×C4⋊C4D411yescharacteristic, complemented
140C2×C3×C4⋊C4D411yescharacteristic, complemented
141C2×C3×C4⋊C4D412yescomplemented
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4—22no—
151C2×C3×C22⋊C4D411yescharacteristic, complemented
152C2×C3×C22⋊C4D412yescomplemented
153C2×C3×C22⋊C4C2311yescharacteristic
154C2×C3×C22⋊C4C2312yes—
155C2×C3×C22⋊C4C2312yes—
156C2×C3×C22⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4C2312yes—
158C2×C3×C22⋊C4C2311yescharacteristic
159C2×C3×C42—21no—
160C2×C3×C42D411yescharacteristic, complemented
161C3×#99—24no—
162C3×#99—42no—
163C3×#99—42no—
164C3×#95—21no—
165C3×#95—21no—
166C3×#95—21no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—21no—
170C3×#95—21no—
171C24×C4C22×C311yescharacteristic
172#553—21no—
173#553—22no—
174#552—21no—
175#551—22no—
176#548—21no—
177#546—21no—
178#539—21no—
179#538—21no—
180#534C22×C312yes—
181#529—21no—
182#525—21no—
183C2×C22⋊Q8—21no—
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×#121—21no—
186C2×#121C22×C311yescharacteristic
187C2×#120C22×C311yescharacteristic
188C2×#120C22×C312yes—
189#518C22×C312yes—
190C2×C4×D4—21no—
191C2×C4×D4C22×C311yescharacteristic
192C2×#99C22×C312yes—
193C2×#99C22×C312yes—
194C2×#99C22×C312yes—
195#386—22no—
196#386—21no—
197#386C22×C312yes—
198#386C22×C311yescharacteristic
199#385—22no—
200#385—21no—
201#385C22×C312yes—
202#385C22×C311yescharacteristic
203#380—21no—
204#380—21no—
205#380C22×C311yescharacteristic
206#380C22×C311yescharacteristic
207#379C22×C312yes—
208#379C22×C311yescharacteristic
209C4×C22⋊C4—21no—
210C4×C22⋊C4C22×C311yescharacteristic
211#342C22×C312yes—
212#342C22×C312yes—
213#342C22×C312yes—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—42no—
221C24×C3—42no—
222C24×C3C2×D412yes—
223C24×C3C2×D411yescharacteristic
224C24×C3#4112yescomplemented
225C24×C3C2411yescharacteristic
226C3×#41—82no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—42no—
230C2×C3×D4—24no—
231C2×C3×D4—21no—
232C2×C3×D4—22no—
233C2×C3×D4—21no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—22no—
239C2×C3×D4—21no—
240C2×C3×D4—22no—
241C2×C3×D4—21no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—22no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—24no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4—42no—
277C22×C3×C4—42no—
278C22×C3×C4—42no—
279C22×C3×C4—41no—
280C22×C3×C4—41no—
281C22×C3×C4—41no—
282C22×C3×C4—41no—
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D411yescharacteristic
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D411yescharacteristic
295C3×C4⋊C4—22no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—42no—
308C3×C4⋊C4—42no—
309C3×C4⋊C4—42no—
310C3×C4⋊C4—44no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—21no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—21no—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—21no—
323C3×C22⋊C4—22no—
324C3×C22⋊C4—21no—
325C3×C22⋊C4—21no—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—22no—
328C3×C22⋊C4—22no—
329C3×C22⋊C4—21no—
330C3×C22⋊C4—22no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—21no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4#4112yescomplemented
341C3×C42—22no—
342C3×C42—22no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—42no—
346C25C23×C311yescharacteristic
347C2×#41—21no—
348C22×Q8C3×D411yescharacteristic, complemented
349C22×D4—21no—
350C22×D4—22no—
351C22×D4C3×D411yescharacteristic, complemented
352C22×D4C23×C311yescharacteristic
353C22×D4C23×C312yes—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—44no—
361C23×C4C3×D411yescharacteristic, complemented
362C23×C4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364#126—22no—
365#126—22no—
366#126—22no—
367#125—21no—
368#125—22no—
369#124—21no—
370#124—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—44no—
383#121—21no—
384#121—22no—
385#121—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—22no—
390#121—22no—
391#121—44no—
392#120—22no—
393#120—22no—
394#120—22no—
395#120—22no—
396#120—24no—
397#120—42no—
398C4×Q8—21no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—44no—
410#117—21no—
411#117—22no—
412#117—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4C3×D411yescharacteristic, complemented
418C2×C4⋊C4C3×D411yescharacteristic, complemented
419C2×C4⋊C4C3×D411yescharacteristic, complemented
420C2×C4⋊C4C3×D412yescomplemented
421C2×C22⋊C4—22no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4C3×D411yescharacteristic, complemented
431C2×C22⋊C4C3×D412yescomplemented
432C2×C22⋊C4C23×C312yes—
433C2×C22⋊C4C23×C311yescharacteristic
434C2×C22⋊C4C23×C312yes—
435C2×C22⋊C4C23×C311yescharacteristic
436C2×C22⋊C4C23×C312yes—
437C2×C22⋊C4C23×C311yescharacteristic
438C2×C42—21no—
439C2×C42C3×D411yescharacteristic, complemented
440#99—24no—
441#99—42no—
442#99—42no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—22no—
447#95—22no—
448#95—21no—
449#95—21no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—21no—
460C23×C3—22no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—41no—
466C23×C3—44no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—42no—
480C23×C3—42no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3C22×D411yescharacteristic
486C23×C3C22×D411yescharacteristic
487C23×C3C22×D411yescharacteristic
488C23×C3C2×#4111yescharacteristic
489C23×C3C2×#4111yescharacteristic
490C23×C3H(5,𝔽2)11yescharacteristic
491C23×C32−1+411yescharacteristic
492C3×Q8—42no—
493C3×Q8—81no—
494C3×D4—48no—
495C3×D4—42no—
496C3×D4—42no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—42no—
501C3×D4—42no—
502C3×D4—41no—
503C3×D4—42no—
504C3×D4—81no—
505C3×D4—82no—
506C3×D4—82no—
507C3×D4—88no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—44no—
529C2×C3×C4—44no—
530C2×C3×C4—44no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—44no—
538C2×C3×C4—42no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—41no—
542C2×C3×C4—42no—
543C2×C3×C4—41no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—42no—
547C2×C3×C4—41no—
548C2×C3×C4—42no—
549C2×C3×C4—41no—
550C2×C3×C4—42no—
551C2×C3×C4—42no—
552C2×C3×C4—81no—
553C2×C3×C4—82no—
554C2×C3×C4—82no—
555C2×C3×C4#12011yescharacteristic
556C2×C3×C4#12011yescharacteristic
557C2×C3×C4#12011yescharacteristic
558C2×C3×C4#12011yescharacteristic
559C24—21no—
560C24—21no—
561C24—21no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—42no—
566C24—42no—
567C24C2×C3×D412yes—
568C24C2×C3×D411yescharacteristic
569C24C3×#4112yescomplemented
570C24C24×C311yescharacteristic
571#41—82no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—42no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4C2×C3×D411yescharacteristic
629C22×C4C2×C3×D412yes—
630C22×C4C2×C3×D411yescharacteristic
631C22×C4C2×C3×D411yescharacteristic
632C22×C4C2×C3×D411yescharacteristic
633C22×C4C2×C3×D411yescharacteristic
634C22×C4C2×C3×D412yes—
635C22×C4C2×C3×D411yescharacteristic
636C22×C4C2×C3×D412yes—
637C22×C4C2×C3×D411yescharacteristic
638C22×C4C2×C3×D411yescharacteristic
639C22×C4C2×C3×D411yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—24no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—21no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—21no—
678C22⋊C4—44no—
679C22⋊C4—42no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—42no—
685C22⋊C4C3×#4112yescomplemented
686C42—22no—
687C42—22no—
688C42—21no—
689C42—21no—
690C42—42no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—42no—
719C22×C3—41no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—41no—
723C22×C3—82no—
724C22×C3—81no—
725C22×C3—82no—
726C22×C3C2×#12011yescharacteristic
727C22×C3#52511yescharacteristic
728C22×C3#53711yescharacteristic
729C22×C3#54611yescharacteristic
730C22×C3#54711yescharacteristic
731C22×C3#54811yescharacteristic
732C22×C3#55011yescharacteristic
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—42no—
737C3×C4—41no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4—41no—
741C3×C4—42no—
742C3×C4—41no—
743C3×C4—42no—
744C3×C4—82no—
745C3×C4—81no—
746C3×C4—82no—
747C3×C4B(4,𝔽2)12yes—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—44no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—41no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23C22×C3×D411yescharacteristic
784C23C22×C3×D411yescharacteristic
785C23C22×C3×D411yescharacteristic
786C23C2×C3×#4111yescharacteristic
787C23C2×C3×#4111yescharacteristic
788C23C3×H(5,𝔽2)11yescharacteristic
789C23C3×2−1+411yescharacteristic
790Q8—42no—
791Q8—81no—
792D4—48no—
793D4—42no—
794D4—42no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—41no—
801D4—42no—
802D4—81no—
803D4—82no—
804D4—82no—
805D4—88no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—81no—
851C2×C4—82no—
852C2×C4—82no—
853C2×C4C3×#12011yescharacteristic
854C2×C4C3×#12011yescharacteristic
855C2×C4C3×#12011yescharacteristic
856C2×C4C3×#12011yescharacteristic
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—44no—
864C2×C3—81no—
865C2×C3—82no—
866C2×C3#240711yescharacteristic
867C2×C3C2×B(4,𝔽2)11yescharacteristic
868C2×C3#302511yescharacteristic
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—82no—
902C22—81no—
903C22—82no—
904C22C2×C3×#12011yescharacteristic
905C22C3×#52511yescharacteristic
906C22C3×#53711yescharacteristic
907C22C3×#54611yescharacteristic
908C22C3×#54711yescharacteristic
909C22C3×#54811yescharacteristic
910C22C3×#55011yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—42no—
915C4—41no—
916C4—42no—
917C4—42no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—42no—
922C4—82no—
923C4—82no—
924C4—81no—
925C4C3×B(4,𝔽2)12yes—
926C3#2414011yescharacteristic, direct product factor, Sylow
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C3×#240711yescharacteristic
937C2C2×C3×B(4,𝔽2)11yescharacteristic
938C2C3×#302511yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3505C2semidirect
2. C3×#2848C2semidirect
3. C3×#2847C2semidirect
4. C3×C4×#120C2semidirect
5. C3×#2044C2semidirect
6. C3×#2021C2semidirect
7. C3×#1996C2semidirect
8. C3×#1964C2semidirect
9. C3×#1889C2semidirect
10. C3×#1867C2semidirect
11. C3×#1799C2semidirect
12. #24140C3direct (N × H)
56. #3505C2×C3semidirect
57. #2848C2×C3semidirect
58. #2847C2×C3semidirect
59. C4×#120C2×C3semidirect
60. #2044C2×C3semidirect
61. #2021C2×C3semidirect
62. #1996C2×C3semidirect
63. #1964C2×C3semidirect
64. #1889C2×C3semidirect
65. #1867C2×C3semidirect
66. #1799C2×C3semidirect
69. C22×C3×Q8D4semidirect
72. C22×C3×D4D4semidirect
82. C23×C3×C4D4semidirect
138. C2×C3×C4⋊C4D4semidirect
139. C2×C3×C4⋊C4D4semidirect
140. C2×C3×C4⋊C4D4semidirect
141. C2×C3×C4⋊C4D4semidirect
151. C2×C3×C22⋊C4D4semidirect
152. C2×C3×C22⋊C4D4semidirect
160. C2×C3×C42D4semidirect
224. C24×C3#41semidirect
340. C3×C22⋊C4#41semidirect
348. C22×Q8C3×D4semidirect
351. C22×D4C3×D4semidirect
361. C23×C4C3×D4semidirect
417. C2×C4⋊C4C3×D4semidirect
418. C2×C4⋊C4C3×D4semidirect
419. C2×C4⋊C4C3×D4semidirect
420. C2×C4⋊C4C3×D4semidirect
430. C2×C22⋊C4C3×D4semidirect
431. C2×C22⋊C4C3×D4semidirect
439. C2×C42C3×D4semidirect
569. C24C3×#41semidirect
685. C22⋊C4C3×#41semidirect
926. C3#24140direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35052
C3×#28482
C3×#28472
C3×C4×#1202
C3×#20442
C3×#20212
C3×#19962
C3×#19642
C3×#18892
C3×#18672
C3×#17992
#241403