Finite Group Databasebeta

← C3×#23920 #10642527

Subgroups — C3×#23920 #10642527

Order 768.

2272 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
1C2×C3×#525C211yesmaximal, characteristic, complemented
2C22×C3×#121C211yesmaximal, characteristic, complemented
3C2×C3×#449C212yesmaximal, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5C2×C3×#447C211yesmaximal, characteristic, complemented
6C3×#2000C212yesmaximal, complemented
7C3×#1999C212yesmaximal, complemented
8C3×#1875C212yesmaximal, complemented
9C3×#1874C211yesmaximal, characteristic, complemented
10C3×#1872C211yesmaximal, characteristic, complemented
11C3×#1779C211yesmaximal, characteristic, complemented
12#23920C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic, complemented
14C23×C3×D4—21no—
15C23×C3×D4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C22×C3×SD16C2212yescomplemented
18C22×C3×D8C2212yescomplemented
19C3×#525—24no—
20C3×#525—24no—
21C2×C3×#123—21no—
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic, complemented
24C2×C3×#121—21no—
25C2×C3×#121—21no—
26C2×C3×#121—28no—
27C2×C3×#121C2212yes—
28C2×C3×#121C2212yes—
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic, complemented
31C2×C3×#120—21no—
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4—21no—
34C2×C3×#117C2211yescharacteristic, complemented
35C22×C3×C4⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4—21no—
37C3×#450—24no—
38C3×#449—28no—
39C3×#447—24no—
40C2×C3×#103C2212yescomplemented
41C2×C3×#102C2212yescomplemented
42C2×C3×#102C2212yescomplemented
43C2×C3×#102C2212yescomplemented
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2212yescomplemented
47C2×C3×C22⋊C8C2212yescomplemented
48C3×#340C2212yescomplemented
49C3×#340C2212yescomplemented
50C2×#525C2×C311yescharacteristic, complemented
51C22×#121C2×C311yescharacteristic, complemented
52C2×#449C2×C312yescomplemented
53C2×#450C2×C311yescharacteristic, complemented
54C2×#447C2×C311yescharacteristic, complemented
55#2000C2×C312yescomplemented
56#1999C2×C312yescomplemented
57#1875C2×C312yescomplemented
58#1874C2×C311yescharacteristic, complemented
59#1872C2×C311yescharacteristic, complemented
60#1779C2×C311yescharacteristic, complemented
61C25×C3—21no—
62C25×C3D411yescharacteristic
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—24no—
66C2×C3×#41—42no—
67C22×C3×Q8C2311yescharacteristic
68C22×C3×D4—28no—
69C22×C3×D4—22no—
70C22×C3×D4—22no—
71C22×C3×D4—21no—
72C22×C3×D4—21no—
73C22×C3×D4—21no—
74C22×C3×D4—24no—
75C22×C3×D4—21no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—42no—
79C22×C3×D4—44no—
80C22×C3×D4—44no—
81C22×C3×D4C2312yes—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—24no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—21no—
88C23×C3×C4—42no—
89C23×C3×C4D411yescharacteristic
90C23×C3×C4D411yescharacteristic
91C23×C3×C4D411yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C2×C3×SD16—24no—
96C2×C3×SD16—24no—
97C2×C3×SD16—42no—
98C2×C3×D8—24no—
99C2×C3×D8—24no—
100C2×C3×D8—42no—
101C22×C3×C8C2312yes—
102C22×C3×C8C2312yes—
103C3×#123—28no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8D414yescomplemented
108C3×#121—28no—
109C3×#121—28no—
110C3×#121—24no—
111C3×#121—22no—
112C3×#121—24no—
113C3×#121—22no—
114C3×#121—24no—
115C3×#121—22no—
116C3×#121D418yescomplemented
117C3×#121D414yescomplemented
118C3×#120—28no—
119C3×C4×D4—28no—
120C3×C4×D4—28no—
121C3×#117—22no—
122C3×#117—22no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—24no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—28no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C42—21no—
139C3×#103—24no—
140C3×#102—24no—
141C3×#102—24no—
142C3×#102—24no—
143C3×C22⋊C8—22no—
144C3×C22⋊C8—22no—
145C3×C22⋊C8—24no—
146C3×C22⋊C8—42no—
147C22×#41C22×C311yescharacteristic, complemented
148C23×D4—21no—
149C23×D4C22×C311yescharacteristic
150C24×C4C22×C311yescharacteristic
151C22×SD16C22×C312yescomplemented
152C22×D8C22×C312yescomplemented
153#525—24no—
154#525—24no—
155C2×#123—21no—
156C2×C22⋊Q8C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic, complemented
158C2×#121—21no—
159C2×#121—21no—
160C2×#121—28no—
161C2×#121C22×C312yes—
162C2×#121C22×C311yescharacteristic
163C2×#121C22×C312yes—
164C2×#121C22×C311yescharacteristic, complemented
165C2×#120—21no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×#117C22×C311yescharacteristic, complemented
169C22×C4⋊C4C22×C311yescharacteristic
170C22×C22⋊C4—21no—
171#450—24no—
172#449—28no—
173#447—24no—
174C2×#103C22×C312yescomplemented
175C2×#102C22×C312yescomplemented
176C2×#102C22×C312yescomplemented
177C2×#102C22×C312yescomplemented
178C2×C22⋊C8C22×C311yescharacteristic
179C2×C22⋊C8C22×C311yescharacteristic
180C2×C22⋊C8C22×C312yescomplemented
181C2×C22⋊C8C22×C312yescomplemented
182#340C22×C312yescomplemented
183#340C22×C312yescomplemented
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—24no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—21no—
192C24×C3—41no—
193C24×C3—41no—
194C24×C3—42no—
195C24×C3—42no—
196C24×C3—42no—
197C24×C3—42no—
198C24×C3—42no—
199C24×C3—42no—
200C24×C3C2×D411yescharacteristic
201C24×C3C2×D411yescharacteristic
202C24×C3C2×D411yescharacteristic
203C3×#41—48no—
204C3×#41—48no—
205C2×C3×Q8—21no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8C2×D412yescomplemented
209C2×C3×D4—24no—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—28no—
213C2×C3×D4—24no—
214C2×C3×D4—28no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—48no—
224C2×C3×D4—48no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—432no—
228C2×C3×D4—44no—
229C2×C3×D4—44no—
230C2×C3×D4—44no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—44no—
237C2×C3×D4—42no—
238C2×C3×D4C2×D414yes—
239C2×C3×D4C2×D412yescomplemented
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—41no—
262C22×C3×C4—41no—
263C22×C3×C4—41no—
264C22×C3×C4—48no—
265C22×C3×C4—48no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2411yescharacteristic
277C3×SD16—48no—
278C3×D8—48no—
279C2×C3×C8—22no—
280C2×C3×C8—22no—
281C2×C3×C8—22no—
282C2×C3×C8—22no—
283C2×C3×C8—22no—
284C2×C3×C8—22no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—22no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D414yes—
292C3×C4⋊C4C2×D412yescomplemented
293C3×C4⋊C4C2×D412yescomplemented
294C3×C22⋊C4—28no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—28no—
300C3×C22⋊C4—24no—
301C3×C42—24no—
302C25—21no—
303C25C3×D411yescharacteristic
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—24no—
307C2×#41—42no—
308C22×Q8C23×C311yescharacteristic
309C22×D4—28no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—24no—
316C22×D4—21no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—42no—
320C22×D4—44no—
321C22×D4—44no—
322C22×D4C23×C312yes—
323C22×D4C23×C311yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—24no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4C3×D411yescharacteristic
331C23×C4C3×D411yescharacteristic
332C23×C4C3×D411yescharacteristic
333C23×C4C23×C311yescharacteristic
334C23×C4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C2×SD16—24no—
337C2×SD16—24no—
338C2×SD16—42no—
339C2×D8—24no—
340C2×D8—24no—
341C2×D8—42no—
342C22×C8C23×C312yes—
343C22×C8C23×C312yes—
344#123—28no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8C3×D414yescomplemented
349#121—28no—
350#121—28no—
351#121—24no—
352#121—22no—
353#121—24no—
354#121—22no—
355#121—24no—
356#121—22no—
357#121C3×D418yescomplemented
358#121C3×D414yescomplemented
359#120—28no—
360C4×D4—28no—
361C4×D4—28no—
362#117—22no—
363#117—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4C23×C312yes—
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C22⋊C4—28no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42—21no—
380#103—24no—
381#102—24no—
382#102—24no—
383#102—24no—
384C22⋊C8—22no—
385C22⋊C8—22no—
386C22⋊C8—24no—
387C22⋊C8—42no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—28no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—24no—
407C23×C3—44no—
408C23×C3—44no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—44no—
412C23×C3—48no—
413C23×C3—48no—
414C23×C3—48no—
415C23×C3—44no—
416C23×C3—41no—
417C23×C3—42no—
418C23×C3—41no—
419C23×C3—42no—
420C23×C3—41no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—42no—
428C23×C3—84no—
429C23×C3—84no—
430C23×C3—84no—
431C23×C3—84no—
432C23×C3#12012yes—
433C23×C3#12012yes—
434C23×C3#13512yes—
435C23×C3AGL(1,ℤ/8)12yes—
436C23×C3AGL(1,ℤ/8)12yes—
437C23×C3C22×D411yescharacteristic
438C3×Q8—24no—
439C3×Q8—42no—
440C3×D4—24no—
441C3×D4—24no—
442C3×D4—24no—
443C3×D4—48no—
444C3×D4—48no—
445C3×D4—416no—
446C3×D4—416no—
447C3×D4—48no—
448C3×D4—48no—
449C3×D4—42no—
450C3×D4—42no—
451C3×D4—42no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—24no—
466C2×C3×C4—21no—
467C2×C3×C4—44no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4—48no—
471C2×C3×C4—48no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—42no—
481C2×C3×C4—42no—
482C2×C3×C4#12012yes—
483C2×C3×C4#12012yes—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4H(5,𝔽2)12yes—
488C3×C8—42no—
489C3×C8—42no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—24no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—22no—
498C24—41no—
499C24—41no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—42no—
506C24C2×C3×D411yescharacteristic
507C24C2×C3×D411yescharacteristic
508C24C2×C3×D411yescharacteristic
509#41—48no—
510#41—48no—
511C2×Q8—21no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8C2×C3×D412yescomplemented
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—28no—
519C2×D4—24no—
520C2×D4—28no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—42no—
532C2×D4—432no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4C2×C3×D414yes—
545C2×D4C2×C3×D412yescomplemented
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4C2×C3×D411yescharacteristic
577C22×C4C2×C3×D411yescharacteristic
578C22×C4C2×C3×D411yescharacteristic
579C22×C4C2×C3×D414yes—
580C22×C4C2×C3×D412yes—
581C22×C4C2×C3×D412yes—
582C22×C4C24×C311yescharacteristic
583SD16—48no—
584D8—48no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4C2×C3×D414yes—
598C4⋊C4C2×C3×D412yescomplemented
599C4⋊C4C2×C3×D412yescomplemented
600C22⋊C4—28no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—28no—
606C22⋊C4—24no—
607C42—24no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—416no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—42no—
630C22×C3—44no—
631C22×C3—42no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—42no—
635C22×C3—816no—
636C22×C3—81no—
637C22×C3—82no—
638C22×C3—81no—
639C22×C3—82no—
640C22×C3—82no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—82no—
644C22×C3#44914yescomplemented
645C22×C3C2×#12011yescharacteristic
646C22×C3C2×#12011yescharacteristic
647C22×C3#53411yescharacteristic
648C22×C3C2×#13511yescharacteristic
649C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
650C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
651C22×C3#57511yescharacteristic
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—44no—
658C3×C4—42no—
659C3×C4D4212yes—
660C3×C4D4212yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—28no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—24no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—48no—
686C23—48no—
687C23—48no—
688C23—44no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—41no—
700C23—42no—
701C23—84no—
702C23—84no—
703C23—84no—
704C23—84no—
705C23C3×#12012yes—
706C23C3×#12012yes—
707C23C3×#13512yes—
708C23C3×AGL(1,ℤ/8)12yes—
709C23C3×AGL(1,ℤ/8)12yes—
710C23C22×C3×D411yescharacteristic
711Q8—24no—
712Q8—42no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—48no—
717D4—416no—
718D4—416no—
719D4—48no—
720D4—48no—
721D4—48no—
722D4—42no—
723D4—42no—
724D4—42no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—21no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4C3×#12012yes—
756C2×C4C3×#12012yes—
757C2×C4C22×C3×D412yes—
758C2×C4C22×C3×D411yescharacteristic
759C2×C4C22×C3×D411yescharacteristic
760C2×C4C3×H(5,𝔽2)12yes—
761C8—42no—
762C8—42no—
763C2×C3—24no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—82no—
767C2×C3—84no—
768C2×C3#240311yescharacteristic
769C2×C3C2×#44911yescharacteristic
770C2×C3#300211yescharacteristic
771C2×C3#300311yescharacteristic
772C2×C3#300611yescharacteristic
773C2×C3#318811yescharacteristic
774C2×C3#319411yescharacteristic
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—416no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—42no—
802C22—816no—
803C22—82no—
804C22—81no—
805C22—82no—
806C22—81no—
807C22—82no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22C3×#44914yescomplemented
812C22C2×C3×#12011yescharacteristic
813C22C2×C3×#12011yescharacteristic
814C22C3×#53411yescharacteristic
815C22C2×C3×#13511yescharacteristic
816C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
817C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
818C22C3×#57511yescharacteristic
819C4—22no—
820C4—22no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—42no—
826C4C3×D4212yes—
827C4C3×D4212yes—
828C3#2392011yescharacteristic, direct product factor, Sylow
829C2—24no—
830C2—42no—
831C2—42no—
832C2—84no—
833C2—82no—
834C2C3×#240311yescharacteristic
835C2C2×C3×#44911yescharacteristic
836C2C3×#300211yescharacteristic
837C2C3×#300311yescharacteristic
838C2C3×#300611yescharacteristic
839C2C3×#318811yescharacteristic
840C2C3×#319411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#525C2semidirect
2. C22×C3×#121C2semidirect
3. C2×C3×#449C2semidirect
4. C2×C3×#450C2semidirect
5. C2×C3×#447C2semidirect
6. C3×#2000C2semidirect
7. C3×#1999C2semidirect
8. C3×#1875C2semidirect
9. C3×#1874C2semidirect
10. C3×#1872C2semidirect
11. C3×#1779C2semidirect
12. #23920C3direct (N × H)
13. C22×C3×#41C22semidirect
17. C22×C3×SD16C22semidirect
18. C22×C3×D8C22semidirect
23. C2×C3×C22⋊Q8C22semidirect
30. C2×C3×#121C22semidirect
34. C2×C3×#117C22semidirect
40. C2×C3×#103C22semidirect
41. C2×C3×#102C22semidirect
42. C2×C3×#102C22semidirect
43. C2×C3×#102C22semidirect
46. C2×C3×C22⋊C8C22semidirect
47. C2×C3×C22⋊C8C22semidirect
48. C3×#340C22semidirect
49. C3×#340C22semidirect
50. C2×#525C2×C3semidirect
51. C22×#121C2×C3semidirect
52. C2×#449C2×C3semidirect
53. C2×#450C2×C3semidirect
54. C2×#447C2×C3semidirect
55. #2000C2×C3semidirect
56. #1999C2×C3semidirect
57. #1875C2×C3semidirect
58. #1874C2×C3semidirect
59. #1872C2×C3semidirect
60. #1779C2×C3semidirect
107. C3×C22⋊Q8D4semidirect
116. C3×#121D4semidirect
117. C3×#121D4semidirect
147. C22×#41C22×C3semidirect
151. C22×SD16C22×C3semidirect
152. C22×D8C22×C3semidirect
157. C2×C22⋊Q8C22×C3semidirect
164. C2×#121C22×C3semidirect
168. C2×#117C22×C3semidirect
174. C2×#103C22×C3semidirect
175. C2×#102C22×C3semidirect
176. C2×#102C22×C3semidirect
177. C2×#102C22×C3semidirect
180. C2×C22⋊C8C22×C3semidirect
181. C2×C22⋊C8C22×C3semidirect
182. #340C22×C3semidirect
183. #340C22×C3semidirect
208. C2×C3×Q8C2×D4semidirect
239. C2×C3×D4C2×D4semidirect
292. C3×C4⋊C4C2×D4semidirect
293. C3×C4⋊C4C2×D4semidirect
348. C22⋊Q8C3×D4semidirect
357. #121C3×D4semidirect
358. #121C3×D4semidirect
514. C2×Q8C2×C3×D4semidirect
545. C2×D4C2×C3×D4semidirect
598. C4⋊C4C2×C3×D4semidirect
599. C4⋊C4C2×C3×D4semidirect
644. C22×C3#449semidirect
811. C22C3×#449semidirect
828. C3#23920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C22×C3×#1212
C2×C3×#4492
C2×C3×#4502
C2×C3×#4472
C3×#20002
C3×#19992
C3×#18752
C3×#18742
C3×#18722
C3×#17792
#239203