Finite Group Databasebeta

← C3×#15137 #10633744

Subgroups — C3×#15137 #10633744

Order 768.

1438 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#398C212yesmaximal
2C2×C3×#389C211yesmaximal, characteristic
3C2×C3×#389C211yesmaximal, characteristic
4C2×C3×#389C211yesmaximal, characteristic
5C2×C3×#384C211yesmaximal, characteristic
6C3×#1444C212yesmaximal
7C3×#1442C212yesmaximal
8C3×#1441C212yesmaximal
9C3×C4⋊#95C211yesmaximal, characteristic
10C3×C4⋊#95C211yesmaximal, characteristic
11C3×C4×#95C211yesmaximal, characteristic
12#15137C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2212yes—
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C3×#398—28no—
26C3×#389—24no—
27C3×#389—24no—
28C3×#389—24no—
29C3×#384—24no—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×#398C2×C312yes—
42C2×#389C2×C311yescharacteristic
43C2×#389C2×C311yescharacteristic
44C2×#389C2×C311yescharacteristic
45C2×#384C2×C311yescharacteristic
46#1444C2×C312yes—
47#1442C2×C312yes—
48#1441C2×C312yes—
49C4⋊#95C2×C311yescharacteristic
50C4⋊#95C2×C311yescharacteristic
51C4×#95C2×C311yescharacteristic
52C23×C3×C4C2312yes—
53C23×C3×C4C2311yescharacteristic
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—22no—
68C2×C3×C4⋊C4—22no—
69C2×C3×C4⋊C4—24no—
70C2×C3×C4⋊C4—24no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—24no—
73C2×C3×C4⋊C4—24no—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—42no—
83C2×C3×C4⋊C4—42no—
84C2×C3×C4⋊C4—42no—
85C2×C3×C4⋊C4—42no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C4⋊C4D414yes—
88C2×C3×C4⋊C4D414yes—
89C2×C3×C4⋊C4Q814yes—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×C3×C42—22no—
93C2×C3×C42—22no—
94C2×C3×C42—22no—
95C2×C3×C42—22no—
96C2×C3×C42—22no—
97C2×C3×C42—22no—
98C2×C3×C42Q814yes—
99C3×#95—24no—
100C3×#95—24no—
101C3×#95—24no—
102C3×#95—24no—
103C3×#95—24no—
104C3×#95—22no—
105C3×#95—24no—
106C3×#95—22no—
107C3×#95—42no—
108C3×#95D414yes—
109C3×#95Q814yes—
110C22×C4⋊C4C22×C311yescharacteristic
111C22×C4⋊C4C22×C312yes—
112C22×C4⋊C4C22×C312yes—
113C22×C4⋊C4C22×C312yes—
114C22×C4⋊C4C22×C312yes—
115C22×C4⋊C4C22×C312yes—
116C22×C4⋊C4C22×C311yescharacteristic
117C22×C4⋊C4C22×C311yescharacteristic
118C22×C4⋊C4C22×C311yescharacteristic
119C22×C42C22×C311yescharacteristic
120C22×C42C22×C311yescharacteristic
121C22×C42C22×C311yescharacteristic
122#398—28no—
123#389—24no—
124#389—24no—
125#389—24no—
126#384—24no—
127C2×#95C22×C312yes—
128C2×#95C22×C312yes—
129C2×#95C22×C311yescharacteristic
130C2×#95C22×C311yescharacteristic
131C2×#95C22×C312yes—
132C2×#95C22×C312yes—
133C2×#95C22×C312yes—
134C2×#95C22×C312yes—
135C2×#95C22×C312yes—
136C2×#95C22×C311yescharacteristic
137C2×#95C22×C311yescharacteristic
138C24×C3C2411yescharacteristic
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×D414yes—
198C22×C3×C4C2×D414yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×Q812yes—
204C22×C3×C4C2×Q812yes—
205C22×C3×C4C2×Q814yes—
206C22×C3×C4C2×Q812yes—
207C22×C3×C4C2×Q812yes—
208C22×C3×C4C2×Q812yes—
209C22×C3×C4C2×Q812yes—
210C22×C3×C4C2×Q812yes—
211C22×C3×C4#4112yes—
212C22×C3×C4#4112yes—
213C22×C3×C4#4112yes—
214C22×C3×C4#4112yes—
215C22×C3×C4#4112yes—
216C3×C4⋊C4—28no—
217C3×C4⋊C4—28no—
218C3×C4⋊C4—28no—
219C3×C4⋊C4—48no—
220C3×C4⋊C4—48no—
221C3×C4⋊C4—48no—
222C3×C4⋊C4—48no—
223C3×C4⋊C4—48no—
224C3×C4⋊C4—44no—
225C3×C42—28no—
226C3×C42—44no—
227C3×C42—44no—
228C23×C4C23×C312yes—
229C23×C4C23×C312yes—
230C23×C4C23×C311yescharacteristic
231C23×C4C23×C312yes—
232C23×C4C23×C311yescharacteristic
233C23×C4C23×C312yes—
234C23×C4C23×C311yescharacteristic
235C23×C4C23×C311yescharacteristic
236C23×C4C23×C311yescharacteristic
237C23×C4C23×C311yescharacteristic
238C23×C4C23×C311yescharacteristic
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4C3×D414yes—
264C2×C4⋊C4C3×D414yes—
265C2×C4⋊C4C3×Q814yes—
266C2×C42—22no—
267C2×C42—22no—
268C2×C42—22no—
269C2×C42—22no—
270C2×C42—22no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42C3×Q814yes—
275#95—24no—
276#95—24no—
277#95—24no—
278#95—24no—
279#95—24no—
280#95—22no—
281#95—24no—
282#95—22no—
283#95—42no—
284#95C3×D414yes—
285#95C3×Q814yes—
286C23×C3C22×D411yescharacteristic
287C23×C3C22×D411yescharacteristic
288C23×C3C22×D411yescharacteristic
289C23×C3C22×Q811yescharacteristic
290C23×C3C22×Q811yescharacteristic
291C23×C3C22×Q811yescharacteristic
292C23×C3C2×#4111yescharacteristic
293C23×C3C2×#4111yescharacteristic
294C23×C3C2×#4111yescharacteristic
295C23×C3C2×#4111yescharacteristic
296C23×C3C2×#4111yescharacteristic
297C23×C3H(5,𝔽2)11yescharacteristic
298C23×C3H(5,𝔽2)11yescharacteristic
299C23×C32−1+411yescharacteristic
300C23×C32−1+411yescharacteristic
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—24no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—24no—
332C2×C3×C4—22no—
333C2×C3×C4—24no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—42no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4#12114yes—
370C2×C3×C4C22⋊Q814yes—
371C2×C3×C4C22⋊Q814yes—
372C2×C3×C4#12314yes—
373C2×C3×C4#12514yes—
374C2×C3×C4#12514yes—
375C2×C3×C4#12514yes—
376C2×C3×C4C4⋊Q814yes—
377C2×C3×C4C4⋊Q814yes—
378C24C24×C311yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4C2×C3×D412yes—
437C22×C4C2×C3×D414yes—
438C22×C4C2×C3×D414yes—
439C22×C4C2×C3×D412yes—
440C22×C4C2×C3×D412yes—
441C22×C4C2×C3×D412yes—
442C22×C4C2×C3×D412yes—
443C22×C4C2×C3×Q812yes—
444C22×C4C2×C3×Q812yes—
445C22×C4C2×C3×Q814yes—
446C22×C4C2×C3×Q812yes—
447C22×C4C2×C3×Q812yes—
448C22×C4C2×C3×Q812yes—
449C22×C4C2×C3×Q812yes—
450C22×C4C2×C3×Q812yes—
451C22×C4C3×#4112yes—
452C22×C4C3×#4112yes—
453C22×C4C3×#4112yes—
454C22×C4C3×#4112yes—
455C22×C4C3×#4112yes—
456C4⋊C4—28no—
457C4⋊C4—28no—
458C4⋊C4—28no—
459C4⋊C4—48no—
460C4⋊C4—48no—
461C4⋊C4—48no—
462C4⋊C4—48no—
463C4⋊C4—48no—
464C4⋊C4—44no—
465C42—28no—
466C42—44no—
467C42—44no—
468C22×C3C2×#12111yescharacteristic
469C22×C3C2×C22⋊Q811yescharacteristic
470C22×C3C2×C22⋊Q811yescharacteristic
471C22×C3C2×#12311yescharacteristic
472C22×C3C2×#12511yescharacteristic
473C22×C3C2×#12511yescharacteristic
474C22×C3C2×#12511yescharacteristic
475C22×C3C2×C4⋊Q811yescharacteristic
476C22×C3C2×C4⋊Q811yescharacteristic
477C22×C3#53211yescharacteristic
478C22×C3#53211yescharacteristic
479C22×C3#53311yescharacteristic
480C22×C3#53311yescharacteristic
481C22×C3#54011yescharacteristic
482C22×C3#54111yescharacteristic
483C22×C3#54211yescharacteristic
484C22×C3#54211yescharacteristic
485C22×C3#54411yescharacteristic
486C22×C3#54411yescharacteristic
487C22×C3D4211yescharacteristic
488C22×C3D4211yescharacteristic
489C22×C3#54611yescharacteristic
490C22×C3#54711yescharacteristic
491C22×C3#54711yescharacteristic
492C22×C3#54811yescharacteristic
493C22×C3D4×Q811yescharacteristic
494C22×C3D4×Q811yescharacteristic
495C22×C3D4×Q811yescharacteristic
496C22×C3#55011yescharacteristic
497C22×C3#55211yescharacteristic
498C22×C3#55311yescharacteristic
499C22×C3#55411yescharacteristic
500C22×C3#55411yescharacteristic
501C22×C3#55711yescharacteristic
502C22×C3Q8211yescharacteristic
503C3×C4—24no—
504C3×C4—24no—
505C3×C4—44no—
506C3×C4—42no—
507C3×C4—42no—
508C3×C4—44no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—44no—
512C3×C4—82no—
513C3×C4#39818yescomplemented
514C23C22×C3×D411yescharacteristic
515C23C22×C3×D411yescharacteristic
516C23C22×C3×D411yescharacteristic
517C23C22×C3×Q811yescharacteristic
518C23C22×C3×Q811yescharacteristic
519C23C22×C3×Q811yescharacteristic
520C23C2×C3×#4111yescharacteristic
521C23C2×C3×#4111yescharacteristic
522C23C2×C3×#4111yescharacteristic
523C23C2×C3×#4111yescharacteristic
524C23C2×C3×#4111yescharacteristic
525C23C3×H(5,𝔽2)11yescharacteristic
526C23C3×H(5,𝔽2)11yescharacteristic
527C23C3×2−1+411yescharacteristic
528C23C3×2−1+411yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4C3×#12114yes—
598C2×C4C3×C22⋊Q814yes—
599C2×C4C3×C22⋊Q814yes—
600C2×C4C3×#12314yes—
601C2×C4C3×#12514yes—
602C2×C4C3×#12514yes—
603C2×C4C3×#12514yes—
604C2×C4C3×C4⋊Q814yes—
605C2×C4C3×C4⋊Q814yes—
606C2×C3C2×#39811yescharacteristic
607C2×C3#242211yescharacteristic
608C2×C3#242311yescharacteristic
609C2×C3#242811yescharacteristic
610C2×C3#242911yescharacteristic
611C2×C3#244011yescharacteristic
612C2×C3#244211yescharacteristic
613C2×C3#245111yescharacteristic
614C2×C3#245211yescharacteristic
615C2×C3#250611yescharacteristic
616C2×C3#250711yescharacteristic
617C2×C3#255111yescharacteristic
618C2×C3#255211yescharacteristic
619C2×C3#264711yescharacteristic
620C2×C3#285911yescharacteristic
621C22C2×C3×#12111yescharacteristic
622C22C2×C3×C22⋊Q811yescharacteristic
623C22C2×C3×C22⋊Q811yescharacteristic
624C22C2×C3×#12311yescharacteristic
625C22C2×C3×#12511yescharacteristic
626C22C2×C3×#12511yescharacteristic
627C22C2×C3×#12511yescharacteristic
628C22C2×C3×C4⋊Q811yescharacteristic
629C22C2×C3×C4⋊Q811yescharacteristic
630C22C3×#53211yescharacteristic
631C22C3×#53211yescharacteristic
632C22C3×#53311yescharacteristic
633C22C3×#53311yescharacteristic
634C22C3×#54011yescharacteristic
635C22C3×#54111yescharacteristic
636C22C3×#54211yescharacteristic
637C22C3×#54211yescharacteristic
638C22C3×#54411yescharacteristic
639C22C3×#54411yescharacteristic
640C22C3×D4211yescharacteristic
641C22C3×D4211yescharacteristic
642C22C3×#54611yescharacteristic
643C22C3×#54711yescharacteristic
644C22C3×#54711yescharacteristic
645C22C3×#54811yescharacteristic
646C22C3×D4×Q811yescharacteristic
647C22C3×D4×Q811yescharacteristic
648C22C3×D4×Q811yescharacteristic
649C22C3×#55011yescharacteristic
650C22C3×#55211yescharacteristic
651C22C3×#55311yescharacteristic
652C22C3×#55411yescharacteristic
653C22C3×#55411yescharacteristic
654C22C3×#55711yescharacteristic
655C22C3×Q8211yescharacteristic
656C4—24no—
657C4—24no—
658C4—44no—
659C4—42no—
660C4—42no—
661C4—44no—
662C4—42no—
663C4—42no—
664C4—44no—
665C4—82no—
666C4C3×#39818yescomplemented
667C3#1513711yescharacteristic, direct product factor, Sylow
668C2C2×C3×#39811yescharacteristic
669C2C3×#242211yescharacteristic
670C2C3×#242311yescharacteristic
671C2C3×#242811yescharacteristic
672C2C3×#242911yescharacteristic
673C2C3×#244011yescharacteristic
674C2C3×#244211yescharacteristic
675C2C3×#245111yescharacteristic
676C2C3×#245211yescharacteristic
677C2C3×#250611yescharacteristic
678C2C3×#250711yescharacteristic
679C2C3×#255111yescharacteristic
680C2C3×#255211yescharacteristic
681C2C3×#264711yescharacteristic
682C2C3×#285911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
12. #15137C3direct (N × H)
513. C3×C4#398semidirect
666. C4C3×#398semidirect
667. C3#15137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3982
C2×C3×#3892
C2×C3×#3842
C3×#14442
C3×#14422
C3×#14412
C3×C4⋊#952
C3×C4×#952
#151373