Finite Group Databasebeta

← C3×#15133 #10633740

Subgroups — C3×#15133 #10633740

Order 768.

1454 conjugacy classes of subgroups.

The subgroup lattice has 690 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×#384C211yesmaximal, characteristic
5C2×C3×C4×C4⋊C4C211yesmaximal, characteristic
6C3×#1441C212yesmaximal
7C3×#1441C212yesmaximal
8C3×#1441C212yesmaximal
9C3×C4⋊#95C211yesmaximal, characteristic
10C3×C4⋊#95C211yesmaximal, characteristic
11C3×C4⋊#95C211yesmaximal, characteristic
12#15133C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×C4⋊C4C2212yes—
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C3×#398—28no—
27C3×#389—24no—
28C3×#389—24no—
29C3×#384—24no—
30C3×C4×C4⋊C4—24no—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×#398C2×C312yes—
42C2×#389C2×C311yescharacteristic
43C2×#389C2×C311yescharacteristic
44C2×#384C2×C311yescharacteristic
45C2×C4×C4⋊C4C2×C311yescharacteristic
46#1441C2×C312yes—
47#1441C2×C312yes—
48#1441C2×C312yes—
49C4⋊#95C2×C311yescharacteristic
50C4⋊#95C2×C311yescharacteristic
51C4⋊#95C2×C311yescharacteristic
52C23×C3×C4C2312yes—
53C23×C3×C4C2312yes—
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
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—22no—
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—24no—
72C2×C3×C4⋊C4—24no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C4⋊C4—42no—
88C2×C3×C4⋊C4—42no—
89C2×C3×C4⋊C4D414yes—
90C2×C3×C4⋊C4D414yes—
91C2×C3×C4⋊C4Q814yes—
92C2×C3×C4⋊C4Q814yes—
93C2×C3×C42—22no—
94C2×C3×C42—22no—
95C2×C3×C42—22no—
96C2×C3×C42—22no—
97C2×C3×C42—22no—
98C2×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42D414yes—
101C2×C3×C42Q814yes—
102C3×#95—22no—
103C3×#95—22no—
104C3×#95—24no—
105C3×#95—24no—
106C3×#95—24no—
107C3×#95—24no—
108C3×#95—24no—
109C3×#95—42no—
110C3×#95—42no—
111C3×#95—42no—
112C22×C4⋊C4C22×C312yes—
113C22×C4⋊C4C22×C311yescharacteristic
114C22×C4⋊C4C22×C311yescharacteristic
115C22×C4⋊C4C22×C312yes—
116C22×C4⋊C4C22×C312yes—
117C22×C4⋊C4C22×C312yes—
118C22×C4⋊C4C22×C311yescharacteristic
119C22×C4⋊C4C22×C311yescharacteristic
120C22×C4⋊C4C22×C311yescharacteristic
121C22×C4⋊C4C22×C311yescharacteristic
122C22×C42C22×C311yescharacteristic
123C22×C42C22×C311yescharacteristic
124C22×C42C22×C311yescharacteristic
125#398—28no—
126#389—24no—
127#389—24no—
128#384—24no—
129C4×C4⋊C4—24no—
130C2×#95C22×C312yes—
131C2×#95C22×C312yes—
132C2×#95C22×C312yes—
133C2×#95C22×C311yescharacteristic
134C2×#95C22×C311yescharacteristic
135C2×#95C22×C312yes—
136C2×#95C22×C312yes—
137C2×#95C22×C312yes—
138C2×#95C22×C312yes—
139C2×#95C22×C312yes—
140C24×C3C2411yescharacteristic
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—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—22no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
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×C4—22no—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D414yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×Q812yes—
206C22×C3×C4C2×Q814yes—
207C22×C3×C4C2×Q812yes—
208C22×C3×C4C2×Q812yes—
209C22×C3×C4C2×Q812yes—
210C22×C3×C4C2×Q812yes—
211C22×C3×C4C2×Q812yes—
212C22×C3×C4C2×Q812yes—
213C22×C3×C4#4112yes—
214C22×C3×C4#4112yes—
215C22×C3×C4#4112yes—
216C22×C3×C4#4112yes—
217C22×C3×C4#4112yes—
218C3×C4⋊C4—28no—
219C3×C4⋊C4—28no—
220C3×C4⋊C4—28no—
221C3×C4⋊C4—28no—
222C3×C4⋊C4—48no—
223C3×C4⋊C4—48no—
224C3×C4⋊C4—48no—
225C3×C4⋊C4—48no—
226C3×C4⋊C4—44no—
227C3×C4⋊C4—44no—
228C3×C42—28no—
229C3×C42—28no—
230C3×C42—44no—
231C23×C4C23×C312yes—
232C23×C4C23×C312yes—
233C23×C4C23×C312yes—
234C23×C4C23×C311yescharacteristic
235C23×C4C23×C312yes—
236C23×C4C23×C311yescharacteristic
237C23×C4C23×C311yescharacteristic
238C23×C4C23×C311yescharacteristic
239C23×C4C23×C311yescharacteristic
240C23×C4C23×C311yescharacteristic
241C23×C4C23×C311yescharacteristic
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4C3×D414yes—
269C2×C4⋊C4C3×D414yes—
270C2×C4⋊C4C3×Q814yes—
271C2×C4⋊C4C3×Q814yes—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—22no—
279C2×C42C3×D414yes—
280C2×C42C3×Q814yes—
281#95—22no—
282#95—22no—
283#95—24no—
284#95—24no—
285#95—24no—
286#95—24no—
287#95—24no—
288#95—42no—
289#95—42no—
290#95—42no—
291C23×C3C22×D411yescharacteristic
292C23×C3C22×D411yescharacteristic
293C23×C3C22×D411yescharacteristic
294C23×C3C22×Q811yescharacteristic
295C23×C3C22×Q811yescharacteristic
296C23×C3C22×Q811yescharacteristic
297C23×C3C2×#4111yescharacteristic
298C23×C3C2×#4111yescharacteristic
299C23×C3C2×#4111yescharacteristic
300C23×C3C2×#4111yescharacteristic
301C23×C3C2×#4111yescharacteristic
302C23×C3H(5,𝔽2)11yescharacteristic
303C23×C3H(5,𝔽2)11yescharacteristic
304C23×C32−1+411yescharacteristic
305C23×C32−1+411yescharacteristic
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—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—24no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
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—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4#12114yes—
374C2×C3×C4#12114yes—
375C2×C3×C4C22⋊Q814yes—
376C2×C3×C4C22⋊Q814yes—
377C2×C3×C4C22⋊Q814yes—
378C2×C3×C4#12314yes—
379C2×C3×C4#12514yes—
380C2×C3×C4#12514yes—
381C2×C3×C4C4⋊Q814yes—
382C2×C3×C4C4⋊Q814yes—
383C24C24×C311yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4C2×C3×D412yes—
441C22×C4C2×C3×D414yes—
442C22×C4C2×C3×D412yes—
443C22×C4C2×C3×D412yes—
444C22×C4C2×C3×D412yes—
445C22×C4C2×C3×D412yes—
446C22×C4C2×C3×D412yes—
447C22×C4C2×C3×D412yes—
448C22×C4C2×C3×Q812yes—
449C22×C4C2×C3×Q814yes—
450C22×C4C2×C3×Q812yes—
451C22×C4C2×C3×Q812yes—
452C22×C4C2×C3×Q812yes—
453C22×C4C2×C3×Q812yes—
454C22×C4C2×C3×Q812yes—
455C22×C4C2×C3×Q812yes—
456C22×C4C3×#4112yes—
457C22×C4C3×#4112yes—
458C22×C4C3×#4112yes—
459C22×C4C3×#4112yes—
460C22×C4C3×#4112yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—48no—
466C4⋊C4—48no—
467C4⋊C4—48no—
468C4⋊C4—48no—
469C4⋊C4—44no—
470C4⋊C4—44no—
471C42—28no—
472C42—28no—
473C42—44no—
474C22×C3C2×#12111yescharacteristic
475C22×C3C2×#12111yescharacteristic
476C22×C3C2×C22⋊Q811yescharacteristic
477C22×C3C2×C22⋊Q811yescharacteristic
478C22×C3C2×C22⋊Q811yescharacteristic
479C22×C3C2×#12311yescharacteristic
480C22×C3C2×#12511yescharacteristic
481C22×C3C2×#12511yescharacteristic
482C22×C3C2×C4⋊Q811yescharacteristic
483C22×C3C2×C4⋊Q811yescharacteristic
484C22×C3#53211yescharacteristic
485C22×C3#53311yescharacteristic
486C22×C3#53311yescharacteristic
487C22×C3#53711yescharacteristic
488C22×C3#53711yescharacteristic
489C22×C3#54011yescharacteristic
490C22×C3#54111yescharacteristic
491C22×C3#54411yescharacteristic
492C22×C3#54411yescharacteristic
493C22×C3D4211yescharacteristic
494C22×C3#54611yescharacteristic
495C22×C3#54711yescharacteristic
496C22×C3#54811yescharacteristic
497C22×C3D4×Q811yescharacteristic
498C22×C3D4×Q811yescharacteristic
499C22×C3#55011yescharacteristic
500C22×C3#55211yescharacteristic
501C22×C3#55311yescharacteristic
502C22×C3#55411yescharacteristic
503C22×C3#55411yescharacteristic
504C22×C3#55611yescharacteristic
505C22×C3#55711yescharacteristic
506C22×C3#55711yescharacteristic
507C22×C3Q8211yescharacteristic
508C22×C3#55911yescharacteristic
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—44no—
516C3×C4—44no—
517C3×C4—82no—
518C3×C4—82no—
519C3×C4#39818yescomplemented
520C23C22×C3×D411yescharacteristic
521C23C22×C3×D411yescharacteristic
522C23C22×C3×D411yescharacteristic
523C23C22×C3×Q811yescharacteristic
524C23C22×C3×Q811yescharacteristic
525C23C22×C3×Q811yescharacteristic
526C23C2×C3×#4111yescharacteristic
527C23C2×C3×#4111yescharacteristic
528C23C2×C3×#4111yescharacteristic
529C23C2×C3×#4111yescharacteristic
530C23C2×C3×#4111yescharacteristic
531C23C3×H(5,𝔽2)11yescharacteristic
532C23C3×H(5,𝔽2)11yescharacteristic
533C23C3×2−1+411yescharacteristic
534C23C3×2−1+411yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
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×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4C3×#12114yes—
603C2×C4C3×#12114yes—
604C2×C4C3×C22⋊Q814yes—
605C2×C4C3×C22⋊Q814yes—
606C2×C4C3×C22⋊Q814yes—
607C2×C4C3×#12314yes—
608C2×C4C3×#12514yes—
609C2×C4C3×#12514yes—
610C2×C4C3×C4⋊Q814yes—
611C2×C4C3×C4⋊Q814yes—
612C2×C3C2×#39811yescharacteristic
613C2×C3#241611yescharacteristic
614C2×C3#241711yescharacteristic
615C2×C3#244511yescharacteristic
616C2×C3#244611yescharacteristic
617C2×C3#250611yescharacteristic
618C2×C3#250711yescharacteristic
619C2×C3#253811yescharacteristic
620C2×C3#255011yescharacteristic
621C2×C3#255111yescharacteristic
622C2×C3#255211yescharacteristic
623C2×C3#257011yescharacteristic
624C2×C3#258211yescharacteristic
625C2×C3#262911yescharacteristic
626C2×C3#285711yescharacteristic
627C22C2×C3×#12111yescharacteristic
628C22C2×C3×#12111yescharacteristic
629C22C2×C3×C22⋊Q811yescharacteristic
630C22C2×C3×C22⋊Q811yescharacteristic
631C22C2×C3×C22⋊Q811yescharacteristic
632C22C2×C3×#12311yescharacteristic
633C22C2×C3×#12511yescharacteristic
634C22C2×C3×#12511yescharacteristic
635C22C2×C3×C4⋊Q811yescharacteristic
636C22C2×C3×C4⋊Q811yescharacteristic
637C22C3×#53211yescharacteristic
638C22C3×#53311yescharacteristic
639C22C3×#53311yescharacteristic
640C22C3×#53711yescharacteristic
641C22C3×#53711yescharacteristic
642C22C3×#54011yescharacteristic
643C22C3×#54111yescharacteristic
644C22C3×#54411yescharacteristic
645C22C3×#54411yescharacteristic
646C22C3×D4211yescharacteristic
647C22C3×#54611yescharacteristic
648C22C3×#54711yescharacteristic
649C22C3×#54811yescharacteristic
650C22C3×D4×Q811yescharacteristic
651C22C3×D4×Q811yescharacteristic
652C22C3×#55011yescharacteristic
653C22C3×#55211yescharacteristic
654C22C3×#55311yescharacteristic
655C22C3×#55411yescharacteristic
656C22C3×#55411yescharacteristic
657C22C3×#55611yescharacteristic
658C22C3×#55711yescharacteristic
659C22C3×#55711yescharacteristic
660C22C3×Q8211yescharacteristic
661C22C3×#55911yescharacteristic
662C4—24no—
663C4—24no—
664C4—24no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—44no—
669C4—44no—
670C4—82no—
671C4—82no—
672C4C3×#39818yescomplemented
673C3#1513311yescharacteristic, direct product factor, Sylow
674C2C2×C3×#39811yescharacteristic
675C2C3×#241611yescharacteristic
676C2C3×#241711yescharacteristic
677C2C3×#244511yescharacteristic
678C2C3×#244611yescharacteristic
679C2C3×#250611yescharacteristic
680C2C3×#250711yescharacteristic
681C2C3×#253811yescharacteristic
682C2C3×#255011yescharacteristic
683C2C3×#255111yescharacteristic
684C2C3×#255211yescharacteristic
685C2C3×#257011yescharacteristic
686C2C3×#258211yescharacteristic
687C2C3×#262911yescharacteristic
688C2C3×#285711yescharacteristic
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. #15133C3direct (N × H)
519. C3×C4#398semidirect
672. C4C3×#398semidirect
673. C3#15133direct (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
C2×C3×C4×C4⋊C42
C3×#14412
C3×C4⋊#952
#151333