Finite Group Databasebeta

← C3×#14029 #10632636

Subgroups — C3×#14029 #10632636

Order 768.

1470 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic
2C2×C3×#387C212yesmaximal
3C2×C3×#384C211yesmaximal, characteristic
4C2×C3×C4×C4⋊C4C211yesmaximal, characteristic
5C3×#1445C212yesmaximal
6C3×#1441C212yesmaximal
7C3×#1436C212yesmaximal
8C3×C4⋊#95C211yesmaximal, characteristic
9C3×C4⋊#95C211yesmaximal, characteristic
10C3×C4⋊#95C211yesmaximal, characteristic
11C3×C4×#95C211yesmaximal, characteristic
12#14029C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2212yes—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C42C2211yescharacteristic
21C22×C3×C42C2212yes—
22C22×C3×C42C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C3×#389—24no—
25C3×#387—28no—
26C3×#384C418yescomplemented
27C3×C4×C4⋊C4—24no—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×#389C2×C311yescharacteristic
41C2×#387C2×C312yes—
42C2×#384C2×C311yescharacteristic
43C2×C4×C4⋊C4C2×C311yescharacteristic
44#1445C2×C312yes—
45#1441C2×C312yes—
46#1436C2×C312yes—
47C4⋊#95C2×C311yescharacteristic
48C4⋊#95C2×C311yescharacteristic
49C4⋊#95C2×C311yescharacteristic
50C4×#95C2×C311yescharacteristic
51C23×C3×C4C2312yes—
52C23×C3×C4C2312yes—
53C23×C3×C4C2312yes—
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—24no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—24no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—22no—
68C2×C3×C4⋊C4—22no—
69C2×C3×C4⋊C4—22no—
70C2×C3×C4⋊C4—24no—
71C2×C3×C4⋊C4—24no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—42no—
76C2×C3×C4⋊C4—42no—
77C2×C3×C4⋊C4—42no—
78C2×C3×C4⋊C4C2×C418yes—
79C2×C3×C4⋊C4C2×C414yes—
80C2×C3×C4⋊C4C2×C414yes—
81C2×C3×C4⋊C4C2×C418yes—
82C2×C3×C4⋊C4D414yes—
83C2×C3×C42—22no—
84C2×C3×C42—22no—
85C2×C3×C42—22no—
86C2×C3×C42—22no—
87C2×C3×C42—24no—
88C2×C3×C42—24no—
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×C3×C42—42no—
93C2×C3×C42C2×C414yes—
94C2×C3×C42Q814yes—
95C3×#95—24no—
96C3×#95—24no—
97C3×#95—24no—
98C3×#95—24no—
99C3×#95—24no—
100C3×#95—22no—
101C3×#95—22no—
102C3×#95—24no—
103C3×#95—42no—
104C3×#95—42no—
105C3×#95D414yes—
106C3×#95Q814yes—
107C22×C4⋊C4C22×C311yescharacteristic
108C22×C4⋊C4C22×C312yes—
109C22×C4⋊C4C22×C311yescharacteristic
110C22×C4⋊C4C22×C311yescharacteristic
111C22×C4⋊C4C22×C312yes—
112C22×C4⋊C4C22×C311yescharacteristic
113C22×C4⋊C4C22×C312yes—
114C22×C42C22×C311yescharacteristic
115C22×C42C22×C312yes—
116C22×C42C22×C311yescharacteristic
117C22×C42C22×C311yescharacteristic
118#389—24no—
119#387—28no—
120#384C3×C418yescomplemented
121C4×C4⋊C4—24no—
122C2×#95C22×C311yescharacteristic
123C2×#95C22×C311yescharacteristic
124C2×#95C22×C312yes—
125C2×#95C22×C312yes—
126C2×#95C22×C312yes—
127C2×#95C22×C312yes—
128C2×#95C22×C312yes—
129C2×#95C22×C312yes—
130C2×#95C22×C312yes—
131C2×#95C22×C312yes—
132C2×#95C22×C311yescharacteristic
133C2×#95C22×C311yescharacteristic
134C24×C3C2411yescharacteristic
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
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—22no—
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—21no—
158C22×C3×C4—21no—
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—22no—
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—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
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×C4C22×C414yes—
191C22×C3×C4C22×C414yes—
192C22×C3×C4C22×C412yes—
193C22×C3×C4C22×C412yes—
194C22×C3×C4C22×C412yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D414yes—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×Q812yes—
201C22×C3×C4C2×Q812yes—
202C22×C3×C4C2×Q812yes—
203C22×C3×C4C2×Q812yes—
204C22×C3×C4C2×Q812yes—
205C22×C3×C4C2×Q812yes—
206C22×C3×C4#4112yes—
207C22×C3×C4#4112yes—
208C22×C3×C4#4112yes—
209C22×C3×C4#4112yes—
210C22×C3×C4#4112yes—
211C22×C3×C4#4112yes—
212C3×C4⋊C4—216no—
213C3×C4⋊C4—28no—
214C3×C4⋊C4—28no—
215C3×C4⋊C4—28no—
216C3×C4⋊C4—48no—
217C3×C4⋊C4—48no—
218C3×C4⋊C4—44no—
219C3×C42—28no—
220C3×C42—28no—
221C3×C42—48no—
222C3×C42—44no—
223C23×C4C23×C312yes—
224C23×C4C23×C312yes—
225C23×C4C23×C312yes—
226C23×C4C23×C312yes—
227C23×C4C23×C311yescharacteristic
228C23×C4C23×C311yescharacteristic
229C23×C4C23×C311yescharacteristic
230C23×C4C23×C311yescharacteristic
231C23×C4C23×C311yescharacteristic
232C23×C4C23×C311yescharacteristic
233C23×C4C23×C311yescharacteristic
234C2×C4⋊C4—22no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4C2×C3×C418yes—
251C2×C4⋊C4C2×C3×C414yes—
252C2×C4⋊C4C2×C3×C414yes—
253C2×C4⋊C4C2×C3×C418yes—
254C2×C4⋊C4C3×D414yes—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—22no—
259C2×C42—24no—
260C2×C42—24no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42—22no—
264C2×C42—42no—
265C2×C42C2×C3×C414yes—
266C2×C42C3×Q814yes—
267#95—24no—
268#95—24no—
269#95—24no—
270#95—24no—
271#95—24no—
272#95—22no—
273#95—22no—
274#95—24no—
275#95—42no—
276#95—42no—
277#95C3×D414yes—
278#95C3×Q814yes—
279C23×C3C23×C411yescharacteristic
280C23×C3C22×D411yescharacteristic
281C23×C3C22×D411yescharacteristic
282C23×C3C22×Q811yescharacteristic
283C23×C3C22×Q811yescharacteristic
284C23×C3C2×#4111yescharacteristic
285C23×C3C2×#4111yescharacteristic
286C23×C3C2×#4111yescharacteristic
287C23×C3C2×#4111yescharacteristic
288C23×C3C2×#4111yescharacteristic
289C23×C3C2×#4111yescharacteristic
290C23×C3H(5,𝔽2)11yescharacteristic
291C23×C3H(5,𝔽2)11yescharacteristic
292C23×C32−1+411yescharacteristic
293C23×C32−1+411yescharacteristic
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
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—24no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—42no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4#11714yes—
362C2×C3×C4C4×D414yes—
363C2×C3×C4C4×D414yes—
364C2×C3×C4C4×Q814yes—
365C2×C3×C4C4×Q814yes—
366C2×C3×C4C22⋊Q814yes—
367C2×C3×C4#12314yes—
368C2×C3×C4#12514yes—
369C2×C3×C4#12614yes—
370C2×C3×C4C4⋊Q814yes—
371C24C24×C311yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
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—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4C22×C3×C414yes—
428C22×C4C22×C3×C414yes—
429C22×C4C22×C3×C412yes—
430C22×C4C22×C3×C412yes—
431C22×C4C22×C3×C412yes—
432C22×C4C2×C3×D412yes—
433C22×C4C2×C3×D414yes—
434C22×C4C2×C3×D412yes—
435C22×C4C2×C3×D412yes—
436C22×C4C2×C3×D412yes—
437C22×C4C2×C3×Q812yes—
438C22×C4C2×C3×Q812yes—
439C22×C4C2×C3×Q812yes—
440C22×C4C2×C3×Q812yes—
441C22×C4C2×C3×Q812yes—
442C22×C4C2×C3×Q812yes—
443C22×C4C3×#4112yes—
444C22×C4C3×#4112yes—
445C22×C4C3×#4112yes—
446C22×C4C3×#4112yes—
447C22×C4C3×#4112yes—
448C22×C4C3×#4112yes—
449C4⋊C4—216no—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—48no—
454C4⋊C4—48no—
455C4⋊C4—44no—
456C42—28no—
457C42—28no—
458C42—48no—
459C42—44no—
460C22×C3C2×#11711yescharacteristic
461C22×C3C2×C4×D411yescharacteristic
462C22×C3C2×C4×D411yescharacteristic
463C22×C3C2×C4×Q811yescharacteristic
464C22×C3C2×C4×Q811yescharacteristic
465C22×C3#51811yescharacteristic
466C22×C3#51911yescharacteristic
467C22×C3C2×C22⋊Q811yescharacteristic
468C22×C3C2×#12311yescharacteristic
469C22×C3C2×#12511yescharacteristic
470C22×C3C2×#12611yescharacteristic
471C22×C3C2×C4⋊Q811yescharacteristic
472C22×C3#53211yescharacteristic
473C22×C3#53311yescharacteristic
474C22×C3#53311yescharacteristic
475C22×C3#54211yescharacteristic
476C22×C3#54211yescharacteristic
477C22×C3#54411yescharacteristic
478C22×C3#54411yescharacteristic
479C22×C3D4211yescharacteristic
480C22×C3#54711yescharacteristic
481C22×C3#54711yescharacteristic
482C22×C3#54711yescharacteristic
483C22×C3D4×Q811yescharacteristic
484C22×C3#55011yescharacteristic
485C22×C3#55011yescharacteristic
486C22×C3#55211yescharacteristic
487C22×C3#55211yescharacteristic
488C22×C3#55311yescharacteristic
489C22×C3#55311yescharacteristic
490C22×C3#55411yescharacteristic
491C22×C3#55411yescharacteristic
492C22×C3#55611yescharacteristic
493C22×C3#55711yescharacteristic
494C22×C3#55911yescharacteristic
495C3×C4—24no—
496C3×C4—24no—
497C3×C4—24no—
498C3×C4—44no—
499C3×C4—44no—
500C3×C4—44no—
501C3×C4—42no—
502C3×C4—42no—
503C3×C4—42no—
504C3×C4—82no—
505C3×C4#38718yescomplemented
506C23C23×C3×C411yescharacteristic
507C23C22×C3×D411yescharacteristic
508C23C22×C3×D411yescharacteristic
509C23C22×C3×Q811yescharacteristic
510C23C22×C3×Q811yescharacteristic
511C23C2×C3×#4111yescharacteristic
512C23C2×C3×#4111yescharacteristic
513C23C2×C3×#4111yescharacteristic
514C23C2×C3×#4111yescharacteristic
515C23C2×C3×#4111yescharacteristic
516C23C2×C3×#4111yescharacteristic
517C23C3×H(5,𝔽2)11yescharacteristic
518C23C3×H(5,𝔽2)11yescharacteristic
519C23C3×2−1+411yescharacteristic
520C23C3×2−1+411yescharacteristic
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
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—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4C3×#11714yes—
589C2×C4C3×C4×D414yes—
590C2×C4C3×C4×D414yes—
591C2×C4C3×C4×Q814yes—
592C2×C4C3×C4×Q814yes—
593C2×C4C3×C22⋊Q814yes—
594C2×C4C3×#12314yes—
595C2×C4C3×#12514yes—
596C2×C4C3×#12614yes—
597C2×C4C3×C4⋊Q814yes—
598C2×C3C2×#38711yescharacteristic
599C2×C3C4×C4⋊Q811yescharacteristic
600C2×C3#233111yescharacteristic
601C2×C3#234411yescharacteristic
602C2×C3#234511yescharacteristic
603C2×C3#236511yescharacteristic
604C2×C3#236611yescharacteristic
605C2×C3#242211yescharacteristic
606C2×C3#242311yescharacteristic
607C2×C3#244011yescharacteristic
608C2×C3#244111yescharacteristic
609C2×C3#251111yescharacteristic
610C2×C3#251211yescharacteristic
611C2×C3#255211yescharacteristic
612C2×C3#257011yescharacteristic
613C22C2×C3×#11711yescharacteristic
614C22C2×C3×C4×D411yescharacteristic
615C22C2×C3×C4×D411yescharacteristic
616C22C2×C3×C4×Q811yescharacteristic
617C22C2×C3×C4×Q811yescharacteristic
618C22C3×#51811yescharacteristic
619C22C3×#51911yescharacteristic
620C22C2×C3×C22⋊Q811yescharacteristic
621C22C2×C3×#12311yescharacteristic
622C22C2×C3×#12511yescharacteristic
623C22C2×C3×#12611yescharacteristic
624C22C2×C3×C4⋊Q811yescharacteristic
625C22C3×#53211yescharacteristic
626C22C3×#53311yescharacteristic
627C22C3×#53311yescharacteristic
628C22C3×#54211yescharacteristic
629C22C3×#54211yescharacteristic
630C22C3×#54411yescharacteristic
631C22C3×#54411yescharacteristic
632C22C3×D4211yescharacteristic
633C22C3×#54711yescharacteristic
634C22C3×#54711yescharacteristic
635C22C3×#54711yescharacteristic
636C22C3×D4×Q811yescharacteristic
637C22C3×#55011yescharacteristic
638C22C3×#55011yescharacteristic
639C22C3×#55211yescharacteristic
640C22C3×#55211yescharacteristic
641C22C3×#55311yescharacteristic
642C22C3×#55311yescharacteristic
643C22C3×#55411yescharacteristic
644C22C3×#55411yescharacteristic
645C22C3×#55611yescharacteristic
646C22C3×#55711yescharacteristic
647C22C3×#55911yescharacteristic
648C4—24no—
649C4—24no—
650C4—24no—
651C4—44no—
652C4—44no—
653C4—44no—
654C4—42no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4C3×#38718yescomplemented
659C3#1402911yescharacteristic, direct product factor, Sylow
660C2C2×C3×#38711yescharacteristic
661C2C3×C4×C4⋊Q811yescharacteristic
662C2C3×#233111yescharacteristic
663C2C3×#234411yescharacteristic
664C2C3×#234511yescharacteristic
665C2C3×#236511yescharacteristic
666C2C3×#236611yescharacteristic
667C2C3×#242211yescharacteristic
668C2C3×#242311yescharacteristic
669C2C3×#244011yescharacteristic
670C2C3×#244111yescharacteristic
671C2C3×#251111yescharacteristic
672C2C3×#251211yescharacteristic
673C2C3×#255211yescharacteristic
674C2C3×#257011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
12. #14029C3direct (N × H)
26. C3×#384C4semidirect
120. #384C3×C4semidirect
505. C3×C4#387semidirect
658. C4C3×#387semidirect
659. C3#14029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C2×C3×#3872
C2×C3×#3842
C2×C3×C4×C4⋊C42
C3×#14452
C3×#14412
C3×#14362
C3×C4⋊#952
C3×C4×#952
#140293