Finite Group Databasebeta

← C3×#15138 #10633745

Subgroups — C3×#15138 #10633745

Order 768.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C212yesmaximal, complemented
2C2×C3×#390C211yesmaximal, characteristic
3C2×C3×#390C211yesmaximal, characteristic
4C2×C3×#390C211yesmaximal, characteristic
5C2×C3×#389C211yesmaximal, characteristic, complemented
6C3×#1440C212yesmaximal, complemented
7C3×#1440C212yesmaximal, complemented
8C3×#1439C212yesmaximal, complemented
9C3×C4⋊#95C211yesmaximal, characteristic, complemented
10C3×C4⋊#95C211yesmaximal, characteristic, complemented
11C3×C4×#95C211yesmaximal, characteristic, complemented
12#15138C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2212yes—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C42C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C22×C3×C42C2211yescharacteristic
27C3×#397—28no—
28C3×#390—24no—
29C3×#390—24no—
30C3×#390—24no—
31C3×#389—24no—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2211yescharacteristic
41C2×#397C2×C312yescomplemented
42C2×#390C2×C311yescharacteristic
43C2×#390C2×C311yescharacteristic
44C2×#390C2×C311yescharacteristic
45C2×#389C2×C311yescharacteristic, complemented
46#1440C2×C312yescomplemented
47#1440C2×C312yescomplemented
48#1439C2×C312yescomplemented
49C4⋊#95C2×C311yescharacteristic, complemented
50C4⋊#95C2×C311yescharacteristic, complemented
51C4×#95C2×C311yescharacteristic, complemented
52C25×C3C2312yes—
53C22×C3×D4—22no—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4D414yes—
60C23×C3×C4C2312yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2312yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—24no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—42no—
81C2×C3×C4⋊C4D414yes—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×C3×C42—22no—
103C2×C3×C42—22no—
104C2×C3×C42—22no—
105C2×C3×C42—22no—
106C2×C3×C42—22no—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C3×#95—24no—
110C3×#95—24no—
111C3×#95—24no—
112C3×#95—22no—
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—42no—
116C3×#95—42no—
117C3×#95D414yescomplemented
118C23×D4C22×C311yescharacteristic
119C22×C4⋊C4C22×C311yescharacteristic
120C22×C4⋊C4C22×C311yescharacteristic
121C22×C4⋊C4C22×C312yes—
122C22×C4⋊C4C22×C311yescharacteristic
123C22×C22⋊C4C22×C312yes—
124C22×C22⋊C4C22×C312yes—
125C22×C22⋊C4C22×C312yes—
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C42C22×C311yescharacteristic
130C22×C42C22×C311yescharacteristic
131C22×C42C22×C311yescharacteristic
132#397—28no—
133#390—24no—
134#390—24no—
135#390—24no—
136#389—24no—
137C2×#95C22×C312yes—
138C2×#95C22×C312yes—
139C2×#95C22×C311yescharacteristic
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C311yescharacteristic
142C2×#95C22×C312yes—
143C2×#95C22×C312yes—
144C2×#95C22×C312yes—
145C2×#95C22×C311yescharacteristic
146C24×C3—22no—
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3C2×D414yes—
161C24×C3C2411yescharacteristic
162C2×C3×D4—28no—
163C2×C3×D4—28no—
164C2×C3×D4—28no—
165C2×C3×D4—44no—
166C2×C3×D4—44no—
167C2×C3×D4—44no—
168C2×C3×D4—44no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4C2×D414yes—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4#4112yes—
232C22×C3×C4#4112yes—
233C22×C3×C4#4112yes—
234C22×C3×C4#4112yes—
235C22×C3×C4#4112yes—
236C22×C3×C4#4112yes—
237C22×C3×C4#4112yes—
238C22×C3×C4#4112yes—
239C3×C4⋊C4—28no—
240C3×C4⋊C4—48no—
241C3×C4⋊C4—44no—
242C3×C4⋊C4—44no—
243C3×C22⋊C4—48no—
244C3×C22⋊C4—48no—
245C3×C22⋊C4—48no—
246C3×C22⋊C4—48no—
247C3×C22⋊C4—48no—
248C3×C22⋊C4—48no—
249C3×C42—44no—
250C3×C42—44no—
251C3×C42—44no—
252C25C23×C312yes—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4C3×D414yes—
260C23×C4C23×C312yes—
261C23×C4C23×C312yes—
262C23×C4C23×C312yes—
263C23×C4C23×C311yescharacteristic
264C23×C4C23×C311yescharacteristic
265C23×C4C23×C311yescharacteristic
266C23×C4C23×C311yescharacteristic
267C23×C4C23×C311yescharacteristic
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C311yescharacteristic
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4C3×D414yes—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—22no—
313#95—22no—
314#95—22no—
315#95—42no—
316#95—42no—
317#95C3×D414yescomplemented
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3C22×D411yescharacteristic
354C23×C3C22×D411yescharacteristic
355C23×C3C22×D411yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4111yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3C2×#4111yescharacteristic
362C23×C3C2×#4111yescharacteristic
363C23×C3C2×#4111yescharacteristic
364C23×C3H(5,𝔽2)11yescharacteristic
365C23×C3H(5,𝔽2)11yescharacteristic
366C23×C3H(5,𝔽2)11yescharacteristic
367C23×C32−1+411yescharacteristic
368C3×D4—416no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—42no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4#12114yes—
433C2×C3×C4#12314yes—
434C2×C3×C4#12314yes—
435C2×C3×C4#12314yes—
436C2×C3×C4#12414yes—
437C2×C3×C4#12614yes—
438C2×C3×C4#12614yes—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24C2×C3×D414yes—
454C24C24×C311yescharacteristic
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4C2×C3×D412yes—
519C22×C4C2×C3×D412yes—
520C22×C4C2×C3×D414yes—
521C22×C4C2×C3×D412yes—
522C22×C4C2×C3×D412yes—
523C22×C4C2×C3×D412yes—
524C22×C4C3×#4112yes—
525C22×C4C3×#4112yes—
526C22×C4C3×#4112yes—
527C22×C4C3×#4112yes—
528C22×C4C3×#4112yes—
529C22×C4C3×#4112yes—
530C22×C4C3×#4112yes—
531C22×C4C3×#4112yes—
532C4⋊C4—28no—
533C4⋊C4—48no—
534C4⋊C4—44no—
535C4⋊C4—44no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—48no—
539C22⋊C4—48no—
540C22⋊C4—48no—
541C22⋊C4—48no—
542C42—44no—
543C42—44no—
544C42—44no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—44no—
548C22×C3—44no—
549C22×C3—44no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—82no—
553C22×C3—82no—
554C22×C3—82no—
555C22×C3—82no—
556C22×C3—82no—
557C22×C3—82no—
558C22×C3—82no—
559C22×C3—82no—
560C22×C3C2×#12111yescharacteristic
561C22×C3C2×#12311yescharacteristic
562C22×C3C2×#12311yescharacteristic
563C22×C3C2×#12311yescharacteristic
564C22×C3C2×#12411yescharacteristic
565C22×C3C2×#12611yescharacteristic
566C22×C3C2×#12611yescharacteristic
567C22×C3#52911yescharacteristic
568C22×C3#52911yescharacteristic
569C22×C3#52911yescharacteristic
570C22×C3#53211yescharacteristic
571C22×C3#53211yescharacteristic
572C22×C3#53211yescharacteristic
573C22×C3#54011yescharacteristic
574C22×C3#54011yescharacteristic
575C22×C3#54011yescharacteristic
576C22×C3#54211yescharacteristic
577C22×C3#54211yescharacteristic
578C22×C3#54211yescharacteristic
579C22×C3D4211yescharacteristic
580C22×C3D4211yescharacteristic
581C22×C3#54611yescharacteristic
582C22×C3#54611yescharacteristic
583C22×C3#54611yescharacteristic
584C22×C3#54711yescharacteristic
585C22×C3#54711yescharacteristic
586C22×C3#54811yescharacteristic
587C22×C3#55011yescharacteristic
588C22×C3#55011yescharacteristic
589C22×C3#55311yescharacteristic
590C22×C3#55311yescharacteristic
591C22×C3#55511yescharacteristic
592C22×C3#55611yescharacteristic
593C22×C3#55911yescharacteristic
594C22×C3#55911yescharacteristic
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—42no—
599C3×C4—44no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—82no—
603C3×C4—82no—
604C3×C4#39718yescomplemented
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23C22×C3×D411yescharacteristic
641C23C22×C3×D411yescharacteristic
642C23C22×C3×D411yescharacteristic
643C23C2×C3×#4111yescharacteristic
644C23C2×C3×#4111yescharacteristic
645C23C2×C3×#4111yescharacteristic
646C23C2×C3×#4111yescharacteristic
647C23C2×C3×#4111yescharacteristic
648C23C2×C3×#4111yescharacteristic
649C23C2×C3×#4111yescharacteristic
650C23C2×C3×#4111yescharacteristic
651C23C3×H(5,𝔽2)11yescharacteristic
652C23C3×H(5,𝔽2)11yescharacteristic
653C23C3×H(5,𝔽2)11yescharacteristic
654C23C3×2−1+411yescharacteristic
655D4—416no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4C3×#12114yes—
720C2×C4C3×#12314yes—
721C2×C4C3×#12314yes—
722C2×C4C3×#12314yes—
723C2×C4C3×#12414yes—
724C2×C4C3×#12614yes—
725C2×C4C3×#12614yes—
726C2×C3—84no—
727C2×C3C2×#39711yescharacteristic
728C2×C3#242011yescharacteristic
729C2×C3#242211yescharacteristic
730C2×C3#242711yescharacteristic
731C2×C3#242811yescharacteristic
732C2×C3#244511yescharacteristic
733C2×C3#244511yescharacteristic
734C2×C3#244711yescharacteristic
735C2×C3#244811yescharacteristic
736C2×C3#249011yescharacteristic
737C2×C3#249111yescharacteristic
738C2×C3#251211yescharacteristic
739C2×C3#251311yescharacteristic
740C2×C3#264411yescharacteristic
741C2×C3#286011yescharacteristic
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×C3×#12111yescharacteristic
758C22C2×C3×#12311yescharacteristic
759C22C2×C3×#12311yescharacteristic
760C22C2×C3×#12311yescharacteristic
761C22C2×C3×#12411yescharacteristic
762C22C2×C3×#12611yescharacteristic
763C22C2×C3×#12611yescharacteristic
764C22C3×#52911yescharacteristic
765C22C3×#52911yescharacteristic
766C22C3×#52911yescharacteristic
767C22C3×#53211yescharacteristic
768C22C3×#53211yescharacteristic
769C22C3×#53211yescharacteristic
770C22C3×#54011yescharacteristic
771C22C3×#54011yescharacteristic
772C22C3×#54011yescharacteristic
773C22C3×#54211yescharacteristic
774C22C3×#54211yescharacteristic
775C22C3×#54211yescharacteristic
776C22C3×D4211yescharacteristic
777C22C3×D4211yescharacteristic
778C22C3×#54611yescharacteristic
779C22C3×#54611yescharacteristic
780C22C3×#54611yescharacteristic
781C22C3×#54711yescharacteristic
782C22C3×#54711yescharacteristic
783C22C3×#54811yescharacteristic
784C22C3×#55011yescharacteristic
785C22C3×#55011yescharacteristic
786C22C3×#55311yescharacteristic
787C22C3×#55311yescharacteristic
788C22C3×#55511yescharacteristic
789C22C3×#55611yescharacteristic
790C22C3×#55911yescharacteristic
791C22C3×#55911yescharacteristic
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—44no—
797C4—42no—
798C4—42no—
799C4—82no—
800C4—82no—
801C4C3×#39718yescomplemented
802C3#1513811yescharacteristic, direct product factor, Sylow
803C2—84no—
804C2C2×C3×#39711yescharacteristic
805C2C3×#242011yescharacteristic
806C2C3×#242211yescharacteristic
807C2C3×#242711yescharacteristic
808C2C3×#242811yescharacteristic
809C2C3×#244511yescharacteristic
810C2C3×#244511yescharacteristic
811C2C3×#244711yescharacteristic
812C2C3×#244811yescharacteristic
813C2C3×#249011yescharacteristic
814C2C3×#249111yescharacteristic
815C2C3×#251211yescharacteristic
816C2C3×#251311yescharacteristic
817C2C3×#264411yescharacteristic
818C2C3×#286011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#397C2semidirect
5. C2×C3×#389C2semidirect
6. C3×#1440C2semidirect
7. C3×#1440C2semidirect
8. C3×#1439C2semidirect
9. C3×C4⋊#95C2semidirect
10. C3×C4⋊#95C2semidirect
11. C3×C4×#95C2semidirect
12. #15138C3direct (N × H)
41. C2×#397C2×C3semidirect
45. C2×#389C2×C3semidirect
46. #1440C2×C3semidirect
47. #1440C2×C3semidirect
48. #1439C2×C3semidirect
49. C4⋊#95C2×C3semidirect
50. C4⋊#95C2×C3semidirect
51. C4×#95C2×C3semidirect
117. C3×#95D4semidirect
317. #95C3×D4semidirect
604. C3×C4#397semidirect
801. C4C3×#397semidirect
802. C3#15138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3902
C2×C3×#3892
C3×#14402
C3×#14392
C3×C4⋊#952
C3×C4×#952
#151383