Finite Group Databasebeta

← C3×#16655 #10635262

Subgroups — C3×#16655 #10635262

Order 768.

2118 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic
4C2×C3×#390C211yesmaximal, characteristic, complemented
5C3×#1441C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1439C212yesmaximal, complemented
9C3×#1438C212yesmaximal, complemented
10C3×#1438C212yesmaximal, complemented
11C3×#1434C211yesmaximal, characteristic, complemented
12#16655C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C2×C3×#126—24no—
16C2×C3×#126—24no—
17C2×C3×#126—24no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C22⋊C4C2212yes—
30C22×C3×C22⋊C4C2212yes—
31C22×C3×C42C2211yescharacteristic
32C3×#394—24no—
33C3×#392—24no—
34C3×#390—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C22×#126C2×C311yescharacteristic, complemented
43C2×#394C2×C311yescharacteristic, complemented
44C2×#392C2×C311yescharacteristic
45C2×#390C2×C311yescharacteristic, complemented
46#1441C2×C311yescharacteristic, complemented
47#1439C2×C312yescomplemented
48#1439C2×C312yescomplemented
49#1439C2×C311yescharacteristic, complemented
50#1438C2×C312yescomplemented
51#1438C2×C312yescomplemented
52#1434C2×C311yescharacteristic, complemented
53C25×C3C2311yescharacteristic
54C25×C3C2312yes—
55C22×C3×D4—24no—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—24no—
62C22×C3×D4—42no—
63C22×C3×D4—42no—
64C22×C3×D4—42no—
65C22×C3×D4—42no—
66C22×C3×D4—42no—
67C23×C3×C4C2312yes—
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2312yes—
75C23×C3×C4C2311yescharacteristic
76C3×#126—232no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C4⋊C4D414yescomplemented
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—42no—
104C2×C3×C22⋊C4—42no—
105C2×C3×C22⋊C4—42no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4—42no—
109C2×C3×C22⋊C4—42no—
110C2×C3×C22⋊C4—42no—
111C2×C3×C22⋊C4—42no—
112C2×C3×C22⋊C4—42no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4D414yes—
115C2×C3×C42—22no—
116C2×C3×C42—22no—
117C2×C3×C42D414yescomplemented
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—24no—
121C3×#95—42no—
122C3×#95—42no—
123C3×#95—42no—
124C3×#95—42no—
125C23×D4C22×C311yescharacteristic
126C23×D4C22×C312yes—
127C2×#126—24no—
128C2×#126—24no—
129C2×#126—24no—
130C22×C4⋊C4C22×C311yescharacteristic
131C22×C4⋊C4C22×C311yescharacteristic
132C22×C4⋊C4C22×C311yescharacteristic
133C22×C4⋊C4C22×C311yescharacteristic
134C22×C22⋊C4C22×C311yescharacteristic
135C22×C22⋊C4C22×C311yescharacteristic
136C22×C22⋊C4C22×C312yes—
137C22×C22⋊C4C22×C312yes—
138C22×C22⋊C4C22×C311yescharacteristic
139C22×C22⋊C4C22×C312yes—
140C22×C22⋊C4C22×C312yes—
141C22×C22⋊C4C22×C312yes—
142C22×C22⋊C4C22×C312yes—
143C22×C42C22×C311yescharacteristic
144#394—24no—
145#392—24no—
146#390—24no—
147C2×#95C22×C311yescharacteristic
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C312yes—
150C2×#95C22×C312yes—
151C2×#95C22×C312yes—
152C2×#95C22×C312yes—
153C2×#95C22×C312yes—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—21no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—22no—
178C24×C3C2×D412yes—
179C24×C3#4114yes—
180C24×C3C2411yescharacteristic
181C2×C3×D4—28no—
182C2×C3×D4—48no—
183C2×C3×D4—48no—
184C2×C3×D4—48no—
185C2×C3×D4—48no—
186C2×C3×D4—44no—
187C2×C3×D4—48no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—44no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
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—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4#4114yes—
248C3×C4⋊C4—28no—
249C3×C4⋊C4—28no—
250C3×C4⋊C4—28no—
251C3×C4⋊C4—44no—
252C3×C22⋊C4—28no—
253C3×C22⋊C4—28no—
254C3×C22⋊C4—28no—
255C3×C22⋊C4—48no—
256C3×C22⋊C4—48no—
257C3×C22⋊C4—48no—
258C3×C22⋊C4—48no—
259C3×C22⋊C4—48no—
260C3×C22⋊C4—48no—
261C3×C42—28no—
262C25C23×C311yescharacteristic
263C25C23×C312yes—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—24no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—42no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—42no—
276C23×C4C23×C312yes—
277C23×C4C23×C312yes—
278C23×C4C23×C311yescharacteristic
279C23×C4C23×C311yescharacteristic
280C23×C4C23×C311yescharacteristic
281C23×C4C23×C311yescharacteristic
282C23×C4C23×C311yescharacteristic
283C23×C4C23×C312yes—
284C23×C4C23×C311yescharacteristic
285#126—232no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4C3×D414yescomplemented
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4C3×D414yes—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42C3×D414yescomplemented
327#95—22no—
328#95—22no—
329#95—24no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334C23×C3—22no—
335C23×C3—24no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—42no—
347C23×C3—41no—
348C23×C3—42no—
349C23×C3—41no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3C22×D411yescharacteristic
393C23×C3C22×D411yescharacteristic
394C23×C3C22×D411yescharacteristic
395C23×C3C2×#4112yes—
396C23×C3C2×#4112yes—
397C23×C3H(5,𝔽2)11yescharacteristic
398C23×C3H(5,𝔽2)11yescharacteristic
399C23×C3H(5,𝔽2)11yescharacteristic
400C23×C3H(5,𝔽2)12yes—
401C23×C3H(5,𝔽2)12yes—
402C23×C32−1+411yescharacteristic
403C3×D4—416no—
404C3×D4—432no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4#12014yes—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—21no—
483C24—22no—
484C24C2×C3×D412yes—
485C24C3×#4114yes—
486C24C24×C311yescharacteristic
487C2×D4—28no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—44no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—44no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4C2×C3×D412yes—
546C22×C4C2×C3×D412yes—
547C22×C4C2×C3×D412yes—
548C22×C4C2×C3×D412yes—
549C22×C4C2×C3×D412yes—
550C22×C4C2×C3×D412yes—
551C22×C4C2×C3×D412yes—
552C22×C4C2×C3×D412yes—
553C22×C4C3×#4114yes—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—44no—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—28no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C42—28no—
568C22×C3—44no—
569C22×C3—42no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—42no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—42no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—82no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3—82no—
584C22×C3—81no—
585C22×C3—82no—
586C22×C3—81no—
587C22×C3—82no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3—82no—
594C22×C3C2×#12011yescharacteristic
595C22×C3#52511yescharacteristic
596C22×C3#53211yescharacteristic
597C22×C3#53511yescharacteristic
598C22×C3#53511yescharacteristic
599C22×C3#53511yescharacteristic
600C22×C3#53511yescharacteristic
601C22×C3#53511yescharacteristic
602C22×C3#53711yescharacteristic
603C22×C3#53711yescharacteristic
604C22×C3#53711yescharacteristic
605C22×C3#53812yes—
606C22×C3#53812yes—
607C22×C3#53912yes—
608C22×C3#54212yes—
609C22×C3#54612yes—
610C22×C3#54612yes—
611C22×C3#54612yes—
612C22×C3#55012yes—
613C22×C3#55112yes—
614C22×C3#55312yes—
615C22×C3#56012yes—
616C22×C3#56012yes—
617C3×C4—24no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—44no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—82no—
625C3×C4—82no—
626C23—22no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23C22×C3×D411yescharacteristic
685C23C22×C3×D411yescharacteristic
686C23C22×C3×D411yescharacteristic
687C23C2×C3×#4112yes—
688C23C2×C3×#4112yes—
689C23C3×H(5,𝔽2)11yescharacteristic
690C23C3×H(5,𝔽2)11yescharacteristic
691C23C3×H(5,𝔽2)12yes—
692C23C3×H(5,𝔽2)12yes—
693C23C3×H(5,𝔽2)11yescharacteristic
694C23C3×2−1+411yescharacteristic
695D4—416no—
696D4—432no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4C3×#12014yes—
752C2×C3—84no—
753C2×C3—82no—
754C2×C3#240411yescharacteristic
755C2×C3#243111yescharacteristic
756C2×C3#260311yescharacteristic
757C2×C3#261511yescharacteristic
758C2×C3#263611yescharacteristic
759C2×C3#266211yescharacteristic
760C2×C3#268512yes—
761C2×C3#269112yes—
762C2×C3#270512yes—
763C2×C3#271412yes—
764C2×C3#281811yescharacteristic
765C22—44no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—81no—
778C22—82no—
779C22—81no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—81no—
788C22—82no—
789C22—81no—
790C22—82no—
791C22C2×C3×#12011yescharacteristic
792C22C3×#52511yescharacteristic
793C22C3×#53211yescharacteristic
794C22C3×#53511yescharacteristic
795C22C3×#53511yescharacteristic
796C22C3×#53511yescharacteristic
797C22C3×#53511yescharacteristic
798C22C3×#53511yescharacteristic
799C22C3×#53711yescharacteristic
800C22C3×#53711yescharacteristic
801C22C3×#53711yescharacteristic
802C22C3×#53812yes—
803C22C3×#53812yes—
804C22C3×#53912yes—
805C22C3×#54212yes—
806C22C3×#54612yes—
807C22C3×#54612yes—
808C22C3×#54612yes—
809C22C3×#55012yes—
810C22C3×#55112yes—
811C22C3×#55312yes—
812C22C3×#56012yes—
813C22C3×#56012yes—
814C4—24no—
815C4—42no—
816C4—44no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—82no—
822C4—82no—
823C3#1665511yescharacteristic, direct product factor, Sylow
824C2—84no—
825C2—82no—
826C2C3×#240411yescharacteristic
827C2C3×#243111yescharacteristic
828C2C3×#260311yescharacteristic
829C2C3×#261511yescharacteristic
830C2C3×#263611yescharacteristic
831C2C3×#266211yescharacteristic
832C2C3×#268512yes—
833C2C3×#269112yes—
834C2C3×#270512yes—
835C2C3×#271412yes—
836C2C3×#281811yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#126C2semidirect
2. C2×C3×#394C2semidirect
4. C2×C3×#390C2semidirect
5. C3×#1441C2semidirect
6. C3×#1439C2semidirect
7. C3×#1439C2semidirect
8. C3×#1439C2semidirect
9. C3×#1438C2semidirect
10. C3×#1438C2semidirect
11. C3×#1434C2semidirect
12. #16655C3direct (N × H)
42. C22×#126C2×C3semidirect
43. C2×#394C2×C3semidirect
45. C2×#390C2×C3semidirect
46. #1441C2×C3semidirect
47. #1439C2×C3semidirect
48. #1439C2×C3semidirect
49. #1439C2×C3semidirect
50. #1438C2×C3semidirect
51. #1438C2×C3semidirect
52. #1434C2×C3semidirect
87. C2×C3×C4⋊C4D4semidirect
117. C2×C3×C42D4semidirect
296. C2×C4⋊C4C3×D4semidirect
326. C2×C42C3×D4semidirect
823. C3#16655direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1262
C2×C3×#3942
C2×C3×#3922
C2×C3×#3902
C3×#14412
C3×#14392
C3×#14382
C3×#14342
#166553