Finite Group Databasebeta

← C3×#15673 #10634280

Subgroups — C3×#15673 #10634280

Order 768.

2602 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic, complemented
2C22×C3×#121C211yesmaximal, characteristic
3C2×C3×#395C211yesmaximal, characteristic, complemented
4C2×C3×#394C212yesmaximal, complemented
5C2×C3×#393C211yesmaximal, characteristic, complemented
6C3×#1439C212yesmaximal, complemented
7C3×#1438C212yesmaximal, complemented
8C3×#1438C211yesmaximal, characteristic, complemented
9C3×#1437C211yesmaximal, characteristic, complemented
10C3×#1436C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal, complemented
12#15673C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C23×C3×D4C2211yescharacteristic
17C24×C3×C4C2211yescharacteristic
18C2×C3×#124—24no—
19C2×C3×#124—28no—
20C2×C3×#121—24no—
21C2×C3×#121—24no—
22C2×C3×#121—24no—
23C22×C3×C4⋊C4C2212yes—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C22⋊C4C2212yes—
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2212yes—
32C22×C3×C22⋊C4C2212yes—
33C22×C3×C42C2211yescharacteristic
34C3×#395—24no—
35C3×#394—28no—
36C3×#393—24no—
37C2×C3×#95C2212yes—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2212yes—
43C2×C3×#95C2212yes—
44C22×#124C2×C311yescharacteristic, complemented
45C22×#121C2×C311yescharacteristic
46C2×#395C2×C311yescharacteristic, complemented
47C2×#394C2×C312yescomplemented
48C2×#393C2×C311yescharacteristic, complemented
49#1439C2×C312yescomplemented
50#1438C2×C312yescomplemented
51#1438C2×C311yescharacteristic, complemented
52#1437C2×C311yescharacteristic, complemented
53#1436C2×C311yescharacteristic, complemented
54C22⋊#95C2×C312yescomplemented
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C22×C3×Q8—24no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—22no—
62C22×C3×Q8—42no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—24no—
68C22×C3×D4—24no—
69C22×C3×D4—22no—
70C22×C3×D4—22no—
71C22×C3×D4—22no—
72C22×C3×D4—22no—
73C22×C3×D4—24no—
74C22×C3×D4—42no—
75C22×C3×D4—42no—
76C22×C3×D4—42no—
77C22×C3×D4D414yes—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—24no—
82C23×C3×C4—42no—
83C23×C3×C4C2312yes—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2312yes—
87C23×C3×C4C2312yes—
88C23×C3×C4C2312yes—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C3×#124—232no—
92C3×#121—232no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—24no—
96C2×C3×C4⋊C4—24no—
97C2×C3×C4⋊C4—42no—
98C2×C3×C4⋊C4D414yes—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—24no—
116C2×C3×C22⋊C4—42no—
117C2×C3×C22⋊C4—42no—
118C2×C3×C22⋊C4—42no—
119C2×C3×C22⋊C4—42no—
120C2×C3×C22⋊C4—42no—
121C2×C3×C22⋊C4D414yes—
122C2×C3×C22⋊C4D418yescomplemented
123C2×C3×C42—24no—
124C2×C3×C42—22no—
125C3×#95—24no—
126C3×#95—22no—
127C3×#95—24no—
128C3×#95—22no—
129C3×#95—24no—
130C3×#95—24no—
131C3×#95—42no—
132C23×Q8C22×C311yescharacteristic
133C23×D4C22×C311yescharacteristic
134C23×D4C22×C311yescharacteristic
135C23×D4C22×C311yescharacteristic
136C24×C4C22×C311yescharacteristic
137C2×#124—24no—
138C2×#124—28no—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—24no—
142C22×C4⋊C4C22×C312yes—
143C22×C4⋊C4C22×C311yescharacteristic
144C22×C22⋊C4C22×C311yescharacteristic
145C22×C22⋊C4C22×C312yes—
146C22×C22⋊C4C22×C312yes—
147C22×C22⋊C4C22×C312yes—
148C22×C22⋊C4C22×C312yes—
149C22×C22⋊C4C22×C311yescharacteristic
150C22×C22⋊C4C22×C312yes—
151C22×C22⋊C4C22×C312yes—
152C22×C42C22×C311yescharacteristic
153#395—24no—
154#394—28no—
155#393—24no—
156C2×#95C22×C312yes—
157C2×#95C22×C311yescharacteristic
158C2×#95C22×C312yes—
159C2×#95C22×C312yes—
160C2×#95C22×C311yescharacteristic
161C2×#95C22×C312yes—
162C2×#95C22×C312yes—
163C24×C3—21no—
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—21no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3C2×D412yes—
187C24×C3C2×D412yes—
188C24×C3C2×D414yes—
189C24×C3C2×D412yes—
190C24×C3C2411yescharacteristic
191C2×C3×Q8—28no—
192C2×C3×Q8—48no—
193C2×C3×Q8—48no—
194C2×C3×Q8—44no—
195C2×C3×Q8—44no—
196C2×C3×D4—28no—
197C2×C3×D4—28no—
198C2×C3×D4—28no—
199C2×C3×D4—28no—
200C2×C3×D4—44no—
201C2×C3×D4—48no—
202C2×C3×D4—48no—
203C2×C3×D4—48no—
204C2×C3×D4—48no—
205C2×C3×D4—48no—
206C2×C3×D4—44no—
207C2×C3×D4—48no—
208C2×C3×D4—44no—
209C2×C3×D4—44no—
210C2×C3×D4—44no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—28no—
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—21no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
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×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—48no—
251C22×C3×C4—48no—
252C22×C3×C4—44no—
253C22×C3×C4—44no—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2×D414yes—
256C22×C3×C4C2×D414yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
262C22×C3×C4#4114yes—
263C22×C3×C4#4114yes—
264C3×C4⋊C4—28no—
265C3×C4⋊C4—48no—
266C3×C22⋊C4—28no—
267C3×C22⋊C4—216no—
268C3×C22⋊C4—216no—
269C3×C22⋊C4—28no—
270C3×C22⋊C4—48no—
271C3×C22⋊C4—48no—
272C3×C22⋊C4—48no—
273C3×C22⋊C4—48no—
274C3×C42—28no—
275C25C23×C311yescharacteristic
276C25C23×C311yescharacteristic
277C25C23×C311yescharacteristic
278C22×Q8—24no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—42no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—24no—
288C22×D4—24no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—24no—
294C22×D4—42no—
295C22×D4—42no—
296C22×D4—42no—
297C22×D4C3×D414yes—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—24no—
302C23×C4—42no—
303C23×C4C23×C312yes—
304C23×C4C23×C312yes—
305C23×C4C23×C312yes—
306C23×C4C23×C311yescharacteristic
307C23×C4C23×C311yescharacteristic
308C23×C4C23×C312yes—
309C23×C4C23×C311yescharacteristic
310C23×C4C23×C311yescharacteristic
311#124—232no—
312#121—232no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4C3×D414yes—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4C3×D414yes—
342C2×C22⋊C4C3×D418yescomplemented
343C2×C42—24no—
344C2×C42—22no—
345#95—24no—
346#95—22no—
347#95—24no—
348#95—22no—
349#95—24no—
350#95—24no—
351#95—42no—
352C23×C3—22no—
353C23×C3—24no—
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—42no—
386C23×C3—41no—
387C23×C3—42no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3#12014yes—
415C23×C3C22×D411yescharacteristic
416C23×C3C22×D411yescharacteristic
417C23×C3C22×D411yescharacteristic
418C23×C3C22×D412yes—
419C23×C3C2×#4112yes—
420C23×C3C2×#4112yes—
421C23×C3H(5,𝔽2)12yes—
422C23×C3H(5,𝔽2)12yes—
423C23×C32−1+412yes—
424C3×Q8—416no—
425C3×D4—416no—
426C3×D4—416no—
427C3×D4—416no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—24no—
437C2×C3×C4—22no—
438C2×C3×C4—24no—
439C2×C3×C4—22no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—416no—
450C2×C3×C4—41no—
451C2×C3×C4—42no—
452C2×C3×C4—41no—
453C2×C3×C4—42no—
454C2×C3×C4—41no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—41no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4#12014yes—
476C2×C3×C4#12414yescomplemented
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24C2×C3×D412yes—
501C24C2×C3×D412yes—
502C24C2×C3×D414yes—
503C24C2×C3×D412yes—
504C24C24×C311yescharacteristic
505C2×Q8—28no—
506C2×Q8—48no—
507C2×Q8—48no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—44no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—44no—
521C2×D4—48no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4C2×C3×D412yes—
569C22×C4C2×C3×D414yes—
570C22×C4C2×C3×D414yes—
571C22×C4C2×C3×D412yes—
572C22×C4C2×C3×D412yes—
573C22×C4C2×C3×D412yes—
574C22×C4C2×C3×D412yes—
575C22×C4C2×C3×D412yes—
576C22×C4C3×#4114yes—
577C22×C4C3×#4114yes—
578C4⋊C4—28no—
579C4⋊C4—48no—
580C22⋊C4—28no—
581C22⋊C4—216no—
582C22⋊C4—216no—
583C22⋊C4—28no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C42—28no—
589C22×C3—24no—
590C22×C3—28no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—44no—
608C22×C3—82no—
609C22×C3—82no—
610C22×C3—82no—
611C22×C3—82no—
612C22×C3—82no—
613C22×C3—82no—
614C22×C3—82no—
615C22×C3—82no—
616C22×C3C2×#12011yescharacteristic
617C22×C3C2×#12011yescharacteristic
618C22×C3C2×#12411yescharacteristic
619C22×C3#53212yes—
620C22×C3#53211yescharacteristic
621C22×C3#53411yescharacteristic
622C22×C3#53511yescharacteristic
623C22×C3#53611yescharacteristic
624C22×C3#53712yes—
625C22×C3#53812yes—
626C22×C3#54212yes—
627C22×C3D4212yes—
628C22×C3D4212yes—
629C22×C3#54612yes—
630C22×C3#54612yes—
631C22×C3#54612yes—
632C22×C3#54712yes—
633C22×C3#54712yes—
634C22×C3#54812yes—
635C22×C3#55512yes—
636C22×C3#56212yes—
637C3×C4—24no—
638C3×C4—24no—
639C3×C4—42no—
640C3×C4—44no—
641C3×C4—44no—
642C3×C4—44no—
643C3×C4—42no—
644C3×C4—82no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23C3×#12014yes—
708C23C22×C3×D411yescharacteristic
709C23C22×C3×D411yescharacteristic
710C23C22×C3×D411yescharacteristic
711C23C22×C3×D412yes—
712C23C2×C3×#4112yes—
713C23C2×C3×#4112yes—
714C23C3×H(5,𝔽2)12yes—
715C23C3×H(5,𝔽2)12yes—
716C23C3×2−1+412yes—
717Q8—416no—
718D4—416no—
719D4—416no—
720D4—416no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—416no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4C3×#12014yes—
769C2×C4C3×#12414yescomplemented
770C2×C3—44no—
771C2×C3—82no—
772C2×C3—82no—
773C2×C3#240311yescharacteristic
774C2×C3#243012yes—
775C2×C3#243211yescharacteristic
776C2×C3#243511yescharacteristic
777C2×C3#249112yes—
778C2×C3#255512yes—
779C2×C3#267212yes—
780C2×C3#267612yes—
781C2×C3#268612yes—
782C22—24no—
783C22—28no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22C2×C3×#12011yescharacteristic
810C22C2×C3×#12011yescharacteristic
811C22C2×C3×#12411yescharacteristic
812C22C3×#53212yes—
813C22C3×#53211yescharacteristic
814C22C3×#53411yescharacteristic
815C22C3×#53511yescharacteristic
816C22C3×#53611yescharacteristic
817C22C3×#53712yes—
818C22C3×#53812yes—
819C22C3×#54212yes—
820C22C3×D4212yes—
821C22C3×D4212yes—
822C22C3×#54612yes—
823C22C3×#54612yes—
824C22C3×#54612yes—
825C22C3×#54712yes—
826C22C3×#54712yes—
827C22C3×#54812yes—
828C22C3×#55512yes—
829C22C3×#56212yes—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—44no—
834C4—44no—
835C4—44no—
836C4—42no—
837C4—82no—
838C3#1567311yescharacteristic, direct product factor, Sylow
839C2—44no—
840C2—82no—
841C2—82no—
842C2C3×#240311yescharacteristic
843C2C3×#243012yes—
844C2C3×#243211yescharacteristic
845C2C3×#243511yescharacteristic
846C2C3×#249112yes—
847C2C3×#255512yes—
848C2C3×#267212yes—
849C2C3×#267612yes—
850C2C3×#268612yes—
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC22×C3×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#124C2semidirect
3. C2×C3×#395C2semidirect
4. C2×C3×#394C2semidirect
5. C2×C3×#393C2semidirect
6. C3×#1439C2semidirect
7. C3×#1438C2semidirect
8. C3×#1438C2semidirect
9. C3×#1437C2semidirect
10. C3×#1436C2semidirect
11. C3×C22⋊#95C2semidirect
12. #15673C3direct (N × H)
44. C22×#124C2×C3semidirect
46. C2×#395C2×C3semidirect
47. C2×#394C2×C3semidirect
48. C2×#393C2×C3semidirect
49. #1439C2×C3semidirect
50. #1438C2×C3semidirect
51. #1438C2×C3semidirect
52. #1437C2×C3semidirect
53. #1436C2×C3semidirect
54. C22⋊#95C2×C3semidirect
122. C2×C3×C22⋊C4D4semidirect
342. C2×C22⋊C4C3×D4semidirect
476. C2×C3×C4#124semidirect
769. C2×C4C3×#124semidirect
838. C3#15673direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C22×C3×#1212
C2×C3×#3952
C2×C3×#3942
C2×C3×#3932
C3×#14392
C3×#14382
C3×#14372
C3×#14362
C3×C22⋊#952
#156733