Finite Group Databasebeta

← C3×#763336 #72271604

Subgroups — C3×#763336 #72271604

Order 1536.

18480 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#535C212yesmaximal, complemented
2C2×C3×#2433C214yesmaximal, complemented
3C3×#15947C214yesmaximal, complemented
4C3×#15763C214yesmaximal, complemented
5C3×#15258C218yesmaximal, complemented
6C3×#15124C214yesmaximal, complemented
7C3×#14136C214yesmaximal, complemented
8C3×#13851C211yesmaximal, characteristic, complemented
9#763336C311yesmaximal, characteristic, direct product factor, Sylow
10C23×C3×#41C2211yescharacteristic
11C24×C3×D4C2212yescomplemented
12C2×C3×#535—232no—
13C2×C3×#535—216no—
14C22×C3×#127C2214yes—
15C22×C3×#127C2214yes—
16C22×C3×#124C2214yescomplemented
17C22×C3×#121C2214yes—
18C22×C3×#121C2214yescomplemented
19C22×C3×#120C2214yes—
20C22×C3×#120C2214yescomplemented
21C22×C3×#120C22116yescomplemented
22C22×C3×#117C2212yescomplemented
23C3×#2433—232no—
24C2×C3×#392C22116yescomplemented
25C2×C3×#392C22116yescomplemented
26C2×C3×#390C2218yescomplemented
27C2×C3×C4×C22⋊C4C2214yescomplemented
28C2×C3×C4×C22⋊C4C2212yescomplemented
29C3×#1446C2212yescomplemented
30C3×#1438C2212yes—
31C3×#1438C22116yescomplemented
32C3×#1438C2214yescomplemented
33C3×#1438C22116yescomplemented
34C3×#1437C22116yescomplemented
35C3×C4⋊#95C2214yescomplemented
36C22×#535C2×C312yescomplemented
37C2×#2433C2×C314yescomplemented
38#15947C2×C314yescomplemented
39#15763C2×C314yescomplemented
40#15258C2×C318yescomplemented
41#15124C2×C314yescomplemented
42#14136C2×C314yescomplemented
43#13851C2×C311yescharacteristic, complemented
44C26×C3C2314yes—
45C22×C3×#41—216no—
46C22×C3×#41—44no—
47C22×C3×#41D418yescomplemented
48C23×C3×Q8C2311yescharacteristic
49C23×C3×D4—216no—
50C23×C3×D4—28no—
51C23×C3×D4—216no—
52C23×C3×D4—48no—
53C23×C3×D4C2314yes—
54C23×C3×D4C2314yes—
55C23×C3×D4C2311yescharacteristic
56C23×C3×D4C2312yes—
57C23×C3×D4C23116yes—
58C23×C3×D4C2318yes—
59C23×C3×D4C2318yes—
60C24×C3×C4C2311yescharacteristic
61C24×C3×C4C2312yes—
62C3×#535—2256no—
63C2×C3×#127—232no—
64C2×C3×#127—216no—
65C2×C3×#127—232no—
66C2×C3×#127—48no—
67C2×C3×#124—216no—
68C2×C3×#124—232no—
69C2×C3×#121—216no—
70C2×C3×#121—216no—
71C2×C3×#121—216no—
72C2×C3×#121—216no—
73C2×C3×#121—216no—
74C2×C3×#121D4132yescomplemented
75C2×C3×#120—216no—
76C2×C3×#120—232no—
77C2×C3×#120—216no—
78C2×C3×#120—264no—
79C2×C3×#120—232no—
80C2×C3×#120—464no—
81C2×C3×#117—28no—
82C2×C3×#117—216no—
83C22×C3×C4⋊C4C2314yes—
84C22×C3×C22⋊C4C2314yes—
85C22×C3×C22⋊C4C2318yes—
86C22×C3×C22⋊C4C2318yes—
87C22×C3×C22⋊C4C23132yes—
88C22×C3×C22⋊C4C2314yes—
89C22×C3×C22⋊C4C2318yes—
90C22×C3×C42C2314yes—
91C22×C3×C42C2314yes—
92C3×#392—264no—
93C3×#392—432no—
94C3×#390—232no—
95C3×C4×C22⋊C4—216no—
96C3×C4×C22⋊C4—44no—
97C2×C3×#95C2318yes—
98C2×C3×#95C23116yes—
99C2×C3×#95C2314yes—
100C23×#41C22×C311yescharacteristic
101C24×D4C22×C312yescomplemented
102C2×#535—216no—
103C2×#535—232no—
104C22×#127C22×C314yes—
105C22×#127C22×C314yes—
106C22×#124C22×C314yescomplemented
107C22×#121C22×C314yes—
108C22×#121C22×C314yescomplemented
109C22×#120C22×C314yes—
110C22×#120C22×C314yescomplemented
111C22×#120C22×C3116yescomplemented
112C22×#117C22×C312yescomplemented
113#2433—232no—
114C2×#392C22×C3116yescomplemented
115C2×#392C22×C3116yescomplemented
116C2×#390C22×C318yescomplemented
117C2×C4×C22⋊C4C22×C314yescomplemented
118C2×C4×C22⋊C4C22×C312yescomplemented
119#1446C22×C312yescomplemented
120#1438C22×C312yes—
121#1438C22×C3116yescomplemented
122#1438C22×C314yescomplemented
123#1438C22×C3116yescomplemented
124#1437C22×C3116yescomplemented
125C4⋊#95C22×C314yescomplemented
126C25×C3—216no—
127C25×C3—28no—
128C25×C3—216no—
129C25×C3—48no—
130C25×C3—432no—
131C25×C3C2411yescharacteristic
132C25×C3C2418yes—
133C25×C3C2412yes—
134C2×C3×#41—264no—
135C2×C3×#41—416no—
136C2×C3×#41—464no—
137C22×C3×Q8—28no—
138C22×C3×Q8—42no—
139C22×C3×Q8C2×D414yes—
140C22×C3×D4—264no—
141C22×C3×D4—216no—
142C22×C3×D4—28no—
143C22×C3×D4—28no—
144C22×C3×D4—216no—
145C22×C3×D4—216no—
146C22×C3×D4—216no—
147C22×C3×D4—216no—
148C22×C3×D4—264no—
149C22×C3×D4—216no—
150C22×C3×D4—28no—
151C22×C3×D4—28no—
152C22×C3×D4—28no—
153C22×C3×D4—28no—
154C22×C3×D4—216no—
155C22×C3×D4—216no—
156C22×C3×D4—216no—
157C22×C3×D4—232no—
158C22×C3×D4—4128no—
159C22×C3×D4—48no—
160C22×C3×D4—44no—
161C22×C3×D4—42no—
162C22×C3×D4—432no—
163C22×C3×D4—432no—
164C22×C3×D4—432no—
165C22×C3×D4—416no—
166C22×C3×D4—416no—
167C22×C3×D4—432no—
168C22×C3×D4—432no—
169C22×C3×D4C2×D4116yes—
170C22×C3×D4C2×D414yes—
171C22×C3×D4C2×D418yes—
172C22×C3×D4C2×D4132yes—
173C23×C3×C4—28no—
174C23×C3×C4—28no—
175C23×C3×C4—28no—
176C23×C3×C4—24no—
177C23×C3×C4C2×D414yes—
178C23×C3×C4C2×D4116yes—
179C23×C3×C4C2×D418yes—
180C23×C3×C4C2411yescharacteristic
181C23×C3×C4C2418yes—
182C23×C3×C4C2418yes—
183C23×C3×C4C2412yes—
184C23×C3×C4C2411yescharacteristic
185C3×#127—2128no—
186C3×#127—464no—
187C3×#124—2128no—
188C3×#121—2128no—
189C3×#121—2128no—
190C3×#120—2128no—
191C3×#120—2128no—
192C3×#120—4256no—
193C3×#117—264no—
194C2×C3×C4⋊C4—28no—
195C2×C3×C4⋊C4—28no—
196C2×C3×C4⋊C4C2×D4116yes—
197C2×C3×C22⋊C4—216no—
198C2×C3×C22⋊C4—28no—
199C2×C3×C22⋊C4—216no—
200C2×C3×C22⋊C4—216no—
201C2×C3×C22⋊C4—216no—
202C2×C3×C22⋊C4—216no—
203C2×C3×C22⋊C4—216no—
204C2×C3×C22⋊C4—216no—
205C2×C3×C22⋊C4—232no—
206C2×C3×C22⋊C4—264no—
207C2×C3×C22⋊C4—216no—
208C2×C3×C22⋊C4—264no—
209C2×C3×C22⋊C4—44no—
210C2×C3×C22⋊C4—432no—
211C2×C3×C22⋊C4C2×D4132yes—
212C2×C3×C42—216no—
213C2×C3×C42—28no—
214C2×C3×C42—216no—
215C2×C3×C42—28no—
216C3×#95—216no—
217C3×#95—44no—
218C3×#95—416no—
219C26C23×C314yes—
220C22×#41—216no—
221C22×#41—44no—
222C22×#41C3×D418yescomplemented
223C23×Q8C23×C311yescharacteristic
224C23×D4—216no—
225C23×D4—28no—
226C23×D4—216no—
227C23×D4—48no—
228C23×D4C23×C314yes—
229C23×D4C23×C314yes—
230C23×D4C23×C311yescharacteristic
231C23×D4C23×C312yes—
232C23×D4C23×C318yes—
233C23×D4C23×C3116yes—
234C23×D4C23×C318yes—
235C24×C4C23×C311yescharacteristic
236C24×C4C23×C312yes—
237#535—2256no—
238C2×#127—232no—
239C2×#127—216no—
240C2×#127—232no—
241C2×#127—48no—
242C2×#124—216no—
243C2×#124—232no—
244C2×#121—216no—
245C2×#121—216no—
246C2×#121—216no—
247C2×#121—216no—
248C2×#121—216no—
249C2×#121C3×D4132yescomplemented
250C2×#120—216no—
251C2×#120—232no—
252C2×#120—216no—
253C2×#120—264no—
254C2×#120—232no—
255C2×#120—464no—
256C2×#117—28no—
257C2×#117—216no—
258C22×C4⋊C4C23×C314yes—
259C22×C22⋊C4C23×C314yes—
260C22×C22⋊C4C23×C318yes—
261C22×C22⋊C4C23×C318yes—
262C22×C22⋊C4C23×C314yes—
263C22×C22⋊C4C23×C3132yes—
264C22×C22⋊C4C23×C318yes—
265C22×C42C23×C314yes—
266C22×C42C23×C314yes—
267#392—264no—
268#392—432no—
269#390—232no—
270C4×C22⋊C4—216no—
271C4×C22⋊C4—44no—
272C2×#95C23×C318yes—
273C2×#95C23×C3116yes—
274C2×#95C23×C314yes—
275C24×C3—24no—
276C24×C3—216no—
277C24×C3—24no—
278C24×C3—232no—
279C24×C3—28no—
280C24×C3—28no—
281C24×C3—216no—
282C24×C3—24no—
283C24×C3—232no—
284C24×C3—232no—
285C24×C3—216no—
286C24×C3—28no—
287C24×C3—22no—
288C24×C3—464no—
289C24×C3—416no—
290C24×C3—464no—
291C24×C3—416no—
292C24×C3—832no—
293C24×C3—832no—
294C24×C3—832no—
295C24×C3—832no—
296C24×C3—832no—
297C24×C3—832no—
298C24×C3C22×D4116yes—
299C24×C3C22×D412yes—
300C24×C3C22×D414yes—
301C24×C3C22×D418yes—
302C24×C3C2511yescharacteristic
303C3×#41—4128no—
304C2×C3×Q8—216no—
305C2×C3×Q8—44no—
306C2×C3×Q8—416no—
307C2×C3×D4—232no—
308C2×C3×D4—216no—
309C2×C3×D4—216no—
310C2×C3×D4—264no—
311C2×C3×D4—264no—
312C2×C3×D4—216no—
313C2×C3×D4—232no—
314C2×C3×D4—264no—
315C2×C3×D4—48no—
316C2×C3×D4—44no—
317C2×C3×D4—464no—
318C2×C3×D4—432no—
319C2×C3×D4—416no—
320C2×C3×D4—4256no—
321C2×C3×D4—464no—
322C2×C3×D4—4128no—
323C2×C3×D4—416no—
324C2×C3×D4—464no—
325C2×C3×D4—416no—
326C2×C3×D4—416no—
327C2×C3×D4—416no—
328C2×C3×D4—432no—
329C2×C3×D4—832no—
330C2×C3×D4—832no—
331C2×C3×D4—832no—
332C2×C3×D4—832no—
333C2×C3×D4—832no—
334C2×C3×D4—832no—
335C2×C3×D4—864no—
336C2×C3×D4—832no—
337C22×C3×C4—24no—
338C22×C3×C4—24no—
339C22×C3×C4—216no—
340C22×C3×C4—216no—
341C22×C3×C4—264no—
342C22×C3×C4—216no—
343C22×C3×C4—28no—
344C22×C3×C4—28no—
345C22×C3×C4—24no—
346C22×C3×C4—28no—
347C22×C3×C4—22no—
348C22×C3×C4—28no—
349C22×C3×C4—232no—
350C22×C3×C4—216no—
351C22×C3×C4—216no—
352C22×C3×C4—28no—
353C22×C3×C4—416no—
354C22×C3×C4#120132yescomplemented
355C22×C3×C4C22×D4116yes—
356C22×C3×C4C22×D412yes—
357C22×C3×C4C22×D418yes—
358C22×C3×C4C22×D414yes—
359C22×C3×C4C22×D412yes—
360C22×C3×C4C22×D418yes—
361C22×C3×C4H(5,𝔽2)116yes—
362C22×C3×C4H(5,𝔽2)14yes—
363C3×C4⋊C4—232no—
364C3×C22⋊C4—232no—
365C3×C22⋊C4—264no—
366C3×C22⋊C4—264no—
367C3×C22⋊C4—264no—
368C3×C22⋊C4—416no—
369C3×C22⋊C4—4128no—
370C3×C42—232no—
371C3×C42—416no—
372C25—216no—
373C25—28no—
374C25—216no—
375C25—48no—
376C25—432no—
377C25C24×C318yes—
378C25C24×C311yescharacteristic
379C25C24×C312yes—
380C2×#41—264no—
381C2×#41—416no—
382C2×#41—464no—
383C22×Q8—28no—
384C22×Q8—42no—
385C22×Q8C2×C3×D414yes—
386C22×D4—264no—
387C22×D4—28no—
388C22×D4—216no—
389C22×D4—28no—
390C22×D4—216no—
391C22×D4—216no—
392C22×D4—216no—
393C22×D4—216no—
394C22×D4—264no—
395C22×D4—28no—
396C22×D4—28no—
397C22×D4—28no—
398C22×D4—28no—
399C22×D4—216no—
400C22×D4—216no—
401C22×D4—216no—
402C22×D4—216no—
403C22×D4—232no—
404C22×D4—4128no—
405C22×D4—48no—
406C22×D4—44no—
407C22×D4—42no—
408C22×D4—432no—
409C22×D4—432no—
410C22×D4—432no—
411C22×D4—416no—
412C22×D4—416no—
413C22×D4—432no—
414C22×D4—432no—
415C22×D4C2×C3×D4116yes—
416C22×D4C2×C3×D414yes—
417C22×D4C2×C3×D418yes—
418C22×D4C2×C3×D4132yes—
419C23×C4—28no—
420C23×C4—28no—
421C23×C4—28no—
422C23×C4—24no—
423C23×C4C2×C3×D414yes—
424C23×C4C2×C3×D418yes—
425C23×C4C2×C3×D4116yes—
426C23×C4C24×C311yescharacteristic
427C23×C4C24×C318yes—
428C23×C4C24×C318yes—
429C23×C4C24×C312yes—
430C23×C4C24×C311yescharacteristic
431#127—2128no—
432#127—464no—
433#124—2128no—
434#121—2128no—
435#121—2128no—
436#120—2128no—
437#120—2128no—
438#120—4256no—
439#117—264no—
440C2×C4⋊C4—28no—
441C2×C4⋊C4—28no—
442C2×C4⋊C4C2×C3×D4116yes—
443C2×C22⋊C4—28no—
444C2×C22⋊C4—216no—
445C2×C22⋊C4—216no—
446C2×C22⋊C4—216no—
447C2×C22⋊C4—216no—
448C2×C22⋊C4—216no—
449C2×C22⋊C4—216no—
450C2×C22⋊C4—216no—
451C2×C22⋊C4—232no—
452C2×C22⋊C4—264no—
453C2×C22⋊C4—264no—
454C2×C22⋊C4—216no—
455C2×C22⋊C4—432no—
456C2×C22⋊C4—44no—
457C2×C22⋊C4C2×C3×D4132yes—
458C2×C42—216no—
459C2×C42—28no—
460C2×C42—216no—
461C2×C42—28no—
462#95—216no—
463#95—44no—
464#95—416no—
465C23×C3—24no—
466C23×C3—24no—
467C23×C3—216no—
468C23×C3—216no—
469C23×C3—216no—
470C23×C3—216no—
471C23×C3—216no—
472C23×C3—24no—
473C23×C3—22no—
474C23×C3—232no—
475C23×C3—232no—
476C23×C3—28no—
477C23×C3—232no—
478C23×C3—464no—
479C23×C3—48no—
480C23×C3—48no—
481C23×C3—48no—
482C23×C3—48no—
483C23×C3—48no—
484C23×C3—48no—
485C23×C3—44no—
486C23×C3—416no—
487C23×C3—432no—
488C23×C3—48no—
489C23×C3—416no—
490C23×C3—48no—
491C23×C3—432no—
492C23×C3—416no—
493C23×C3—416no—
494C23×C3—416no—
495C23×C3—44no—
496C23×C3—432no—
497C23×C3—432no—
498C23×C3—44no—
499C23×C3—864no—
500C23×C3—864no—
501C23×C3—8256no—
502C23×C3—864no—
503C23×C3C2×#12018yes—
504C23×C3C23×D411yescharacteristic
505C23×C3C23×D414yes—
506C23×C3C2×H(5,𝔽2)12yes—
507C23×C3C2×H(5,𝔽2)18yes—
508C3×Q8—416no—
509C3×D4—432no—
510C3×D4—464no—
511C3×D4—416no—
512C3×D4—464no—
513C3×D4—864no—
514C3×D4—864no—
515C3×D4—8128no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—216no—
519C2×C3×C4—264no—
520C2×C3×C4—216no—
521C2×C3×C4—24no—
522C2×C3×C4—22no—
523C2×C3×C4—232no—
524C2×C3×C4—232no—
525C2×C3×C4—216no—
526C2×C3×C4—48no—
527C2×C3×C4—44no—
528C2×C3×C4—416no—
529C2×C3×C4—416no—
530C2×C3×C4—416no—
531C2×C3×C4—48no—
532C2×C3×C4—416no—
533C2×C3×C4C2×#12018yes—
534C2×C3×C4C2×#12018yes—
535C2×C3×C4#53414yes—
536C2×C3×C4D42116yes—
537C24—24no—
538C24—216no—
539C24—24no—
540C24—232no—
541C24—28no—
542C24—28no—
543C24—216no—
544C24—24no—
545C24—28no—
546C24—232no—
547C24—22no—
548C24—232no—
549C24—216no—
550C24—464no—
551C24—416no—
552C24—464no—
553C24—416no—
554C24—832no—
555C24—832no—
556C24—832no—
557C24—832no—
558C24—832no—
559C24—832no—
560C24C22×C3×D4116yes—
561C24C22×C3×D412yes—
562C24C22×C3×D414yes—
563C24C22×C3×D418yes—
564C24C25×C311yescharacteristic
565#41—4128no—
566C2×Q8—216no—
567C2×Q8—44no—
568C2×Q8—416no—
569C2×D4—232no—
570C2×D4—216no—
571C2×D4—216no—
572C2×D4—264no—
573C2×D4—264no—
574C2×D4—216no—
575C2×D4—232no—
576C2×D4—264no—
577C2×D4—48no—
578C2×D4—44no—
579C2×D4—464no—
580C2×D4—432no—
581C2×D4—416no—
582C2×D4—4256no—
583C2×D4—464no—
584C2×D4—4128no—
585C2×D4—416no—
586C2×D4—464no—
587C2×D4—416no—
588C2×D4—416no—
589C2×D4—416no—
590C2×D4—432no—
591C2×D4—832no—
592C2×D4—832no—
593C2×D4—832no—
594C2×D4—832no—
595C2×D4—832no—
596C2×D4—832no—
597C2×D4—864no—
598C2×D4—832no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—216no—
602C22×C4—216no—
603C22×C4—264no—
604C22×C4—216no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—24no—
608C22×C4—28no—
609C22×C4—22no—
610C22×C4—28no—
611C22×C4—232no—
612C22×C4—216no—
613C22×C4—216no—
614C22×C4—28no—
615C22×C4—416no—
616C22×C4C3×#120132yescomplemented
617C22×C4C22×C3×D4116yes—
618C22×C4C22×C3×D412yes—
619C22×C4C22×C3×D418yes—
620C22×C4C22×C3×D414yes—
621C22×C4C22×C3×D412yes—
622C22×C4C22×C3×D418yes—
623C22×C4C3×H(5,𝔽2)116yes—
624C22×C4C3×H(5,𝔽2)14yes—
625C4⋊C4—232no—
626C22⋊C4—232no—
627C22⋊C4—264no—
628C22⋊C4—264no—
629C22⋊C4—264no—
630C22⋊C4—4128no—
631C22⋊C4—416no—
632C42—232no—
633C42—416no—
634C22×C3—28no—
635C22×C3—216no—
636C22×C3—432no—
637C22×C3—48no—
638C22×C3—48no—
639C22×C3—464no—
640C22×C3—42no—
641C22×C3—416no—
642C22×C3—44no—
643C22×C3—48no—
644C22×C3—416no—
645C22×C3—416no—
646C22×C3—8128no—
647C22×C3—88no—
648C22×C3—832no—
649C22×C3—816no—
650C22×C3—816no—
651C22×C3C22×#12012yes—
652C22×C3C2×#53411yescharacteristic
653C22×C3C2×D4214yes—
654C22×C3#348418yes—
655C22×C3#349818yes—
656C22×C3#349814yes—
657C22×C3#353714yes—
658C22×C3#354914yes—
659C3×C4—28no—
660C3×C4—416no—
661C3×C4—42no—
662C3×C4—416no—
663C3×C4#240318yes—
664C23—24no—
665C23—24no—
666C23—216no—
667C23—216no—
668C23—216no—
669C23—216no—
670C23—216no—
671C23—24no—
672C23—22no—
673C23—232no—
674C23—232no—
675C23—28no—
676C23—232no—
677C23—464no—
678C23—48no—
679C23—48no—
680C23—48no—
681C23—48no—
682C23—48no—
683C23—48no—
684C23—44no—
685C23—416no—
686C23—432no—
687C23—48no—
688C23—416no—
689C23—48no—
690C23—432no—
691C23—416no—
692C23—416no—
693C23—416no—
694C23—44no—
695C23—432no—
696C23—432no—
697C23—44no—
698C23—864no—
699C23—864no—
700C23—8256no—
701C23—864no—
702C23C2×C3×#12018yes—
703C23C23×C3×D411yescharacteristic
704C23C23×C3×D414yes—
705C23C2×C3×H(5,𝔽2)12yes—
706C23C2×C3×H(5,𝔽2)18yes—
707Q8—416no—
708D4—432no—
709D4—464no—
710D4—416no—
711D4—464no—
712D4—864no—
713D4—864no—
714D4—8128no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—216no—
718C2×C4—264no—
719C2×C4—216no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—232no—
723C2×C4—232no—
724C2×C4—216no—
725C2×C4—48no—
726C2×C4—44no—
727C2×C4—416no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—48no—
731C2×C4—416no—
732C2×C4C2×C3×#12018yes—
733C2×C4C2×C3×#12018yes—
734C2×C4C3×#53414yes—
735C2×C4C3×D42116yes—
736C2×C3—48no—
737C2×C3—82no—
738C2×C3—816no—
739C2×C3C2×#240311yescharacteristic
740C2×C3#3552714yes—
741C2×C3#3729712yes—
742C2×C3#4487018yes—
743C22—28no—
744C22—216no—
745C22—432no—
746C22—48no—
747C22—48no—
748C22—464no—
749C22—42no—
750C22—416no—
751C22—44no—
752C22—48no—
753C22—416no—
754C22—416no—
755C22—8128no—
756C22—832no—
757C22—88no—
758C22—816no—
759C22—816no—
760C22C22×C3×#12012yes—
761C22C2×C3×#53411yescharacteristic
762C22C2×C3×D4214yes—
763C22C3×#348418yes—
764C22C3×#349818yes—
765C22C3×#349814yes—
766C22C3×#353714yes—
767C22C3×#354914yes—
768C4—28no—
769C4—416no—
770C4—42no—
771C4—416no—
772C4C3×#240318yes—
773C3#76333611yescharacteristic, direct product factor, Sylow
774C2—48no—
775C2—816no—
776C2—82no—
777C2C2×C3×#240311yescharacteristic
778C2C3×#3552714yes—
779C2C3×#3729712yes—
780C2C3×#4487018yes—
subgroupG/H
center, socleC24×C3C25
commutator, Frattini, cosocleC24C25×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#535C2semidirect
2. C2×C3×#2433C2semidirect
3. C3×#15947C2semidirect
4. C3×#15763C2semidirect
5. C3×#15258C2semidirect
6. C3×#15124C2semidirect
7. C3×#14136C2semidirect
8. C3×#13851C2semidirect
9. #763336C3direct (N × H)
11. C24×C3×D4C22semidirect
16. C22×C3×#124C22semidirect
18. C22×C3×#121C22semidirect
20. C22×C3×#120C22semidirect
21. C22×C3×#120C22semidirect
22. C22×C3×#117C22semidirect
24. C2×C3×#392C22semidirect
25. C2×C3×#392C22semidirect
26. C2×C3×#390C22semidirect
27. C2×C3×C4×C22⋊C4C22semidirect
28. C2×C3×C4×C22⋊C4C22semidirect
29. C3×#1446C22semidirect
31. C3×#1438C22semidirect
32. C3×#1438C22semidirect
33. C3×#1438C22semidirect
34. C3×#1437C22semidirect
35. C3×C4⋊#95C22semidirect
36. C22×#535C2×C3semidirect
37. C2×#2433C2×C3semidirect
38. #15947C2×C3semidirect
39. #15763C2×C3semidirect
40. #15258C2×C3semidirect
41. #15124C2×C3semidirect
42. #14136C2×C3semidirect
43. #13851C2×C3semidirect
47. C22×C3×#41D4semidirect
74. C2×C3×#121D4semidirect
101. C24×D4C22×C3semidirect
106. C22×#124C22×C3semidirect
108. C22×#121C22×C3semidirect
110. C22×#120C22×C3semidirect
111. C22×#120C22×C3semidirect
112. C22×#117C22×C3semidirect
114. C2×#392C22×C3semidirect
115. C2×#392C22×C3semidirect
116. C2×#390C22×C3semidirect
117. C2×C4×C22⋊C4C22×C3semidirect
118. C2×C4×C22⋊C4C22×C3semidirect
119. #1446C22×C3semidirect
121. #1438C22×C3semidirect
122. #1438C22×C3semidirect
123. #1438C22×C3semidirect
124. #1437C22×C3semidirect
125. C4⋊#95C22×C3semidirect
222. C22×#41C3×D4semidirect
249. C2×#121C3×D4semidirect
354. C22×C3×C4#120semidirect
616. C22×C4C3×#120semidirect
773. C3#763336direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#5352
C2×C3×#24332
C3×#159472
C3×#157632
C3×#152582
C3×#151242
C3×#141362
C3×#138512
#7633363