Finite Group Databasebeta

← C2×#86467 #11702035

Subgroups — C2×#86467 #11702035

Order 768.

7302 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#540C211yesmaximal, characteristic, complemented
2#86467C2132yesmaximal, direct product factor
3C2×#5719C211yesmaximal, characteristic, complemented
4C2×#5716C211yesmaximal, characteristic, complemented
5C2×#5698C211yesmaximal, characteristic, complemented
6C2×#5688C211yesmaximal, characteristic, complemented
7C2×#5660C214yesmaximal, complemented
8C2×#5649C214yesmaximal, complemented
9C2×#5613C214yesmaximal, complemented
10C2×#5603C212yesmaximal, complemented
11C2×#5600C214yesmaximal, complemented
12C2×#5606C212yesmaximal, complemented
13C2×#5561C212yesmaximal, complemented
14C2×C4×#237C212yesmaximal, complemented
15C2×D3×#117C211yesmaximal, characteristic, complemented
16C2×#5518C211yesmaximal, characteristic, complemented
17C2×#3455—31nomaximal, Sylow
18C22×#237C2212yes—
19C23×C4×D3C2211yescharacteristic
20C3×#540C22116yescomplemented
21C2×C3×#127C2211yescharacteristic, complemented
22C2×C3×#125C2211yescharacteristic, complemented
23C2×C3×#123C2214yescomplemented
24C2×C3×#121C2212yes—
25C2×C3×#121C2214yes—
26C2×C3×C4×D4C2212yescomplemented
27C2×C3×#117C2211yescharacteristic
28C2×#939C2214yes—
29C2×#938C2212yes—
30C2×#938C2214yes—
31C2×#937C2214yes—
32C2×#936C2214yes—
33C2×#936C2212yescomplemented
34C2×#935C2214yes—
35C2×#935C2214yescomplemented
36C2×D4×Dic3C2214yes—
37C2×D4×Dic3C2214yescomplemented
38C2×D4×Dic3C2212yescomplemented
39C2×#929C2214yes—
40C2×C4×#67C2214yes—
41C2×#926C2211yescharacteristic
42C2×#924C2212yes—
43C2×#924C2214yescomplemented
44C22×C4×Dic3C2214yescomplemented
45#5719C22116yescomplemented
46#5716C22116yescomplemented
47#5698C22116yescomplemented
48#5688C22116yescomplemented
49#5660C22164yescomplemented
50#5649C22164yescomplemented
51#5613C22164yescomplemented
52#5606C22132yescomplemented
53#5603C22132yescomplemented
54#5600C22164yescomplemented
55#5561C22132yescomplemented
56C4×#237C22132yescomplemented
57D3×#117C22116yescomplemented
58#5518C22116yescomplemented
59C2×#898C2214yes—
60C2×#897C2212yes—
61C2×#896C2214yes—
62C2×#892C2212yes—
63C2×#892C2212yes—
64C2×D3×C4⋊C4C2212yes—
65C2×#890C2214yescomplemented
66C2×#889C2214yescomplemented
67C2×#888C2212yescomplemented
68C2×#887C2214yescomplemented
69C2×#887C2212yescomplemented
70C2×#885C2214yes—
71C2×#883C2214yes—
72C2×#67⋊C4C2214yes—
73C2×#67⋊C4C2214yes—
74C2×D3×C22⋊C4C2212yes—
75C2×#879C2214yes—
76C2×#879C2214yescomplemented
77C2×#879C2214yescomplemented
78C2×#878C2214yescomplemented
79C2×#877C2212yes—
80C2×#877C2214yescomplemented
81C2×#872C2211yescharacteristic
82C2×#872C2211yescharacteristic
83C2×C42×D3C2211yescharacteristic
84C2×C42×D3C2211yescharacteristic
85C2×#870C2211yescharacteristic, complemented
86C2×#869C2211yescharacteristic, complemented
87C2×C4×Dic6C2212yescomplemented
88#3455—332no—
89C2×#542—32no—
90C2×#542—32no—
91C2×#541—31no—
92C2×#541—31no—
93C2×#540—31no—
94C2×#540D311yescharacteristic, complemented
95C2×#539—34no—
96C2×#538—34no—
97C2×#533—31no—
98C2×#532—31no—
99C2×#529—34no—
100C2×#529—34no—
101C2×#525—32no—
102C2×C4×#41—32no—
103C22×#117—31no—
104C24×D3C2311yescharacteristic
105C22×C3×D4C2312yes—
106C22×C3×D4C2314yes—
107C22×C3×D4C2314yes—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2314yes—
110C22×#67C2314yes—
111C22×#67C2314yes—
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2314yes—
114C23×Dic3C2314yes—
115C2×#237—216no—
116C2×#237C23116yes—
117C22×C4×D3—28no—
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2311yescharacteristic
121C22×C4×D3C2318yes—
122C22×C4×D3C2312yes—
123C22×C4×D3C2312yes—
124C22×C4×D3C2311yescharacteristic
125C22×Dic6C2312yes—
126C22×Dic6C2314yes—
127C3×#127C2318yescomplemented
128C3×#125C2318yescomplemented
129C3×#123C23132yescomplemented
130C3×#121C23132yes—
131C3×#121C23116yes—
132C3×C4×D4C23116yescomplemented
133C3×#117C2318yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×#217C2312yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148#939C23132yes—
149#938C23132yes—
150#938C23116yes—
151#937C23132yes—
152#936C23132yes—
153#936C23116yescomplemented
154#935C23132yes—
155#935C23132yescomplemented
156D4×Dic3C23132yes—
157D4×Dic3C23132yescomplemented
158D4×Dic3C23116yescomplemented
159#929C23132yes—
160C4×#67C23132yes—
161C2×(C2×D3)⋊C4C2312yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165#926C2318yes—
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2314yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2314yes—
170#924C23116yes—
171#924C23132yescomplemented
172C2×Dic3⋊C4C2314yes—
173C2×Dic3⋊C4C2314yes—
174C2×Dic3⋊C4C2312yes—
175C2×Dic3⋊C4C2312yes—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×C4×Dic3C2314yes—
180C2×C4×Dic3C2311yescharacteristic
181C2×C4×Dic3C2311yescharacteristic
182C2×C4×Dic3C2312yes—
183C2×C4×Dic3C2312yes—
184C2×C4×Dic3C2314yes—
185C2×C4×Dic3C2314yes—
186C2×C4×Dic3C23132yescomplemented
187#898C23132yes—
188#897C23116yes—
189#896C23132yes—
190#892C23116yes—
191#892C23116yes—
192D3×C4⋊C4C23116yes—
193#890C23132yescomplemented
194#889C23132yescomplemented
195#888C23116yescomplemented
196#887C23132yescomplemented
197#887C23116yescomplemented
198#885C23132yes—
199#883C23132yes—
200#67⋊C4C23132yes—
201#67⋊C4C23132yes—
202D3×C22⋊C4C23116yes—
203#879C23132yes—
204#879C23132yescomplemented
205#879C23132yescomplemented
206#878C23132yescomplemented
207#877C23116yes—
208#877C23132yescomplemented
209#872C2318yes—
210#872C2318yes—
211C42×D3C2318yes—
212C42×D3C2318yes—
213#870C2318yescomplemented
214#869C2318yescomplemented
215C4×Dic6C23116yescomplemented
216C22×#41—32no—
217C24×C4—31no—
218#542—332no—
219#542—332no—
220#541—316no—
221#541—316no—
222#540—316no—
223#540C2×D3116yescomplemented
224#539—364no—
225#538—364no—
226#533—316no—
227#532—316no—
228C2×C4⋊Q8—32no—
229C2×C4⋊Q8—31no—
230C2×#127C2×D311yescharacteristic, complemented
231#529—364no—
232#529—364no—
233C2×#126—34no—
234C2×#126—34no—
235C2×#126—34no—
236C2×#126—34no—
237C2×#125—34no—
238C2×#125—34no—
239C2×#125—31no—
240C2×#125C2×D311yescharacteristic, complemented
241C2×#124—34no—
242C2×#124—32no—
243C2×#124—34no—
244#525—332no—
245C2×#123—34no—
246C2×#123—34no—
247C2×#123—34no—
248C2×#123—34no—
249C2×#123C2×D314yescomplemented
250C2×C22⋊Q8—32no—
251C2×C22⋊Q8—34no—
252C2×C22⋊Q8—32no—
253C2×C22⋊Q8—34no—
254C2×C22⋊Q8—34no—
255C2×#121—32no—
256C2×#121—34no—
257C2×#121—34no—
258C2×#121C2×D312yes—
259C2×#121C2×D314yes—
260C2×#120—34no—
261C4×#41—332no—
262C2×C4×Q8—32no—
263C2×C4×Q8—34no—
264C2×C4×Q8—32no—
265C2×C4×D4—32no—
266C2×C4×D4—34no—
267C2×C4×D4—34no—
268C2×C4×D4—34no—
269C2×C4×D4—34no—
270C2×C4×D4—34no—
271C2×C4×D4C2×D312yescomplemented
272C2×#117—31no—
273C2×#117—316no—
274C2×#117—32no—
275C2×#117—32no—
276C2×#117—32no—
277C2×#117—34no—
278C2×#117—31no—
279C2×#117—31no—
280C2×#117C2×D311yescharacteristic
281C22×C4⋊C4—32no—
282C22×C22⋊C4—32no—
283C22×C42—34no—
284C22×C42—31no—
285C22×C42—31no—
286C24×C3C2411yescharacteristic
287C24×C3C2414yes—
288C23×D3—24no—
289C23×D3—44no—
290C23×D3C2411yescharacteristic
291C23×D3C2411yescharacteristic
292C23×D3C2414yes—
293C2×C3×D4—28no—
294C2×C3×D4—48no—
295C2×C3×D4—48no—
296C2×C3×D4C2418yes—
297C2×C3×D4C24116yes—
298C2×C3×D4C24116yes—
299C22×C3×C4—24no—
300C22×C3×C4—48no—
301C22×C3×C4C2412yes—
302C22×C3×C4C2414yes—
303C22×C3×C4C2412yes—
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2414yes—
306C22×C3×C4C24116yes—
307C22×C3×C4C2411yescharacteristic
308C2×#67—216no—
309C2×#67—48no—
310C2×#67C24116yes—
311C2×#67C24116yes—
312C22×Dic3—24no—
313C22×Dic3—216no—
314C22×Dic3—48no—
315C22×Dic3C2414yes—
316C22×Dic3C24116yes—
317C22×Dic3C2412yes—
318C22×Dic3C2414yes—
319C22×Dic3C2414yes—
320C22×Dic3C2412yes—
321C22×Dic3C2411yescharacteristic
322C22×Dic3C24116yes—
323C22×Dic3C2411yescharacteristic
324#237—264no—
325C2×C4×D3—24no—
326C2×C4×D3—24no—
327C2×C4×D3—24no—
328C2×C4×D3—232no—
329C2×C4×D3—44no—
330C2×C4×D3—44no—
331C2×C4×D3#4118yes—
332C2×C4×D3C2414yes—
333C2×C4×D3C2414yes—
334C2×C4×D3C2414yes—
335C2×C4×D3C2418yes—
336C2×C4×D3C2418yes—
337C2×C4×D3C2414yes—
338C2×Dic6—28no—
339C2×Dic6—48no—
340C2×Dic6C2418yes—
341C2×Dic6C24116yes—
342C3×C4⋊C4C2418yes—
343C3×C4⋊C4C24116yes—
344C3×C4⋊C4C2418yes—
345C3×C22⋊C4C2418yes—
346C3×C22⋊C4C24116yes—
347C3×C22⋊C4C24116yes—
348C3×C42C2414yes—
349C3×C42C2414yes—
350#217C2418yes—
351#217C24116yes—
352#217C24116yes—
353#217C24116yes—
354#217C24116yes—
355#217C24116yes—
356(C2×D3)⋊C4C2418yes—
357(C2×D3)⋊C4C2418yes—
358(C2×D3)⋊C4C24116yes—
359(C2×D3)⋊C4C24116yes—
360C4⋊Dic3C2418yes—
361C4⋊Dic3C24116yes—
362C4⋊Dic3C2418yes—
363C4⋊Dic3C24116yes—
364Dic3⋊C4C24116yes—
365Dic3⋊C4C24116yes—
366Dic3⋊C4C2418yes—
367Dic3⋊C4C2418yes—
368Dic3⋊C4C24116yes—
369Dic3⋊C4C24116yes—
370Dic3⋊C4C24116yes—
371C4×Dic3C24116yes—
372C4×Dic3C2414yes—
373C4×Dic3C2414yes—
374C4×Dic3C2418yes—
375C4×Dic3C2418yes—
376C4×Dic3C24116yes—
377C4×Dic3C24116yes—
378C25—31no—
379C2×#41—316no—
380C2×#41—616no—
381C22×Q8—32no—
382C22×Q8—34no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4C22×D312yes—
386C22×D4C22×D314yes—
387C22×D4C22×D314yes—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—34no—
391C23×C4—34no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—38no—
396C23×C4—32no—
397C23×C4—32no—
398C23×C4—68no—
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D314yes—
401C4⋊Q8—316no—
402C4⋊Q8—38no—
403#127C22×D318yescomplemented
404#126—332no—
405#126—332no—
406#126—332no—
407#126—332no—
408#125—332no—
409#125—332no—
410#125—38no—
411#125C22×D318yescomplemented
412#124—332no—
413#124—316no—
414#124—332no—
415#123—332no—
416#123—332no—
417#123—332no—
418#123—332no—
419#123C22×D3132yescomplemented
420C22⋊Q8—316no—
421C22⋊Q8—332no—
422C22⋊Q8—316no—
423C22⋊Q8—332no—
424C22⋊Q8—332no—
425#121—316no—
426#121—332no—
427#121—332no—
428#121C22×D3116yes—
429#121C22×D3132yes—
430#120—332no—
431C4×Q8—316no—
432C4×Q8—332no—
433C4×Q8—316no—
434C4×D4—316no—
435C4×D4—332no—
436C4×D4—332no—
437C4×D4—332no—
438C4×D4—332no—
439C4×D4—332no—
440C4×D4C22×D3116yescomplemented
441#117—38no—
442#117—316no—
443#117—316no—
444#117—316no—
445#117—332no—
446#117—38no—
447#117—38no—
448#117C22×D318yes—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—32no—
452C2×C4⋊C4—32no—
453C2×C4⋊C4—34no—
454C2×C4⋊C4—34no—
455C2×C4⋊C4—34no—
456C2×C4⋊C4—34no—
457C2×C4⋊C4—34no—
458C2×C4⋊C4—34no—
459C2×C4⋊C4—34no—
460C2×C4⋊C4—316no—
461C2×C4⋊C4C22×D312yes—
462C2×C4⋊C4C22×D312yes—
463C2×C4⋊C4C22×D314yes—
464C2×C22⋊C4—32no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—34no—
469C2×C22⋊C4—34no—
470C2×C22⋊C4—32no—
471C2×C22⋊C4—32no—
472C2×C22⋊C4—34no—
473C2×C22⋊C4—34no—
474C2×C22⋊C4—316no—
475C2×C22⋊C4C22×D312yes—
476C2×C22⋊C4C22×D314yes—
477C2×C22⋊C4C22×D314yes—
478C2×C42—32no—
479C2×C42—32no—
480C2×C42—34no—
481C2×C42—31no—
482C2×C42—31no—
483C2×C42—34no—
484C2×C42—34no—
485C2×C42—332no—
486C2×C42—38no—
487C2×C42—38no—
488C2×C42C22×D311yescharacteristic
489C2×C42C22×D311yescharacteristic
490C23×C3—28no—
491C23×C3—22no—
492C23×C3—28no—
493C23×C3—28no—
494C23×C3—24no—
495C23×C3C2512yes—
496C23×C3C2518yes—
497C23×C3C2511yescharacteristic
498C22×D3—24no—
499C22×D3—22no—
500C22×D3—24no—
501C22×D3—28no—
502C22×D3—48no—
503C22×D3—416no—
504C22×D3C2×#4114yes—
505C22×D3C2512yes—
506C22×D3C2512yes—
507C3×D4—216no—
508C3×D4—416no—
509C3×D4—416no—
510C2×C3×C4—22no—
511C2×C3×C4—28no—
512C2×C3×C4—24no—
513C2×C3×C4—24no—
514C2×C3×C4—28no—
515C2×C3×C4—416no—
516C2×C3×C4C2×#4114yes—
517C2×C3×C4C2514yes—
518C2×C3×C4C2518yes—
519C2×C3×C4C2514yes—
520C2×C3×C4C2512yes—
521C2×C3×C4C2512yes—
522#67—232no—
523#67—416no—
524C2×Dic3—28no—
525C2×Dic3—22no—
526C2×Dic3—24no—
527C2×Dic3—28no—
528C2×Dic3—24no—
529C2×Dic3—28no—
530C2×Dic3—232no—
531C2×Dic3—416no—
532C2×Dic3C2×#4114yes—
533C2×Dic3C2514yes—
534C2×Dic3C2518yes—
535C2×Dic3C2518yes—
536C2×Dic3C2514yes—
537C2×Dic3C2512yes—
538C2×Dic3C2512yes—
539C4×D3—28no—
540C4×D3—28no—
541C4×D3—28no—
542C4×D3—48no—
543C4×D3—48no—
544C4×D3C2×#41116yes—
545Dic6—216no—
546Dic6—416no—
547C24—31no—
548C24—31no—
549C24—34no—
550C24—64no—
551C24—124no—
552C24C23×D311yescharacteristic
553C24C23×D314yes—
554#41—664no—
555C2×Q8—38no—
556C2×Q8—316no—
557C2×Q8—68no—
558C2×Q8—128no—
559C2×D4—28no—
560C2×D4—316no—
561C2×D4—316no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—616no—
565C2×D4—128no—
566C2×D4C23×D318yes—
567C2×D4C23×D3116yes—
568C2×D4C23×D3116yes—
569C22×C4—24no—
570C22×C4—31no—
571C22×C4—38no—
572C22×C4—34no—
573C22×C4—316no—
574C22×C4—34no—
575C22×C4—32no—
576C22×C4—32no—
577C22×C4—34no—
578C22×C4—34no—
579C22×C4—31no—
580C22×C4—316no—
581C22×C4—34no—
582C22×C4—34no—
583C22×C4—34no—
584C22×C4—38no—
585C22×C4—38no—
586C22×C4—48no—
587C22×C4—64no—
588C22×C4—632no—
589C22×C4—64no—
590C22×C4—64no—
591C22×C4—616no—
592C22×C4—64no—
593C22×C4—124no—
594C22×C4—124no—
595C22×C4—128no—
596C22×C4C23×D314yes—
597C22×C4C23×D312yes—
598C22×C4C23×D314yes—
599C22×C4C23×D312yes—
600C22×C4C23×D311yescharacteristic
601C22×C4C23×D3116yes—
602C22×C4C23×D311yescharacteristic
603C4⋊C4—38no—
604C4⋊C4—38no—
605C4⋊C4—38no—
606C4⋊C4—38no—
607C4⋊C4—316no—
608C4⋊C4—316no—
609C4⋊C4—316no—
610C4⋊C4—316no—
611C4⋊C4—316no—
612C4⋊C4—316no—
613C4⋊C4—316no—
614C4⋊C4C23×D318yes—
615C4⋊C4C23×D318yes—
616C4⋊C4C23×D3116yes—
617C22⋊C4—38no—
618C22⋊C4—316no—
619C22⋊C4—316no—
620C22⋊C4—316no—
621C22⋊C4—316no—
622C22⋊C4—316no—
623C22⋊C4—38no—
624C22⋊C4—38no—
625C22⋊C4—316no—
626C22⋊C4—316no—
627C22⋊C4C23×D318yes—
628C22⋊C4C23×D3116yes—
629C22⋊C4C23×D3116yes—
630C42—38no—
631C42—38no—
632C42—316no—
633C42—34no—
634C42—34no—
635C42—316no—
636C42—316no—
637C42C23×D314yes—
638C42C23×D314yes—
639C22×C3—28no—
640C22×C3—22no—
641C22×C3—28no—
642C22×C3—28no—
643C22×C3—24no—
644C22×C3—44no—
645C22×C3—416no—
646C22×C3C22×#4112yes—
647C22×C3#58514yes—
648C22×C3C2611yescharacteristic
649C2×D3—24no—
650C2×D3—28no—
651C2×D3—22no—
652C2×D3—24no—
653C2×D3—416no—
654C2×D3—44no—
655C2×D3C22×#4114yes—
656C3×C4—22no—
657C3×C4—28no—
658C3×C4—24no—
659C3×C4—24no—
660C3×C4C22×#4114yes—
661Dic3—28no—
662Dic3—22no—
663Dic3—24no—
664Dic3—28no—
665Dic3—24no—
666Dic3C22×#4114yes—
667C23—22no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—24no—
672C23—34no—
673C23—32no—
674C23—32no—
675C23—68no—
676C23—64no—
677C23—62no—
678C23—64no—
679C23—128no—
680C23—1216no—
681C23C24×D312yes—
682C23C24×D318yes—
683C23C24×D311yescharacteristic
684Q8—616no—
685Q8—1216no—
686D4—216no—
687D4—416no—
688D4—416no—
689D4—632no—
690D4—1216no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—34no—
697C2×C4—32no—
698C2×C4—316no—
699C2×C4—34no—
700C2×C4—34no—
701C2×C4—38no—
702C2×C4—38no—
703C2×C4—32no—
704C2×C4—416no—
705C2×C4—68no—
706C2×C4—68no—
707C2×C4—68no—
708C2×C4—632no—
709C2×C4—62no—
710C2×C4—68no—
711C2×C4—64no—
712C2×C4—68no—
713C2×C4—64no—
714C2×C4—68no—
715C2×C4—128no—
716C2×C4—128no—
717C2×C4—1216no—
718C2×C4D3×#4114yes—
719C2×C4C24×D314yes—
720C2×C4C24×D318yes—
721C2×C4C24×D314yes—
722C2×C4C24×D312yes—
723C2×C4C24×D312yes—
724C2×C3—42no—
725C2×C3—48no—
726C2×C3#345514yescomplemented
727C2×C3C23×#4111yescharacteristic
728C2×C3C2×#58512yes—
729D3—24no—
730D3—42no—
731C22—22no—
732C22—28no—
733C22—28no—
734C22—28no—
735C22—24no—
736C22—34no—
737C22—44no—
738C22—416no—
739C22—64no—
740C22—68no—
741C22—62no—
742C22—64no—
743C22—1216no—
744C22—124no—
745C22C2×D3×#4112yes—
746C22#596614yes—
747C22C25×D311yescharacteristic
748C4—22no—
749C4—24no—
750C4—28no—
751C4—24no—
752C4—34no—
753C4—62no—
754C4—68no—
755C4—64no—
756C4—68no—
757C4—64no—
758C4C2×D3×#4114yes—
759C3C2×#345511yescharacteristic, complemented, Sylow
760C2—42no—
761C2—48no—
762C2—64no—
763C2—122no—
764C2#8646714yesdirect product factor
765C2C22×D3×#4111yescharacteristic
766C2C2×#596612yes—
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#540C2
socleC23×C3C25
hypercenterC2×#540D3
hypocenterC3C2×#3455
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×C3×#540C2semidirect
2. #86467C2direct (N × H)
3. C2×#5719C2semidirect
4. C2×#5716C2semidirect
5. C2×#5698C2semidirect
6. C2×#5688C2semidirect
7. C2×#5660C2semidirect
8. C2×#5649C2semidirect
9. C2×#5613C2semidirect
10. C2×#5603C2semidirect
11. C2×#5600C2semidirect
12. C2×#5606C2semidirect
13. C2×#5561C2semidirect
14. C2×C4×#237C2semidirect
15. C2×D3×#117C2semidirect
16. C2×#5518C2semidirect
20. C3×#540C22semidirect
21. C2×C3×#127C22semidirect
22. C2×C3×#125C22semidirect
23. C2×C3×#123C22semidirect
26. C2×C3×C4×D4C22semidirect
33. C2×#936C22semidirect
35. C2×#935C22semidirect
37. C2×D4×Dic3C22semidirect
38. C2×D4×Dic3C22semidirect
43. C2×#924C22semidirect
44. C22×C4×Dic3C22semidirect
45. #5719C22semidirect
46. #5716C22semidirect
47. #5698C22semidirect
48. #5688C22semidirect
49. #5660C22semidirect
50. #5649C22semidirect
51. #5613C22semidirect
52. #5606C22semidirect
53. #5603C22semidirect
54. #5600C22semidirect
55. #5561C22semidirect
56. C4×#237C22semidirect
57. D3×#117C22semidirect
58. #5518C22semidirect
65. C2×#890C22semidirect
66. C2×#889C22semidirect
67. C2×#888C22semidirect
68. C2×#887C22semidirect
69. C2×#887C22semidirect
76. C2×#879C22semidirect
77. C2×#879C22semidirect
78. C2×#878C22semidirect
80. C2×#877C22semidirect
85. C2×#870C22semidirect
86. C2×#869C22semidirect
87. C2×C4×Dic6C22semidirect
94. C2×#540D3semidirect
127. C3×#127C23semidirect
128. C3×#125C23semidirect
129. C3×#123C23semidirect
132. C3×C4×D4C23semidirect
153. #936C23semidirect
155. #935C23semidirect
157. D4×Dic3C23semidirect
158. D4×Dic3C23semidirect
171. #924C23semidirect
186. C2×C4×Dic3C23semidirect
193. #890C23semidirect
194. #889C23semidirect
195. #888C23semidirect
196. #887C23semidirect
197. #887C23semidirect
204. #879C23semidirect
205. #879C23semidirect
206. #878C23semidirect
208. #877C23semidirect
213. #870C23semidirect
214. #869C23semidirect
215. C4×Dic6C23semidirect
223. #540C2×D3semidirect
230. C2×#127C2×D3semidirect
240. C2×#125C2×D3semidirect
249. C2×#123C2×D3semidirect
271. C2×C4×D4C2×D3semidirect
403. #127C22×D3semidirect
411. #125C22×D3semidirect
419. #123C22×D3semidirect
440. C4×D4C22×D3semidirect
726. C2×C3#3455semidirect
759. C3C2×#3455semidirect
764. C2#86467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5402
#864672
C2×#57192
C2×#57162
C2×#56982
C2×#56882
C2×#56602
C2×#56492
C2×#56132
C2×#56032
C2×#56002
C2×#56062
C2×#55612
C2×C4×#2372
C2×D3×#1172
C2×#55182
C2×#34553