Finite Group Databasebeta

← C2×#74587 #11001066

Subgroups — C2×#74587 #11001066

Order 768.

3354 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic3C211yesmaximal, characteristic, complemented
2C22×#898C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic
5C2×#4990C211yesmaximal, characteristic, complemented
6C2×#4978C211yesmaximal, characteristic, complemented
7C2×#4980C211yesmaximal, characteristic, complemented
8C2×#4958C211yesmaximal, characteristic
9C2×#4958C211yesmaximal, characteristic
10C2×#4950C211yesmaximal, characteristic, complemented
11C2×#4946C211yesmaximal, characteristic, complemented
12#74587C2116yesmaximal, direct product factor
13C2×#4670C211yesmaximal, characteristic, complemented
14C2×#4669C211yesmaximal, characteristic, complemented
15C2×#4654C211yesmaximal, characteristic, complemented
16C2×#4651C211yesmaximal, characteristic, complemented
17C2×#2852—31nomaximal, Sylow
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3—28no—
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2218yescomplemented
43C2×#898—28no—
44C2×#898C2218yescomplemented
45C3×#385C2218yescomplemented
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48#5213C2218yes—
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4990C2218yescomplemented
60#4980C2218yescomplemented
61#4978C2218yescomplemented
62#4958C2218yes—
63#4958C2218yes—
64#4950C2218yescomplemented
65#4946C2218yescomplemented
66#4670C2218yescomplemented
67#4669C2218yescomplemented
68#4654C2218yescomplemented
69#4651C2218yescomplemented
70C22×#126—31no—
71C23×C42—31no—
72#2852—316no—
73C2×#388—31no—
74C2×#388—31no—
75C2×#388—31no—
76C2×#387—31no—
77C2×#387—31no—
78C2×#387—31no—
79C2×#386—31no—
80C2×#386—31no—
81C2×#386—31no—
82C2×#385—31no—
83C2×#385—31no—
84C2×#385D311yescharacteristic, complemented
85C2×#383—31no—
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C23×C3×C4—24no—
89C23×C3×C4—24no—
90C23×C3×C4—24no—
91C23×C3×C4C2314yes—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—24no—
99C22×#67—24no—
100C22×#67—24no—
101C22×#67C2314yes—
102C23×Dic3—24no—
103C23×Dic3—24no—
104C23×Dic3—24no—
105C23×Dic3—24no—
106C23×Dic3—24no—
107C23×Dic3—24no—
108C23×Dic3C2314yes—
109C23×Dic3C2314yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4—24no—
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C22⋊C4—24no—
122C2×C3×C22⋊C4—24no—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2314yes—
125C2×#217—24no—
126C2×#217C2314yes—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×C4⋊Dic3—24no—
140C2×C4⋊Dic3—24no—
141C2×C4⋊Dic3C2314yes—
142C2×C4⋊Dic3C2314yes—
143C2×Dic3⋊C4—24no—
144C2×Dic3⋊C4—24no—
145C2×Dic3⋊C4C2314yes—
146C2×Dic3⋊C4C2314yes—
147C2×C4×Dic3—24no—
148C2×C4×Dic3—24no—
149C2×C4×Dic3—24no—
150C2×C4×Dic3—232no—
151C2×C4×Dic3D418yescomplemented
152C2×C4×Dic3C2314yes—
153C2×C4×Dic3C2314yes—
154C2×C4×Dic3C2314yes—
155C2×C4×Dic3C2314yes—
156#898—232no—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C23×D4—31no—
170C24×C4—31no—
171C24×C4—31no—
172C24×C4C2×D311yescharacteristic
173C2×#126—38no—
174C2×#126—68no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C4⋊C4C2×D311yescharacteristic
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C42—31no—
191C22×C42—38no—
192C22×C42—31no—
193C22×C42—31no—
194C22×C42—31no—
195C22×C42—68no—
196#388—38no—
197#388—38no—
198#388—38no—
199#387—38no—
200#387—38no—
201#387—38no—
202#386—38no—
203#386—38no—
204#386—38no—
205#385—38no—
206#385—38no—
207#385C2×D318yescomplemented
208#383—38no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3#4114yes—
226C24×C3#4114yes—
227C24×C3#4114yes—
228C24×C3C2412yes—
229C24×C3C2411yescharacteristic
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3C2412yes—
238C22×C3×C4—232no—
239C22×C3×C4—22no—
240C22×C3×C4—28no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—28no—
245C22×C3×C4—28no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4C2×D414yes—
259C22×C3×C4#4114yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C2×#67—28no—
267C2×#67—28no—
268C2×#67—28no—
269C2×#67—416no—
270C22×Dic3—232no—
271C22×Dic3—232no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—28no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—28no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—28no—
283C22×Dic3—28no—
284C22×Dic3—28no—
285C22×Dic3—28no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3C2×D414yes—
296C22×Dic3C2×D414yes—
297C22×Dic3#4114yes—
298C22×Dic3#4114yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C22×Dic3C2412yes—
306C3×C4⋊C4—28no—
307C3×C4⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—28no—
310#217—28no—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4—28no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—28no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317C4⋊Dic3—28no—
318C4⋊Dic3—28no—
319Dic3⋊C4—28no—
320Dic3⋊C4—28no—
321C4×Dic3—28no—
322C4×Dic3—28no—
323C4×Dic3—28no—
324C4×Dic3C2×D4116yescomplemented
325C25—31no—
326C25C22×D311yescharacteristic
327C22×D4—34no—
328C22×D4—64no—
329C22×D4—64no—
330C22×D4—64no—
331C23×C4—24no—
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—34no—
339C23×C4—34no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—64no—
344C23×C4—64no—
345C23×C4—64no—
346C23×C4—64no—
347C23×C4—64no—
348C23×C4—64no—
349C23×C4C22×D314yes—
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356#126—632no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—34no—
361C2×C4⋊C4—34no—
362C2×C4⋊C4—34no—
363C2×C4⋊C4—64no—
364C2×C4⋊C4—64no—
365C2×C4⋊C4—64no—
366C2×C4⋊C4—64no—
367C2×C4⋊C4C22×D314yes—
368C2×C4⋊C4C22×D314yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—34no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—64no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4C22×D314yes—
386C2×C22⋊C4C22×D314yes—
387C2×C42—38no—
388C2×C42—34no—
389C2×C42—34no—
390C2×C42—34no—
391C2×C42—34no—
392C2×C42—632no—
393C2×C42—64no—
394C2×C42—64no—
395C2×C42—64no—
396#95—34no—
397#95—34no—
398#95—34no—
399#95—34no—
400#95—34no—
401#95—34no—
402#95—34no—
403#95—34no—
404#95—34no—
405#95—34no—
406#95C22×D314yes—
407#95C22×D314yes—
408C23×C3—28no—
409C23×C3—28no—
410C23×C3—28no—
411C23×C3—28no—
412C23×C3—28no—
413C23×C3—28no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3#126116yescomplemented
419C23×C3C22×D412yes—
420C23×C3C2×#4114yes—
421C23×C3C2×#4112yes—
422C23×C3C2×#4114yes—
423C23×C3C2×#4112yes—
424C23×C3C2×#4112yes—
425C23×C3C2×#4114yes—
426C23×C3C2×#4112yes—
427C23×C3C2×#4112yes—
428C23×C3C2×#4112yes—
429C23×C3C2511yescharacteristic
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—44no—
438C22×D3—44no—
439C22×D3—44no—
440C22×D3—44no—
441C22×D3—44no—
442C22×D3—44no—
443C22×D3—44no—
444C2×C3×C4—232no—
445C2×C3×C4—28no—
446C2×C3×C4—28no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4C22×D414yes—
468C2×C3×C4C2×#4114yes—
469#67—416no—
470C2×Dic3—232no—
471C2×Dic3—232no—
472C2×Dic3—28no—
473C2×Dic3—28no—
474C2×Dic3—28no—
475C2×Dic3—28no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—44no—
494C2×Dic3—44no—
495C2×Dic3—44no—
496C2×Dic3C22×D414yes—
497C2×Dic3C22×D414yes—
498C2×Dic3C2×#4114yes—
499C2×Dic3C2×#4114yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—32no—
505C24—62no—
506C24—62no—
507C24—62no—
508C24—62no—
509C24—62no—
510C24—62no—
511C24—62no—
512C24#23514yes—
513C24#23714yes—
514C24#23914yes—
515C24C23×D312yes—
516C24C23×D311yescharacteristic
517C2×D4—68no—
518C2×D4—68no—
519C2×D4—68no—
520C2×D4—1216no—
521C22×C4—232no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—22no—
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—34no—
542C22×C4—34no—
543C22×C4—34no—
544C22×C4—34no—
545C22×C4—32no—
546C22×C4—32no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—68no—
553C22×C4—68no—
554C22×C4—68no—
555C22×C4—68no—
556C22×C4—632no—
557C22×C4—632no—
558C22×C4—68no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—68no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4D3×D414yes—
578C22×C4#23714yes—
579C22×C4C23×D312yes—
580C22×C4C23×D312yes—
581C22×C4C23×D312yes—
582C22×C4C23×D312yes—
583C22×C4C23×D312yes—
584C22×C4C23×D312yes—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—68no—
588C4⋊C4—68no—
589C4⋊C4—68no—
590C4⋊C4—68no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—68no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—68no—
597C22⋊C4—68no—
598C22⋊C4—68no—
599C22⋊C4—68no—
600C42—316no—
601C42—68no—
602C42—68no—
603C42—68no—
604C22×C3—232no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3#52514yes—
612C22×C3#52514yes—
613C22×C3#52514yes—
614C22×C3C2×#12614yes—
615C22×C3C2×#12618yescomplemented
616C22×C3#52914yes—
617C22×C3#52914yes—
618C22×C3#52914yes—
619C22×C3C23×D411yescharacteristic
620C22×C3C22×#4111yescharacteristic
621C22×C3C22×#4111yescharacteristic
622C22×C3C22×#4111yescharacteristic
623C22×C3C22×#4111yescharacteristic
624C22×C3C22×#4111yescharacteristic
625C22×C3C22×#4111yescharacteristic
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—88no—
634C3×C4—24no—
635C3×C4—24no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—42no—
640Dic3—24no—
641Dic3—24no—
642Dic3—24no—
643Dic3—24no—
644Dic3—42no—
645Dic3—42no—
646Dic3—42no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—124no—
665C23—124no—
666C23—124no—
667C23—124no—
668C23—124no—
669C23—124no—
670C23—124no—
671C23#898116yescomplemented
672C23C2×#23514yes—
673C23C2×#23512yes—
674C23C2×D3×D412yes—
675C23C2×#23714yes—
676C23C2×#23712yes—
677C23C2×#23712yes—
678C23C2×#23914yes—
679C23C2×#23912yes—
680C23D3×#4112yes—
681C23D3×#4112yes—
682C23C24×D311yescharacteristic
683D4—1216no—
684C2×C4—232no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—34no—
704C2×C4—34no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—632no—
712C2×C4—632no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—68no—
722C2×C4—68no—
723C2×C4—68no—
724C2×C4—68no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—124no—
735C2×C4—124no—
736C2×C4—124no—
737C2×C4C2×D3×D414yes—
738C2×C4C2×#23714yes—
739C2×C3—28no—
740C2×C3#285218yescomplemented
741C2×C3C2×#52511yescharacteristic
742C2×C3C2×#52511yescharacteristic
743C2×C3C2×#52511yescharacteristic
744C2×C3C22×#12611yescharacteristic
745C2×C3C2×#52911yescharacteristic
746C2×C3C2×#52911yescharacteristic
747C2×C3C2×#52911yescharacteristic
748D3—82no—
749C22—24no—
750C22—232no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22—248no—
764C22C2×#89814yes—
765C22C2×#89818yescomplemented
766C22#553814yes—
767C22#554714yes—
768C22#558614yes—
769C22#562414yes—
770C22#562714yes—
771C22#564914yes—
772C22C22×#23511yescharacteristic
773C22C22×D3×D411yescharacteristic
774C22C22×#23711yescharacteristic
775C22C22×#23711yescharacteristic
776C22C22×#23911yescharacteristic
777C22C2×D3×#4111yescharacteristic
778C22C2×D3×#4111yescharacteristic
779C4—24no—
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—64no—
786C4—64no—
787C4—64no—
788C4—64no—
789C4—122no—
790C4—122no—
791C4—122no—
792C3C2×#285211yescharacteristic, complemented, Sylow
793C2—28no—
794C2—242no—
795C2#7458718yesdirect product factor
796C2C22×#89811yescharacteristic
797C2C2×#553811yescharacteristic
798C2C2×#554711yescharacteristic
799C2C2×#558611yescharacteristic
800C2C2×#562711yescharacteristic
801C2C2×#562411yescharacteristic
802C2C2×#564911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#385C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#385D3
hypocenterC3C2×#2852
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C23×C4×Dic3C2semidirect
2. C22×#898C2semidirect
3. C2×C3×#385C2semidirect
5. C2×#4990C2semidirect
6. C2×#4978C2semidirect
7. C2×#4980C2semidirect
10. C2×#4950C2semidirect
11. C2×#4946C2semidirect
12. #74587C2direct (N × H)
13. C2×#4670C2semidirect
14. C2×#4669C2semidirect
15. C2×#4654C2semidirect
16. C2×#4651C2semidirect
42. C22×C4×Dic3C22semidirect
44. C2×#898C22semidirect
45. C3×#385C22semidirect
59. #4990C22semidirect
60. #4980C22semidirect
61. #4978C22semidirect
64. #4950C22semidirect
65. #4946C22semidirect
66. #4670C22semidirect
67. #4669C22semidirect
68. #4654C22semidirect
69. #4651C22semidirect
84. C2×#385D3semidirect
151. C2×C4×Dic3D4semidirect
207. #385C2×D3semidirect
324. C4×Dic3C2×D4semidirect
418. C23×C3#126semidirect
615. C22×C3C2×#126semidirect
671. C23#898semidirect
740. C2×C3#2852semidirect
765. C22C2×#898semidirect
792. C3C2×#2852semidirect
795. C2#74587direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×Dic32
C22×#8982
C2×C3×#3852
C2×#52132
C2×#49902
C2×#49782
C2×#49802
C2×#49582
C2×#49502
C2×#49462
#745872
C2×#46702
C2×#46692
C2×#46542
C2×#46512
C2×#28523