Finite Group Databasebeta

← #10972961

Subgroups — #10972961

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#117C211yesmaximal, characteristic
2C2×#5500C211yesmaximal, characteristic, complemented
3C3×#2317C211yesmaximal, characteristic, complemented
4#82267C211yesmaximal, characteristic
5#82234C211yesmaximal, characteristic, complemented
6#82232C211yesmaximal, characteristic, complemented
7C2×#4987C211yesmaximal, characteristic
8#76288C212yesmaximal, complemented
9#76285C212yesmaximal, complemented
10#76251C212yesmaximal, complemented
11#76250C212yesmaximal, complemented
12#74607C214yesmaximal
13#74414C214yesmaximal, complemented
14#74327C212yesmaximal, complemented
15#74326C212yesmaximal, complemented
16#74163C212yesmaximal, complemented
17#74162C212yesmaximal, complemented
18#35253—31nomaximal, Sylow
19C23×C4×D3C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2212yes—
24C2×#926C2211yescharacteristic
25C2×#926C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C2×#924C2214yes—
28D3×#117—28no—
29C2×#896C2214yes—
30C2×#892C2211yescharacteristic
31C2×#892C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×D3×C4⋊C4C2211yescharacteristic
34#5500—28no—
35C2×#890C2212yescomplemented
36C2×#890C2212yescomplemented
37C2×#888C2212yescomplemented
38C2×#888C2212yescomplemented
39C2×D3×C22⋊C4C2212yes—
40C2×#877C2212yes—
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43C3×#389C2212yescomplemented
44C3×#389C2212yescomplemented
45C3×#385C2214yes—
46C3×#384C2212yescomplemented
47C3×#382C2212yescomplemented
48C2×C3⋊#95C2212yes—
49#4994C2214yes—
50#4993C2214yes—
51#4989C2214yes—
52#4987C2211yescharacteristic
53#4987C2212yes—
54#4987C2212yes—
55#4987C2212yes—
56#4987C2212yes—
57#4987C2211yescharacteristic
58#4987C2211yescharacteristic
59#4987C2211yescharacteristic
60#4983C2214yescomplemented
61#4980C2214yescomplemented
62#4979C2214yescomplemented
63#4977C2212yescomplemented
64#4976C2214yescomplemented
65#4975C2212yescomplemented
66#4972C2212yescomplemented
67#4972C2212yescomplemented
68#4955C2212yes—
69#4946C2214yes—
70#4943C2212yes—
71#4942C2214yes—
72C4×(C2×D3)⋊C4C2212yes—
73C4×(C2×D3)⋊C4C2212yes—
74#4928C2212yescomplemented
75#4928C2212yescomplemented
76#4928C2212yescomplemented
77#4928C2212yescomplemented
78#4676C2214yes—
79#4673C2214yes—
80#4668C2214yes—
81#4667C2214yes—
82#4658C2214yescomplemented
83#4657C2214yescomplemented
84#4652C2214yescomplemented
85#4646C2214yescomplemented
86C2×#544—31no—
87C22×#117—31no—
88#2857—32no—
89#2851—32no—
90#2629—32no—
91#2628—32no—
92#2442—32no—
93#2441—32no—
94#2440—32no—
95#2439—32no—
96#2438—34no—
97#2437—34no—
98#2317—31no—
99#2317D311yescharacteristic, complemented
100#2316—31no—
101#2280—31no—
102C2×#380—31no—
103C24×D3C2311yescharacteristic
104C23×C3×C4C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2312yes—
108C22×C4×D3—24no—
109C22×C4×D3—24no—
110C22×C4×D3Q818yescomplemented
111C22×C4×D3C2312yes—
112C22×C4×D3C2312yes—
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×Dic6C2314yes—
118C3×#117—24no—
119C3×#117—24no—
120C2×C3×C4⋊C4—24no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C42C2312yes—
132C2×C3×C42C2312yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×(C2×D3)⋊C4—44no—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144#926—24no—
145#926D418yes—
146C2×C4⋊Dic3—24no—
147C2×C4⋊Dic3C2314yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154#924—216no—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2312yes—
167#896—48no—
168#892—24no—
169#892—24no—
170D3×C4⋊C4—24no—
171D3×C4⋊C4—24no—
172#890—28no—
173#890—28no—
174#888—28no—
175#888—28no—
176D3×C22⋊C4—28no—
177#877—28no—
178#872—28no—
179C42×D3—28no—
180C3×#95C2314yes—
181C3×#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C24×C4—31no—
193#544—68no—
194C2×C4⋊Q8—32no—
195C2×C4⋊Q8—32no—
196C2×#125—32no—
197C2×#125—32no—
198C2×C22⋊Q8—34no—
199C2×C22⋊Q8—34no—
200C2×#117—31no—
201C2×#117—31no—
202C2×#117—31no—
203C2×#117—31no—
204C2×#117—32no—
205C2×#117—32no—
206C2×#117—68no—
207C2×#117C2×D311yescharacteristic
208C2×#117C2×D311yescharacteristic
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C22⋊C4—32no—
214C22×C22⋊C4—32no—
215C22×C42—32no—
216#400—34no—
217#399—34no—
218#398—34no—
219#398—34no—
220#396—34no—
221#396—34no—
222#395—34no—
223#393—34no—
224#391—34no—
225#389—32no—
226#389—32no—
227#389—34no—
228#389—32no—
229#389—32no—
230#389—32no—
231#389—32no—
232#389C2×D312yescomplemented
233#389C2×D312yescomplemented
234#387—34no—
235#387—34no—
236#385—34no—
237#385—34no—
238#385—34no—
239#385C2×D314yes—
240#384—32no—
241#384C2×D312yescomplemented
242#382—32no—
243#382C2×D312yescomplemented
244#381—32no—
245#380—31no—
246#380—32no—
247#380—31no—
248#380—31no—
249#380—32no—
250#380—31no—
251#380—32no—
252#380—32no—
253#380—34no—
254#380—34no—
255#379—32no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C2×#95—32no—
259C24×C3C2411yescharacteristic
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3—41no—
265C23×D3—41no—
266C23×D3C2×Q814yes—
267C23×D3C2411yescharacteristic
268C23×D3C2411yescharacteristic
269C22×C3×C4—24no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2×Q814yes—
274C22×C3×C4#4114yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2414yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—24no—
285C22×Dic3—42no—
286C22×Dic3—42no—
287C22×Dic3C2×Q814yes—
288C22×Dic3C2414yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2411yescharacteristic
295C2×C4×D3—232no—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—22no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—42no—
309C2×C4×D3—42no—
310C2×C4×D3C2×Q814yes—
311C2×C4×D3C2×Q814yes—
312C2×C4×D3C2×Q814yes—
313C2×C4×D3C2×Q814yes—
314C2×Dic6—28no—
315C2×Dic6—44no—
316C2×Dic6—44no—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—44no—
324C3×C4⋊C4—44no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—24no—
327C3×C42—24no—
328C3×C42—24no—
329#217—24no—
330#217C2×D418yes—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339C4⋊Dic3—22no—
340C4⋊Dic3—22no—
341C4⋊Dic3—24no—
342C4⋊Dic3—24no—
343C4⋊Dic3—28no—
344C4⋊Dic3C2×D414yes—
345C4⋊Dic3C2×D414yes—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—28no—
349Dic3⋊C4—28no—
350Dic3⋊C4—44no—
351Dic3⋊C4—44no—
352Dic3⋊C4—44no—
353Dic3⋊C4—44no—
354C4×Dic3—24no—
355C4×Dic3—24no—
356C4×Dic3—24no—
357C4×Dic3C2×D418yes—
358C25—31no—
359C22×Q8—34no—
360C23×C4—31no—
361C23×C4—38no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—32no—
367C23×C4—32no—
368C23×C4—32no—
369C23×C4—64no—
370C23×C4—64no—
371C23×C4C22×D312yes—
372C23×C4C22×D311yescharacteristic
373C4⋊Q8—68no—
374C4⋊Q8—68no—
375#125—68no—
376#125—68no—
377C22⋊Q8—616no—
378C22⋊Q8—128no—
379#117—24no—
380#117—24no—
381#117—38no—
382#117—68no—
383#117—68no—
384#117—64no—
385#117—64no—
386#117—64no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—64no—
404C2×C4⋊C4—64no—
405C2×C4⋊C4—64no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D312yes—
409C2×C4⋊C4C22×D312yes—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D314yes—
413C2×C4⋊C4C22×D314yes—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—68no—
425C2×C22⋊C4—124no—
426C2×C22⋊C4C22×D312yes—
427C2×C22⋊C4C22×D312yes—
428C2×C42—32no—
429C2×C42—32no—
430C2×C42—32no—
431C2×C42—32no—
432C2×C42—68no—
433C2×C42C22×D312yes—
434C2×C42C22×D312yes—
435#95—34no—
436#95—34no—
437#95—32no—
438#95—32no—
439#95—32no—
440#95—32no—
441#95—34no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95C22×D314yes—
446#95C22×D314yes—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3C22×D412yes—
452C23×C3C22×Q812yes—
453C23×C3C2×#4112yes—
454C23×C3C2511yescharacteristic
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—28no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—28no—
467C22×D3—44no—
468C22×D3—44no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3—44no—
472C22×D3C22×Q812yes—
473C22×D3C22×Q812yes—
474C22×D3H(5,𝔽2)12yes—
475C22×D32−1+412yes—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—84no—
492C2×C3×C4C22⋊Q8116yescomplemented
493C2×C3×C4C22×D412yes—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×Q812yes—
496C2×C3×C4C22×Q812yes—
497C2×C3×C4C2×#4112yes—
498C2×C3×C4C2×#4112yes—
499C2×Dic3—28no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—24no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—24no—
516C2×Dic3—22no—
517C2×Dic3—84no—
518C2×Dic3C22×D414yes—
519C2×Dic3C22×D414yes—
520C2×Dic3C22×Q812yes—
521C2×Dic3C22×Q812yes—
522C4×D3—28no—
523C4×D3—28no—
524C4×D3—28no—
525C4×D3—28no—
526C4×D3—48no—
527C4×D3—48no—
528Dic6—88no—
529C24—31no—
530C24—31no—
531C24—34no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24—121no—
537C24—121no—
538C24C23×D311yescharacteristic
539C2×Q8—68no—
540C2×Q8—124no—
541C2×Q8—124no—
542C22×C4—24no—
543C22×C4—34no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—32no—
547C22×C4—32no—
548C22×C4—34no—
549C22×C4—34no—
550C22×C4—34no—
551C22×C4—34no—
552C22×C4—34no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—64no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—632no—
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—64no—
573C22×C4—122no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4#23514yes—
578C22×C4D3×D414yes—
579C22×C4D3×Q814yes—
580C22×C4C23×D312yes—
581C22×C4C23×D312yes—
582C22×C4C23×D312yes—
583C22×C4C23×D314yes—
584C22×C4C23×D312yes—
585C22×C4C23×D311yescharacteristic
586C22×C4C23×D311yescharacteristic
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—34no—
594C4⋊C4—34no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—68no—
600C4⋊C4—68no—
601C4⋊C4—68no—
602C4⋊C4—64no—
603C4⋊C4—64no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—124no—
607C4⋊C4—124no—
608C4⋊C4—124no—
609C4⋊C4—124no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—38no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—68no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C22⋊C4—64no—
619C22⋊C4—124no—
620C22⋊C4—122no—
621C22⋊C4—122no—
622C42—24no—
623C42—24no—
624C42—38no—
625C42—64no—
626C42—64no—
627C42—64no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3C2×C22⋊Q814yes—
635C22×C3C23×D411yescharacteristic
636C22×C3C23×Q811yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×2−1+411yescharacteristic
640C22×C3#58511yescharacteristic
641C22×C3#58511yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—416no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3#54414yescomplemented
657C3×C4—44no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4C2×C22⋊Q814yes—
663C3×C4C2×C22⋊Q814yes—
664Dic3—22no—
665Dic3—22no—
666Dic3—24no—
667Dic3—24no—
668Dic3—42no—
669Dic3—42no—
670Dic3—44no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—32no—
676C23—32no—
677C23—32no—
678C23—32no—
679C23—68no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—68no—
691C23—124no—
692C23—124no—
693C23—124no—
694C23—124no—
695C23—124no—
696C23C2×#23512yes—
697C23C2×D3×D412yes—
698C23C2×D3×Q812yes—
699C23C24×D311yescharacteristic
700Q8—248no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—34no—
717C2×C4—34no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—68no—
729C2×C4—68no—
730C2×C4—68no—
731C2×C4—68no—
732C2×C4—68no—
733C2×C4—64no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—64no—
742C2×C4—84no—
743C2×C4—128no—
744C2×C4—128no—
745C2×C4—244no—
746C2×C4#896116yescomplemented
747C2×C4C2×#23512yes—
748C2×C4C2×#23512yes—
749C2×C4C2×D3×D412yes—
750C2×C4C2×D3×D412yes—
751C2×C4C2×D3×Q812yes—
752C2×C4C2×D3×Q812yes—
753C2×C3—24no—
754C2×C3C22×C22⋊Q811yescharacteristic
755C2×C3C2×#54411yescharacteristic
756C2×C3#345811yescharacteristic
757C2×C3#348811yescharacteristic
758C2×C3#348911yescharacteristic
759C2×C3#349411yescharacteristic
760C2×C3#349511yescharacteristic
761D3—24no—
762D3—42no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—34no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22—1216no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22C2×#89614yes—
785C22C22×#23511yescharacteristic
786C22C22×D3×D411yescharacteristic
787C22C22×D3×Q811yescharacteristic
788C22D3×H(5,𝔽2)11yescharacteristic
789C22#596611yescharacteristic
790C22D3×2−1+411yescharacteristic
791C22#596811yescharacteristic
792C4—44no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—64no—
798C4—64no—
799C4—62no—
800C4—62no—
801C4—122no—
802C4—122no—
803C4—124no—
804C4C2×#89614yes—
805C4C2×#89614yes—
806C3#3525311yescharacteristic, complemented, Sylow
807C2—24no—
808C2—64no—
809C2—122no—
810C2C22×#89611yescharacteristic
811C2#8590311yescharacteristic
812C2#8590411yescharacteristic
813C2#8633111yescharacteristic
814C2#8635611yescharacteristic
815C2#8658111yescharacteristic
816C2D3×#54411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2317C2
prime radicalC24×D3C23
hypercenter#2317D3
hypocenterC3#35253
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#5500C2semidirect
3. C3×#2317C2semidirect
5. #82234C2semidirect
6. #82232C2semidirect
8. #76288C2semidirect
9. #76285C2semidirect
10. #76251C2semidirect
11. #76250C2semidirect
13. #74414C2semidirect
14. #74327C2semidirect
15. #74326C2semidirect
16. #74163C2semidirect
17. #74162C2semidirect
35. C2×#890C22semidirect
36. C2×#890C22semidirect
37. C2×#888C22semidirect
38. C2×#888C22semidirect
43. C3×#389C22semidirect
44. C3×#389C22semidirect
46. C3×#384C22semidirect
47. C3×#382C22semidirect
60. #4983C22semidirect
61. #4980C22semidirect
62. #4979C22semidirect
63. #4977C22semidirect
64. #4976C22semidirect
65. #4975C22semidirect
66. #4972C22semidirect
67. #4972C22semidirect
74. #4928C22semidirect
75. #4928C22semidirect
76. #4928C22semidirect
77. #4928C22semidirect
82. #4658C22semidirect
83. #4657C22semidirect
84. #4652C22semidirect
85. #4646C22semidirect
99. #2317D3semidirect
110. C22×C4×D3Q8semidirect
232. #389C2×D3semidirect
233. #389C2×D3semidirect
241. #384C2×D3semidirect
243. #382C2×D3semidirect
492. C2×C3×C4C22⋊Q8semidirect
656. C2×D3#544semidirect
746. C2×C4#896semidirect
806. C3#35253semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1172
C2×#55002
C3×#23172
#822672
#822342
#822322
C2×#49872
#762882
#762852
#762512
#762502
#746072
#744142
#743272
#743262
#741632
#741622
#352533