Finite Group Databasebeta

← C2×#83508 #11670313

Subgroups — C2×#83508 #11670313

Order 768.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic, complemented
2C22×#951C211yesmaximal, characteristic, complemented
3C22×#932C211yesmaximal, characteristic, complemented
4C2×#5552C211yesmaximal, characteristic, complemented
5C2×#5238C211yesmaximal, characteristic, complemented
6C2×#5218C211yesmaximal, characteristic, complemented
7#83508C2116yesmaximal, direct product factor
8C2×#5054C211yesmaximal, characteristic, complemented
9C2×#5059C211yesmaximal, characteristic, complemented
10C2×#5047C211yesmaximal, characteristic, complemented
11C2×#5052C211yesmaximal, characteristic, complemented
12C2×#5040C211yesmaximal, characteristic, complemented
13C2×#5039C211yesmaximal, characteristic, complemented
14C2×C4×#214C211yesmaximal, characteristic, complemented
15C2×#5016C211yesmaximal, characteristic, complemented
16C2×#5012C211yesmaximal, characteristic, complemented
17C2×#3275—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C23×Dic6C2211yescharacteristic, complemented
22C3×#546—24no—
23C3×#546C2218yescomplemented
24C2×C3×#124C2211yescharacteristic
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#120—21no—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C22⋊C4—21no—
33C2×#951—28no—
34C2×#951C2218yescomplemented
35C22×#216C2211yescharacteristic, complemented
36C22×#216C2211yescharacteristic, complemented
37C22×#215C2211yescharacteristic, complemented
38C2×#939—21no—
39C22×#214C2211yescharacteristic
40C22×#214C2211yescharacteristic
41C22×#214C2211yescharacteristic
42C22×#214C2211yescharacteristic
43C2×#932—28no—
44C2×#932C2218yescomplemented
45C22×#213C2211yescharacteristic
46C22×#213C2211yescharacteristic
47C2×#930C2211yescharacteristic, complemented
48C2×#924C2211yescharacteristic
49C22×#208C2211yescharacteristic
50C22×#208C2211yescharacteristic, complemented
51#5552—24no—
52#5552C2218yescomplemented
53C2×#896—21no—
54C2×#885—21no—
55C2×#67⋊C4—21no—
56C2×#875C2211yescharacteristic, complemented
57C2×C4×Dic6C2211yescharacteristic, complemented
58#5238C2218yescomplemented
59C2×#835C2211yescharacteristic, complemented
60#5218C2218yescomplemented
61C2×#832C2211yescharacteristic
62C2×#832C2211yescharacteristic
63C2×#830C2211yescharacteristic
64C2×#830C2211yescharacteristic, complemented
65#5059C2218yescomplemented
66#5054C2218yescomplemented
67#5052C2218yescomplemented
68#5047C2218yescomplemented
69#5040C2218yescomplemented
70#5039C2218yescomplemented
71C4×#214C2218yescomplemented
72#5016C2218yescomplemented
73#5012C2218yescomplemented
74C2×#810C2211yescharacteristic, complemented
75C2×#810C2211yescharacteristic, complemented
76C2×#809C2211yescharacteristic, complemented
77C2×#808C2211yescharacteristic, complemented
78C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
79C2×C4×C3⋊C8C2211yescharacteristic, complemented
80C22×#137—31no—
81C22×AGL(1,ℤ/8)—31no—
82C2×#548—31no—
83C2×#546D311yescharacteristic, complemented
84#3275—316no—
85C2×#495—31no—
86C2×#470—31no—
87C2×#469—31no—
88C2×#464—31no—
89C2×#463—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#448—31no—
93C2×#450—31no—
94C2×C4×SD16—31no—
95C2×#436—31no—
96C25×C3—21no—
97C2×C3×#41—22no—
98C2×C3×#41—24no—
99C2×C3×#41—42no—
100C2×C3×#41C2314yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4—24no—
103C22×C3×D4—21no—
104C22×C3×D4—21no—
105C22×C3×D4—21no—
106C22×C3×D4—22no—
107C22×C3×D4—42no—
108C22×C3×D4D411yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C22×C3×D4C2314yes—
111C22×C3×D4C2311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—21no—
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C22×#67—21no—
117C22×#67—21no—
118C23×Dic3—21no—
119C2×#235—22no—
120C2×#235—24no—
121C2×#235—42no—
122C2×#235C2314yes—
123C22×D12C2311yescharacteristic
124C22×C4×D3—21no—
125C22×Dic6—24no—
126C22×Dic6—21no—
127C22×Dic6—22no—
128C22×Dic6—42no—
129C22×Dic6C2311yescharacteristic
130C22×Dic6C2311yescharacteristic
131C22×Dic6C2314yescomplemented
132C3×#124—22no—
133C3×#124C2314yes—
134C3×#123—28no—
135C3×C22⋊Q8—22no—
136C3×C22⋊Q8C2314yes—
137C3×#121—22no—
138C3×#121—28no—
139C3×#121C2314yes—
140C3×#120—28no—
141C3×C4×D4—22no—
142C3×C4×D4D414yes—
143C3×C4×D4C2314yes—
144C3×C4×D4C2314yes—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4D411yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—28no—
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C22⋊C4D411yescharacteristic
156C2×C3×C42C2311yescharacteristic
157C2×#217—21no—
158#951—232no—
159C2×#216—24no—
160C2×#216—24no—
161C2×#216C2314yescomplemented
162C2×#216C2314yescomplemented
163C2×#215—42no—
164C2×#215C2314yescomplemented
165#939—28no—
166C2×#214—24no—
167C2×#214—24no—
168C2×#214—42no—
169C2×#214D418yescomplemented
170C2×#214C2314yes—
171C2×#214C2314yes—
172C2×#214C2314yes—
173C2×#214C2314yes—
174#932—232no—
175C2×#213—24no—
176C2×#213—24no—
177C2×#213C2314yes—
178C2×#213C2314yes—
179#930—22no—
180#930C2314yescomplemented
181C2×(C2×D3)⋊C4—21no—
182C2×(C2×D3)⋊C4—21no—
183C2×(C2×D3)⋊C4—21no—
184C2×C4⋊Dic3C2311yescharacteristic
185#924—22no—
186#924C2314yes—
187C2×Dic3⋊C4—21no—
188C2×Dic3⋊C4—21no—
189C2×C4×Dic3—21no—
190C2×#208—24no—
191C2×#208—24no—
192C2×#208C2314yes—
193C2×#208C2314yescomplemented
194C22×C3⋊C8C2311yescharacteristic
195C22×C3⋊C8C2311yescharacteristic
196C22×C3⋊C8C2311yescharacteristic
197C22×C3⋊C8C2311yescharacteristic
198#896—28no—
199#885—28no—
200#67⋊C4—28no—
201#875—22no—
202#875C2314yescomplemented
203C4×Dic6—22no—
204C4×Dic6C2314yescomplemented
205#835C2314yescomplemented
206#832C2314yes—
207#832C2314yes—
208#830C2314yes—
209#830C2314yescomplemented
210#810C2314yescomplemented
211#810C2314yescomplemented
212#809C2314yescomplemented
213#808C2314yescomplemented
214C4⋊(C3⋊C8)C2314yescomplemented
215C4×C3⋊C8C2314yescomplemented
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×Q8—31no—
219C23×D4C2×D311yescharacteristic
220C2×#137—38no—
221C2×#137—68no—
222C2×AGL(1,ℤ/8)—38no—
223C2×AGL(1,ℤ/8)—68no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
234C22×M16—31no—
235#548—38no—
236#548—64no—
237#546—24no—
238#546C2×D318yescomplemented
239C2×#124—31no—
240C2×#124—61no—
241C2×#124C2×D311yescharacteristic
242C2×#123—21no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—61no—
245C2×C22⋊Q8C2×D311yescharacteristic
246C2×#121—21no—
247C2×#121—31no—
248C2×#121—61no—
249C2×#121C2×D311yescharacteristic
250C2×#120—21no—
251C2×C4×Q8—31no—
252C2×C4×D4—61no—
253C2×C4×D4C2×D311yescharacteristic
254C2×C4×D4C2×D311yescharacteristic
255C22×C22⋊C4—21no—
256#495—38no—
257#470—38no—
258#469—38no—
259#464—38no—
260#463—38no—
261#452—38no—
262#450—38no—
263#449—38no—
264#448—38no—
265C4×SD16—38no—
266#436—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3—24no—
281C24×C3—44no—
282C24×C3—44no—
283C24×C3—82no—
284C24×C3C2×D411yescharacteristic
285C24×C3C2×D411yescharacteristic
286C23×D3—21no—
287C3×#41—28no—
288C3×#41—44no—
289C3×#41—48no—
290C2×C3×Q8—21no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8C2412yes—
294C2×C3×D4—28no—
295C2×C3×D4—24no—
296C2×C3×D4—24no—
297C2×C3×D4—21no—
298C2×C3×D4—22no—
299C2×C3×D4—24no—
300C2×C3×D4—21no—
301C2×C3×D4—22no—
302C2×C3×D4—22no—
303C2×C3×D4—44no—
304C2×C3×D4—48no—
305C2×C3×D4—42no—
306C2×C3×D4—44no—
307C2×C3×D4—44no—
308C2×C3×D4—82no—
309C2×C3×D4C2×D414yes—
310C2×C3×D4C2×D414yes—
311C2×C3×D4C2412yes—
312C2×C3×D4C2412yes—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—24no—
320C22×C3×C4—24no—
321C22×C3×C4—44no—
322C22×C3×C4—82no—
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D411yescharacteristic
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2412yes—
330C22×C3×C4C2412yes—
331C22×C3×C4C2411yescharacteristic
332C2×#67—24no—
333C2×#67—24no—
334C2×#67—44no—
335C2×#67—44no—
336C22×Dic3—21no—
337C22×Dic3—24no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—44no—
341#235—28no—
342#235—44no—
343#235—48no—
344C2×D12—22no—
345C2×D12—22no—
346C2×D12—21no—
347C2×D12C2412yes—
348C2×C4×D3—24no—
349C2×C4×D3—44no—
350C2×Dic6—21no—
351C2×Dic6—22no—
352C2×Dic6—22no—
353C2×Dic6—22no—
354C2×Dic6—28no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6—44no—
358C2×Dic6—48no—
359C2×Dic6—44no—
360C2×Dic6C2×D414yes—
361C2×Dic6C2412yes—
362C2×Dic6C2412yes—
363C3×C4⋊C4—24no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4C2×D414yes—
366C3×C4⋊C4C2412yes—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—24no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—24no—
372C3×C22⋊C4C2×D414yes—
373C3×C22⋊C4C2×D414yes—
374C3×C42C2×D412yes—
375C3×C42C2412yes—
376#217—24no—
377#216—28no—
378#216—28no—
379#215—44no—
380#214—28no—
381#214—28no—
382#214—44no—
383#214C2×D4116yescomplemented
384#213—28no—
385#213—28no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389C4⋊Dic3—21no—
390C4⋊Dic3C2412yes—
391Dic3⋊C4—24no—
392Dic3⋊C4—24no—
393C4×Dic3—24no—
394#208—28no—
395#208—28no—
396C2×C3⋊C8—22no—
397C2×C3⋊C8—22no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8C2×D414yes—
400C2×C3⋊C8C2412yes—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404C25—21no—
405C2×#41—22no—
406C2×#41—24no—
407C2×#41—34no—
408C2×#41—42no—
409C2×#41—64no—
410C2×#41—62no—
411C2×#41—122no—
412C2×#41C22×D314yes—
413C22×Q8—31no—
414C22×Q8—31no—
415C22×Q8—34no—
416C22×Q8—64no—
417C22×Q8—61no—
418C22×Q8—62no—
419C22×Q8—122no—
420C22×Q8C22×D311yescharacteristic
421C22×D4—24no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—22no—
426C22×D4—31no—
427C22×D4—42no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4#6711yescharacteristic
431C22×D4C22×D311yescharacteristic
432C22×D4C22×D314yes—
433C22×D4C22×D311yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—61no—
437C23×C4—61no—
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440#137—632no—
441AGL(1,ℤ/8)—632no—
442C2×Q16—34no—
443C2×Q16—34no—
444C2×Q16—64no—
445C2×Q16—64no—
446C2×SD16—38no—
447C2×SD16—34no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—64no—
453C2×SD16—64no—
454C2×SD16—122no—
455C2×SD16—122no—
456C2×D8—34no—
457C2×D8—34no—
458C2×D8—64no—
459C2×D8—64no—
460C2×M16—34no—
461C2×M16—34no—
462C2×M16—64no—
463C2×M16—64no—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8—31no—
467C22×C8—31no—
468#124—22no—
469#124—34no—
470#124—68no—
471#124—62no—
472#124C22×D314yes—
473#123—28no—
474C22⋊Q8—22no—
475C22⋊Q8—34no—
476C22⋊Q8—62no—
477C22⋊Q8—68no—
478C22⋊Q8C22×D314yes—
479#121—22no—
480#121—28no—
481#121—34no—
482#121—68no—
483#121—62no—
484#121C22×D314yes—
485#120—28no—
486C4×Q8—34no—
487C4×Q8—62no—
488C4×D4—22no—
489C4×D4—68no—
490C4×D4#6714yes—
491C4×D4C22×D314yes—
492C4×D4C22×D314yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4#6711yescharacteristic
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—28no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4#6711yescharacteristic
510C2×C22⋊C4#6711yescharacteristic
511C2×C42—61no—
512C2×C42C22×D311yescharacteristic
513#106—34no—
514C4⋊C8—34no—
515#103—34no—
516#103—34no—
517#103—34no—
518#102—34no—
519#102—34no—
520#102—34no—
521C22⋊C8—34no—
522C22⋊C8—34no—
523C4×C8—34no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—24no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—48no—
534C23×C3—48no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—84no—
541C23×C3—816no—
542C23×C3C22×D412yes—
543C23×C3C22×D412yes—
544C23×C3C22×D411yescharacteristic
545C22×D3—22no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—42no—
549C3×Q8—22no—
550C3×Q8—22no—
551C3×Q8—42no—
552C3×D4—24no—
553C3×D4—22no—
554C3×D4—22no—
555C3×D4—22no—
556C3×D4—44no—
557C3×D4—48no—
558C3×D4—48no—
559C3×D4—42no—
560C3×D4—84no—
561C3×D4C22×D414yes—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—24no—
567C2×C3×C4—24no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—48no—
575C2×C3×C4—42no—
576C2×C3×C4—42no—
577C2×C3×C4—84no—
578C2×C3×C4C22×D412yes—
579C2×C3×C4C22×D412yes—
580C2×C3×C4C22×D412yes—
581C2×C3×C4C22×D412yes—
582C2×C3×C4C22×D412yes—
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4H(5,𝔽2)12yes—
585C2×C3×C4C2511yescharacteristic
586#67—48no—
587#67—48no—
588C2×Dic3—24no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—48no—
593C2×Dic3—42no—
594C2×Dic3—42no—
595D12—22no—
596D12—22no—
597D12—42no—
598C4×D3—48no—
599Dic6—24no—
600Dic6—22no—
601Dic6—22no—
602Dic6—22no—
603Dic6—48no—
604Dic6—42no—
605Dic6C22×D414yes—
606C3⋊C8—22no—
607C3⋊C8—22no—
608C3⋊C8—22no—
609C3⋊C8C22×D414yes—
610C24—21no—
611C24—21no—
612C24—24no—
613C24—44no—
614C24—44no—
615C24—61no—
616C24—82no—
617C24C2×#6711yescharacteristic
618C24C2×#6711yescharacteristic
619#41—28no—
620#41—44no—
621#41—48no—
622#41—68no—
623#41—124no—
624#41—128no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—34no—
629C2×Q8—32no—
630C2×Q8—32no—
631C2×Q8—68no—
632C2×Q8—62no—
633C2×Q8—61no—
634C2×Q8—64no—
635C2×Q8—61no—
636C2×Q8—62no—
637C2×Q8—62no—
638C2×Q8—124no—
639C2×Q8—124no—
640C2×Q8—128no—
641C2×Q8C23×D312yes—
642C2×D4—28no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—32no—
652C2×D4—44no—
653C2×D4—48no—
654C2×D4—42no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—61no—
662C2×D4—82no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4D3×D414yes—
666C2×D4C2×#6714yes—
667C2×D4C23×D312yes—
668C2×D4C23×D312yes—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—44no—
678C22×C4—61no—
679C22×C4—64no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—64no—
683C22×C4—82no—
684C22×C4—124no—
685C22×C4—124no—
686C22×C4C2×#6712yes—
687C22×C4C2×#6712yes—
688C22×C4C2×#6711yescharacteristic
689C22×C4C2×#6711yescharacteristic
690C22×C4C2×#6711yescharacteristic
691C22×C4C2×#6711yescharacteristic
692C22×C4C23×D312yes—
693C22×C4C23×D312yes—
694C22×C4C23×D311yescharacteristic
695Q16—68no—
696Q16—68no—
697SD16—316no—
698SD16—68no—
699SD16—68no—
700SD16—124no—
701SD16—124no—
702D8—68no—
703D8—68no—
704M16—68no—
705M16—68no—
706C2×C8—34no—
707C2×C8—32no—
708C2×C8—32no—
709C2×C8—32no—
710C2×C8—32no—
711C2×C8—62no—
712C2×C8—62no—
713C2×C8—62no—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—32no—
717C4⋊C4—61no—
718C4⋊C4—64no—
719C4⋊C4—64no—
720C4⋊C4C2×#6714yes—
721C4⋊C4C23×D312yes—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C22⋊C4C2×#6714yes—
732C22⋊C4C2×#6714yes—
733C42—64no—
734C42C2×#6712yes—
735C42C23×D312yes—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—24no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—44no—
744C22×C3—44no—
745C22×C3—48no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—816no—
752C22×C3—84no—
753C22×C3D4212yes—
754C22×C3#57512yes—
755C22×C3#57712yes—
756C22×C3C23×D411yescharacteristic
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—84no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—42no—
766C3×C4—42no—
767C3×C4D4212yes—
768C3×C4C23×D411yescharacteristic
769C3×C4C2×H(5,𝔽2)11yescharacteristic
770Dic3—24no—
771Dic3—42no—
772Dic3—42no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—48no—
783C23—48no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—62no—
790C23—84no—
791C23—816no—
792C23—122no—
793C23—122no—
794C23—122no—
795C23C22×#6712yes—
796C23C22×#6712yes—
797C23C22×#6711yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—34no—
801Q8—42no—
802Q8—62no—
803Q8—64no—
804Q8—62no—
805Q8—62no—
806Q8—128no—
807Q8—122no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—24no—
812D4—44no—
813D4—48no—
814D4—48no—
815D4—42no—
816D4—62no—
817D4—62no—
818D4—84no—
819D4—128no—
820D4—128no—
821D4—122no—
822D4C2×D3×D414yes—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—48no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—62no—
839C2×C4—64no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—84no—
843C2×C4—128no—
844C2×C4—128no—
845C2×C4—122no—
846C2×C4—122no—
847C2×C4C2×D3×D412yes—
848C2×C4#100412yes—
849C2×C4C22×#6712yes—
850C2×C4C22×#6712yes—
851C2×C4C22×#6712yes—
852C2×C4C22×#6712yes—
853C2×C4C22×#6711yescharacteristic
854C2×C4C24×D311yescharacteristic
855C8—34no—
856C8—62no—
857C8—62no—
858C8—62no—
859C2×C3—42no—
860C2×C3—42no—
861C2×C3—44no—
862C2×C3—82no—
863C2×C3#327514yescomplemented
864C2×C3C2×D4211yescharacteristic
865C2×C3C2×#57511yescharacteristic
866C2×C3C2×#57711yescharacteristic
867D3—82no—
868C22—22no—
869C22—22no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—48no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—816no—
884C22—84no—
885C22—122no—
886C22—122no—
887C22—122no—
888C22—244no—
889C22D4×#6712yes—
890C22#582212yes—
891C22#583612yes—
892C22C23×#6711yescharacteristic
893C4—22no—
894C4—22no—
895C4—22no—
896C4—22no—
897C4—42no—
898C4—42no—
899C4—64no—
900C4—122no—
901C4—122no—
902C4D4×#6712yes—
903C4C22×D3×D411yescharacteristic
904C4C2×#100411yescharacteristic
905C3C2×#327511yescharacteristic, complemented, Sylow
906C2—42no—
907C2—42no—
908C2—44no—
909C2—82no—
910C2—242no—
911C2#8350814yesdirect product factor
912C2C2×D4×#6711yescharacteristic
913C2C2×#582211yescharacteristic
914C2C2×#583611yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#546C2
socleC23×C3C22×D4
hypercenterC2×#546D3
hypocenterC3C2×#3275
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×C3×#546C2semidirect
2. C22×#951C2semidirect
3. C22×#932C2semidirect
4. C2×#5552C2semidirect
5. C2×#5238C2semidirect
6. C2×#5218C2semidirect
7. #83508C2direct (N × H)
8. C2×#5054C2semidirect
9. C2×#5059C2semidirect
10. C2×#5047C2semidirect
11. C2×#5052C2semidirect
12. C2×#5040C2semidirect
13. C2×#5039C2semidirect
14. C2×C4×#214C2semidirect
15. C2×#5016C2semidirect
16. C2×#5012C2semidirect
21. C23×Dic6C22semidirect
23. C3×#546C22semidirect
34. C2×#951C22semidirect
35. C22×#216C22semidirect
36. C22×#216C22semidirect
37. C22×#215C22semidirect
44. C2×#932C22semidirect
47. C2×#930C22semidirect
50. C22×#208C22semidirect
52. #5552C22semidirect
56. C2×#875C22semidirect
57. C2×C4×Dic6C22semidirect
58. #5238C22semidirect
59. C2×#835C22semidirect
60. #5218C22semidirect
64. C2×#830C22semidirect
65. #5059C22semidirect
66. #5054C22semidirect
67. #5052C22semidirect
68. #5047C22semidirect
69. #5040C22semidirect
70. #5039C22semidirect
71. C4×#214C22semidirect
72. #5016C22semidirect
73. #5012C22semidirect
74. C2×#810C22semidirect
75. C2×#810C22semidirect
76. C2×#809C22semidirect
77. C2×#808C22semidirect
78. C2×C4⋊(C3⋊C8)C22semidirect
79. C2×C4×C3⋊C8C22semidirect
83. C2×#546D3semidirect
131. C22×Dic6C23semidirect
161. C2×#216C23semidirect
162. C2×#216C23semidirect
164. C2×#215C23semidirect
169. C2×#214D4semidirect
180. #930C23semidirect
193. C2×#208C23semidirect
202. #875C23semidirect
204. C4×Dic6C23semidirect
205. #835C23semidirect
209. #830C23semidirect
210. #810C23semidirect
211. #810C23semidirect
212. #809C23semidirect
213. #808C23semidirect
214. C4⋊(C3⋊C8)C23semidirect
215. C4×C3⋊C8C23semidirect
238. #546C2×D3semidirect
383. #214C2×D4semidirect
863. C2×C3#3275semidirect
905. C3C2×#3275semidirect
911. C2#83508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C22×#9512
C22×#9322
C2×#55522
C2×#52382
C2×#52182
#835082
C2×#50542
C2×#50592
C2×#50472
C2×#50522
C2×#50402
C2×#50392
C2×C4×#2142
C2×#50162
C2×#50122
C2×#32753