Finite Group Databasebeta

← C2×#83505 #11670387

Subgroups — C2×#83505 #11670387

Order 768.

3074 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C23×#213C211yesmaximal, characteristic, complemented
4C2×#5550C211yesmaximal, characteristic, complemented
5C2×#5238C211yesmaximal, characteristic, complemented
6C2×#5218C211yesmaximal, characteristic, complemented
7#83505C2116yesmaximal, direct product factor
8C2×#5057C211yesmaximal, characteristic, complemented
9C2×#5059C211yesmaximal, characteristic, complemented
10C2×#5046C211yesmaximal, characteristic, complemented
11C2×#5051C211yesmaximal, characteristic, complemented
12C2×#5037C211yesmaximal, characteristic, complemented
13C2×#5038C211yesmaximal, characteristic, complemented
14C2×#5016C211yesmaximal, characteristic, complemented
15C2×D4×C3⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×#213C211yesmaximal, characteristic, complemented
17C2×#3280—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic, complemented
19C23×C3×D4C2211yescharacteristic
20C22×#235C2211yescharacteristic, complemented
21C23×D12C2211yescharacteristic
22C3×#546—24no—
23C3×#546C2218yescomplemented
24C2×C3×#124C2211yescharacteristic, complemented
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic, complemented
29C2×C3×#120—21no—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic, complemented
32C22×C3×C22⋊C4—21no—
33C2×#950—28no—
34C2×#950C2218yescomplemented
35C22×#216C2211yescharacteristic, complemented
36C22×#215C2211yescharacteristic, complemented
37C22×#215C2211yescharacteristic, complemented
38C2×#937—21no—
39C22×#214C2211yescharacteristic, complemented
40C22×#214C2211yescharacteristic, complemented
41C22×#213—28no—
42C22×#213C2211yescharacteristic
43C22×#213C2211yescharacteristic
44C22×#213C2211yescharacteristic
45C22×#213C2211yescharacteristic
46C22×#213C2218yescomplemented
47C2×#930C2211yescharacteristic, complemented
48C2×#924C2211yescharacteristic
49C23×C3⋊C8C2211yescharacteristic
50C23×C3⋊C8C2211yescharacteristic, complemented
51#5550—24no—
52#5550C2218yescomplemented
53C2×#894—21no—
54C2×#884—21no—
55C2×D3×C22⋊C4—21no—
56C2×#875C2211yescharacteristic, complemented
57C2×C4×D12C2211yescharacteristic, complemented
58#5238C2218yescomplemented
59C2×#835C2211yescharacteristic, complemented
60#5218C2218yescomplemented
61C2×#832C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic, complemented
63C2×#830C2211yescharacteristic
64C2×#830C2211yescharacteristic, complemented
65#5059C2218yescomplemented
66#5057C2218yescomplemented
67#5051C2218yescomplemented
68#5046C2218yescomplemented
69#5038C2218yescomplemented
70#5037C2218yescomplemented
71#5016C2218yescomplemented
72C4×#213C2218yescomplemented
73D4×C3⋊C8C2218yescomplemented
74C2×#810C2211yescharacteristic, complemented
75C2×#809C2211yescharacteristic, complemented
76C2×#809C2211yescharacteristic, complemented
77C2×#807C2211yescharacteristic, complemented
78C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
79C2×C4×C3⋊C8C2211yescharacteristic, complemented
80C22×#135—31no—
81C23×D8—31no—
82C2×#546—31no—
83C2×#546D311yescharacteristic, complemented
84#3280—316no—
85C2×#495—31no—
86C2×#467—31no—
87C2×#466—31no—
88C2×#463—31no—
89C2×#463—31no—
90C2×#449—31no—
91C2×#449—31no—
92C2×#450—31no—
93C2×#450—31no—
94C2×C4×D8—31no—
95C2×C8×D4—31no—
96C25×C3—21no—
97C24×D3—21no—
98C2×C3×#41—22no—
99C2×C3×#41—24no—
100C2×C3×#41—42no—
101C2×C3×#41C2314yescomplemented
102C22×C3×Q8C2311yescharacteristic
103C22×C3×D4—24no—
104C22×C3×D4—21no—
105C22×C3×D4—21no—
106C22×C3×D4—21no—
107C22×C3×D4—22no—
108C22×C3×D4—42no—
109C22×C3×D4D411yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C22×C3×D4C2314yes—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4—21no—
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C22×#67—21no—
118C22×#67—21no—
119C2×#235—22no—
120C2×#235—24no—
121C2×#235—42no—
122C2×#235C2314yescomplemented
123C22×D12—24no—
124C22×D12—21no—
125C22×D12—22no—
126C22×D12—42no—
127C22×D12C2311yescharacteristic
128C22×D12C2314yes—
129C22×D12C2311yescharacteristic
130C22×C4×D3—21no—
131C22×C4×D3—21no—
132C22×Dic6C2311yescharacteristic
133C3×#124—22no—
134C3×#124C2314yescomplemented
135C3×#123—28no—
136C3×C22⋊Q8—22no—
137C3×C22⋊Q8C2314yes—
138C3×#121—22no—
139C3×#121—28no—
140C3×#121C2314yescomplemented
141C3×#120—28no—
142C3×C4×D4—22no—
143C3×C4×D4D414yes—
144C3×C4×D4C2314yes—
145C3×C4×D4C2314yescomplemented
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4D411yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—28no—
155C2×C3×C22⋊C4D411yescharacteristic
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C42C2311yescharacteristic
158C2×#217—21no—
159#950—232no—
160C2×#216—24no—
161C2×#216C2314yescomplemented
162C2×#215—24no—
163C2×#215—42no—
164C2×#215C2314yescomplemented
165C2×#215C2314yescomplemented
166#937—28no—
167C2×#214—24no—
168C2×#214—42no—
169C2×#214C2314yescomplemented
170C2×#214C2314yescomplemented
171C2×#213—24no—
172C2×#213—24no—
173C2×#213—232no—
174C2×#213—24no—
175C2×#213D418yescomplemented
176C2×#213C2314yes—
177C2×#213C2314yes—
178C2×#213C2314yes—
179C2×#213C2314yes—
180#930—22no—
181#930C2314yescomplemented
182C2×(C2×D3)⋊C4—21no—
183C2×(C2×D3)⋊C4—21no—
184C2×(C2×D3)⋊C4—21no—
185C2×(C2×D3)⋊C4—21no—
186C2×C4⋊Dic3C2311yescharacteristic
187#924—22no—
188#924C2314yes—
189C2×Dic3⋊C4—21no—
190C22×C3⋊C8—24no—
191C22×C3⋊C8—24no—
192C22×C3⋊C8C2311yescharacteristic
193C22×C3⋊C8C2311yescharacteristic
194C22×C3⋊C8C2311yescharacteristic
195C22×C3⋊C8C2314yes—
196C22×C3⋊C8C2311yescharacteristic
197C22×C3⋊C8C2314yescomplemented
198#894—28no—
199#884—28no—
200D3×C22⋊C4—28no—
201#875—22no—
202#875C2314yescomplemented
203C4×D12—22no—
204C4×D12C2314yescomplemented
205#835C2314yescomplemented
206#832C2314yescomplemented
207#832C2314yescomplemented
208#830C2314yes—
209#830C2314yescomplemented
210#810C2314yescomplemented
211#809C2314yescomplemented
212#809C2314yescomplemented
213#807C2314yescomplemented
214C4⋊(C3⋊C8)C2314yescomplemented
215C4×C3⋊C8C2314yescomplemented
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic, complemented
218C23×D4—31no—
219C23×D4C2×D311yescharacteristic
220C2×#135—38no—
221C2×#135—68no—
222C22×Q16—31no—
223C22×SD16—31no—
224C22×SD16—31no—
225C22×SD16—31no—
226C22×SD16—31no—
227C22×D8—31no—
228C22×D8—31no—
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—38no—
232C22×D8—68no—
233C23×C8—31no—
234C23×C8—31no—
235#546—24no—
236#546—38no—
237#546—64no—
238#546C2×D318yescomplemented
239C2×#124—31no—
240C2×#124C2×D311yescharacteristic, complemented
241C2×#123—21no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8C2×D311yescharacteristic
245C2×#121—21no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121C2×D311yescharacteristic, complemented
249C2×#120—21no—
250C2×#120—61no—
251C2×C4×D4—31no—
252C2×C4×D4C2×D311yescharacteristic
253C2×C4×D4C2×D311yescharacteristic, complemented
254C22×C22⋊C4—21no—
255C22×C22⋊C4—61no—
256#495—38no—
257#467—38no—
258#466—38no—
259#463—38no—
260#463—38no—
261#450—38no—
262#450—38no—
263#449—38no—
264#449—38no—
265C4×D8—38no—
266C8×D4—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#102—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—
287C23×D3—21no—
288C23×D3—24no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—82no—
292C3×#41—28no—
293C3×#41—44no—
294C3×#41—48no—
295C2×C3×Q8—21no—
296C2×C3×Q8—22no—
297C2×C3×Q8—22no—
298C2×C3×Q8C2412yes—
299C2×C3×D4—24no—
300C2×C3×D4—28no—
301C2×C3×D4—24no—
302C2×C3×D4—24no—
303C2×C3×D4—21no—
304C2×C3×D4—22no—
305C2×C3×D4—24no—
306C2×C3×D4—21no—
307C2×C3×D4—22no—
308C2×C3×D4—22no—
309C2×C3×D4—44no—
310C2×C3×D4—48no—
311C2×C3×D4—44no—
312C2×C3×D4—44no—
313C2×C3×D4—82no—
314C2×C3×D4C2×D414yes—
315C2×C3×D4C2×D414yes—
316C2×C3×D4C2412yes—
317C2×C3×D4C2412yes—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—24no—
325C22×C3×C4—24no—
326C22×C3×C4—44no—
327C22×C3×C4—82no—
328C22×C3×C4C2×D411yescharacteristic
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2412yes—
335C22×C3×C4C2412yes—
336C22×C3×C4C2411yescharacteristic
337C2×#67—24no—
338C2×#67—24no—
339C2×#67—44no—
340C2×#67—82no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343#235—28no—
344#235—44no—
345#235—48no—
346C2×D12—21no—
347C2×D12—22no—
348C2×D12—22no—
349C2×D12—22no—
350C2×D12—28no—
351C2×D12—21no—
352C2×D12—24no—
353C2×D12—44no—
354C2×D12—48no—
355C2×D12—44no—
356C2×D12C2×D414yes—
357C2×D12C2412yes—
358C2×D12C2412yes—
359C2×C4×D3—24no—
360C2×C4×D3—24no—
361C2×C4×D3—44no—
362C2×C4×D3—82no—
363C2×Dic6—22no—
364C2×Dic6—22no—
365C2×Dic6—21no—
366C2×Dic6C2412yes—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4C2×D414yes—
370C3×C4⋊C4C2412yes—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—24no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C22⋊C4—24no—
376C3×C22⋊C4C2×D414yes—
377C3×C22⋊C4C2×D414yes—
378C3×C42C2×D412yes—
379C3×C42C2412yes—
380#217—24no—
381#216—28no—
382#215—28no—
383#215—44no—
384#214—28no—
385#214—44no—
386#213—28no—
387#213—28no—
388#213—28no—
389#213C2×D4116yescomplemented
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394C4⋊Dic3—21no—
395C4⋊Dic3C2412yes—
396Dic3⋊C4—24no—
397C2×C3⋊C8—22no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8—22no—
400C2×C3⋊C8—28no—
401C2×C3⋊C8—28no—
402C2×C3⋊C8C2×D414yes—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405C2×C3⋊C8C2412yes—
406C2×C3⋊C8C2412yes—
407C25—21no—
408C25—61no—
409C2×#41—22no—
410C2×#41—24no—
411C2×#41—34no—
412C2×#41—42no—
413C2×#41—64no—
414C2×#41—62no—
415C2×#41—122no—
416C2×#41C22×D314yescomplemented
417C22×Q8—31no—
418C22×Q8C22×D311yescharacteristic
419C22×D4—24no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—22no—
424C22×D4—31no—
425C22×D4—31no—
426C22×D4—34no—
427C22×D4—42no—
428C22×D4—64no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—62no—
433C22×D4—122no—
434C22×D4#6711yescharacteristic
435C22×D4C22×D311yescharacteristic
436C22×D4C22×D314yes—
437C22×D4C22×D311yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—61no—
441C23×C4—61no—
442C23×C4C22×D311yescharacteristic
443C23×C4C22×D311yescharacteristic
444#135—632no—
445C2×Q16—34no—
446C2×Q16—64no—
447C2×SD16—34no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—64no—
452C2×SD16—64no—
453C2×SD16—122no—
454C2×SD16—122no—
455C2×D8—38no—
456C2×D8—34no—
457C2×D8—34no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—64no—
461C2×D8—632no—
462C2×D8—64no—
463C2×D8—64no—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8—34no—
467C22×C8—31no—
468C22×C8—34no—
469C22×C8—31no—
470C22×C8—64no—
471C22×C8—64no—
472#124—22no—
473#124—34no—
474#124—62no—
475#124C22×D314yescomplemented
476#123—28no—
477#123—68no—
478C22⋊Q8—22no—
479C22⋊Q8—34no—
480C22⋊Q8—62no—
481C22⋊Q8C22×D314yes—
482#121—22no—
483#121—28no—
484#121—34no—
485#121—62no—
486#121—68no—
487#121C22×D314yescomplemented
488#120—28no—
489#120—68no—
490C4×D4—22no—
491C4×D4—34no—
492C4×D4—62no—
493C4×D4#6714yes—
494C4×D4C22×D314yes—
495C4×D4C22×D314yescomplemented
496C2×C4⋊C4—21no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4#6711yescharacteristic
500C2×C4⋊C4C22×D311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—28no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—68no—
513C2×C22⋊C4#6711yescharacteristic
514C2×C22⋊C4#6711yescharacteristic
515C2×C42C22×D311yescharacteristic
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103—34no—
520#102—34no—
521#102—34no—
522#102—34no—
523#102—34no—
524C22⋊C8—34no—
525C22⋊C8—34no—
526C4×C8—34no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—24no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—48no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—48no—
541C23×C3—42no—
542C23×C3—84no—
543C23×C3—816no—
544C23×C3#13514yescomplemented
545C23×C3C22×D412yes—
546C23×C3C22×D412yes—
547C23×C3C22×D411yescharacteristic
548C22×D3—24no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—48no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—48no—
557C22×D3—42no—
558C22×D3—84no—
559C22×D3—816no—
560C3×Q8—22no—
561C3×Q8—22no—
562C3×Q8—42no—
563C3×D4—28no—
564C3×D4—24no—
565C3×D4—22no—
566C3×D4—22no—
567C3×D4—22no—
568C3×D4—48no—
569C3×D4—48no—
570C3×D4—42no—
571C3×D4—84no—
572C3×D4C22×D414yes—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—24no—
578C2×C3×C4—24no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—48no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—84no—
589C2×C3×C4C22×D412yes—
590C2×C3×C4C22×D412yes—
591C2×C3×C4C22×D412yes—
592C2×C3×C4C22×D412yes—
593C2×C3×C4C22×D412yes—
594C2×C3×C4C22×D411yescharacteristic
595C2×C3×C4H(5,𝔽2)12yes—
596C2×C3×C4C2511yescharacteristic
597#67—48no—
598#67—84no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—42no—
602C2×Dic3—42no—
603D12—24no—
604D12—22no—
605D12—22no—
606D12—22no—
607D12—48no—
608D12—42no—
609D12C22×D414yes—
610C4×D3—48no—
611C4×D3—84no—
612Dic6—22no—
613Dic6—22no—
614Dic6—42no—
615C3⋊C8—22no—
616C3⋊C8—22no—
617C3⋊C8—22no—
618C3⋊C8C22×D414yes—
619C24—21no—
620C24—21no—
621C24—24no—
622C24—44no—
623C24—44no—
624C24—61no—
625C24—61no—
626C24—64no—
627C24—82no—
628C24—124no—
629C24—124no—
630C24—242no—
631C24C2×#6711yescharacteristic
632C24C2×#6711yescharacteristic
633#41—28no—
634#41—44no—
635#41—48no—
636#41—68no—
637#41—124no—
638#41—128no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—32no—
643C2×Q8—61no—
644C2×Q8—62no—
645C2×Q8—62no—
646C2×Q8C23×D312yes—
647C2×D4—24no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—24no—
656C2×D4—21no—
657C2×D4—34no—
658C2×D4—32no—
659C2×D4—32no—
660C2×D4—44no—
661C2×D4—48no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—68no—
665C2×D4—64no—
666C2×D4—64no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—61no—
671C2×D4—64no—
672C2×D4—61no—
673C2×D4—82no—
674C2×D4—124no—
675C2×D4—128no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4D3×D414yes—
680C2×D4C2×#6714yes—
681C2×D4C23×D312yes—
682C2×D4C23×D312yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—44no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—64no—
695C22×C4—64no—
696C22×C4—82no—
697C22×C4—124no—
698C22×C4—242no—
699C22×C4C2×#6712yes—
700C22×C4C2×#6712yes—
701C22×C4C2×#6711yescharacteristic
702C22×C4C2×#6711yescharacteristic
703C22×C4C2×#6711yescharacteristic
704C22×C4C2×#6711yescharacteristic
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C22×C4C23×D311yescharacteristic
708Q16—68no—
709SD16—68no—
710SD16—68no—
711SD16—124no—
712SD16—124no—
713D8—316no—
714D8—68no—
715D8—68no—
716D8—68no—
717C2×C8—34no—
718C2×C8—32no—
719C2×C8—32no—
720C2×C8—32no—
721C2×C8—32no—
722C2×C8—68no—
723C2×C8—68no—
724C2×C8—62no—
725C2×C8—62no—
726C2×C8—62no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—32no—
730C4⋊C4—61no—
731C4⋊C4—64no—
732C4⋊C4C2×#6714yes—
733C4⋊C4C23×D312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—24no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4C2×#6714yes—
745C22⋊C4C2×#6714yes—
746C42C2×#6712yes—
747C42C23×D312yes—
748C22×C3—22no—
749C22×C3—28no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—24no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—44no—
756C22×C3—48no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—816no—
763C22×C3—84no—
764C22×C3D4212yes—
765C22×C3C2×#13512yes—
766C22×C3C2×#13514yescomplemented
767C22×C3#57612yes—
768C22×C3C23×D411yescharacteristic
769C2×D3—24no—
770C2×D3—48no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—42no—
775C2×D3—42no—
776C2×D3—816no—
777C2×D3—84no—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4D4212yes—
785C3×C4C23×D411yescharacteristic
786C3×C4C2×H(5,𝔽2)11yescharacteristic
787Dic3—42no—
788Dic3—42no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—24no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—48no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—48no—
803C23—42no—
804C23—62no—
805C23—64no—
806C23—62no—
807C23—84no—
808C23—816no—
809C23—128no—
810C23—122no—
811C23—122no—
812C23—122no—
813C23—122no—
814C23—128no—
815C23—122no—
816C23—244no—
817C23—2416no—
818C23#95014yescomplemented
819C23C22×#6712yes—
820C23C22×#6712yes—
821C23C22×#6711yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—42no—
825Q8—62no—
826Q8—62no—
827Q8—122no—
828D4—28no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—24no—
833D4—34no—
834D4—48no—
835D4—48no—
836D4—42no—
837D4—62no—
838D4—62no—
839D4—62no—
840D4—64no—
841D4—84no—
842D4—128no—
843D4—128no—
844D4—122no—
845D4—244no—
846D4C2×D3×D414yes—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—48no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—84no—
865C2×C4—128no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—244no—
869C2×C4C2×D3×D412yes—
870C2×C4#100412yes—
871C2×C4C22×#6712yes—
872C2×C4C22×#6712yes—
873C2×C4C22×#6712yes—
874C2×C4C22×#6712yes—
875C2×C4C22×#6711yescharacteristic
876C2×C4C24×D311yescharacteristic
877C8—34no—
878C8—62no—
879C8—62no—
880C8—62no—
881C2×C3—24no—
882C2×C3—42no—
883C2×C3—44no—
884C2×C3—82no—
885C2×C3#328014yescomplemented
886C2×C3C2×D4211yescharacteristic
887C2×C3C22×#13511yescharacteristic
888C2×C3C2×#57611yescharacteristic
889D3—44no—
890D3—82no—
891C22—28no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—24no—
896C22—22no—
897C22—22no—
898C22—44no—
899C22—48no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—64no—
906C22—816no—
907C22—84no—
908C22—128no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—2416no—
915C22—244no—
916C22D4×#6712yes—
917C22C2×#95012yes—
918C22C2×#95014yescomplemented
919C22#583512yes—
920C22C23×#6711yescharacteristic
921C4—22no—
922C4—22no—
923C4—22no—
924C4—22no—
925C4—42no—
926C4—42no—
927C4—122no—
928C4—122no—
929C4D4×#6712yes—
930C4C22×D3×D411yescharacteristic
931C4C2×#100411yescharacteristic
932C3C2×#328011yescharacteristic, complemented, Sylow
933C2—24no—
934C2—42no—
935C2—44no—
936C2—82no—
937C2—124no—
938C2—242no—
939C2#8350514yesdirect product factor
940C2C2×D4×#6711yescharacteristic
941C2C22×#95011yescharacteristic
942C2C2×#583511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#546C2
socleC23×C3C22×D4
hypercenterC2×#546D3
hypocenterC3C2×#3280
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×#950C2semidirect
3. C23×#213C2semidirect
4. C2×#5550C2semidirect
5. C2×#5238C2semidirect
6. C2×#5218C2semidirect
7. #83505C2direct (N × H)
8. C2×#5057C2semidirect
9. C2×#5059C2semidirect
10. C2×#5046C2semidirect
11. C2×#5051C2semidirect
12. C2×#5037C2semidirect
13. C2×#5038C2semidirect
14. C2×#5016C2semidirect
15. C2×D4×C3⋊C8C2semidirect
16. C2×C4×#213C2semidirect
18. C22×C3×#41C22semidirect
20. C22×#235C22semidirect
23. C3×#546C22semidirect
24. C2×C3×#124C22semidirect
28. C2×C3×#121C22semidirect
31. C2×C3×C4×D4C22semidirect
34. C2×#950C22semidirect
35. C22×#216C22semidirect
36. C22×#215C22semidirect
37. C22×#215C22semidirect
39. C22×#214C22semidirect
40. C22×#214C22semidirect
46. C22×#213C22semidirect
47. C2×#930C22semidirect
50. C23×C3⋊C8C22semidirect
52. #5550C22semidirect
56. C2×#875C22semidirect
57. C2×C4×D12C22semidirect
58. #5238C22semidirect
59. C2×#835C22semidirect
60. #5218C22semidirect
61. C2×#832C22semidirect
62. C2×#832C22semidirect
64. C2×#830C22semidirect
65. #5059C22semidirect
66. #5057C22semidirect
67. #5051C22semidirect
68. #5046C22semidirect
69. #5038C22semidirect
70. #5037C22semidirect
71. #5016C22semidirect
72. C4×#213C22semidirect
73. D4×C3⋊C8C22semidirect
74. C2×#810C22semidirect
75. C2×#809C22semidirect
76. C2×#809C22semidirect
77. C2×#807C22semidirect
78. C2×C4⋊(C3⋊C8)C22semidirect
79. C2×C4×C3⋊C8C22semidirect
83. C2×#546D3semidirect
101. C2×C3×#41C23semidirect
122. C2×#235C23semidirect
134. C3×#124C23semidirect
140. C3×#121C23semidirect
145. C3×C4×D4C23semidirect
161. C2×#216C23semidirect
164. C2×#215C23semidirect
165. C2×#215C23semidirect
169. C2×#214C23semidirect
170. C2×#214C23semidirect
175. C2×#213D4semidirect
181. #930C23semidirect
197. C22×C3⋊C8C23semidirect
202. #875C23semidirect
204. C4×D12C23semidirect
205. #835C23semidirect
206. #832C23semidirect
207. #832C23semidirect
209. #830C23semidirect
210. #810C23semidirect
211. #809C23semidirect
212. #809C23semidirect
213. #807C23semidirect
214. C4⋊(C3⋊C8)C23semidirect
215. C4×C3⋊C8C23semidirect
217. C22×#41C2×D3semidirect
238. #546C2×D3semidirect
240. C2×#124C2×D3semidirect
248. C2×#121C2×D3semidirect
253. C2×C4×D4C2×D3semidirect
389. #213C2×D4semidirect
416. C2×#41C22×D3semidirect
475. #124C22×D3semidirect
487. #121C22×D3semidirect
495. C4×D4C22×D3semidirect
544. C23×C3#135semidirect
766. C22×C3C2×#135semidirect
818. C23#950semidirect
885. C2×C3#3280semidirect
918. C22C2×#950semidirect
932. C3C2×#3280semidirect
939. C2#83505direct (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×#9502
C23×#2132
C2×#55502
C2×#52382
C2×#52182
#835052
C2×#50572
C2×#50592
C2×#50462
C2×#50512
C2×#50372
C2×#50382
C2×#50162
C2×D4×C3⋊C82
C2×C4×#2132
C2×#32803