Finite Group Databasebeta

← C2×#80266 #11670203

Subgroups — C2×#80266 #11670203

Order 768.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5834C211yesmaximal, characteristic, complemented
2C22×#949C211yesmaximal, characteristic, complemented
3C22×#919C211yesmaximal, characteristic, complemented
4C2×#5630C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×#5185C211yesmaximal, characteristic, complemented
7C2×#5172C211yesmaximal, characteristic, complemented
8C2×#5176C211yesmaximal, characteristic, complemented
9C2×#5049C211yesmaximal, characteristic, complemented
10#80266C2116yesmaximal, direct product factor
11C2×#4810C211yesmaximal, characteristic, complemented
12C2×#4817C211yesmaximal, characteristic, complemented
13C2×#4786C211yesmaximal, characteristic, complemented
14C2×#4775C211yesmaximal, characteristic, complemented
15C2×#4732C211yesmaximal, characteristic, complemented
16C2×#4728C211yesmaximal, characteristic, complemented
17C2×#3268—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×#239C2211yescharacteristic, complemented
21C23×D12C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic, complemented
24C2×C3×C22⋊Q8C2211yescharacteristic
25#5834—24no—
26#5834C2218yescomplemented
27C2×#949—28no—
28C2×#949C2218yescomplemented
29C2×#947C2211yescharacteristic
30C2×Q8×Dic3C2211yescharacteristic, complemented
31C22×#215C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C22×#215C2211yescharacteristic, complemented
34C2×#940—21no—
35C2×#940C2211yescharacteristic, complemented
36C2×#938—21no—
37C2×#938C2211yescharacteristic, complemented
38C22×#213C2211yescharacteristic
39C22×#213C2211yescharacteristic
40C2×#930—21no—
41C2×#930C2211yescharacteristic
42C2×C4×#67—21no—
43C2×C4×#67C2211yescharacteristic
44C22×#208C2211yescharacteristic
45C2×#919—28no—
46C2×#919C2218yescomplemented
47C22×D24C2211yescharacteristic
48C22×D24C2211yescharacteristic
49C22×D3×C8C2211yescharacteristic, complemented
50#5630—24no—
51#5630C2218yescomplemented
52C2×#895—21no—
53C2×#895C2211yescharacteristic
54C2×#894—21no—
55C2×#893C2211yescharacteristic
56C2×#882—21no—
57C2×D3×C22⋊C4—21no—
58C3×#452C2218yescomplemented
59C2×C3×#103C2211yescharacteristic, complemented
60C2×C3×#102C2211yescharacteristic, complemented
61C2×C3×C22⋊C8C2211yescharacteristic
62C2×#835C2211yescharacteristic, complemented
63#5185C2218yescomplemented
64#5176C2218yescomplemented
65#5172C2218yescomplemented
66C2×#821C2211yescharacteristic
67C2×#821C2211yescharacteristic
68C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
69C2×#815C2211yescharacteristic, complemented
70C2×Dic3⋊C8C2211yescharacteristic, complemented
71#5049C2218yescomplemented
72C2×#809C2211yescharacteristic, complemented
73C2×#807C2211yescharacteristic, complemented
74#4817C2218yescomplemented
75#4810C2218yescomplemented
76#4786C2218yescomplemented
77#4775C2218yescomplemented
78#4732C2218yescomplemented
79#4728C2218yescomplemented
80C22×AGL(1,ℤ/8)—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#546—31no—
84#3268—316no—
85C2×#496—31no—
86C2×#468—31no—
87C2×#466—31no—
88C2×#464—31no—
89C2×#459—31no—
90C2×#452D311yescharacteristic, complemented
91C2×#449—31no—
92C2×#449—31no—
93C2×#447—31no—
94C2×#440—31no—
95C2×#435—31no—
96C24×D3—21no—
97C2×C3×#41—22no—
98C2×C3×#41—24no—
99C2×C3×#41—42no—
100C2×C3×#41C2314yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×Q8C2311yescharacteristic
103C22×C3×D4—21no—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C22×#67—21no—
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67D411yescharacteristic
112C2×#239—22no—
113C2×#239—22no—
114C2×#239—24no—
115C2×#239—24no—
116C2×#239—42no—
117C2×#239—42no—
118C2×#239C2314yes—
119C2×#239C2314yescomplemented
120C22×D12—24no—
121C22×D12—21no—
122C22×D12—21no—
123C22×D12—21no—
124C22×D12—22no—
125C22×D12—21no—
126C22×D12—42no—
127C22×D12C2311yescharacteristic
128C22×D12C2311yescharacteristic
129C22×D12C2314yes—
130C22×D12C2311yescharacteristic
131C22×C4×D3—21no—
132C22×C4×D3—21no—
133C22×C4×D3—21no—
134C22×C4×D3C2311yescharacteristic
135C2×C3×Q16—24no—
136C2×C3×Q16C2314yescomplemented
137C2×C3×SD16—42no—
138C2×C3×SD16C2314yescomplemented
139C22×C3×C8C2311yescharacteristic
140C22×C3×C8C2311yescharacteristic
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8C2314yes—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C22⋊C4—21no—
146C2×#217—21no—
147C2×#217D411yescharacteristic
148#949—232no—
149#947—22no—
150#947C2314yes—
151Q8×Dic3—22no—
152Q8×Dic3C2314yescomplemented
153C2×#215—24no—
154C2×#215—24no—
155C2×#215D418yescomplemented
156C2×#215C2314yes—
157C2×#215C2314yes—
158C2×#215C2314yescomplemented
159#940—28no—
160#940—22no—
161#940C2314yescomplemented
162#938—22no—
163#938—28no—
164#938C2314yescomplemented
165C2×#213—24no—
166C2×#213—24no—
167C2×#213C2314yes—
168C2×#213C2314yes—
169#930—22no—
170#930—28no—
171#930C2314yes—
172C4×#67—28no—
173C4×#67D414yes—
174C4×#67C2314yes—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4—21no—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4D411yescharacteristic
181C2×C4⋊Dic3—21no—
182C2×C4⋊Dic3C2311yescharacteristic
183C2×Dic3⋊C4D411yescharacteristic
184C2×C4×Dic3—21no—
185C2×C4×Dic3C2311yescharacteristic
186C2×#208—24no—
187C2×#208C2314yes—
188C22×C3⋊C8C2311yescharacteristic
189C22×C3⋊C8C2311yescharacteristic
190#919—232no—
191C2×D24—24no—
192C2×D24—42no—
193C2×D24C2314yes—
194C2×D24C2314yes—
195C2×D3×C8—24no—
196C2×D3×C8C2314yescomplemented
197#895—22no—
198#895—28no—
199#895C2314yes—
200#894—28no—
201#893—22no—
202#893C2314yes—
203#882—28no—
204D3×C22⋊C4—28no—
205C3×#103C2314yescomplemented
206C3×#102C2314yescomplemented
207C3×C22⋊C8C2314yes—
208#835C2314yescomplemented
209#821C2314yes—
210#821C2314yes—
211(C2×D3)⋊C8C2314yescomplemented
212#815C2314yescomplemented
213Dic3⋊C8C2314yescomplemented
214#809C2314yescomplemented
215#807C2314yescomplemented
216C22×#41—31no—
217C22×#41—31no—
218C22×#41C2×D311yescharacteristic
219C23×D4—31no—
220C2×AGL(1,ℤ/8)—38no—
221C2×AGL(1,ℤ/8)—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16C2×D311yescharacteristic, complemented
225C22×SD16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16C2×D311yescharacteristic, complemented
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
234C23×C8—31no—
235#550—38no—
236#550—64no—
237#546—38no—
238#546—64no—
239C2×#127—31no—
240C2×#127—61no—
241C2×#124—31no—
242C2×#123—61no—
243C2×C22⋊Q8C2×D311yescharacteristic
244C2×#121—31no—
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#120—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C22⋊C4—61no—
256#496—38no—
257#468—38no—
258#466—38no—
259#464—38no—
260#459—38no—
261#452C2×D318yescomplemented
262#449—38no—
263#449—38no—
264#447—38no—
265#440—38no—
266#435—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103C2×D311yescharacteristic, complemented
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic, complemented
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic
277C2×#97—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—24no—
284C23×D3—44no—
285C23×D3—44no—
286C23×D3—82no—
287C23×D3C2×D411yescharacteristic
288C3×#41—28no—
289C3×#41—44no—
290C3×#41—48no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8—22no—
296C2×C3×Q8C2×D414yes—
297C2×C3×Q8C2412yes—
298C2×C3×Q8C2412yes—
299C2×C3×D4—24no—
300C2×C3×D4—22no—
301C2×C3×D4—21no—
302C2×C3×D4—22no—
303C2×C3×D4—44no—
304C2×C3×D4C2412yes—
305C22×C3×C4—21no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—24no—
311C22×C3×C4—44no—
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2412yes—
315C22×C3×C4C2411yescharacteristic
316C2×#67—24no—
317C2×#67—24no—
318C2×#67—24no—
319C2×#67—24no—
320C2×#67—42no—
321C2×#67—44no—
322C2×#67—82no—
323C2×#67—82no—
324C2×#67—82no—
325C2×#67C2×D414yes—
326C22×Dic3—21no—
327C22×Dic3C2×D411yescharacteristic
328C22×Dic3C2×D411yescharacteristic
329C22×Dic3C2×D411yescharacteristic
330#239—28no—
331#239—28no—
332#239—44no—
333#239—44no—
334#239—48no—
335#239—48no—
336C2×D12—21no—
337C2×D12—22no—
338C2×D12—22no—
339C2×D12—22no—
340C2×D12—22no—
341C2×D12—22no—
342C2×D12—28no—
343C2×D12—24no—
344C2×D12—24no—
345C2×D12—24no—
346C2×D12—21no—
347C2×D12—21no—
348C2×D12—24no—
349C2×D12—44no—
350C2×D12—48no—
351C2×D12—44no—
352C2×D12—44no—
353C2×D12—44no—
354C2×D12—82no—
355C2×D12C2×D414yes—
356C2×D12C2412yes—
357C2×D12C2412yes—
358C2×D12C2412yes—
359C2×C4×D3—22no—
360C2×C4×D3—22no—
361C2×C4×D3—24no—
362C2×C4×D3—24no—
363C2×C4×D3—24no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—82no—
367C2×C4×D3C2×D412yes—
368C2×C4×D3C2412yes—
369C3×Q16—28no—
370C3×SD16—44no—
371C2×C3×C8—22no—
372C2×C3×C8—22no—
373C2×C3×C8C2412yes—
374C2×C3×C8C2412yes—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—24no—
377C3×C4⋊C4C2412yes—
378C3×C22⋊C4—24no—
379#217—24no—
380#217C2×D414yes—
381#215—28no—
382#215—28no—
383#215C2×D4116yescomplemented
384#213—28no—
385#213—28no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4C2×D414yes—
392C4⋊Dic3—21no—
393C4⋊Dic3—24no—
394C4⋊Dic3C2412yes—
395Dic3⋊C4C2×D414yes—
396C4×Dic3—24no—
397C4×Dic3C2×D412yes—
398C4×Dic3C2412yes—
399#208—28no—
400C2×C3⋊C8—22no—
401C2×C3⋊C8C2×D414yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404D24—28no—
405D24—44no—
406D3×C8—28no—
407C25—61no—
408C2×#41—22no—
409C2×#41—24no—
410C2×#41—34no—
411C2×#41—34no—
412C2×#41—42no—
413C2×#41—62no—
414C2×#41—62no—
415C2×#41—64no—
416C2×#41—64no—
417C2×#41—122no—
418C2×#41—122no—
419C2×#41C22×D314yes—
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D311yescharacteristic
422C22×D4—21no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—31no—
426C22×D4—31no—
427C22×D4—34no—
428C22×D4—64no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—61no—
435C22×D4—61no—
436C22×D4—61no—
437C22×D4—62no—
438C22×D4—122no—
439C22×D4C22×D311yescharacteristic
440C23×C4—21no—
441C23×C4—31no—
442C23×C4—61no—
443C23×C4—61no—
444C23×C4—61no—
445C23×C4C22×D311yescharacteristic
446AGL(1,ℤ/8)—632no—
447#135—632no—
448C2×Q16—24no—
449C2×Q16C22×D314yescomplemented
450C2×SD16—38no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—34no—
454C2×SD16—42no—
455C2×SD16—64no—
456C2×SD16—64no—
457C2×SD16C22×D314yescomplemented
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—34no—
461C2×D8—34no—
462C2×D8—64no—
463C2×D8—64no—
464C2×D8—64no—
465C2×D8—122no—
466C2×M16—34no—
467C2×M16—64no—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8—34no—
471C22×C8—64no—
472C22×C8C22×D311yescharacteristic
473C22×C8C22×D311yescharacteristic
474#127—34no—
475#127—62no—
476#127—68no—
477#124—34no—
478#124—62no—
479#123—68no—
480C22⋊Q8—22no—
481C22⋊Q8C22×D314yes—
482#121—34no—
483#121—34no—
484#121—34no—
485#121—68no—
486#121—68no—
487#121—68no—
488#121—62no—
489#121—62no—
490#121—62no—
491#120—68no—
492C4×Q8—34no—
493C4×Q8—62no—
494C4×D4—34no—
495C4×D4—34no—
496C4×D4—34no—
497C4×D4—62no—
498C4×D4—68no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4C22×D311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—68no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C22⋊C4—61no—
514C2×C42—31no—
515C2×C42—61no—
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103C22×D314yescomplemented
520#102—34no—
521#102—34no—
522#102—34no—
523#102C22×D314yescomplemented
524C22⋊C8—34no—
525C22⋊C8C22×D314yes—
526#97—34no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3C22×D412yes—
535C23×C3C22×D411yescharacteristic
536C22×D3—22no—
537C22×D3—24no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—48no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—48no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—84no—
554C22×D3—816no—
555C22×D3C22×D412yes—
556C3×Q8—24no—
557C3×Q8—22no—
558C3×Q8—22no—
559C3×Q8—22no—
560C3×Q8—42no—
561C3×Q8C22×D414yes—
562C3×D4—22no—
563C3×D4—22no—
564C3×D4—48no—
565C3×D4—42no—
566C2×C3×C4—24no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—24no—
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×C4C22×D412yes—
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D412yes—
580C2×C3×C4H(5,𝔽2)12yes—
581C2×C3×C4C2511yescharacteristic
582#67—44no—
583#67—48no—
584#67—84no—
585#67—84no—
586#67—84no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—42no—
592C2×Dic3C22×D412yes—
593C2×Dic3C22×D412yes—
594C2×Dic3C22×D412yes—
595D12—24no—
596D12—22no—
597D12—22no—
598D12—22no—
599D12—22no—
600D12—22no—
601D12—48no—
602D12—48no—
603D12—48no—
604D12—42no—
605D12—42no—
606D12—84no—
607D12C22×D414yes—
608C4×D3—24no—
609C4×D3—22no—
610C4×D3—22no—
611C4×D3—48no—
612C4×D3—48no—
613C4×D3—84no—
614C3×C8—22no—
615C3×C8—22no—
616C3⋊C8—22no—
617C3⋊C8C22×D414yes—
618C24—21no—
619C24—31no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—64no—
624C24—124no—
625C24—124no—
626C24—242no—
627C24D3×D411yescharacteristic
628#41—28no—
629#41—44no—
630#41—48no—
631#41—68no—
632#41—68no—
633#41—124no—
634#41—124no—
635#41—128no—
636#41—128no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8D3×D414yes—
643C2×Q8C23×D312yes—
644C2×Q8C23×D312yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—34no—
650C2×D4—34no—
651C2×D4—32no—
652C2×D4—32no—
653C2×D4—32no—
654C2×D4—44no—
655C2×D4—68no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—64no—
661C2×D4—64no—
662C2×D4—64no—
663C2×D4—61no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—64no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—62no—
670C2×D4—62no—
671C2×D4—62no—
672C2×D4—124no—
673C2×D4—128no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—122no—
678C2×D4—124no—
679C2×D4—242no—
680C2×D4—242no—
681C2×D4—242no—
682C2×D4—242no—
683C2×D4C23×D312yes—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—44no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—64no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—61no—
702C22×C4—124no—
703C22×C4—124no—
704C22×C4—242no—
705C22×C4D3×D412yes—
706C22×C4D3×D411yescharacteristic
707C22×C4C23×D312yes—
708C22×C4C23×D311yescharacteristic
709Q16—28no—
710SD16—316no—
711SD16—44no—
712SD16—68no—
713SD16—68no—
714D8—68no—
715D8—68no—
716D8—68no—
717D8—124no—
718M16—68no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—34no—
722C2×C8—32no—
723C2×C8—32no—
724C2×C8—68no—
725C2×C8—62no—
726C2×C8C23×D312yes—
727C2×C8C23×D312yes—
728C4⋊C4—24no—
729C4⋊C4—21no—
730C4⋊C4—34no—
731C4⋊C4—32no—
732C4⋊C4—64no—
733C4⋊C4—61no—
734C4⋊C4C23×D312yes—
735C22⋊C4—24no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C42—32no—
745C42—32no—
746C42—64no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—44no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—84no—
755C22×C3D4212yes—
756C22×C3#57512yes—
757C22×C3#57612yes—
758C22×C3C23×D411yescharacteristic
759C2×D3—22no—
760C2×D3—24no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—44no—
764C2×D3—48no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—816no—
774C2×D3—84no—
775C2×D3—84no—
776C3×C4—24no—
777C3×C4—22no—
778C3×C4—42no—
779C3×C4—42no—
780C3×C4D4212yes—
781C3×C4C23×D411yescharacteristic
782C3×C4C2×H(5,𝔽2)11yescharacteristic
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—42no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—32no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—64no—
800C23—62no—
801C23—62no—
802C23—128no—
803C23—128no—
804C23—122no—
805C23—122no—
806C23—122no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—244no—
813C23—2416no—
814C23C2×D3×D412yes—
815C23C2×D3×D411yescharacteristic
816Q8—22no—
817Q8—24no—
818Q8—22no—
819Q8—22no—
820Q8—42no—
821Q8C2×D3×D414yes—
822D4—22no—
823D4—22no—
824D4—34no—
825D4—48no—
826D4—42no—
827D4—62no—
828D4—62no—
829D4—62no—
830D4—62no—
831D4—62no—
832D4—64no—
833D4—128no—
834D4—128no—
835D4—128no—
836D4—124no—
837D4—128no—
838D4—122no—
839D4—122no—
840D4—244no—
841D4—244no—
842D4—244no—
843D4—244no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—48no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—64no—
864C2×C4—62no—
865C2×C4—128no—
866C2×C4—128no—
867C2×C4—122no—
868C2×C4—244no—
869C2×C4C2×D3×D412yes—
870C2×C4C2×D3×D412yes—
871C2×C4C2×D3×D411yescharacteristic
872C2×C4#100412yes—
873C2×C4C24×D311yescharacteristic
874C8—22no—
875C8—22no—
876C8—34no—
877C8—62no—
878C2×C3—42no—
879C2×C3—82no—
880C2×C3#326814yescomplemented
881C2×C3C2×D4211yescharacteristic
882C2×C3C2×#57511yescharacteristic
883C2×C3C2×#57611yescharacteristic
884D3—42no—
885D3—44no—
886D3—82no—
887D3—82no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—44no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—64no—
899C22—84no—
900C22—124no—
901C22—128no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—2416no—
911C22—244no—
912C22—244no—
913C22#559012yes—
914C22#576912yes—
915C22#577712yes—
916C22C22×D3×D411yescharacteristic
917C4—22no—
918C4—24no—
919C4—42no—
920C4—42no—
921C4—62no—
922C4—62no—
923C4—62no—
924C4—122no—
925C4#559012yes—
926C4C22×D3×D411yescharacteristic
927C4C2×#100411yescharacteristic
928C3C2×#326811yescharacteristic, complemented, Sylow
929C2—42no—
930C2—82no—
931C2—122no—
932C2—124no—
933C2—242no—
934C2—242no—
935C2#8026614yesdirect product factor
936C2C2×#559011yescharacteristic
937C2C2×#576911yescharacteristic
938C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
hypercenterC2×#452D3
hypocenterC3C2×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#5834C2semidirect
2. C22×#949C2semidirect
3. C22×#919C2semidirect
4. C2×#5630C2semidirect
5. C2×C3×#452C2semidirect
6. C2×#5185C2semidirect
7. C2×#5172C2semidirect
8. C2×#5176C2semidirect
9. C2×#5049C2semidirect
10. #80266C2direct (N × H)
11. C2×#4810C2semidirect
12. C2×#4817C2semidirect
13. C2×#4786C2semidirect
14. C2×#4775C2semidirect
15. C2×#4732C2semidirect
16. C2×#4728C2semidirect
20. C22×#239C22semidirect
22. C22×C3×Q16C22semidirect
23. C22×C3×SD16C22semidirect
26. #5834C22semidirect
28. C2×#949C22semidirect
30. C2×Q8×Dic3C22semidirect
33. C22×#215C22semidirect
35. C2×#940C22semidirect
37. C2×#938C22semidirect
46. C2×#919C22semidirect
49. C22×D3×C8C22semidirect
51. #5630C22semidirect
58. C3×#452C22semidirect
59. C2×C3×#103C22semidirect
60. C2×C3×#102C22semidirect
62. C2×#835C22semidirect
63. #5185C22semidirect
64. #5176C22semidirect
65. #5172C22semidirect
68. C2×(C2×D3)⋊C8C22semidirect
69. C2×#815C22semidirect
70. C2×Dic3⋊C8C22semidirect
71. #5049C22semidirect
72. C2×#809C22semidirect
73. C2×#807C22semidirect
74. #4817C22semidirect
75. #4810C22semidirect
76. #4786C22semidirect
77. #4775C22semidirect
78. #4732C22semidirect
79. #4728C22semidirect
90. C2×#452D3semidirect
119. C2×#239C23semidirect
136. C2×C3×Q16C23semidirect
138. C2×C3×SD16C23semidirect
152. Q8×Dic3C23semidirect
155. C2×#215D4semidirect
158. C2×#215C23semidirect
161. #940C23semidirect
164. #938C23semidirect
196. C2×D3×C8C23semidirect
205. C3×#103C23semidirect
206. C3×#102C23semidirect
208. #835C23semidirect
211. (C2×D3)⋊C8C23semidirect
212. #815C23semidirect
213. Dic3⋊C8C23semidirect
214. #809C23semidirect
215. #807C23semidirect
224. C22×Q16C2×D3semidirect
228. C22×SD16C2×D3semidirect
261. #452C2×D3semidirect
270. C2×#103C2×D3semidirect
274. C2×#102C2×D3semidirect
383. #215C2×D4semidirect
449. C2×Q16C22×D3semidirect
457. C2×SD16C22×D3semidirect
519. #103C22×D3semidirect
523. #102C22×D3semidirect
880. C2×C3#3268semidirect
928. C3C2×#3268semidirect
935. C2#80266direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58342
C22×#9492
C22×#9192
C2×#56302
C2×C3×#4522
C2×#51852
C2×#51722
C2×#51762
C2×#50492
#802662
C2×#48102
C2×#48172
C2×#47862
C2×#47752
C2×#47322
C2×#47282
C2×#32683