Finite Group Databasebeta

← C2×#80117 #11672113

Subgroups — C2×#80117 #11672113

Order 768.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5834C211yesmaximal, characteristic, complemented
2C2×#5611C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×#5232C211yesmaximal, characteristic, complemented
5C2×#5172C211yesmaximal, characteristic, complemented
6C2×Dic3×SD16C211yesmaximal, characteristic, complemented
7C2×#5159C211yesmaximal, characteristic, complemented
8C2×#5150C211yesmaximal, characteristic, complemented
9C2×#5039C211yesmaximal, characteristic, complemented
10#80117C2116yesmaximal, direct product factor
11C2×#4803C211yesmaximal, characteristic, complemented
12C2×#4791C211yesmaximal, characteristic, complemented
13C2×#4777C211yesmaximal, characteristic, complemented
14C2×#4760C211yesmaximal, characteristic, complemented
15C2×#4729C211yesmaximal, characteristic, complemented
16C2×#4735C211yesmaximal, characteristic, complemented
17C2×#3332—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×#237—21no—
21C22×C3×SD16C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24#5834—24no—
25#5834C2218yescomplemented
26C2×Q8×Dic3C2211yescharacteristic
27C2×#940—21no—
28C2×#940C2211yescharacteristic
29C2×#938—21no—
30C2×#938C2211yescharacteristic
31C2×#938C2211yescharacteristic
32C2×#935—21no—
33C2×D4×Dic3C2211yescharacteristic
34C22×#213C2211yescharacteristic
35C2×#930—21no—
36C2×#930C2211yescharacteristic
37C2×C4×#67—21no—
38C2×C4×#67C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×#208C2211yescharacteristic
41C22×ΓL(1,𝔽25)C2211yescharacteristic
42#5611—24no—
43#5611C2218yescomplemented
44C2×D3×C4⋊C4C2211yescharacteristic
45C2×#888C2211yescharacteristic
46C2×#883—21no—
47C2×#878—21no—
48C3×#449C2218yescomplemented
49C2×C3×#103C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×C22⋊C8C2211yescharacteristic
52#5232C2218yescomplemented
53C2×#835C2211yescharacteristic
54C2×#835C2211yescharacteristic
55C2×#832C2211yescharacteristic
56C2×#832C2211yescharacteristic
57C2×#832C2211yescharacteristic
58#5172C2218yescomplemented
59Dic3×SD16C2218yescomplemented
60#5159C2218yescomplemented
61#5150C2218yescomplemented
62C2×#821C2211yescharacteristic
63C2×#821C2211yescharacteristic
64C2×(C2×D3)⋊C8C2211yescharacteristic
65C2×#817C2211yescharacteristic
66C2×#817C2211yescharacteristic
67C2×Dic3⋊C8C2211yescharacteristic
68C2×C8×Dic3C2211yescharacteristic
69#5039C2218yescomplemented
70C2×#809C2211yescharacteristic
71C2×#808C2211yescharacteristic
72#4803C2218yescomplemented
73#4791C2218yescomplemented
74#4777C2218yescomplemented
75#4760C2218yescomplemented
76#4735C2218yescomplemented
77#4729C2218yescomplemented
78C2×#550—31no—
79C2×#547—31no—
80#3332—316no—
81C2×#486—31no—
82C2×#481—31no—
83C2×#481—31no—
84C2×#475—31no—
85C2×#469—31no—
86C2×#469—31no—
87C2×#459—31no—
88C2×#449—31no—
89C2×#449D311yescharacteristic, complemented
90C2×C4×SD16—31no—
91C2×#436—31no—
92C2×#417—31no—
93C2×#417—31no—
94C2×C3×#41—22no—
95C2×C3×#41—24no—
96C2×C3×#41—42no—
97C2×C3×#41C2314yes—
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C22×#67—21no—
106C22×#67—21no—
107C22×#67—21no—
108C22×#67—21no—
109C22×#67—21no—
110C22×#67D411yescharacteristic
111C23×Dic3—21no—
112C23×Dic3—21no—
113C2×#239—22no—
114C2×#239—24no—
115C2×#239—42no—
116C2×#239C2314yes—
117C2×#237—28no—
118C2×#237—48no—
119C22×D12—21no—
120C22×D12C2311yescharacteristic
121C22×C4×D3—21no—
122C22×C4×D3—21no—
123C22×C4×D3C2311yescharacteristic
124C22×Dic6—21no—
125C2×C3×SD16—24no—
126C2×C3×SD16C2314yes—
127C2×C3×D8—42no—
128C2×C3×D8C2314yes—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×#121—22no—
132C3×#121C2314yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×#217—21no—
136C2×#217—21no—
137C2×#217—21no—
138C2×#217D411yescharacteristic
139Q8×Dic3—22no—
140Q8×Dic3C2314yes—
141#940—28no—
142#940—22no—
143#940C2314yes—
144#938—22no—
145#938—22no—
146#938—28no—
147#938C2314yes—
148#938C2314yes—
149#935—28no—
150D4×Dic3—22no—
151D4×Dic3C2314yes—
152C2×#213—42no—
153C2×#213C2314yes—
154#930—22no—
155#930—28no—
156#930C2314yes—
157C4×#67—28no—
158C4×#67D414yes—
159C4×#67C2314yes—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4D411yescharacteristic
162C2×C4⋊Dic3—21no—
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3—21no—
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2314yes—
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4—21no—
171C2×Dic3⋊C4D411yescharacteristic
172C2×C4×Dic3—21no—
173C2×C4×Dic3C2311yescharacteristic
174C2×#208—42no—
175C2×#208C2314yes—
176C22×C3⋊C8C2311yescharacteristic
177C22×C3⋊C8C2311yescharacteristic
178C2×ΓL(1,𝔽25)—42no—
179C2×ΓL(1,𝔽25)C2314yes—
180D3×C4⋊C4—22no—
181D3×C4⋊C4C2314yes—
182#888—22no—
183#888C2314yes—
184#883—28no—
185#878—28no—
186C3×#103C2314yes—
187C3×#102C2314yes—
188C3×C22⋊C8C2314yes—
189#835C2314yes—
190#835C2314yes—
191#832C2314yes—
192#832C2314yes—
193#832C2314yes—
194#821C2314yes—
195#821C2314yes—
196(C2×D3)⋊C8C2314yes—
197#817C2314yes—
198#817C2314yes—
199Dic3⋊C8C2314yes—
200C8×Dic3C2314yes—
201#809C2314yes—
202#808C2314yes—
203C22×#41—31no—
204C22×#41—61no—
205C22×#41C2×D311yescharacteristic
206C22×SD16C2×D311yescharacteristic
207C22×D8—31no—
208C22×D8C2×D311yescharacteristic
209C22×M16—31no—
210C22×M16—31no—
211#550—38no—
212#550—64no—
213#547—38no—
214#547—64no—
215C2×C4⋊Q8—31no—
216C2×#127—31no—
217C2×#127—61no—
218C2×#123—61no—
219C2×#123—61no—
220C2×C22⋊Q8—61no—
221C2×#121—31no—
222C2×#121—31no—
223C2×#121—31no—
224C2×#121—61no—
225C2×#121—61no—
226C2×#121C2×D311yescharacteristic
227C2×C4×Q8—31no—
228C2×C4×D4—31no—
229C2×C4×D4—31no—
230C2×C4×D4—61no—
231C22×C4⋊C4—31no—
232C22×C4⋊C4—31no—
233#486—38no—
234#481—38no—
235#481—38no—
236#475—38no—
237#469—38no—
238#469—38no—
239#459—38no—
240#449—38no—
241#449C2×D318yescomplemented
242C4×SD16—38no—
243#436—38no—
244C2×#106—31no—
245C2×#106—31no—
246C2×#106—31no—
247C2×C4⋊C8—31no—
248#417—38no—
249#417—38no—
250C2×#103—31no—
251C2×#103—31no—
252C2×#103C2×D311yescharacteristic
253C2×#102—31no—
254C2×#102—31no—
255C2×#102—31no—
256C2×#102—31no—
257C2×#102—31no—
258C2×#102—31no—
259C2×#102C2×D311yescharacteristic
260C2×C22⋊C8—31no—
261C2×C22⋊C8C2×D311yescharacteristic
262C2×C4×C8—31no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3C2×D411yescharacteristic
266C23×D3—21no—
267C23×D3C2×D411yescharacteristic
268C3×#41—28no—
269C3×#41—44no—
270C3×#41—48no—
271C2×C3×Q8—21no—
272C2×C3×Q8—22no—
273C2×C3×Q8#4114yescomplemented
274C2×C3×Q8C2412yes—
275C2×C3×D4—24no—
276C2×C3×D4—24no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4C2412yes—
286C2×C3×D4C2412yes—
287C22×C3×C4—21no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—21no—
291C22×C3×C4—24no—
292C22×C3×C4—44no—
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2411yescharacteristic
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—82no—
306C2×#67—82no—
307C2×#67—82no—
308C2×#67C2×D414yes—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—24no—
313C22×Dic3—24no—
314C22×Dic3—44no—
315C22×Dic3—44no—
316C22×Dic3C2×D411yescharacteristic
317C22×Dic3C2×D411yescharacteristic
318C22×Dic3C2×D411yescharacteristic
319#239—28no—
320#239—44no—
321#239—48no—
322#237—432no—
323C2×D12—22no—
324C2×D12—22no—
325C2×D12—24no—
326C2×D12—21no—
327C2×D12—44no—
328C2×D12C2412yes—
329C2×C4×D3—22no—
330C2×C4×D3—22no—
331C2×C4×D3—24no—
332C2×C4×D3—24no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3C2×D412yes—
336C2×C4×D3C2412yes—
337C2×Dic6—24no—
338C2×Dic6—44no—
339C3×SD16—28no—
340C3×D8—44no—
341C2×C3×C8—22no—
342C2×C3×C8—22no—
343C2×C3×C8C2412yes—
344C2×C3×C8C2412yes—
345C3×C4⋊C4—21no—
346C3×C4⋊C4C2412yes—
347C3×C22⋊C4—24no—
348#217—24no—
349#217—24no—
350#217—24no—
351#217C2×D414yes—
352#213—44no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4C2×D414yes—
355C4⋊Dic3—24no—
356C4⋊Dic3—21no—
357C4⋊Dic3—21no—
358C4⋊Dic3—21no—
359C4⋊Dic3—24no—
360C4⋊Dic3C2412yes—
361C4⋊Dic3C2412yes—
362C4⋊Dic3C2412yes—
363Dic3⋊C4—24no—
364Dic3⋊C4—24no—
365Dic3⋊C4C2×D414yes—
366C4×Dic3—24no—
367C4×Dic3C2×D412yes—
368C4×Dic3C2412yes—
369#208—44no—
370C2×C3⋊C8—22no—
371C2×C3⋊C8—22no—
372C2×C3⋊C8C2412yes—
373C2×C3⋊C8C2412yes—
374ΓL(1,𝔽25)—44no—
375C2×#41—22no—
376C2×#41—24no—
377C2×#41—34no—
378C2×#41—42no—
379C2×#41—62no—
380C2×#41—68no—
381C2×#41—64no—
382C2×#41—122no—
383C2×#41—128no—
384C2×#41C22×D314yes—
385C22×Q8—61no—
386C22×Q8C22×D311yescharacteristic
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—31no—
390C22×D4—31no—
391C22×D4—61no—
392C22×D4—61no—
393C22×D4—61no—
394C22×D4—61no—
395C22×D4—61no—
396C22×D4—61no—
397C22×D4C22×D311yescharacteristic
398C22×D4C22×D311yescharacteristic
399C23×C4—21no—
400C23×C4—31no—
401C23×C4—61no—
402C23×C4—61no—
403C23×C4—61no—
404C23×C4—61no—
405C23×C4C22×D311yescharacteristic
406C2×SD16—24no—
407C2×SD16C22×D314yes—
408C2×D8—34no—
409C2×D8—42no—
410C2×D8—122no—
411C2×D8C22×D314yes—
412C2×M16—34no—
413C2×M16—34no—
414C2×M16—122no—
415C2×M16—122no—
416C22×C8—31no—
417C22×C8—31no—
418C22×C8C22×D311yescharacteristic
419C22×C8C22×D311yescharacteristic
420C4⋊Q8—34no—
421C4⋊Q8—62no—
422#127—34no—
423#127—62no—
424#127—68no—
425#123—68no—
426#123—68no—
427C22⋊Q8—68no—
428#121—22no—
429#121—34no—
430#121—34no—
431#121—34no—
432#121—68no—
433#121—68no—
434#121—62no—
435#121—62no—
436#121—62no—
437#121C22×D314yes—
438C4×Q8—34no—
439C4×Q8—62no—
440C4×D4—34no—
441C4×D4—34no—
442C4×D4—34no—
443C4×D4—62no—
444C4×D4—68no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—34no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—34no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—61no—
453C2×C4⋊C4—61no—
454C2×C4⋊C4—61no—
455C2×C4⋊C4—61no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4C22×D311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—61no—
462C2×C22⋊C4—61no—
463C2×C22⋊C4—61no—
464C2×C22⋊C4—61no—
465C2×C42—31no—
466C2×C42—61no—
467#106—34no—
468#106—34no—
469#106—34no—
470C4⋊C8—34no—
471#103—34no—
472#103—34no—
473#103C22×D314yes—
474#102—34no—
475#102—34no—
476#102—34no—
477#102—34no—
478#102—34no—
479#102—34no—
480#102C22×D314yes—
481C22⋊C8—34no—
482C22⋊C8C22×D314yes—
483C4×C8—34no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3C22×D412yes—
496C23×C3C22×D411yescharacteristic
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—42no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3C22×D412yes—
505C3×Q8—24no—
506C3×Q8—22no—
507C3×Q8C2×#4114yescomplemented
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—48no—
513C3×D4—48no—
514C3×D4—42no—
515C3×D4—42no—
516C2×C3×C4—24no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—24no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—48no—
524C2×C3×C4—42no—
525C2×C3×C4C22×D412yes—
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C2×#4112yes—
528C2×C3×C4H(5,𝔽2)12yes—
529C2×C3×C4C2511yescharacteristic
530#67—28no—
531#67—48no—
532#67—48no—
533#67—84no—
534#67—84no—
535#67—84no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—48no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544C2×Dic3—42no—
545C2×Dic3—48no—
546C2×Dic3AGL(1,ℤ/8)14yes—
547C2×Dic3C22×D412yes—
548C2×Dic3C22×D412yes—
549C2×Dic3C22×D412yes—
550D12—22no—
551D12—22no—
552D12—48no—
553D12—42no—
554C4×D3—24no—
555C4×D3—22no—
556C4×D3—22no—
557C4×D3—48no—
558C4×D3—48no—
559Dic6—48no—
560C3×C8—22no—
561C3×C8—22no—
562C3⋊C8—22no—
563C3⋊C8—22no—
564C24—21no—
565C24—21no—
566C24—31no—
567C24—61no—
568C24D3×D411yescharacteristic
569#41—28no—
570#41—44no—
571#41—48no—
572#41—68no—
573#41—124no—
574#41—128no—
575#41—1232no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—64no—
579C2×Q8—124no—
580C2×Q8#23714yescomplemented
581C2×Q8C23×D312yes—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—34no—
591C2×D4—32no—
592C2×D4—44no—
593C2×D4—44no—
594C2×D4—64no—
595C2×D4—64no—
596C2×D4—64no—
597C2×D4—64no—
598C2×D4—64no—
599C2×D4—64no—
600C2×D4—64no—
601C2×D4—61no—
602C2×D4—62no—
603C2×D4—62no—
604C2×D4—124no—
605C2×D4—124no—
606C2×D4—124no—
607C2×D4—242no—
608C2×D4—242no—
609C2×D4—242no—
610C2×D4C23×D312yes—
611C2×D4C23×D312yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—44no—
623C22×C4—64no—
624C22×C4—64no—
625C22×C4—64no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—64no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—124no—
633C22×C4—124no—
634C22×C4—124no—
635C22×C4—124no—
636C22×C4D3×D412yes—
637C22×C4D3×D411yescharacteristic
638C22×C4C23×D312yes—
639C22×C4C23×D311yescharacteristic
640SD16—28no—
641D8—44no—
642D8—124no—
643M16—124no—
644M16—124no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—32no—
648C2×C8—32no—
649C2×C8—62no—
650C2×C8—62no—
651C2×C8C23×D312yes—
652C2×C8C23×D312yes—
653C4⋊C4—21no—
654C4⋊C4—34no—
655C4⋊C4—32no—
656C4⋊C4—32no—
657C4⋊C4—32no—
658C4⋊C4—64no—
659C4⋊C4—64no—
660C4⋊C4—64no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—64no—
664C4⋊C4—61no—
665C4⋊C4C23×D312yes—
666C22⋊C4—24no—
667C22⋊C4—34no—
668C22⋊C4—34no—
669C22⋊C4—64no—
670C22⋊C4—64no—
671C22⋊C4—64no—
672C22⋊C4—64no—
673C42—32no—
674C42—32no—
675C42—64no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—44no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—84no—
687C22×C3—84no—
688C22×C3#54612yes—
689C22×C3C2×AGL(1,ℤ/8)12yes—
690C22×C3#57712yes—
691C22×C3C23×D411yescharacteristic
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—44no—
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—84no—
700C3×C4—24no—
701C3×C4—22no—
702C3×C4—42no—
703C3×C4#54612yes—
704C3×C4C22×#4111yescharacteristic
705C3×C4C2×H(5,𝔽2)11yescharacteristic
706Dic3—22no—
707Dic3—22no—
708Dic3—42no—
709Dic3—42no—
710Dic3—42no—
711Dic3C2×AGL(1,ℤ/8)14yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—32no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—62no—
725C23—62no—
726C23—62no—
727C23—62no—
728C23—122no—
729C23—122no—
730C23—122no—
731C23C2×D3×D412yes—
732C23C2×D3×D411yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8—128no—
736Q8C2×#23714yescomplemented
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—42no—
744D4—42no—
745D4—68no—
746D4—62no—
747D4—62no—
748D4—128no—
749D4—128no—
750D4—128no—
751D4—122no—
752D4—244no—
753D4—244no—
754D4—244no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—32no—
763C2×C4—34no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—48no—
767C2×C4—42no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—64no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—128no—
777C2×C4—128no—
778C2×C4—128no—
779C2×C4—128no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4C2×D3×D412yes—
784C2×C4C2×D3×D411yescharacteristic
785C2×C4C2×#23712yes—
786C2×C4#100412yes—
787C2×C4C24×D311yescharacteristic
788C8—22no—
789C8—22no—
790C8—62no—
791C8—62no—
792C2×C3—42no—
793C2×C3—82no—
794C2×C3—82no—
795C2×C3#333214yescomplemented
796C2×C3C2×#54611yescharacteristic
797C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
798C2×C3C2×#57711yescharacteristic
799D3—42no—
800D3—82no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—62no—
812C22—62no—
813C22—62no—
814C22—84no—
815C22—84no—
816C22—124no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—244no—
821C22#559112yes—
822C22#577012yes—
823C22D3×AGL(1,ℤ/8)12yes—
824C22C22×D3×D411yescharacteristic
825C4—22no—
826C4—24no—
827C4—34no—
828C4—42no—
829C4—62no—
830C4—62no—
831C4—122no—
832C4—122no—
833C4—122no—
834C4#559112yes—
835C4C22×#23711yescharacteristic
836C4C2×#100411yescharacteristic
837C3C2×#333211yescharacteristic, complemented, Sylow
838C2—42no—
839C2—82no—
840C2—82no—
841C2—122no—
842C2—242no—
843C2#8011714yesdirect product factor
844C2C2×#559111yescharacteristic
845C2C2×#577011yescharacteristic
846C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3C2×#3332
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5834C2semidirect
2. C2×#5611C2semidirect
3. C2×C3×#449C2semidirect
4. C2×#5232C2semidirect
5. C2×#5172C2semidirect
6. C2×Dic3×SD16C2semidirect
7. C2×#5159C2semidirect
8. C2×#5150C2semidirect
9. C2×#5039C2semidirect
10. #80117C2direct (N × H)
11. C2×#4803C2semidirect
12. C2×#4791C2semidirect
13. C2×#4777C2semidirect
14. C2×#4760C2semidirect
15. C2×#4729C2semidirect
16. C2×#4735C2semidirect
25. #5834C22semidirect
43. #5611C22semidirect
48. C3×#449C22semidirect
52. #5232C22semidirect
58. #5172C22semidirect
59. Dic3×SD16C22semidirect
60. #5159C22semidirect
61. #5150C22semidirect
69. #5039C22semidirect
72. #4803C22semidirect
73. #4791C22semidirect
74. #4777C22semidirect
75. #4760C22semidirect
76. #4735C22semidirect
77. #4729C22semidirect
89. C2×#449D3semidirect
241. #449C2×D3semidirect
273. C2×C3×Q8#41semidirect
507. C3×Q8C2×#41semidirect
580. C2×Q8#237semidirect
736. Q8C2×#237semidirect
795. C2×C3#3332semidirect
837. C3C2×#3332semidirect
843. C2#80117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58342
C2×#56112
C2×C3×#4492
C2×#52322
C2×#51722
C2×Dic3×SD162
C2×#51592
C2×#51502
C2×#50392
#801172
C2×#48032
C2×#47912
C2×#47772
C2×#47602
C2×#47292
C2×#47352
C2×#33323