Finite Group Databasebeta

← C2×#81638 #11664422

Subgroups — C2×#81638 #11664422

Order 768.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5689C211yesmaximal, characteristic, complemented
2C2×#5674C211yesmaximal, characteristic
3C2×C3×#488C211yesmaximal, characteristic, complemented
4C2×#5067C211yesmaximal, characteristic, complemented
5C2×#5055C211yesmaximal, characteristic, complemented
6#81638C2116yesmaximal, direct product factor
7C2×#4803C211yesmaximal, characteristic, complemented
8C2×#4804C211yesmaximal, characteristic, complemented
9C2×#4794C211yesmaximal, characteristic, complemented
10C2×#4800C211yesmaximal, characteristic, complemented
11C2×#4770C211yesmaximal, characteristic, complemented
12C2×D3×#102C211yesmaximal, characteristic, complemented
13C2×#4764C211yesmaximal, characteristic, complemented
14C2×#4760C211yesmaximal, characteristic, complemented
15C2×#4694C211yesmaximal, characteristic, complemented
16C2×#4689C211yesmaximal, characteristic, complemented
17C2×#3136—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×D3×D4C2211yescharacteristic
20C2×C3×#125C2211yescharacteristic, complemented
21C2×C3×#124C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26#5689—24no—
27#5689C2218yescomplemented
28#5674—24no—
29#5674C2218yes—
30C2×#897—21no—
31C2×#896—21no—
32C2×#892C2211yescharacteristic
33C2×D3×C4⋊C4C2211yescharacteristic
34C2×#890C2211yescharacteristic, complemented
35C2×#889—21no—
36C2×#888—21no—
37C2×#888C2211yescharacteristic, complemented
38C2×#884—21no—
39C2×#884—21no—
40C2×#882—21no—
41C2×#882—21no—
42C2×#874C2211yescharacteristic
43C2×#872C2211yescharacteristic
44C2×#869C2211yescharacteristic, complemented
45C3×#488C2218yescomplemented
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×C4×C8C2211yescharacteristic, complemented
51C2×#835C2211yescharacteristic, complemented
52C2×#835C2211yescharacteristic, complemented
53C2×#832C2211yescharacteristic
54C2×#832C2211yescharacteristic
55C2×#821C2211yescharacteristic
56C2×#821C2211yescharacteristic
57C2×#821C2211yescharacteristic, complemented
58C2×#821C2211yescharacteristic, complemented
59C2×#815C2211yescharacteristic, complemented
60C2×C8×Dic3C2211yescharacteristic, complemented
61#5067C2218yescomplemented
62#5055C2218yescomplemented
63C2×#809C2211yescharacteristic
64C2×#809C2211yescharacteristic
65C2×#809C2211yescharacteristic, complemented
66C2×#809C2211yescharacteristic, complemented
67C2×#803C2211yescharacteristic, complemented
68#4804C2218yescomplemented
69#4803C2218yescomplemented
70#4800C2218yescomplemented
71#4794C2218yescomplemented
72#4770C2218yescomplemented
73D3×#102C2218yescomplemented
74#4764C2218yescomplemented
75#4760C2218yescomplemented
76#4694C2218yescomplemented
77#4689C2218yescomplemented
78C2×#544—31no—
79C2×#535—31no—
80#3136—316no—
81C2×#490—31no—
82C2×#490—31no—
83C2×#489—31no—
84C2×#489—31no—
85C2×#488—31no—
86C2×#488D311yescharacteristic, complemented
87C2×#486—31no—
88C2×#486—31no—
89C2×#417—31no—
90C2×#418—31no—
91C2×#416—31no—
92C22×#102—31no—
93C2×#405—31no—
94C24×D3—21no—
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4C2311yescharacteristic
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C2×#239—22no—
101C2×#239—24no—
102C2×#239—24no—
103C2×#239C2314yes—
104C2×D3×D4—22no—
105C2×D3×D4—24no—
106C2×D3×D4—24no—
107C2×D3×D4C2314yes—
108C22×D12—21no—
109C22×D12—21no—
110C22×D12—21no—
111C22×D12C2311yescharacteristic
112C22×D12C2311yescharacteristic
113C22×C4×D3—21no—
114C22×C4×D3—21no—
115C22×C4×D3C2311yescharacteristic
116C22×Dic6—21no—
117C22×Dic6—21no—
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C3×#125—22no—
121C3×#125C2314yescomplemented
122C3×#124—22no—
123C3×#124C2314yes—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C42C2311yescharacteristic
131#947—22no—
132#947C2314yes—
133#940—22no—
134#940C2314yes—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4D411yescharacteristic
139C2×(C2×D3)⋊C4D411yescharacteristic
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4D411yescharacteristic
148C2×Dic3⋊C4D411yescharacteristic
149C2×C4×Dic3—21no—
150C2×C4×Dic3C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C2×ΓL(1,𝔽25)—24no—
154C2×ΓL(1,𝔽25)C2314yes—
155C2×D3×C8—24no—
156C2×D3×C8C2314yes—
157#897—28no—
158#896—28no—
159#892—22no—
160#892C2314yes—
161D3×C4⋊C4—22no—
162D3×C4⋊C4C2314yes—
163#890—22no—
164#890C2314yescomplemented
165#889—28no—
166#888—28no—
167#888—22no—
168#888C2314yescomplemented
169#884—28no—
170#884—28no—
171#882—28no—
172#882—28no—
173#874—22no—
174#874C2314yes—
175#872D414yes—
176#872C2314yes—
177#869—22no—
178#869C2314yescomplemented
179C3×#103C2314yescomplemented
180C3×#103C2314yescomplemented
181C3×#102C2314yes—
182C3×#102C2314yes—
183C3×C4×C8C2314yescomplemented
184#835C2314yescomplemented
185#835C2314yescomplemented
186#832C2314yes—
187#832C2314yes—
188#821C2314yes—
189#821C2314yes—
190#821C2314yescomplemented
191#821C2314yescomplemented
192#815C2314yescomplemented
193C8×Dic3C2314yescomplemented
194#809C2314yes—
195#809C2314yes—
196#809C2314yescomplemented
197#809C2314yescomplemented
198#803C2314yescomplemented
199C22×#41—31no—
200C23×D4—31no—
201C22×M16—31no—
202C23×C8—31no—
203#544—38no—
204#544—64no—
205#535—38no—
206#535—64no—
207C2×C4⋊Q8—31no—
208C2×C4⋊Q8—31no—
209C2×C4⋊Q8—61no—
210C2×#127—31no—
211C2×#127—31no—
212C2×#125—31no—
213C2×#125—61no—
214C2×#125C2×D311yescharacteristic, complemented
215C2×#124—31no—
216C2×#124C2×D311yescharacteristic
217C2×C22⋊Q8—61no—
218C2×C22⋊Q8—61no—
219C2×#121—61no—
220C2×#121—61no—
221C2×#120—61no—
222C2×#120—61no—
223C2×#117—31no—
224C2×#117—31no—
225C22×C4⋊C4—31no—
226#490—38no—
227#490—38no—
228#489—38no—
229#489—38no—
230#488—38no—
231#488C2×D318yescomplemented
232#486—38no—
233#486—38no—
234#418—38no—
235#417—38no—
236#416—38no—
237C2×#103—31no—
238C2×#103—31no—
239C2×#103C2×D311yescharacteristic, complemented
240C2×#103C2×D311yescharacteristic, complemented
241C2×#102—31no—
242C2×#102—31no—
243C2×#102—31no—
244C2×#102—31no—
245C2×#102—31no—
246C2×#102—31no—
247C2×#102—31no—
248C2×#102—31no—
249C2×#102—31no—
250C2×#102—31no—
251C2×#102—38no—
252C2×#102C2×D311yescharacteristic
253C2×#102C2×D311yescharacteristic
254#405—38no—
255C2×#97—31no—
256C2×#97—31no—
257C2×C4×C8—31no—
258C2×C4×C8C2×D311yescharacteristic, complemented
259C24×C3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—24no—
263C23×D3—44no—
264C23×D3—82no—
265C23×D3—82no—
266C23×D3C2×D411yescharacteristic
267C2×C3×Q8—21no—
268C2×C3×Q8—22no—
269C2×C3×Q8—22no—
270C2×C3×Q8C2412yes—
271C2×C3×D4—21no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C2×C3×D4C2412yes—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—24no—
284C2×#67—44no—
285C2×#67—82no—
286C2×#67—82no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3C2×D411yescharacteristic
290C22×Dic3C2×D411yescharacteristic
291C22×Dic3C2×D411yescharacteristic
292#239—28no—
293#239—28no—
294#239—48no—
295D3×D4—28no—
296D3×D4—28no—
297D3×D4—48no—
298C2×D12—22no—
299C2×D12—22no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—24no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—24no—
306C2×D12—24no—
307C2×D12—44no—
308C2×D12—82no—
309C2×D12—82no—
310C2×D12C2412yes—
311C2×D12C2412yes—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3—44no—
315C2×C4×D3—82no—
316C2×C4×D3C2×D412yes—
317C2×C4×D3#4114yes—
318C2×C4×D3#4114yes—
319C2×C4×D3C2412yes—
320C2×Dic6—24no—
321C2×Dic6—24no—
322C2×Dic6—82no—
323C2×Dic6—82no—
324C2×C3×C8—22no—
325C2×C3×C8—22no—
326C2×C3×C8C2412yes—
327C2×C3×C8C2412yes—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—24no—
330C3×C4⋊C4—24no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4C2412yes—
333C3×C4⋊C4C2412yes—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—24no—
336C3×C42C2×D412yes—
337C3×C42C2412yes—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4C2×D414yes—
342(C2×D3)⋊C4C2×D414yes—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—24no—
346C4⋊Dic3—24no—
347C4⋊Dic3C2412yes—
348C4⋊Dic3C2412yes—
349Dic3⋊C4—24no—
350Dic3⋊C4—24no—
351Dic3⋊C4—24no—
352Dic3⋊C4C2×D414yes—
353Dic3⋊C4C2×D414yes—
354C4×Dic3—24no—
355C4×Dic3C2×D412yes—
356C4×Dic3C2412yes—
357C2×C3⋊C8—22no—
358C2×C3⋊C8—22no—
359C2×C3⋊C8C2412yes—
360C2×C3⋊C8C2412yes—
361ΓL(1,𝔽25)—28no—
362D3×C8—28no—
363C25—61no—
364C2×#41—34no—
365C2×#41—62no—
366C2×#41—64no—
367C2×#41—64no—
368C22×Q8—61no—
369C22×Q8—61no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—34no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—61no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4—61no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4C22×D311yescharacteristic
384C23×C4—31no—
385C23×C4—61no—
386C23×C4—61no—
387C2×M16—34no—
388C2×M16—64no—
389C22×C8—31no—
390C22×C8—31no—
391C22×C8—34no—
392C22×C8—64no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395C4⋊Q8—34no—
396C4⋊Q8—34no—
397C4⋊Q8—62no—
398C4⋊Q8—68no—
399C4⋊Q8—62no—
400#127—34no—
401#127—34no—
402#127—62no—
403#127—62no—
404#125—22no—
405#125—34no—
406#125—62no—
407#125—68no—
408#125C22×D314yescomplemented
409#124—22no—
410#124—34no—
411#124—62no—
412#124C22×D314yes—
413C22⋊Q8—68no—
414C22⋊Q8—68no—
415#121—68no—
416#121—68no—
417#120—68no—
418#120—68no—
419#117—34no—
420#117—34no—
421#117—34no—
422#117—62no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—61no—
432C2×C4⋊C4—61no—
433C2×C4⋊C4—61no—
434C2×C4⋊C4—61no—
435C2×C4⋊C4—61no—
436C2×C4⋊C4C22×D311yescharacteristic
437C2×C4⋊C4C22×D311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—61no—
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445C2×C42—31no—
446C2×C42—61no—
447C2×C42C22×D311yescharacteristic
448#103—34no—
449#103—34no—
450#103C22×D314yescomplemented
451#103C22×D314yescomplemented
452#102—34no—
453#102—34no—
454#102—34no—
455#102—34no—
456#102—34no—
457#102—34no—
458#102—34no—
459#102—34no—
460#102—34no—
461#102—34no—
462#102C22×D314yes—
463#102C22×D314yes—
464#97—34no—
465#97—34no—
466C4×C8—34no—
467C4×C8C22×D314yescomplemented
468C23×C3—22no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3—42no—
472C23×C3C22×D411yescharacteristic
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—48no—
484C22×D3—84no—
485C22×D3—84no—
486C22×D3—816no—
487C22×D3#12414yes—
488C22×D3C22×D412yes—
489C3×Q8—22no—
490C3×Q8—22no—
491C3×Q8—42no—
492C3×D4—22no—
493C3×D4—22no—
494C3×D4—42no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4C22×D412yes—
504C2×C3×C4C22×D412yes—
505C2×C3×C4C22×D411yescharacteristic
506C2×C3×C4C2×#4112yes—
507C2×C3×C4C2×#4112yes—
508C2×C3×C4C2511yescharacteristic
509#67—48no—
510#67—84no—
511#67—84no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—42no—
517C2×Dic3—42no—
518C2×Dic3#12414yes—
519C2×Dic3C22×D412yes—
520C2×Dic3C22×D412yes—
521C2×Dic3C22×D412yes—
522D12—22no—
523D12—22no—
524D12—22no—
525D12—22no—
526D12—48no—
527D12—42no—
528D12—42no—
529D12—84no—
530D12—84no—
531C4×D3—48no—
532C4×D3—84no—
533C4×D3#12418yes—
534C4×D3C2×#4114yes—
535C4×D3C2×#4114yes—
536Dic6—84no—
537Dic6—84no—
538C3×C8—22no—
539C3×C8—22no—
540C3⋊C8—22no—
541C3⋊C8—22no—
542C24—21no—
543C24—31no—
544C24—64no—
545C24—61no—
546C24—61no—
547C24—124no—
548C24—242no—
549C24—242no—
550#41—68no—
551#41—68no—
552#41—128no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—64no—
557C2×Q8—64no—
558C2×Q8—242no—
559C2×Q8—242no—
560C2×Q8C23×D312yes—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—32no—
565C2×D4—32no—
566C2×D4—64no—
567C2×D4—68no—
568C2×D4—68no—
569C2×D4—64no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—128no—
581C2×D4—124no—
582C2×D4—124no—
583C2×D4—242no—
584C2×D4—242no—
585C2×D4—242no—
586C2×D4—242no—
587C2×D4C23×D312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—32no—
593C22×C4—34no—
594C22×C4—34no—
595C22×C4—32no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—124no—
603C22×C4—242no—
604C22×C4D3×D411yescharacteristic
605C22×C4D3×D411yescharacteristic
606C22×C4C23×D311yescharacteristic
607M16—68no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—32no—
611C2×C8—32no—
612C2×C8—68no—
613C2×C8—62no—
614C2×C8—62no—
615C2×C8C23×D312yes—
616C2×C8C23×D312yes—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—34no—
622C4⋊C4—34no—
623C4⋊C4—32no—
624C4⋊C4—32no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—64no—
628C4⋊C4—64no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—64no—
632C4⋊C4C23×D312yes—
633C4⋊C4C23×D312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—34no—
637C22⋊C4—34no—
638C22⋊C4—64no—
639C22⋊C4—64no—
640C22⋊C4—64no—
641C42—32no—
642C42—32no—
643C42—64no—
644C42D3×D412yes—
645C42C23×D312yes—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—84no—
650C22×C3C2×#12412yes—
651C22×C3#57612yes—
652C22×C3#57712yes—
653C22×C3C23×D411yescharacteristic
654C2×D3—28no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—816no—
664C2×D3—84no—
665C2×D3—84no—
666C2×D3C2×#12414yes—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4C2×#12412yes—
673C3×C4C22×#4111yescharacteristic
674C3×C4C22×#4111yescharacteristic
675Dic3—22no—
676Dic3—22no—
677Dic3—42no—
678Dic3—42no—
679Dic3C2×#12414yes—
680C23—22no—
681C23—34no—
682C23—32no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—128no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—244no—
698C23—244no—
699C23—2416no—
700C23C2×D3×D411yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—244no—
705Q8—244no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—62no—
710D4—62no—
711D4—62no—
712D4—62no—
713D4—128no—
714D4—128no—
715D4—122no—
716D4—122no—
717D4—244no—
718D4—244no—
719D4—244no—
720D4—244no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—34no—
727C2×C4—32no—
728C2×C4—38no—
729C2×C4—34no—
730C2×C4—34no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—128no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—244no—
744C2×C4C2×D3×D412yes—
745C2×C4C2×D3×D412yes—
746C2×C4C2×D3×D411yescharacteristic
747C2×C4D3×#4112yes—
748C2×C4D3×#4112yes—
749C2×C4C24×D311yescharacteristic
750C8—22no—
751C8—22no—
752C8—62no—
753C8—62no—
754C2×C3—82no—
755C2×C3#313614yescomplemented
756C2×C3C22×#12411yescharacteristic
757C2×C3C2×#57611yescharacteristic
758C2×C3C2×#57711yescharacteristic
759D3—24no—
760D3—82no—
761D3—82no—
762C22—34no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—62no—
767C22—62no—
768C22—68no—
769C22—84no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—2416no—
777C22—244no—
778C22—244no—
779C22D3×#12412yes—
780C22#576912yes—
781C22#577012yes—
782C22C22×D3×D411yescharacteristic
783C4—22no—
784C4—22no—
785C4—34no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—62no—
790C4—62no—
791C4—122no—
792C4—122no—
793C4D3×#12412yes—
794C4C2×D3×#4111yescharacteristic
795C4C2×D3×#4111yescharacteristic
796C3C2×#313611yescharacteristic, complemented, Sylow
797C2—64no—
798C2—82no—
799C2—242no—
800C2—242no—
801C2#8163814yesdirect product factor
802C2C2×D3×#12411yescharacteristic
803C2C2×#576911yescharacteristic
804C2C2×#577011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#488C2
socleC23×C3C22×D4
prime radicalC2×#5674C2
hypercenterC2×#488D3
hypocenterC3C2×#3136
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#5689C2semidirect
3. C2×C3×#488C2semidirect
4. C2×#5067C2semidirect
5. C2×#5055C2semidirect
6. #81638C2direct (N × H)
7. C2×#4803C2semidirect
8. C2×#4804C2semidirect
9. C2×#4794C2semidirect
10. C2×#4800C2semidirect
11. C2×#4770C2semidirect
12. C2×D3×#102C2semidirect
13. C2×#4764C2semidirect
14. C2×#4760C2semidirect
15. C2×#4694C2semidirect
16. C2×#4689C2semidirect
20. C2×C3×#125C22semidirect
27. #5689C22semidirect
34. C2×#890C22semidirect
37. C2×#888C22semidirect
44. C2×#869C22semidirect
45. C3×#488C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#103C22semidirect
50. C2×C3×C4×C8C22semidirect
51. C2×#835C22semidirect
52. C2×#835C22semidirect
57. C2×#821C22semidirect
58. C2×#821C22semidirect
59. C2×#815C22semidirect
60. C2×C8×Dic3C22semidirect
61. #5067C22semidirect
62. #5055C22semidirect
65. C2×#809C22semidirect
66. C2×#809C22semidirect
67. C2×#803C22semidirect
68. #4804C22semidirect
69. #4803C22semidirect
70. #4800C22semidirect
71. #4794C22semidirect
72. #4770C22semidirect
73. D3×#102C22semidirect
74. #4764C22semidirect
75. #4760C22semidirect
76. #4694C22semidirect
77. #4689C22semidirect
86. C2×#488D3semidirect
121. C3×#125C23semidirect
164. #890C23semidirect
168. #888C23semidirect
178. #869C23semidirect
179. C3×#103C23semidirect
180. C3×#103C23semidirect
183. C3×C4×C8C23semidirect
184. #835C23semidirect
185. #835C23semidirect
190. #821C23semidirect
191. #821C23semidirect
192. #815C23semidirect
193. C8×Dic3C23semidirect
196. #809C23semidirect
197. #809C23semidirect
198. #803C23semidirect
214. C2×#125C2×D3semidirect
231. #488C2×D3semidirect
239. C2×#103C2×D3semidirect
240. C2×#103C2×D3semidirect
258. C2×C4×C8C2×D3semidirect
408. #125C22×D3semidirect
450. #103C22×D3semidirect
451. #103C22×D3semidirect
467. C4×C8C22×D3semidirect
755. C2×C3#3136semidirect
796. C3C2×#3136semidirect
801. C2#81638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56892
C2×#56742
C2×C3×#4882
C2×#50672
C2×#50552
#816382
C2×#48032
C2×#48042
C2×#47942
C2×#48002
C2×#47702
C2×D3×#1022
C2×#47642
C2×#47602
C2×#46942
C2×#46892
C2×#31363