Finite Group Databasebeta

← C2×#79554 #11672002

Subgroups — C2×#79554 #11672002

Order 768.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5550C211yesmaximal, characteristic
2C2×#5541C211yesmaximal, characteristic, complemented
3C2×C3×#436C211yesmaximal, characteristic, complemented
4C2×#5137C211yesmaximal, characteristic, complemented
5C2×#5134C211yesmaximal, characteristic, complemented
6C2×#5133C211yesmaximal, characteristic, complemented
7C2×#5131C211yesmaximal, characteristic, complemented
8#79554C2116yesmaximal, direct product factor
9C2×#4845C211yesmaximal, characteristic, complemented
10C2×#4847C211yesmaximal, characteristic, complemented
11C2×#4733C211yesmaximal, characteristic, complemented
12C2×#4731C211yesmaximal, characteristic, complemented
13C2×#4735C211yesmaximal, characteristic, complemented
14C2×#4723C211yesmaximal, characteristic, complemented
15C2×C4×#204C211yesmaximal, characteristic, complemented
16C2×#4697C211yesmaximal, characteristic, complemented
17C2×#3323—31nomaximal, Sylow
18C22×#235C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic, complemented
22C2×C3×C4×D4C2211yescharacteristic
23C2×#937—21no—
24C2×#935—21no—
25C2×#930C2211yescharacteristic
26C2×#926C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic, complemented
28C2×#924C2211yescharacteristic
29C2×#924C2211yescharacteristic
30C2×#924C2211yescharacteristic, complemented
31C22×Dic12C2211yescharacteristic, complemented
32C22×#204C2211yescharacteristic
33C22×#204C2211yescharacteristic
34#5550—24no—
35#5550C2218yes—
36#5541—24no—
37#5541C2218yescomplemented
38C2×#894—21no—
39C2×#889—21no—
40C2×#884—21no—
41C2×D3×C22⋊C4—21no—
42C2×#879—21no—
43C2×#877—21no—
44C2×#875C2211yescharacteristic
45C2×C4×D12C2211yescharacteristic
46C2×#870C2211yescharacteristic, complemented
47C2×C4×Dic6C2211yescharacteristic, complemented
48C3×#436C2218yescomplemented
49C2×C3×C4⋊C8C2211yescharacteristic, complemented
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×C22⋊C8C2211yescharacteristic, complemented
52C2×C3×C4×C8C2211yescharacteristic, complemented
53#5137C2218yescomplemented
54#5134C2218yescomplemented
55#5133C2218yescomplemented
56#5131C2218yescomplemented
57C2×#821C2211yescharacteristic
58C2×#821C2211yescharacteristic
59C2×#821C2211yescharacteristic
60C2×#821C2211yescharacteristic
61C2×#821C2211yescharacteristic
62C2×#821C2211yescharacteristic
63C2×#818C2211yescharacteristic, complemented
64C2×#817C2211yescharacteristic, complemented
65C2×#817C2211yescharacteristic, complemented
66C2×#816C2211yescharacteristic, complemented
67C2×#816C2211yescharacteristic, complemented
68C2×#816C2211yescharacteristic, complemented
69C2×#816C2211yescharacteristic, complemented
70#4847C2218yescomplemented
71#4845C2218yescomplemented
72#4735C2218yescomplemented
73#4733C2218yescomplemented
74#4731C2218yescomplemented
75#4723C2218yescomplemented
76#4697C2218yescomplemented
77C4×#204C2218yescomplemented
78C2×#552—31no—
79C2×#546—31no—
80#3323—316no—
81C2×#488—31no—
82C2×#481—31no—
83C2×#485—31no—
84C2×#478—31no—
85C2×#470—31no—
86C2×#468—31no—
87C2×#464—31no—
88C2×#452—31no—
89C2×#450—31no—
90C2×C4×SD16—31no—
91C2×#436D311yescharacteristic, complemented
92C2×#417—31no—
93C2×#418—31no—
94C24×D3—21no—
95C22×C3×D4D411yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C22×#67—21no—
100C23×Dic3—21no—
101C2×#235—22no—
102C2×#235—24no—
103C2×#235—42no—
104C2×#235C2314yes—
105C22×D12—24no—
106C22×D12—21no—
107C22×D12—22no—
108C22×D12—42no—
109C22×D12C2311yescharacteristic
110C22×D12C2314yes—
111C22×D12C2311yescharacteristic
112C22×C4×D3—21no—
113C22×C4×D3—21no—
114C22×Dic6C2311yescharacteristic
115C22×Dic6C2311yescharacteristic
116C2×C3×M16—42no—
117C2×C3×M16—42no—
118C2×C3×M16C2314yes—
119C2×C3×M16C2314yescomplemented
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C3×C4×D4D414yes—
125C3×C4×D4C2314yes—
126C2×C3×C4⋊C4D411yescharacteristic
127C2×C3×C22⋊C4D411yescharacteristic
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×#217—21no—
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134#937—28no—
135#935—28no—
136#930—22no—
137#930C2314yes—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142#926—22no—
143#926C2314yes—
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2314yescomplemented
151#924—22no—
152#924—22no—
153#924—22no—
154#924C2314yes—
155#924C2314yes—
156#924C2314yescomplemented
157C2×Dic3⋊C4—21no—
158C2×Dic3⋊C4—21no—
159C2×Dic3⋊C4—21no—
160C2×Dic3⋊C4—21no—
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—21no—
163C2×C4×Dic3—21no—
164C2×C4×Dic3—21no—
165C2×Dic12—42no—
166C2×Dic12C2314yescomplemented
167C2×#204—24no—
168C2×#204—42no—
169C2×#204C2314yes—
170C2×#204C2314yes—
171#894—28no—
172#889—28no—
173#884—28no—
174D3×C22⋊C4—28no—
175#879—28no—
176#877—28no—
177#875—22no—
178#875C2314yes—
179C4×D12—22no—
180C4×D12C2314yes—
181#870—22no—
182#870C2314yescomplemented
183C4×Dic6—22no—
184C4×Dic6C2314yescomplemented
185C3×C4⋊C8C2314yescomplemented
186C3×C22⋊C8C2314yes—
187C3×C22⋊C8C2314yescomplemented
188C3×C4×C8C2314yescomplemented
189#821C2314yes—
190#821C2314yes—
191#821C2314yes—
192#821C2314yes—
193#821C2314yes—
194#821C2314yes—
195#818C2314yescomplemented
196#817C2314yescomplemented
197#817C2314yescomplemented
198#816C2314yescomplemented
199#816C2314yescomplemented
200#816C2314yescomplemented
201#816C2314yescomplemented
202C22×#41—31no—
203C23×D4—31no—
204C22×Q16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×M16C2×D311yescharacteristic
208C22×M16C2×D311yescharacteristic, complemented
209#552—38no—
210#552—64no—
211#546—38no—
212#546—64no—
213C2×#126—61no—
214C2×#125—31no—
215C2×#125—61no—
216C2×#124—31no—
217C2×#123—61no—
218C2×#123—61no—
219C2×C22⋊Q8—31no—
220C2×C22⋊Q8—31no—
221C2×C22⋊Q8—31no—
222C2×#121—31no—
223C2×#121—61no—
224C2×#120—61no—
225C2×C4×Q8—31no—
226C2×C4×D4—31no—
227C2×C4×D4C2×D311yescharacteristic
228C2×#117—31no—
229C2×#117—61no—
230C22×C4⋊C4—31no—
231C22×C22⋊C4—61no—
232#488—38no—
233#485—38no—
234#481—38no—
235#478—38no—
236#470—38no—
237#468—38no—
238#464—38no—
239#452—38no—
240#450—38no—
241C4×SD16—38no—
242#436C2×D318yescomplemented
243C2×#107—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×C4⋊C8C2×D311yescharacteristic, complemented
247#418—38no—
248#417—38no—
249C2×#103—31no—
250C2×#103—31no—
251C2×#103—31no—
252C2×#103—31no—
253C2×#102—31no—
254C2×#102—31no—
255C2×#102—31no—
256C2×#102—31no—
257C2×#102—31no—
258C2×#102—31no—
259C2×C22⋊C8C2×D311yescharacteristic
260C2×C22⋊C8C2×D311yescharacteristic, complemented
261C2×C4×C8C2×D311yescharacteristic, complemented
262C24×C3C2×D411yescharacteristic
263C24×C3C2×D411yescharacteristic
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—24no—
267C23×D3—44no—
268C23×D3—44no—
269C23×D3—82no—
270C2×C3×D4—42no—
271C2×C3×D4C2×D414yes—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2411yescharacteristic
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—44no—
288C2×#67—82no—
289C22×Dic3—24no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—44no—
297#235—28no—
298#235—44no—
299#235—48no—
300C2×D12—21no—
301C2×D12—22no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—28no—
305C2×D12—21no—
306C2×D12—24no—
307C2×D12—44no—
308C2×D12—48no—
309C2×D12—44no—
310C2×D12#4114yes—
311C2×D12C2412yes—
312C2×D12C2412yes—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—44no—
316C2×C4×D3—82no—
317C2×Dic6—22no—
318C2×Dic6—22no—
319C2×Dic6—22no—
320C2×Dic6—22no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6C2412yes—
324C2×Dic6C2412yes—
325C3×M16—44no—
326C3×M16—44no—
327C2×C3×C8—22no—
328C2×C3×C8—22no—
329C2×C3×C8—22no—
330C2×C3×C8—22no—
331C2×C3×C8C2412yes—
332C2×C3×C8C2412yes—
333C2×C3×C8C2412yes—
334C2×C3×C8C2412yes—
335C3×C4⋊C4C2×D414yes—
336C3×C22⋊C4C2×D414yes—
337C3×C22⋊C4C2×D414yes—
338C3×C42C2×D412yes—
339C3×C42C2412yes—
340#217—24no—
341#217—24no—
342#217—24no—
343#217—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—24no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352C4⋊Dic3—24no—
353C4⋊Dic3C2412yes—
354C4⋊Dic3C2412yes—
355C4⋊Dic3C2412yes—
356C4⋊Dic3C2412yes—
357Dic3⋊C4—24no—
358Dic3⋊C4—24no—
359Dic3⋊C4—24no—
360Dic3⋊C4—24no—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363C4×Dic3—24no—
364C4×Dic3—24no—
365Dic12—44no—
366#204—28no—
367#204—44no—
368C25—61no—
369C2×#41—34no—
370C2×#41—64no—
371C2×#41—62no—
372C2×#41—122no—
373C22×Q8—31no—
374C22×Q8—31no—
375C22×D4—31no—
376C22×D4—31no—
377C22×D4—34no—
378C22×D4—64no—
379C22×D4—61no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—62no—
383C22×D4—122no—
384C22×D4D1211yescharacteristic
385C23×C4—61no—
386C23×C4—61no—
387C23×C4—61no—
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C2×Q16—34no—
391C2×Q16—122no—
392C2×SD16—34no—
393C2×SD16—34no—
394C2×SD16—64no—
395C2×SD16—122no—
396C2×M16—42no—
397C2×M16—42no—
398C2×M16C22×D314yes—
399C2×M16C22×D314yescomplemented
400C22×C8C22×D311yescharacteristic
401C22×C8C22×D311yescharacteristic
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#126—68no—
405#125—34no—
406#125—68no—
407#125—62no—
408#124—34no—
409#124—62no—
410#123—68no—
411#123—68no—
412C22⋊Q8—34no—
413C22⋊Q8—34no—
414C22⋊Q8—34no—
415C22⋊Q8—62no—
416C22⋊Q8—62no—
417C22⋊Q8—62no—
418#121—34no—
419#121—62no—
420#121—68no—
421#120—68no—
422C4×Q8—34no—
423C4×Q8—62no—
424C4×D4—34no—
425C4×D4—62no—
426C4×D4D1214yes—
427C4×D4C22×D314yes—
428#117—34no—
429#117—62no—
430#117—68no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—61no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—61no—
439C2×C4⋊C4—61no—
440C2×C4⋊C4—61no—
441C2×C4⋊C4—61no—
442C2×C4⋊C4—61no—
443C2×C4⋊C4—61no—
444C2×C4⋊C4D1211yescharacteristic
445C2×C22⋊C4—61no—
446C2×C22⋊C4—61no—
447C2×C22⋊C4—61no—
448C2×C22⋊C4—61no—
449C2×C22⋊C4—61no—
450C2×C22⋊C4—61no—
451C2×C22⋊C4—61no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—68no—
454C2×C22⋊C4D1211yescharacteristic
455C2×C22⋊C4D1211yescharacteristic
456C2×C42—61no—
457C2×C42—61no—
458C2×C42C22×D311yescharacteristic
459#107—34no—
460#106—34no—
461#106—34no—
462C4⋊C8C22×D314yescomplemented
463#103—34no—
464#103—34no—
465#103—34no—
466#103—34no—
467#102—34no—
468#102—34no—
469#102—34no—
470#102—34no—
471#102—34no—
472#102—34no—
473C22⋊C8C22×D314yes—
474C22⋊C8C22×D314yescomplemented
475C4×C8C22×D314yescomplemented
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3C22×D412yes—
483C23×C3C22×D412yes—
484C23×C3C22×D411yescharacteristic
485C22×D3—24no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—48no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—48no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—84no—
496C22×D3—816no—
497C3×D4—44no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—24no—
503C2×C3×C4—24no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4C22×D412yes—
509C2×C3×C4C22×D412yes—
510C2×C3×C4C22×D412yes—
511C2×C3×C4C22×D412yes—
512C2×C3×C4C22×D411yescharacteristic
513C2×C3×C4C2×#4112yes—
514C2×C3×C4H(5,𝔽2)12yes—
515C2×C3×C4C2511yescharacteristic
516#67—48no—
517#67—84no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—48no—
525C2×Dic3—42no—
526C2×Dic3—42no—
527C2×Dic3—42no—
528C2×Dic3—42no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531D12—24no—
532D12—22no—
533D12—22no—
534D12—22no—
535D12—48no—
536D12—42no—
537D12C2×#4114yes—
538C4×D3—48no—
539C4×D3—84no—
540Dic6—22no—
541Dic6—22no—
542Dic6—22no—
543Dic6—22no—
544Dic6—42no—
545Dic6—42no—
546C3×C8—22no—
547C3×C8—22no—
548C3×C8—22no—
549C3×C8—22no—
550C24—61no—
551C24—61no—
552C24—64no—
553C24—124no—
554C24—124no—
555C24—242no—
556C24C2×D1211yescharacteristic
557C24C2×D1211yescharacteristic
558#41—68no—
559#41—124no—
560#41—128no—
561C2×Q8—32no—
562C2×Q8—32no—
563C2×Q8—61no—
564C2×Q8—61no—
565C2×Q8—62no—
566C2×Q8—62no—
567C2×Q8—62no—
568C2×Q8—62no—
569C2×D4—34no—
570C2×D4—32no—
571C2×D4—32no—
572C2×D4—42no—
573C2×D4—68no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—61no—
577C2×D4—64no—
578C2×D4—61no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4—62no—
582C2×D4—124no—
583C2×D4—128no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—242no—
587C2×D4C2×D1214yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—64no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—124no—
602C22×C4—124no—
603C22×C4—242no—
604C22×C4C2×D1212yes—
605C22×C4C2×D1212yes—
606C22×C4C2×D1211yescharacteristic
607C22×C4C2×D1211yescharacteristic
608C22×C4C2×D1211yescharacteristic
609C22×C4C2×D1211yescharacteristic
610C22×C4C23×D312yes—
611C22×C4C23×D312yes—
612C22×C4C23×D311yescharacteristic
613Q16—124no—
614SD16—68no—
615SD16—124no—
616M16—44no—
617M16—44no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8C23×D312yes—
623C2×C8C23×D312yes—
624C2×C8C23×D312yes—
625C2×C8C23×D312yes—
626C4⋊C4—32no—
627C4⋊C4—32no—
628C4⋊C4—32no—
629C4⋊C4—32no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—64no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—64no—
641C4⋊C4C2×D1214yes—
642C22⋊C4—64no—
643C22⋊C4—64no—
644C22⋊C4—64no—
645C22⋊C4—64no—
646C22⋊C4—64no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4C2×D1214yes—
651C22⋊C4C2×D1214yes—
652C42—64no—
653C42—64no—
654C42C2×D1212yes—
655C42C23×D312yes—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3#54612yes—
665C22×C3#57512yes—
666C22×C3#57712yes—
667C22×C3C23×D411yescharacteristic
668C2×D3—24no—
669C2×D3—48no—
670C2×D3—42no—
671C2×D3—42no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—816no—
676C2×D3—84no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4#54612yes—
682C3×C4C22×#4111yescharacteristic
683C3×C4C2×H(5,𝔽2)11yescharacteristic
684Dic3—42no—
685Dic3—42no—
686Dic3—42no—
687Dic3—42no—
688Dic3—42no—
689Dic3—42no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—62no—
697C23—64no—
698C23—62no—
699C23—128no—
700C23—128no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23—244no—
707C23—2416no—
708C23C22×D1212yes—
709C23C22×D1212yes—
710C23C22×D1211yescharacteristic
711Q8—62no—
712Q8—62no—
713Q8—62no—
714Q8—62no—
715Q8—122no—
716Q8—122no—
717D4—34no—
718D4—44no—
719D4—62no—
720D4—62no—
721D4—62no—
722D4—64no—
723D4—128no—
724D4—128no—
725D4—122no—
726D4—244no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—128no—
744C2×C4—128no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—244no—
752C2×C4C22×D1212yes—
753C2×C4C22×D1212yes—
754C2×C4C22×D1212yes—
755C2×C4C22×D1212yes—
756C2×C4C22×D1211yescharacteristic
757C2×C4#100412yes—
758C2×C4D3×#4112yes—
759C2×C4C24×D311yescharacteristic
760C8—22no—
761C8—22no—
762C8—22no—
763C8—22no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3#332314yescomplemented
767C2×C3C2×#54611yescharacteristic
768C2×C3C2×#57511yescharacteristic
769C2×C3C2×#57711yescharacteristic
770D3—44no—
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—44no—
779C22—44no—
780C22—64no—
781C22—122no—
782C22—122no—
783C22—128no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—2416no—
788C22—244no—
789C22#555412yes—
790C22#574812yes—
791C22#575112yes—
792C22C23×D1211yescharacteristic
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—122no—
798C4—122no—
799C4—122no—
800C4—122no—
801C4—122no—
802C4—122no—
803C4#555412yes—
804C4C2×#100411yescharacteristic
805C4C2×D3×#4111yescharacteristic
806C3C2×#332311yescharacteristic, complemented, Sylow
807C2—42no—
808C2—42no—
809C2—124no—
810C2—242no—
811C2#7955414yesdirect product factor
812C2C2×#555411yescharacteristic
813C2C2×#574811yescharacteristic
814C2C2×#575111yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#436C2
socleC23×C3C22×D4
prime radicalC2×#5550C2
hypercenterC2×#436D3
hypocenterC3C2×#3323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#5541C2semidirect
3. C2×C3×#436C2semidirect
4. C2×#5137C2semidirect
5. C2×#5134C2semidirect
6. C2×#5133C2semidirect
7. C2×#5131C2semidirect
8. #79554C2direct (N × H)
9. C2×#4845C2semidirect
10. C2×#4847C2semidirect
11. C2×#4733C2semidirect
12. C2×#4731C2semidirect
13. C2×#4735C2semidirect
14. C2×#4723C2semidirect
15. C2×C4×#204C2semidirect
16. C2×#4697C2semidirect
21. C22×C3×M16C22semidirect
27. C22×C4⋊Dic3C22semidirect
30. C2×#924C22semidirect
31. C22×Dic12C22semidirect
37. #5541C22semidirect
46. C2×#870C22semidirect
47. C2×C4×Dic6C22semidirect
48. C3×#436C22semidirect
49. C2×C3×C4⋊C8C22semidirect
51. C2×C3×C22⋊C8C22semidirect
52. C2×C3×C4×C8C22semidirect
53. #5137C22semidirect
54. #5134C22semidirect
55. #5133C22semidirect
56. #5131C22semidirect
63. C2×#818C22semidirect
64. C2×#817C22semidirect
65. C2×#817C22semidirect
66. C2×#816C22semidirect
67. C2×#816C22semidirect
68. C2×#816C22semidirect
69. C2×#816C22semidirect
70. #4847C22semidirect
71. #4845C22semidirect
72. #4735C22semidirect
73. #4733C22semidirect
74. #4731C22semidirect
75. #4723C22semidirect
76. #4697C22semidirect
77. C4×#204C22semidirect
91. C2×#436D3semidirect
119. C2×C3×M16C23semidirect
150. C2×C4⋊Dic3C23semidirect
156. #924C23semidirect
166. C2×Dic12C23semidirect
182. #870C23semidirect
184. C4×Dic6C23semidirect
185. C3×C4⋊C8C23semidirect
187. C3×C22⋊C8C23semidirect
188. C3×C4×C8C23semidirect
195. #818C23semidirect
196. #817C23semidirect
197. #817C23semidirect
198. #816C23semidirect
199. #816C23semidirect
200. #816C23semidirect
201. #816C23semidirect
208. C22×M16C2×D3semidirect
242. #436C2×D3semidirect
246. C2×C4⋊C8C2×D3semidirect
260. C2×C22⋊C8C2×D3semidirect
261. C2×C4×C8C2×D3semidirect
399. C2×M16C22×D3semidirect
462. C4⋊C8C22×D3semidirect
474. C22⋊C8C22×D3semidirect
475. C4×C8C22×D3semidirect
766. C2×C3#3323semidirect
806. C3C2×#3323semidirect
811. C2#79554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55502
C2×#55412
C2×C3×#4362
C2×#51372
C2×#51342
C2×#51332
C2×#51312
#795542
C2×#48452
C2×#48472
C2×#47332
C2×#47312
C2×#47352
C2×#47232
C2×C4×#2042
C2×#46972
C2×#33233