Finite Group Databasebeta

← C2×#83501 #11672000

Subgroups — C2×#83501 #11672000

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×C3×#546C211yesmaximal, characteristic
2C2×#5541C211yesmaximal, characteristic, complemented
3C2×#5239C211yesmaximal, characteristic, complemented
4C2×#5232C211yesmaximal, characteristic, complemented
5C2×#5218C211yesmaximal, characteristic, complemented
6C2×#5215C211yesmaximal, characteristic, complemented
7#83501C2116yesmaximal, direct product factor
8C2×#5054C211yesmaximal, characteristic, complemented
9C2×#5056C211yesmaximal, characteristic, complemented
10C2×#5052C211yesmaximal, characteristic, complemented
11C2×#5045C211yesmaximal, characteristic, complemented
12C2×#5042C211yesmaximal, characteristic, complemented
13C2×#5034C211yesmaximal, characteristic, complemented
14C2×C4×#214C211yesmaximal, characteristic, complemented
15C2×#5012C211yesmaximal, characteristic, complemented
16C2×#5009C211yesmaximal, characteristic, complemented
17C2×#3323—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C3×#546—24no—
21C3×#546C2218yes—
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121—21no—
26C2×C3×#121C2211yescharacteristic
27C2×C3×#120—21no—
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C22×C3×C22⋊C4—21no—
31C22×#216C2211yescharacteristic, complemented
32C2×#935—21no—
33C22×#214C2211yescharacteristic
34C22×#214C2211yescharacteristic
35C2×#926C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic, complemented
37C2×#924C2211yescharacteristic
38C2×#924C2211yescharacteristic, complemented
39C22×#208C2211yescharacteristic
40C22×#208C2211yescharacteristic, complemented
41#5541—24no—
42#5541C2218yescomplemented
43C2×#889—21no—
44C2×#879—21no—
45C2×#877—21no—
46C2×#870C2211yescharacteristic, complemented
47C2×C4×Dic6C2211yescharacteristic, complemented
48#5239C2218yescomplemented
49#5232C2218yescomplemented
50C2×#835C2211yescharacteristic, complemented
51C2×#835C2211yescharacteristic, complemented
52C2×#835C2211yescharacteristic, complemented
53#5218C2218yescomplemented
54#5215C2218yescomplemented
55C2×#832C2211yescharacteristic
56C2×#832C2211yescharacteristic
57C2×#832C2211yescharacteristic
58C2×#832C2211yescharacteristic
59C2×#832C2211yescharacteristic
60C2×#832C2211yescharacteristic
61C2×#830C2211yescharacteristic
62C2×#830C2211yescharacteristic, complemented
63#5056C2218yescomplemented
64#5054C2218yescomplemented
65#5052C2218yescomplemented
66#5045C2218yescomplemented
67#5042C2218yescomplemented
68#5034C2218yescomplemented
69C4×#214C2218yescomplemented
70#5012C2218yescomplemented
71#5009C2218yescomplemented
72C2×#810C2211yescharacteristic, complemented
73C2×#808C2211yescharacteristic, complemented
74C2×#808C2211yescharacteristic, complemented
75C2×#807C2211yescharacteristic, complemented
76C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
77C2×C4×C3⋊C8C2211yescharacteristic, complemented
78C2×#552—31no—
79C2×#546D311yescharacteristic
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×#436—31no—
92C2×#417—31no—
93C2×#418—31no—
94C25×C3—21no—
95C2×C3×#41—22no—
96C2×C3×#41—24no—
97C2×C3×#41—42no—
98C2×C3×#41C2314yes—
99C22×C3×Q8C2311yescharacteristic
100C22×C3×D4—24no—
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4—21no—
104C22×C3×D4—22no—
105C22×C3×D4—42no—
106C22×C3×D4D411yescharacteristic
107C22×C3×D4C2311yescharacteristic
108C22×C3×D4C2314yes—
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×Dic3—21no—
115C22×Dic6C2311yescharacteristic
116C3×#124—22no—
117C3×#124C2314yes—
118C3×#123—28no—
119C3×C22⋊Q8—22no—
120C3×C22⋊Q8C2314yes—
121C3×#121—22no—
122C3×#121—28no—
123C3×#121C2314yes—
124C3×#120—28no—
125C3×C4×D4—22no—
126C3×C4×D4D414yes—
127C3×C4×D4C2314yes—
128C3×C4×D4C2314yes—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4D411yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—28no—
138C2×C3×C22⋊C4D411yescharacteristic
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×#217—21no—
142C2×#217—21no—
143C2×#217—21no—
144C2×#216—42no—
145C2×#216C2314yescomplemented
146#935—28no—
147C2×#214—24no—
148C2×#214—42no—
149C2×#214C2314yes—
150C2×#214C2314yes—
151#926—22no—
152#926C2314yes—
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2314yescomplemented
159#924—22no—
160#924—22no—
161#924C2314yes—
162#924C2314yescomplemented
163C2×Dic3⋊C4—21no—
164C2×Dic3⋊C4—21no—
165C2×Dic3⋊C4—21no—
166C2×Dic3⋊C4—21no—
167C2×Dic3⋊C4—21no—
168C2×C4×Dic3—21no—
169C2×C4×Dic3—21no—
170C2×#208—42no—
171C2×#208—42no—
172C2×#208C2314yes—
173C2×#208C2314yescomplemented
174C22×C3⋊C8C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177C22×C3⋊C8C2311yescharacteristic
178#889—28no—
179#879—28no—
180#877—28no—
181#870—22no—
182#870C2314yescomplemented
183C4×Dic6—22no—
184C4×Dic6C2314yescomplemented
185#835C2314yescomplemented
186#835C2314yescomplemented
187#835C2314yescomplemented
188#832C2314yes—
189#832C2314yes—
190#832C2314yes—
191#832C2314yes—
192#832C2314yes—
193#832C2314yes—
194#830C2314yes—
195#830C2314yescomplemented
196#810C2314yescomplemented
197#808C2314yescomplemented
198#808C2314yescomplemented
199#807C2314yescomplemented
200C4⋊(C3⋊C8)C2314yescomplemented
201C4×C3⋊C8C2314yescomplemented
202C22×#41C2×D311yescharacteristic
203C23×D4C2×D311yescharacteristic
204C22×Q16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×M16—31no—
208C22×M16—31no—
209#552—38no—
210#552—64no—
211#546—24no—
212#546C2×D318yes—
213C2×#126—61no—
214C2×#125—31no—
215C2×#125—61no—
216C2×#124C2×D311yescharacteristic
217C2×#123—21no—
218C2×#123—61no—
219C2×C22⋊Q8—31no—
220C2×C22⋊Q8—31no—
221C2×C22⋊Q8C2×D311yescharacteristic
222C2×#121—21no—
223C2×#121C2×D311yescharacteristic
224C2×#120—21no—
225C2×C4×Q8—31no—
226C2×C4×D4C2×D311yescharacteristic
227C2×C4×D4C2×D311yescharacteristic
228C2×#117—31no—
229C2×#117—61no—
230C22×C4⋊C4—31no—
231C22×C22⋊C4—21no—
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#436—38no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×C4⋊C8—31no—
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⋊C8—31no—
260C2×C22⋊C8—31no—
261C2×C4×C8—31no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—24no—
265C24×C3—44no—
266C24×C3—44no—
267C24×C3—82no—
268C24×C3C2×D411yescharacteristic
269C24×C3C2×D411yescharacteristic
270C3×#41—28no—
271C3×#41—44no—
272C3×#41—48no—
273C2×C3×Q8—21no—
274C2×C3×Q8—22no—
275C2×C3×Q8—22no—
276C2×C3×Q8C2412yes—
277C2×C3×D4—28no—
278C2×C3×D4—24no—
279C2×C3×D4—24no—
280C2×C3×D4—21no—
281C2×C3×D4—24no—
282C2×C3×D4—21no—
283C2×C3×D4—22no—
284C2×C3×D4—22no—
285C2×C3×D4—22no—
286C2×C3×D4—44no—
287C2×C3×D4—48no—
288C2×C3×D4—42no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
291C2×C3×D4—82no—
292C2×C3×D4C2×D414yes—
293C2×C3×D4#4114yes—
294C2×C3×D4C2412yes—
295C2×C3×D4C2412yes—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—24no—
303C22×C3×C4—24no—
304C22×C3×C4—44no—
305C22×C3×C4—82no—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2412yes—
313C22×C3×C4C2412yes—
314C22×C3×C4C2411yescharacteristic
315C22×Dic3—24no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—44no—
321C2×Dic6—22no—
322C2×Dic6—22no—
323C2×Dic6—21no—
324C2×Dic6C2412yes—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4C2×D414yes—
328C3×C4⋊C4C2412yes—
329C3×C22⋊C4—24no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4—24no—
332C3×C22⋊C4—24no—
333C3×C22⋊C4—24no—
334C3×C22⋊C4C2×D414yes—
335C3×C22⋊C4C2×D414yes—
336C3×C42C2×D412yes—
337C3×C42C2412yes—
338#217—24no—
339#217—24no—
340#217—24no—
341#216—44no—
342#214—28no—
343#214—44no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—24no—
348C4⋊Dic3C2412yes—
349C4⋊Dic3C2412yes—
350C4⋊Dic3C2412yes—
351Dic3⋊C4—24no—
352Dic3⋊C4—24no—
353Dic3⋊C4—24no—
354Dic3⋊C4—24no—
355Dic3⋊C4—24no—
356C4×Dic3—24no—
357C4×Dic3—24no—
358#208—44no—
359#208—44no—
360C2×C3⋊C8—22no—
361C2×C3⋊C8—22no—
362C2×C3⋊C8—22no—
363C2×C3⋊C8—22no—
364C2×C3⋊C8C2412yes—
365C2×C3⋊C8C2412yes—
366C2×C3⋊C8C2412yes—
367C2×C3⋊C8C2412yes—
368C25—21no—
369C2×#41—22no—
370C2×#41—24no—
371C2×#41—42no—
372C2×#41C22×D314yes—
373C22×Q8—31no—
374C22×Q8C22×D311yescharacteristic
375C22×D4—24no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—22no—
380C22×D4—42no—
381C22×D4#6711yescharacteristic
382C22×D4C22×D311yescharacteristic
383C22×D4C22×D314yes—
384C22×D4C22×D311yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
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—34no—
397C2×M16—34no—
398C2×M16—122no—
399C2×M16—122no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8—31no—
403C22×C8—31no—
404#126—68no—
405#125—34no—
406#125—68no—
407#125—62no—
408#124—22no—
409#124C22×D314yes—
410#123—28no—
411#123—68no—
412C22⋊Q8—22no—
413C22⋊Q8—34no—
414C22⋊Q8—34no—
415C22⋊Q8—62no—
416C22⋊Q8—62no—
417C22⋊Q8C22×D314yes—
418#121—22no—
419#121—28no—
420#121C22×D314yes—
421#120—28no—
422C4×Q8—34no—
423C4×Q8—62no—
424C4×D4—22no—
425C4×D4#6714yes—
426C4×D4C22×D314yes—
427C4×D4C22×D314yes—
428#117—34no—
429#117—62no—
430#117—68no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—34no—
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#6711yescharacteristic
444C2×C4⋊C4C22×D311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—61no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—61no—
454C2×C22⋊C4#6711yescharacteristic
455C2×C22⋊C4#6711yescharacteristic
456C2×C42—61no—
457C2×C42—61no—
458C2×C42C22×D311yescharacteristic
459#107—34no—
460#106—34no—
461#106—34no—
462C4⋊C8—34no—
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⋊C8—34no—
474C22⋊C8—34no—
475C4×C8—34no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—24no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—48no—
486C23×C3—48no—
487C23×C3—42no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—84no—
493C23×C3—816no—
494C23×C3C22×D412yes—
495C23×C3C22×D412yes—
496C23×C3C22×D411yescharacteristic
497C3×Q8—22no—
498C3×Q8—22no—
499C3×Q8—42no—
500C3×D4—24no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—44no—
505C3×D4—48no—
506C3×D4—48no—
507C3×D4—42no—
508C3×D4—84no—
509C3×D4C2×#4114yes—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—24no—
515C2×C3×C4—24no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—48no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—84no—
526C2×C3×C4C22×D412yes—
527C2×C3×C4C22×D412yes—
528C2×C3×C4C22×D412yes—
529C2×C3×C4C22×D412yes—
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C2×#4112yes—
532C2×C3×C4H(5,𝔽2)12yes—
533C2×C3×C4C2511yescharacteristic
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—48no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543Dic6—22no—
544Dic6—22no—
545Dic6—42no—
546C3⋊C8—22no—
547C3⋊C8—22no—
548C3⋊C8—22no—
549C3⋊C8—22no—
550C24—21no—
551C24—21no—
552C24—24no—
553C24—44no—
554C24—44no—
555C24—82no—
556C24C2×#6711yescharacteristic
557C24C2×#6711yescharacteristic
558#41—28no—
559#41—44no—
560#41—48no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—32no—
565C2×Q8—61no—
566C2×Q8—62no—
567C2×Q8—62no—
568C2×Q8C23×D312yes—
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—44no—
579C2×D4—48no—
580C2×D4—42no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—82no—
584C2×D4#23714yes—
585C2×D4C2×#6714yes—
586C2×D4C23×D312yes—
587C2×D4C23×D312yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—64no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—82no—
603C22×C4—124no—
604C22×C4C2×#6712yes—
605C22×C4C2×#6712yes—
606C22×C4C2×#6711yescharacteristic
607C22×C4C2×#6711yescharacteristic
608C22×C4C2×#6711yescharacteristic
609C22×C4C2×#6711yescharacteristic
610C22×C4C23×D312yes—
611C22×C4C23×D312yes—
612C22×C4C23×D311yescharacteristic
613Q16—124no—
614SD16—68no—
615SD16—124no—
616M16—124no—
617M16—124no—
618C2×C8—32no—
619C2×C8—32no—
620C2×C8—32no—
621C2×C8—32no—
622C2×C8—62no—
623C2×C8—62no—
624C2×C8—62no—
625C2×C8—62no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—32no—
629C4⋊C4—32no—
630C4⋊C4—32no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—64no—
634C4⋊C4—61no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4C2×#6714yes—
641C4⋊C4C23×D312yes—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4C2×#6714yes—
651C22⋊C4C2×#6714yes—
652C42—64no—
653C42—64no—
654C42C2×#6712yes—
655C42C23×D312yes—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—24no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—48no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—816no—
672C22×C3—84no—
673C22×C3#54612yes—
674C22×C3#57512yes—
675C22×C3#57712yes—
676C22×C3C23×D411yescharacteristic
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4#54612yes—
684C3×C4C22×#4111yescharacteristic
685C3×C4C2×H(5,𝔽2)11yescharacteristic
686Dic3—42no—
687Dic3—42no—
688Dic3—42no—
689Dic3—42no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—48no—
700C23—48no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—84no—
707C23—816no—
708C23C22×#6712yes—
709C23C22×#6712yes—
710C23C22×#6711yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—62no—
715Q8—62no—
716Q8—122no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—24no—
721D4—44no—
722D4—48no—
723D4—48no—
724D4—42no—
725D4—84no—
726D4C2×#23714yes—
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—22no—
738C2×C4—22no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—84no—
747C2×C4—128no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4C2×#23712yes—
753C2×C4#100412yes—
754C2×C4C22×#6712yes—
755C2×C4C22×#6712yes—
756C2×C4C22×#6712yes—
757C2×C4C22×#6712yes—
758C2×C4C22×#6711yescharacteristic
759C2×C4C24×D311yescharacteristic
760C8—62no—
761C8—62no—
762C8—62no—
763C8—62no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—44no—
767C2×C3—82no—
768C2×C3#332314yescomplemented
769C2×C3C2×#54611yescharacteristic
770C2×C3C2×#57511yescharacteristic
771C2×C3C2×#57711yescharacteristic
772C22—22no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—48no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—816no—
788C22—84no—
789C22#580612yes—
790C22#582212yes—
791C22#583612yes—
792C22C23×#6711yescharacteristic
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—42no—
798C4—42no—
799C4—122no—
800C4—122no—
801C4—122no—
802C4—122no—
803C4#580612yes—
804C4C22×#23711yescharacteristic
805C4C2×#100411yescharacteristic
806C3C2×#332311yescharacteristic, complemented, Sylow
807C2—42no—
808C2—42no—
809C2—44no—
810C2—82no—
811C2#8350114yesdirect product factor
812C2C2×#580611yescharacteristic
813C2C2×#582211yescharacteristic
814C2C2×#583611yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
Fitting, prime radicalC2×C3×#546C2
socleC23×C3C22×D4
hypercenterC2×#546D3
hypocenterC3C2×#3323
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
2. C2×#5541C2semidirect
3. C2×#5239C2semidirect
4. C2×#5232C2semidirect
5. C2×#5218C2semidirect
6. C2×#5215C2semidirect
7. #83501C2direct (N × H)
8. C2×#5054C2semidirect
9. C2×#5056C2semidirect
10. C2×#5052C2semidirect
11. C2×#5045C2semidirect
12. C2×#5042C2semidirect
13. C2×#5034C2semidirect
14. C2×C4×#214C2semidirect
15. C2×#5012C2semidirect
16. C2×#5009C2semidirect
31. C22×#216C22semidirect
36. C22×C4⋊Dic3C22semidirect
38. C2×#924C22semidirect
40. C22×#208C22semidirect
42. #5541C22semidirect
46. C2×#870C22semidirect
47. C2×C4×Dic6C22semidirect
48. #5239C22semidirect
49. #5232C22semidirect
50. C2×#835C22semidirect
51. C2×#835C22semidirect
52. C2×#835C22semidirect
53. #5218C22semidirect
54. #5215C22semidirect
62. C2×#830C22semidirect
63. #5056C22semidirect
64. #5054C22semidirect
65. #5052C22semidirect
66. #5045C22semidirect
67. #5042C22semidirect
68. #5034C22semidirect
69. C4×#214C22semidirect
70. #5012C22semidirect
71. #5009C22semidirect
72. C2×#810C22semidirect
73. C2×#808C22semidirect
74. C2×#808C22semidirect
75. C2×#807C22semidirect
76. C2×C4⋊(C3⋊C8)C22semidirect
77. C2×C4×C3⋊C8C22semidirect
145. C2×#216C23semidirect
158. C2×C4⋊Dic3C23semidirect
162. #924C23semidirect
173. C2×#208C23semidirect
182. #870C23semidirect
184. C4×Dic6C23semidirect
185. #835C23semidirect
186. #835C23semidirect
187. #835C23semidirect
195. #830C23semidirect
196. #810C23semidirect
197. #808C23semidirect
198. #808C23semidirect
199. #807C23semidirect
200. C4⋊(C3⋊C8)C23semidirect
201. C4×C3⋊C8C23semidirect
768. C2×C3#3323semidirect
806. C3C2×#3323semidirect
811. C2#83501direct (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
C2×#55412
C2×#52392
C2×#52322
C2×#52182
C2×#52152
#835012
C2×#50542
C2×#50562
C2×#50522
C2×#50452
C2×#50422
C2×#50342
C2×C4×#2142
C2×#50122
C2×#50092
C2×#33233