Finite Group Databasebeta

← C2×#80554 #11670222

Subgroups — C2×#80554 #11670222

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#915C211yesmaximal, characteristic, complemented
2C22×#912C211yesmaximal, characteristic, complemented
3C2×#5677C211yesmaximal, characteristic, complemented
4C2×#5555C211yesmaximal, characteristic, complemented
5C2×C3×#463C211yesmaximal, characteristic, complemented
6C2×#5173C211yesmaximal, characteristic, complemented
7C2×#5158C211yesmaximal, characteristic, complemented
8C2×#5060C211yesmaximal, characteristic, complemented
9C2×#5018C211yesmaximal, characteristic, complemented
10#80554C2116yesmaximal, direct product factor
11C2×#4849C211yesmaximal, characteristic, complemented
12C2×#4836C211yesmaximal, characteristic, complemented
13C2×#4813C211yesmaximal, characteristic, complemented
14C2×#4809C211yesmaximal, characteristic, complemented
15C2×#4780C211yesmaximal, characteristic, complemented
16C2×#4783C211yesmaximal, characteristic, complemented
17C2×#3269—31nomaximal, Sylow
18C22×D3×Q8C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C22×#237C2211yescharacteristic
21C22×#237C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#124C2211yescharacteristic
25C2×C3×C4×D4C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C22×#216C2211yescharacteristic
28C22×#216C2211yescharacteristic
29C2×#938C2211yescharacteristic
30C22×#214C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C22×#214C2211yescharacteristic
33C2×#930—21no—
34C22×C4⋊Dic3—21no—
35C2×#915—28no—
36C2×#915C2218yescomplemented
37C2×#912—28no—
38C2×#912C2218yescomplemented
39C22×Dic12C2211yescharacteristic
40C22×Dic12C2211yescharacteristic
41C22×ΓL(1,𝔽25)C2211yescharacteristic
42C22×D3×C8C2211yescharacteristic
43#5677—24no—
44#5677C2218yescomplemented
45#5555—24no—
46#5555C2218yescomplemented
47C2×#897C2211yescharacteristic
48C2×#897C2211yescharacteristic
49C2×#886—21no—
50C2×#886—21no—
51C2×#885—21no—
52C2×#884—21no—
53C2×#67⋊C4—21no—
54C2×#878—21no—
55C2×C4×D12C2211yescharacteristic
56C2×#869C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic
58C3×#463C2218yescomplemented
59C2×C3×C4⋊C8C2211yescharacteristic
60C2×C3×#103C2211yescharacteristic
61C2×C3×#102C2211yescharacteristic
62C2×#832C2211yescharacteristic
63#5173C2218yescomplemented
64#5158C2218yescomplemented
65C2×(C2×D3)⋊C8C2211yescharacteristic
66C2×(C2×D3)⋊C8C2211yescharacteristic
67C2×#816C2211yescharacteristic
68C2×#816C2211yescharacteristic
69#5060C2218yescomplemented
70#5018C2218yescomplemented
71C2×#810C2211yescharacteristic
72C2×#807C2211yescharacteristic
73C2×#803C2211yescharacteristic
74#4849C2218yescomplemented
75#4836C2218yescomplemented
76#4813C2218yescomplemented
77#4809C2218yescomplemented
78#4783C2218yescomplemented
79#4780C2218yescomplemented
80C22×#137—31no—
81C22×#135—31no—
82C2×#548—31no—
83C2×#547—31no—
84#3269—316no—
85C2×#497—31no—
86C2×#468—31no—
87C2×#467—31no—
88C2×#462—31no—
89C2×#463D311yescharacteristic, complemented
90C2×#452—31no—
91C2×#452—31no—
92C2×#449—31no—
93C2×#451—31no—
94C2×#440—31no—
95C2×#435—31no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4C2311yescharacteristic
98C22×C3×D4C2311yescharacteristic
99C23×C3×C4—21no—
100C22×#67—21no—
101C22×#67—21no—
102C22×#67—21no—
103C22×#67—21no—
104C23×Dic3—21no—
105C23×Dic3—21no—
106C23×Dic3—21no—
107C2×D3×Q8—22no—
108C2×D3×Q8—24no—
109C2×D3×Q8—42no—
110C2×D3×Q8C2314yes—
111C2×#237—24no—
112C2×#237—24no—
113C2×#237—22no—
114C2×#237—22no—
115C2×#237—22no—
116C2×#237—24no—
117C2×#237—42no—
118C2×#237—42no—
119C2×#237—42no—
120C2×#237C2314yes—
121C2×#237C2314yes—
122C2×#237C2314yes—
123C22×D12D411yescharacteristic
124C22×C4×D3—21no—
125C22×C4×D3C2311yescharacteristic
126C22×C4×D3C2311yescharacteristic
127C22×Dic6—21no—
128C22×Dic6C2311yescharacteristic
129C22×Dic6C2311yescharacteristic
130C22×Dic6C2311yescharacteristic
131C2×C3×SD16—24no—
132C2×C3×SD16C2314yes—
133C2×C3×D8—24no—
134C2×C3×D8C2314yes—
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C3×#124—22no—
138C3×#124C2314yes—
139C3×C4×D4—22no—
140C3×C4×D4C2314yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C42C2311yescharacteristic
146C2×#217—21no—
147#946—22no—
148#946C2314yes—
149C2×#216—24no—
150C2×#216—42no—
151C2×#216C2314yes—
152C2×#216C2314yes—
153#938—22no—
154#938C2314yes—
155C2×#214—24no—
156C2×#214—42no—
157C2×#214D418yescomplemented
158C2×#214C2314yes—
159C2×#214C2314yes—
160C2×#214C2314yes—
161#930—28no—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4—21no—
165C2×(C2×D3)⋊C4D411yescharacteristic
166C2×(C2×D3)⋊C4D411yescharacteristic
167C2×C4⋊Dic3—21no—
168C2×C4⋊Dic3—21no—
169C2×C4⋊Dic3—21no—
170C2×C4⋊Dic3—21no—
171C2×C4⋊Dic3—28no—
172C2×C4⋊Dic3D411yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×Dic3⋊C4—21no—
175C2×Dic3⋊C4—21no—
176C2×C4×Dic3—21no—
177C22×C3⋊C8C2311yescharacteristic
178C22×C3⋊C8C2311yescharacteristic
179#915—232no—
180#912—232no—
181C2×Dic12—24no—
182C2×Dic12—24no—
183C2×Dic12C2314yes—
184C2×Dic12C2314yes—
185C2×ΓL(1,𝔽25)—24no—
186C2×ΓL(1,𝔽25)C2314yes—
187C2×D3×C8—24no—
188C2×D3×C8C2314yes—
189#897—22no—
190#897—22no—
191#897C2314yes—
192#897C2314yes—
193#886—28no—
194#886—28no—
195#885—28no—
196#884—28no—
197#67⋊C4—28no—
198#878—28no—
199C4×D12D414yes—
200C4×D12C2314yes—
201#869—22no—
202#869C2314yes—
203C4×Dic6—22no—
204C4×Dic6C2314yes—
205C3×C4⋊C8C2314yes—
206C3×#103C2314yes—
207C3×#102C2314yes—
208#832C2314yes—
209(C2×D3)⋊C8C2314yes—
210(C2×D3)⋊C8C2314yes—
211#816C2314yes—
212#816C2314yes—
213#810C2314yes—
214#807C2314yes—
215#803C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41—31no—
219C23×Q8—31no—
220C2×#137—38no—
221C2×#137—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×Q16—31no—
227C22×Q16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×SD16C2×D311yescharacteristic
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C23×C8—31no—
235#548—38no—
236#548—64no—
237#547—38no—
238#547—64no—
239C2×C4⋊Q8—31no—
240C2×#124—61no—
241C2×#124C2×D311yescharacteristic
242C2×#123—61no—
243C2×#123—61no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—31no—
246C2×C22⋊Q8—31no—
247C2×C22⋊Q8—61no—
248C2×#121—31no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—61no—
254C2×C4×D4C2×D311yescharacteristic
255C22×C4⋊C4—61no—
256#497—38no—
257#468—38no—
258#467—38no—
259#463C2×D318yescomplemented
260#462—38no—
261#452—38no—
262#452—38no—
263#451—38no—
264#449—38no—
265#440—38no—
266#435—38no—
267C2×#107—31no—
268C2×C4⋊C8C2×D311yescharacteristic
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103C2×D311yescharacteristic
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C24×C3—21no—
279C24×C3—21no—
280C23×D3C2×D411yescharacteristic
281C23×D3C2×D411yescharacteristic
282C2×C3×Q8—21no—
283C2×C3×Q8—22no—
284C2×C3×Q8—22no—
285C2×C3×Q8C2412yes—
286C2×C3×D4—21no—
287C2×C3×D4—22no—
288C2×C3×D4—21no—
289C2×C3×D4—22no—
290C2×C3×D4—22no—
291C2×C3×D4C2×D414yes—
292C2×C3×D4C2412yes—
293C2×C3×D4C2412yes—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—24no—
297C22×C3×C4—44no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—44no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—24no—
314C22×Dic3—24no—
315C22×Dic3—24no—
316C22×Dic3—44no—
317C22×Dic3—44no—
318C22×Dic3—44no—
319C22×Dic3C2×D411yescharacteristic
320C22×Dic3C2×D411yescharacteristic
321D3×Q8—28no—
322D3×Q8—44no—
323D3×Q8—48no—
324#237—28no—
325#237—28no—
326#237—28no—
327#237—44no—
328#237—44no—
329#237—44no—
330#237—48no—
331#237—48no—
332#237—48no—
333C2×D12—42no—
334C2×D12C2×D414yes—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—24no—
340C2×C4×D3—44no—
341C2×C4×D3C2×D412yes—
342C2×C4×D3C2×D412yes—
343C2×C4×D3C2412yes—
344C2×C4×D3C2412yes—
345C2×Dic6—21no—
346C2×Dic6—22no—
347C2×Dic6—22no—
348C2×Dic6—22no—
349C2×Dic6—22no—
350C2×Dic6—22no—
351C2×Dic6—21no—
352C2×Dic6—21no—
353C2×Dic6—24no—
354C2×Dic6—44no—
355C2×Dic6C2×D414yes—
356C2×Dic6C2412yes—
357C2×Dic6C2412yes—
358C2×Dic6C2412yes—
359C3×SD16—28no—
360C3×D8—28no—
361C2×C3×C8—22no—
362C2×C3×C8—22no—
363C2×C3×C8C2412yes—
364C2×C3×C8C2412yes—
365C3×C4⋊C4—21no—
366C3×C4⋊C4C2412yes—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—24no—
369C3×C22⋊C4—24no—
370C3×C42C2×D412yes—
371C3×C42C2412yes—
372#217—24no—
373#216—28no—
374#216—44no—
375#214—28no—
376#214—44no—
377#214C2×D4116yescomplemented
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4C2×D414yes—
382(C2×D3)⋊C4C2×D414yes—
383C4⋊Dic3—21no—
384C4⋊Dic3—24no—
385C4⋊Dic3—24no—
386C4⋊Dic3—24no—
387C4⋊Dic3—24no—
388C4⋊Dic3C2×D414yes—
389C4⋊Dic3C2412yes—
390Dic3⋊C4—24no—
391Dic3⋊C4—24no—
392C4×Dic3—24no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8C2×D414yes—
395C2×C3⋊C8C2412yes—
396C2×C3⋊C8C2412yes—
397Dic12—28no—
398Dic12—28no—
399ΓL(1,𝔽25)—28no—
400D3×C8—28no—
401C2×#41—34no—
402C2×#41—34no—
403C2×#41—34no—
404C2×#41—62no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—64no—
408C2×#41—64no—
409C2×#41—64no—
410C2×#41—122no—
411C2×#41—122no—
412C2×#41—122no—
413C22×Q8—34no—
414C22×Q8—31no—
415C22×Q8—31no—
416C22×Q8—31no—
417C22×Q8—61no—
418C22×Q8—62no—
419C22×Q8—64no—
420C22×Q8—122no—
421C22×Q8C22×D311yescharacteristic
422C22×D4—31no—
423C22×D4—61no—
424C22×D4—61no—
425C22×D4—61no—
426C22×D4—61no—
427C22×D4C22×D311yescharacteristic
428C22×D4C22×D311yescharacteristic
429C23×C4—21no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—61no—
433C23×C4—61no—
434C23×C4—61no—
435C23×C4—61no—
436#137—632no—
437#135—632no—
438C2×Q16—34no—
439C2×Q16—34no—
440C2×Q16—34no—
441C2×Q16—34no—
442C2×Q16—64no—
443C2×Q16—64no—
444C2×Q16—64no—
445C2×Q16—122no—
446C2×SD16—24no—
447C2×SD16—38no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—64no—
452C2×SD16—122no—
453C2×SD16C22×D314yes—
454C2×D8—24no—
455C2×D8C22×D314yes—
456C2×M16—34no—
457C2×M16—64no—
458C22×C8—31no—
459C22×C8—31no—
460C22×C8—34no—
461C22×C8—64no—
462C22×C8C22×D311yescharacteristic
463C22×C8C22×D311yescharacteristic
464C4⋊Q8—34no—
465C4⋊Q8—62no—
466#124—22no—
467#124—68no—
468#124C22×D314yes—
469#123—68no—
470#123—68no—
471C22⋊Q8—34no—
472C22⋊Q8—34no—
473C22⋊Q8—34no—
474C22⋊Q8—68no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478#121—34no—
479#121—68no—
480#121—68no—
481#121—62no—
482C4×Q8—34no—
483C4×Q8—62no—
484C4×D4—22no—
485C4×D4—34no—
486C4×D4—34no—
487C4×D4—68no—
488C4×D4C22×D314yes—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—68no—
492C2×C4⋊C4—61no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C42—61no—
509C2×C42C22×D311yescharacteristic
510#107—34no—
511C4⋊C8C22×D314yes—
512#103—34no—
513#103—34no—
514#103—34no—
515#103C22×D314yes—
516#102—34no—
517#102C22×D314yes—
518C22⋊C8—34no—
519C22⋊C8—34no—
520#97—34no—
521C23×C3—24no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—42no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3C22×D411yescharacteristic
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3C22×D412yes—
537C22×D3C22×D412yes—
538C3×Q8—22no—
539C3×Q8—22no—
540C3×Q8—42no—
541C3×D4—24no—
542C3×D4—22no—
543C3×D4—22no—
544C3×D4—22no—
545C3×D4—42no—
546C3×D4C22×D414yes—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—48no—
552C2×C3×C4—42no—
553C2×C3×C4—42no—
554C2×C3×C4C22×D412yes—
555C2×C3×C4C22×D412yes—
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×D412yes—
558C2×C3×C4H(5,𝔽2)12yes—
559C2×C3×C4C2511yescharacteristic
560#67—48no—
561#67—48no—
562#67—48no—
563#67—48no—
564C2×Dic3—24no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—48no—
572C2×Dic3—48no—
573C2×Dic3—48no—
574C2×Dic3—42no—
575C2×Dic3—42no—
576C2×Dic3—42no—
577C2×Dic3C22×D412yes—
578C2×Dic3C22×D412yes—
579D12—44no—
580C4×D3—24no—
581C4×D3—24no—
582C4×D3—22no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—22no—
586C4×D3—48no—
587Dic6—24no—
588Dic6—22no—
589Dic6—22no—
590Dic6—22no—
591Dic6—22no—
592Dic6—22no—
593Dic6—48no—
594Dic6—42no—
595Dic6—42no—
596Dic6C22×D414yes—
597C3×C8—22no—
598C3×C8—22no—
599C3⋊C8—22no—
600C3⋊C8C22×D414yes—
601C24—21no—
602C24—21no—
603C24—31no—
604C24—31no—
605#41—68no—
606#41—68no—
607#41—68no—
608#41—124no—
609#41—124no—
610#41—124no—
611#41—128no—
612#41—128no—
613#41—128no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8—22no—
617C2×Q8—34no—
618C2×Q8—32no—
619C2×Q8—32no—
620C2×Q8—32no—
621C2×Q8—64no—
622C2×Q8—61no—
623C2×Q8—61no—
624C2×Q8—61no—
625C2×Q8—62no—
626C2×Q8—68no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—124no—
632C2×Q8—124no—
633C2×Q8—128no—
634C2×Q8C23×D312yes—
635C2×D4—21no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—34no—
641C2×D4—64no—
642C2×D4—64no—
643C2×D4—64no—
644C2×D4—64no—
645C2×D4—122no—
646C2×D4—124no—
647C2×D4—124no—
648C2×D4—124no—
649C2×D4—124no—
650C2×D4D3×D414yes—
651C2×D4C23×D312yes—
652C2×D4C23×D312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—44no—
663C22×C4—64no—
664C22×C4—64no—
665C22×C4—64no—
666C22×C4—64no—
667C22×C4—61no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—124no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4—124no—
679C22×C4D3×D411yescharacteristic
680C22×C4D3×D411yescharacteristic
681C22×C4C23×D311yescharacteristic
682Q16—68no—
683Q16—68no—
684Q16—68no—
685Q16—124no—
686SD16—28no—
687SD16—316no—
688SD16—68no—
689SD16—124no—
690D8—28no—
691M16—68no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—34no—
695C2×C8—32no—
696C2×C8—32no—
697C2×C8—68no—
698C2×C8—62no—
699C2×C8C23×D312yes—
700C2×C8C23×D312yes—
701C4⋊C4—21no—
702C4⋊C4—34no—
703C4⋊C4—32no—
704C4⋊C4—64no—
705C4⋊C4—64no—
706C4⋊C4—64no—
707C4⋊C4—61no—
708C4⋊C4—64no—
709C4⋊C4—64no—
710C4⋊C4—64no—
711C4⋊C4C23×D312yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—34no—
716C22⋊C4—34no—
717C22⋊C4—64no—
718C22⋊C4—64no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C42—64no—
722C42D3×D412yes—
723C42C23×D312yes—
724C22×C3—24no—
725C22×C3—48no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—84no—
732C22×C3D4212yes—
733C22×C3#57512yes—
734C22×C3#57812yes—
735C22×C3C23×D411yescharacteristic
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—44no—
743C2×D3—44no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4D4212yes—
749C3×C4C23×D411yescharacteristic
750C3×C4C2×H(5,𝔽2)11yescharacteristic
751Dic3—24no—
752Dic3—22no—
753Dic3—22no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—24no—
759C23—22no—
760C23—32no—
761C23—32no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23C2×D3×D411yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—34no—
777Q8—42no—
778Q8—62no—
779Q8—64no—
780Q8—62no—
781Q8—62no—
782Q8—62no—
783Q8—62no—
784Q8—128no—
785Q8—122no—
786Q8—122no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—24no—
791D4—42no—
792D4—124no—
793D4—128no—
794D4—128no—
795D4—128no—
796D4—128no—
797D4C2×D3×D414yes—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—48no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—64no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—64no—
816C2×C4—64no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—128no—
821C2×C4—128no—
822C2×C4—128no—
823C2×C4—128no—
824C2×C4—122no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4C2×D3×D412yes—
828C2×C4C2×D3×D412yes—
829C2×C4C2×D3×D412yes—
830C2×C4C2×D3×D411yescharacteristic
831C2×C4#100912yes—
832C2×C4C24×D311yescharacteristic
833C8—22no—
834C8—22no—
835C8—34no—
836C8—62no—
837C2×C3—44no—
838C2×C3—82no—
839C2×C3#326914yescomplemented
840C2×C3C2×D4211yescharacteristic
841C2×C3C2×#57511yescharacteristic
842C2×C3C2×#57811yescharacteristic
843D3—42no—
844D3—42no—
845C22—24no—
846C22—42no—
847C22—42no—
848C22—48no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—84no—
859C22—124no—
860C22—124no—
861C22#560912yes—
862C22#577112yes—
863C22#577312yes—
864C22C22×D3×D411yescharacteristic
865C4—22no—
866C4—22no—
867C4—42no—
868C4—42no—
869C4—62no—
870C4—62no—
871C4—64no—
872C4—122no—
873C4—122no—
874C4—122no—
875C4#560912yes—
876C4C22×D3×D411yescharacteristic
877C4C2×#100911yescharacteristic
878C3C2×#326911yescharacteristic, complemented, Sylow
879C2—44no—
880C2—82no—
881C2—122no—
882C2—122no—
883C2#8055414yesdirect product factor
884C2C2×#560911yescharacteristic
885C2C2×#577111yescharacteristic
886C2C2×#577311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
hypercenterC2×#463D3
hypocenterC3C2×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#915C2semidirect
2. C22×#912C2semidirect
3. C2×#5677C2semidirect
4. C2×#5555C2semidirect
5. C2×C3×#463C2semidirect
6. C2×#5173C2semidirect
7. C2×#5158C2semidirect
8. C2×#5060C2semidirect
9. C2×#5018C2semidirect
10. #80554C2direct (N × H)
11. C2×#4849C2semidirect
12. C2×#4836C2semidirect
13. C2×#4813C2semidirect
14. C2×#4809C2semidirect
15. C2×#4780C2semidirect
16. C2×#4783C2semidirect
36. C2×#915C22semidirect
38. C2×#912C22semidirect
44. #5677C22semidirect
46. #5555C22semidirect
58. C3×#463C22semidirect
63. #5173C22semidirect
64. #5158C22semidirect
69. #5060C22semidirect
70. #5018C22semidirect
74. #4849C22semidirect
75. #4836C22semidirect
76. #4813C22semidirect
77. #4809C22semidirect
78. #4783C22semidirect
79. #4780C22semidirect
89. C2×#463D3semidirect
157. C2×#214D4semidirect
259. #463C2×D3semidirect
377. #214C2×D4semidirect
839. C2×C3#3269semidirect
878. C3C2×#3269semidirect
883. C2#80554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9152
C22×#9122
C2×#56772
C2×#55552
C2×C3×#4632
C2×#51732
C2×#51582
C2×#50602
C2×#50182
#805542
C2×#48492
C2×#48362
C2×#48132
C2×#48092
C2×#47802
C2×#47832
C2×#32693