Finite Group Databasebeta

← C2×#81549 #11671998

Subgroups — C2×#81549 #11671998

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×#5630C211yesmaximal, characteristic
2C2×#5529C211yesmaximal, characteristic, complemented
3C2×C3×#485C211yesmaximal, characteristic, complemented
4C2×#5052C211yesmaximal, characteristic, complemented
5C2×#5001C211yesmaximal, characteristic, complemented
6#81549C2116yesmaximal, direct product factor
7C2×#4891C211yesmaximal, characteristic, complemented
8C2×#4886C211yesmaximal, characteristic, complemented
9C2×#4863C211yesmaximal, characteristic, complemented
10C2×#4852C211yesmaximal, characteristic, complemented
11C2×#4798C211yesmaximal, characteristic, complemented
12C2×#4808C211yesmaximal, characteristic, complemented
13C2×#4803C211yesmaximal, characteristic, complemented
14C2×#4800C211yesmaximal, characteristic, complemented
15C2×#4731C211yesmaximal, characteristic, complemented
16C2×#4729C211yesmaximal, characteristic, complemented
17C2×#3323—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C22×#216C2211yescharacteristic, complemented
24C2×C4×#67C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×#208C2211yescharacteristic
27C22×#204C2211yescharacteristic
28C22×#204C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30#5630—24no—
31#5630C2218yes—
32#5529—24no—
33#5529C2218yescomplemented
34C2×#897C2211yescharacteristic, complemented
35C2×#895—21no—
36C2×#895C2211yescharacteristic
37C2×#894—21no—
38C2×#893C2211yescharacteristic
39C2×D3×C4⋊C4C2211yescharacteristic, complemented
40C2×#890C2211yescharacteristic, complemented
41C2×#887C2211yescharacteristic, complemented
42C2×#883—21no—
43C2×#882—21no—
44C2×D3×C22⋊C4—21no—
45C2×#879—21no—
46C2×#872—21no—
47C2×#870—21no—
48C3×#485C2218yescomplemented
49C2×C3×#107C2211yescharacteristic, complemented
50C2×C3×#106C2211yescharacteristic, complemented
51C2×C3×#103C2211yescharacteristic, complemented
52C2×C3×#103C2211yescharacteristic, complemented
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×#835C2211yescharacteristic, complemented
55C2×#821C2211yescharacteristic
56C2×#821C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C2×Dic3⋊C8C2211yescharacteristic, complemented
59C2×C8×Dic3C2211yescharacteristic, complemented
60#5052C2218yescomplemented
61#5001C2218yescomplemented
62C2×#810C2211yescharacteristic, complemented
63C2×#809C2211yescharacteristic
64C2×#809C2211yescharacteristic
65C2×#809C2211yescharacteristic
66C2×#809C2211yescharacteristic
67C2×#808C2211yescharacteristic, complemented
68#4891C2218yescomplemented
69#4886C2218yescomplemented
70#4863C2218yescomplemented
71#4852C2218yescomplemented
72#4808C2218yescomplemented
73#4803C2218yescomplemented
74#4800C2218yescomplemented
75#4798C2218yescomplemented
76#4731C2218yescomplemented
77#4729C2218yescomplemented
78C2×#552—31no—
79C2×#546—31no—
80#3323—316no—
81C2×#488—31no—
82C2×#481—31no—
83C2×#485D311yescharacteristic, complemented
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—
94C24×D3—21no—
95C22×C3×Q8C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67D411yescharacteristic
98C2×#239—22no—
99C2×#239—24no—
100C2×#239—42no—
101C2×#239C2314yes—
102C22×D12—24no—
103C22×D12—21no—
104C22×D12—21no—
105C22×D12—22no—
106C22×D12—21no—
107C22×D12—42no—
108C22×D12C2311yescharacteristic
109C22×D12C2314yes—
110C22×D12C2311yescharacteristic
111C22×C4×D3—21no—
112C22×C4×D3—21no—
113C22×C4×D3—21no—
114C22×C4×D3C2311yescharacteristic
115C22×Dic6C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C3×C22⋊Q8—22no—
119C3×C22⋊Q8C2314yes—
120C3×#117—22no—
121C3×#117C2314yes—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C42—21no—
129C2×#217—21no—
130C2×#217D411yescharacteristic
131#947—22no—
132#947C2314yes—
133C2×#216—42no—
134C2×#216C2314yescomplemented
135C4×#67D414yes—
136C4×#67C2314yes—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4D411yescharacteristic
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3C2311yescharacteristic
146#924—22no—
147#924C2314yes—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4—21no—
152C2×Dic3⋊C4D411yescharacteristic
153C2×C4×Dic3—21no—
154C2×C4×Dic3C2311yescharacteristic
155C2×#208—42no—
156C2×#208C2314yes—
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159C2×#204—24no—
160C2×#204—42no—
161C2×#204C2314yes—
162C2×#204C2314yes—
163C2×ΓL(1,𝔽25)—42no—
164C2×ΓL(1,𝔽25)C2314yescomplemented
165#897—22no—
166#897C2314yescomplemented
167#895—22no—
168#895—28no—
169#895C2314yes—
170#894—28no—
171#893—22no—
172#893C2314yes—
173D3×C4⋊C4—22no—
174D3×C4⋊C4C2314yescomplemented
175#890—22no—
176#890C2314yescomplemented
177#887—22no—
178#887C2314yescomplemented
179#883—28no—
180#882—28no—
181D3×C22⋊C4—28no—
182#879—28no—
183#872—28no—
184#870—28no—
185C3×#107C2314yescomplemented
186C3×#106C2314yescomplemented
187C3×#103C2314yescomplemented
188C3×#103C2314yescomplemented
189C3×C22⋊C8C2314yes—
190#835C2314yescomplemented
191#821C2314yes—
192#821C2314yes—
193(C2×D3)⋊C8C2314yescomplemented
194Dic3⋊C8C2314yescomplemented
195C8×Dic3C2314yescomplemented
196#810C2314yescomplemented
197#809C2314yes—
198#809C2314yes—
199#809C2314yes—
200#809C2314yes—
201#808C2314yescomplemented
202C22×#41—31no—
203C23×D4—31no—
204C22×Q16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×M16—31no—
208C22×M16—31no—
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⋊Q8C2×D311yescharacteristic
222C2×#121—31no—
223C2×#121—61no—
224C2×#120—61no—
225C2×C4×Q8—31no—
226C2×C4×D4—31no—
227C2×C4×D4—31no—
228C2×#117—61no—
229C2×#117C2×D311yescharacteristic
230C22×C4⋊C4—31no—
231C22×C22⋊C4—61no—
232#488—38no—
233#485C2×D318yescomplemented
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×#107C2×D311yescharacteristic, complemented
244C2×#106—31no—
245C2×#106C2×D311yescharacteristic, complemented
246C2×C4⋊C8—31no—
247#418—38no—
248#417—38no—
249C2×#103—31no—
250C2×#103—31no—
251C2×#103C2×D311yescharacteristic, complemented
252C2×#103C2×D311yescharacteristic, complemented
253C2×#102—31no—
254C2×#102—31no—
255C2×#102—31no—
256C2×#102—31no—
257C2×#102—31no—
258C2×#102—31no—
259C2×C22⋊C8—31no—
260C2×C22⋊C8C2×D311yescharacteristic
261C2×C4×C8—31no—
262C24×C3C2×D411yescharacteristic
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—24no—
266C23×D3—44no—
267C23×D3—44no—
268C23×D3—82no—
269C23×D3C2×D411yescharacteristic
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8—22no—
273C2×C3×Q8C2412yes—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2411yescharacteristic
284C2×#67—42no—
285C2×#67C2×D414yes—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290C22×Dic3C2×D411yescharacteristic
291#239—28no—
292#239—44no—
293#239—48no—
294C2×D12—21no—
295C2×D12—22no—
296C2×D12—22no—
297C2×D12—22no—
298C2×D12—28no—
299C2×D12—24no—
300C2×D12—24no—
301C2×D12—21no—
302C2×D12—24no—
303C2×D12—44no—
304C2×D12—48no—
305C2×D12—44no—
306C2×D12—44no—
307C2×D12—82no—
308C2×D12#4114yes—
309C2×D12C2412yes—
310C2×D12C2412yes—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—44no—
317C2×C4×D3—44no—
318C2×C4×D3—82no—
319C2×C4×D3C2×D412yes—
320C2×C4×D3C2412yes—
321C2×Dic6—22no—
322C2×Dic6—22no—
323C2×Dic6—21no—
324C2×Dic6C2412yes—
325C2×C3×C8—22no—
326C2×C3×C8—22no—
327C2×C3×C8C2412yes—
328C2×C3×C8C2412yes—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—24no—
333C3×C4⋊C4C2412yes—
334C3×C4⋊C4C2412yes—
335C3×C4⋊C4C2412yes—
336C3×C22⋊C4—24no—
337C3×C22⋊C4—24no—
338C3×C42—24no—
339#217—24no—
340#217C2×D414yes—
341#216—44no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4C2×D414yes—
348C4⋊Dic3—21no—
349C4⋊Dic3—24no—
350C4⋊Dic3—24no—
351C4⋊Dic3C2412yes—
352Dic3⋊C4—24no—
353Dic3⋊C4—24no—
354Dic3⋊C4—24no—
355Dic3⋊C4—24no—
356Dic3⋊C4C2×D414yes—
357C4×Dic3—24no—
358C4×Dic3C2×D412yes—
359C4×Dic3C2412yes—
360#208—44no—
361C2×C3⋊C8—22no—
362C2×C3⋊C8—22no—
363C2×C3⋊C8C2412yes—
364C2×C3⋊C8C2412yes—
365#204—28no—
366#204—44no—
367ΓL(1,𝔽25)—44no—
368C25—61no—
369C2×#41—34no—
370C2×#41—62no—
371C2×#41—64no—
372C2×#41—122no—
373C22×Q8—31no—
374C22×Q8C22×D311yescharacteristic
375C22×D4—31no—
376C22×D4—31no—
377C22×D4—31no—
378C22×D4—34no—
379C22×D4—64no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4—62no—
384C22×D4—122no—
385C23×C4—31no—
386C23×C4—61no—
387C23×C4—61no—
388C23×C4—61no—
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×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—22no—
413C22⋊Q8—34no—
414C22⋊Q8—34no—
415C22⋊Q8—62no—
416C22⋊Q8—62no—
417C22⋊Q8C22×D314yes—
418#121—34no—
419#121—68no—
420#121—62no—
421#120—68no—
422C4×Q8—34no—
423C4×Q8—62no—
424C4×D4—34no—
425C4×D4—34no—
426C4×D4—34no—
427C4×D4—62no—
428#117—22no—
429#117—68no—
430#117C22×D314yes—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4—61no—
437C2×C4⋊C4—61no—
438C2×C4⋊C4—61no—
439C2×C4⋊C4—61no—
440C2×C4⋊C4—61no—
441C2×C4⋊C4—61no—
442C2×C4⋊C4C22×D311yescharacteristic
443C2×C4⋊C4C22×D311yescharacteristic
444C2×C4⋊C4C22×D311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—31no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—68no—
450C2×C22⋊C4—61no—
451C2×C22⋊C4—61no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455C2×C22⋊C4—61no—
456C2×C42—21no—
457C2×C42—31no—
458C2×C42—61no—
459#107C22×D314yescomplemented
460#106—34no—
461#106C22×D314yescomplemented
462C4⋊C8—34no—
463#103—34no—
464#103—34no—
465#103C22×D314yescomplemented
466#103C22×D314yescomplemented
467#102—34no—
468#102—34no—
469#102—34no—
470#102—34no—
471#102—34no—
472#102—34no—
473C22⋊C8—34no—
474C22⋊C8C22×D314yes—
475C4×C8—34no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3C22×D412yes—
480C23×C3C22×D411yescharacteristic
481C22×D3—22no—
482C22×D3—24no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—48no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—48no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—84no—
495C22×D3—816no—
496C22×D3C22×D412yes—
497C3×Q8—22no—
498C3×Q8—22no—
499C3×Q8—42no—
500C2×C3×C4—22no—
501C2×C3×C4—24no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4C22×D412yes—
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C2×#4112yes—
515C2×C3×C4H(5,𝔽2)12yes—
516C2×C3×C4C2511yescharacteristic
517#67—44no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—42no—
524C2×Dic3—42no—
525C2×Dic3C22×D412yes—
526C2×Dic3C22×D412yes—
527C2×Dic3C22×D412yes—
528D12—24no—
529D12—22no—
530D12—22no—
531D12—22no—
532D12—48no—
533D12—48no—
534D12—42no—
535D12—84no—
536D12C2×#4114yes—
537C4×D3—24no—
538C4×D3—22no—
539C4×D3—22no—
540C4×D3—48no—
541C4×D3—48no—
542C4×D3—84no—
543Dic6—22no—
544Dic6—22no—
545Dic6—42no—
546C3×C8—22no—
547C3×C8—22no—
548C3⋊C8—22no—
549C3⋊C8—22no—
550C24—31no—
551C24—61no—
552C24—61no—
553C24—64no—
554C24—124no—
555C24—124no—
556C24—242no—
557C24D3×D411yescharacteristic
558#41—68no—
559#41—124no—
560#41—128no—
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—34no—
570C2×D4—34no—
571C2×D4—32no—
572C2×D4—32no—
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—122no—
587C2×D4—242no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—124no—
607C22×C4—124no—
608C22×C4—242no—
609C22×C4D3×D412yes—
610C22×C4D3×D411yescharacteristic
611C22×C4C23×D312yes—
612C22×C4C23×D311yescharacteristic
613Q16—124no—
614SD16—68no—
615SD16—124no—
616M16—124no—
617M16—124no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—32no—
621C2×C8—32no—
622C2×C8—62no—
623C2×C8—62no—
624C2×C8C23×D312yes—
625C2×C8C23×D312yes—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—34no—
631C4⋊C4—32no—
632C4⋊C4—64no—
633C4⋊C4—64no—
634C4⋊C4—64no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—61no—
638C4⋊C4—64no—
639C4⋊C4C23×D312yes—
640C4⋊C4C23×D312yes—
641C4⋊C4C23×D312yes—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—34no—
645C22⋊C4—34no—
646C22⋊C4—64no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C42—24no—
653C42—32no—
654C42—32no—
655C42—64no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—44no—
660C22×C3#54612yes—
661C22×C3#57512yes—
662C22×C3#57712yes—
663C22×C3C23×D411yescharacteristic
664C2×D3—22no—
665C2×D3—24no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—44no—
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—42no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—42no—
682C3×C4#54612yes—
683C3×C4C22×#4111yescharacteristic
684C3×C4C2×H(5,𝔽2)11yescharacteristic
685Dic3—22no—
686Dic3—22no—
687Dic3—22no—
688Dic3—42no—
689Dic3—42no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—32no—
694C23—62no—
695C23—64no—
696C23—62no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23—128no—
701C23—128no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23—244no—
708C23—2416no—
709C23C2×D3×D412yes—
710C23C2×D3×D411yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—62no—
715Q8—62no—
716Q8—122no—
717D4—34no—
718D4—64no—
719D4—62no—
720D4—62no—
721D4—62no—
722D4—128no—
723D4—128no—
724D4—124no—
725D4—122no—
726D4—244no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—64no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—128no—
751C2×C4—128no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—244no—
755C2×C4C2×D3×D412yes—
756C2×C4C2×D3×D411yescharacteristic
757C2×C4D3×#4112yes—
758C2×C4#100912yes—
759C2×C4C24×D311yescharacteristic
760C8—22no—
761C8—22no—
762C8—62no—
763C8—62no—
764C2×C3—42no—
765C2×C3#332314yescomplemented
766C2×C3C2×#54611yescharacteristic
767C2×C3C2×#57511yescharacteristic
768C2×C3C2×#57711yescharacteristic
769D3—42no—
770D3—44no—
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22—64no—
780C22—124no—
781C22—128no—
782C22—122no—
783C22—122no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—2416no—
788C22—244no—
789C22#565412yes—
790C22#577012yes—
791C22#577712yes—
792C22C22×D3×D411yescharacteristic
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—62no—
799C4—62no—
800C4—62no—
801C4—122no—
802C4—122no—
803C4#565412yes—
804C4C2×D3×#4111yescharacteristic
805C4C2×#100911yescharacteristic
806C3C2×#332311yescharacteristic, complemented, Sylow
807C2—42no—
808C2—122no—
809C2—124no—
810C2—242no—
811C2#8154914yesdirect product factor
812C2C2×#565411yescharacteristic
813C2C2×#577011yescharacteristic
814C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#485C2
socleC23×C3C22×D4
prime radicalC2×#5630C2
hypercenterC2×#485D3
hypocenterC3C2×#3323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#5529C2semidirect
3. C2×C3×#485C2semidirect
4. C2×#5052C2semidirect
5. C2×#5001C2semidirect
6. #81549C2direct (N × H)
7. C2×#4891C2semidirect
8. C2×#4886C2semidirect
9. C2×#4863C2semidirect
10. C2×#4852C2semidirect
11. C2×#4798C2semidirect
12. C2×#4808C2semidirect
13. C2×#4803C2semidirect
14. C2×#4800C2semidirect
15. C2×#4731C2semidirect
16. C2×#4729C2semidirect
23. C22×#216C22semidirect
29. C22×ΓL(1,𝔽25)C22semidirect
33. #5529C22semidirect
34. C2×#897C22semidirect
39. C2×D3×C4⋊C4C22semidirect
40. C2×#890C22semidirect
41. C2×#887C22semidirect
48. C3×#485C22semidirect
49. C2×C3×#107C22semidirect
50. C2×C3×#106C22semidirect
51. C2×C3×#103C22semidirect
52. C2×C3×#103C22semidirect
54. C2×#835C22semidirect
57. C2×(C2×D3)⋊C8C22semidirect
58. C2×Dic3⋊C8C22semidirect
59. C2×C8×Dic3C22semidirect
60. #5052C22semidirect
61. #5001C22semidirect
62. C2×#810C22semidirect
67. C2×#808C22semidirect
68. #4891C22semidirect
69. #4886C22semidirect
70. #4863C22semidirect
71. #4852C22semidirect
72. #4808C22semidirect
73. #4803C22semidirect
74. #4800C22semidirect
75. #4798C22semidirect
76. #4731C22semidirect
77. #4729C22semidirect
83. C2×#485D3semidirect
134. C2×#216C23semidirect
164. C2×ΓL(1,𝔽25)C23semidirect
166. #897C23semidirect
174. D3×C4⋊C4C23semidirect
176. #890C23semidirect
178. #887C23semidirect
185. C3×#107C23semidirect
186. C3×#106C23semidirect
187. C3×#103C23semidirect
188. C3×#103C23semidirect
190. #835C23semidirect
193. (C2×D3)⋊C8C23semidirect
194. Dic3⋊C8C23semidirect
195. C8×Dic3C23semidirect
196. #810C23semidirect
201. #808C23semidirect
233. #485C2×D3semidirect
243. C2×#107C2×D3semidirect
245. C2×#106C2×D3semidirect
251. C2×#103C2×D3semidirect
252. C2×#103C2×D3semidirect
459. #107C22×D3semidirect
461. #106C22×D3semidirect
465. #103C22×D3semidirect
466. #103C22×D3semidirect
765. C2×C3#3323semidirect
806. C3C2×#3323semidirect
811. C2#81549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56302
C2×#55292
C2×C3×#4852
C2×#50522
C2×#50012
#815492
C2×#48912
C2×#48862
C2×#48632
C2×#48522
C2×#47982
C2×#48082
C2×#48032
C2×#48002
C2×#47312
C2×#47292
C2×#33233