Finite Group Databasebeta

← C2×#78903 #11672001

Subgroups — C2×#78903 #11672001

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×#5829C211yesmaximal, characteristic
2C2×#5513C211yesmaximal, characteristic, complemented
3C2×C3×#417C211yesmaximal, characteristic, complemented
4C2×#5239C211yesmaximal, characteristic, complemented
5C2×#5134C211yesmaximal, characteristic, complemented
6C2×#5128C211yesmaximal, characteristic, complemented
7C2×#4968C211yesmaximal, characteristic, complemented
8#78903C2116yesmaximal, direct product factor
9C2×#4798C211yesmaximal, characteristic, complemented
10C2×#4816C211yesmaximal, characteristic, complemented
11C2×#4800C211yesmaximal, characteristic, complemented
12C2×#4814C211yesmaximal, characteristic, complemented
13C2×#4776C211yesmaximal, characteristic, complemented
14C2×#4770C211yesmaximal, characteristic, complemented
15C2×#4766C211yesmaximal, characteristic, complemented
16C2×#4758C211yesmaximal, characteristic, complemented
17C2×#3323—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×D3×D4C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic, complemented
21C22×C3×C4⋊C4C2211yescharacteristic, complemented
22#5829—24no—
23#5829C2218yes—
24C2×#947C2211yescharacteristic
25C2×#946C2211yescharacteristic
26C22×#216C2211yescharacteristic, complemented
27C2×#939—21no—
28C2×#937—21no—
29C2×D4×Dic3C2211yescharacteristic
30C22×#214C2211yescharacteristic
31C2×#930C2211yescharacteristic
32C2×#929—21no—
33C2×#929—21no—
34C2×C4×#67C2211yescharacteristic
35C22×(C2×D3)⋊C4—21no—
36C2×#926—21no—
37C2×#924C2211yescharacteristic, complemented
38C22×#204C2211yescharacteristic
39C22×ΓL(1,𝔽25)C2211yescharacteristic
40#5513—24no—
41#5513C2218yescomplemented
42C2×#898—21no—
43C2×#897C2211yescharacteristic
44C2×#892C2211yescharacteristic
45C2×#890C2211yescharacteristic, complemented
46C2×#889—21no—
47C2×#887C2211yescharacteristic, complemented
48C3×#417C2218yescomplemented
49C2×C3×#103C2211yescharacteristic, complemented
50C2×C3×#103C2211yescharacteristic, complemented
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53#5239C2218yescomplemented
54C2×#835C2211yescharacteristic, complemented
55C2×#832C2211yescharacteristic
56C2×#830C2211yescharacteristic, complemented
57#5134C2218yescomplemented
58#5128C2218yescomplemented
59C2×#821C2211yescharacteristic
60C2×(C2×D3)⋊C8C2211yescharacteristic
61C2×#818C2211yescharacteristic, complemented
62C2×#816C2211yescharacteristic, complemented
63C2×Dic3⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic3C2211yescharacteristic, complemented
65#4968C2218yescomplemented
66C2×#809C2211yescharacteristic
67C2×#809C2211yescharacteristic
68C2×#808C2211yescharacteristic, complemented
69C2×#808C2211yescharacteristic, complemented
70#4816C2218yescomplemented
71#4814C2218yescomplemented
72#4800C2218yescomplemented
73#4798C2218yescomplemented
74#4776C2218yescomplemented
75#4770C2218yescomplemented
76#4766C2218yescomplemented
77#4758C2218yescomplemented
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×#436—31no—
92C2×#417D311yescharacteristic, complemented
93C2×#418—31no—
94C24×D3—21no—
95C2×C3×#41—22no—
96C2×C3×#41—24no—
97C2×C3×#41—42no—
98C2×C3×#41C2314yes—
99C22×C3×Q8C2311yescharacteristic
100C22×C3×D4—21no—
101C22×C3×D4C2311yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C22×#67—21no—
106C22×#67—21no—
107C22×#67D411yescharacteristic
108C23×Dic3—21no—
109C2×D3×D4—24no—
110C2×D3×D4—22no—
111C2×D3×D4—42no—
112C2×D3×D4C2314yes—
113C22×D12C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×Dic6C2311yescharacteristic
116C2×C3×M16—42no—
117C2×C3×M16C2314yescomplemented
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2314yescomplemented
125C2×#217—21no—
126C2×#217—21no—
127C2×#217D411yescharacteristic
128#947—22no—
129#947C2314yes—
130#946—22no—
131#946C2314yes—
132C2×#216—42no—
133C2×#216C2314yescomplemented
134#939—28no—
135#937—28no—
136D4×Dic3—22no—
137D4×Dic3C2314yes—
138C2×#214—24no—
139C2×#214C2314yes—
140#930—22no—
141#930C2314yes—
142#929—28no—
143#929—28no—
144C4×#67D414yes—
145C4×#67C2314yes—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—28no—
153C2×(C2×D3)⋊C4D411yescharacteristic
154#926—28no—
155C2×C4⋊Dic3—21no—
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159#924—22no—
160#924C2314yescomplemented
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—21no—
163C2×Dic3⋊C4—21no—
164C2×Dic3⋊C4—21no—
165C2×Dic3⋊C4D411yescharacteristic
166C2×C4×Dic3—21no—
167C2×C4×Dic3—21no—
168C2×C4×Dic3C2311yescharacteristic
169C22×C3⋊C8C2311yescharacteristic
170C22×C3⋊C8C2311yescharacteristic
171C2×#204—42no—
172C2×#204C2314yes—
173C2×ΓL(1,𝔽25)—42no—
174C2×ΓL(1,𝔽25)C2314yes—
175#898—28no—
176#897—22no—
177#897C2314yes—
178#892—22no—
179#892C2314yes—
180#890—22no—
181#890C2314yescomplemented
182#889—28no—
183#887—22no—
184#887C2314yescomplemented
185C3×#103C2314yescomplemented
186C3×#103C2314yescomplemented
187C3×#102C2314yes—
188C3×#102C2314yes—
189#835C2314yescomplemented
190#832C2314yes—
191#830C2314yescomplemented
192#821C2314yes—
193(C2×D3)⋊C8C2314yes—
194#818C2314yescomplemented
195#816C2314yescomplemented
196Dic3⋊C8C2314yescomplemented
197C8×Dic3C2314yescomplemented
198#809C2314yes—
199#809C2314yes—
200#808C2314yescomplemented
201#808C2314yescomplemented
202C22×#41C2×D311yescharacteristic
203C23×D4—31no—
204C22×Q16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×M16—31no—
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×D4—31no—
228C2×#117—31no—
229C2×#117—61no—
230C22×C4⋊C4C2×D311yescharacteristic, complemented
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#436—38no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×C4⋊C8—31no—
247#418—38no—
248#417C2×D318yescomplemented
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×#102C2×D311yescharacteristic
258C2×#102C2×D311yescharacteristic
259C2×C22⋊C8—31no—
260C2×C22⋊C8—31no—
261C2×C4×C8—31no—
262C24×C3—21no—
263C24×C3C2×D411yescharacteristic
264C23×D3—21no—
265C23×D3—24no—
266C23×D3—44no—
267C23×D3—44no—
268C23×D3—82no—
269C23×D3C2×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—24no—
278C2×C3×D4—21no—
279C2×C3×D4—22no—
280C2×C3×D4—44no—
281C2×C3×D4#4114yes—
282C2×C3×D4C2412yes—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—44no—
291C22×C3×C4—44no—
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2411yescharacteristic
296C2×#67—24no—
297C2×#67—24no—
298C2×#67—42no—
299C2×#67—44no—
300C2×#67—82no—
301C2×#67C2×D414yes—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—24no—
306C22×Dic3—82no—
307C22×Dic3C2×D411yescharacteristic
308C22×Dic3C2×D411yescharacteristic
309C22×Dic3C2×D411yescharacteristic
310D3×D4—28no—
311D3×D4—44no—
312D3×D4—48no—
313C2×D12—22no—
314C2×D12—22no—
315C2×D12—21no—
316C2×D12C2412yes—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3C2×D412yes—
320C2×C4×D3C2412yes—
321C2×Dic6—22no—
322C2×Dic6—22no—
323C2×Dic6—21no—
324C2×Dic6C2412yes—
325C3×M16—44no—
326C2×C3×C8—22no—
327C2×C3×C8—22no—
328C2×C3×C8C2412yes—
329C2×C3×C8C2412yes—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—24no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4C2412yes—
334C3×C4⋊C4C2412yes—
335#217—24no—
336#217—24no—
337#217C2×D414yes—
338#216—44no—
339#214—28no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4C2×D414yes—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—24no—
350C4⋊Dic3—24no—
351C4⋊Dic3C2412yes—
352C4⋊Dic3C2412yes—
353Dic3⋊C4—24no—
354Dic3⋊C4—24no—
355Dic3⋊C4—24no—
356Dic3⋊C4—24no—
357Dic3⋊C4C2×D414yes—
358C4×Dic3—24no—
359C4×Dic3—24no—
360C4×Dic3C2×D412yes—
361C4×Dic3C2412yes—
362C2×C3⋊C8—22no—
363C2×C3⋊C8—22no—
364C2×C3⋊C8C2412yes—
365C2×C3⋊C8C2412yes—
366#204—44no—
367ΓL(1,𝔽25)—44no—
368C25—61no—
369C2×#41—22no—
370C2×#41—24no—
371C2×#41—42no—
372C2×#41C22×D314yes—
373C22×Q8—31no—
374C22×Q8C22×D311yescharacteristic
375C22×D4—21no—
376C22×D4—31no—
377C22×D4—34no—
378C22×D4—31no—
379C22×D4—62no—
380C22×D4—61no—
381C22×D4—64no—
382C22×D4—61no—
383C22×D4—122no—
384C22×D4C22×D311yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—31no—
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—42no—
398C2×M16—122no—
399C2×M16C22×D314yescomplemented
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#126—68no—
405#125—34no—
406#125—62no—
407#125—68no—
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—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—34no—
429#117—68no—
430#117—62no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
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×D314yescomplemented
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—68no—
448C2×C22⋊C4—61no—
449C2×C22⋊C4—61no—
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—31no—
457C2×C42—61no—
458C2×C42—61no—
459#107—34no—
460#106—34no—
461#106—34no—
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#102C22×D314yes—
472#102C22×D314yes—
473C22⋊C8—34no—
474C22⋊C8—34no—
475C4×C8—34no—
476C23×C3—24no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—42no—
482C23×C3—42no—
483C23×C3C22×D412yes—
484C23×C3C22×D411yescharacteristic
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—48no—
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—
500C3×D4—24no—
501C3×D4—22no—
502C3×D4—48no—
503C3×D4C2×#4114yes—
504C2×C3×C4—22no—
505C2×C3×C4—24no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—48no—
512C2×C3×C4—48no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C2×#4112yes—
519C2×C3×C4H(5,𝔽2)12yes—
520C2×C3×C4C2511yescharacteristic
521#67—44no—
522#67—48no—
523#67—84no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—42no—
533C2×Dic3—84no—
534C2×Dic3C22×D412yes—
535C2×Dic3C22×D412yes—
536C2×Dic3C22×D412yes—
537D12—22no—
538D12—22no—
539D12—42no—
540C4×D3—24no—
541C4×D3—22no—
542C4×D3—22no—
543Dic6—22no—
544Dic6—22no—
545Dic6—42no—
546C3×C8—22no—
547C3×C8—22no—
548C3⋊C8—22no—
549C3⋊C8—22no—
550C24—21no—
551C24—31no—
552C24—64no—
553C24—61no—
554C24—124no—
555C24—124no—
556C24—242no—
557C24D3×D411yescharacteristic
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—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—34no—
573C2×D4—32no—
574C2×D4—44no—
575C2×D4—64no—
576C2×D4—68no—
577C2×D4—64no—
578C2×D4—62no—
579C2×D4—61no—
580C2×D4—62no—
581C2×D4—124no—
582C2×D4—128no—
583C2×D4—122no—
584C2×D4—124no—
585C2×D4—242no—
586C2×D4#23514yes—
587C2×D4C23×D312yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—64no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—242no—
609C22×C4D3×D412yes—
610C22×C4D3×D411yescharacteristic
611C22×C4C23×D312yes—
612C22×C4C23×D311yescharacteristic
613Q16—124no—
614SD16—68no—
615SD16—124no—
616M16—44no—
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—21no—
627C4⋊C4—21no—
628C4⋊C4—24no—
629C4⋊C4—34no—
630C4⋊C4—32no—
631C4⋊C4—32no—
632C4⋊C4—64no—
633C4⋊C4—64no—
634C4⋊C4—64no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—64no—
640C4⋊C4C23×D312yes—
641C4⋊C4C23×D312yes—
642C22⋊C4—34no—
643C22⋊C4—34no—
644C22⋊C4—64no—
645C22⋊C4—64no—
646C22⋊C4—64no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C42—32no—
653C42—32no—
654C42—64no—
655C42—64no—
656C22×C3—24no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—48no—
661C22×C3—44no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3#54612yes—
665C22×C3#57512yes—
666C22×C3#57712yes—
667C22×C3C23×D411yescharacteristic
668C2×D3—22no—
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—44no—
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#54612yes—
682C3×C4C22×#4111yescharacteristic
683C3×C4C2×H(5,𝔽2)11yescharacteristic
684Dic3—22no—
685Dic3—22no—
686Dic3—22no—
687Dic3—42no—
688Dic3—42no—
689Dic3—42no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—32no—
696C23—42no—
697C23—42no—
698C23—62no—
699C23—62no—
700C23—62no—
701C23—62no—
702C23—128no—
703C23—128no—
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—22no—
718D4—24no—
719D4—48no—
720D4—62no—
721D4—62no—
722D4—124no—
723D4—128no—
724D4—122no—
725D4—244no—
726D4C2×#23514yes—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—64no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—244no—
755C2×C4C2×#23512yes—
756C2×C4C2×D3×D412yes—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4#100412yes—
759C2×C4C24×D311yescharacteristic
760C8—22no—
761C8—22no—
762C8—62no—
763C8—62no—
764C2×C3—44no—
765C2×C3—42no—
766C2×C3#332314yescomplemented
767C2×C3C2×#54611yescharacteristic
768C2×C3C2×#57511yescharacteristic
769C2×C3C2×#57711yescharacteristic
770D3—42no—
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—44no—
777C22—48no—
778C22—42no—
779C22—42no—
780C22—62no—
781C22—62no—
782C22—62no—
783C22—124no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—2416no—
788C22—244no—
789C22#549012yes—
790C22#577312yes—
791C22#577812yes—
792C22C22×D3×D411yescharacteristic
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—62no—
798C4—62no—
799C4—62no—
800C4—122no—
801C4—122no—
802C4—122no—
803C4#549012yes—
804C4C22×#23511yescharacteristic
805C4C2×#100411yescharacteristic
806C3C2×#332311yescharacteristic, complemented, Sylow
807C2—42no—
808C2—44no—
809C2—122no—
810C2—242no—
811C2#7890314yesdirect product factor
812C2C2×#549011yescharacteristic
813C2C2×#577311yescharacteristic
814C2C2×#577811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#417C2
socleC23×C3C22×D4
prime radicalC2×#5829C2
hypercenterC2×#417D3
hypocenterC3C2×#3323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#5513C2semidirect
3. C2×C3×#417C2semidirect
4. C2×#5239C2semidirect
5. C2×#5134C2semidirect
6. C2×#5128C2semidirect
7. C2×#4968C2semidirect
8. #78903C2direct (N × H)
9. C2×#4798C2semidirect
10. C2×#4816C2semidirect
11. C2×#4800C2semidirect
12. C2×#4814C2semidirect
13. C2×#4776C2semidirect
14. C2×#4770C2semidirect
15. C2×#4766C2semidirect
16. C2×#4758C2semidirect
20. C22×C3×M16C22semidirect
21. C22×C3×C4⋊C4C22semidirect
26. C22×#216C22semidirect
37. C2×#924C22semidirect
41. #5513C22semidirect
45. C2×#890C22semidirect
47. C2×#887C22semidirect
48. C3×#417C22semidirect
49. C2×C3×#103C22semidirect
50. C2×C3×#103C22semidirect
53. #5239C22semidirect
54. C2×#835C22semidirect
56. C2×#830C22semidirect
57. #5134C22semidirect
58. #5128C22semidirect
61. C2×#818C22semidirect
62. C2×#816C22semidirect
63. C2×Dic3⋊C8C22semidirect
64. C2×C8×Dic3C22semidirect
65. #4968C22semidirect
68. C2×#808C22semidirect
69. C2×#808C22semidirect
70. #4816C22semidirect
71. #4814C22semidirect
72. #4800C22semidirect
73. #4798C22semidirect
74. #4776C22semidirect
75. #4770C22semidirect
76. #4766C22semidirect
77. #4758C22semidirect
92. C2×#417D3semidirect
117. C2×C3×M16C23semidirect
124. C2×C3×C4⋊C4C23semidirect
133. C2×#216C23semidirect
160. #924C23semidirect
181. #890C23semidirect
184. #887C23semidirect
185. C3×#103C23semidirect
186. C3×#103C23semidirect
189. #835C23semidirect
191. #830C23semidirect
194. #818C23semidirect
195. #816C23semidirect
196. Dic3⋊C8C23semidirect
197. C8×Dic3C23semidirect
200. #808C23semidirect
201. #808C23semidirect
208. C22×M16C2×D3semidirect
230. C22×C4⋊C4C2×D3semidirect
248. #417C2×D3semidirect
251. C2×#103C2×D3semidirect
252. C2×#103C2×D3semidirect
399. C2×M16C22×D3semidirect
444. C2×C4⋊C4C22×D3semidirect
465. #103C22×D3semidirect
466. #103C22×D3semidirect
766. C2×C3#3323semidirect
806. C3C2×#3323semidirect
811. C2#78903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58292
C2×#55132
C2×C3×#4172
C2×#52392
C2×#51342
C2×#51282
C2×#49682
#789032
C2×#47982
C2×#48162
C2×#48002
C2×#48142
C2×#47762
C2×#47702
C2×#47662
C2×#47582
C2×#33233