Finite Group Databasebeta

← C2×#78902 #11671985

Subgroups — C2×#78902 #11671985

Order 768.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5829C211yesmaximal, characteristic, complemented
2C2×#5514C211yesmaximal, characteristic, complemented
3C2×C3×#417C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5135C211yesmaximal, characteristic, complemented
6C2×#5128C211yesmaximal, characteristic, complemented
7C2×#4967C211yesmaximal, characteristic, complemented
8#78902C2116yesmaximal, direct product factor
9C2×#4819C211yesmaximal, characteristic, complemented
10C2×#4815C211yesmaximal, characteristic, complemented
11C2×#4812C211yesmaximal, characteristic, complemented
12C2×#4800C211yesmaximal, characteristic, complemented
13C2×#4773C211yesmaximal, characteristic, complemented
14C2×#4770C211yesmaximal, characteristic, complemented
15C2×#4763C211yesmaximal, characteristic, complemented
16C2×#4756C211yesmaximal, characteristic, complemented
17C2×#3322—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×D3×D4C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic, complemented
21C22×C3×C4⋊C4C2211yescharacteristic, complemented
22#5829—24no—
23#5829C2218yescomplemented
24C2×#947C2211yescharacteristic
25C2×#946C2211yescharacteristic
26C22×#215C2211yescharacteristic, complemented
27C2×#939—21no—
28C2×#937—21no—
29C2×D4×Dic3C2211yescharacteristic
30C22×#213C2211yescharacteristic
31C2×#930—21no—
32C2×#930C2211yescharacteristic
33C2×#930C2211yescharacteristic, complemented
34C2×#929—21no—
35C2×C4×#67—21no—
36C2×C4×#67C2211yescharacteristic
37C22×(C2×D3)⋊C4—21no—
38C22×D24C2211yescharacteristic
39C22×ΓL(1,𝔽25)C2211yescharacteristic
40#5514—24no—
41#5514C2218yescomplemented
42C2×#898—21no—
43C2×#895C2211yescharacteristic
44C2×#894—21no—
45C2×#893C2211yescharacteristic, complemented
46C2×#892C2211yescharacteristic
47C2×#890C2211yescharacteristic, complemented
48C3×#417C2218yescomplemented
49C2×C3×#103C2211yescharacteristic, complemented
50C2×C3×#103C2211yescharacteristic, complemented
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53#5238C2218yescomplemented
54C2×#835C2211yescharacteristic, complemented
55C2×#832C2211yescharacteristic
56C2×#830C2211yescharacteristic, complemented
57#5135C2218yescomplemented
58#5128C2218yescomplemented
59C2×#821C2211yescharacteristic
60C2×#821C2211yescharacteristic, complemented
61C2×(C2×D3)⋊C8C2211yescharacteristic
62C2×#817C2211yescharacteristic, complemented
63C2×Dic3⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic3C2211yescharacteristic, complemented
65#4967C2218yescomplemented
66C2×#809C2211yescharacteristic
67C2×#809C2211yescharacteristic
68C2×#807C2211yescharacteristic, complemented
69C2×#807C2211yescharacteristic, complemented
70#4819C2218yescomplemented
71#4815C2218yescomplemented
72#4812C2218yescomplemented
73#4800C2218yescomplemented
74#4773C2218yescomplemented
75#4770C2218yescomplemented
76#4763C2218yescomplemented
77#4756C2218yescomplemented
78C2×#553—31no—
79C2×#546—31no—
80#3322—316no—
81C2×#488—31no—
82C2×#485—31no—
83C2×#480—31no—
84C2×#478—31no—
85C2×#469—31no—
86C2×#468—31no—
87C2×#463—31no—
88C2×#449—31no—
89C2×#447—31no—
90C2×C4×D8—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×#67—21no—
108C22×#67D411yescharacteristic
109C23×Dic3—21no—
110C2×D3×D4—24no—
111C2×D3×D4—22no—
112C2×D3×D4—42no—
113C2×D3×D4C2314yes—
114C22×D12—21no—
115C22×D12C2311yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×C4×D3C2311yescharacteristic
119C2×C3×M16—42no—
120C2×C3×M16C2314yescomplemented
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2314yescomplemented
128C2×#217—21no—
129C2×#217D411yescharacteristic
130#947—22no—
131#947C2314yes—
132#946—22no—
133#946C2314yes—
134C2×#215—42no—
135C2×#215C2314yescomplemented
136#939—28no—
137#937—28no—
138D4×Dic3—22no—
139D4×Dic3C2314yes—
140C2×#213—24no—
141C2×#213C2314yes—
142#930—22no—
143#930—22no—
144#930—28no—
145#930C2314yes—
146#930C2314yescomplemented
147#929—28no—
148C4×#67—28no—
149C4×#67D414yes—
150C4×#67C2314yes—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4—21no—
154C2×(C2×D3)⋊C4—21no—
155C2×(C2×D3)⋊C4—21no—
156C2×(C2×D3)⋊C4—21no—
157C2×(C2×D3)⋊C4—21no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—28no—
160C2×(C2×D3)⋊C4D411yescharacteristic
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×Dic3⋊C4—21no—
165C2×Dic3⋊C4—21no—
166C2×Dic3⋊C4D411yescharacteristic
167C2×C4×Dic3—21no—
168C2×C4×Dic3C2311yescharacteristic
169C22×C3⋊C8C2311yescharacteristic
170C22×C3⋊C8C2311yescharacteristic
171C2×D24—42no—
172C2×D24C2314yes—
173C2×ΓL(1,𝔽25)—42no—
174C2×ΓL(1,𝔽25)C2314yes—
175#898—28no—
176#895—22no—
177#895C2314yes—
178#894—28no—
179#893—22no—
180#893C2314yescomplemented
181#892—22no—
182#892C2314yes—
183#890—22no—
184#890C2314yescomplemented
185C3×#103C2314yescomplemented
186C3×#103C2314yescomplemented
187C3×#102C2314yes—
188C3×#102C2314yes—
189#835C2314yescomplemented
190#832C2314yes—
191#830C2314yescomplemented
192#821C2314yes—
193#821C2314yescomplemented
194(C2×D3)⋊C8C2314yes—
195#817C2314yescomplemented
196Dic3⋊C8C2314yescomplemented
197C8×Dic3C2314yescomplemented
198#809C2314yes—
199#809C2314yes—
200#807C2314yescomplemented
201#807C2314yescomplemented
202C22×#41C2×D311yescharacteristic
203C23×D4—31no—
204C22×SD16—31no—
205C22×D8—31no—
206C22×D8—31no—
207C22×M16—31no—
208C22×M16C2×D311yescharacteristic, complemented
209#553—38no—
210#553—64no—
211#546—38no—
212#546—64no—
213C2×#126—61no—
214C2×#125—31no—
215C2×#124—31no—
216C2×#123—61no—
217C2×#123—61no—
218C2×C22⋊Q8—31no—
219C2×#121—31no—
220C2×#121—31no—
221C2×#121—31no—
222C2×#121—61no—
223C2×#121—61no—
224C2×#120—61no—
225C2×C4×D4—31no—
226C2×C4×D4—31no—
227C2×C4×D4—31no—
228C2×C4×D4—61no—
229C2×#117—31no—
230C22×C4⋊C4C2×D311yescharacteristic, complemented
231C22×C22⋊C4—61no—
232#488—38no—
233#485—38no—
234#480—38no—
235#478—38no—
236#469—38no—
237#468—38no—
238#463—38no—
239#449—38no—
240#447—38no—
241C4×D8—38no—
242#436—38no—
243C2×#107—31no—
244C2×#107—31no—
245C2×#106—31no—
246C2×C4⋊C8—31no—
247#418—38no—
248#417C2×D318yescomplemented
249C2×#103—31no—
250C2×#103C2×D311yescharacteristic, complemented
251C2×#103C2×D311yescharacteristic, complemented
252C2×#102—31no—
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—21no—
266C23×D3—24no—
267C23×D3—44no—
268C23×D3—44no—
269C23×D3—82no—
270C23×D3C2×D411yescharacteristic
271C3×#41—28no—
272C3×#41—44no—
273C3×#41—48no—
274C2×C3×Q8—21no—
275C2×C3×Q8—22no—
276C2×C3×Q8—22no—
277C2×C3×Q8C2412yes—
278C2×C3×D4—24no—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—44no—
282C2×C3×D4#4114yes—
283C2×C3×D4C2412yes—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—44no—
292C22×C3×C4—82no—
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2411yescharacteristic
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—42no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—82no—
304C2×#67C2×D414yes—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—24no—
308C22×Dic3—82no—
309C22×Dic3C2×D411yescharacteristic
310C22×Dic3C2×D411yescharacteristic
311C22×Dic3C2×D411yescharacteristic
312D3×D4—28no—
313D3×D4—44no—
314D3×D4—48no—
315C2×D12—22no—
316C2×D12—22no—
317C2×D12—22no—
318C2×D12—22no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12—24no—
322C2×D12—82no—
323C2×D12C2412yes—
324C2×D12C2412yes—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3—24no—
328C2×C4×D3—82no—
329C2×C4×D3C2×D412yes—
330C2×C4×D3C2412yes—
331C3×M16—44no—
332C2×C3×C8—22no—
333C2×C3×C8—22no—
334C2×C3×C8C2412yes—
335C2×C3×C8C2412yes—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4C2412yes—
340C3×C4⋊C4C2412yes—
341#217—24no—
342#217C2×D414yes—
343#215—44no—
344#213—28no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349(C2×D3)⋊C4—24no—
350(C2×D3)⋊C4—24no—
351(C2×D3)⋊C4—24no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4C2×D414yes—
354C4⋊Dic3—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—24no—
357C4⋊Dic3C2412yes—
358C4⋊Dic3C2412yes—
359Dic3⋊C4—24no—
360Dic3⋊C4—24no—
361Dic3⋊C4C2×D414yes—
362C4×Dic3—24no—
363C4×Dic3C2×D412yes—
364C4×Dic3C2412yes—
365C2×C3⋊C8—22no—
366C2×C3⋊C8—22no—
367C2×C3⋊C8C2412yes—
368C2×C3⋊C8C2412yes—
369D24—44no—
370ΓL(1,𝔽25)—44no—
371C25—61no—
372C2×#41—22no—
373C2×#41—24no—
374C2×#41—42no—
375C2×#41C22×D314yes—
376C22×Q8C22×D311yescharacteristic
377C22×D4—21no—
378C22×D4—31no—
379C22×D4—34no—
380C22×D4—31no—
381C22×D4—31no—
382C22×D4—61no—
383C22×D4—62no—
384C22×D4—61no—
385C22×D4—64no—
386C22×D4—61no—
387C22×D4—61no—
388C22×D4—122no—
389C22×D4C22×D311yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—31no—
393C23×C4—61no—
394C23×C4—61no—
395C23×C4C22×D311yescharacteristic
396C2×SD16—34no—
397C2×SD16—122no—
398C2×D8—34no—
399C2×D8—34no—
400C2×D8—64no—
401C2×D8—122no—
402C2×M16—34no—
403C2×M16—42no—
404C2×M16—122no—
405C2×M16C22×D314yescomplemented
406C22×C8—31no—
407C22×C8—31no—
408C22×C8C22×D311yescharacteristic
409C22×C8C22×D311yescharacteristic
410#126—68no—
411#125—34no—
412#125—62no—
413#124—34no—
414#124—62no—
415#123—68no—
416#123—68no—
417C22⋊Q8—34no—
418C22⋊Q8—62no—
419#121—34no—
420#121—34no—
421#121—34no—
422#121—68no—
423#121—62no—
424#121—68no—
425#121—62no—
426#121—62no—
427#120—68no—
428C4×D4—34no—
429C4×D4—34no—
430C4×D4—34no—
431C4×D4—34no—
432C4×D4—62no—
433C4×D4—62no—
434C4×D4—68no—
435#117—34no—
436#117—62no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—61no—
443C2×C4⋊C4—61no—
444C2×C4⋊C4—61no—
445C2×C4⋊C4C22×D311yescharacteristic
446C2×C4⋊C4C22×D311yescharacteristic
447C2×C4⋊C4C22×D314yescomplemented
448C2×C22⋊C4—31no—
449C2×C22⋊C4—31no—
450C2×C22⋊C4—68no—
451C2×C22⋊C4—61no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455C2×C22⋊C4—61no—
456C2×C22⋊C4—61no—
457C2×C22⋊C4—61no—
458C2×C22⋊C4—61no—
459C2×C22⋊C4—61no—
460C2×C42—31no—
461C2×C42—61no—
462#107—34no—
463#107—34no—
464#106—34no—
465C4⋊C8—34no—
466#103—34no—
467#103C22×D314yescomplemented
468#103C22×D314yescomplemented
469#102—34no—
470#102—34no—
471#102—34no—
472#102—34no—
473#102—34no—
474#102C22×D314yes—
475#102C22×D314yes—
476C22⋊C8—34no—
477C22⋊C8—34no—
478C4×C8—34no—
479C23×C3—24no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—42no—
485C23×C3—42no—
486C23×C3C22×D412yes—
487C23×C3C22×D411yescharacteristic
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—48no—
494C22×D3—48no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—84no—
502C22×D3—816no—
503C22×D3C22×D412yes—
504C3×Q8—22no—
505C3×Q8—22no—
506C3×Q8—42no—
507C3×D4—24no—
508C3×D4—22no—
509C3×D4—48no—
510C3×D4C2×#4114yes—
511C2×C3×C4—22no—
512C2×C3×C4—24no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—48no—
519C2×C3×C4—42no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—84no—
523C2×C3×C4C22×D412yes—
524C2×C3×C4C22×D411yescharacteristic
525C2×C3×C4C2×#4112yes—
526C2×C3×C4H(5,𝔽2)12yes—
527C2×C3×C4C2511yescharacteristic
528#67—44no—
529#67—48no—
530#67—48no—
531#67—84no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539C2×Dic3—84no—
540C2×Dic3C22×D412yes—
541C2×Dic3C22×D412yes—
542C2×Dic3C22×D412yes—
543D12—22no—
544D12—22no—
545D12—22no—
546D12—22no—
547D12—42no—
548D12—42no—
549D12—84no—
550C4×D3—24no—
551C4×D3—22no—
552C4×D3—22no—
553C4×D3—84no—
554C3×C8—22no—
555C3×C8—22no—
556C3⋊C8—22no—
557C3⋊C8—22no—
558C24—21no—
559C24—31no—
560C24—64no—
561C24—61no—
562C24—61no—
563C24—124no—
564C24—124no—
565C24—242no—
566C24D3×D411yescharacteristic
567#41—28no—
568#41—44no—
569#41—48no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8C23×D312yes—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—34no—
578C2×D4—32no—
579C2×D4—32no—
580C2×D4—44no—
581C2×D4—64no—
582C2×D4—64no—
583C2×D4—68no—
584C2×D4—64no—
585C2×D4—64no—
586C2×D4—62no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—62no—
591C2×D4—62no—
592C2×D4—124no—
593C2×D4—128no—
594C2×D4—122no—
595C2×D4—124no—
596C2×D4—124no—
597C2×D4—242no—
598C2×D4—242no—
599C2×D4#23514yes—
600C2×D4C23×D312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—32no—
612C22×C4—32no—
613C22×C4—44no—
614C22×C4—64no—
615C22×C4—64no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—82no—
621C22×C4—242no—
622C22×C4—242no—
623C22×C4D3×D412yes—
624C22×C4D3×D411yescharacteristic
625C22×C4C23×D312yes—
626C22×C4C23×D311yescharacteristic
627SD16—124no—
628D8—68no—
629D8—124no—
630M16—44no—
631M16—124no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—32no—
635C2×C8—32no—
636C2×C8—62no—
637C2×C8—62no—
638C2×C8C23×D312yes—
639C2×C8C23×D312yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—24no—
643C4⋊C4—34no—
644C4⋊C4—32no—
645C4⋊C4—32no—
646C4⋊C4—64no—
647C4⋊C4—64no—
648C4⋊C4—64no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4C23×D312yes—
652C4⋊C4C23×D312yes—
653C22⋊C4—34no—
654C22⋊C4—34no—
655C22⋊C4—64no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—64no—
660C22⋊C4—64no—
661C22⋊C4—64no—
662C22⋊C4—64no—
663C22⋊C4—64no—
664C42—32no—
665C42—32no—
666C42—64no—
667C22×C3—24no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—48no—
672C22×C3—44no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3#54612yes—
676C22×C3#57512yes—
677C22×C3#57612yes—
678C22×C3C23×D411yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—44no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3—816no—
690C2×D3—84no—
691C2×D3—84no—
692C3×C4—22no—
693C3×C4—42no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4#54612yes—
697C3×C4C22×#4111yescharacteristic
698C3×C4C2×H(5,𝔽2)11yescharacteristic
699Dic3—22no—
700Dic3—22no—
701Dic3—22no—
702Dic3—42no—
703Dic3—42no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—32no—
710C23—42no—
711C23—42no—
712C23—62no—
713C23—62no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—128no—
718C23—128no—
719C23—122no—
720C23—122no—
721C23—122no—
722C23—122no—
723C23—122no—
724C23—122no—
725C23—244no—
726C23—2416no—
727C23C2×D3×D412yes—
728C23C2×D3×D411yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—42no—
732D4—22no—
733D4—24no—
734D4—48no—
735D4—62no—
736D4—62no—
737D4—62no—
738D4—62no—
739D4—124no—
740D4—128no—
741D4—128no—
742D4—122no—
743D4—122no—
744D4—244no—
745D4—244no—
746D4C2×#23514yes—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—48no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—64no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—84no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—244no—
773C2×C4—244no—
774C2×C4C2×#23512yes—
775C2×C4C2×D3×D412yes—
776C2×C4C2×D3×D411yescharacteristic
777C2×C4#100412yes—
778C2×C4C24×D311yescharacteristic
779C8—22no—
780C8—22no—
781C8—62no—
782C8—62no—
783C2×C3—44no—
784C2×C3—42no—
785C2×C3#332214yescomplemented
786C2×C3C2×#54611yescharacteristic
787C2×C3C2×#57511yescharacteristic
788C2×C3C2×#57611yescharacteristic
789D3—42no—
790D3—82no—
791D3—82no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—44no—
797C22—48no—
798C22—42no—
799C22—42no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—124no—
804C22—122no—
805C22—122no—
806C22—122no—
807C22—122no—
808C22—122no—
809C22—122no—
810C22—2416no—
811C22—244no—
812C22—244no—
813C22#549012yes—
814C22#577412yes—
815C22#577712yes—
816C22C22×D3×D411yescharacteristic
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—62no—
822C4—62no—
823C4—62no—
824C4—122no—
825C4—122no—
826C4#549012yes—
827C4C22×#23511yescharacteristic
828C4C2×#100411yescharacteristic
829C3C2×#332211yescharacteristic, complemented, Sylow
830C2—42no—
831C2—44no—
832C2—122no—
833C2—242no—
834C2—242no—
835C2#7890214yesdirect product factor
836C2C2×#549011yescharacteristic
837C2C2×#577411yescharacteristic
838C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#417C2
socleC23×C3C22×D4
hypercenterC2×#417D3
hypocenterC3C2×#3322
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
1. C2×#5829C2semidirect
2. C2×#5514C2semidirect
3. C2×C3×#417C2semidirect
4. C2×#5238C2semidirect
5. C2×#5135C2semidirect
6. C2×#5128C2semidirect
7. C2×#4967C2semidirect
8. #78902C2direct (N × H)
9. C2×#4819C2semidirect
10. C2×#4815C2semidirect
11. C2×#4812C2semidirect
12. C2×#4800C2semidirect
13. C2×#4773C2semidirect
14. C2×#4770C2semidirect
15. C2×#4763C2semidirect
16. C2×#4756C2semidirect
20. C22×C3×M16C22semidirect
21. C22×C3×C4⋊C4C22semidirect
23. #5829C22semidirect
26. C22×#215C22semidirect
33. C2×#930C22semidirect
41. #5514C22semidirect
45. C2×#893C22semidirect
47. C2×#890C22semidirect
48. C3×#417C22semidirect
49. C2×C3×#103C22semidirect
50. C2×C3×#103C22semidirect
53. #5238C22semidirect
54. C2×#835C22semidirect
56. C2×#830C22semidirect
57. #5135C22semidirect
58. #5128C22semidirect
60. C2×#821C22semidirect
62. C2×#817C22semidirect
63. C2×Dic3⋊C8C22semidirect
64. C2×C8×Dic3C22semidirect
65. #4967C22semidirect
68. C2×#807C22semidirect
69. C2×#807C22semidirect
70. #4819C22semidirect
71. #4815C22semidirect
72. #4812C22semidirect
73. #4800C22semidirect
74. #4773C22semidirect
75. #4770C22semidirect
76. #4763C22semidirect
77. #4756C22semidirect
92. C2×#417D3semidirect
120. C2×C3×M16C23semidirect
127. C2×C3×C4⋊C4C23semidirect
135. C2×#215C23semidirect
146. #930C23semidirect
180. #893C23semidirect
184. #890C23semidirect
185. C3×#103C23semidirect
186. C3×#103C23semidirect
189. #835C23semidirect
191. #830C23semidirect
193. #821C23semidirect
195. #817C23semidirect
196. Dic3⋊C8C23semidirect
197. C8×Dic3C23semidirect
200. #807C23semidirect
201. #807C23semidirect
208. C22×M16C2×D3semidirect
230. C22×C4⋊C4C2×D3semidirect
248. #417C2×D3semidirect
250. C2×#103C2×D3semidirect
251. C2×#103C2×D3semidirect
405. C2×M16C22×D3semidirect
447. C2×C4⋊C4C22×D3semidirect
467. #103C22×D3semidirect
468. #103C22×D3semidirect
785. C2×C3#3322semidirect
829. C3C2×#3322semidirect
835. C2#78902direct (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×#55142
C2×C3×#4172
C2×#52382
C2×#51352
C2×#51282
C2×#49672
#789022
C2×#48192
C2×#48152
C2×#48122
C2×#48002
C2×#47732
C2×#47702
C2×#47632
C2×#47562
C2×#33223