Finite Group Databasebeta

← C2×#81332 #11671908

Subgroups — C2×#81332 #11671908

Order 768.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5599C211yesmaximal, characteristic
2C2×#5513C211yesmaximal, characteristic, complemented
3C2×C3×#481C211yesmaximal, characteristic, complemented
4C2×#5042C211yesmaximal, characteristic, complemented
5C2×#4966C211yesmaximal, characteristic, complemented
6#81332C2116yesmaximal, direct product factor
7C2×#4857C211yesmaximal, characteristic, complemented
8C2×#4866C211yesmaximal, characteristic, complemented
9C2×#4864C211yesmaximal, characteristic, complemented
10C2×#4853C211yesmaximal, characteristic, complemented
11C2×#4762C211yesmaximal, characteristic, complemented
12C2×#4783C211yesmaximal, characteristic, complemented
13C2×#4772C211yesmaximal, characteristic, complemented
14C2×#4764C211yesmaximal, characteristic, complemented
15C2×#4733C211yesmaximal, characteristic, complemented
16C2×#4728C211yesmaximal, characteristic, complemented
17C2×#3317—31nomaximal, Sylow
18C22×#237C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C2×#940—21no—
23C2×#940C2211yescharacteristic
24C2×#939—21no—
25C22×#214C2211yescharacteristic
26C2×#929—21no—
27C2×C4×#67C2211yescharacteristic
28C2×#926—21no—
29C2×#924C2211yescharacteristic
30C22×#208C2211yescharacteristic
31C22×Dic12C2211yescharacteristic
32C22×#204C2211yescharacteristic
33C22×D3×C8C2211yescharacteristic
34#5599—24no—
35#5599C2218yes—
36#5513—24no—
37#5513C2218yescomplemented
38C2×#898—21no—
39C2×#897C2211yescharacteristic
40C2×#895C2211yescharacteristic
41C2×#892C2211yescharacteristic
42C2×#890C2211yescharacteristic
43C2×#889—21no—
44C2×#887C2211yescharacteristic
45C2×#887C2211yescharacteristic
46C2×#884—21no—
47C2×#67⋊C4—21no—
48C3×#481C2218yescomplemented
49C2×C3×#106C2211yescharacteristic
50C2×C3×#106C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×#832C2211yescharacteristic
55C2×#821C2211yescharacteristic
56C2×(C2×D3)⋊C8C2211yescharacteristic
57C2×#816C2211yescharacteristic
58C2×#815C2211yescharacteristic
59C2×Dic3⋊C8C2211yescharacteristic
60#5042C2218yescomplemented
61C2×#810C2211yescharacteristic
62C2×#810C2211yescharacteristic
63C2×#810C2211yescharacteristic
64#4966C2218yescomplemented
65C2×#809C2211yescharacteristic
66C2×#809C2211yescharacteristic
67C2×#807C2211yescharacteristic
68#4866C2218yescomplemented
69#4864C2218yescomplemented
70#4857C2218yescomplemented
71#4853C2218yescomplemented
72#4783C2218yescomplemented
73#4772C2218yescomplemented
74#4764C2218yescomplemented
75#4762C2218yescomplemented
76#4733C2218yescomplemented
77#4728C2218yescomplemented
78C2×#552—31no—
79C2×#550—31no—
80#3317—316no—
81C2×#490—31no—
82C2×#481D311yescharacteristic, complemented
83C2×#482—31no—
84C2×#479—31no—
85C2×#468—31no—
86C2×#465—31no—
87C2×#460—31no—
88C2×#452—31no—
89C2×#452—31no—
90C2×#441—31no—
91C2×#435—31no—
92C2×#417—31no—
93C2×#416—31no—
94C22×C3×D4—21no—
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C22×#67—21no—
102C22×#67D411yescharacteristic
103C23×Dic3—21no—
104C2×#237—22no—
105C2×#237—24no—
106C2×#237—42no—
107C2×#237C2314yes—
108C2×#235—22no—
109C2×#235—24no—
110C2×#235—42no—
111C2×#235C2314yes—
112C22×D12—21no—
113C22×D12C2311yescharacteristic
114C22×C4×D3—21no—
115C22×C4×D3C2311yescharacteristic
116C22×Dic6C2311yescharacteristic
117C22×Dic6C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C3×#121—22no—
121C3×#121C2314yes—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C22⋊C4—21no—
129C2×#217—21no—
130C2×#217D411yescharacteristic
131#940—28no—
132#940—22no—
133#940C2314yes—
134#939—28no—
135C2×#214—42no—
136C2×#214C2314yes—
137#929—28no—
138C4×#67D414yes—
139C4×#67C2314yes—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4D411yescharacteristic
144#926—28no—
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3C2311yescharacteristic
148#924—22no—
149#924C2314yes—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4—21no—
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4—21no—
154C2×Dic3⋊C4D411yescharacteristic
155C2×C4×Dic3—21no—
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C2×#208—42no—
160C2×#208C2314yes—
161C22×C3⋊C8C2311yescharacteristic
162C22×C3⋊C8C2311yescharacteristic
163C2×Dic12—24no—
164C2×Dic12C2314yes—
165C2×#204—42no—
166C2×#204C2314yes—
167C2×D3×C8—42no—
168C2×D3×C8C2314yes—
169#898—28no—
170#897—22no—
171#897C2314yes—
172#895—22no—
173#895C2314yes—
174#892—22no—
175#892C2314yes—
176#890—22no—
177#890C2314yes—
178#889—28no—
179#887—22no—
180#887—22no—
181#887C2314yes—
182#887C2314yes—
183#884—28no—
184#67⋊C4—28no—
185C3×#106C2314yes—
186C3×#106C2314yes—
187C3×#102C2314yes—
188C3×#102C2314yes—
189C3×C22⋊C8C2314yes—
190#832C2314yes—
191#821C2314yes—
192(C2×D3)⋊C8C2314yes—
193#816C2314yes—
194#815C2314yes—
195Dic3⋊C8C2314yes—
196#810C2314yes—
197#810C2314yes—
198#810C2314yes—
199#809C2314yes—
200#809C2314yes—
201#807C2314yes—
202C22×#41—31no—
203C22×#41—31no—
204C22×Q16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×M16—31no—
208C23×C8—31no—
209#552—38no—
210#552—64no—
211#550—38no—
212#550—64no—
213C2×#127—31no—
214C2×#127—61no—
215C2×#126—61no—
216C2×#125—31no—
217C2×#125—61no—
218C2×#123—61no—
219C2×C22⋊Q8—31no—
220C2×C22⋊Q8—31no—
221C2×#121—31no—
222C2×#121—61no—
223C2×#121—61no—
224C2×#121C2×D311yescharacteristic
225C2×C4×Q8—31no—
226C2×C4×Q8—31no—
227C2×C4×D4—31no—
228C2×C4×D4—61no—
229C2×#117—31no—
230C2×#117—61no—
231C22×C4⋊C4C2×D311yescharacteristic
232#490—38no—
233#482—38no—
234#481C2×D318yescomplemented
235#479—38no—
236#468—38no—
237#465—38no—
238#460—38no—
239#452—38no—
240#452—38no—
241#441—38no—
242#435—38no—
243C2×#107—31no—
244C2×#106C2×D311yescharacteristic
245C2×#106C2×D311yescharacteristic
246C2×C4⋊C8—31no—
247#417—38no—
248#416—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×#102C2×D311yescharacteristic
258C2×#102C2×D311yescharacteristic
259C2×C22⋊C8—31no—
260C2×C22⋊C8C2×D311yescharacteristic
261C2×#97—31no—
262C24×C3—21no—
263C24×C3C2×D411yescharacteristic
264C23×D3—21no—
265C23×D3C2×D411yescharacteristic
266C2×C3×D4—24no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—82no—
271C2×C3×D4C2412yes—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—24no—
278C22×C3×C4—44no—
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2411yescharacteristic
283C2×#67—24no—
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—42no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—82no—
292C2×#67C2×D414yes—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—24no—
297C22×Dic3—44no—
298C22×Dic3C2×D411yescharacteristic
299C22×Dic3C2×D411yescharacteristic
300C22×Dic3C2×D411yescharacteristic
301#237—28no—
302#237—44no—
303#237—48no—
304#235—28no—
305#235—44no—
306#235—48no—
307C2×D12—22no—
308C2×D12—22no—
309C2×D12—21no—
310C2×D12—24no—
311C2×D12—82no—
312C2×D12C2412yes—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—24no—
316C2×C4×D3—44no—
317C2×C4×D3C2×D412yes—
318C2×C4×D3C2412yes—
319C2×Dic6—21no—
320C2×Dic6—22no—
321C2×Dic6—22no—
322C2×Dic6—22no—
323C2×Dic6—21no—
324C2×Dic6#4114yes—
325C2×Dic6C2412yes—
326C2×Dic6C2412yes—
327C2×C3×C8—22no—
328C2×C3×C8—22no—
329C2×C3×C8C2412yes—
330C2×C3×C8C2412yes—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—24no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4C2412yes—
336C3×C4⋊C4C2412yes—
337C3×C4⋊C4C2412yes—
338C3×C22⋊C4—24no—
339#217—24no—
340#217C2×D414yes—
341#214—44no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4C2×D414yes—
346C4⋊Dic3—21no—
347C4⋊Dic3—24no—
348C4⋊Dic3—24no—
349C4⋊Dic3C2412yes—
350Dic3⋊C4—24no—
351Dic3⋊C4—24no—
352Dic3⋊C4—24no—
353Dic3⋊C4—24no—
354Dic3⋊C4C2×D414yes—
355C4×Dic3—24no—
356C4×Dic3—24no—
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—
365Dic12—28no—
366#204—44no—
367D3×C8—44no—
368C2×#41—34no—
369C2×#41—34no—
370C2×#41—64no—
371C2×#41—62no—
372C2×#41—62no—
373C2×#41—64no—
374C2×#41—122no—
375C2×#41—122no—
376C22×Q8—31no—
377C22×Q8—31no—
378C22×D4—21no—
379C22×D4—31no—
380C22×D4—31no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4—61no—
384C22×D4—61no—
385C22×D4—61no—
386C22×D4C22×D311yescharacteristic
387C23×C4—21no—
388C23×C4—31no—
389C23×C4—61no—
390C23×C4—61no—
391C23×C4C22×D311yescharacteristic
392C2×Q16—34no—
393C2×Q16—64no—
394C2×SD16—34no—
395C2×SD16—34no—
396C2×SD16—122no—
397C2×SD16—122no—
398C2×M16—34no—
399C2×M16—122no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8—34no—
403C22×C8—122no—
404C22×C8C22×D311yescharacteristic
405C22×C8C22×D311yescharacteristic
406#127—34no—
407#127—62no—
408#127—68no—
409#126—68no—
410#125—34no—
411#125—62no—
412#125—68no—
413#123—68no—
414C22⋊Q8—34no—
415C22⋊Q8—34no—
416C22⋊Q8—62no—
417C22⋊Q8—62no—
418#121—22no—
419#121—34no—
420#121—68no—
421#121—68no—
422#121—62no—
423#121C22×D314yes—
424C4×Q8—34no—
425C4×Q8—34no—
426C4×Q8—62no—
427C4×Q8—62no—
428C4×D4—34no—
429C4×D4—34no—
430C4×D4—68no—
431#117—34no—
432#117—68no—
433#117—62no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—61no—
439C2×C4⋊C4—61no—
440C2×C4⋊C4—61no—
441C2×C4⋊C4—61no—
442C2×C4⋊C4—61no—
443C2×C4⋊C4—61no—
444C2×C4⋊C4C22×D311yescharacteristic
445C2×C4⋊C4C22×D311yescharacteristic
446C2×C4⋊C4C22×D314yes—
447C2×C4⋊C4C22×D311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—31no—
450C2×C22⋊C4—31no—
451C2×C22⋊C4—61no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455C2×C42—31no—
456C2×C42—61no—
457C2×C42—61no—
458C2×C42—61no—
459#107—34no—
460#106C22×D314yes—
461#106C22×D314yes—
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#102C22×D314yes—
472#102C22×D314yes—
473C22⋊C8—34no—
474C22⋊C8C22×D314yes—
475#97—34no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—42no—
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—42no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3C22×D412yes—
493C3×D4—22no—
494C3×D4—22no—
495C3×D4—42no—
496C3×D4—84no—
497C2×C3×C4—22no—
498C2×C3×C4—24no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—48no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508C2×C3×C4C22×D412yes—
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C2×#4112yes—
511C2×C3×C4H(5,𝔽2)12yes—
512C2×C3×C4C2511yescharacteristic
513#67—44no—
514#67—48no—
515#67—48no—
516#67—48no—
517#67—84no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—48no—
526C2×Dic3—42no—
527C2×Dic3—42no—
528C2×Dic3C22×D412yes—
529C2×Dic3C22×D412yes—
530C2×Dic3C22×D412yes—
531D12—22no—
532D12—22no—
533D12—42no—
534D12—84no—
535C4×D3—24no—
536C4×D3—22no—
537C4×D3—22no—
538C4×D3—48no—
539Dic6—24no—
540Dic6—22no—
541Dic6—22no—
542Dic6—22no—
543Dic6—42no—
544Dic6C2×#4114yes—
545C3×C8—22no—
546C3×C8—22no—
547C3⋊C8—22no—
548C3⋊C8—22no—
549C24—21no—
550C24—31no—
551C24—61no—
552C24D3×D411yescharacteristic
553#41—68no—
554#41—68no—
555#41—124no—
556#41—128no—
557#41—124no—
558#41—128no—
559C2×Q8—34no—
560C2×Q8—32no—
561C2×Q8—32no—
562C2×Q8—61no—
563C2×Q8—61no—
564C2×Q8—62no—
565C2×Q8—62no—
566C2×Q8—62no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—34no—
572C2×D4—32no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—61no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4—82no—
582C2×D4—122no—
583C2×D4—124no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—242no—
587C2×D4—242no—
588C2×D4C23×D312yes—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—44no—
601C22×C4—64no—
602C22×C4—61no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—64no—
608C22×C4—124no—
609C22×C4—124no—
610C22×C4D3×D412yes—
611C22×C4D3×D411yescharacteristic
612C22×C4C23×D312yes—
613C22×C4C23×D311yescharacteristic
614Q16—68no—
615SD16—124no—
616SD16—124no—
617M16—124no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—32no—
621C2×C8—32no—
622C2×C8—62no—
623C2×C8—62no—
624C2×C8—124no—
625C2×C8C23×D312yes—
626C2×C8C23×D312yes—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—24no—
630C4⋊C4—21no—
631C4⋊C4—34no—
632C4⋊C4—32no—
633C4⋊C4—64no—
634C4⋊C4—64no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—61no—
639C4⋊C4—64no—
640C4⋊C4C23×D312yes—
641C4⋊C4C23×D312yes—
642C4⋊C4C23×D312yes—
643C22⋊C4—24no—
644C22⋊C4—34no—
645C22⋊C4—34no—
646C22⋊C4—64no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C42—32no—
651C42—32no—
652C42—64no—
653C42—64no—
654C42—64no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—44no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—84no—
663C22×C3#54612yes—
664C22×C3#57512yes—
665C22×C3#57712yes—
666C22×C3C23×D411yescharacteristic
667C2×D3—22no—
668C2×D3—22no—
669C2×D3—22no—
670C2×D3—44no—
671C2×D3—42no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—84no—
675C3×C4—22no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4#54612yes—
680C3×C4C22×#4111yescharacteristic
681C3×C4C2×H(5,𝔽2)11yescharacteristic
682Dic3—24no—
683Dic3—22no—
684Dic3—22no—
685Dic3—22no—
686Dic3—42no—
687Dic3—42no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—32no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—62no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23C2×D3×D412yes—
704C23C2×D3×D411yescharacteristic
705Q8—34no—
706Q8—64no—
707Q8—62no—
708Q8—62no—
709Q8—62no—
710Q8—122no—
711D4—22no—
712D4—22no—
713D4—42no—
714D4—62no—
715D4—62no—
716D4—84no—
717D4—124no—
718D4—128no—
719D4—128no—
720D4—128no—
721D4—122no—
722D4—244no—
723D4—244no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—48no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—62no—
739C2×C4—64no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—64no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—128no—
749C2×C4—128no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4C2×D3×D412yes—
753C2×C4C2×D3×D411yescharacteristic
754C2×C4D3×#4112yes—
755C2×C4#100912yes—
756C2×C4C24×D311yescharacteristic
757C8—22no—
758C8—22no—
759C8—62no—
760C8—62no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3#331714yescomplemented
764C2×C3C2×#54611yescharacteristic
765C2×C3C2×#57511yescharacteristic
766C2×C3C2×#57711yescharacteristic
767D3—42no—
768D3—82no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—44no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22—84no—
780C22—124no—
781C22—122no—
782C22—122no—
783C22—122no—
784C22—244no—
785C22#565412yes—
786C22#576212yes—
787C22#577312yes—
788C22C22×D3×D411yescharacteristic
789C4—22no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—62no—
794C4—62no—
795C4—62no—
796C4—64no—
797C4—122no—
798C4—122no—
799C4#565412yes—
800C4C2×D3×#4111yescharacteristic
801C4C2×#100911yescharacteristic
802C3C2×#331711yescharacteristic, complemented, Sylow
803C2—42no—
804C2—82no—
805C2—122no—
806C2—242no—
807C2#8133214yesdirect product factor
808C2C2×#565411yescharacteristic
809C2C2×#576211yescharacteristic
810C2C2×#577311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#481C2
socleC23×C3C22×D4
prime radicalC2×#5599C2
hypercenterC2×#481D3
hypocenterC3C2×#3317
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#5513C2semidirect
3. C2×C3×#481C2semidirect
4. C2×#5042C2semidirect
5. C2×#4966C2semidirect
6. #81332C2direct (N × H)
7. C2×#4857C2semidirect
8. C2×#4866C2semidirect
9. C2×#4864C2semidirect
10. C2×#4853C2semidirect
11. C2×#4762C2semidirect
12. C2×#4783C2semidirect
13. C2×#4772C2semidirect
14. C2×#4764C2semidirect
15. C2×#4733C2semidirect
16. C2×#4728C2semidirect
37. #5513C22semidirect
48. C3×#481C22semidirect
60. #5042C22semidirect
64. #4966C22semidirect
68. #4866C22semidirect
69. #4864C22semidirect
70. #4857C22semidirect
71. #4853C22semidirect
72. #4783C22semidirect
73. #4772C22semidirect
74. #4764C22semidirect
75. #4762C22semidirect
76. #4733C22semidirect
77. #4728C22semidirect
82. C2×#481D3semidirect
234. #481C2×D3semidirect
763. C2×C3#3317semidirect
802. C3C2×#3317semidirect
807. C2#81332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55992
C2×#55132
C2×C3×#4812
C2×#50422
C2×#49662
#813322
C2×#48572
C2×#48662
C2×#48642
C2×#48532
C2×#47622
C2×#47832
C2×#47722
C2×#47642
C2×#47332
C2×#47282
C2×#33173