Finite Group Databasebeta

← C2×#81523 #11665809

Subgroups — C2×#81523 #11665809

Order 768.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5524C211yesmaximal, characteristic
3C2×C3×#485C211yesmaximal, characteristic, complemented
4C2×#5047C211yesmaximal, characteristic, complemented
5C2×#4996C211yesmaximal, characteristic, complemented
6#81523C2116yesmaximal, direct product factor
7C2×#4884C211yesmaximal, characteristic, complemented
8C2×#4886C211yesmaximal, characteristic, complemented
9C2×#4863C211yesmaximal, characteristic, complemented
10C2×#4867C211yesmaximal, characteristic, complemented
11C2×#4816C211yesmaximal, characteristic, complemented
12C2×#4812C211yesmaximal, characteristic, complemented
13C2×#4809C211yesmaximal, characteristic, complemented
14C2×#4806C211yesmaximal, characteristic, complemented
15C2×#4733C211yesmaximal, characteristic, complemented
16C2×#4726C211yesmaximal, characteristic, complemented
17C2×#3196—31nomaximal, Sylow
18C22×D3×Q8C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#117C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C22×#216C2211yescharacteristic, complemented
25C22×#215C2211yescharacteristic, complemented
26C2×#924C2211yescharacteristic
27C22×Dic12C2211yescharacteristic, complemented
28C22×#204C2211yescharacteristic, complemented
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C22×ΓL(1,𝔽25)C2211yescharacteristic
31D3×C22⋊Q8—24no—
32D3×C22⋊Q8C2218yescomplemented
33#5524—24no—
34#5524C2218yes—
35C2×#897C2211yescharacteristic
36C2×#897C2211yescharacteristic
37C2×#897C2211yescharacteristic
38C2×#896—21no—
39C2×#895C2211yescharacteristic
40C2×#895C2211yescharacteristic
41C2×D3×C4⋊C4—21no—
42C2×D3×C4⋊C4C2211yescharacteristic
43C2×#886—21no—
44C2×#882—21no—
45C2×D3×C22⋊C4—21no—
46C2×#878—21no—
47C2×C4×D12—21no—
48C2×C4×D12—21no—
49C3×#485C2218yescomplemented
50C2×C3×#107C2211yescharacteristic, complemented
51C2×C3×#106C2211yescharacteristic, complemented
52C2×C3×#103C2211yescharacteristic, complemented
53C2×C3×#103C2211yescharacteristic, complemented
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×#830C2211yescharacteristic
56C2×#821C2211yescharacteristic, complemented
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×(C2×D3)⋊C8C2211yescharacteristic
59C2×#816C2211yescharacteristic, complemented
60#5047C2218yescomplemented
61#4996C2218yescomplemented
62C2×#810C2211yescharacteristic, complemented
63C2×#810C2211yescharacteristic, complemented
64C2×#810C2211yescharacteristic, complemented
65C2×#809C2211yescharacteristic, complemented
66C2×#808C2211yescharacteristic, complemented
67C2×#807C2211yescharacteristic, complemented
68#4886C2218yescomplemented
69#4884C2218yescomplemented
70#4867C2218yescomplemented
71#4863C2218yescomplemented
72#4816C2218yescomplemented
73#4812C2218yescomplemented
74#4809C2218yescomplemented
75#4806C2218yescomplemented
76#4733C2218yescomplemented
77#4726C2218yescomplemented
78C2×#525—31no—
79C22×C22⋊Q8—31no—
80#3196—316no—
81C2×#484—31no—
82C2×#481—31no—
83C2×#485—31no—
84C2×#485D311yescharacteristic, complemented
85C2×#470—31no—
86C2×#470—31no—
87C2×#468—31no—
88C2×#468—31no—
89C2×#452—31no—
90C2×#452—31no—
91C2×#451—31no—
92C2×#448—31no—
93C2×#407—31no—
94C24×D3D411yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—21no—
98C23×Dic3D411yescharacteristic
99C2×D3×Q8—22no—
100C2×D3×Q8—42no—
101C2×D3×Q8—42no—
102C2×D3×Q8C2314yes—
103C2×#235—22no—
104C2×#235—42no—
105C2×#235—42no—
106C2×#235C2314yes—
107C22×D12—21no—
108C22×D12—21no—
109C22×D12C2311yescharacteristic
110C22×C4×D3—21no—
111C22×C4×D3—21no—
112C22×C4×D3—21no—
113C22×C4×D3—42no—
114C22×C4×D3—42no—
115C22×C4×D3D411yescharacteristic
116C22×C4×D3D411yescharacteristic
117C22×C4×D3D414yes—
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2314yes—
121C22×Dic6—21no—
122C22×Dic6C2311yescharacteristic
123C22×Dic6C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C22×C3×C8C2311yescharacteristic
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8C2314yes—
128C3×#117—22no—
129C3×#117C2314yes—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C42—21no—
137C2×#217—21no—
138#946—22no—
139#946C2314yes—
140C2×#216—42no—
141C2×#216C2314yescomplemented
142C2×#215—42no—
143C2×#215C2314yescomplemented
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×C4⋊Dic3—21no—
151C2×C4⋊Dic3—21no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3C2311yescharacteristic
154#924—22no—
155#924C2314yes—
156C2×Dic3⋊C4—21no—
157C2×Dic3⋊C4—21no—
158C2×Dic3⋊C4—21no—
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C2×Dic12—42no—
162C2×Dic12C2314yescomplemented
163C2×#204—42no—
164C2×#204C2314yescomplemented
165C2×ΓL(1,𝔽25)—42no—
166C2×ΓL(1,𝔽25)—42no—
167C2×ΓL(1,𝔽25)C2314yes—
168C2×ΓL(1,𝔽25)C2314yes—
169#897—22no—
170#897—22no—
171#897—22no—
172#897C2314yes—
173#897C2314yes—
174#897C2314yes—
175#896—28no—
176#895—22no—
177#895—22no—
178#895C2314yes—
179#895C2314yes—
180D3×C4⋊C4—28no—
181D3×C4⋊C4—22no—
182D3×C4⋊C4C2314yes—
183#886—28no—
184#882—28no—
185D3×C22⋊C4—28no—
186#878—28no—
187C4×D12—28no—
188C4×D12—28no—
189C3×#107C2314yescomplemented
190C3×#106C2314yescomplemented
191C3×#103C2314yescomplemented
192C3×#103C2314yescomplemented
193C3×C22⋊C8C2314yes—
194#830C2314yes—
195#821C2314yescomplemented
196(C2×D3)⋊C8C2314yes—
197(C2×D3)⋊C8C2314yes—
198#816C2314yescomplemented
199#810C2314yescomplemented
200#810C2314yescomplemented
201#810C2314yescomplemented
202#809C2314yescomplemented
203#808C2314yescomplemented
204#807C2314yescomplemented
205C22×#41—31no—
206C23×Q8—31no—
207C24×C4—31no—
208C22×Q16—31no—
209C22×Q16—31no—
210C22×SD16—31no—
211C22×SD16—31no—
212C22×M16—31no—
213C22×M16—31no—
214#525—38no—
215#525—64no—
216C2×#123—61no—
217C2×C22⋊Q8—31no—
218C2×C22⋊Q8—31no—
219C2×C22⋊Q8—38no—
220C2×C22⋊Q8—31no—
221C2×C22⋊Q8—31no—
222C2×C22⋊Q8—31no—
223C2×C22⋊Q8—61no—
224C2×C22⋊Q8—61no—
225C2×C22⋊Q8—64no—
226C2×C22⋊Q8C2×D311yescharacteristic
227C2×#121—31no—
228C2×#121—31no—
229C2×#120—61no—
230C2×C4×D4—61no—
231C2×C4×D4—61no—
232C2×#117C2×D311yescharacteristic
233C22×C4⋊C4—31no—
234C22×C4⋊C4—61no—
235C22×C22⋊C4—61no—
236#485—38no—
237#485C2×D318yescomplemented
238#484—38no—
239#481—38no—
240#470—38no—
241#470—38no—
242#468—38no—
243#468—38no—
244#452—38no—
245#452—38no—
246#451—38no—
247#448—38no—
248C2×#107—31no—
249C2×#107C2×D311yescharacteristic, complemented
250C2×#106—31no—
251C2×#106C2×D311yescharacteristic, complemented
252C2×#103—31no—
253C2×#103—31no—
254C2×#103—31no—
255C2×#103—31no—
256C2×#103C2×D311yescharacteristic, complemented
257C2×#103C2×D311yescharacteristic, complemented
258C2×#102—31no—
259C2×#102—31no—
260#407—38no—
261C2×C22⋊C8—31no—
262C2×C22⋊C8—31no—
263C2×C22⋊C8—31no—
264C2×C22⋊C8C2×D311yescharacteristic
265C24×C3C2×D411yescharacteristic
266C23×D3—24no—
267C23×D3—21no—
268C23×D3—42no—
269C23×D3—42no—
270C23×D3C2×D411yescharacteristic
271C23×D3C2×D411yescharacteristic
272C23×D3C2×D414yes—
273C2×C3×Q8—21no—
274C2×C3×Q8—22no—
275C2×C3×Q8—22no—
276C2×C3×Q8C2412yes—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2411yescharacteristic
287C2×#67—24no—
288C2×#67—44no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—42no—
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295C22×Dic3C2×D414yes—
296D3×Q8—44no—
297D3×Q8—44no—
298D3×Q8—48no—
299#235—44no—
300#235—44no—
301#235—48no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—24no—
305C2×D12—24no—
306C2×D12—21no—
307C2×D12—44no—
308C2×D12—44no—
309C2×D12C2412yes—
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—48no—
318C2×C4×D3—44no—
319C2×C4×D3—44no—
320C2×C4×D3—42no—
321C2×C4×D3—42no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3C2×D412yes—
326C2×C4×D3C2×D412yes—
327C2×C4×D3C2×D414yes—
328C2×C4×D3C2×D414yes—
329C2×C4×D3C2412yes—
330C2×C4×D3C2412yes—
331C2×Dic6—22no—
332C2×Dic6—22no—
333C2×Dic6—22no—
334C2×Dic6—22no—
335C2×Dic6—21no—
336C2×Dic6—21no—
337C2×Dic6—24no—
338C2×Dic6—44no—
339C2×Dic6C2412yes—
340C2×Dic6C2412yes—
341C2×C3×C8—22no—
342C2×C3×C8—22no—
343C2×C3×C8C2412yes—
344C2×C3×C8C2412yes—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4C2412yes—
350C3×C4⋊C4C2412yes—
351C3×C4⋊C4C2412yes—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—24no—
354C3×C42—24no—
355#217—24no—
356#216—44no—
357#215—44no—
358(C2×D3)⋊C4—24no—
359(C2×D3)⋊C4—24no—
360(C2×D3)⋊C4—24no—
361(C2×D3)⋊C4—24no—
362(C2×D3)⋊C4—24no—
363(C2×D3)⋊C4—24no—
364C4⋊Dic3—21no—
365C4⋊Dic3—24no—
366C4⋊Dic3—24no—
367C4⋊Dic3—24no—
368C4⋊Dic3C2412yes—
369Dic3⋊C4—24no—
370Dic3⋊C4—24no—
371Dic3⋊C4—24no—
372C2×C3⋊C8—22no—
373C2×C3⋊C8—22no—
374C2×C3⋊C8C2412yes—
375C2×C3⋊C8C2412yes—
376Dic12—44no—
377#204—44no—
378ΓL(1,𝔽25)—44no—
379ΓL(1,𝔽25)—44no—
380C25—31no—
381C2×#41—34no—
382C2×#41—62no—
383C2×#41—122no—
384C2×#41—122no—
385C22×Q8—34no—
386C22×Q8—31no—
387C22×Q8—31no—
388C22×Q8—61no—
389C22×Q8—62no—
390C22×Q8—122no—
391C22×Q8—122no—
392C22×Q8C22×D311yescharacteristic
393C22×D4—31no—
394C22×D4—61no—
395C22×D4—61no—
396C22×D4—61no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—34no—
403C23×C4—34no—
404C23×C4—61no—
405C23×C4—61no—
406C23×C4—61no—
407C23×C4—122no—
408C23×C4—122no—
409C23×C4C22×D311yescharacteristic
410C2×Q16—34no—
411C2×Q16—34no—
412C2×Q16—122no—
413C2×Q16—122no—
414C2×SD16—34no—
415C2×SD16—34no—
416C2×SD16—122no—
417C2×SD16—122no—
418C2×M16—34no—
419C2×M16—34no—
420C2×M16—122no—
421C2×M16—122no—
422C22×C8—31no—
423C22×C8—31no—
424C22×C8C22×D311yescharacteristic
425C22×C8C22×D311yescharacteristic
426#123—68no—
427C22⋊Q8—22no—
428C22⋊Q8—34no—
429C22⋊Q8—34no—
430C22⋊Q8—34no—
431C22⋊Q8—34no—
432C22⋊Q8—34no—
433C22⋊Q8—68no—
434C22⋊Q8—68no—
435C22⋊Q8—62no—
436C22⋊Q8—62no—
437C22⋊Q8—62no—
438C22⋊Q8—62no—
439C22⋊Q8—62no—
440C22⋊Q8C22×D314yes—
441#121—34no—
442#121—34no—
443#121—62no—
444#121—62no—
445#120—68no—
446C4×D4—68no—
447C4×D4—68no—
448#117—22no—
449#117C22×D314yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—34no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—68no—
455C2×C4⋊C4—61no—
456C2×C4⋊C4—61no—
457C2×C4⋊C4—61no—
458C2×C4⋊C4—61no—
459C2×C4⋊C4—61no—
460C2×C4⋊C4—61no—
461C2×C4⋊C4C22×D311yescharacteristic
462C2×C4⋊C4C22×D311yescharacteristic
463C2×C4⋊C4C22×D311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—68no—
467C2×C22⋊C4—61no—
468C2×C22⋊C4—61no—
469C2×C22⋊C4—61no—
470C2×C22⋊C4—61no—
471C2×C22⋊C4—61no—
472C2×C22⋊C4—61no—
473C2×C22⋊C4—61no—
474C2×C42—21no—
475#107—34no—
476#107C22×D314yescomplemented
477#106—34no—
478#106C22×D314yescomplemented
479#103—34no—
480#103—34no—
481#103—34no—
482#103—34no—
483#103C22×D314yescomplemented
484#103C22×D314yescomplemented
485#102—34no—
486#102—34no—
487C22⋊C8—34no—
488C22⋊C8—34no—
489C22⋊C8—34no—
490C22⋊C8C22×D314yes—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3C22×D412yes—
495C23×C3C22×D411yescharacteristic
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—28no—
502C22×D3—22no—
503C22×D3—44no—
504C22×D3—44no—
505C22×D3—416no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3#13714yes—
510C22×D3C22×D412yes—
511C22×D3C22×D412yes—
512C3×Q8—22no—
513C3×Q8—22no—
514C3×Q8—42no—
515C2×C3×C4—22no—
516C2×C3×C4—24no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4C22×D412yes—
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4H(5,𝔽2)12yes—
530C2×C3×C4H(5,𝔽2)12yes—
531C2×C3×C4C2511yescharacteristic
532#67—48no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—44no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3C22×D412yes—
543C2×Dic3C22×D412yes—
544D12—22no—
545D12—22no—
546D12—48no—
547D12—48no—
548D12—42no—
549C4×D3—24no—
550C4×D3—24no—
551C4×D3—22no—
552C4×D3—22no—
553C4×D3—22no—
554C4×D3—22no—
555C4×D3—44no—
556C4×D3—44no—
557C4×D3—48no—
558C4×D3—48no—
559C4×D3—48no—
560Dic6—22no—
561Dic6—22no—
562Dic6—22no—
563Dic6—22no—
564Dic6—48no—
565Dic6—42no—
566Dic6—42no—
567C3×C8—22no—
568C3×C8—22no—
569C3⋊C8—22no—
570C3⋊C8—22no—
571C24—31no—
572C24—31no—
573C24—34no—
574C24—64no—
575C24—61no—
576C24—122no—
577C24—122no—
578C24D3×D411yescharacteristic
579#41—124no—
580#41—124no—
581#41—128no—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—32no—
586C2×Q8—32no—
587C2×Q8—64no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—62no—
591C2×Q8—62no—
592C2×Q8—62no—
593C2×Q8—62no—
594C2×Q8—124no—
595C2×Q8—124no—
596C2×Q8—124no—
597C2×Q8—128no—
598C2×Q8C23×D312yes—
599C2×D4—32no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—64no—
603C2×D4—61no—
604C2×D4—62no—
605C2×D4—62no—
606C2×D4—124no—
607C2×D4—124no—
608C2×D4—124no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—34no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—34no—
623C22×C4—34no—
624C22×C4—64no—
625C22×C4—64no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—64no—
634C22×C4—128no—
635C22×C4—124no—
636C22×C4—124no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4—124no—
640C22×C4—124no—
641C22×C4—124no—
642C22×C4—122no—
643C22×C4D3×D412yes—
644C22×C4D3×D411yescharacteristic
645C22×C4C23×D312yes—
646C22×C4C23×D311yescharacteristic
647Q16—124no—
648Q16—124no—
649SD16—124no—
650SD16—124no—
651M16—124no—
652M16—124no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—32no—
656C2×C8—32no—
657C2×C8—62no—
658C2×C8—62no—
659C2×C8C23×D312yes—
660C2×C8C23×D312yes—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—32no—
666C4⋊C4—64no—
667C4⋊C4—64no—
668C4⋊C4—64no—
669C4⋊C4—64no—
670C4⋊C4—64no—
671C4⋊C4—61no—
672C4⋊C4—64no—
673C4⋊C4C23×D312yes—
674C4⋊C4C23×D312yes—
675C4⋊C4C23×D312yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—64no—
685C42—24no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—44no—
690C22×C3#53412yes—
691C22×C3C2×#13712yes—
692C22×C3#57512yes—
693C22×C3C23×D411yescharacteristic
694C2×D3—22no—
695C2×D3—28no—
696C2×D3—22no—
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—416no—
701C2×D3—44no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—84no—
706C2×D3C2×#13714yes—
707C3×C4—22no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—42no—
712C3×C4#53412yes—
713C3×C4C2×H(5,𝔽2)11yescharacteristic
714C3×C4C2×H(5,𝔽2)11yescharacteristic
715Dic3—22no—
716Dic3—22no—
717Dic3—42no—
718Dic3—42no—
719Dic3—42no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—32no—
724C23—34no—
725C23—32no—
726C23—68no—
727C23—62no—
728C23—62no—
729C23—62no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23—124no—
734C23—124no—
735C23—1216no—
736C23—122no—
737C23—122no—
738C23—122no—
739C23C2×D3×D412yes—
740C23C2×D3×D411yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—62no—
745Q8—62no—
746Q8—62no—
747Q8—62no—
748Q8—128no—
749Q8—122no—
750Q8—122no—
751D4—62no—
752D4—62no—
753D4—128no—
754D4—128no—
755D4—128no—
756D4—122no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—64no—
774C2×C4—64no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—124no—
783C2×C4—124no—
784C2×C4—128no—
785C2×C4—128no—
786C2×C4—128no—
787C2×C4—124no—
788C2×C4—122no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4C2×D3×D412yes—
792C2×C4C2×D3×D411yescharacteristic
793C2×C4#100912yes—
794C2×C4#100912yes—
795C2×C4C24×D311yescharacteristic
796C8—22no—
797C8—22no—
798C8—62no—
799C8—62no—
800C2×C3—42no—
801C2×C3#319614yescomplemented
802C2×C3C2×#53411yescharacteristic
803C2×C3C22×#13711yescharacteristic
804C2×C3C2×#57511yescharacteristic
805D3—24no—
806D3—42no—
807D3—82no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—34no—
812C22—44no—
813C22—68no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—62no—
819C22—1216no—
820C22—124no—
821C22—122no—
822C22—122no—
823C22—122no—
824C22—244no—
825C22#565312yes—
826C22#576812yes—
827C22D3×#13712yes—
828C22C22×D3×D411yescharacteristic
829C4—22no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—62no—
835C4—62no—
836C4—122no—
837C4—122no—
838C4—122no—
839C4#565312yes—
840C4C2×#100911yescharacteristic
841C4C2×#100911yescharacteristic
842C3C2×#319611yescharacteristic, complemented, Sylow
843C2—42no—
844C2—64no—
845C2—122no—
846C2—242no—
847C2#8152314yesdirect product factor
848C2C2×#565311yescharacteristic
849C2C2×#576811yescharacteristic
850C2C2×D3×#13711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#485C2
socleC23×C3C22×D4
prime radicalC2×#5524C2
hypercenterC2×#485D3
hypocenterC3C2×#3196
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
1. C2×D3×C22⋊Q8C2semidirect
3. C2×C3×#485C2semidirect
4. C2×#5047C2semidirect
5. C2×#4996C2semidirect
6. #81523C2direct (N × H)
7. C2×#4884C2semidirect
8. C2×#4886C2semidirect
9. C2×#4863C2semidirect
10. C2×#4867C2semidirect
11. C2×#4816C2semidirect
12. C2×#4812C2semidirect
13. C2×#4809C2semidirect
14. C2×#4806C2semidirect
15. C2×#4733C2semidirect
16. C2×#4726C2semidirect
24. C22×#216C22semidirect
25. C22×#215C22semidirect
27. C22×Dic12C22semidirect
28. C22×#204C22semidirect
32. D3×C22⋊Q8C22semidirect
49. C3×#485C22semidirect
50. C2×C3×#107C22semidirect
51. C2×C3×#106C22semidirect
52. C2×C3×#103C22semidirect
53. C2×C3×#103C22semidirect
56. C2×#821C22semidirect
59. C2×#816C22semidirect
60. #5047C22semidirect
61. #4996C22semidirect
62. C2×#810C22semidirect
63. C2×#810C22semidirect
64. C2×#810C22semidirect
65. C2×#809C22semidirect
66. C2×#808C22semidirect
67. C2×#807C22semidirect
68. #4886C22semidirect
69. #4884C22semidirect
70. #4867C22semidirect
71. #4863C22semidirect
72. #4816C22semidirect
73. #4812C22semidirect
74. #4809C22semidirect
75. #4806C22semidirect
76. #4733C22semidirect
77. #4726C22semidirect
84. C2×#485D3semidirect
141. C2×#216C23semidirect
143. C2×#215C23semidirect
162. C2×Dic12C23semidirect
164. C2×#204C23semidirect
189. C3×#107C23semidirect
190. C3×#106C23semidirect
191. C3×#103C23semidirect
192. C3×#103C23semidirect
195. #821C23semidirect
198. #816C23semidirect
199. #810C23semidirect
200. #810C23semidirect
201. #810C23semidirect
202. #809C23semidirect
203. #808C23semidirect
204. #807C23semidirect
237. #485C2×D3semidirect
249. C2×#107C2×D3semidirect
251. C2×#106C2×D3semidirect
256. C2×#103C2×D3semidirect
257. C2×#103C2×D3semidirect
476. #107C22×D3semidirect
478. #106C22×D3semidirect
483. #103C22×D3semidirect
484. #103C22×D3semidirect
801. C2×C3#3196semidirect
842. C3C2×#3196semidirect
847. C2#81523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊Q82
C2×#55242
C2×C3×#4852
C2×#50472
C2×#49962
#815232
C2×#48842
C2×#48862
C2×#48632
C2×#48672
C2×#48162
C2×#48122
C2×#48092
C2×#48062
C2×#47332
C2×#47262
C2×#31963