Finite Group Databasebeta

← C2×#83549 #11670448

Subgroups — C2×#83549 #11670448

Order 768.

2794 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C23×#216C211yesmaximal, characteristic, complemented
4C2×#5552C211yesmaximal, characteristic, complemented
5C2×#5239C211yesmaximal, characteristic, complemented
6C2×#5227C211yesmaximal, characteristic, complemented
7#83549C2116yesmaximal, direct product factor
8C2×#5054C211yesmaximal, characteristic, complemented
9C2×#5059C211yesmaximal, characteristic, complemented
10C2×#5047C211yesmaximal, characteristic, complemented
11C2×#5051C211yesmaximal, characteristic, complemented
12C2×#5040C211yesmaximal, characteristic, complemented
13C2×#5038C211yesmaximal, characteristic, complemented
14C2×#5028C211yesmaximal, characteristic, complemented
15C2×C4×#216C211yesmaximal, characteristic, complemented
16C2×D4×C3⋊C8C211yesmaximal, characteristic, complemented
17C2×#3285—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C3×#548—24no—
23C3×#548C2218yescomplemented
24C2×C3×#124—21no—
25C2×C3×#124C2211yescharacteristic
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121—21no—
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×#950—28no—
34C2×#950C2218yescomplemented
35C22×#216—28no—
36C22×#216C2211yescharacteristic
37C22×#216C2211yescharacteristic
38C22×#216C2211yescharacteristic
39C22×#216C2211yescharacteristic
40C22×#216C2218yescomplemented
41C22×#215C2211yescharacteristic
42C22×#215C2211yescharacteristic
43C2×#939—21no—
44C22×#214C2211yescharacteristic
45C22×#214C2211yescharacteristic
46C22×#213C2211yescharacteristic
47C2×#930C2211yescharacteristic
48C2×#924C2211yescharacteristic
49C23×C3⋊C8C2211yescharacteristic
50C23×C3⋊C8C2211yescharacteristic
51#5552—24no—
52#5552C2218yescomplemented
53C2×#896—21no—
54C2×#885—21no—
55C2×#67⋊C4—21no—
56C2×#875C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic
58#5239C2218yescomplemented
59#5227C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#832C2211yescharacteristic
63C2×#830C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5059C2218yescomplemented
66#5054C2218yescomplemented
67#5051C2218yescomplemented
68#5047C2218yescomplemented
69#5040C2218yescomplemented
70#5038C2218yescomplemented
71C4×#216C2218yescomplemented
72#5028C2218yescomplemented
73D4×C3⋊C8C2218yescomplemented
74C2×#810C2211yescharacteristic
75C2×#810C2211yescharacteristic
76C2×#809C2211yescharacteristic
77C2×#807C2211yescharacteristic
78C2×C4⋊(C3⋊C8)C2211yescharacteristic
79C2×C4×C3⋊C8C2211yescharacteristic
80C22×#135—31no—
81C23×Q16—31no—
82C2×#548—31no—
83C2×#548D311yescharacteristic, complemented
84#3285—316no—
85C2×#495—31no—
86C2×#467—31no—
87C2×#466—31no—
88C2×#464—31no—
89C2×#464—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#448—31no—
93C2×#448—31no—
94C2×C4×Q16—31no—
95C2×C8×D4—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8—21no—
101C22×C3×Q8—22no—
102C22×C3×Q8—24no—
103C22×C3×Q8—42no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2314yes—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4—21no—
108C22×C3×D4—21no—
109C22×C3×D4D411yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4—21no—
112C23×C3×C4—21no—
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C22×#67—21no—
116C22×#67—21no—
117C23×Dic3—21no—
118C2×#235—22no—
119C2×#235—24no—
120C2×#235—42no—
121C2×#235C2314yes—
122C22×D12C2311yescharacteristic
123C22×C4×D3—21no—
124C22×Dic6—24no—
125C22×Dic6—21no—
126C22×Dic6—22no—
127C22×Dic6—42no—
128C22×Dic6C2311yescharacteristic
129C22×Dic6C2314yes—
130C22×Dic6C2311yescharacteristic
131C3×#124—28no—
132C3×#124—22no—
133C3×#124C2314yes—
134C3×C22⋊Q8—22no—
135C3×C22⋊Q8—28no—
136C3×C22⋊Q8C2314yes—
137C3×#121—28no—
138C3×#121—22no—
139C3×#121C2314yes—
140C3×C4×Q8—22no—
141C3×C4×Q8C2314yes—
142C3×C4×D4—28no—
143C3×C4×D4D414yes—
144C3×C4×D4C2314yes—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4D411yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4D411yescharacteristic
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C42—21no—
156C2×C3×C42C2311yescharacteristic
157C2×#217—21no—
158#950—232no—
159C2×#216—24no—
160C2×#216—24no—
161C2×#216—232no—
162C2×#216—24no—
163C2×#216D418yescomplemented
164C2×#216C2314yes—
165C2×#216C2314yes—
166C2×#216C2314yes—
167C2×#216C2314yes—
168C2×#215—24no—
169C2×#215—42no—
170C2×#215C2314yes—
171C2×#215C2314yes—
172#939—28no—
173C2×#214—24no—
174C2×#214—42no—
175C2×#214C2314yes—
176C2×#214C2314yes—
177C2×#213—24no—
178C2×#213C2314yes—
179#930—22no—
180#930C2314yes—
181C2×(C2×D3)⋊C4—21no—
182C2×(C2×D3)⋊C4—21no—
183C2×(C2×D3)⋊C4—21no—
184C2×C4⋊Dic3C2311yescharacteristic
185#924—22no—
186#924C2314yes—
187C2×Dic3⋊C4—21no—
188C2×Dic3⋊C4—21no—
189C2×C4×Dic3—21no—
190C22×C3⋊C8—24no—
191C22×C3⋊C8—24no—
192C22×C3⋊C8C2311yescharacteristic
193C22×C3⋊C8C2311yescharacteristic
194C22×C3⋊C8C2311yescharacteristic
195C22×C3⋊C8C2314yes—
196C22×C3⋊C8C2314yes—
197C22×C3⋊C8C2311yescharacteristic
198#896—28no—
199#885—28no—
200#67⋊C4—28no—
201#875—22no—
202#875C2314yes—
203C4×Dic6—22no—
204C4×Dic6C2314yes—
205#835C2314yes—
206#835C2314yes—
207#832C2314yes—
208#830C2314yes—
209#830C2314yes—
210#810C2314yes—
211#810C2314yes—
212#809C2314yes—
213#807C2314yes—
214C4⋊(C3⋊C8)C2314yes—
215C4×C3⋊C8C2314yes—
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×Q8—31no—
219C23×Q8C2×D311yescharacteristic
220C2×#135—38no—
221C2×#135—68no—
222C22×Q16—31no—
223C22×Q16—31no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×Q16—38no—
227C22×Q16—68no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×SD16—31no—
232C22×D8—31no—
233C23×C8—31no—
234C23×C8—31no—
235#548—24no—
236#548—38no—
237#548—64no—
238#548C2×D318yescomplemented
239C2×#124—21no—
240C2×#124—31no—
241C2×#124—61no—
242C2×#124C2×D311yescharacteristic
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—61no—
246C2×C22⋊Q8C2×D311yescharacteristic
247C2×#121—21no—
248C2×#121—31no—
249C2×#121—61no—
250C2×#121C2×D311yescharacteristic
251C2×C4×Q8—31no—
252C2×C4×Q8C2×D311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—61no—
255C2×C4×D4C2×D311yescharacteristic
256#495—38no—
257#467—38no—
258#466—38no—
259#464—38no—
260#464—38no—
261#452—38no—
262#452—38no—
263#448—38no—
264#448—38no—
265C4×Q16—38no—
266C8×D4—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C3×#41—28no—
283C3×#41—44no—
284C3×#41—48no—
285C2×C3×Q8—21no—
286C2×C3×Q8—24no—
287C2×C3×Q8—21no—
288C2×C3×Q8—22no—
289C2×C3×Q8—28no—
290C2×C3×Q8—22no—
291C2×C3×Q8—22no—
292C2×C3×Q8—44no—
293C2×C3×Q8—44no—
294C2×C3×Q8—48no—
295C2×C3×Q8C2×D414yes—
296C2×C3×Q8C2412yes—
297C2×C3×Q8C2412yes—
298C2×C3×D4—24no—
299C2×C3×D4—24no—
300C2×C3×D4—24no—
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—22no—
304C2×C3×D4—44no—
305C2×C3×D4—44no—
306C2×C3×D4C2×D414yes—
307C2×C3×D4C2412yes—
308C22×C3×C4—21no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—24no—
316C22×C3×C4—24no—
317C22×C3×C4—44no—
318C22×C3×C4—44no—
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2412yes—
326C22×C3×C4C2412yes—
327C22×C3×C4C2411yescharacteristic
328C2×#67—24no—
329C2×#67—24no—
330C2×#67—44no—
331C2×#67—44no—
332C22×Dic3—21no—
333C22×Dic3—24no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—44no—
337#235—28no—
338#235—44no—
339#235—48no—
340C2×D12—22no—
341C2×D12—22no—
342C2×D12—21no—
343C2×D12C2412yes—
344C2×C4×D3—24no—
345C2×C4×D3—44no—
346C2×Dic6—21no—
347C2×Dic6—22no—
348C2×Dic6—22no—
349C2×Dic6—22no—
350C2×Dic6—28no—
351C2×Dic6—21no—
352C2×Dic6—24no—
353C2×Dic6—44no—
354C2×Dic6—48no—
355C2×Dic6—44no—
356C2×Dic6C2×D414yes—
357C2×Dic6C2412yes—
358C2×Dic6C2412yes—
359C3×C4⋊C4—24no—
360C3×C4⋊C4—24no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4C2×D414yes—
363C3×C4⋊C4C2412yes—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—24no—
368C3×C22⋊C4C2×D414yes—
369C3×C22⋊C4C2×D414yes—
370C3×C42—24no—
371C3×C42C2×D412yes—
372C3×C42C2412yes—
373#217—24no—
374#216—28no—
375#216—28no—
376#216—28no—
377#216C2×D4116yescomplemented
378#215—28no—
379#215—44no—
380#214—28no—
381#214—44no—
382#213—28no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386C4⋊Dic3—21no—
387C4⋊Dic3C2412yes—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390C4×Dic3—24no—
391C2×C3⋊C8—22no—
392C2×C3⋊C8—22no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8—28no—
395C2×C3⋊C8—28no—
396C2×C3⋊C8C2×D414yes—
397C2×C3⋊C8C2412yes—
398C2×C3⋊C8C2412yes—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401C2×#41—22no—
402C2×#41—24no—
403C2×#41—34no—
404C2×#41—42no—
405C2×#41—64no—
406C2×#41—62no—
407C2×#41—122no—
408C2×#41C22×D314yes—
409C22×Q8—21no—
410C22×Q8—22no—
411C22×Q8—24no—
412C22×Q8—31no—
413C22×Q8—31no—
414C22×Q8—34no—
415C22×Q8—42no—
416C22×Q8—64no—
417C22×Q8—61no—
418C22×Q8—62no—
419C22×Q8—122no—
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D314yes—
422C22×Q8C22×D311yescharacteristic
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—31no—
426C22×D4—61no—
427C22×D4—61no—
428C22×D4#6711yescharacteristic
429C22×D4C22×D311yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—61no—
433C23×C4—61no—
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436#135—632no—
437C2×Q16—38no—
438C2×Q16—34no—
439C2×Q16—34no—
440C2×Q16—34no—
441C2×Q16—34no—
442C2×Q16—64no—
443C2×Q16—632no—
444C2×Q16—64no—
445C2×Q16—64no—
446C2×SD16—34no—
447C2×SD16—34no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—64no—
451C2×SD16—64no—
452C2×SD16—122no—
453C2×SD16—122no—
454C2×D8—34no—
455C2×D8—64no—
456C22×C8—31no—
457C22×C8—31no—
458C22×C8—31no—
459C22×C8—34no—
460C22×C8—34no—
461C22×C8—31no—
462C22×C8—64no—
463C22×C8—64no—
464#124—28no—
465#124—22no—
466#124—34no—
467#124—68no—
468#124—62no—
469#124C22×D314yes—
470C22⋊Q8—22no—
471C22⋊Q8—28no—
472C22⋊Q8—34no—
473C22⋊Q8—62no—
474C22⋊Q8—68no—
475C22⋊Q8C22×D314yes—
476#121—28no—
477#121—22no—
478#121—34no—
479#121—68no—
480#121—62no—
481#121C22×D314yes—
482C4×Q8—22no—
483C4×Q8—34no—
484C4×Q8—62no—
485C4×Q8C22×D314yes—
486C4×D4—28no—
487C4×D4—68no—
488C4×D4#6714yes—
489C4×D4C22×D314yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4#6711yescharacteristic
496C2×C4⋊C4C22×D311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—61no—
502C2×C22⋊C4—61no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4#6711yescharacteristic
506C2×C22⋊C4#6711yescharacteristic
507C2×C42—21no—
508C2×C42—61no—
509C2×C42C22×D311yescharacteristic
510#107—34no—
511C4⋊C8—34no—
512#103—34no—
513#103—34no—
514#103—34no—
515#103—34no—
516#102—34no—
517#102—34no—
518C22⋊C8—34no—
519C22⋊C8—34no—
520C4×C8—34no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3#13514yescomplemented
531C23×C3C22×D412yes—
532C23×C3C22×D412yes—
533C23×C3C22×D411yescharacteristic
534C22×D3—22no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—42no—
538C3×Q8—24no—
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—22no—
542C3×Q8—48no—
543C3×Q8—42no—
544C3×Q8C22×D414yes—
545C3×D4—28no—
546C3×D4—22no—
547C3×D4—22no—
548C3×D4—48no—
549C3×D4—48no—
550C3×D4—42no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—24no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—24no—
558C2×C3×C4—24no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—48no—
566C2×C3×C4—48no—
567C2×C3×C4—42no—
568C2×C3×C4—42no—
569C2×C3×C4C22×D412yes—
570C2×C3×C4C22×D412yes—
571C2×C3×C4C22×D412yes—
572C2×C3×C4C22×D412yes—
573C2×C3×C4C22×D412yes—
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4H(5,𝔽2)12yes—
576C2×C3×C4C2511yescharacteristic
577#67—48no—
578#67—48no—
579C2×Dic3—24no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—48no—
584C2×Dic3—42no—
585C2×Dic3—42no—
586D12—22no—
587D12—22no—
588D12—42no—
589C4×D3—48no—
590Dic6—24no—
591Dic6—22no—
592Dic6—22no—
593Dic6—22no—
594Dic6—48no—
595Dic6—42no—
596Dic6C22×D414yes—
597C3⋊C8—22no—
598C3⋊C8—22no—
599C3⋊C8—22no—
600C3⋊C8C22×D414yes—
601C24—21no—
602C24—61no—
603C24C2×#6711yescharacteristic
604C24C2×#6711yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608#41—68no—
609#41—124no—
610#41—128no—
611C2×Q8—22no—
612C2×Q8—21no—
613C2×Q8—24no—
614C2×Q8—21no—
615C2×Q8—28no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—34no—
619C2×Q8—32no—
620C2×Q8—32no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—48no—
624C2×Q8—68no—
625C2×Q8—62no—
626C2×Q8—61no—
627C2×Q8—64no—
628C2×Q8—61no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—124no—
632C2×Q8—124no—
633C2×Q8—128no—
634C2×Q8D3×D414yes—
635C2×Q8C23×D312yes—
636C2×Q8C23×D312yes—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—32no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—64no—
647C2×D4—64no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4—61no—
651C2×D4—124no—
652C2×D4—124no—
653C2×D4C2×#6714yes—
654C2×D4C23×D312yes—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—61no—
667C22×C4—64no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—64no—
671C22×C4—124no—
672C22×C4—124no—
673C22×C4C2×#6712yes—
674C22×C4C2×#6712yes—
675C22×C4C2×#6711yescharacteristic
676C22×C4C2×#6711yescharacteristic
677C22×C4C2×#6711yescharacteristic
678C22×C4C2×#6711yescharacteristic
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C22×C4C23×D311yescharacteristic
682Q16—316no—
683Q16—68no—
684Q16—68no—
685Q16—68no—
686SD16—68no—
687SD16—68no—
688SD16—124no—
689SD16—124no—
690D8—68no—
691C2×C8—34no—
692C2×C8—32no—
693C2×C8—32no—
694C2×C8—32no—
695C2×C8—32no—
696C2×C8—68no—
697C2×C8—68no—
698C2×C8—62no—
699C2×C8—62no—
700C2×C8—62no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—21no—
704C4⋊C4—32no—
705C4⋊C4—61no—
706C4⋊C4—64no—
707C4⋊C4—64no—
708C4⋊C4C2×#6714yes—
709C4⋊C4C23×D312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C22⋊C4C2×#6714yes—
719C22⋊C4C2×#6714yes—
720C42—24no—
721C42—64no—
722C42C2×#6712yes—
723C42C23×D312yes—
724C22×C3—22no—
725C22×C3—28no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—44no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—84no—
735C22×C3D4212yes—
736C22×C3C2×#13512yes—
737C22×C3C2×#13514yescomplemented
738C22×C3#57812yes—
739C22×C3C23×D411yescharacteristic
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—84no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—24no—
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4D4212yes—
752C3×C4C23×D411yescharacteristic
753C3×C4C2×H(5,𝔽2)11yescharacteristic
754Dic3—24no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—62no—
767C23—122no—
768C23—122no—
769C23—122no—
770C23#95014yescomplemented
771C23C22×#6712yes—
772C23C22×#6712yes—
773C23C22×#6711yescharacteristic
774Q8—22no—
775Q8—24no—
776Q8—22no—
777Q8—22no—
778Q8—34no—
779Q8—48no—
780Q8—42no—
781Q8—62no—
782Q8—64no—
783Q8—62no—
784Q8—62no—
785Q8—128no—
786Q8—122no—
787Q8C2×D3×D414yes—
788D4—28no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—42no—
794D4—62no—
795D4—62no—
796D4—128no—
797D4—128no—
798D4—122no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—62no—
818C2×C4—64no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—128no—
822C2×C4—128no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4C2×D3×D412yes—
826C2×C4#100412yes—
827C2×C4C22×#6712yes—
828C2×C4C22×#6712yes—
829C2×C4C22×#6712yes—
830C2×C4C22×#6712yes—
831C2×C4C22×#6711yescharacteristic
832C2×C4C24×D311yescharacteristic
833C8—34no—
834C8—62no—
835C8—62no—
836C8—62no—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3—82no—
840C2×C3#328514yescomplemented
841C2×C3C2×D4211yescharacteristic
842C2×C3C22×#13511yescharacteristic
843C2×C3C2×#57811yescharacteristic
844D3—82no—
845C22—28no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—44no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—84no—
856C22—122no—
857C22—122no—
858C22—122no—
859C22—244no—
860C22D4×#6712yes—
861C22C2×#95012yes—
862C22C2×#95014yescomplemented
863C22#583812yes—
864C22C23×#6711yescharacteristic
865C4—22no—
866C4—22no—
867C4—24no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—64no—
873C4—122no—
874C4—122no—
875C4D4×#6712yes—
876C4C22×D3×D411yescharacteristic
877C4C2×#100411yescharacteristic
878C3C2×#328511yescharacteristic, complemented, Sylow
879C2—24no—
880C2—42no—
881C2—82no—
882C2—242no—
883C2#8354914yesdirect product factor
884C2C2×D4×#6711yescharacteristic
885C2C22×#95011yescharacteristic
886C2C2×#583811yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#548C2
socleC23×C3C22×D4
hypercenterC2×#548D3
hypocenterC3C2×#3285
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C22×#950C2semidirect
3. C23×#216C2semidirect
4. C2×#5552C2semidirect
5. C2×#5239C2semidirect
6. C2×#5227C2semidirect
7. #83549C2direct (N × H)
8. C2×#5054C2semidirect
9. C2×#5059C2semidirect
10. C2×#5047C2semidirect
11. C2×#5051C2semidirect
12. C2×#5040C2semidirect
13. C2×#5038C2semidirect
14. C2×#5028C2semidirect
15. C2×C4×#216C2semidirect
16. C2×D4×C3⋊C8C2semidirect
23. C3×#548C22semidirect
34. C2×#950C22semidirect
40. C22×#216C22semidirect
52. #5552C22semidirect
58. #5239C22semidirect
59. #5227C22semidirect
65. #5059C22semidirect
66. #5054C22semidirect
67. #5051C22semidirect
68. #5047C22semidirect
69. #5040C22semidirect
70. #5038C22semidirect
71. C4×#216C22semidirect
72. #5028C22semidirect
73. D4×C3⋊C8C22semidirect
83. C2×#548D3semidirect
163. C2×#216D4semidirect
238. #548C2×D3semidirect
377. #216C2×D4semidirect
530. C23×C3#135semidirect
737. C22×C3C2×#135semidirect
770. C23#950semidirect
840. C2×C3#3285semidirect
862. C22C2×#950semidirect
878. C3C2×#3285semidirect
883. C2#83549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C22×#9502
C23×#2162
C2×#55522
C2×#52392
C2×#52272
#835492
C2×#50542
C2×#50592
C2×#50472
C2×#50512
C2×#50402
C2×#50382
C2×#50282
C2×C4×#2162
C2×D4×C3⋊C82
C2×#32853