Finite Group Databasebeta

← C2×#80268 #11670310

Subgroups — C2×#80268 #11670310

Order 768.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5831C211yesmaximal, characteristic, complemented
2C22×#949C211yesmaximal, characteristic, complemented
3C22×#918C211yesmaximal, characteristic, complemented
4C2×#5630C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×#5185C211yesmaximal, characteristic, complemented
7C2×#5172C211yesmaximal, characteristic, complemented
8C2×#5168C211yesmaximal, characteristic, complemented
9C2×#5052C211yesmaximal, characteristic, complemented
10#80268C2116yesmaximal, direct product factor
11C2×#4806C211yesmaximal, characteristic, complemented
12C2×#4788C211yesmaximal, characteristic, complemented
13C2×#4787C211yesmaximal, characteristic, complemented
14C2×#4782C211yesmaximal, characteristic, complemented
15C2×#4731C211yesmaximal, characteristic, complemented
16C2×#4729C211yesmaximal, characteristic, complemented
17C2×#3275—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×D3×Q8C2211yescharacteristic, complemented
21C23×D12C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic, complemented
24C2×C3×C22⋊Q8C2211yescharacteristic
25#5831—24no—
26#5831C2218yescomplemented
27C2×#949—28no—
28C2×#949C2218yescomplemented
29C2×#947C2211yescharacteristic
30C2×Q8×Dic3C2211yescharacteristic, complemented
31C22×#216C2211yescharacteristic, complemented
32C22×#215C2211yescharacteristic
33C22×#215C2211yescharacteristic
34C2×#938—21no—
35C2×#938C2211yescharacteristic, complemented
36C2×#936—21no—
37C2×#936C2211yescharacteristic, complemented
38C22×#213C2211yescharacteristic
39C22×#213C2211yescharacteristic
40C2×C4×#67—21no—
41C2×C4×#67C2211yescharacteristic
42C2×#924—21no—
43C2×#924C2211yescharacteristic
44C22×#208C2211yescharacteristic
45C2×#918—28no—
46C2×#918C2218yescomplemented
47C22×#204C2211yescharacteristic
48C22×#204C2211yescharacteristic
49C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
50#5630—24no—
51#5630C2218yescomplemented
52C2×#895—21no—
53C2×#895C2211yescharacteristic
54C2×#894—21no—
55C2×#893C2211yescharacteristic
56C2×#882—21no—
57C2×D3×C22⋊C4—21no—
58C3×#452C2218yescomplemented
59C2×C3×#103C2211yescharacteristic, complemented
60C2×C3×#102C2211yescharacteristic, complemented
61C2×C3×C22⋊C8C2211yescharacteristic
62C2×#835C2211yescharacteristic, complemented
63#5185C2218yescomplemented
64#5172C2218yescomplemented
65#5168C2218yescomplemented
66C2×#821C2211yescharacteristic
67C2×#821C2211yescharacteristic
68C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
69C2×Dic3⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic3C2211yescharacteristic, complemented
71#5052C2218yescomplemented
72C2×#810C2211yescharacteristic, complemented
73C2×#808C2211yescharacteristic, complemented
74#4806C2218yescomplemented
75#4788C2218yescomplemented
76#4787C2218yescomplemented
77#4782C2218yescomplemented
78#4731C2218yescomplemented
79#4729C2218yescomplemented
80C22×#137—31no—
81C22×AGL(1,ℤ/8)—31no—
82C2×#548—31no—
83C2×#546—31no—
84#3275—316no—
85C2×#495—31no—
86C2×#470—31no—
87C2×#469—31no—
88C2×#464—31no—
89C2×#463—31no—
90C2×#452D311yescharacteristic, complemented
91C2×#449—31no—
92C2×#448—31no—
93C2×#450—31no—
94C2×C4×SD16—31no—
95C2×#436—31no—
96C24×D3—21no—
97C2×C3×#41—22no—
98C2×C3×#41—24no—
99C2×C3×#41—42no—
100C2×C3×#41C2314yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×Q8C2311yescharacteristic
103C22×C3×D4—21no—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C22×#67—21no—
108C22×#67D411yescharacteristic
109C2×#239—22no—
110C2×#239—24no—
111C2×#239—42no—
112C2×#239C2314yes—
113C2×D3×Q8—22no—
114C2×D3×Q8—24no—
115C2×D3×Q8—42no—
116C2×D3×Q8C2314yescomplemented
117C22×D12—24no—
118C22×D12—21no—
119C22×D12—21no—
120C22×D12—22no—
121C22×D12—21no—
122C22×D12—42no—
123C22×D12C2311yescharacteristic
124C22×D12C2314yes—
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—21no—
128C22×C4×D3—21no—
129C22×C4×D3C2311yescharacteristic
130C22×Dic6—21no—
131C22×Dic6C2311yescharacteristic
132C2×C3×Q16—24no—
133C2×C3×Q16C2314yescomplemented
134C2×C3×SD16—42no—
135C2×C3×SD16C2314yescomplemented
136C22×C3×C8C2311yescharacteristic
137C22×C3×C8C2311yescharacteristic
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8C2314yes—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×#217—21no—
144C2×#217—21no—
145C2×#217—21no—
146C2×#217—21no—
147C2×#217D411yescharacteristic
148#949—232no—
149#947—22no—
150#947C2314yes—
151Q8×Dic3—22no—
152Q8×Dic3C2314yescomplemented
153C2×#216—24no—
154C2×#216C2314yescomplemented
155C2×#215—24no—
156C2×#215D418yescomplemented
157C2×#215C2314yes—
158C2×#215C2314yes—
159#938—28no—
160#938—22no—
161#938C2314yescomplemented
162#936—28no—
163#936—22no—
164#936C2314yescomplemented
165C2×#213—24no—
166C2×#213—24no—
167C2×#213C2314yes—
168C2×#213C2314yes—
169C4×#67—28no—
170C4×#67D414yes—
171C4×#67C2314yes—
172C2×(C2×D3)⋊C4—21no—
173C2×(C2×D3)⋊C4—21no—
174C2×(C2×D3)⋊C4—21no—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4D411yescharacteristic
177C2×C4⋊Dic3—21no—
178C2×C4⋊Dic3C2311yescharacteristic
179#924—22no—
180#924—28no—
181#924C2314yes—
182C2×Dic3⋊C4—21no—
183C2×Dic3⋊C4D411yescharacteristic
184C2×C4×Dic3—21no—
185C2×C4×Dic3C2311yescharacteristic
186C2×#208—24no—
187C2×#208C2314yes—
188C22×C3⋊C8C2311yescharacteristic
189C22×C3⋊C8C2311yescharacteristic
190#918—232no—
191C2×#204—24no—
192C2×#204—42no—
193C2×#204C2314yes—
194C2×#204C2314yes—
195C2×ΓL(1,𝔽25)—24no—
196C2×ΓL(1,𝔽25)C2314yescomplemented
197#895—22no—
198#895—28no—
199#895C2314yes—
200#894—28no—
201#893—22no—
202#893C2314yes—
203#882—28no—
204D3×C22⋊C4—28no—
205C3×#103C2314yescomplemented
206C3×#102C2314yescomplemented
207C3×C22⋊C8C2314yes—
208#835C2314yescomplemented
209#821C2314yes—
210#821C2314yes—
211(C2×D3)⋊C8C2314yescomplemented
212Dic3⋊C8C2314yescomplemented
213C8×Dic3C2314yescomplemented
214#810C2314yescomplemented
215#808C2314yescomplemented
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×Q8—31no—
219C23×D4—31no—
220C2×#137—38no—
221C2×#137—68no—
222C2×AGL(1,ℤ/8)—38no—
223C2×AGL(1,ℤ/8)—68no—
224C22×Q16—31no—
225C22×Q16C2×D311yescharacteristic, complemented
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16C2×D311yescharacteristic, complemented
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
234C22×M16—31no—
235#548—38no—
236#548—64no—
237#546—38no—
238#546—64no—
239C2×#124—31no—
240C2×#124—31no—
241C2×#124—61no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—61no—
245C2×C22⋊Q8C2×D311yescharacteristic
246C2×#121—31no—
247C2×#121—31no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#120—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C22⋊C4—61no—
256#495—38no—
257#470—38no—
258#469—38no—
259#464—38no—
260#463—38no—
261#452C2×D318yescomplemented
262#450—38no—
263#449—38no—
264#448—38no—
265C4×SD16—38no—
266#436—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103C2×D311yescharacteristic, complemented
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic, complemented
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—24no—
283C23×D3—44no—
284C23×D3—44no—
285C23×D3—82no—
286C23×D3C2×D411yescharacteristic
287C3×#41—28no—
288C3×#41—44no—
289C3×#41—48no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8C2×D414yes—
296C2×C3×Q8C2412yes—
297C2×C3×Q8C2412yes—
298C2×C3×D4—24no—
299C2×C3×D4—22no—
300C2×C3×D4—21no—
301C2×C3×D4—22no—
302C2×C3×D4—44no—
303C2×C3×D4C2412yes—
304C22×C3×C4—21no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—24no—
310C22×C3×C4—44no—
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2412yes—
314C22×C3×C4C2411yescharacteristic
315C2×#67—24no—
316C2×#67—42no—
317C2×#67—44no—
318C2×#67C2×D414yes—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3C2×D411yescharacteristic
322C22×Dic3C2×D411yescharacteristic
323C22×Dic3C2×D411yescharacteristic
324#239—28no—
325#239—44no—
326#239—48no—
327D3×Q8—28no—
328D3×Q8—44no—
329D3×Q8—48no—
330C2×D12—21no—
331C2×D12—22no—
332C2×D12—22no—
333C2×D12—22no—
334C2×D12—28no—
335C2×D12—24no—
336C2×D12—24no—
337C2×D12—21no—
338C2×D12—24no—
339C2×D12—44no—
340C2×D12—48no—
341C2×D12—44no—
342C2×D12—44no—
343C2×D12—82no—
344C2×D12C2×D414yes—
345C2×D12C2412yes—
346C2×D12C2412yes—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—24no—
350C2×C4×D3—24no—
351C2×C4×D3—24no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—82no—
355C2×C4×D3C2×D412yes—
356C2×C4×D3C2412yes—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—21no—
360C2×Dic6—24no—
361C2×Dic6—44no—
362C2×Dic6C2412yes—
363C3×Q16—28no—
364C3×SD16—44no—
365C2×C3×C8—22no—
366C2×C3×C8—22no—
367C2×C3×C8C2412yes—
368C2×C3×C8C2412yes—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—24no—
371C3×C4⋊C4C2412yes—
372C3×C22⋊C4—24no—
373#217—24no—
374#217—24no—
375#217—24no—
376#217—24no—
377#217C2×D414yes—
378#216—28no—
379#215—28no—
380#215C2×D4116yescomplemented
381#213—28no—
382#213—28no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4C2×D414yes—
388C4⋊Dic3—21no—
389C4⋊Dic3—24no—
390C4⋊Dic3C2412yes—
391Dic3⋊C4—24no—
392Dic3⋊C4C2×D414yes—
393C4×Dic3—24no—
394C4×Dic3C2×D412yes—
395C4×Dic3C2412yes—
396#208—28no—
397C2×C3⋊C8—22no—
398C2×C3⋊C8C2×D414yes—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401#204—28no—
402#204—44no—
403ΓL(1,𝔽25)—28no—
404C25—61no—
405C2×#41—22no—
406C2×#41—24no—
407C2×#41—34no—
408C2×#41—42no—
409C2×#41—62no—
410C2×#41—64no—
411C2×#41—122no—
412C2×#41C22×D314yes—
413C22×Q8—34no—
414C22×Q8—31no—
415C22×Q8—61no—
416C22×Q8—62no—
417C22×Q8—64no—
418C22×Q8—122no—
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D311yescharacteristic
421C22×D4—21no—
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—34no—
426C22×D4—64no—
427C22×D4—61no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—62no—
432C22×D4—122no—
433C22×D4C22×D311yescharacteristic
434C23×C4—21no—
435C23×C4—31no—
436C23×C4—61no—
437C23×C4—61no—
438C23×C4—61no—
439C23×C4C22×D311yescharacteristic
440#137—632no—
441AGL(1,ℤ/8)—632no—
442C2×Q16—24no—
443C2×Q16—34no—
444C2×Q16—64no—
445C2×Q16C22×D314yescomplemented
446C2×SD16—38no—
447C2×SD16—34no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—42no—
452C2×SD16—64no—
453C2×SD16—64no—
454C2×SD16—122no—
455C2×SD16C22×D314yescomplemented
456C2×D8—34no—
457C2×D8—34no—
458C2×D8—64no—
459C2×D8—64no—
460C2×M16—34no—
461C2×M16—34no—
462C2×M16—64no—
463C2×M16—64no—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8C22×D311yescharacteristic
467C22×C8C22×D311yescharacteristic
468#124—34no—
469#124—34no—
470#124—62no—
471#124—62no—
472#124—68no—
473#123—68no—
474C22⋊Q8—22no—
475C22⋊Q8—34no—
476C22⋊Q8—68no—
477C22⋊Q8—62no—
478C22⋊Q8C22×D314yes—
479#121—34no—
480#121—34no—
481#121—68no—
482#121—62no—
483#121—62no—
484#121—68no—
485#120—68no—
486C4×Q8—34no—
487C4×Q8—62no—
488C4×D4—34no—
489C4×D4—34no—
490C4×D4—34no—
491C4×D4—62no—
492C4×D4—68no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—68no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C42—31no—
512C2×C42—61no—
513#106—34no—
514C4⋊C8—34no—
515#103—34no—
516#103—34no—
517#103C22×D314yescomplemented
518#102—34no—
519#102—34no—
520#102C22×D314yescomplemented
521C22⋊C8—34no—
522C22⋊C8C22×D314yes—
523C4×C8—34no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3C22×D412yes—
532C23×C3C22×D411yescharacteristic
533C22×D3—22no—
534C22×D3—24no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—48no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—48no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—84no—
547C22×D3—816no—
548C22×D3C22×D412yes—
549C3×Q8—24no—
550C3×Q8—22no—
551C3×Q8—22no—
552C3×Q8—22no—
553C3×Q8—42no—
554C3×Q8C22×D414yes—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—48no—
558C3×D4—42no—
559C2×C3×C4—24no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—24no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—48no—
568C2×C3×C4—42no—
569C2×C3×C4—42no—
570C2×C3×C4C22×D412yes—
571C2×C3×C4C22×D411yescharacteristic
572C2×C3×C4C22×D412yes—
573C2×C3×C4H(5,𝔽2)12yes—
574C2×C3×C4C2511yescharacteristic
575#67—44no—
576#67—48no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—42no—
583C2×Dic3—42no—
584C2×Dic3C22×D412yes—
585C2×Dic3C22×D412yes—
586C2×Dic3C22×D412yes—
587D12—24no—
588D12—22no—
589D12—22no—
590D12—22no—
591D12—48no—
592D12—48no—
593D12—42no—
594D12—84no—
595D12C22×D414yes—
596C4×D3—24no—
597C4×D3—22no—
598C4×D3—22no—
599C4×D3—48no—
600C4×D3—48no—
601C4×D3—84no—
602Dic6—22no—
603Dic6—22no—
604Dic6—48no—
605Dic6—42no—
606C3×C8—22no—
607C3×C8—22no—
608C3⋊C8—22no—
609C3⋊C8C22×D414yes—
610C24—21no—
611C24—31no—
612C24—61no—
613C24—61no—
614C24—64no—
615C24—124no—
616C24—124no—
617C24—242no—
618C24D3×D411yescharacteristic
619#41—28no—
620#41—44no—
621#41—48no—
622#41—68no—
623#41—124no—
624#41—128no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—32no—
631C2×Q8—64no—
632C2×Q8—61no—
633C2×Q8—68no—
634C2×Q8—62no—
635C2×Q8—62no—
636C2×Q8—124no—
637C2×Q8—124no—
638C2×Q8—128no—
639C2×Q8D3×D414yes—
640C2×Q8C23×D312yes—
641C2×Q8C23×D312yes—
642C2×D4—24no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—34no—
647C2×D4—34no—
648C2×D4—32no—
649C2×D4—32no—
650C2×D4—44no—
651C2×D4—68no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—61no—
656C2×D4—62no—
657C2×D4—64no—
658C2×D4—61no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—124no—
662C2×D4—128no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—122no—
666C2×D4—124no—
667C2×D4—242no—
668C2×D4C23×D312yes—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—44no—
681C22×C4—64no—
682C22×C4—64no—
683C22×C4—64no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—242no—
691C22×C4D3×D412yes—
692C22×C4D3×D411yescharacteristic
693C22×C4C23×D312yes—
694C22×C4C23×D311yescharacteristic
695Q16—28no—
696Q16—68no—
697SD16—316no—
698SD16—44no—
699SD16—68no—
700SD16—68no—
701SD16—124no—
702D8—68no—
703D8—68no—
704M16—68no—
705M16—68no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—34no—
709C2×C8—32no—
710C2×C8—32no—
711C2×C8—62no—
712C2×C8C23×D312yes—
713C2×C8C23×D312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—34no—
717C4⋊C4—32no—
718C4⋊C4—64no—
719C4⋊C4—61no—
720C4⋊C4—64no—
721C4⋊C4C23×D312yes—
722C22⋊C4—24no—
723C22⋊C4—34no—
724C22⋊C4—34no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C22⋊C4—64no—
732C22⋊C4—64no—
733C42—32no—
734C42—32no—
735C42—64no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—44no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—84no—
744C22×C3D4212yes—
745C22×C3#57512yes—
746C22×C3#57712yes—
747C22×C3C23×D411yescharacteristic
748C2×D3—22no—
749C2×D3—24no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—44no—
753C2×D3—48no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—816no—
760C2×D3—84no—
761C3×C4—24no—
762C3×C4—22no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4D4212yes—
766C3×C4C23×D411yescharacteristic
767C3×C4C2×H(5,𝔽2)11yescharacteristic
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—42no—
772Dic3—42no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—32no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—64no—
786C23—62no—
787C23—128no—
788C23—128no—
789C23—122no—
790C23—122no—
791C23—122no—
792C23—122no—
793C23—122no—
794C23—244no—
795C23—2416no—
796C23C2×D3×D412yes—
797C23C2×D3×D411yescharacteristic
798Q8—22no—
799Q8—24no—
800Q8—22no—
801Q8—22no—
802Q8—42no—
803Q8—62no—
804Q8—62no—
805Q8—128no—
806Q8—122no—
807Q8C2×D3×D414yes—
808D4—22no—
809D4—22no—
810D4—34no—
811D4—48no—
812D4—42no—
813D4—62no—
814D4—62no—
815D4—62no—
816D4—64no—
817D4—128no—
818D4—128no—
819D4—124no—
820D4—128no—
821D4—122no—
822D4—244no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—48no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—64no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—128no—
846C2×C4—128no—
847C2×C4—122no—
848C2×C4—122no—
849C2×C4—244no—
850C2×C4C2×D3×D412yes—
851C2×C4C2×D3×D412yes—
852C2×C4C2×D3×D411yescharacteristic
853C2×C4#100412yes—
854C2×C4C24×D311yescharacteristic
855C8—22no—
856C8—22no—
857C8—34no—
858C8—62no—
859C2×C3—42no—
860C2×C3—82no—
861C2×C3#327514yescomplemented
862C2×C3C2×D4211yescharacteristic
863C2×C3C2×#57511yescharacteristic
864C2×C3C2×#57711yescharacteristic
865D3—42no—
866D3—44no—
867D3—82no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—44no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—64no—
879C22—84no—
880C22—124no—
881C22—128no—
882C22—122no—
883C22—122no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22—2416no—
888C22—244no—
889C22#559012yes—
890C22#577012yes—
891C22#577712yes—
892C22C22×D3×D411yescharacteristic
893C4—22no—
894C4—24no—
895C4—42no—
896C4—42no—
897C4—62no—
898C4—62no—
899C4—62no—
900C4—122no—
901C4—122no—
902C4#559012yes—
903C4C22×D3×D411yescharacteristic
904C4C2×#100411yescharacteristic
905C3C2×#327511yescharacteristic, complemented, Sylow
906C2—42no—
907C2—82no—
908C2—122no—
909C2—124no—
910C2—242no—
911C2#8026814yesdirect product factor
912C2C2×#559011yescharacteristic
913C2C2×#577011yescharacteristic
914C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
hypercenterC2×#452D3
hypocenterC3C2×#3275
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#5831C2semidirect
2. C22×#949C2semidirect
3. C22×#918C2semidirect
4. C2×#5630C2semidirect
5. C2×C3×#452C2semidirect
6. C2×#5185C2semidirect
7. C2×#5172C2semidirect
8. C2×#5168C2semidirect
9. C2×#5052C2semidirect
10. #80268C2direct (N × H)
11. C2×#4806C2semidirect
12. C2×#4788C2semidirect
13. C2×#4787C2semidirect
14. C2×#4782C2semidirect
15. C2×#4731C2semidirect
16. C2×#4729C2semidirect
20. C22×D3×Q8C22semidirect
22. C22×C3×Q16C22semidirect
23. C22×C3×SD16C22semidirect
26. #5831C22semidirect
28. C2×#949C22semidirect
30. C2×Q8×Dic3C22semidirect
31. C22×#216C22semidirect
35. C2×#938C22semidirect
37. C2×#936C22semidirect
46. C2×#918C22semidirect
49. C22×ΓL(1,𝔽25)C22semidirect
51. #5630C22semidirect
58. C3×#452C22semidirect
59. C2×C3×#103C22semidirect
60. C2×C3×#102C22semidirect
62. C2×#835C22semidirect
63. #5185C22semidirect
64. #5172C22semidirect
65. #5168C22semidirect
68. C2×(C2×D3)⋊C8C22semidirect
69. C2×Dic3⋊C8C22semidirect
70. C2×C8×Dic3C22semidirect
71. #5052C22semidirect
72. C2×#810C22semidirect
73. C2×#808C22semidirect
74. #4806C22semidirect
75. #4788C22semidirect
76. #4787C22semidirect
77. #4782C22semidirect
78. #4731C22semidirect
79. #4729C22semidirect
90. C2×#452D3semidirect
116. C2×D3×Q8C23semidirect
133. C2×C3×Q16C23semidirect
135. C2×C3×SD16C23semidirect
152. Q8×Dic3C23semidirect
154. C2×#216C23semidirect
156. C2×#215D4semidirect
161. #938C23semidirect
164. #936C23semidirect
196. C2×ΓL(1,𝔽25)C23semidirect
205. C3×#103C23semidirect
206. C3×#102C23semidirect
208. #835C23semidirect
211. (C2×D3)⋊C8C23semidirect
212. Dic3⋊C8C23semidirect
213. C8×Dic3C23semidirect
214. #810C23semidirect
215. #808C23semidirect
225. C22×Q16C2×D3semidirect
230. C22×SD16C2×D3semidirect
261. #452C2×D3semidirect
271. C2×#103C2×D3semidirect
274. C2×#102C2×D3semidirect
380. #215C2×D4semidirect
445. C2×Q16C22×D3semidirect
455. C2×SD16C22×D3semidirect
517. #103C22×D3semidirect
520. #102C22×D3semidirect
861. C2×C3#3275semidirect
905. C3C2×#3275semidirect
911. C2#80268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58312
C22×#9492
C22×#9182
C2×#56302
C2×C3×#4522
C2×#51852
C2×#51722
C2×#51682
C2×#50522
#802682
C2×#48062
C2×#47882
C2×#47872
C2×#47822
C2×#47312
C2×#47292
C2×#32753