Finite Group Databasebeta

← C2×#80062 #11670320

Subgroups — C2×#80062 #11670320

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×#5817C211yesmaximal, characteristic, complemented
2C22×#942C211yesmaximal, characteristic, complemented
3C22×#914C211yesmaximal, characteristic, complemented
4C2×#5612C211yesmaximal, characteristic, complemented
5C2×C3×#448C211yesmaximal, characteristic, complemented
6C2×#5169C211yesmaximal, characteristic, complemented
7C2×#5168C211yesmaximal, characteristic, complemented
8C2×#5166C211yesmaximal, characteristic, complemented
9C2×#5039C211yesmaximal, characteristic, complemented
10#80062C2116yesmaximal, direct product factor
11C2×#4819C211yesmaximal, characteristic, complemented
12C2×#4816C211yesmaximal, characteristic, complemented
13C2×#4808C211yesmaximal, characteristic, complemented
14C2×#4788C211yesmaximal, characteristic, complemented
15C2×#4734C211yesmaximal, characteristic, complemented
16C2×#4729C211yesmaximal, characteristic, complemented
17C2×#3275—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic, complemented
19C22×#239C2211yescharacteristic
20C22×D3×D4C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25#5817—24no—
26#5817C2218yescomplemented
27C2×#947—21no—
28C2×#947C2211yescharacteristic, complemented
29C2×#946—21no—
30C2×#946C2211yescharacteristic
31C2×Q8×Dic3C2211yescharacteristic, complemented
32C22×#216C2211yescharacteristic, complemented
33C22×#216C2211yescharacteristic, complemented
34C2×#942—28no—
35C2×#942C2218yescomplemented
36C22×#215C2211yescharacteristic
37C22×#215C2211yescharacteristic
38C2×#938—21no—
39C2×#937—21no—
40C2×#936C2211yescharacteristic
41C22×#213C2211yescharacteristic
42C2×#930—21no—
43C2×#930C2211yescharacteristic, complemented
44C2×C4×#67—21no—
45C2×C4×#67C2211yescharacteristic
46C22×#208C2211yescharacteristic, complemented
47C2×#914—28no—
48C2×#914C2218yescomplemented
49C22×D24C2211yescharacteristic
50C22×#204C2211yescharacteristic, complemented
51C22×ΓL(1,𝔽25)C2211yescharacteristic
52#5612—24no—
53#5612C2218yescomplemented
54C2×#897C2211yescharacteristic
55C2×#893C2211yescharacteristic
56C2×#883—21no—
57C2×D3×C22⋊C4—21no—
58C3×#448C2218yescomplemented
59C2×C3×#103C2211yescharacteristic, complemented
60C2×C3×#103C2211yescharacteristic, complemented
61C2×C3×C22⋊C8C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic
63#5169C2218yescomplemented
64#5168C2218yescomplemented
65#5166C2218yescomplemented
66C2×#821C2211yescharacteristic
67C2×(C2×D3)⋊C8C2211yescharacteristic
68C2×#816C2211yescharacteristic, complemented
69C2×Dic3⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic3C2211yescharacteristic, complemented
71#5039C2218yescomplemented
72C2×#809C2211yescharacteristic, complemented
73C2×#808C2211yescharacteristic, complemented
74#4819C2218yescomplemented
75#4816C2218yescomplemented
76#4808C2218yescomplemented
77#4788C2218yescomplemented
78#4734C2218yescomplemented
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×#452—31no—
91C2×#449—31no—
92C2×#448D311yescharacteristic, complemented
93C2×#450—31no—
94C2×C4×SD16—31no—
95C2×#436—31no—
96C24×D3—21no—
97C22×C3×Q8—21no—
98C22×C3×Q8—22no—
99C22×C3×Q8—24no—
100C22×C3×Q8—42no—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×Q8C2311yescharacteristic
103C22×C3×Q8C2314yescomplemented
104C22×C3×D4—21no—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67D411yescharacteristic
112C2×#239—22no—
113C2×#239—24no—
114C2×#239—42no—
115C2×#239C2314yes—
116C2×D3×D4—24no—
117C2×D3×D4—22no—
118C2×D3×D4—42no—
119C2×D3×D4C2314yes—
120C2×#235—22no—
121C2×#235—24no—
122C2×#235—42no—
123C2×#235C2314yes—
124C22×D12—21no—
125C22×D12C2311yescharacteristic
126C22×D12C2311yescharacteristic
127C22×C4×D3—21no—
128C22×C4×D3—21no—
129C22×C4×D3—21no—
130C22×C4×D3C2311yescharacteristic
131C22×Dic6C2311yescharacteristic
132C2×C3×SD16—24no—
133C2×C3×SD16—42no—
134C2×C3×SD16C2314yes—
135C2×C3×SD16C2314yes—
136C22×C3×C8C2311yescharacteristic
137C22×C3×C8C2311yescharacteristic
138C3×#121—22no—
139C3×#121C2314yes—
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C22⋊C4—21no—
142C2×#217—21no—
143C2×#217—21no—
144C2×#217D411yescharacteristic
145#947—28no—
146#947—22no—
147#947C2314yescomplemented
148#946—22no—
149#946—28no—
150#946C2314yes—
151Q8×Dic3—22no—
152Q8×Dic3C2314yescomplemented
153C2×#216—24no—
154C2×#216—24no—
155C2×#216C2314yescomplemented
156C2×#216C2314yescomplemented
157#942—232no—
158C2×#215—24no—
159C2×#215D418yescomplemented
160C2×#215C2314yes—
161C2×#215C2314yes—
162#938—28no—
163#937—28no—
164#936—22no—
165#936C2314yes—
166C2×#213—24no—
167C2×#213C2314yes—
168#930—22no—
169#930—28no—
170#930C2314yescomplemented
171C4×#67—28no—
172C4×#67D414yes—
173C4×#67C2314yes—
174C2×(C2×D3)⋊C4—21no—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4—21no—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4D411yescharacteristic
181C2×C4⋊Dic3—21no—
182C2×C4⋊Dic3—21no—
183C2×C4⋊Dic3C2311yescharacteristic
184C2×Dic3⋊C4—21no—
185C2×Dic3⋊C4D411yescharacteristic
186C2×C4×Dic3—21no—
187C2×C4×Dic3C2311yescharacteristic
188C2×#208—24no—
189C2×#208C2314yescomplemented
190C22×C3⋊C8C2311yescharacteristic
191C22×C3⋊C8C2311yescharacteristic
192#914—232no—
193C2×D24—24no—
194C2×D24C2314yes—
195C2×#204—42no—
196C2×#204C2314yescomplemented
197C2×ΓL(1,𝔽25)—24no—
198C2×ΓL(1,𝔽25)C2314yes—
199#897—22no—
200#897C2314yes—
201#893—22no—
202#893C2314yes—
203#883—28no—
204D3×C22⋊C4—28no—
205C3×#103C2314yescomplemented
206C3×#103C2314yescomplemented
207C3×C22⋊C8C2314yescomplemented
208#832C2314yes—
209#821C2314yes—
210(C2×D3)⋊C8C2314yes—
211#816C2314yescomplemented
212Dic3⋊C8C2314yescomplemented
213C8×Dic3C2314yescomplemented
214#809C2314yescomplemented
215#808C2314yescomplemented
216C22×#41—31no—
217C22×#41—31no—
218C23×Q8C2×D311yescharacteristic, complemented
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×Q16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16C2×D311yescharacteristic
230C22×SD16C2×D311yescharacteristic
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—31no—
245C2×C22⋊Q8—61no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#121C2×D311yescharacteristic
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#452—38no—
262#450—38no—
263#449—38no—
264#448C2×D318yescomplemented
265C4×SD16—38no—
266#436—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103C2×D311yescharacteristic, complemented
271C2×#103C2×D311yescharacteristic, complemented
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic, complemented
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
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—24no—
290C2×C3×Q8—22no—
291C2×C3×Q8—28no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—44no—
295C2×C3×Q8—44no—
296C2×C3×Q8—48no—
297C2×C3×Q8C2×D414yes—
298C2×C3×Q8C2412yes—
299C2×C3×Q8C2412yes—
300C2×C3×D4—24no—
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—22no—
304C2×C3×D4—82no—
305C2×C3×D4C2412yes—
306C22×C3×C4—21no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—24no—
312C22×C3×C4—44no—
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2412yes—
316C22×C3×C4C2411yescharacteristic
317C2×#67—24no—
318C2×#67—24no—
319C2×#67—24no—
320C2×#67—42no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67C2×D414yes—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3C2×D411yescharacteristic
328C22×Dic3C2×D411yescharacteristic
329C22×Dic3C2×D411yescharacteristic
330#239—28no—
331#239—44no—
332#239—48no—
333D3×D4—28no—
334D3×D4—44no—
335D3×D4—48no—
336#235—28no—
337#235—44no—
338#235—48no—
339C2×D12—21no—
340C2×D12—22no—
341C2×D12—22no—
342C2×D12—22no—
343C2×D12—24no—
344C2×D12—21no—
345C2×D12—44no—
346C2×D12C2×D414yes—
347C2×D12C2412yes—
348C2×D12C2412yes—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—24no—
352C2×C4×D3—24no—
353C2×C4×D3—24no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—82no—
357C2×C4×D3C2×D412yes—
358C2×C4×D3C2412yes—
359C2×Dic6—22no—
360C2×Dic6—22no—
361C2×Dic6—21no—
362C2×Dic6C2412yes—
363C3×SD16—28no—
364C3×SD16—44no—
365C2×C3×C8—22no—
366C2×C3×C8—22no—
367C2×C3×C8C2412yes—
368C2×C3×C8C2412yes—
369C3×C4⋊C4—21no—
370C3×C4⋊C4C2412yes—
371C3×C22⋊C4—24no—
372#217—24no—
373#217—24no—
374#217C2×D414yes—
375#216—28no—
376#216—28no—
377#215—28no—
378#215C2×D4116yescomplemented
379#213—28no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4C2×D414yes—
387C4⋊Dic3—21no—
388C4⋊Dic3—24no—
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—
401D24—28no—
402#204—44no—
403ΓL(1,𝔽25)—28no—
404C25—61no—
405C2×#41—34no—
406C2×#41—34no—
407C2×#41—64no—
408C2×#41—62no—
409C2×#41—62no—
410C2×#41—64no—
411C2×#41—122no—
412C2×#41—122no—
413C22×Q8—21no—
414C22×Q8—22no—
415C22×Q8—24no—
416C22×Q8—31no—
417C22×Q8—42no—
418C22×Q8C22×D311yescharacteristic
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D314yescomplemented
421C22×D4—21no—
422C22×D4—31no—
423C22×D4—34no—
424C22×D4—31no—
425C22×D4—31no—
426C22×D4—61no—
427C22×D4—62no—
428C22×D4—61no—
429C22×D4—64no—
430C22×D4—61no—
431C22×D4—61no—
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—34no—
443C2×Q16—34no—
444C2×Q16—64no—
445C2×Q16—64no—
446C2×SD16—24no—
447C2×SD16—38no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—42no—
452C2×SD16—64no—
453C2×SD16—122no—
454C2×SD16C22×D314yes—
455C2×SD16C22×D314yes—
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—34no—
475C22⋊Q8—34no—
476C22⋊Q8—62no—
477C22⋊Q8—68no—
478C22⋊Q8—62no—
479#121—22no—
480#121—34no—
481#121—68no—
482#121—68no—
483#121—62no—
484#121C22×D314yes—
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—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—61no—
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#103C22×D314yescomplemented
517#103C22×D314yescomplemented
518#102—34no—
519#102—34no—
520#102—34no—
521C22⋊C8—34no—
522C22⋊C8C22×D314yescomplemented
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—48no—
541C22×D3—42no—
542C22×D3—42no—
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—48no—
554C3×Q8—42no—
555C3×Q8C22×D414yes—
556C3×D4—22no—
557C3×D4—22no—
558C3×D4—42no—
559C3×D4—84no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—22no—
563C2×C3×C4—24no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—48no—
569C2×C3×C4—42no—
570C2×C3×C4—42no—
571C2×C3×C4C22×D412yes—
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D412yes—
574C2×C3×C4H(5,𝔽2)12yes—
575C2×C3×C4C2511yescharacteristic
576#67—44no—
577#67—48no—
578#67—48no—
579#67—48no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—42no—
586C2×Dic3—42no—
587C2×Dic3C22×D412yes—
588C2×Dic3C22×D412yes—
589C2×Dic3C22×D412yes—
590D12—24no—
591D12—22no—
592D12—22no—
593D12—22no—
594D12—48no—
595D12—42no—
596D12C22×D414yes—
597C4×D3—24no—
598C4×D3—22no—
599C4×D3—22no—
600C4×D3—48no—
601C4×D3—48no—
602C4×D3—84no—
603Dic6—22no—
604Dic6—22no—
605Dic6—42no—
606C3×C8—22no—
607C3×C8—22no—
608C3⋊C8—22no—
609C3⋊C8C22×D414yes—
610C24—21no—
611C24—31no—
612C24—64no—
613C24—61no—
614C24—61no—
615C24—124no—
616C24—124no—
617C24—242no—
618C24D3×D411yescharacteristic
619#41—68no—
620#41—68no—
621#41—124no—
622#41—128no—
623#41—124no—
624#41—128no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—24no—
628C2×Q8—22no—
629C2×Q8—28no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—32no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—48no—
636C2×Q8—61no—
637C2×Q8—62no—
638C2×Q8—62no—
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—64no—
651C2×D4—64no—
652C2×D4—68no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—61no—
656C2×D4—62no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—82no—
661C2×D4—124no—
662C2×D4—124no—
663C2×D4—128no—
664C2×D4—122no—
665C2×D4—124no—
666C2×D4—124no—
667C2×D4—124no—
668C2×D4C23×D312yes—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—21no—
674C22×C4—21no—
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—62no—
684C22×C4—62no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—64no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—242no—
691C22×C4D3×D412yes—
692C22×C4D3×D411yescharacteristic
693C22×C4C23×D312yes—
694C22×C4C23×D311yescharacteristic
695Q16—68no—
696Q16—68no—
697SD16—28no—
698SD16—316no—
699SD16—44no—
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—21no—
715C4⋊C4—34no—
716C4⋊C4—32no—
717C4⋊C4—64no—
718C4⋊C4—64no—
719C4⋊C4—64no—
720C4⋊C4—61no—
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—22no—
762C3×C4—24no—
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—48no—
803Q8—42no—
804Q8—62no—
805Q8—62no—
806Q8—122no—
807Q8C2×D3×D414yes—
808D4—22no—
809D4—22no—
810D4—34no—
811D4—42no—
812D4—62no—
813D4—62no—
814D4—62no—
815D4—64no—
816D4—84no—
817D4—128no—
818D4—124no—
819D4—128no—
820D4—128no—
821D4—128no—
822D4—122no—
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—122no—
881C22—122no—
882C22—124no—
883C22—128no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22—2416no—
888C22—244no—
889C22#559012yes—
890C22#576212yes—
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#8006214yesdirect product factor
912C2C2×#559011yescharacteristic
913C2C2×#576211yescharacteristic
914C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#448C2
socleC23×C3C22×D4
hypercenterC2×#448D3
hypocenterC3C2×#3275
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#5817C2semidirect
2. C22×#942C2semidirect
3. C22×#914C2semidirect
4. C2×#5612C2semidirect
5. C2×C3×#448C2semidirect
6. C2×#5169C2semidirect
7. C2×#5168C2semidirect
8. C2×#5166C2semidirect
9. C2×#5039C2semidirect
10. #80062C2direct (N × H)
11. C2×#4819C2semidirect
12. C2×#4816C2semidirect
13. C2×#4808C2semidirect
14. C2×#4788C2semidirect
15. C2×#4734C2semidirect
16. C2×#4729C2semidirect
18. C23×C3×Q8C22semidirect
26. #5817C22semidirect
28. C2×#947C22semidirect
31. C2×Q8×Dic3C22semidirect
32. C22×#216C22semidirect
33. C22×#216C22semidirect
35. C2×#942C22semidirect
43. C2×#930C22semidirect
46. C22×#208C22semidirect
48. C2×#914C22semidirect
50. C22×#204C22semidirect
53. #5612C22semidirect
58. C3×#448C22semidirect
59. C2×C3×#103C22semidirect
60. C2×C3×#103C22semidirect
61. C2×C3×C22⋊C8C22semidirect
63. #5169C22semidirect
64. #5168C22semidirect
65. #5166C22semidirect
68. C2×#816C22semidirect
69. C2×Dic3⋊C8C22semidirect
70. C2×C8×Dic3C22semidirect
71. #5039C22semidirect
72. C2×#809C22semidirect
73. C2×#808C22semidirect
74. #4819C22semidirect
75. #4816C22semidirect
76. #4808C22semidirect
77. #4788C22semidirect
78. #4734C22semidirect
79. #4729C22semidirect
92. C2×#448D3semidirect
103. C22×C3×Q8C23semidirect
147. #947C23semidirect
152. Q8×Dic3C23semidirect
155. C2×#216C23semidirect
156. C2×#216C23semidirect
159. C2×#215D4semidirect
170. #930C23semidirect
189. C2×#208C23semidirect
196. C2×#204C23semidirect
205. C3×#103C23semidirect
206. C3×#103C23semidirect
207. C3×C22⋊C8C23semidirect
211. #816C23semidirect
212. Dic3⋊C8C23semidirect
213. C8×Dic3C23semidirect
214. #809C23semidirect
215. #808C23semidirect
218. C23×Q8C2×D3semidirect
264. #448C2×D3semidirect
270. C2×#103C2×D3semidirect
271. C2×#103C2×D3semidirect
276. C2×C22⋊C8C2×D3semidirect
378. #215C2×D4semidirect
420. C22×Q8C22×D3semidirect
516. #103C22×D3semidirect
517. #103C22×D3semidirect
522. C22⋊C8C22×D3semidirect
861. C2×C3#3275semidirect
905. C3C2×#3275semidirect
911. C2#80062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58172
C22×#9422
C22×#9142
C2×#56122
C2×C3×#4482
C2×#51692
C2×#51682
C2×#51662
C2×#50392
#800622
C2×#48192
C2×#48162
C2×#48082
C2×#47882
C2×#47342
C2×#47292
C2×#32753