Finite Group Databasebeta

← C2×#81830 #11670316

Subgroups — C2×#81830 #11670316

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
1C22×#918C211yesmaximal, characteristic, complemented
2C22×#911C211yesmaximal, characteristic, complemented
3C2×#5677C211yesmaximal, characteristic, complemented
4C2×#5676C211yesmaximal, characteristic, complemented
5C2×C3×#495C211yesmaximal, characteristic, complemented
6C2×#5189C211yesmaximal, characteristic, complemented
7C2×#5173C211yesmaximal, characteristic, complemented
8C2×#5172C211yesmaximal, characteristic, complemented
9C2×#5170C211yesmaximal, characteristic, complemented
10C2×#5169C211yesmaximal, characteristic, complemented
11C2×#5159C211yesmaximal, characteristic, complemented
12C2×#5054C211yesmaximal, characteristic, complemented
13C2×#5057C211yesmaximal, characteristic, complemented
14#81830C2116yesmaximal, direct product factor
15C2×C4×#204C211yesmaximal, characteristic, complemented
16C2×#4688C211yesmaximal, characteristic, complemented
17C2×#3275—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×D3×Q8C2211yescharacteristic, complemented
20C22×#237C2211yescharacteristic
21C22×D3×D4C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic, complemented
25C22×C3×D8C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic, complemented
28C2×#946C2211yescharacteristic
29C2×#946C2211yescharacteristic
30C22×#216C2211yescharacteristic, complemented
31C22×#215C2211yescharacteristic
32C2×#938C2211yescharacteristic
33C2×#938C2211yescharacteristic, complemented
34C22×#214C2211yescharacteristic
35C22×#213C2211yescharacteristic
36C2×#918—28no—
37C2×#918C2218yescomplemented
38C2×#911—28no—
39C2×#911C2218yescomplemented
40C22×#204C2211yescharacteristic
41C22×ΓL(1,𝔽25)C2211yescharacteristic
42C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
43#5677—24no—
44#5677C2218yescomplemented
45#5676—24no—
46#5676C2218yescomplemented
47C2×#885—21no—
48C2×#884—21no—
49C2×#884—21no—
50C2×#883—21no—
51C2×#882—21no—
52C2×#67⋊C4—21no—
53C2×D3×C22⋊C4—21no—
54C2×#878—21no—
55C2×C4×D12C2211yescharacteristic
56C2×C4×D12C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic, complemented
58C3×#495C2218yescomplemented
59C2×C3×C4×C8C2211yescharacteristic, complemented
60C2×#835C2211yescharacteristic, complemented
61C2×#835C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic
63C2×#832C2211yescharacteristic, complemented
64#5189C2218yescomplemented
65#5173C2218yescomplemented
66#5172C2218yescomplemented
67#5170C2218yescomplemented
68#5169C2218yescomplemented
69#5159C2218yescomplemented
70C2×#821C2211yescharacteristic
71C2×(C2×D3)⋊C8C2211yescharacteristic
72C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
73C2×#817C2211yescharacteristic, complemented
74C2×#816C2211yescharacteristic, complemented
75#5057C2218yescomplemented
76#5054C2218yescomplemented
77C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
78C4×#204C2218yescomplemented
79#4688C2218yescomplemented
80C22×#137—31no—
81C22×AGL(1,ℤ/8)—31no—
82C2×#548—31no—
83C2×#546—31no—
84#3275—316no—
85C2×#495D311yescharacteristic, complemented
86C2×#470—31no—
87C2×#469—31no—
88C2×#464—31no—
89C2×#463—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#448—31no—
93C2×#450—31no—
94C2×C4×SD16—31no—
95C2×#436—31no—
96C24×D3—21no—
97C22×C3×Q8C2311yescharacteristic
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C22×#67—21no—
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C23×Dic3—21no—
106C2×#239—22no—
107C2×#239—24no—
108C2×#239—42no—
109C2×#239C2314yes—
110C2×D3×Q8—22no—
111C2×D3×Q8—24no—
112C2×D3×Q8—42no—
113C2×D3×Q8C2314yescomplemented
114C2×#237—22no—
115C2×#237—24no—
116C2×#237—42no—
117C2×#237C2314yes—
118C2×D3×D4—24no—
119C2×D3×D4—22no—
120C2×D3×D4—42no—
121C2×D3×D4C2314yes—
122C22×D12—21no—
123C22×D12D411yescharacteristic
124C22×D12C2311yescharacteristic
125C22×C4×D3—21no—
126C22×C4×D3—21no—
127C22×C4×D3—21no—
128C22×C4×D3C2311yescharacteristic
129C22×C4×D3C2311yescharacteristic
130C22×Dic6—21no—
131C22×Dic6C2311yescharacteristic
132C2×C3×Q16—24no—
133C2×C3×Q16C2314yescomplemented
134C2×C3×SD16—42no—
135C2×C3×SD16—42no—
136C2×C3×SD16C2314yes—
137C2×C3×SD16C2314yescomplemented
138C2×C3×D8—24no—
139C2×C3×D8C2314yes—
140C22×C3×C8C2311yescharacteristic
141C22×C3×C8C2311yescharacteristic
142C3×#124—22no—
143C3×#124—22no—
144C3×#124C2314yes—
145C3×#124C2314yescomplemented
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C42C2311yescharacteristic
151C2×#217—21no—
152C2×#217—21no—
153#946—22no—
154#946—22no—
155#946C2314yes—
156#946C2314yes—
157C2×#216—24no—
158C2×#216C2314yescomplemented
159C2×#215—24no—
160C2×#215C2314yes—
161#938—22no—
162#938—22no—
163#938C2314yes—
164#938C2314yescomplemented
165C2×#214—24no—
166C2×#214C2314yes—
167C2×#213—24no—
168C2×#213C2314yes—
169C2×(C2×D3)⋊C4—21no—
170C2×(C2×D3)⋊C4—21no—
171C2×(C2×D3)⋊C4—21no—
172C2×(C2×D3)⋊C4D411yescharacteristic
173C2×(C2×D3)⋊C4D411yescharacteristic
174C2×C4⋊Dic3D411yescharacteristic
175C2×C4⋊Dic3C2311yescharacteristic
176C2×C4⋊Dic3C2311yescharacteristic
177C2×Dic3⋊C4—21no—
178C2×Dic3⋊C4—21no—
179C2×Dic3⋊C4—21no—
180C2×C4×Dic3—21no—
181C22×C3⋊C8C2311yescharacteristic
182C22×C3⋊C8C2311yescharacteristic
183#918—232no—
184#911—232no—
185C2×#204D418yescomplemented
186C2×#204C2314yes—
187C2×ΓL(1,𝔽25)—24no—
188C2×ΓL(1,𝔽25)—24no—
189C2×ΓL(1,𝔽25)C2314yes—
190C2×ΓL(1,𝔽25)C2314yescomplemented
191#885—28no—
192#884—28no—
193#884—28no—
194#883—28no—
195#882—28no—
196#67⋊C4—28no—
197D3×C22⋊C4—28no—
198#878—28no—
199C4×D12—22no—
200C4×D12D414yes—
201C4×D12C2314yes—
202C4×D12C2314yes—
203C4×Dic6—22no—
204C4×Dic6C2314yescomplemented
205C3×C4×C8C2314yescomplemented
206#835C2314yescomplemented
207#835C2314yescomplemented
208#832C2314yes—
209#832C2314yescomplemented
210#821C2314yes—
211(C2×D3)⋊C8C2314yes—
212(C2×D3)⋊C8C2314yescomplemented
213#817C2314yescomplemented
214#816C2314yescomplemented
215C4⋊(C3⋊C8)C2314yescomplemented
216C22×#41—31no—
217C22×#41—31no—
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×SD16C2×D311yescharacteristic
230C22×SD16C2×D311yescharacteristic, complemented
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C22×M16—31no—
235#548—38no—
236#548—64no—
237#546—38no—
238#546—64no—
239C2×#124—61no—
240C2×#124C2×D311yescharacteristic
241C2×#124C2×D311yescharacteristic, complemented
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—61no—
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#495C2×D318yescomplemented
257#470—38no—
258#469—38no—
259#464—38no—
260#463—38no—
261#452—38no—
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×#103—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8C2×D311yescharacteristic, complemented
278C24×C3—21no—
279C24×C3—21no—
280C23×D3—21no—
281C23×D3—24no—
282C23×D3—44no—
283C23×D3—44no—
284C23×D3—82no—
285C23×D3C2×D411yescharacteristic
286C23×D3C2×D411yescharacteristic
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8C2412yes—
294C2×C3×Q8C2412yes—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—22no—
300C2×C3×D4—22no—
301C2×C3×D4C2412yes—
302C2×C3×D4C2412yes—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C2×#67—24no—
309C2×#67—24no—
310C2×#67—24no—
311C2×#67—24no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—82no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—24no—
320C22×Dic3—44no—
321C22×Dic3C2×D411yescharacteristic
322C22×Dic3C2×D411yescharacteristic
323#239—28no—
324#239—44no—
325#239—48no—
326D3×Q8—28no—
327D3×Q8—44no—
328D3×Q8—48no—
329#237—28no—
330#237—44no—
331#237—48no—
332D3×D4—28no—
333D3×D4—44no—
334D3×D4—48no—
335C2×D12—21no—
336C2×D12—22no—
337C2×D12—24no—
338C2×D12—42no—
339C2×D12—44no—
340C2×D12C2×D414yes—
341C2×D12C2×D414yes—
342C2×D12C2412yes—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—24no—
348C2×C4×D3—24no—
349C2×C4×D3—24no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—82no—
353C2×C4×D3C2×D412yes—
354C2×C4×D3C2×D412yes—
355C2×C4×D3C2412yes—
356C2×C4×D3C2412yes—
357C2×Dic6—21no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—44no—
361C2×Dic6C2×D414yes—
362C2×Dic6C2412yes—
363C3×Q16—28no—
364C3×SD16—44no—
365C3×SD16—44no—
366C3×D8—28no—
367C2×C3×C8—22no—
368C2×C3×C8C2×D414yes—
369C2×C3×C8C2412yes—
370C2×C3×C8C2412yes—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—24no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C42C2×D412yes—
376C3×C42C2412yes—
377#217—24no—
378#217—24no—
379#216—28no—
380#215—28no—
381#214—28no—
382#213—28no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4C2×D414yes—
387(C2×D3)⋊C4C2×D414yes—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3C2×D414yes—
391C4⋊Dic3C2412yes—
392C4⋊Dic3C2412yes—
393Dic3⋊C4—24no—
394Dic3⋊C4—24no—
395Dic3⋊C4—24no—
396C4×Dic3—24no—
397C2×C3⋊C8—22no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401#204C2×D4116yescomplemented
402ΓL(1,𝔽25)—28no—
403ΓL(1,𝔽25)—28no—
404C25—61no—
405C2×#41—34no—
406C2×#41—34no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—64no—
410C2×#41—64no—
411C2×#41—122no—
412C2×#41—122no—
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—34no—
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—61no—
425C22×D4—62no—
426C22×D4—61no—
427C22×D4—64no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—122no—
432C22×D4C22×D311yescharacteristic
433C22×D4C22×D311yescharacteristic
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—61no—
437C23×C4—61no—
438C23×C4—61no—
439C23×C4—61no—
440#137—632no—
441AGL(1,ℤ/8)—632no—
442C2×Q16—24no—
443C2×Q16—34no—
444C2×Q16—64no—
445C2×Q16C22×D314yescomplemented
446C2×SD16—34no—
447C2×SD16—34no—
448C2×SD16—38no—
449C2×SD16—34no—
450C2×SD16—42no—
451C2×SD16—42no—
452C2×SD16—64no—
453C2×SD16—64no—
454C2×SD16C22×D314yes—
455C2×SD16C22×D314yescomplemented
456C2×D8—24no—
457C2×D8—34no—
458C2×D8—64no—
459C2×D8C22×D314yes—
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—22no—
469#124—22no—
470#124—68no—
471#124C22×D314yes—
472#124C22×D314yescomplemented
473#123—68no—
474C22⋊Q8—34no—
475C22⋊Q8—34no—
476C22⋊Q8—68no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479#121—34no—
480#121—34no—
481#121—68no—
482#121—68no—
483#121—62no—
484#121—62no—
485#120—68no—
486C4×Q8—34no—
487C4×Q8—62no—
488C4×D4—34no—
489C4×D4—34no—
490C4×D4—34no—
491C4×D4—68no—
492C4×D4—62no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4—61no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—68no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C42—61no—
512C2×C42C22×D311yescharacteristic
513#106—34no—
514C4⋊C8—34no—
515#103—34no—
516#103—34no—
517#103—34no—
518#102—34no—
519#102—34no—
520#102—34no—
521C22⋊C8—34no—
522C22⋊C8—34no—
523C4×C8C22×D314yescomplemented
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3C22×D411yescharacteristic
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—24no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—48no—
542C22×D3—48no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—84no—
546C22×D3—816no—
547C22×D3C22×D412yes—
548C22×D3C22×D412yes—
549C3×Q8—22no—
550C3×Q8—22no—
551C3×Q8—22no—
552C3×Q8—22no—
553C3×Q8—42no—
554C3×Q8—42no—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—22no—
558C3×D4—22no—
559C3×D4—42no—
560C3×D4—42no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4C22×D412yes—
568C2×C3×C4C22×D412yes—
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C22×D412yes—
571C2×C3×C4H(5,𝔽2)12yes—
572C2×C3×C4C2511yescharacteristic
573#67—48no—
574#67—48no—
575#67—48no—
576#67—84no—
577C2×Dic3—24no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—48no—
584C2×Dic3—42no—
585C2×Dic3—42no—
586C2×Dic3C22×D412yes—
587C2×Dic3C22×D412yes—
588D12—24no—
589D12—22no—
590D12—44no—
591D12—48no—
592D12C22×D414yes—
593C4×D3—24no—
594C4×D3—24no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—22no—
598C4×D3—22no—
599C4×D3—48no—
600C4×D3—48no—
601C4×D3—84no—
602Dic6—24no—
603Dic6—22no—
604Dic6—48no—
605Dic6C22×D414yes—
606C3×C8—22no—
607C3×C8C22×D414yes—
608C3⋊C8—22no—
609C3⋊C8—22no—
610C24—21no—
611C24—21no—
612C24—31no—
613C24—31no—
614C24—64no—
615C24—61no—
616C24—124no—
617C24—124no—
618C24—242no—
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—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—34no—
632C2×Q8—32no—
633C2×Q8—64no—
634C2×Q8—61no—
635C2×Q8—62no—
636C2×Q8—68no—
637C2×Q8—124no—
638C2×Q8—124no—
639C2×Q8—128no—
640C2×Q8C23×D312yes—
641C2×Q8C23×D312yes—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—34no—
649C2×D4—34no—
650C2×D4—32no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—68no—
654C2×D4—64no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—122no—
660C2×D4—124no—
661C2×D4—124no—
662C2×D4—128no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—124no—
666C2×D4—242no—
667C2×D4C23×D312yes—
668C2×D4C23×D312yes—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—64no—
678C22×C4—64no—
679C22×C4—64no—
680C22×C4—61no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—64no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—242no—
692C22×C4D3×D411yescharacteristic
693C22×C4D3×D411yescharacteristic
694C22×C4C23×D311yescharacteristic
695Q16—28no—
696Q16—68no—
697SD16—316no—
698SD16—44no—
699SD16—44no—
700SD16—68no—
701SD16—68no—
702D8—28no—
703D8—68no—
704M16—68no—
705M16—68no—
706C2×C8—22no—
707C2×C8—32no—
708C2×C8—32no—
709C2×C8—62no—
710C2×C8—62no—
711C2×C8D3×D414yes—
712C2×C8C23×D312yes—
713C2×C8C23×D312yes—
714C4⋊C4—34no—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—64no—
718C4⋊C4—64no—
719C4⋊C4—61no—
720C4⋊C4—61no—
721C4⋊C4—64no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—24no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C22⋊C4—64no—
732C22⋊C4—64no—
733C42—64no—
734C42D3×D412yes—
735C42C23×D312yes—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—84no—
743C22×C3—84no—
744C22×C3D4212yes—
745C22×C3#57512yes—
746C22×C3#57712yes—
747C22×C3C23×D411yescharacteristic
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—24no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—44no—
756C2×D3—44no—
757C2×D3—48no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—816no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4D4212yes—
766C3×C4C23×D411yescharacteristic
767C3×C4C2×H(5,𝔽2)11yescharacteristic
768Dic3—24no—
769Dic3—22no—
770Dic3—22no—
771Dic3—42no—
772Dic3—42no—
773C23—22no—
774C23—22no—
775C23—32no—
776C23—32no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—64no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—128no—
792C23—128no—
793C23—122no—
794C23—122no—
795C23—244no—
796C23—2416no—
797C23C2×D3×D411yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—22no—
802Q8—34no—
803Q8—42no—
804Q8—42no—
805Q8—62no—
806Q8—64no—
807Q8—128no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—34no—
813D4—42no—
814D4—42no—
815D4—62no—
816D4—64no—
817D4—124no—
818D4—128no—
819D4—128no—
820D4—128no—
821D4—128no—
822D4—244no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—64no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—64no—
840C2×C4—64no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—128no—
844C2×C4—128no—
845C2×C4—128no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—244no—
849C2×C4C2×D3×D412yes—
850C2×C4C2×D3×D412yes—
851C2×C4C2×D3×D412yes—
852C2×C4C2×D3×D411yescharacteristic
853C2×C4#100412yes—
854C2×C4C24×D311yescharacteristic
855C8—22no—
856C8—62no—
857C8—62no—
858C8C2×D3×D414yes—
859C2×C3—82no—
860C2×C3—82no—
861C2×C3#327514yescomplemented
862C2×C3C2×D4211yescharacteristic
863C2×C3C2×#57511yescharacteristic
864C2×C3C2×#57711yescharacteristic
865D3—42no—
866D3—42no—
867D3—44no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—64no—
881C22—84no—
882C22—84no—
883C22—122no—
884C22—122no—
885C22—124no—
886C22—124no—
887C22—128no—
888C22—2416no—
889C22#571712yes—
890C22#576812yes—
891C22#577012yes—
892C22C22×D3×D411yescharacteristic
893C4—22no—
894C4—22no—
895C4—42no—
896C4—42no—
897C4—62no—
898C4—62no—
899C4—64no—
900C4—122no—
901C4—122no—
902C4#571712yes—
903C4C22×D3×D411yescharacteristic
904C4C2×#100411yescharacteristic
905C3C2×#327511yescharacteristic, complemented, Sylow
906C2—82no—
907C2—82no—
908C2—122no—
909C2—122no—
910C2—124no—
911C2#8183014yesdirect product factor
912C2C2×#571711yescharacteristic
913C2C2×#576811yescharacteristic
914C2C2×#577011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#495C2
socleC23×C3C22×D4
hypercenterC2×#495D3
hypocenterC3C2×#3275
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C22×#918C2semidirect
2. C22×#911C2semidirect
3. C2×#5677C2semidirect
4. C2×#5676C2semidirect
5. C2×C3×#495C2semidirect
6. C2×#5189C2semidirect
7. C2×#5173C2semidirect
8. C2×#5172C2semidirect
9. C2×#5170C2semidirect
10. C2×#5169C2semidirect
11. C2×#5159C2semidirect
12. C2×#5054C2semidirect
13. C2×#5057C2semidirect
14. #81830C2direct (N × H)
15. C2×C4×#204C2semidirect
16. C2×#4688C2semidirect
19. C22×D3×Q8C22semidirect
22. C22×C3×Q16C22semidirect
24. C22×C3×SD16C22semidirect
27. C2×C3×#124C22semidirect
30. C22×#216C22semidirect
33. C2×#938C22semidirect
37. C2×#918C22semidirect
39. C2×#911C22semidirect
42. C22×ΓL(1,𝔽25)C22semidirect
44. #5677C22semidirect
46. #5676C22semidirect
57. C2×C4×Dic6C22semidirect
58. C3×#495C22semidirect
59. C2×C3×C4×C8C22semidirect
60. C2×#835C22semidirect
61. C2×#835C22semidirect
63. C2×#832C22semidirect
64. #5189C22semidirect
65. #5173C22semidirect
66. #5172C22semidirect
67. #5170C22semidirect
68. #5169C22semidirect
69. #5159C22semidirect
72. C2×(C2×D3)⋊C8C22semidirect
73. C2×#817C22semidirect
74. C2×#816C22semidirect
75. #5057C22semidirect
76. #5054C22semidirect
77. C2×C4⋊(C3⋊C8)C22semidirect
78. C4×#204C22semidirect
79. #4688C22semidirect
85. C2×#495D3semidirect
113. C2×D3×Q8C23semidirect
133. C2×C3×Q16C23semidirect
137. C2×C3×SD16C23semidirect
145. C3×#124C23semidirect
158. C2×#216C23semidirect
164. #938C23semidirect
185. C2×#204D4semidirect
190. C2×ΓL(1,𝔽25)C23semidirect
204. C4×Dic6C23semidirect
205. C3×C4×C8C23semidirect
206. #835C23semidirect
207. #835C23semidirect
209. #832C23semidirect
212. (C2×D3)⋊C8C23semidirect
213. #817C23semidirect
214. #816C23semidirect
215. C4⋊(C3⋊C8)C23semidirect
225. C22×Q16C2×D3semidirect
230. C22×SD16C2×D3semidirect
241. C2×#124C2×D3semidirect
256. #495C2×D3semidirect
277. C2×C4×C8C2×D3semidirect
401. #204C2×D4semidirect
445. C2×Q16C22×D3semidirect
455. C2×SD16C22×D3semidirect
472. #124C22×D3semidirect
523. C4×C8C22×D3semidirect
861. C2×C3#3275semidirect
905. C3C2×#3275semidirect
911. C2#81830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9182
C22×#9112
C2×#56772
C2×#56762
C2×C3×#4952
C2×#51892
C2×#51732
C2×#51722
C2×#51702
C2×#51692
C2×#51592
C2×#50542
C2×#50572
#818302
C2×C4×#2042
C2×#46882
C2×#32753