Finite Group Databasebeta

← C2×#80243 #11670288

Subgroups — C2×#80243 #11670288

Order 768.

3042 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5829C211yesmaximal, characteristic, complemented
2C22×#949C211yesmaximal, characteristic, complemented
3C22×#914C211yesmaximal, characteristic, complemented
4C2×#5630C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×#5187C211yesmaximal, characteristic, complemented
7C2×#5191C211yesmaximal, characteristic, complemented
8C2×#5165C211yesmaximal, characteristic, complemented
9C2×#5049C211yesmaximal, characteristic, complemented
10#80243C2116yesmaximal, direct product factor
11C2×#4819C211yesmaximal, characteristic, complemented
12C2×#4812C211yesmaximal, characteristic, complemented
13C2×#4773C211yesmaximal, characteristic, complemented
14C2×#4756C211yesmaximal, characteristic, complemented
15C2×#4732C211yesmaximal, characteristic, complemented
16C2×#4729C211yesmaximal, characteristic, complemented
17C2×#3273—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×D3×D4C2211yescharacteristic, complemented
21C23×D12C2211yescharacteristic, complemented
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic, complemented
24C2×C3×C22⋊Q8C2211yescharacteristic, complemented
25#5829—24no—
26#5829C2218yescomplemented
27C2×#949—28no—
28C2×#949C2218yescomplemented
29C2×#947C2211yescharacteristic, complemented
30C2×#947C2211yescharacteristic, complemented
31C2×#946C2211yescharacteristic, complemented
32C22×#215C2211yescharacteristic, complemented
33C22×#215C2211yescharacteristic, complemented
34C22×#215C2211yescharacteristic, complemented
35C2×#939—21no—
36C2×#937—21no—
37C2×D4×Dic3C2211yescharacteristic, complemented
38C22×#213C2211yescharacteristic
39C22×#213C2211yescharacteristic
40C2×#930C2211yescharacteristic
41C2×#929—21no—
42C2×C4×#67C2211yescharacteristic
43C22×(C2×D3)⋊C4—21no—
44C22×#208C2211yescharacteristic, complemented
45C2×#914—28no—
46C2×#914C2218yescomplemented
47C22×D24C2211yescharacteristic
48C22×D24C2211yescharacteristic
49C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
50#5630—24no—
51#5630C2218yescomplemented
52C2×#895—21no—
53C2×#895C2211yescharacteristic
54C2×#894—21no—
55C2×#893C2211yescharacteristic, complemented
56C2×#882—21no—
57C2×D3×C22⋊C4—21no—
58C3×#452C2218yescomplemented
59C2×C3×#103C2211yescharacteristic, complemented
60C2×C3×#102C2211yescharacteristic, complemented
61C2×C3×C22⋊C8C2211yescharacteristic, complemented
62C2×#835C2211yescharacteristic, complemented
63#5191C2218yescomplemented
64#5187C2218yescomplemented
65#5165C2218yescomplemented
66C2×#821C2211yescharacteristic, complemented
67C2×#821C2211yescharacteristic, complemented
68C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
69C2×Dic3⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic3C2211yescharacteristic, complemented
71#5049C2218yescomplemented
72C2×#809C2211yescharacteristic, complemented
73C2×#807C2211yescharacteristic, complemented
74#4819C2218yescomplemented
75#4812C2218yescomplemented
76#4773C2218yescomplemented
77#4756C2218yescomplemented
78#4732C2218yescomplemented
79#4729C2218yescomplemented
80C22×AGL(1,ℤ/8)—31no—
81C22×AGL(1,ℤ/8)—31no—
82C2×#546—31no—
83C2×#546—31no—
84#3273—316no—
85C2×#495—31no—
86C2×#468—31no—
87C2×#468—31no—
88C2×#463—31no—
89C2×#463—31no—
90C2×#452—31no—
91C2×#452D311yescharacteristic, complemented
92C2×#447—31no—
93C2×#447—31no—
94C2×C4×D8—31no—
95C2×#436—31no—
96C24×D3—21no—
97C24×D3—21no—
98C2×C3×#41—22no—
99C2×C3×#41—24no—
100C2×C3×#41—42no—
101C2×C3×#41C2314yes—
102C22×C3×Q8C2311yescharacteristic
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4—21no—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C22×#67—21no—
110C22×#67D411yescharacteristic
111C23×Dic3—21no—
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×D4C2314yescomplemented
120C22×D12—24no—
121C22×D12—21no—
122C22×D12—21no—
123C22×D12—22no—
124C22×D12—21no—
125C22×D12—42no—
126C22×D12C2311yescharacteristic
127C22×D12C2311yescharacteristic
128C22×D12C2311yescharacteristic
129C22×D12C2314yescomplemented
130C22×C4×D3—21no—
131C22×C4×D3—21no—
132C22×C4×D3C2311yescharacteristic
133C2×C3×Q16—42no—
134C2×C3×Q16C2314yescomplemented
135C2×C3×SD16—24no—
136C2×C3×SD16C2314yescomplemented
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C3×C22⋊Q8—22no—
140C3×C22⋊Q8C2314yescomplemented
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C22⋊C4—21no—
144C2×#217—21no—
145C2×#217D411yescharacteristic
146#949—232no—
147#947—22no—
148#947—22no—
149#947C2314yescomplemented
150#947C2314yescomplemented
151#946—22no—
152#946C2314yescomplemented
153C2×#215—24no—
154C2×#215—24no—
155C2×#215—24no—
156C2×#215C2314yescomplemented
157C2×#215C2314yescomplemented
158C2×#215C2314yescomplemented
159#939—28no—
160#937—28no—
161D4×Dic3—22no—
162D4×Dic3C2314yescomplemented
163C2×#213—24no—
164C2×#213D418yescomplemented
165C2×#213C2314yes—
166C2×#213C2314yes—
167#930—22no—
168#930C2314yes—
169#929—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)⋊C4—21no—
177C2×(C2×D3)⋊C4—21no—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4—28no—
181C2×(C2×D3)⋊C4D411yescharacteristic
182C2×C4⋊Dic3C2311yescharacteristic
183C2×Dic3⋊C4—21no—
184C2×Dic3⋊C4D411yescharacteristic
185C2×C4×Dic3C2311yescharacteristic
186C2×#208—24no—
187C2×#208C2314yescomplemented
188C22×C3⋊C8C2311yescharacteristic
189C22×C3⋊C8C2311yescharacteristic
190#914—232no—
191C2×D24—24no—
192C2×D24—42no—
193C2×D24C2314yes—
194C2×D24C2314yes—
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#893C2314yescomplemented
203#882—28no—
204D3×C22⋊C4—28no—
205C3×#103C2314yescomplemented
206C3×#102C2314yescomplemented
207C3×C22⋊C8C2314yescomplemented
208#835C2314yescomplemented
209#821C2314yescomplemented
210#821C2314yescomplemented
211(C2×D3)⋊C8C2314yescomplemented
212Dic3⋊C8C2314yescomplemented
213C8×Dic3C2314yescomplemented
214#809C2314yescomplemented
215#807C2314yescomplemented
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×D4—31no—
219C23×D4—31no—
220C2×AGL(1,ℤ/8)—38no—
221C2×AGL(1,ℤ/8)—38no—
222C2×AGL(1,ℤ/8)—68no—
223C2×AGL(1,ℤ/8)—68no—
224C22×Q16C2×D311yescharacteristic, complemented
225C22×SD16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16C2×D311yescharacteristic, complemented
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
234C22×M16—31no—
235#546—38no—
236#546—38no—
237#546—64no—
238#546—64no—
239C2×#124—31no—
240C2×#124—31no—
241C2×#123—61no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8C2×D311yescharacteristic, complemented
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#120—61no—
250C2×#120—61no—
251C2×C4×D4—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C22×C22⋊C4—61no—
255C22×C22⋊C4—61no—
256#495—38no—
257#468—38no—
258#468—38no—
259#463—38no—
260#463—38no—
261#452—38no—
262#452C2×D318yescomplemented
263#447—38no—
264#447—38no—
265C4×D8—38no—
266#436—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103C2×D311yescharacteristic, complemented
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic, complemented
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—21no—
283C23×D3—24no—
284C23×D3—24no—
285C23×D3—44no—
286C23×D3—44no—
287C23×D3—44no—
288C23×D3—44no—
289C23×D3—82no—
290C23×D3—82no—
291C23×D3C2×D411yescharacteristic
292C3×#41—28no—
293C3×#41—44no—
294C3×#41—48no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—22no—
298C2×C3×Q8—22no—
299C2×C3×Q8—22no—
300C2×C3×Q8—22no—
301C2×C3×Q8C2412yes—
302C2×C3×Q8C2412yes—
303C2×C3×D4—24no—
304C2×C3×D4—21no—
305C2×C3×D4—22no—
306C2×C3×D4—44no—
307C2×C3×D4C2×D414yes—
308C2×C3×D4C2412yes—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—24no—
315C22×C3×C4—44no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D412yes—
318C22×C3×C4C2412yes—
319C22×C3×C4C2411yescharacteristic
320C2×#67—24no—
321C2×#67—24no—
322C2×#67—42no—
323C2×#67—44no—
324C2×#67—82no—
325C2×#67C2×D414yes—
326C22×Dic3—21no—
327C22×Dic3—24no—
328C22×Dic3—82no—
329C22×Dic3C2×D411yescharacteristic
330C22×Dic3C2×D411yescharacteristic
331C22×Dic3C2×D411yescharacteristic
332#239—28no—
333#239—44no—
334#239—48no—
335D3×D4—28no—
336D3×D4—44no—
337D3×D4—48no—
338C2×D12—21no—
339C2×D12—22no—
340C2×D12—22no—
341C2×D12—22no—
342C2×D12—22no—
343C2×D12—22no—
344C2×D12—28no—
345C2×D12—24no—
346C2×D12—24no—
347C2×D12—21no—
348C2×D12—21no—
349C2×D12—24no—
350C2×D12—44no—
351C2×D12—48no—
352C2×D12—44no—
353C2×D12—44no—
354C2×D12—82no—
355C2×D12C2×D414yes—
356C2×D12C2412yes—
357C2×D12C2412yes—
358C2×D12C2412yes—
359C2×C4×D3—22no—
360C2×C4×D3—22no—
361C2×C4×D3—24no—
362C2×C4×D3—24no—
363C2×C4×D3—44no—
364C2×C4×D3—82no—
365C2×C4×D3C2×D412yes—
366C2×C4×D3C2412yes—
367C3×Q16—44no—
368C3×SD16—28no—
369C2×C3×C8—22no—
370C2×C3×C8—22no—
371C2×C3×C8C2412yes—
372C2×C3×C8C2412yes—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—24no—
375C3×C4⋊C4C2412yes—
376C3×C22⋊C4—24no—
377#217—24no—
378#217C2×D414yes—
379#215—28no—
380#215—28no—
381#215—28no—
382#213—28no—
383#213C2×D4116yescomplemented
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4C2×D414yes—
393C4⋊Dic3—21no—
394C4⋊Dic3C2412yes—
395Dic3⋊C4—24no—
396Dic3⋊C4C2×D414yes—
397C4×Dic3C2×D412yes—
398C4×Dic3C2412yes—
399#208—28no—
400C2×C3⋊C8—22no—
401C2×C3⋊C8C2×D414yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404D24—28no—
405D24—44no—
406ΓL(1,𝔽25)—28no—
407C25—61no—
408C25—61no—
409C2×#41—22no—
410C2×#41—24no—
411C2×#41—34no—
412C2×#41—42no—
413C2×#41—62no—
414C2×#41—64no—
415C2×#41—122no—
416C2×#41C22×D314yes—
417C22×Q8C22×D311yescharacteristic
418C22×Q8C22×D311yescharacteristic
419C22×D4—21no—
420C22×D4—31no—
421C22×D4—34no—
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—34no—
426C22×D4—64no—
427C22×D4—61no—
428C22×D4—61no—
429C22×D4—62no—
430C22×D4—61no—
431C22×D4—64no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—62no—
435C22×D4—122no—
436C22×D4—122no—
437C22×D4C22×D311yescharacteristic
438C23×C4—21no—
439C23×C4—31no—
440C23×C4—61no—
441C23×C4—61no—
442C23×C4—61no—
443C23×C4C22×D311yescharacteristic
444AGL(1,ℤ/8)—632no—
445AGL(1,ℤ/8)—632no—
446C2×Q16—42no—
447C2×Q16C22×D314yescomplemented
448C2×SD16—24no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—64no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16C22×D314yescomplemented
456C2×D8—38no—
457C2×D8—34no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—34no—
461C2×D8—64no—
462C2×D8—64no—
463C2×D8—122no—
464C2×M16—34no—
465C2×M16—34no—
466C2×M16—64no—
467C2×M16—64no—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8C22×D311yescharacteristic
471C22×C8C22×D311yescharacteristic
472#124—34no—
473#124—34no—
474#124—62no—
475#124—62no—
476#123—68no—
477#123—68no—
478C22⋊Q8—22no—
479C22⋊Q8—34no—
480C22⋊Q8—62no—
481C22⋊Q8C22×D314yescomplemented
482#121—34no—
483#121—34no—
484#121—68no—
485#121—68no—
486#121—62no—
487#121—62no—
488#120—68no—
489#120—68no—
490C4×D4—34no—
491C4×D4—34no—
492C4×D4—34no—
493C4×D4—34no—
494C4×D4—62no—
495C4×D4—62no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4C22×D311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—68no—
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×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C22⋊C4—61no—
514C2×C22⋊C4—61no—
515C2×C42—31no—
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103C22×D314yescomplemented
520#102—34no—
521#102—34no—
522#102—34no—
523#102C22×D314yescomplemented
524C22⋊C8—34no—
525C22⋊C8C22×D314yescomplemented
526C4×C8—34no—
527C23×C3—24no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3C22×D412yes—
535C23×C3C22×D411yescharacteristic
536C22×D3—22no—
537C22×D3—24no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—48no—
544C22×D3—48no—
545C22×D3—48no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—48no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—84no—
556C22×D3—84no—
557C22×D3—816no—
558C22×D3—816no—
559C22×D3C22×D412yes—
560C3×Q8—22no—
561C3×Q8—22no—
562C3×Q8—22no—
563C3×Q8—22no—
564C3×Q8—42no—
565C3×Q8—42no—
566C3×D4—24no—
567C3×D4—22no—
568C3×D4—48no—
569C3×D4C22×D414yes—
570C2×C3×C4—22no—
571C2×C3×C4—24no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—48no—
578C2×C3×C4—42no—
579C2×C3×C4—42no—
580C2×C3×C4—42no—
581C2×C3×C4C22×D412yes—
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D412yes—
584C2×C3×C4H(5,𝔽2)12yes—
585C2×C3×C4C2511yescharacteristic
586#67—44no—
587#67—48no—
588#67—84no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—42no—
594C2×Dic3—84no—
595C2×Dic3C22×D412yes—
596C2×Dic3C22×D412yes—
597C2×Dic3C22×D412yes—
598D12—24no—
599D12—22no—
600D12—22no—
601D12—22no—
602D12—22no—
603D12—22no—
604D12—48no—
605D12—48no—
606D12—42no—
607D12—42no—
608D12—84no—
609D12C22×D414yes—
610C4×D3—24no—
611C4×D3—22no—
612C4×D3—22no—
613C4×D3—48no—
614C4×D3—84no—
615C3×C8—22no—
616C3×C8—22no—
617C3⋊C8—22no—
618C3⋊C8C22×D414yes—
619C24—21no—
620C24—31no—
621C24—64no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—64no—
626C24—124no—
627C24—124no—
628C24—124no—
629C24—124no—
630C24—242no—
631C24—242no—
632C24D3×D411yescharacteristic
633#41—28no—
634#41—44no—
635#41—48no—
636#41—68no—
637#41—124no—
638#41—128no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8C23×D312yes—
646C2×Q8C23×D312yes—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—34no—
651C2×D4—34no—
652C2×D4—32no—
653C2×D4—32no—
654C2×D4—32no—
655C2×D4—44no—
656C2×D4—68no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—68no—
661C2×D4—64no—
662C2×D4—61no—
663C2×D4—62no—
664C2×D4—62no—
665C2×D4—64no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—62no—
671C2×D4—124no—
672C2×D4—128no—
673C2×D4—124no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—128no—
677C2×D4—122no—
678C2×D4—124no—
679C2×D4—242no—
680C2×D4—242no—
681C2×D4D3×D414yes—
682C2×D4C23×D312yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—44no—
695C22×C4—64no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—61no—
701C22×C4—124no—
702C22×C4—242no—
703C22×C4—242no—
704C22×C4D3×D412yes—
705C22×C4D3×D411yescharacteristic
706C22×C4C23×D312yes—
707C22×C4C23×D311yescharacteristic
708Q16—44no—
709SD16—28no—
710SD16—68no—
711SD16—68no—
712SD16—68no—
713D8—316no—
714D8—68no—
715D8—68no—
716D8—124no—
717M16—68no—
718M16—68no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—34no—
722C2×C8—32no—
723C2×C8—32no—
724C2×C8—62no—
725C2×C8C23×D312yes—
726C2×C8C23×D312yes—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—34no—
730C4⋊C4—32no—
731C4⋊C4—64no—
732C4⋊C4—61no—
733C4⋊C4C23×D312yes—
734C22⋊C4—24no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—64no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—64no—
745C22⋊C4—64no—
746C42—32no—
747C42—32no—
748C22×C3—24no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—44no—
753C22×C3—48no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3D4212yes—
757C22×C3#57512yes—
758C22×C3#57612yes—
759C22×C3C23×D411yescharacteristic
760C2×D3—22no—
761C2×D3—24no—
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—44no—
765C2×D3—48no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—816no—
775C2×D3—816no—
776C2×D3—84no—
777C2×D3—84no—
778C3×C4—22no—
779C3×C4—42no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4D4212yes—
783C3×C4C23×D411yescharacteristic
784C3×C4C2×H(5,𝔽2)11yescharacteristic
785Dic3—22no—
786Dic3—22no—
787Dic3—22no—
788Dic3—42no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—24no—
794C23—32no—
795C23—42no—
796C23—42no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—64no—
802C23—62no—
803C23—62no—
804C23—128no—
805C23—128no—
806C23—128no—
807C23—128no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23—122no—
816C23—244no—
817C23—244no—
818C23—2416no—
819C23—2416no—
820C23C2×D3×D412yes—
821C23C2×D3×D411yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—22no—
825Q8—22no—
826Q8—42no—
827Q8—42no—
828D4—22no—
829D4—24no—
830D4—34no—
831D4—48no—
832D4—62no—
833D4—62no—
834D4—62no—
835D4—62no—
836D4—62no—
837D4—64no—
838D4—128no—
839D4—128no—
840D4—124no—
841D4—128no—
842D4—122no—
843D4—122no—
844D4—244no—
845D4—244no—
846D4C2×D3×D414yes—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—48no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—64no—
867C2×C4—62no—
868C2×C4—128no—
869C2×C4—122no—
870C2×C4—244no—
871C2×C4—244no—
872C2×C4C2×D3×D412yes—
873C2×C4C2×D3×D412yes—
874C2×C4C2×D3×D411yescharacteristic
875C2×C4#100412yes—
876C2×C4C24×D311yescharacteristic
877C8—22no—
878C8—22no—
879C8—34no—
880C8—62no—
881C2×C3—42no—
882C2×C3—44no—
883C2×C3#327314yescomplemented
884C2×C3C2×D4211yescharacteristic
885C2×C3C2×#57511yescharacteristic
886C2×C3C2×#57611yescharacteristic
887D3—42no—
888D3—44no—
889D3—82no—
890D3—82no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—44no—
896C22—48no—
897C22—42no—
898C22—42no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—64no—
903C22—124no—
904C22—128no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—2416no—
914C22—2416no—
915C22—244no—
916C22—244no—
917C22#559012yes—
918C22#576912yes—
919C22#577712yes—
920C22C22×D3×D411yescharacteristic
921C4—22no—
922C4—42no—
923C4—42no—
924C4—42no—
925C4—62no—
926C4—62no—
927C4—62no—
928C4—122no—
929C4#559012yes—
930C4C22×D3×D411yescharacteristic
931C4C2×#100411yescharacteristic
932C3C2×#327311yescharacteristic, complemented, Sylow
933C2—42no—
934C2—44no—
935C2—122no—
936C2—124no—
937C2—242no—
938C2—242no—
939C2#8024314yesdirect product factor
940C2C2×#559011yescharacteristic
941C2C2×#576911yescharacteristic
942C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
hypercenterC2×#452D3
hypocenterC3C2×#3273
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×#5829C2semidirect
2. C22×#949C2semidirect
3. C22×#914C2semidirect
4. C2×#5630C2semidirect
5. C2×C3×#452C2semidirect
6. C2×#5187C2semidirect
7. C2×#5191C2semidirect
8. C2×#5165C2semidirect
9. C2×#5049C2semidirect
10. #80243C2direct (N × H)
11. C2×#4819C2semidirect
12. C2×#4812C2semidirect
13. C2×#4773C2semidirect
14. C2×#4756C2semidirect
15. C2×#4732C2semidirect
16. C2×#4729C2semidirect
20. C22×D3×D4C22semidirect
21. C23×D12C22semidirect
22. C22×C3×Q16C22semidirect
23. C22×C3×SD16C22semidirect
24. C2×C3×C22⋊Q8C22semidirect
26. #5829C22semidirect
28. C2×#949C22semidirect
29. C2×#947C22semidirect
30. C2×#947C22semidirect
31. C2×#946C22semidirect
32. C22×#215C22semidirect
33. C22×#215C22semidirect
34. C22×#215C22semidirect
37. C2×D4×Dic3C22semidirect
44. C22×#208C22semidirect
46. C2×#914C22semidirect
49. C22×ΓL(1,𝔽25)C22semidirect
51. #5630C22semidirect
55. C2×#893C22semidirect
58. C3×#452C22semidirect
59. C2×C3×#103C22semidirect
60. C2×C3×#102C22semidirect
61. C2×C3×C22⋊C8C22semidirect
62. C2×#835C22semidirect
63. #5191C22semidirect
64. #5187C22semidirect
65. #5165C22semidirect
66. C2×#821C22semidirect
67. C2×#821C22semidirect
68. C2×(C2×D3)⋊C8C22semidirect
69. C2×Dic3⋊C8C22semidirect
70. C2×C8×Dic3C22semidirect
71. #5049C22semidirect
72. C2×#809C22semidirect
73. C2×#807C22semidirect
74. #4819C22semidirect
75. #4812C22semidirect
76. #4773C22semidirect
77. #4756C22semidirect
78. #4732C22semidirect
79. #4729C22semidirect
91. C2×#452D3semidirect
119. C2×D3×D4C23semidirect
129. C22×D12C23semidirect
134. C2×C3×Q16C23semidirect
136. C2×C3×SD16C23semidirect
140. C3×C22⋊Q8C23semidirect
149. #947C23semidirect
150. #947C23semidirect
152. #946C23semidirect
156. C2×#215C23semidirect
157. C2×#215C23semidirect
158. C2×#215C23semidirect
162. D4×Dic3C23semidirect
164. C2×#213D4semidirect
187. C2×#208C23semidirect
196. C2×ΓL(1,𝔽25)C23semidirect
202. #893C23semidirect
205. C3×#103C23semidirect
206. C3×#102C23semidirect
207. C3×C22⋊C8C23semidirect
208. #835C23semidirect
209. #821C23semidirect
210. #821C23semidirect
211. (C2×D3)⋊C8C23semidirect
212. Dic3⋊C8C23semidirect
213. C8×Dic3C23semidirect
214. #809C23semidirect
215. #807C23semidirect
224. C22×Q16C2×D3semidirect
228. C22×SD16C2×D3semidirect
244. C2×C22⋊Q8C2×D3semidirect
262. #452C2×D3semidirect
270. C2×#103C2×D3semidirect
274. C2×#102C2×D3semidirect
276. C2×C22⋊C8C2×D3semidirect
383. #213C2×D4semidirect
447. C2×Q16C22×D3semidirect
455. C2×SD16C22×D3semidirect
481. C22⋊Q8C22×D3semidirect
519. #103C22×D3semidirect
523. #102C22×D3semidirect
525. C22⋊C8C22×D3semidirect
883. C2×C3#3273semidirect
932. C3C2×#3273semidirect
939. C2#80243direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58292
C22×#9492
C22×#9142
C2×#56302
C2×C3×#4522
C2×#51872
C2×#51912
C2×#51652
C2×#50492
#802432
C2×#48192
C2×#48122
C2×#47732
C2×#47562
C2×#47322
C2×#47292
C2×#32733