Finite Group Databasebeta

← C2×#21446869 #29707003

Subgroups — C2×#21446869 #29707003

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic, complemented
2C2×#16840326C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839768C211yesmaximal, characteristic, complemented
5C2×#16839736C211yesmaximal, characteristic, complemented
6#21446869C218yesmaximal, direct product factor
7C2×#16839533C211yesmaximal, characteristic, complemented
8C2×C61×#575C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C2×#14519802—22no—
11C2×#14519802—22no—
12C2×#14519802—22no—
13C2×#14519802—22no—
14C2×#14519802—22no—
15C2×#14519802C2214yescomplemented
16C22×#11758201—21no—
17C22×#11758199—21no—
18C22×#11758194C2211yescharacteristic
19#16840326—22no—
20#16840326—22no—
21#16840326—22no—
22#16840326C2214yescomplemented
23C2×#14519773—21no—
24C2×#14519766—21no—
25C2×#14519751—22no—
26C2×#14519745—22no—
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#16839779—22no—
30#16839779C2214yescomplemented
31C2×#14519704—22no—
32#16839768—22no—
33#16839768C2214yescomplemented
34C2×#14519699—22no—
35#16839736—22no—
36#16839736C2214yescomplemented
37C2×#14519692—22no—
38#16839533C2214yescomplemented
39C22×#41×C61C2211yescharacteristic
40C22×#41×C61C2211yescharacteristic
41C61×#575—22no—
42C61×#575—22no—
43C61×#575—22no—
44C61×#575C2214yescomplemented
45C2×#137×C61—21no—
46C2×#137×C61—21no—
47C2×AGL(1,ℤ/8)×C61—21no—
48C2×AGL(1,ℤ/8)×C61—21no—
49C2×#135×C61—22no—
50C22×M16×C61C2211yescharacteristic
51C24×D61—21no—
52C22×D244—21no—
53C22×D244—21no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244D412yes—
64C22×D244D412yes—
65C22×D244C2312yes—
66C22×C22⋊D61—24no—
67#14519802—28no—
68#14519802—28no—
69#14519802—28no—
70#14519802—28no—
71C2×#11758201—24no—
72C2×#11758201—24no—
73C2×#11758201—24no—
74C2×#11758199—24no—
75C2×#11758199—24no—
76C2×#11758199—24no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194D412yescomplemented
81C2×#11758194D412yescomplemented
82C2×#11758194C2312yes—
83C22×#92418—21no—
84#14519773—24no—
85#14519773—24no—
86#14519766—24no—
87#14519766—24no—
88#14519751—28no—
89#14519751—28no—
90#14519745—28no—
91#14519745—28no—
92#14519736—21no—
93#14519736—21no—
94#14519736—21no—
95#14519736—21no—
96#14519736—21no—
97#14519736D412yes—
98#14519736C2312yes—
99#14519736C2312yes—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61D412yes—
104C2×#11758198—24no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107#14519704—28no—
108#14519699—28no—
109#14519692—28no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61—21no—
130C2×#41×C61D412yes—
131C2×#41×C61D412yescomplemented
132C2×#41×C61C2312yes—
133C2×#41×C61C2312yes—
134C22×Q8×C61D411yescharacteristic
135C22×Q8×C61D411yescharacteristic, complemented
136C22×D4×C61—21no—
137C22×D4×C61—21no—
138C22×D4×C61D411yescharacteristic
139C22×D4×C61D411yescharacteristic, complemented
140C23×C4×C61—21no—
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143#137×C61—24no—
144#137×C61—24no—
145#137×C61—24no—
146#137×C61—24no—
147AGL(1,ℤ/8)×C61—24no—
148AGL(1,ℤ/8)×C61—24no—
149AGL(1,ℤ/8)×C61—24no—
150AGL(1,ℤ/8)×C61—24no—
151#135×C61—28no—
152#135×C61—28no—
153C2×Q16×C61—22no—
154C2×SD16×C61—22no—
155C2×SD16×C61—22no—
156C2×D8×C61—22no—
157C2×M16×C61—21no—
158C2×M16×C61—21no—
159C2×M16×C61—21no—
160C2×M16×C61—21no—
161C2×M16×C61D412yescomplemented
162C2×M16×C61C2312yes—
163C22×C8×C61D412yescomplemented
164C24×C61—21no—
165C24×C61—21no—
166C24×C61C2×D411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—41no—
171C23×D61—41no—
172C23×D61—41no—
173C23×D61—41no—
174C23×D61—84no—
175#41×C61—22no—
176#41×C61—22no—
177#41×C61—22no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—22no—
181#41×C61—22no—
182#41×C61—22no—
183#41×C61—22no—
184#41×C61—22no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—22no—
190#41×C61—22no—
191#41×C61—41no—
192#41×C61—41no—
193#41×C61—41no—
194#41×C61—41no—
195#41×C61—41no—
196#41×C61—41no—
197#41×C61—41no—
198#41×C61—41no—
199#41×C61—41no—
200#41×C61—41no—
201#41×C61—41no—
202#41×C61—41no—
203#41×C61—41no—
204#41×C61—41no—
205#41×C61—41no—
206#41×C61—41no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61C2×D412yes—
218C2×Q8×C61C2×D412yescomplemented
219C2×D4×C61—22no—
220C2×D4×C61—22no—
221C2×D4×C61—22no—
222C2×D4×C61—22no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—41no—
234C2×D4×C61—41no—
235C2×D4×C61—41no—
236C2×D4×C61—41no—
237C2×D4×C61—41no—
238C2×D4×C61—41no—
239C2×D4×C61—41no—
240C2×D4×C61—41no—
241C2×D4×C61C2×D412yes—
242C2×D4×C61C2×D412yescomplemented
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—22no—
246C22×C4×C61—22no—
247C22×C4×C61—22no—
248C22×C4×C61—22no—
249C22×C4×C61—41no—
250C22×C4×C61—41no—
251C22×C4×C61—41no—
252C22×C4×C61—41no—
253C22×C4×C61—41no—
254C22×C4×C61—41no—
255C22×C4×C61—41no—
256C22×C4×C61—41no—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61#4111yescharacteristic
269C22×C4×C61#4111yescharacteristic
270C22×C4×C61C2411yescharacteristic
271C2×C22⋊D61—216no—
272C2×C22⋊D61—88no—
273C22×Dic61—22no—
274C22×Dic61—41no—
275C2×D244—22no—
276C2×D244—22no—
277C2×D244—22no—
278C2×D244—22no—
279C2×D244—22no—
280C2×D244—22no—
281C2×D244—22no—
282C2×D244—22no—
283C2×D244—22no—
284C2×D244—22no—
285C2×D244—22no—
286C2×D244—22no—
287C2×D244—22no—
288C2×D244—22no—
289C2×D244—22no—
290C2×D244—41no—
291C2×D244—41no—
292C2×D244—41no—
293C2×D244—41no—
294C2×D244—41no—
295C2×D244—41no—
296C2×D244—41no—
297C2×D244—41no—
298C2×D244—41no—
299C2×D244—41no—
300C2×D244—41no—
301C2×D244—41no—
302C2×D244C2×D414yes—
303Q16×C61—28no—
304SD16×C61—28no—
305SD16×C61—28no—
306D8×C61—28no—
307M16×C61—22no—
308M16×C61—22no—
309M16×C61—22no—
310M16×C61—22no—
311C2×C8×C61—22no—
312C2×C8×C61—22no—
313C2×C8×C61C2×D414yescomplemented
314C22⋊Dic61—22no—
315C22⋊Dic61—22no—
316C22⋊Dic61—41no—
317C22⋊Dic61C2×D414yes—
318#11758201—216no—
319#11758199—216no—
320#11758198—216no—
321C4⋊Dic61—22no—
322C4⋊Dic61—22no—
323C4⋊Dic61—22no—
324C4⋊Dic61—41no—
325C4×Dic61—22no—
326C4×Dic61—22no—
327C4×Dic61—22no—
328C4×Dic61—41no—
329#11758194—22no—
330#11758194—22no—
331#11758194—22no—
332#11758194C2×D414yescomplemented
333C2×#92418—22no—
334C2×#92418—22no—
335C2×#92418—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—42no—
339C23×C61—44no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—82no—
345C23×C61#12011yescharacteristic
346C23×C61#12011yescharacteristic
347C23×C61#12111yescharacteristic
348C23×C61#12111yescharacteristic
349C23×C61#12711yescharacteristic
350C23×C61#12711yescharacteristic
351C23×C61C22×D411yescharacteristic
352C22×D61—24no—
353C22×D61—48no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—84no—
361C22×D61—84no—
362C22×D61—84no—
363C22×D61—84no—
364C22×D61—84no—
365C22×D61—84no—
366Q8×C61—22no—
367Q8×C61—22no—
368Q8×C61—22no—
369Q8×C61—22no—
370Q8×C61—41no—
371Q8×C61—41no—
372Q8×C61—41no—
373Q8×C61—41no—
374D4×C61—22no—
375D4×C61—22no—
376D4×C61—22no—
377D4×C61—22no—
378D4×C61—42no—
379D4×C61—42no—
380D4×C61—42no—
381D4×C61—42no—
382D4×C61—42no—
383D4×C61—42no—
384D4×C61—42no—
385D4×C61—42no—
386D4×C61—41no—
387D4×C61—41no—
388D4×C61—41no—
389D4×C61—41no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—42no—
399C2×C4×C61—42no—
400C2×C4×C61—42no—
401C2×C4×C61—42no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61#12011yescharacteristic
405C2×C4×C61#12011yescharacteristic
406C2×C4×C61#12011yescharacteristic
407C2×C4×C61#12011yescharacteristic
408C2×C4×C61#12011yescharacteristic
409C2×C4×C61#12011yescharacteristic
410C2×C4×C61#12011yescharacteristic
411C2×C4×C61#12011yescharacteristic
412C2×C4×C61#12011yescharacteristic
413C2×C4×C61#12011yescharacteristic
414C2×C4×C61#12111yescharacteristic
415C2×C4×C61#12111yescharacteristic
416C2×C4×C61#12111yescharacteristic
417C2×C4×C61#12111yescharacteristic
418C2×C4×C61#12111yescharacteristic
419C2×C4×C61#12111yescharacteristic
420C2×C4×C61#12111yescharacteristic
421C2×C4×C61#12111yescharacteristic
422C2×C4×C61#12111yescharacteristic
423C2×C4×C61#12111yescharacteristic
424C2×C4×C61#12711yescharacteristic
425C2×C4×C61#12711yescharacteristic
426C2×C4×C61C22×D411yescharacteristic
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61C22×D411yescharacteristic
429C2×C4×C61C22×D411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C2×#4111yescharacteristic
432C22⋊D61—816no—
433C2×Dic61—24no—
434C2×Dic61—44no—
435C2×Dic61—42no—
436C2×Dic61—82no—
437D244—24no—
438D244—24no—
439D244—42no—
440D244—42no—
441D244—42no—
442D244—42no—
443D244—42no—
444D244—42no—
445C8×C61—24no—
446#92418—24no—
447C2×#2008—611nomaximal, Sylow
448C22×C61—22no—
449C22×C61—22no—
450C22×C61—22no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—44no—
456C22×C61—42no—
457C22×C61—42no—
458C22×C61—82no—
459C22×C61—82no—
460C22×C61—82no—
461C22×C61—82no—
462C22×C61—82no—
463C22×C61#39211yescharacteristic
464C22×C61#39211yescharacteristic
465C22×C61#39211yescharacteristic
466C22×C61#39211yescharacteristic
467C22×C61C2×#12011yescharacteristic
468C22×C61C2×#12111yescharacteristic
469C22×C61C2×#12711yescharacteristic
470C2×D61—48no—
471C2×D61—44no—
472C2×D61—84no—
473C2×D61—84no—
474C2×D61—84no—
475C2×D61—84no—
476C2×D61—84no—
477C2×D61—84no—
478C4×C61—42no—
479C4×C61—42no—
480C4×C61#39211yescharacteristic
481C4×C61#39211yescharacteristic
482C4×C61#39211yescharacteristic
483C4×C61#39211yescharacteristic
484C4×C61C2×#12011yescharacteristic
485C4×C61C2×#12011yescharacteristic
486C4×C61C2×#12111yescharacteristic
487C4×C61C2×#12111yescharacteristic
488Dic61—44no—
489Dic61—82no—
490C2×#575D6111yescharacteristic, complemented
491C22×AGL(1,ℤ/8)—611no—
492C2×#535—611no—
493C2×#421—611no—
494C2×#418—611no—
495C2×#410—611no—
496#2008—618no—
497C2×#344—611no—
498C2×C61—21no—
499C2×C61—21no—
500C2×C61—21no—
501C2×C61—21no—
502C2×C61—21no—
503C2×C61—21no—
504C2×C61—82no—
505C2×C61—82no—
506C2×C61#200812yescomplemented
507C2×C61C2×#39211yescharacteristic
508D61—84no—
509C22×#41C2×D6111yescharacteristic
510C22×#41C2×D6111yescharacteristic
511C23×D4—611no—
512#575—22no—
513#575—22no—
514#575—22no—
515#575C2×D6114yescomplemented
516C2×#137—21no—
517C2×#137—21no—
518C2×AGL(1,ℤ/8)—21no—
519C2×AGL(1,ℤ/8)—21no—
520C2×AGL(1,ℤ/8)—614no—
521C2×AGL(1,ℤ/8)—1222no—
522C2×AGL(1,ℤ/8)—1222no—
523C2×AGL(1,ℤ/8)—1222no—
524C2×AGL(1,ℤ/8)—1222no—
525C2×AGL(1,ℤ/8)—1222no—
526C2×#135—22no—
527C22×SD16—1221no—
528C22×D8—1221no—
529C22×M16—611no—
530C22×M16C2×D6111yescharacteristic
531#535—614no—
532#535—1222no—
533#535—1222no—
534#535—1222no—
535C2×#127—1221no—
536C2×#124—1221no—
537C2×#121—1222no—
538C2×#120—1222no—
539C2×#117—611no—
540C2×#117—611no—
541#421—614no—
542#421—1222no—
543C2×#104—1222no—
544#418—614no—
545#418—1222no—
546C2×#102—1222no—
547#410—614no—
548#410—1222no—
549C2×#99—1222no—
550#344—614no—
551C61C2×#200811yescharacteristic, complemented, Sylow
552C25—1221no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41C22⋊D6112yes—
574C2×#41C22⋊D6112yescomplemented
575C2×#41C22×D6112yes—
576C2×#41C22×D6112yes—
577C22×Q8C22⋊D6111yescharacteristic
578C22×Q8C22⋊D6111yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—612no—
582C22×D4—612no—
583C22×D4—612no—
584C22×D4—1224no—
585C22×D4—1221no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C22×D4—1221no—
591C22×D4—1221no—
592C22×D4—1221no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4—1221no—
596C22×D4C22⋊D6111yescharacteristic
597C22×D4C22⋊D6111yescharacteristic, complemented
598C23×C4—21no—
599C23×C4—21no—
600C23×C4C22×D6111yescharacteristic
601#137—24no—
602#137—24no—
603#137—24no—
604#137—24no—
605AGL(1,ℤ/8)—24no—
606AGL(1,ℤ/8)—24no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—24no—
609AGL(1,ℤ/8)—1228no—
610AGL(1,ℤ/8)—1228no—
611AGL(1,ℤ/8)—1228no—
612AGL(1,ℤ/8)—1228no—
613#135—28no—
614#135—28no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—1224no—
619C2×SD16—1224no—
620C2×SD16—1224no—
621C2×D8—22no—
622C2×D8—1224no—
623C2×D8—1224no—
624C2×D8—1224no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—612no—
630C2×M16—612no—
631C2×M16—612no—
632C2×M16—1221no—
633C2×M16—1221no—
634C2×M16—1221no—
635C2×M16C22⋊D6112yescomplemented
636C2×M16C22×D6112yes—
637C22×C8—1221no—
638C22×C8C22⋊D6112yescomplemented
639#127—1224no—
640#127—1224no—
641#124—1224no—
642#124—1224no—
643#121—1228no—
644#121—1228no—
645#120—1228no—
646#120—1228no—
647#117—612no—
648#117—612no—
649#117—612no—
650#117—1221no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C22⋊C4—612no—
658C2×C22⋊C4—1224no—
659C2×C22⋊C4—1221no—
660C2×C42—1221no—
661C2×C42—1221no—
662#104—1228no—
663#102—1228no—
664#99—1228no—
665C24—21no—
666C24—21no—
667C24—1222no—
668C24—1222no—
669C24—1222no—
670C24—4884no—
671C24—2441no—
672C24—2441no—
673C24—2441no—
674C24—2441no—
675C24D4×D6111yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×C22⋊D6112yes—
719C2×Q8C2×C22⋊D6112yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—41no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—614no—
743C2×D4—12216no—
744C2×D4—1222no—
745C2×D4—1222no—
746C2×D4—1222no—
747C2×D4—1222no—
748C2×D4—1222no—
749C2×D4—1222no—
750C2×D4—1222no—
751C2×D4—1222no—
752C2×D4—1222no—
753C2×D4—1222no—
754C2×D4—1222no—
755C2×D4—1222no—
756C2×D4—1222no—
757C2×D4—1222no—
758C2×D4—1222no—
759C2×D4—4888no—
760C2×D4—2441no—
761C2×D4—2441no—
762C2×D4—2441no—
763C2×D4—2441no—
764C2×D4—2441no—
765C2×D4—2441no—
766C2×D4—2441no—
767C2×D4—2441no—
768C2×D4—2441no—
769C2×D4—2441no—
770C2×D4—2441no—
771C2×D4—2441no—
772C2×D4C2×C22⋊D6112yes—
773C2×D4C2×C22⋊D6112yescomplemented
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—1222no—
789C22×C4—2441no—
790C22×C4D4×D6111yescharacteristic
791C22×C4D4×D6111yescharacteristic
792C22×C4D4×D6111yescharacteristic
793C22×C4D4×D6111yescharacteristic
794C22×C4D4×D6111yescharacteristic
795C22×C4#1175822411yescharacteristic
796C22×C4#1175822411yescharacteristic
797C22×C4C2×C22⋊D6111yescharacteristic
798C22×C4C2×C22⋊D6111yescharacteristic
799C22×C4C2×C22⋊D6111yescharacteristic
800C22×C4C2×C22⋊D6111yescharacteristic
801C22×C4C2×C22⋊D6111yescharacteristic
802C22×C4C2×C22⋊D6111yescharacteristic
803C22×C4C23×D6111yescharacteristic
804Q16—28no—
805SD16—28no—
806SD16—28no—
807SD16—12216no—
808D8—28no—
809D8—12216no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—614no—
815M16—1222no—
816M16—1222no—
817M16—1222no—
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—1222no—
821C2×C8—1222no—
822C2×C8—1222no—
823C2×C8C2×C22⋊D6114yescomplemented
824C4⋊C4—1222no—
825C4⋊C4—1222no—
826C4⋊C4—1222no—
827C4⋊C4—2441no—
828C22⋊C4—614no—
829C22⋊C4—12216no—
830C22⋊C4—1222no—
831C22⋊C4—1222no—
832C22⋊C4—2441no—
833C42—1222no—
834C42—1222no—
835C42—1222no—
836C42—2441no—
837C23—22no—
838C23—22no—
839C23—42no—
840C23—44no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—82no—
846C23—1224no—
847C23—4884no—
848C23—4884no—
849C23—4884no—
850C23—4884no—
851C23—4884no—
852C23—4884no—
853C23—2448no—
854C23—2442no—
855C23—2442no—
856C23—2442no—
857C23—2442no—
858C23—2442no—
859C23—2442no—
860C23#1451974511yescharacteristic
861C23#1451974511yescharacteristic
862C23#1451974911yescharacteristic
863C23#1451974911yescharacteristic
864C23#1451977311yescharacteristic
865C23#1451977311yescharacteristic
866C23C2×D4×D6111yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—42no—
880D4—42no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—1224no—
892D4—1224no—
893D4—48816no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898D4—2442no—
899D4—2442no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—1224no—
915C2×C4—4882no—
916C2×C4—2442no—
917C2×C4—2444no—
918C2×C4#1451974511yescharacteristic
919C2×C4#1451974511yescharacteristic
920C2×C4#1451974511yescharacteristic
921C2×C4#1451974511yescharacteristic
922C2×C4#1451974511yescharacteristic
923C2×C4#1451974511yescharacteristic
924C2×C4#1451974611yescharacteristic
925C2×C4#1451974611yescharacteristic
926C2×C4#1451974611yescharacteristic
927C2×C4#1451974611yescharacteristic
928C2×C4#1451974811yescharacteristic
929C2×C4#1451974811yescharacteristic
930C2×C4#1451974811yescharacteristic
931C2×C4#1451974811yescharacteristic
932C2×C4#1451974911yescharacteristic
933C2×C4#1451974911yescharacteristic
934C2×C4#1451974911yescharacteristic
935C2×C4#1451974911yescharacteristic
936C2×C4#1451974911yescharacteristic
937C2×C4#1451974911yescharacteristic
938C2×C4#1451977311yescharacteristic
939C2×C4#1451977311yescharacteristic
940C2×C4C2×D4×D6111yescharacteristic
941C2×C4C2×D4×D6111yescharacteristic
942C2×C4C22×C22⋊D6111yescharacteristic
943C2×C4C22×C22⋊D6111yescharacteristic
944C2×C4C22×C22⋊D6111yescharacteristic
945C2×C4C2×#1175822411yescharacteristic
946C8—24no—
947C8—1224no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—42no—
957C22—42no—
958C22—82no—
959C22—82no—
960C22—82no—
961C22—82no—
962C22—82no—
963C22—4884no—
964C22—4884no—
965C22—4884no—
966C22—4884no—
967C22—4884no—
968C22—4884no—
969C22—2448no—
970C22—2444no—
971C22#1683967011yescharacteristic
972C22#1683967011yescharacteristic
973C22#1683967011yescharacteristic
974C22#1683967011yescharacteristic
975C22C2×#1451974511yescharacteristic
976C22C2×#1451974911yescharacteristic
977C22C2×#1451977311yescharacteristic
978C4—42no—
979C4—42no—
980C4—4882no—
981C4—2444no—
982C4#1683967011yescharacteristic
983C4#1683967011yescharacteristic
984C4#1683967011yescharacteristic
985C4#1683967011yescharacteristic
986C4C2×#1451974511yescharacteristic
987C4C2×#1451974611yescharacteristic
988C4C2×#1451974811yescharacteristic
989C4C2×#1451974911yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—82no—
997C2—82no—
998C2—4884no—
999C2#2144686912yesdirect product factor
1000C2C2×#1683967011yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#575C2
socleC22×C61#392
hypercenterC2×#575D61
hypocenterC61C2×#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C22×#14519802C2semidirect
2. C2×#16840326C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839768C2semidirect
5. C2×#16839736C2semidirect
6. #21446869C2direct (N × H)
7. C2×#16839533C2semidirect
8. C2×C61×#575C2semidirect
15. C2×#14519802C22semidirect
22. #16840326C22semidirect
30. #16839779C22semidirect
33. #16839768C22semidirect
36. #16839736C22semidirect
38. #16839533C22semidirect
44. C61×#575C22semidirect
80. C2×#11758194D4semidirect
81. C2×#11758194D4semidirect
131. C2×#41×C61D4semidirect
135. C22×Q8×C61D4semidirect
139. C22×D4×C61D4semidirect
161. C2×M16×C61D4semidirect
163. C22×C8×C61D4semidirect
218. C2×Q8×C61C2×D4semidirect
242. C2×D4×C61C2×D4semidirect
313. C2×C8×C61C2×D4semidirect
332. #11758194C2×D4semidirect
490. C2×#575D61semidirect
506. C2×C61#2008semidirect
515. #575C2×D61semidirect
551. C61C2×#2008semidirect
574. C2×#41C22⋊D61semidirect
578. C22×Q8C22⋊D61semidirect
597. C22×D4C22⋊D61semidirect
635. C2×M16C22⋊D61semidirect
638. C22×C8C22⋊D61semidirect
719. C2×Q8C2×C22⋊D61semidirect
773. C2×D4C2×C22⋊D61semidirect
823. C2×C8C2×C22⋊D61semidirect
999. C2#21446869direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198022
C2×#168403262
C2×#168397792
C2×#168397682
C2×#168397362
#214468692
C2×#168395332
C2×C61×#5752
C2×#200861