Finite Group Databasebeta

← C2×#21457780 #30556523

Subgroups — C2×#21457780 #30556523

Order 15616.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840416C211yesmaximal, characteristic, complemented
2#21457780C2116yesmaximal, direct product factor
3C2×#16840121C211yesmaximal, characteristic, complemented
4C2×#16840078C211yesmaximal, characteristic, complemented
5C2×#16840090C211yesmaximal, characteristic, complemented
6C2×#16840052C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16839993C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839907C211yesmaximal, characteristic, complemented
11C2×#16839896C211yesmaximal, characteristic, complemented
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839763C211yesmaximal, characteristic, complemented
15C22×#14519698C211yesmaximal, characteristic, complemented
16C2×C61×#546C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758201C2211yescharacteristic, complemented
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758194C2211yescharacteristic, complemented
22C23×#92418C2211yescharacteristic
23#16840416—24no—
24#16840416C2218yescomplemented
25C2×#14519777C2211yescharacteristic, complemented
26C2×#14519761—21no—
27C2×#14519761—21no—
28C2×#14519757—21no—
29C2×#14519751C2211yescharacteristic
30C2×#14519751C2211yescharacteristic, complemented
31C2×C4×D244C2211yescharacteristic, complemented
32C22×C4⋊Dic61C2211yescharacteristic
33C22×C4⋊Dic61C2211yescharacteristic, complemented
34#16840121C2218yescomplemented
35#16840090C2218yescomplemented
36#16840078C2218yescomplemented
37#16840052C2218yescomplemented
38#16840013C2218yescomplemented
39#16839993C2218yescomplemented
40#16839974C2218yescomplemented
41#16839907C2218yescomplemented
42#16839896C2218yescomplemented
43#16839872C2218yescomplemented
44#16839834C2218yescomplemented
45C2×#14519708C2211yescharacteristic, complemented
46C2×#14519708C2211yescharacteristic, complemented
47C2×#14519708C2211yescharacteristic, complemented
48C2×C4⋊#92418C2211yescharacteristic, complemented
49#16839763C2218yescomplemented
50C2×#14519701C2211yescharacteristic, complemented
51C2×#14519701C2211yescharacteristic, complemented
52C2×#14519701C2211yescharacteristic, complemented
53C2×#14519698C2211yescharacteristic
54C2×#14519698C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2218yescomplemented
60C2×#14519697C2211yescharacteristic, complemented
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic, complemented
63C2×#14519688C2211yescharacteristic, complemented
64C22×#41×C61C2211yescharacteristic
65C23×D4×C61C2211yescharacteristic
66C61×#546—24no—
67C61×#546C2218yescomplemented
68C2×#124×C61C2211yescharacteristic
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×#121×C61—21no—
72C2×#121×C61C2211yescharacteristic
73C2×#120×C61—21no—
74C2×C4×D4×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C22×C22⋊C4×C61—21no—
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758201—42no—
87C2×#11758201C2314yescomplemented
88C2×#11758199—24no—
89C2×#11758199—42no—
90C2×#11758199C2314yes—
91C2×#11758199C2314yes—
92C2×#11758194—42no—
93C2×#11758194C2314yescomplemented
94C22×#92418—42no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2314yes—
100#14519777—22no—
101#14519777C2314yescomplemented
102#14519761—28no—
103#14519761—28no—
104#14519757—28no—
105#14519751—22no—
106#14519751—22no—
107#14519751C2314yes—
108#14519751C2314yescomplemented
109C4×D244—22no—
110C4×D244C2314yescomplemented
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61—22no—
113C2×C4⋊Dic61—21no—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—21no—
116C2×C4⋊Dic61C2311yescharacteristic
117C2×C4⋊Dic61C2311yescharacteristic
118C2×C4⋊Dic61C2314yes—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2314yescomplemented
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124#14519708C2314yescomplemented
125#14519708C2314yescomplemented
126#14519708C2314yescomplemented
127C4⋊#92418C2314yescomplemented
128#14519701C2314yescomplemented
129#14519701C2314yescomplemented
130#14519701C2314yescomplemented
131#14519698C2314yes—
132#14519698C2314yes—
133#14519698C2314yes—
134#14519698C2314yes—
135#14519698C2314yes—
136#14519698C2314yes—
137#14519697C2314yescomplemented
138C22⋊#92418C2314yes—
139C22⋊#92418C2314yescomplemented
140#14519688C2314yescomplemented
141C25×C61—21no—
142C2×#41×C61—22no—
143C2×#41×C61—24no—
144C2×#41×C61—42no—
145C2×#41×C61C2314yes—
146C22×Q8×C61C2311yescharacteristic
147C22×D4×C61—24no—
148C22×D4×C61—21no—
149C22×D4×C61—21no—
150C22×D4×C61—22no—
151C22×D4×C61—21no—
152C22×D4×C61—42no—
153C22×D4×C61D411yescharacteristic
154C22×D4×C61C2311yescharacteristic
155C22×D4×C61C2314yes—
156C22×D4×C61C2311yescharacteristic
157C23×C4×C61—21no—
158C23×C4×C61—21no—
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161#124×C61—22no—
162#124×C61C2314yes—
163#123×C61—28no—
164C22⋊Q8×C61—22no—
165C22⋊Q8×C61C2314yes—
166#121×C61—22no—
167#121×C61—28no—
168#121×C61C2314yes—
169#120×C61—28no—
170C4×D4×C61—22no—
171C4×D4×C61D414yes—
172C4×D4×C61C2314yes—
173C4×D4×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61D411yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—28no—
183C2×C22⋊C4×C61D411yescharacteristic
184C2×C22⋊C4×C61D411yescharacteristic
185C2×C42×C61C2311yescharacteristic
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—24no—
189C24×C61—44no—
190C24×C61—44no—
191C24×C61—82no—
192C24×C61C2×D411yescharacteristic
193C24×C61C2×D411yescharacteristic
194C23×D61—21no—
195#41×C61—28no—
196#41×C61—44no—
197#41×C61—48no—
198C2×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61C2412yes—
202C2×D4×C61—24no—
203C2×D4×C61—28no—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—21no—
207C2×D4×C61—24no—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—44no—
213C2×D4×C61—48no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—82no—
217C2×D4×C61C2×D414yes—
218C2×D4×C61#4114yescomplemented
219C2×D4×C61C2412yes—
220C2×D4×C61C2412yes—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—24no—
228C22×C4×C61—24no—
229C22×C4×C61—44no—
230C22×C4×C61—82no—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2412yes—
238C22×C4×C61C2412yes—
239C22×C4×C61C2411yescharacteristic
240C2×C22⋊D61—24no—
241C2×C22⋊D61—24no—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—44no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—24no—
248C22×Dic61—24no—
249C22×Dic61—44no—
250C22×Dic61—44no—
251#11758224—432no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—21no—
255C2×D244C2412yes—
256C2×C4×D61—24no—
257C2×C4×D61—44no—
258C2×Dic122—24no—
259C2×Dic122—44no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C2×D414yes—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—24no—
268C22⋊C4×C61—24no—
269C22⋊C4×C61C2×D414yes—
270C22⋊C4×C61C2×D414yes—
271C42×C61C2×D412yes—
272C42×C61C2412yes—
273#11758201—44no—
274#11758199—28no—
275#11758199—44no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—24no—
283C4⋊Dic61—24no—
284C4⋊Dic61—24no—
285C4⋊Dic61C2412yes—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288#11758194—44no—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418—44no—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297C2×#92418C2412yes—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—24no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—48no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—48no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—84no—
314C23×C61—816no—
315C23×C61AGL(1,ℤ/8)14yes—
316C23×C61C22×D412yes—
317C23×C61C22×D412yes—
318C23×C61C22×D411yescharacteristic
319C22×D61—22no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323Q8×C61—22no—
324Q8×C61—22no—
325Q8×C61—42no—
326D4×C61—28no—
327D4×C61—24no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—48no—
332D4×C61—48no—
333D4×C61—42no—
334D4×C61—84no—
335D4×C61C2×#4114yescomplemented
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—24no—
341C2×C4×C61—24no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—48no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—84no—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D412yes—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C2×#4112yes—
358C2×C4×C61H(5,𝔽2)12yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—48no—
361C22⋊D61—48no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—48no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—48no—
370D244—22no—
371D244—22no—
372D244—42no—
373C4×D61—48no—
374Dic122—48no—
375#92418—22no—
376#92418—22no—
377#92418—22no—
378#92418—22no—
379C2×#3306—611nomaximal, Sylow
380C22×C61—22no—
381C22×C61—28no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—24no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—44no—
388C22×C61—48no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—816no—
395C22×C61—84no—
396C22×C61#54612yes—
397C22×C61C2×AGL(1,ℤ/8)14yes—
398C22×C61C2×AGL(1,ℤ/8)12yes—
399C22×C61#57712yes—
400C22×C61C23×D411yescharacteristic
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—84no—
405C4×C61—22no—
406C4×C61—22no—
407C4×C61—22no—
408C4×C61—22no—
409C4×C61—42no—
410C4×C61—42no—
411C4×C61#54612yes—
412C4×C61C22×#4111yescharacteristic
413C4×C61C2×H(5,𝔽2)11yescharacteristic
414Dic61—42no—
415Dic61—42no—
416Dic61—42no—
417C2×#547—611no—
418C2×#546D6111yescharacteristic, complemented
419#3306—6116no—
420C2×#489—611no—
421C2×#481—611no—
422C2×#483—611no—
423C2×#476—611no—
424C2×#469—611no—
425C2×#465—611no—
426C2×#463—611no—
427C2×#449—611no—
428C2×#447—611no—
429C2×#442—611no—
430C2×#435—611no—
431C2×#417—611no—
432C22×#102—611no—
433C2×C61—24no—
434C2×C61—42no—
435C2×C61—44no—
436C2×C61—82no—
437C2×C61#330614yescomplemented
438C2×C61C2×#54611yescharacteristic
439C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
440C2×C61C2×#57711yescharacteristic
441D61—82no—
442C22×#41—1221no—
443C22×#41C2×D6111yescharacteristic
444C23×D4C2×D6111yescharacteristic
445C22×SD16—611no—
446C22×D8—611no—
447C22×D8—611no—
448C22×M16—611no—
449C23×C8—611no—
450#547—618no—
451#547—1224no—
452#546—24no—
453#546C2×D6118yescomplemented
454C2×C4⋊Q8—611no—
455C2×#124C2×D6111yescharacteristic
456C2×#123—21no—
457C2×#123—1221no—
458C2×#123—1221no—
459C2×C22⋊Q8—1221no—
460C2×C22⋊Q8C2×D6111yescharacteristic
461C2×#121—21no—
462C2×#121—611no—
463C2×#121—611no—
464C2×#121C2×D6111yescharacteristic
465C2×#120—21no—
466C2×C4×D4—611no—
467C2×C4×D4C2×D6111yescharacteristic
468C2×C4×D4C2×D6111yescharacteristic
469C22×C4⋊C4—611no—
470C22×C4⋊C4—611no—
471C22×C22⋊C4—21no—
472#489—618no—
473#483—618no—
474#481—618no—
475#476—618no—
476#469—618no—
477#465—618no—
478#463—618no—
479#449—618no—
480#447—618no—
481#442—618no—
482#435—618no—
483C2×#106—611no—
484C2×#106—611no—
485C2×#106—611no—
486C2×C4⋊C8—611no—
487#417—618no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—618no—
498C2×#102—611no—
499C2×C22⋊C8—611no—
500C2×C22⋊C8—611no—
501C2×#97—611no—
502C61C2×#330611yescharacteristic, complemented, Sylow
503C25—21no—
504C2×#41—22no—
505C2×#41—24no—
506C2×#41—42no—
507C2×#41—1228no—
508C2×#41—2448no—
509C2×#41C22×D6114yes—
510C22×Q8—1221no—
511C22×Q8C22×D6111yescharacteristic
512C22×D4—24no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—42no—
518C22×D4—611no—
519C22×D4—1221no—
520C22×D4—1221no—
521C22×D4C22⋊D6111yescharacteristic
522C22×D4C22×D6111yescharacteristic
523C22×D4C22×D6114yes—
524C22×D4C22×D6111yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4C22×D6111yescharacteristic
531C23×C4C22×D6111yescharacteristic
532C2×SD16—614no—
533C2×SD16—2442no—
534C2×D8—614no—
535C2×D8—614no—
536C2×D8—1224no—
537C2×D8—2442no—
538C2×M16—614no—
539C2×M16—2442no—
540C22×C8—611no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8—614no—
545C22×C8—2442no—
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#124—22no—
549#124C22×D6114yes—
550#123—28no—
551#123—1228no—
552#123—1228no—
553C22⋊Q8—22no—
554C22⋊Q8—1228no—
555C22⋊Q8C22×D6114yes—
556#121—22no—
557#121—28no—
558#121—614no—
559#121—614no—
560#121—1222no—
561#121—1222no—
562#121C22×D6114yes—
563#120—28no—
564C4×D4—22no—
565C4×D4—614no—
566C4×D4—1222no—
567C4×D4C22⋊D6114yes—
568C4×D4C22×D6114yes—
569C4×D4C22×D6114yes—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—614no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4C22⋊D6111yescharacteristic
582C2×C4⋊C4C22×D6111yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—28no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4C22⋊D6111yescharacteristic
593C2×C22⋊C4C22⋊D6111yescharacteristic
594C2×C42C22×D6111yescharacteristic
595#106—614no—
596#106—614no—
597#106—614no—
598C4⋊C8—614no—
599#103—614no—
600#103—614no—
601#103—614no—
602#102—614no—
603#102—614no—
604#102—614no—
605#102—614no—
606#102—614no—
607#102—614no—
608#102—614no—
609C22⋊C8—614no—
610C22⋊C8—614no—
611#97—614no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—44no—
616C24—44no—
617C24—82no—
618C24—1221no—
619C24C2×C22⋊D6111yescharacteristic
620C24C2×C22⋊D6111yescharacteristic
621#41—28no—
622#41—44no—
623#41—48no—
624#41—24432no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—1224no—
629C2×Q8—2444no—
630C2×Q8C23×D6112yes—
631C2×D4—24no—
632C2×D4—28no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—21no—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—44no—
642C2×D4—48no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—82no—
646C2×D4—612no—
647C2×D4—1224no—
648C2×D4—1224no—
649C2×D4—1221no—
650C2×D4—1222no—
651C2×D4—1222no—
652C2×D4—2444no—
653C2×D4—2444no—
654C2×D4#1175822414yescomplemented
655C2×D4C2×C22⋊D6114yes—
656C2×D4C23×D6112yes—
657C2×D4C23×D6112yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—44no—
667C22×C4—82no—
668C22×C4—1224no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—2444no—
675C22×C4—2444no—
676C22×C4—2444no—
677C22×C4C2×C22⋊D6112yes—
678C22×C4C2×C22⋊D6112yes—
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C23×D6112yes—
684C22×C4C23×D6112yes—
685C22×C4C23×D6111yescharacteristic
686SD16—2444no—
687D8—1228no—
688D8—2444no—
689M16—2444no—
690C2×C8—612no—
691C2×C8—612no—
692C2×C8—612no—
693C2×C8—612no—
694C2×C8—1222no—
695C2×C8—1222no—
696C2×C8—1222no—
697C2×C8—1222no—
698C2×C8—2444no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—612no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1224no—
710C4⋊C4C2×C22⋊D6114yes—
711C4⋊C4C23×D6112yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4C2×C22⋊D6114yes—
721C22⋊C4C2×C22⋊D6114yes—
722C42C2×C22⋊D6112yes—
723C42C23×D6112yes—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—22no—
732C23—48no—
733C23—42no—
734C23—42no—
735C23—48no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—84no—
740C23—816no—
741C23—1222no—
742C23—2442no—
743C23—2442no—
744C23—2442no—
745C23#1451980214yes—
746C23C22×C22⋊D6112yes—
747C23C22×C22⋊D6112yes—
748C23C22×C22⋊D6111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—2448no—
753D4—28no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—24no—
758D4—48no—
759D4—48no—
760D4—42no—
761D4—84no—
762D4—1222no—
763D4—1222no—
764D4—2448no—
765D4—2448no—
766D4—2442no—
767D4C2×#1175822414yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—48no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—84no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—2448no—
788C2×C4—2448no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2448no—
793C2×C4C22×C22⋊D6112yes—
794C2×C4C22×C22⋊D6112yes—
795C2×C4C22×C22⋊D6112yes—
796C2×C4C22×C22⋊D6112yes—
797C2×C4C22×C22⋊D6111yescharacteristic
798C2×C4C2×#1175822412yes—
799C2×C4#1451982212yes—
800C2×C4C24×D6111yescharacteristic
801C8—1222no—
802C8—1222no—
803C8—1222no—
804C8—1222no—
805C22—22no—
806C22—22no—
807C22—28no—
808C22—22no—
809C22—24no—
810C22—22no—
811C22—22no—
812C22—42no—
813C22—42no—
814C22—44no—
815C22—48no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—816no—
820C22—84no—
821C22—4884no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22#1684040612yes—
826C22C2×#1451980214yes—
827C22C2×#1451980212yes—
828C22#1684057312yes—
829C22C23×C22⋊D6111yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—2442no—
837C4—2442no—
838C4—2442no—
839C4#1684040612yes—
840C4C22×#1175822411yescharacteristic
841C4C2×#1451982211yescharacteristic
842C2—24no—
843C2—42no—
844C2—44no—
845C2—82no—
846C2—4882no—
847C2#2145778014yesdirect product factor
848C2C2×#1684040611yescharacteristic
849C2C22×#1451980211yescharacteristic
850C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61C2×#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16840416C2semidirect
2. #21457780C2direct (N × H)
3. C2×#16840121C2semidirect
4. C2×#16840078C2semidirect
5. C2×#16840090C2semidirect
6. C2×#16840052C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16839993C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839907C2semidirect
11. C2×#16839896C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839763C2semidirect
15. C22×#14519698C2semidirect
16. C2×C61×#546C2semidirect
18. C22×#11758201C22semidirect
21. C22×#11758194C22semidirect
24. #16840416C22semidirect
25. C2×#14519777C22semidirect
30. C2×#14519751C22semidirect
31. C2×C4×D244C22semidirect
33. C22×C4⋊Dic61C22semidirect
34. #16840121C22semidirect
35. #16840090C22semidirect
36. #16840078C22semidirect
37. #16840052C22semidirect
38. #16840013C22semidirect
39. #16839993C22semidirect
40. #16839974C22semidirect
41. #16839907C22semidirect
42. #16839896C22semidirect
43. #16839872C22semidirect
44. #16839834C22semidirect
45. C2×#14519708C22semidirect
46. C2×#14519708C22semidirect
47. C2×#14519708C22semidirect
48. C2×C4⋊#92418C22semidirect
49. #16839763C22semidirect
50. C2×#14519701C22semidirect
51. C2×#14519701C22semidirect
52. C2×#14519701C22semidirect
59. C2×#14519698C22semidirect
60. C2×#14519697C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×#14519688C22semidirect
67. C61×#546C22semidirect
87. C2×#11758201C23semidirect
93. C2×#11758194C23semidirect
101. #14519777C23semidirect
108. #14519751C23semidirect
110. C4×D244C23semidirect
120. C2×C4⋊Dic61C23semidirect
124. #14519708C23semidirect
125. #14519708C23semidirect
126. #14519708C23semidirect
127. C4⋊#92418C23semidirect
128. #14519701C23semidirect
129. #14519701C23semidirect
130. #14519701C23semidirect
137. #14519697C23semidirect
139. C22⋊#92418C23semidirect
140. #14519688C23semidirect
218. C2×D4×C61#41semidirect
335. D4×C61C2×#41semidirect
418. C2×#546D61semidirect
437. C2×C61#3306semidirect
453. #546C2×D61semidirect
502. C61C2×#3306semidirect
654. C2×D4#11758224semidirect
767. D4C2×#11758224semidirect
847. C2#21457780direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404162
#214577802
C2×#168401212
C2×#168400782
C2×#168400902
C2×#168400522
C2×#168400132
C2×#168399932
C2×#168399742
C2×#168399072
C2×#168398962
C2×#168398722
C2×#168398342
C2×#168397632
C22×#145196982
C2×C61×#5462
C2×#330661