Finite Group Databasebeta

← C2×#21456092 #30548340

Subgroups — C2×#21456092 #30548340

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840384C211yesmaximal, characteristic, complemented
2C2×#16840241C211yesmaximal, characteristic, complemented
3#21456092C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840091C211yesmaximal, characteristic, complemented
6C2×#16840046C211yesmaximal, characteristic, complemented
7C2×#16840050C211yesmaximal, characteristic, complemented
8C2×#16839987C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839921C211yesmaximal, characteristic, complemented
11C2×#16839908C211yesmaximal, characteristic
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839867C211yesmaximal, characteristic, complemented
14C2×C4×#11758190C211yesmaximal, characteristic, complemented
15C2×#16839821C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21#16840384—24no—
22#16840384C2218yescomplemented
23C2×#14519776C2211yescharacteristic
24C2×#14519771—21no—
25C2×#14519766C2211yescharacteristic
26C2×#14519765—21no—
27C2×#14519762—21no—
28C2×#14519755—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519752C2211yescharacteristic
31#16840241—24no—
32#16840241C2218yescomplemented
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519737—21no—
39C2×#14519734C2211yescharacteristic
40C2×#14519733—21no—
41C22×#11758196—21no—
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840091C2218yescomplemented
44#16840082C2218yescomplemented
45#16840050C2218yescomplemented
46#16840046C2218yescomplemented
47#16839987C2218yescomplemented
48#16839979C2218yescomplemented
49#16839921C2218yescomplemented
50#16839908C2218yes—
51#16839872C2218yescomplemented
52#16839867C2218yescomplemented
53C4×#11758190C2218yescomplemented
54#16839821C2218yescomplemented
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C4×SD16×C61C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C2×#11758224—24no—
78C2×#11758224—22no—
79C2×#11758224—24no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C23×Dic61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758202—24no—
92C2×#11758202C2314yes—
93C2×#11758190—24no—
94C2×#11758190C2314yes—
95C2×#11758199—24no—
96C2×#11758199C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519776—22no—
100#14519776C2314yes—
101#14519771—28no—
102#14519766—22no—
103#14519766C2314yes—
104#14519765—28no—
105#14519762—28no—
106#14519755—28no—
107#14519753—22no—
108#14519753C2314yes—
109#14519752—22no—
110#14519752C2314yes—
111C4×Dic122—22no—
112C4×Dic122C2314yes—
113#14519742—22no—
114#14519742C2314yes—
115C4×D244—22no—
116C4×D244C2314yes—
117D4×Dic61—22no—
118D4×Dic61C2314yes—
119C4×C22⋊D61—28no—
120#14519737—28no—
121#14519734D414yes—
122#14519734C2314yes—
123#14519733—28no—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—28no—
132C2×#11758196D411yescharacteristic
133C2×#11758196D411yescharacteristic
134C4⋊C4×D61—22no—
135C4⋊C4×D61C2314yes—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×#11758198D411yescharacteristic
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519709C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519701C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519688C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#106×C61C2314yes—
179#103×C61C2314yes—
180#102×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61#4114yes—
192C2×D4×C61C2412yes—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—82no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—28no—
202C2×C22⋊D61—24no—
203C22×Dic61—28no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—82no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213#11758224—216no—
214#11758224—28no—
215#11758224—28no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244—24no—
220C2×D244—82no—
221C2×D244C2412yes—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—82no—
227C2×C4×D61—82no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2412yes—
230C2×Dic122—21no—
231C2×Dic122—22no—
232C2×Dic122—24no—
233C2×Dic122—82no—
234C2×Dic122#4114yes—
235C2×Dic122C2412yes—
236SD16×C61—28no—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C22⋊C4×C61—24no—
247C42×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C22⋊Dic61—24no—
251#11758202—28no—
252#11758199—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198C2×D414yes—
259#11758198C2×D414yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61C2×D412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279#11758190—28no—
280C23×C61—24no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C22×D412yes—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—42no—
296D4×C61—24no—
297D4×C61—22no—
298D4×C61C2×#4114yes—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—84no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—216no—
315C2×Dic61—216no—
316C2×Dic61—24no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—84no—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329D244—22no—
330D244—22no—
331D244—42no—
332D244—84no—
333C4×D61—24no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—84no—
337C4×D61—84no—
338Dic122—24no—
339Dic122—22no—
340Dic122—84no—
341Dic122C2×#4114yes—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3125—611nomaximal, Sylow
347C22×C61—24no—
348C22×C61—48no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61#52512yes—
352C22×C61#57712yes—
353C22×C61#57712yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—44no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61#52512yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—24no—
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377C2×#542—611no—
378C2×#520—611no—
379#3125—6116no—
380C2×#481—611no—
381C2×#483—611no—
382C2×#475—611no—
383C2×#476—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#452—611no—
387C2×#449—611no—
388C2×#442—611no—
389C2×#441—611no—
390C2×C4×SD16—611no—
391C2×C4×SD16D6111yescharacteristic, complemented
392C2×#433—611no—
393C2×C61—44no—
394C2×C61#312514yescomplemented
395C2×C61C2×#52511yescharacteristic
396C2×C61C2×#57711yescharacteristic
397C2×C61C2×#57711yescharacteristic
398D61—42no—
399D61—82no—
400C22×#41—611no—
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16C2×D6111yescharacteristic
404C22×D8—611no—
405#542—618no—
406#542—1224no—
407C2×C4⋊Q8—611no—
408C2×#126—1221no—
409C2×#124—611no—
410C2×#124—1221no—
411C2×#123—1221no—
412C2×C22⋊Q8—611no—
413C2×C22⋊Q8—1221no—
414C2×#121—611no—
415#520—618no—
416#520—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8C2×D6111yescharacteristic
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×C4×D4—1221no—
423C2×C4×D4—1221no—
424C2×C4×D4C2×D6111yescharacteristic
425C2×#117—611no—
426C2×#117—1221no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—1221no—
429#483—618no—
430#481—618no—
431#476—618no—
432#475—618no—
433#464—618no—
434#463—618no—
435#452—618no—
436#449—618no—
437#442—618no—
438#441—618no—
439C4×SD16—618no—
440C4×SD16C2×D6118yescomplemented
441#433—618no—
442C2×#106—611no—
443C2×#106—611no—
444C2×#106—611no—
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×C4×C8C2×D6111yescharacteristic
460C61C2×#312511yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—1222no—
463C2×#41—1224no—
464C2×#41—1224no—
465C22×Q8—611no—
466C22×Q8—1221no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—611no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4C22×D6111yescharacteristic
472C23×C4—21no—
473C23×C4—611no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C2×Q16—614no—
479C2×Q16—1224no—
480C2×SD16—24no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16C22×D6114yes—
484C2×D8—614no—
485C2×D8—1224no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—614no—
491C4⋊Q8—1222no—
492#126—1228no—
493#124—614no—
494#124—1228no—
495#124—1222no—
496#123—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—1228no—
499C22⋊Q8—1222no—
500#121—614no—
501#121—1222no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8C22×D6114yes—
508C4×D4—22no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—1222no—
512C4×D4—1228no—
513C4×D4—1228no—
514C4×D4—1222no—
515C4×D4C22×D6114yes—
516#117—614no—
517#117—614no—
518#117—1228no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—1222no—
526C2×C4⋊C4—1228no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—21no—
544C2×C42—611no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42C22×D6111yescharacteristic
548#106—614no—
549#106—614no—
550#106—614no—
551#106C22×D6114yes—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103C22×D6114yes—
558#102—614no—
559#102—614no—
560#102—614no—
561#102C22×D6114yes—
562C22⋊C8—614no—
563C22⋊C8—614no—
564#97—614no—
565C4×C8C22×D6114yes—
566C24—21no—
567C24—611no—
568C24—1221no—
569#41—1228no—
570#41—12216no—
571#41—1228no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—614no—
576C2×Q8—612no—
577C2×Q8—1224no—
578C2×Q8—1221no—
579C2×Q8—1222no—
580C2×Q8—4882no—
581C2×Q8C23×D6112yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—612no—
585C2×D4—1224no—
586C2×D4—1224no—
587C2×D4—1228no—
588C2×D4—1221no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—4882no—
592C2×D4#1175822214yes—
593C2×D4C23×D6112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—82no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1228no—
608C22×C4—1221no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1224no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4—4882no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—28no—
622SD16—1228no—
623D8—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1224no—
646C4⋊C4C23×D6112yes—
647C4⋊C4C23×D6112yes—
648C22⋊C4—24no—
649C22⋊C4—614no—
650C22⋊C4—614no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C42—24no—
658C42—612no—
659C42—612no—
660C42—1224no—
661C42—1224no—
662C42D4×D6112yes—
663C42C23×D6112yes—
664C23—24no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—612no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23C2×D4×D6111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—614no—
681Q8—1224no—
682Q8—1222no—
683Q8—4884no—
684D4—24no—
685D4—22no—
686D4—12216no—
687D4—1222no—
688D4—1222no—
689D4—4884no—
690D4—2442no—
691D4C2×#1175822214yes—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—84no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—12216no—
705C2×C4—1222no—
706C2×C4—1224no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1224no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—4884no—
716C2×C4—4884no—
717C2×C4—4884no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4C2×#1175822212yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—24no—
731C22—42no—
732C22—42no—
733C22—48no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—4884no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2444no—
742C22#1684027112yes—
743C22#1684056812yes—
744C22#1684056912yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—1222no—
752C4—1222no—
753C4—1222no—
754C4—1224no—
755C4—2442no—
756C4—2442no—
757C4#1684027112yes—
758C4C2×#41×D6111yescharacteristic
759C4C22×#1175822211yescharacteristic
760C2—44no—
761C2—4882no—
762C2—2442no—
763C2#2145609214yesdirect product factor
764C2C2×#1684027111yescharacteristic
765C2C2×#1684056811yescharacteristic
766C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839908C2
hypercenterC2×C4×SD16D61
hypocenterC61C2×#3125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16840384C2semidirect
2. C2×#16840241C2semidirect
3. #21456092C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840091C2semidirect
6. C2×#16840046C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16839987C2semidirect
9. C2×#16839979C2semidirect
10. C2×#16839921C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839867C2semidirect
14. C2×C4×#11758190C2semidirect
15. C2×#16839821C2semidirect
16. C2×C4×SD16×C61C2semidirect
22. #16840384C22semidirect
32. #16840241C22semidirect
43. #16840091C22semidirect
44. #16840082C22semidirect
45. #16840050C22semidirect
46. #16840046C22semidirect
47. #16839987C22semidirect
48. #16839979C22semidirect
49. #16839921C22semidirect
51. #16839872C22semidirect
52. #16839867C22semidirect
53. C4×#11758190C22semidirect
54. #16839821C22semidirect
72. C4×SD16×C61C22semidirect
391. C2×C4×SD16D61semidirect
394. C2×C61#3125semidirect
440. C4×SD16C2×D61semidirect
460. C61C2×#3125semidirect
763. C2#21456092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403842
C2×#168402412
#214560922
C2×#168400822
C2×#168400912
C2×#168400462
C2×#168400502
C2×#168399872
C2×#168399792
C2×#168399212
C2×#168399082
C2×#168398722
C2×#168398672
C2×C4×#117581902
C2×#168398212
C2×C4×SD16×C612
C2×#312561