Finite Group Databasebeta

← C2×#21456099 #30548347

Subgroups — C2×#21456099 #30548347

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×#16840379C211yesmaximal, characteristic, complemented
2C2×#16840243C211yesmaximal, characteristic, complemented
3#21456099C2116yesmaximal, direct product factor
4C2×#16840092C211yesmaximal, characteristic, complemented
5C2×#16840046C211yesmaximal, characteristic, complemented
6C2×#16840051C211yesmaximal, characteristic, complemented
7C2×#16839983C211yesmaximal, characteristic, complemented
8C2×#16839976C211yesmaximal, characteristic, complemented
9C2×#16839926C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic
11C2×#16839871C211yesmaximal, characteristic, complemented
12C2×#16839868C211yesmaximal, characteristic, complemented
13C2×#16839853C211yesmaximal, characteristic, complemented
14C2×#16839849C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#481C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840379—24no—
23#16840379C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519770—21no—
26C2×#14519764—21no—
27C2×#14519764C2211yescharacteristic
28C2×#14519758—21no—
29C2×#14519756C2211yescharacteristic
30C2×#14519754—21no—
31#16840243—24no—
32#16840243C2218yescomplemented
33C2×#14519742C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519742C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61—21no—
41C2×#14519736C2211yescharacteristic
42C2×#14519735—21no—
43C2×C4⋊C4×D61—21no—
44#16840092C2218yescomplemented
45#16840051C2218yescomplemented
46#16840046C2218yescomplemented
47#16839983C2218yescomplemented
48#16839976C2218yescomplemented
49#16839926C2218yescomplemented
50#16839905C2218yes—
51#16839871C2218yescomplemented
52#16839868C2218yescomplemented
53#16839853C2218yescomplemented
54#16839849C2218yescomplemented
55#16839820C2218yescomplemented
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#481C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C2×Dic244—24no—
91C2×Dic244C2314yes—
92C2×#11758190—24no—
93C2×#11758190C2314yes—
94C2×#11758200—24no—
95C2×#11758200C2314yes—
96C2×#11758199—24no—
97C2×#11758199C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100#14519776—22no—
101#14519776C2314yes—
102#14519770—28no—
103#14519764—28no—
104#14519764—22no—
105#14519764C2314yes—
106#14519758—28no—
107#14519756—22no—
108#14519756C2314yes—
109#14519754—28no—
110#14519742—22no—
111#14519742—22no—
112#14519742—22no—
113#14519742C2314yes—
114#14519742C2314yes—
115#14519742C2314yes—
116D4×Dic61—22no—
117D4×Dic61C2314yes—
118#14519739—22no—
119#14519739—22no—
120#14519739C2314yes—
121#14519739C2314yes—
122C4×C22⋊D61—28no—
123C4×C22⋊D61—28no—
124#14519736D414yes—
125#14519736C2314yes—
126#14519735—28no—
127C2×C4⋊Dic61D411yescharacteristic
128C2×C4⋊Dic61D411yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C4⋊C4×D61—28no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61D411yescharacteristic
141C2×C22⋊Dic61D411yescharacteristic
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519708C2314yes—
150#14519708C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519700C2314yes—
155#14519700C2314yes—
156#14519700C2314yes—
157#14519699C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C23×C4×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#121×C61—22no—
169#121×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—22no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2314yes—
176C2×C22⋊C4×C61—21no—
177#106×C61C2314yes—
178#106×C61C2314yes—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C2×D4×C61—24no—
186C2×D4×C61—21no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—82no—
190C2×D4×C61C2412yes—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
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×D412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—28no—
203C2×C22⋊D61—24no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—82no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213#11758222—216no—
214#11758222—28no—
215#11758222—28no—
216C2×D244—21no—
217C2×D244—22no—
218C2×D244#4114yes—
219C2×D244C2412yes—
220C2×C4×D61—28no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—82no—
225C2×C4×D61—82no—
226C2×Dic122—21no—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—21no—
231C2×Dic122—24no—
232C2×Dic122—82no—
233C2×Dic122#4114yes—
234C2×Dic122C2412yes—
235C2×Dic122C2412yes—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C22⋊C4×C61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61C2×D414yes—
253C22⋊Dic61C2×D414yes—
254#11758200—28no—
255#11758199—28no—
256#11758198—24no—
257#11758198—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2×D414yes—
260C4⋊Dic61C2×D414yes—
261C4⋊Dic61C2412yes—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61C2×D412yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2412yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278Dic244—28no—
279#11758190—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—24no—
290C22×D61—22no—
291C22×D61—42no—
292C22×D61—42no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—42no—
296D4×C61—84no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
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×D411yescharacteristic
310C2×C4×C61C2×#4112yes—
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2511yescharacteristic
313C22⋊D61—216no—
314C2×Dic61—24no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—84no—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329D244—24no—
330D244—22no—
331D244C2×#4114yes—
332C4×D61—216no—
333C4×D61—84no—
334C4×D61—84no—
335Dic122—24no—
336Dic122—22no—
337Dic122—22no—
338Dic122—22no—
339Dic122—42no—
340Dic122—84no—
341Dic122C2×#4114yes—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3125—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—44no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—84no—
355C22×C61#52512yes—
356C22×C61#57712yes—
357C22×C61#57712yes—
358C22×C61C23×D411yescharacteristic
359C2×D61—24no—
360C2×D61—48no—
361C2×D61—42no—
362C2×D61—42no—
363C4×C61—22no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61#52512yes—
368C4×C61C22×#4111yescharacteristic
369C4×C61C22×#4111yescharacteristic
370Dic61—24no—
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377C2×#542—611no—
378C2×#520—611no—
379#3125—6116no—
380C2×#481D6111yescharacteristic, complemented
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×SD16—611no—
392C2×#433—611no—
393C2×C61—42no—
394C2×C61—82no—
395C2×C61#312514yescomplemented
396C2×C61C2×#52511yescharacteristic
397C2×C61C2×#57711yescharacteristic
398C2×C61C2×#57711yescharacteristic
399D61—44no—
400C22×#41—611no—
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
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×#121C2×D6111yescharacteristic
415#520—618no—
416#520—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×C4×D4—1221no—
425C2×#117—611no—
426C2×#117—1221no—
427C22×C4⋊C4—1221no—
428C22×C4⋊C4C2×D6111yescharacteristic
429#483—618no—
430#481C2×D6118yescomplemented
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×SD16—618no—
441#433—618no—
442C2×#106—611no—
443C2×#106—611no—
444C2×#106C2×D6111yescharacteristic
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102C2×D6111yescharacteristic
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8C2×D6111yescharacteristic
458C2×#97—611no—
459C2×C4×C8—611no—
460C61C2×#312511yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—1224no—
463C2×#41—1224no—
464C2×#41—1222no—
465C22×Q8—611no—
466C22×Q8—611no—
467C22×Q8—1221no—
468C22×D4—21no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4C22×D6111yescharacteristic
472C23×C4—21no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4C22×D6111yescharacteristic
478C2×Q16—614no—
479C2×Q16—1224no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
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—1222no—
495#124—1228no—
496#123—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—1228no—
499C22⋊Q8—1222no—
500#121—22no—
501#121C22×D6114yes—
502C4×Q8—614no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8—1222no—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1228no—
515C4×D4—1228no—
516#117—614no—
517#117—614no—
518#117—1228no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1228no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4C22×D6111yescharacteristic
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6114yes—
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—611no—
544C2×C42—611no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42—1221no—
548#106—614no—
549#106—614no—
550#106C22×D6114yes—
551#106C22×D6114yes—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103—614no—
558#102—614no—
559#102—614no—
560#102C22×D6114yes—
561#102C22×D6114yes—
562C22⋊C8—614no—
563C22⋊C8C22×D6114yes—
564#97—614no—
565C4×C8—614no—
566C24—21no—
567C24—1221no—
568C24D4×D6111yescharacteristic
569#41—1228no—
570#41—1228no—
571#41—12216no—
572C2×Q8—614no—
573C2×Q8—612no—
574C2×Q8—612no—
575C2×Q8—1224no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1222no—
579C2×Q8—1222no—
580C2×Q8—1222no—
581C2×Q8—4882no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—82no—
587C2×D4—614no—
588C2×D4—612no—
589C2×D4—1228no—
590C2×D4—1224no—
591C2×D4—1221no—
592C2×D4—1222no—
593C2×D4C23×D6112yes—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1228no—
608C22×C4—1224no—
609C22×C4—1221no—
610C22×C4—1224no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—4882no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4D4×D6112yes—
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—1228no—
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—21no—
636C4⋊C4—614no—
637C4⋊C4—614no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1224no—
645C4⋊C4C23×D6112yes—
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—612no—
658C42—612no—
659C42—612no—
660C42—612no—
661C42—1224no—
662C42—1224no—
663C42—1224no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1224no—
672C23—1222no—
673C23—2442no—
674C23—2442no—
675C23C2×D4×D6112yes—
676C23C2×D4×D6111yescharacteristic
677Q8—614no—
678Q8—1224no—
679Q8—1222no—
680Q8—1222no—
681Q8—1222no—
682Q8—4884no—
683Q8—2442no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—614no—
689D4—12216no—
690D4—1224no—
691D4—1222no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—12216no—
708C2×C4—1224no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—4884no—
717C2×C4—4884no—
718C2×C4—4884no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4#41×D6112yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—1224no—
739C22—2442no—
740C22—2442no—
741C22—2448no—
742C22#1684027012yes—
743C22#1684056812yes—
744C22#1684057212yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—1222no—
751C4—1222no—
752C4—1222no—
753C4—1222no—
754C4—1224no—
755C4—2442no—
756C4—2442no—
757C4#1684027012yes—
758C4C2×#41×D6111yescharacteristic
759C4C2×#41×D6111yescharacteristic
760C2—42no—
761C2—82no—
762C2—2444no—
763C2#2145609914yesdirect product factor
764C2C2×#1684027011yescharacteristic
765C2C2×#1684056811yescharacteristic
766C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#481C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenterC2×#481D61
hypocenterC61C2×#3125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16840379C2semidirect
2. C2×#16840243C2semidirect
3. #21456099C2direct (N × H)
4. C2×#16840092C2semidirect
5. C2×#16840046C2semidirect
6. C2×#16840051C2semidirect
7. C2×#16839983C2semidirect
8. C2×#16839976C2semidirect
9. C2×#16839926C2semidirect
11. C2×#16839871C2semidirect
12. C2×#16839868C2semidirect
13. C2×#16839853C2semidirect
14. C2×#16839849C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#481C2semidirect
23. #16840379C22semidirect
32. #16840243C22semidirect
44. #16840092C22semidirect
45. #16840051C22semidirect
46. #16840046C22semidirect
47. #16839983C22semidirect
48. #16839976C22semidirect
49. #16839926C22semidirect
51. #16839871C22semidirect
52. #16839868C22semidirect
53. #16839853C22semidirect
54. #16839849C22semidirect
55. #16839820C22semidirect
71. C61×#481C22semidirect
380. C2×#481D61semidirect
395. C2×C61#3125semidirect
430. #481C2×D61semidirect
460. C61C2×#3125semidirect
763. C2#21456099direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403792
C2×#168402432
#214560992
C2×#168400922
C2×#168400462
C2×#168400512
C2×#168399832
C2×#168399762
C2×#168399262
C2×#168399052
C2×#168398712
C2×#168398682
C2×#168398532
C2×#168398492
C2×#168398202
C2×C61×#4812
C2×#312561