Finite Group Databasebeta

← C2×#478×D61 #30547478

Subgroups — C2×#478×D61 #30547478

Order 15616.

2574 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×#125×D61C211yesmaximal, characteristic, complemented
2C2×C4×D4×D61C211yesmaximal, characteristic
3C2×#16840065C211yesmaximal, characteristic, complemented
4C2×#16840064C211yesmaximal, characteristic, complemented
5C2×#16840063C211yesmaximal, characteristic, complemented
6C2×#16840062C211yesmaximal, characteristic, complemented
7C2×#16840061C211yesmaximal, characteristic, complemented
8C2×#16840060C211yesmaximal, characteristic, complemented
9C2×#16840059C211yesmaximal, characteristic, complemented
10#478×D61C2116yesmaximal, direct product factor
11C2×#107×D61C211yesmaximal, characteristic, complemented
12C2×#106×D61C211yesmaximal, characteristic, complemented
13C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
14C2×#102×D61C211yesmaximal, characteristic
15C2×#102×D61C211yesmaximal, characteristic
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C23×C4×D61—21no—
19C22×C8×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C2×#14519769C2211yescharacteristic, complemented
22C2×#14519768C2211yescharacteristic, complemented
23C2×#14519768C2211yescharacteristic, complemented
24C2×#14519767—21no—
25C2×#14519767—21no—
26#125×D61—24no—
27#125×D61C2218yescomplemented
28C2×C4×D244C2211yescharacteristic
29C2×D4×Dic61C2211yescharacteristic
30C2×#14519739C2211yescharacteristic
31C2×C4×C22⋊D61—21no—
32C2×#14519737—21no—
33C4×D4×D61—24no—
34C4×D4×D61C2218yes—
35C2×C4⋊C4×D61—21no—
36C2×C4⋊C4×D61—21no—
37C2×C4⋊C4×D61C2211yescharacteristic
38C2×C4⋊C4×D61C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42#16840065C2218yescomplemented
43#16840064C2218yescomplemented
44#16840063C2218yescomplemented
45#16840062C2218yescomplemented
46#16840061C2218yescomplemented
47#16840060C2218yescomplemented
48#16840059C2218yescomplemented
49C2×#14519711C2211yescharacteristic, complemented
50C2×#14519710C2211yescharacteristic, complemented
51C2×#14519710C2211yescharacteristic, complemented
52#107×D61C2218yescomplemented
53C2×#14519709C2211yescharacteristic, complemented
54C2×#14519708C2211yescharacteristic, complemented
55C2×#14519708C2211yescharacteristic, complemented
56#106×D61C2218yescomplemented
57C2×C4⋊#92418C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C4⋊C8×D61C2218yescomplemented
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67#102×D61C2218yes—
68#102×D61C2218yes—
69C2×#125×C61C2211yescharacteristic, complemented
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C2×D4×D61—22no—
81C2×D4×D61—24no—
82C2×D4×D61Q818yes—
83C2×D4×D61C2314yes—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—28no—
91C22×C4×D61—48no—
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—24no—
98C2×C8×D61—24no—
99C2×C8×D61C2314yes—
100C2×C8×D61C2314yes—
101#14519769—22no—
102#14519769C2314yescomplemented
103#14519768—22no—
104#14519768—22no—
105#14519768C2314yescomplemented
106#14519768C2314yescomplemented
107#14519767—28no—
108#14519767—28no—
109C4×D244—22no—
110C4×D244C2314yes—
111D4×Dic61—22no—
112D4×Dic61C2314yes—
113#14519739—22no—
114#14519739C2314yes—
115C4×C22⋊D61—28no—
116#14519737—28no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C4⋊C4×D61—28no—
130C4⋊C4×D61—28no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2314yes—
135C4⋊C4×D61C2314yes—
136C4⋊C4×D61C2314yes—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C22⋊C4×D61—28no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C42×D61D414yes—
145C42×D61C2314yes—
146#14519711C2314yescomplemented
147#14519710C2314yescomplemented
148#14519710C2314yescomplemented
149#14519709C2314yescomplemented
150#14519708C2314yescomplemented
151#14519708C2314yescomplemented
152C4⋊#92418C2314yescomplemented
153#14519706C2314yescomplemented
154#14519706C2314yescomplemented
155#14519699C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519697C2314yes—
160#14519697C2314yes—
161C22×D4×C61C2311yescharacteristic
162C23×C4×C61—21no—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165#125×C61—22no—
166#125×C61C2314yescomplemented
167C4×D4×C61—22no—
168C4×D4×C61C2314yes—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#107×C61C2314yescomplemented
177#106×C61C2314yescomplemented
178C4⋊C8×C61C2314yescomplemented
179#102×C61C2314yes—
180#102×C61C2314yes—
181C24×C61—21no—
182C23×D61—21no—
183C23×D61—28no—
184C23×D61—24no—
185C23×D61—44no—
186C23×D61—44no—
187C23×D61C2×D411yescharacteristic
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61C2×Q814yes—
191C2×D4×C61C2412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—44no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—28no—
201C2×C22⋊D61—24no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—44no—
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210D4×D61—216no—
211D4×D61—28no—
212D4×D61C2×Q8116yes—
213C2×D244—21no—
214C2×D244—22no—
215C2×D244C2×Q814yes—
216C2×D244C2412yes—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—432no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61C2×D414yes—
231C2×C4×D61C2×D414yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×Q814yes—
234C2×C4×D61#4114yes—
235C2×C4×D61C2412yes—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C22⋊C4×C61—24no—
249C42×C61C2×D412yes—
250C42×C61C2412yes—
251C22⋊Dic61—24no—
252#11758198—24no—
253#11758198—24no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2×D414yes—
271C4×Dic61C2×D414yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C8×D61—28no—
278C8×D61—28no—
279C23×C61—24no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61C22×D411yescharacteristic
284C22×D61—24no—
285C22×D61—22no—
286C22×D61—216no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—48no—
290C22×D61—48no—
291C22×D61—432no—
292C22×D61C22⋊Q814yes—
293C22×D61#13514yes—
294C22×D61AGL(1,ℤ/8)14yes—
295C22×D61C22×D412yes—
296D4×C61—24no—
297D4×C61—22no—
298D4×C61C22×Q814yes—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—48no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×Q812yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—216no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—48no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61C22⋊Q814yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328D244—24no—
329D244—22no—
330D244C22×Q814yes—
331C4×D61—28no—
332C4×D61—28no—
333C4×D61—48no—
334C4×D61—48no—
335C4×D61—48no—
336C4×D61—48no—
337C4×D61—48no—
338C4×D61C22⋊Q818yes—
339C4×D61C22×Q814yes—
340C4×D61C2×#4114yes—
341C8×C61—22no—
342C8×C61—22no—
343#92418—22no—
344#92418—22no—
345C22×#478—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—48no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61C2×C22⋊Q812yes—
351C22×C61C2×#13512yes—
352C22×C61C2×AGL(1,ℤ/8)12yes—
353C22×C61C23×D411yescharacteristic
354C2×D61—24no—
355C2×D61—48no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—432no—
359C2×D61#478116yesdirect product factor
360C2×D61C2×C22⋊Q814yes—
361C2×D61C2×#13514yes—
362C2×D61C2×AGL(1,ℤ/8)14yes—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61C2×C22⋊Q812yes—
369C4×C61C23×Q811yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376Dic61C2×C22⋊Q814yes—
377C22×#125—611no—
378C22×C4×D4—611no—
379C2×#478—6116no—
380C2×#478—611no—
381C2×#478—611no—
382C2×#478—611no—
383C2×#478—611no—
384C2×#478—611no—
385C2×#478—611no—
386C2×#478—611no—
387C2×#478D6111yescharacteristic, direct product factor
388C22×#107—611no—
389C22×#106—611no—
390C22×C4⋊C8—611no—
391C22×#102—611no—
392C22×#102—611no—
393C2×C61—44no—
394C2×C61C2×#47814yescomplemented
395C2×C61C22×C22⋊Q811yescharacteristic
396C2×C61C22×#13511yescharacteristic
397C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
398D61—44no—
399D61C2×#47818yesdirect product factor
400C23×D4—611no—
401C24×C4—1221no—
402C23×C8—611no—
403C23×C8—611no—
404C2×#125—618no—
405C2×#125—611no—
406C2×#125—611no—
407C2×#125—611no—
408C2×#125—1221no—
409C2×#125—1221no—
410C2×#125—1224no—
411C2×#125C2×D6111yescharacteristic, complemented
412C2×C4×D4—611no—
413C2×C4×D4—618no—
414C2×C4×D4—611no—
415C2×C4×D4—611no—
416C2×C4×D4—1221no—
417C2×C4×D4—1224no—
418C2×C4×D4—1221no—
419C2×C4×D4C2×D6111yescharacteristic
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—1221no—
424C22×C4⋊C4—1221no—
425C22×C22⋊C4—1221no—
426C22×C42—611no—
427#478—618no—
428#478—618no—
429#478—618no—
430#478—618no—
431#478—618no—
432#478—618no—
433#478—618no—
434#478C2×D6118yesdirect product factor
435C2×#107—611no—
436C2×#107—611no—
437C2×#107—611no—
438C2×#107—618no—
439C2×#107C2×D6111yescharacteristic, complemented
440C2×#106—611no—
441C2×#106—611no—
442C2×#106—611no—
443C2×#106—618no—
444C2×#106C2×D6111yescharacteristic, complemented
445C2×C4⋊C8—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—618no—
449C2×C4⋊C8C2×D6111yescharacteristic, complemented
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—618no—
457C2×#102—618no—
458C2×#102C2×D6111yescharacteristic
459C2×#102C2×D6111yescharacteristic
460C61C22×#47811yescharacteristic, complemented, Sylow
461C25—1221no—
462C22×D4—618no—
463C22×D4—614no—
464C22×D4—611no—
465C22×D4—1222no—
466C22×D4—1224no—
467C22×D4—1221no—
468C22×D4C22×D6111yescharacteristic
469C23×C4—21no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—1221no—
474C23×C4—1228no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—2448no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—614no—
484C22×C8—614no—
485C22×C8—1224no—
486C22×C8—1224no—
487C22×C8C22×D6111yescharacteristic
488C22×C8C22×D6111yescharacteristic
489#125—22no—
490#125—614no—
491#125—614no—
492#125—614no—
493#125—1228no—
494#125—1228no—
495#125—1222no—
496#125—1222no—
497#125—1222no—
498#125C22×D6114yescomplemented
499C4×D4—22no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—614no—
503C4×D4—1228no—
504C4×D4—1222no—
505C4×D4—1228no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4C22×D6114yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1228no—
521C2×C4⋊C4—1228no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—1228no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—614no—
543C2×C42—614no—
544C2×C42C22×D6111yescharacteristic
545#107—614no—
546#107—614no—
547#107—614no—
548#107C22×D6114yescomplemented
549#106—614no—
550#106—614no—
551#106—614no—
552#106C22×D6114yescomplemented
553C4⋊C8—614no—
554C4⋊C8—614no—
555C4⋊C8—614no—
556C4⋊C8C22×D6114yescomplemented
557#102—614no—
558#102—614no—
559#102—614no—
560#102—614no—
561#102—614no—
562#102—614no—
563#102C22×D6114yes—
564#102C22×D6114yes—
565C24—21no—
566C24—611no—
567C24—1224no—
568C24—1228no—
569C24—1221no—
570C24—2444no—
571C24—2444no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—6116no—
575C2×D4—614no—
576C2×D4—612no—
577C2×D4—12216no—
578C2×D4—1228no—
579C2×D4—1224no—
580C2×D4—1228no—
581C2×D4—1221no—
582C2×D4—1222no—
583C2×D4Q8×D6114yes—
584C2×D4C23×D6112yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—44no—
590C22×C4—611no—
591C22×C4—612no—
592C22×C4—614no—
593C22×C4—614no—
594C22×C4—612no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—1224no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1224no—
610C22×C4—2444no—
611C22×C4—24432no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—612no—
623C2×C8—612no—
624C2×C8—1228no—
625C2×C8—1228no—
626C2×C8—1222no—
627C2×C8—1222no—
628C2×C8C23×D6112yes—
629C2×C8C23×D6112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—612no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4C23×D6112yes—
651C4⋊C4C23×D6112yes—
652C4⋊C4C23×D6112yes—
653C22⋊C4—24no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C42—614no—
658C42—614no—
659C42—612no—
660C42—612no—
661C42D4×D6112yes—
662C42C23×D6112yes—
663C23—24no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—614no—
668C23—614no—
669C23—614no—
670C23—612no—
671C23—12216no—
672C23—1224no—
673C23—1222no—
674C23—2448no—
675C23—2448no—
676C23—24432no—
677C23—2442no—
678C23—2442no—
679C23C2×D4×D6111yescharacteristic
680D4—24no—
681D4—22no—
682D4—614no—
683D4—12216no—
684D4—1224no—
685D4—1222no—
686D4C2×Q8×D6114yes—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—48no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—614no—
697C2×C4—612no—
698C2×C4—618no—
699C2×C4—614no—
700C2×C4—614no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—1228no—
704C2×C4—1228no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—2448no—
711C2×C4—2448no—
712C2×C4—2448no—
713C2×C4—2448no—
714C2×C4—2448no—
715C2×C4—2448no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4C2×D4×D6112yes—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4C2×Q8×D6112yes—
723C2×C4#41×D6112yes—
724C2×C4C24×D6111yescharacteristic
725C8—22no—
726C8—22no—
727C8—1222no—
728C8—1222no—
729C22—24no—
730C22—42no—
731C22—42no—
732C22—48no—
733C22—614no—
734C22—614no—
735C22—614no—
736C22—6116no—
737C22—1224no—
738C22—24432no—
739C22—2442no—
740C22—2442no—
741C22—2448no—
742C22C22⋊Q8×D6112yes—
743C22#135×D6112yes—
744C22AGL(1,ℤ/8)×D6112yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—614no—
752C4—1222no—
753C4—1222no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4C22⋊Q8×D6112yes—
758C4C22×Q8×D6111yescharacteristic
759C4C2×#41×D6111yescharacteristic
760C2—44no—
761C2—618no—
762C2—2444no—
763C2#478×D6114yesdirect product factor
764C2C2×C22⋊Q8×D6111yescharacteristic
765C2C2×#135×D6111yescharacteristic
766C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×#478D61
hypocenterC61C22×#478
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#125×D61C2semidirect
3. C2×#16840065C2semidirect
4. C2×#16840064C2semidirect
5. C2×#16840063C2semidirect
6. C2×#16840062C2semidirect
7. C2×#16840061C2semidirect
8. C2×#16840060C2semidirect
9. C2×#16840059C2semidirect
10. #478×D61C2direct (N × H)
11. C2×#107×D61C2semidirect
12. C2×#106×D61C2semidirect
13. C2×C4⋊C8×D61C2semidirect
16. C2×C61×#478C2semidirect
21. C2×#14519769C22semidirect
22. C2×#14519768C22semidirect
23. C2×#14519768C22semidirect
27. #125×D61C22semidirect
42. #16840065C22semidirect
43. #16840064C22semidirect
44. #16840063C22semidirect
45. #16840062C22semidirect
46. #16840061C22semidirect
47. #16840060C22semidirect
48. #16840059C22semidirect
49. C2×#14519711C22semidirect
50. C2×#14519710C22semidirect
51. C2×#14519710C22semidirect
52. #107×D61C22semidirect
53. C2×#14519709C22semidirect
54. C2×#14519708C22semidirect
55. C2×#14519708C22semidirect
56. #106×D61C22semidirect
57. C2×C4⋊#92418C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C4⋊C8×D61C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#478C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×C4⋊C8×C61C22semidirect
102. #14519769C23semidirect
105. #14519768C23semidirect
106. #14519768C23semidirect
146. #14519711C23semidirect
147. #14519710C23semidirect
148. #14519710C23semidirect
149. #14519709C23semidirect
150. #14519708C23semidirect
151. #14519708C23semidirect
152. C4⋊#92418C23semidirect
153. #14519706C23semidirect
154. #14519706C23semidirect
166. #125×C61C23semidirect
176. #107×C61C23semidirect
177. #106×C61C23semidirect
178. C4⋊C8×C61C23semidirect
359. C2×D61#478direct (N × H)
387. C2×#478D61direct (N × H)
394. C2×C61C2×#478semidirect
399. D61C2×#478direct (N × H)
411. C2×#125C2×D61semidirect
434. #478C2×D61direct (N × H)
439. C2×#107C2×D61semidirect
444. C2×#106C2×D61semidirect
449. C2×C4⋊C8C2×D61semidirect
460. C61C22×#478semidirect
498. #125C22×D61semidirect
548. #107C22×D61semidirect
552. #106C22×D61semidirect
556. C4⋊C8C22×D61semidirect
763. C2#478×D61direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D612
C2×C4×D4×D612
C2×#168400652
C2×#168400642
C2×#168400632
C2×#168400622
C2×#168400612
C2×#168400602
C2×#168400592
#478×D612
C2×#107×D612
C2×#106×D612
C2×C4⋊C8×D612
C2×#102×D612
C2×C61×#4782
C22×#47861