Finite Group Databasebeta

← C2×#21455614 #30547522

Subgroups — C2×#21455614 #30547522

Order 15616.

2530 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×#16840318C211yesmaximal, characteristic, complemented
2C2×C4×D4×D61C211yesmaximal, characteristic
3#21455614C2116yesmaximal, direct product factor
4C2×#16840063C211yesmaximal, characteristic, complemented
5C2×#16840062C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840051C211yesmaximal, characteristic, complemented
8C2×#16840050C211yesmaximal, characteristic, complemented
9C2×#16840041C211yesmaximal, characteristic, complemented
10C2×#16840040C211yesmaximal, characteristic, complemented
11C2×#16839803C211yesmaximal, characteristic, complemented
12C2×#16839801C211yesmaximal, characteristic, complemented
13C2×#16839784C211yesmaximal, characteristic, complemented
14C2×#16839765C211yesmaximal, characteristic
15C2×#16839765C211yesmaximal, characteristic
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C23×C4×D61—21no—
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21#16840318—24no—
22#16840318C2218yescomplemented
23C2×#14519776C2211yescharacteristic, complemented
24C2×#14519776C2211yescharacteristic, complemented
25C2×#14519769C2211yescharacteristic, complemented
26C2×#14519755—21no—
27C2×#14519755—21no—
28C2×#14519742—21no—
29C2×#14519742—21no—
30C2×C4×D244C2211yescharacteristic
31C2×D4×Dic61C2211yescharacteristic
32C2×#14519739C2211yescharacteristic
33C2×C4×C22⋊D61—21no—
34C2×#14519737—21no—
35C4×D4×D61—24no—
36C4×D4×D61C2218yes—
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42#16840063C2218yescomplemented
43#16840062C2218yescomplemented
44#16840059C2218yescomplemented
45#16840051C2218yescomplemented
46#16840050C2218yescomplemented
47#16840041C2218yescomplemented
48#16840040C2218yescomplemented
49#16839803C2218yescomplemented
50#16839801C2218yescomplemented
51C2×#14519711C2211yescharacteristic, complemented
52C2×#14519710C2211yescharacteristic, complemented
53C2×#14519710C2211yescharacteristic, complemented
54C2×#14519709C2211yescharacteristic, complemented
55C2×#14519708C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57#16839784C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519706C2211yescharacteristic, complemented
61#16839765C2218yes—
62#16839765C2218yes—
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
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×Dic122—21no—
79C22×Dic122—21no—
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C2×D4×D61—22no—
83C2×D4×D61—24no—
84C2×D4×D61Q818yescomplemented
85C2×D4×D61C2314yes—
86C23×Dic61—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
95C2×#11758189—24no—
96C2×#11758189—24no—
97C2×#11758189C2314yes—
98C2×#11758189C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519776—22no—
102#14519776—22no—
103#14519776C2314yescomplemented
104#14519776C2314yescomplemented
105#14519769—22no—
106#14519769C2314yescomplemented
107#14519755—28no—
108#14519755—28no—
109#14519742—28no—
110#14519742—28no—
111C4×D244—22no—
112C4×D244C2314yes—
113D4×Dic61—22no—
114D4×Dic61C2314yes—
115#14519739—22no—
116#14519739C2314yes—
117C4×C22⋊D61—28no—
118#14519737—28no—
119#14519735—22no—
120#14519735—22no—
121#14519735C2314yes—
122#14519735C2314yes—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C22⋊C4×D61—28no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
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×Q8116yescomplemented
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—432no—
222C2×C4×D61—42no—
223C2×C4×D61—44no—
224C2×C4×D61—44no—
225C2×C4×D61—44no—
226C2×C4×D61C2×D414yes—
227C2×C4×D61C2×D414yes—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2×Q814yes—
230C2×C4×D61#4114yes—
231C2×C4×D61C2412yes—
232C2×Dic122—24no—
233C2×Dic122—24no—
234C2×Dic122—44no—
235C2×Dic122—44no—
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—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2×D414yes—
271C4×Dic61C2×D414yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277#11758189—28no—
278#11758189—28no—
279C23×C61—24no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—22no—
288C22×D61—216no—
289C22×D61—48no—
290C22×D61—432no—
291C22×D61—48no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61C22⋊Q814yes—
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—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—48no—
323C2×Dic61C22⋊Q814yes—
324C2×Dic61AGL(1,ℤ/8)14yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328D244—24no—
329D244—22no—
330D244C22×Q814yes—
331C4×D61—28no—
332C4×D61—44no—
333C4×D61—48no—
334C4×D61—48no—
335C4×D61—48no—
336C4×D61C22⋊Q818yes—
337C4×D61C22×Q814yes—
338C4×D61C2×#4114yes—
339Dic122—48no—
340Dic122—48no—
341C8×C61—22no—
342C8×C61—22no—
343#92418—22no—
344#92418—22no—
345C2×#3077—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—48no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61C2×C22⋊Q812yes—
351C22×C61C2×AGL(1,ℤ/8)12yes—
352C22×C61#57512yes—
353C22×C61C23×D411yescharacteristic
354C2×D61—28no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—24no—
358C2×D61—432no—
359C2×D61—48no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61C2×C22⋊Q814yes—
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—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61C2×C22⋊Q814yes—
376Dic61C2×AGL(1,ℤ/8)14yes—
377C2×#533—611no—
378C22×C4×D4—611no—
379#3077—6116no—
380C2×#478—611no—
381C2×#478—611no—
382C2×#478—611no—
383C2×#478D6111yescharacteristic, complemented
384C2×#476—611no—
385C2×#476—611no—
386C2×#474—611no—
387C2×#474—611no—
388C2×#428—611no—
389C2×#428—611no—
390C2×#423—611no—
391C2×#418—611no—
392C2×#418—611no—
393C2×C61—44no—
394C2×C61#307714yescomplemented
395C2×C61C22×C22⋊Q811yescharacteristic
396C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C61C2×#57511yescharacteristic
398D61—24no—
399D61—44no—
400C23×D4—611no—
401C24×C4—1221no—
402C22×M16—611no—
403C22×M16—611no—
404#533—618no—
405#533—1224no—
406C2×C4⋊Q8—611no—
407C2×C4⋊Q8—611no—
408C2×#125—611no—
409C2×#125C2×D6111yescharacteristic, complemented
410C2×C22⋊Q8—1221no—
411C2×C22⋊Q8—1221no—
412C2×C4×Q8—1221no—
413C2×C4×Q8—1221no—
414C2×C4×D4—611no—
415C2×C4×D4—618no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×C4×D4—1221no—
419C2×C4×D4—1224no—
420C2×C4×D4—1221no—
421C2×C4×D4C2×D6111yescharacteristic
422C2×#117—611no—
423C2×#117—611no—
424C22×C4⋊C4—611no—
425C22×C22⋊C4—1221no—
426C22×C42—611no—
427#478—618no—
428#478—618no—
429#478—618no—
430#478C2×D6118yescomplemented
431#476—618no—
432#476—618no—
433#474—618no—
434#474—618no—
435#428—618no—
436#428—618no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#107C2×D6111yescharacteristic, complemented
441C2×#106—611no—
442C2×#106—611no—
443C2×#106—611no—
444C2×#106C2×D6111yescharacteristic, complemented
445#423—618no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8C2×D6111yescharacteristic, complemented
450#418—618no—
451#418—618no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102C2×D6111yescharacteristic
459C2×#102C2×D6111yescharacteristic
460C61C2×#307711yescharacteristic, complemented, Sylow
461C25—1221no—
462C22×Q8—1221no—
463C22×Q8—1221no—
464C22×D4—618no—
465C22×D4—614no—
466C22×D4—611no—
467C22×D4—1222no—
468C22×D4—1224no—
469C22×D4—1221no—
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—1221no—
476C23×C4—1228no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—2448no—
481C2×M16—614no—
482C2×M16—614no—
483C2×M16—1224no—
484C2×M16—1224no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8C22×D6111yescharacteristic
488C22×C8C22×D6111yescharacteristic
489C4⋊Q8—614no—
490C4⋊Q8—614no—
491C4⋊Q8—1222no—
492C4⋊Q8—1222no—
493#125—22no—
494#125—614no—
495#125—1222no—
496#125C22×D6114yescomplemented
497C22⋊Q8—1228no—
498C22⋊Q8—1228no—
499C4×Q8—1228no—
500C4×Q8—1228no—
501C4×D4—22no—
502C4×D4—614no—
503C4×D4—614no—
504C4×D4—614no—
505C4×D4—1228no—
506C4×D4—1222no—
507C4×D4—1228no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4C22×D6114yes—
511#117—614no—
512#117—614no—
513#117—1222no—
514#117—1222no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C4⋊C4C22×D6111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1228no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—614no—
541C2×C42—614no—
542C2×C42—1221no—
543C2×C42—1221no—
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×Q8—1224no—
573C2×Q8—1224no—
574C2×Q8—2444no—
575C2×Q8—2444no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—6116no—
579C2×D4—614no—
580C2×D4—612no—
581C2×D4—12216no—
582C2×D4—1228no—
583C2×D4—1224no—
584C2×D4—1228no—
585C2×D4—1221no—
586C2×D4—1222no—
587C2×D4Q8×D6114yes—
588C2×D4C23×D6112yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—44no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—612no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—612no—
600C22×C4—611no—
601C22×C4—614no—
602C22×C4—614no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1224no—
611C22×C4—2442no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—24432no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620M16—1228no—
621M16—1228no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—612no—
625C2×C8—612no—
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—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4C23×D6112yes—
647C4⋊C4C23×D6112yes—
648C4⋊C4C23×D6112yes—
649C22⋊C4—24no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C42—614no—
656C42—614no—
657C42—612no—
658C42—612no—
659C42—1224no—
660C42—1224no—
661C42D4×D6112yes—
662C42C23×D6112yes—
663C23—24no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—614no—
668C23—612no—
669C23—12216no—
670C23—1222no—
671C23—1222no—
672C23—1224no—
673C23—1222no—
674C23—2448no—
675C23—2448no—
676C23—24432no—
677C23—2442no—
678C23—2442no—
679C23C2×D4×D6111yescharacteristic
680Q8—2448no—
681Q8—2448no—
682D4—24no—
683D4—22no—
684D4—614no—
685D4—12216no—
686D4—1224no—
687D4—1222no—
688D4C2×Q8×D6114yes—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—614no—
699C2×C4—614no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—618no—
703C2×C4—614no—
704C2×C4—614no—
705C2×C4—612no—
706C2×C4—1228no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—2444no—
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—1222no—
735C22—1222no—
736C22—1228no—
737C22—1224no—
738C22—24432no—
739C22—2442no—
740C22—2442no—
741C22—2448no—
742C22C22⋊Q8×D6112yes—
743C22AGL(1,ℤ/8)×D6112yes—
744C22#1684055912yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—614no—
752C4—614no—
753C4—1222no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4C22⋊Q8×D6112yes—
758C4C22×Q8×D6111yescharacteristic
759C4C2×#41×D6111yescharacteristic
760C2—44no—
761C2—1224no—
762C2—2444no—
763C2#2145561414yesdirect product factor
764C2C2×C22⋊Q8×D6111yescharacteristic
765C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
766C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×#478D61
hypocenterC61C2×#3077
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×#16840318C2semidirect
3. #21455614C2direct (N × H)
4. C2×#16840063C2semidirect
5. C2×#16840062C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840051C2semidirect
8. C2×#16840050C2semidirect
9. C2×#16840041C2semidirect
10. C2×#16840040C2semidirect
11. C2×#16839803C2semidirect
12. C2×#16839801C2semidirect
13. C2×#16839784C2semidirect
16. C2×C61×#478C2semidirect
22. #16840318C22semidirect
23. C2×#14519776C22semidirect
24. C2×#14519776C22semidirect
25. C2×#14519769C22semidirect
42. #16840063C22semidirect
43. #16840062C22semidirect
44. #16840059C22semidirect
45. #16840051C22semidirect
46. #16840050C22semidirect
47. #16840041C22semidirect
48. #16840040C22semidirect
49. #16839803C22semidirect
50. #16839801C22semidirect
51. C2×#14519711C22semidirect
52. C2×#14519710C22semidirect
53. C2×#14519710C22semidirect
54. C2×#14519709C22semidirect
55. C2×#14519708C22semidirect
56. C2×#14519708C22semidirect
57. #16839784C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519706C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#478C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×C4⋊C8×C61C22semidirect
84. C2×D4×D61Q8semidirect
103. #14519776C23semidirect
104. #14519776C23semidirect
106. #14519769C23semidirect
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
212. D4×D61C2×Q8semidirect
383. C2×#478D61semidirect
394. C2×C61#3077semidirect
409. C2×#125C2×D61semidirect
430. #478C2×D61semidirect
440. C2×#107C2×D61semidirect
444. C2×#106C2×D61semidirect
449. C2×C4⋊C8C2×D61semidirect
460. C61C2×#3077semidirect
496. #125C22×D61semidirect
548. #107C22×D61semidirect
552. #106C22×D61semidirect
556. C4⋊C8C22×D61semidirect
763. C2#21455614direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403182
C2×C4×D4×D612
#214556142
C2×#168400632
C2×#168400622
C2×#168400592
C2×#168400512
C2×#168400502
C2×#168400412
C2×#168400402
C2×#168398032
C2×#168398012
C2×#168397842
C2×#168397652
C2×C61×#4782
C2×#307761