Finite Group Databasebeta

← #29680970

Subgroups — #29680970

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×#16839801C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic
4C2×#16839765C211yesmaximal, characteristic
5#21448300C211yesmaximal, characteristic, complemented
6#21446079C211yesmaximal, characteristic, complemented
7#21446078C211yesmaximal, characteristic, complemented
8#21446077C211yesmaximal, characteristic, complemented
9#21446069C211yesmaximal, characteristic, complemented
10#21446068C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446066C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445511C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61—21no—
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×C4×C22⋊D61—21no—
24C2×#14519737—21no—
25C4×D4×D61—24no—
26C4×D4×D61—24no—
27C2×#14519735C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839801—24no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519708C2211yescharacteristic, complemented
36#16839765—24no—
37#16839765C418yescomplemented
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44#16839661C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839658C2211yescharacteristic, complemented
47#16839636—21no—
48#16839633—21no—
49C4⋊C4×Dic61—21no—
50#16839613—21no—
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839517C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C2×D4×D61D414yes—
72C2×D4×D61Q814yes—
73C23×Dic61—21no—
74C22×C4×D61—28no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61—44no—
79C22×C4×D61—44no—
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C2×#11758189—22no—
84C2×#11758189—22no—
85C2×#11758189—22no—
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189C2×C414yescomplemented
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C4×D244—22no—
92C4×D244—22no—
93D4×Dic61—22no—
94D4×Dic61—22no—
95#14519739—22no—
96#14519739—22no—
97C4×C22⋊D61—28no—
98#14519737—28no—
99#14519735—22no—
100#14519735—22no—
101#14519735—22no—
102#14519735C2×C414yescomplemented
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61D414yes—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C22⋊C4×D61—28no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61D411yescharacteristic
121C2×C4×Dic61D411yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C42×D61—22no—
124C42×D61—22no—
125#14519711—22no—
126#14519710—22no—
127#14519708—22no—
128#14519699—22no—
129#14519699C2×C414yescomplemented
130#14519698—22no—
131#14519698C2×C414yescomplemented
132#14519697—22no—
133#14519697C2×C414yescomplemented
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61—21no—
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×D4×C61—22no—
142C4×D4×C61—22no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#106×C61—22no—
150#102×C61—22no—
151#102×C61C2×C414yescomplemented
152#95×C61—21no—
153C24×C61—21no—
154C23×D61—21no—
155C23×D61—24no—
156C23×D61—24no—
157C23×D61—24no—
158C23×D61—42no—
159C23×D61—42no—
160C23×D61—42no—
161C23×D61—42no—
162C23×D61C2×D411yescharacteristic
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61C22×C412yes—
167C2×D4×C61C2×D412yes—
168C2×D4×C61C2×Q812yes—
169C22×C4×C61—24no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178C2×C22⋊D61—24no—
179C2×C22⋊D61—24no—
180C2×C22⋊D61—24no—
181C22×Dic61—24no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190D4×D61—28no—
191D4×D61—28no—
192D4×D61—28no—
193D4×D61C4⋊C4116yescomplemented
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244C22×C412yes—
198C2×D244C2×D412yes—
199C2×D244C2×Q812yes—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—24no—
204C2×C4×D61—24no—
205C2×C4×D61—24no—
206C2×C4×D61—22no—
207C2×C4×D61—432no—
208C2×C4×D61—41no—
209C2×C4×D61—41no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61C22×C412yes—
217C2×C4×D61C2×D412yes—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2×Q812yes—
220C2×C4×D61#4112yes—
221C2×C4×D61#4112yes—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61C22×C412yescomplemented
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—42no—
233C4⋊C4×C61C22×C412yescomplemented
234C4⋊C4×C61C2×D412yes—
235C22⋊C4×C61—24no—
236C42×C61—21no—
237C42×C61—21no—
238C22⋊Dic61—24no—
239#11758198—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198—42no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—42no—
248C4⋊Dic61C22×C412yescomplemented
249C4⋊Dic61C2×D412yes—
250#11758196—24no—
251#11758196—42no—
252#11758196—42no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—24no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258C4×Dic61—42no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418C22×C412yescomplemented
265#11758189—28no—
266#11758189—44no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61C22×D411yescharacteristic
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—216no—
283C22×D61—48no—
284C22×D61—48no—
285C22×D61—48no—
286C22×D61—48no—
287C22×D61—48no—
288C22×D61—48no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61C4×D412yes—
294C22×D61#12012yes—
295C22×D61C22⋊Q812yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61C2×C4⋊C414yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—48no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61AGL(1,ℤ/8)12yes—
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×Q811yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C22⋊D61—216no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—48no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61C4×D412yes—
339C2×Dic61#12012yes—
340C2×Dic61C22⋊Q812yes—
341C2×Dic61AGL(1,ℤ/8)12yes—
342D244—22no—
343D244—22no—
344D244—22no—
345D244C2×C4⋊C414yes—
346C4×D61—28no—
347C4×D61—48no—
348C4×D61—48no—
349C4×D61—44no—
350C4×D61—48no—
351C4×D61C2×C4⋊C414yes—
352C4×D61C4×D414yes—
353C4×D61C22⋊Q814yes—
354C4×D61#12314yes—
355C8×C61—22no—
356C8×C61—41no—
357#92418—22no—
358#92418—41no—
359#20873—611nomaximal, Sylow
360C22×C61—24no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61C2×#12011yescharacteristic
369C22×C61C2×C22⋊Q811yescharacteristic
370C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C61#57511yescharacteristic
373C22×C61#57511yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—24no—
381C2×D61—432no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61#38514yes—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61—41no—
393C4×C61—81no—
394C4×C61C22×C4⋊C411yescharacteristic
395C4×C61C2×C4×D411yescharacteristic
396C4×C61C2×C22⋊Q811yescharacteristic
397C4×C61C2×#12311yescharacteristic
398Dic61—22no—
399Dic61—42no—
400Dic61—42no—
401Dic61—41no—
402Dic61—81no—
403Dic61#38514yes—
404C22×C4×D4—611no—
405C2×#428—611no—
406C2×#418—611no—
407C2×#418—611no—
408#2296—611no—
409#1864—611no—
410#1864—611no—
411#1864—611no—
412#1864D6111yescharacteristic, complemented
413#1862—611no—
414#1862—611no—
415#1862—611no—
416#1862—611no—
417#1736—611no—
418#1728—611no—
419C2×C61—44no—
420C2×C61C2×#38511yescharacteristic
421C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C61#300311yescharacteristic
424C2×C61#300511yescharacteristic
425C2×C61#307711yescharacteristic
426C2×C61#307711yescharacteristic
427D61—24no—
428D61—44no—
429C23×D4—611no—
430C24×C4—1221no—
431C22×M16—611no—
432C22×M16—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×C4×D4—1224no—
439C2×C4×D4—1224no—
440C2×C4×D4C2×D6111yescharacteristic
441C2×#117—611no—
442C2×#117—611no—
443C22×C4⋊C4—611no—
444C22×C22⋊C4—1221no—
445C22×C42—611no—
446#428—1224no—
447C2×#107—611no—
448C2×#107—611no—
449C2×#106—611no—
450C2×#106C2×D6111yescharacteristic, complemented
451#418—618no—
452#418—1224no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102C2×D6111yescharacteristic
460C2×#102C2×D6111yescharacteristic
461#389—611no—
462#389—611no—
463#389—611no—
464#389C2×D6111yescharacteristic, complemented
465#385—1221no—
466#385—1221no—
467C4×C4⋊C4—1221no—
468C4×C4⋊C4—1221no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340C2×D6111yescharacteristic, complemented
473#336—611no—
474#336—611no—
475#336—611no—
476#336C2×D6111yescharacteristic, complemented
477C61#2087311yescharacteristic, complemented, Sylow
478C25—1221no—
479C22×D4—614no—
480C22×D4—614no—
481C22×D4—614no—
482C22×D4—611no—
483C22×D4—1222no—
484C22×D4—1222no—
485C22×D4—1222no—
486C22×D4—1221no—
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4—1228no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4—2444no—
498C23×C4—2444no—
499C2×M16—614no—
500C2×M16—1222no—
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—1222no—
505C22×C8—611no—
506C22×C8—611no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1228no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1228no—
517C4×D4—1222no—
518C4×D4—1222no—
519#117—614no—
520#117—1222no—
521#117—1222no—
522#117—1222no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—1222no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—1228no—
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—611no—
546C2×C42—1222no—
547C2×C42—1222no—
548C2×C42—1221no—
549C2×C42—1221no—
550C2×C42C22×D6111yescharacteristic
551#107—1222no—
552#107—1222no—
553#106—22no—
554#106—1222no—
555#102—22no—
556#102—614no—
557#102—614no—
558#102—614no—
559#102—1222no—
560#102—1222no—
561#102—1222no—
562#102C4×D6114yescomplemented
563#95—21no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567C24—21no—
568C24—611no—
569C24—1224no—
570C24—1224no—
571C24—1224no—
572C24—1221no—
573C24—2442no—
574C24—2442no—
575C24—2442no—
576C24—2442no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—6116no—
581C2×D4—612no—
582C2×D4—612no—
583C2×D4—612no—
584C2×D4—1228no—
585C2×D4—1228no—
586C2×D4—1228no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4C2×C4×D6112yes—
594C2×D4D4×D6112yes—
595C2×D4Q8×D6112yes—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—611no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1224no—
617C22×C4—1222no—
618C22×C4—1224no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—2441no—
623C22×C4—2441no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—24432no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636M16—1228no—
637M16—2444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—612no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8C2×C4×D6112yescomplemented
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—2442no—
663C4⋊C4—2442no—
664C4⋊C4—2442no—
665C4⋊C4C2×C4×D6112yescomplemented
666C4⋊C4D4×D6112yes—
667C22⋊C4—24no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—2442no—
673C42—21no—
674C42—21no—
675C42—1222no—
676C42—1222no—
677C42—1224no—
678C42—1221no—
679C42—1221no—
680C42—2442no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—612no—
689C23—612no—
690C23—612no—
691C23—12216no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—2448no—
700C23—2448no—
701C23—2448no—
702C23—2448no—
703C23—2448no—
704C23—2448no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23C2×D4×D6111yescharacteristic
710D4—22no—
711D4—22no—
712D4—22no—
713D4—614no—
714D4—12216no—
715D4—1222no—
716D4—1222no—
717D4—1222no—
718D4C4⋊C4×D6114yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—48no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—612no—
735C2×C4—612no—
736C2×C4—612no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—612no—
742C2×C4—1228no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1222no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—2448no—
751C2×C4—2448no—
752C2×C4—2444no—
753C2×C4—2448no—
754C2×C4—2448no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4#1451980412yes—
763C2×C4C22×C4×D6111yescharacteristic
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4C2×Q8×D6111yescharacteristic
767C2×C4#41×D6111yescharacteristic
768C2×C4#41×D6111yescharacteristic
769C8—22no—
770C8—41no—
771C8—1222no—
772C8—2441no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—614no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—1224no—
788C22—24432no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C4×D4×D6111yescharacteristic
796C22#120×D6111yescharacteristic
797C22C22⋊Q8×D6111yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22C2×#1451980411yescharacteristic
800C22#1684055811yescharacteristic
801C22#1684055911yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—41no—
806C4—81no—
807C4—614no—
808C4—1222no—
809C4—4881no—
810C4—2442no—
811C4—2442no—
812C4—2441no—
813C4C2×C4⋊C4×D6111yescharacteristic
814C4C4×D4×D6111yescharacteristic
815C4C22⋊Q8×D6111yescharacteristic
816C4#123×D6111yescharacteristic
817C2—44no—
818C2—1224no—
819C2—2444no—
820C2#385×D6111yescharacteristic
821C2C4×#1451980411yescharacteristic
822C2#2145463011yescharacteristic
823C2#2145504711yescharacteristic
824C2#2145505711yescharacteristic
825C2#2145561411yescharacteristic
826C2#2145561711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1864C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1864D61
hypocenterC61#20873
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#16839801C2semidirect
5. #21448300C2semidirect
6. #21446079C2semidirect
7. #21446078C2semidirect
8. #21446077C2semidirect
9. #21446069C2semidirect
10. #21446068C2semidirect
11. #21446067C2semidirect
12. #21446066C2semidirect
13. #21445537C2semidirect
14. #21445511C2semidirect
15. C61×#1864C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519708C22semidirect
37. #16839765C4semidirect
44. #16839661C22semidirect
45. #16839660C22semidirect
46. #16839658C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839517C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
58. C2×#106×C61C22semidirect
61. C61×#389C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
88. C2×#11758189C2×C4semidirect
102. #14519735C2×C4semidirect
129. #14519699C2×C4semidirect
131. #14519698C2×C4semidirect
133. #14519697C2×C4semidirect
151. #102×C61C2×C4semidirect
193. D4×D61C4⋊C4semidirect
227. C2×C8×C61C22×C4semidirect
233. C4⋊C4×C61C22×C4semidirect
248. C4⋊Dic61C22×C4semidirect
264. C2×#92418C22×C4semidirect
412. #1864D61semidirect
450. C2×#106C2×D61semidirect
464. #389C2×D61semidirect
472. #340C2×D61semidirect
476. #336C2×D61semidirect
477. C61#20873semidirect
562. #102C4×D61semidirect
649. C2×C8C2×C4×D61semidirect
665. C4⋊C4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×#168398012
C2×#168397652
#214483002
#214460792
#214460782
#214460772
#214460692
#214460682
#214460672
#214460662
#214455372
#214455112
C61×#18642
#2087361