Finite Group Databasebeta

← #29647433

Subgroups — #29647433

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3#21448200C211yesmaximal, characteristic, complemented
4#21444372C214yesmaximal, complemented
5#21444359C214yesmaximal, complemented
6#21444340C211yesmaximal, characteristic, complemented
7#21444338C211yesmaximal, characteristic, complemented
8#21444335C211yesmaximal, characteristic, complemented
9C61×#1507C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13#16840272—21no—
14#16840272—21no—
15#16840272—21no—
16#16840272—21no—
17#16840272C412yescomplemented
18#16840272C412yescomplemented
19#16840272C2212yes—
20#16840272C2212yes—
21C2×#14519759—21no—
22C2×#14519757C411yescharacteristic, complemented
23C2×#14519756C2211yescharacteristic
24C2×#14519748C411yescharacteristic, complemented
25C2×#14519745—21no—
26C2×D4×Dic61—21no—
27C2×#14519737—21no—
28C2×#14519735C411yescharacteristic, complemented
29C2×#14519734—21no—
30#16839726C2211yescharacteristic
31#16839725—21no—
32#16839724—21no—
33#16839724C2212yescomplemented
34C22⋊C8×D61—21no—
35C22⋊C8×D61C2212yescomplemented
36#16839624C2212yescomplemented
37#16839621C2212yescomplemented
38#16839620—21no—
39#16839617—21no—
40C4×#11758198—21no—
41C4×C22⋊Dic61C2211yescharacteristic
42#16839500C2214yescomplemented
43#16839498C2214yescomplemented
44#16839496C2214yescomplemented
45C2×#121×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#327C2214yescomplemented
49C24×D61D411yescharacteristic
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224—44no—
53C2×#11758224C2×C412yes—
54C2×#11758224C2×C412yes—
55C22×Dic122C2×C411yescharacteristic
56C22×C22⋊D61—21no—
57C22×C22⋊D61—21no—
58C23×Dic61—21no—
59C23×Dic61D411yescharacteristic
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758194—21no—
74C2×#11758189—22no—
75M16×D61—44no—
76C2×C8×D61—22no—
77#14519759—22no—
78#14519759—22no—
79#14519759—22no—
80#14519759—22no—
81#14519757—21no—
82#14519757—21no—
83#14519757C2×C412yes—
84#14519757C2×C412yes—
85#14519756—21no—
86#14519756—21no—
87#14519756C2×C412yes—
88#14519756C2312yes—
89#14519748—21no—
90#14519748—21no—
91#14519748C2×C412yes—
92#14519748C2×C412yes—
93#14519745—22no—
94#14519745—22no—
95#14519745—22no—
96#14519745—22no—
97D4×Dic61—22no—
98D4×Dic61—22no—
99D4×Dic61—22no—
100D4×Dic61—22no—
101#14519737—22no—
102#14519737—22no—
103#14519737—22no—
104#14519737—22no—
105#14519735—21no—
106#14519735—21no—
107#14519735C2×C412yes—
108#14519735C2×C412yes—
109#14519734—44no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61C2×C411yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—22no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C22⋊#92418—21no—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519684—22no—
128#14519684C2312yes—
129C22×D4×C61—21no—
130C22×D4×C61C2×C411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135#121×C61C2×C412yes—
136#121×C61C2312yes—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
143#95×C61C2312yes—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—44no—
160C2×D4×C61C22×C412yes—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—42no—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—44no—
175C2×C22⋊D61—44no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—42no—
182C22×Dic61—44no—
183C22×Dic61C22⋊C411yescharacteristic
184C22×Dic61C22⋊C411yescharacteristic
185C22×Dic61C22⋊C411yescharacteristic
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189#11758224—44no—
190#11758224—44no—
191#11758224—44no—
192#11758224—44no—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22×C411yescharacteristic
214C2×C4×D61C22×C411yescharacteristic
215C2×C4×D61C22×C411yescharacteristic
216C2×C4×D61C22×C411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122—42no—
223C2×Dic122C22×C412yes—
224M16×C61—42no—
225C2×C8×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61C22×C412yes—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—42no—
231C42×C61—42no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—42no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—44no—
242#11758198—44no—
243C4⋊Dic61—21no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246C4⋊Dic61C22×C412yes—
247#11758196—22no—
248#11758196—22no—
249#11758196—44no—
250C4×Dic61—22no—
251C4×Dic61—22no—
252C4×Dic61—42no—
253#11758194—42no—
254C2×#92418—22no—
255#11758189—44no—
256C8×D61—44no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—41no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C22×D411yescharacteristic
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—416no—
286C22×D61C2×C22⋊C411yescharacteristic
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61C2×C22⋊C411yescharacteristic
289C22×D61C2×C22⋊C411yescharacteristic
290D4×C61—42no—
291D4×C61—44no—
292D4×C61—44no—
293D4×C61—42no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C23×C411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C22⋊D61—44no—
310C22⋊D61—44no—
311C22⋊D61—44no—
312C22⋊D61—44no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—44no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—44no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61#9914yes—
348Dic122—42no—
349Dic122—42no—
350C8×C61—42no—
351#92418—42no—
352#17582—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—44no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—84no—
365C22×C61#42112yes—
366C22×C61C22×C22⋊C411yescharacteristic
367C22×C61#57512yes—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61C2×#9912yes—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—42no—
390C4×C61—82no—
391C4×C61C2×#9912yes—
392Dic61—21no—
393Dic61—21no—
394Dic61—21no—
395Dic61—42no—
396Dic61—42no—
397Dic61—82no—
398Dic61C2×#9912yes—
399C2×#525—611no—
400C2×#407—611no—
401#2280—611no—
402#1516—614no—
403#1513—614no—
404#1508—611no—
405#1508—611no—
406#1507—611no—
407#1507D6111yescharacteristic, complemented
408C2×C61—22no—
409C2×C61—22no—
410C2×C61—41no—
411C2×C61—82no—
412C2×C61C22×#9911yescharacteristic
413C2×C61#289611yescharacteristic
414C2×C61C2×#42111yescharacteristic
415D61—22no—
416D61—41no—
417D61—41no—
418D61—41no—
419C22×#41—611no—
420C24×C4—611no—
421C22×M16—1221no—
422#525—612no—
423#525—612no—
424#525—612no—
425#525—612no—
426#525—1221no—
427#525—1221no—
428#525—1221no—
429#525—1221no—
430C2×#123—1221no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—611no—
433C2×#121—611no—
434C2×#121C2×D6111yescharacteristic
435C2×#120—1221no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×#117—611no—
439C2×#117—1221no—
440#407—611no—
441#407—612no—
442#407—1221no—
443#407—1221no—
444#407C2×D6111yescharacteristic
445C2×C22⋊C8—612no—
446C2×C22⋊C8—1221no—
447#381—612no—
448#380—612no—
449#380—1221no—
450#379—1221no—
451C4×C22⋊C4—611no—
452C4×C22⋊C4—1221no—
453C4×C22⋊C4C2×D6111yescharacteristic
454#328—614no—
455#328—614no—
456#327—614no—
457#327C2×D6114yescomplemented
458C61#1758211yescharacteristic, complemented, Sylow
459C25—611no—
460C2×#41—612no—
461C2×#41—612no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—2444no—
465C22×Q8—611no—
466C22×D4—21no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4C4×D6111yescharacteristic
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—1221no—
484C23×C4—2444no—
485C23×C4C22×D6111yescharacteristic
486C2×M16—21no—
487C2×M16—1222no—
488C2×M16—1221no—
489C2×M16—2444no—
490C22×C8—1222no—
491#123—1222no—
492#123—1222no—
493#123—1222no—
494#123—1222no—
495C22⋊Q8—612no—
496C22⋊Q8—612no—
497C22⋊Q8—612no—
498C22⋊Q8—612no—
499C22⋊Q8—1221no—
500C22⋊Q8—1221no—
501C22⋊Q8—1221no—
502C22⋊Q8—1221no—
503#121—21no—
504#121—21no—
505#121—612no—
506#121—612no—
507#121—1221no—
508#121—1221no—
509#121C4×D6112yes—
510#121C22×D6112yes—
511#120—1222no—
512#120—1222no—
513#120—1222no—
514#120—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1222no—
523#117—612no—
524#117—612no—
525#117—1221no—
526#117—1221no—
527#117—2444no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1222no—
532C2×C4⋊C4C4×D6111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—1222no—
541C2×C22⋊C4—1221no—
542C2×C42—21no—
543C2×C42—1221no—
544C2×C42—1221no—
545C22⋊C8—21no—
546C22⋊C8—612no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1221no—
550C22⋊C8C22×D6112yes—
551#95—612no—
552#95—1222no—
553#95C22×D6112yes—
554C24—21no—
555C24—611no—
556C24—611no—
557C24—611no—
558C24—611no—
559C24—611no—
560C24—611no—
561C24—2442no—
562C24—2442no—
563C24—2442no—
564C24D4×D6111yescharacteristic
565#41—2444no—
566#41—2444no—
567#41—2444no—
568#41—2444no—
569C2×Q8—612no—
570C2×Q8—1221no—
571C2×Q8—2442no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—2444no—
582C2×D4—2444no—
583C2×D4C2×C4×D6112yes—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—42no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1222no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2444no—
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4C2×C4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4D4×D6111yescharacteristic
633C22×C4C23×D6111yescharacteristic
634M16—42no—
635M16—2444no—
636M16—2442no—
637C2×C8—22no—
638C2×C8—1222no—
639C2×C8—2444no—
640C4⋊C4—21no—
641C4⋊C4—612no—
642C4⋊C4—1222no—
643C4⋊C4—1222no—
644C4⋊C4—1222no—
645C4⋊C4—1221no—
646C4⋊C4—1222no—
647C4⋊C4—2444no—
648C4⋊C4C2×C4×D6112yes—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—42no—
652C22⋊C4—1222no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—2444no—
661C22⋊C4—2444no—
662C22⋊C4—2442no—
663C42—42no—
664C42—1222no—
665C42—1222no—
666C42—2442no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—611no—
675C23—611no—
676C23—611no—
677C23—611no—
678C23—1222no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—24416no—
697C23C22⋊C4×D6111yescharacteristic
698C23C22⋊C4×D6111yescharacteristic
699C23C2×D4×D6111yescharacteristic
700Q8—2442no—
701Q8—2442no—
702D4—42no—
703D4—44no—
704D4—44no—
705D4—42no—
706D4—2444no—
707D4—2444no—
708D4—2444no—
709D4—2444no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—611no—
722C2×C4—614no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2444no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2444no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4C22⋊C4×D6111yescharacteristic
757C2×C4C22⋊C4×D6111yescharacteristic
758C2×C4C22×C4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C8—42no—
761C8—2442no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—84no—
774C22—612no—
775C22—1221no—
776C22—1221no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—1221no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1221no—
786C22—2444no—
787C22—2444no—
788C22—2444no—
789C22—2444no—
790C22—2444no—
791C22—2444no—
792C22#1683977712yes—
793C22C2×C22⋊C4×D6111yescharacteristic
794C22#1684055812yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—42no—
799C4—82no—
800C4—612no—
801C4—1221no—
802C4—1221no—
803C4—1221no—
804C4—4882no—
805C4—2442no—
806C4—2442no—
807C4#99×D6112yes—
808C2—22no—
809C2—22no—
810C2—41no—
811C2—82no—
812C2—1222no—
813C2—2441no—
814C2—2441no—
815C2—2441no—
816C2C2×#99×D6111yescharacteristic
817C2#2145433311yescharacteristic
818C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1507C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC22×C4×C61C24
hypercenter#1507D61
hypocenterC61#17582
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. #21448200C2semidirect
4. #21444372C2semidirect
5. #21444359C2semidirect
6. #21444340C2semidirect
7. #21444338C2semidirect
8. #21444335C2semidirect
9. C61×#1507C2semidirect
10. C22×#11758224C4semidirect
17. #16840272C4semidirect
18. #16840272C4semidirect
22. C2×#14519757C4semidirect
24. C2×#14519748C4semidirect
28. C2×#14519735C4semidirect
33. #16839724C22semidirect
35. C22⋊C8×D61C22semidirect
36. #16839624C22semidirect
37. #16839621C22semidirect
42. #16839500C22semidirect
43. #16839498C22semidirect
44. #16839496C22semidirect
48. C61×#327C22semidirect
407. #1507D61semidirect
457. #327C2×D61semidirect
458. C61#17582semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
#407×D612
#214482002
#214443722
#214443592
#214443402
#214443382
#214443352
C61×#15072
#1758261