Finite Group Databasebeta

← #29603078

Subgroups — #29603078

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758198C211yesmaximal, characteristic
2C2×#16839652C212yesmaximal, complemented
3C2×#16839617C211yesmaximal, characteristic
4C2×#16839617C211yesmaximal, characteristic
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
6#21444067C212yesmaximal, complemented
7#21444061C212yesmaximal, complemented
8#21444055C212yesmaximal, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444041C211yesmaximal, characteristic, complemented
11C2×C61×#385C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2211yescharacteristic
16C22×#11758198—28no—
17C22×#11758198—24no—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×C4×Dic61C2211yescharacteristic, complemented
25C22×C4×Dic61C2211yescharacteristic, complemented
26#16839652—28no—
27#16839617—24no—
28#16839617C418yescomplemented
29C22⋊C4×Dic61—24no—
30C2×#14519684C2212yescomplemented
31C2×#14519684C2212yescomplemented
32C2×#14519684C2211yescharacteristic, complemented
33C2×#14519684C2211yescharacteristic, complemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C24×C4×C61C2211yescharacteristic
37C22×C4⋊C4×C61C2212yescomplemented
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C61×#385—24no—
41C2×#95×C61C2212yescomplemented
42C24×D61—22no—
43C24×D61—22no—
44C24×D61—24no—
45C24×D61—24no—
46C24×D61—22no—
47C24×D61—22no—
48C24×D61—22no—
49C24×D61—22no—
50C24×D61—42no—
51C24×D61—42no—
52C24×D61C2×C414yes—
53C24×D61C2312yes—
54C23×Dic61—22no—
55C23×Dic61—22no—
56C23×Dic61—24no—
57C23×Dic61—42no—
58C23×Dic61D414yes—
59C23×Dic61C2312yes—
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61C2×C414yes—
70C2×#11758198—232no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—42no—
83C2×#11758198—42no—
84C2×#11758198—42no—
85C2×#11758198—42no—
86C2×#11758198C2×C418yescomplemented
87C2×#11758198C2×C418yescomplemented
88C2×#11758198D418yes—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61—24no—
92C2×C4×Dic61—42no—
93#14519684—24no—
94#14519684—22no—
95#14519684—22no—
96#14519684—24no—
97#14519684—42no—
98#14519684—42no—
99C25×C61C2311yescharacteristic
100C23×C4×C61—22no—
101C23×C4×C61—24no—
102C23×C4×C61—22no—
103C23×C4×C61—22no—
104C23×C4×C61—42no—
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2312yes—
109C2×C4⋊C4×C61—24no—
110C2×C4⋊C4×C61—24no—
111C2×C4⋊C4×C61—42no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61C2×C414yes—
117C2×C22⋊C4×C61D414yes—
118#95×C61—24no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61C22×C412yes—
124C24×C61C2×D412yes—
125C24×C61C2×D412yes—
126C24×C61#4112yes—
127C24×C61#4112yes—
128C24×C61#4112yes—
129C24×C61#4112yes—
130C24×C61C2411yescharacteristic
131C23×D61—216no—
132C23×D61—28no—
133C23×D61—28no—
134C23×D61—28no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—22no—
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—216no—
148C23×D61—28no—
149C23×D61—28no—
150C23×D61—48no—
151C23×D61—48no—
152C23×D61—48no—
153C23×D61—48no—
154C23×D61—48no—
155C23×D61—48no—
156C23×D61—48no—
157C23×D61—48no—
158C23×D61—48no—
159C23×D61—44no—
160C23×D61—44no—
161C23×D61—48no—
162C23×D61—44no—
163C23×D61—44no—
164C23×D61—44no—
165C23×D61—44no—
166C23×D61C22×C414yes—
167C23×D61C2×D414yes—
168C23×D61#4114yes—
169C22×C4×C61—28no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—48no—
191C22×C4×C61—48no—
192C22×C4×C61—44no—
193C22×C4×C61—44no—
194C22×C4×C61C22×C414yes—
195C22×C4×C61C2×D414yes—
196C22×C4×C61C2×D412yes—
197C22×C4×C61C2×D412yes—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—22no—
201C22×Dic61—28no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—22no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—28no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—44no—
223C22×Dic61—48no—
224C22×Dic61—48no—
225C22×Dic61C22×C412yes—
226C22×Dic61C22×C412yes—
227C22×Dic61C2×D412yes—
228C22×Dic61C2×D414yes—
229C22×Dic61C2×D412yes—
230C4⋊C4×C61—48no—
231C22⋊C4×C61—28no—
232C22⋊C4×C61—28no—
233C22⋊Dic61—28no—
234C22⋊Dic61—44no—
235#11758198—216no—
236#11758198—216no—
237#11758198—216no—
238#11758198—48no—
239#11758198—48no—
240#11758198—48no—
241C4×Dic61—44no—
242C4×Dic61—44no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—24no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—24no—
251C23×C61—24no—
252C23×C61—24no—
253C23×C61—24no—
254C23×C61—24no—
255C23×C61—24no—
256C23×C61—24no—
257C23×C61—24no—
258C23×C61—24no—
259C23×C61#11714yes—
260C23×C61C4×D414yes—
261C23×C61C4×D414yes—
262C23×C61#12114yes—
263C23×C61#12314yes—
264C23×C61#12414yes—
265C23×C61#12614yes—
266C23×C61C23×C411yescharacteristic
267C23×C61C22×D411yescharacteristic
268C23×C61C22×D412yes—
269C23×C61C22×D411yescharacteristic
270C23×C61C2×#4111yescharacteristic
271C23×C61C2×#4111yescharacteristic
272C23×C61C2×#4111yescharacteristic
273C23×C61C2×#4111yescharacteristic
274C23×C61C2×#4112yes—
275C23×C61H(5,𝔽2)12yes—
276C23×C61H(5,𝔽2)12yes—
277C22×D61—232no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—24no—
284C22×D61—24no—
285C22×D61—24no—
286C22×D61—24no—
287C22×D61—24no—
288C22×D61—24no—
289C22×D61—24no—
290C22×D61—24no—
291C22×D61—24no—
292C22×D61—24no—
293C22×D61—24no—
294C22×D61—24no—
295C22×D61—24no—
296C22×D61—432no—
297C22×D61—432no—
298C22×D61—416no—
299C22×D61—416no—
300C22×D61—416no—
301C22×D61—432no—
302C22×D61—432no—
303C22×D61—416no—
304C22×D61—416no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—416no—
322C22×D61C4×D418yes—
323C2×C4×C61—24no—
324C2×C4×C61—24no—
325C2×C4×C61—24no—
326C2×C4×C61—24no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—24no—
330C2×C4×C61—24no—
331C2×C4×C61—24no—
332C2×C4×C61—24no—
333C2×C4×C61—416no—
334C2×C4×C61—41no—
335C2×C4×C61—42no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—24no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—24no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—416no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—42no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61#12014yes—
376#13991—611nomaximal, Sylow
377C22×C61—24no—
378C22×C61—28no—
379C22×C61—28no—
380C22×C61—24no—
381C22×C61—24no—
382C22×C61—28no—
383C22×C61—28no—
384C22×C61—24no—
385C22×C61—24no—
386C22×C61—24no—
387C22×C61#38818yescomplemented
388C22×C61C2×#11711yescharacteristic
389C22×C61C2×C4×D412yes—
390C22×C61C2×C4×D411yescharacteristic
391C22×C61C2×C4×D411yescharacteristic
392C22×C61#51812yes—
393C22×C61C2×#12011yescharacteristic
394C22×C61C2×#12111yescharacteristic
395C22×C61C2×#12311yescharacteristic
396C22×C61#52511yescharacteristic
397C22×C61#52512yes—
398C22×C61C2×#12411yescharacteristic
399C22×C61C2×#12611yescharacteristic
400C22×C61#53411yescharacteristic
401C22×C61#53511yescharacteristic
402C22×C61#53812yes—
403C22×C61D4212yes—
404C22×C61#54612yes—
405C22×C61#54612yes—
406C22×C61#54612yes—
407C22×C61#54612yes—
408C22×C61#55112yes—
409C22×C61#55112yes—
410C22×C61#55112yes—
411C2×D61—28no—
412C2×D61—28no—
413C2×D61—28no—
414C2×D61—464no—
415C2×D61—44no—
416C2×D61—44no—
417C2×D61—44no—
418C2×D61—44no—
419C2×D61—44no—
420C2×D61—44no—
421C2×D61—44no—
422C2×D61—44no—
423C2×D61—44no—
424C2×D61—44no—
425C2×D61—44no—
426C2×D61—44no—
427C4×C61—44no—
428C4×C61—42no—
429C4×C61—44no—
430C4×C61—42no—
431Dic61—24no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435Dic61—82no—
436C23×C22⋊C4—611no—
437C2×#388—612no—
438C2×#385D6111yescharacteristic, complemented
439C2×#379—611no—
440C2×#379—611no—
441C2×C4×C22⋊C4—611no—
442#1440—612no—
443#1439—612no—
444#1437—612no—
445C22⋊#95—611no—
446C22⋊#95—611no—
447C2×C61—28no—
448C2×C61C2×#38811yescharacteristic
449C2×C61C4×#12011yescharacteristic
450C2×C61#232111yescharacteristic
451C2×C61#234212yes—
452C2×C61#235812yes—
453C2×C61#240511yescharacteristic
454C2×C61#240811yescharacteristic
455C2×C61#247212yes—
456C2×C61#248012yes—
457C2×C61#248211yescharacteristic
458C2×C61#253411yescharacteristic
459D61—48no—
460C26—611no—
461C24×C4—611no—
462C24×C4C2×D6111yescharacteristic
463C22×C4⋊C4C2×D6112yescomplemented
464C22×C22⋊C4—611no—
465C22×C22⋊C4—612no—
466C22×C22⋊C4—612no—
467C22×C22⋊C4—612no—
468C22×C22⋊C4—611no—
469C22×C22⋊C4—612no—
470C22×C22⋊C4—612no—
471C22×C22⋊C4—612no—
472C22×C22⋊C4—1228no—
473C22×C22⋊C4—1224no—
474C22×C22⋊C4C2×D6111yescharacteristic
475C22×C22⋊C4C2×D6111yescharacteristic
476C22×C42—611no—
477C22×C42—611no—
478#388—1228no—
479#385—24no—
480#379—618no—
481#379—1224no—
482C4×C22⋊C4—1224no—
483C2×#95—612no—
484C2×#95—612no—
485C2×#95—611no—
486C2×#95—611no—
487C2×#95—612no—
488C2×#95—612no—
489C2×#95C2×D6112yescomplemented
490C61#1399111yescharacteristic, complemented, Sylow
491C25—612no—
492C25—614no—
493C25—1224no—
494C25—1224no—
495C25—1222no—
496C25—1222no—
497C25—1222no—
498C25—1222no—
499C25—1222no—
500C25—1222no—
501C25—2442no—
502C25—2442no—
503C25C22×D6111yescharacteristic
504C23×C4—22no—
505C23×C4—24no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—42no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—614no—
514C23×C4—612no—
515C23×C4—1224no—
516C23×C4—1222no—
517C23×C4—1222no—
518C23×C4—2442no—
519C23×C4C22×D6112yes—
520C23×C4C22×D6112yes—
521C23×C4C22×D6111yescharacteristic
522C23×C4C22×D6111yescharacteristic
523C2×C4⋊C4—24no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—42no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—618no—
532C2×C22⋊C4—618no—
533C2×C22⋊C4—618no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1224no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1224no—
538C2×C22⋊C4—1224no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4—12232no—
541C2×C22⋊C4—1222no—
542C2×C22⋊C4—1222no—
543C2×C22⋊C4—1224no—
544C2×C22⋊C4—1224no—
545C2×C22⋊C4—1224no—
546C2×C22⋊C4—1222no—
547C2×C22⋊C4—1222no—
548C2×C22⋊C4—1222no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4—2442no—
555C2×C22⋊C4C4×D6114yes—
556C2×C22⋊C4C22⋊D6114yes—
557C2×C42—1222no—
558C2×C42—1222no—
559C2×C42—1224no—
560C2×C42—2442no—
561#95—24no—
562#95—1222no—
563#95—1222no—
564#95—1224no—
565#95—1224no—
566#95—2442no—
567#95—2442no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—614no—
573C24—614no—
574C24—614no—
575C24—12216no—
576C24—1228no—
577C24—1228no—
578C24—12216no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24—1222no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1228no—
592C24—1228no—
593C24—1228no—
594C24—2448no—
595C24—2448no—
596C24—2448no—
597C24—2448no—
598C24—2448no—
599C24—2448no—
600C24—2448no—
601C24—2448no—
602C24—2448no—
603C24—2444no—
604C24—2444no—
605C24—2448no—
606C24—2444no—
607C24—2444no—
608C24—2444no—
609C24—2444no—
610C24C2×C4×D6112yes—
611C24#1175822212yes—
612C24D4×D6112yes—
613C24#1175822412yes—
614C24#1175822612yes—
615C24#1175822612yes—
616C24C2×C22⋊D6112yes—
617C24C23×D6111yescharacteristic
618C22×C4—28no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—48no—
640C22×C4—48no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—614no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1228no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1228no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—2444no—
673C22×C4—2448no—
674C22×C4—2448no—
675C22×C4C2×C4×D6114yes—
676C22×C4D4×D6114yes—
677C22×C4C2×C22⋊D6112yes—
678C22×C4C2×C22⋊D6112yes—
679C4⋊C4—48no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—12216no—
683C22⋊C4—12216no—
684C22⋊C4—12216no—
685C22⋊C4—1228no—
686C22⋊C4—2448no—
687C22⋊C4—2448no—
688C22⋊C4—2448no—
689C22⋊C4—2444no—
690C42—2444no—
691C42—2444no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—618no—
709C23—12232no—
710C23—1224no—
711C23—1224no—
712C23—1224no—
713C23—1224no—
714C23—1224no—
715C23—1224no—
716C23—1224no—
717C23—1224no—
718C23—1224no—
719C23—1224no—
720C23—1224no—
721C23—1224no—
722C23—1224no—
723C23—1224no—
724C23—1224no—
725C23—1224no—
726C23—1224no—
727C23—1224no—
728C23—24432no—
729C23—24432no—
730C23—24416no—
731C23—24432no—
732C23—24416no—
733C23—24416no—
734C23—24416no—
735C23—24416no—
736C23—24432no—
737C23—2442no—
738C23—2442no—
739C23—2442no—
740C23—2442no—
741C23—2442no—
742C23—2442no—
743C23—2442no—
744C23—2442no—
745C23—2442no—
746C23—2442no—
747C23—2442no—
748C23—2442no—
749C23—2442no—
750C23—24416no—
751C23—2442no—
752C23—2442no—
753C23—2442no—
754C23#1451973514yes—
755C23C4×C22⋊D6114yes—
756C23#1451973914yes—
757C23#1451974914yes—
758C23#1451976214yes—
759C23#1451976614yes—
760C23#1451977214yes—
761C23C22×C4×D6111yescharacteristic
762C23C2×D4×D6112yes—
763C23C2×D4×D6111yescharacteristic
764C23C22×C22⋊D6111yescharacteristic
765C23#41×D6112yes—
766C23C2×#1175822411yescharacteristic
767C23C2×#1175822211yescharacteristic
768C23C2×#1175822611yescharacteristic
769C23C2×#1175822611yescharacteristic
770C23#1451982212yes—
771C23#1451982312yes—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—416no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—614no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1224no—
801C2×C4—1224no—
802C2×C4—1224no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1224no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—24416no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2442no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2442no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4—2442no—
825C22—24no—
826C22—28no—
827C22—28no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—28no—
834C22—28no—
835C22—1228no—
836C22—1228no—
837C22—1228no—
838C22—24464no—
839C22—2444no—
840C22—2444no—
841C22—2444no—
842C22—2444no—
843C22—2444no—
844C22—2444no—
845C22—2444no—
846C22—2444no—
847C22—2444no—
848C22—2444no—
849C22—2444no—
850C22—2444no—
851C22#1683965218yescomplemented
852C22C2×#1451973511yescharacteristic
853C22C4×D4×D6112yes—
854C22C2×C4×C22⋊D6111yescharacteristic
855C22C2×#1451973911yescharacteristic
856C22#1684023412yes—
857C22#120×D6111yescharacteristic
858C22C2×#1451974911yescharacteristic
859C22C2×#1451976211yescharacteristic
860C22#1684027011yescharacteristic
861C22#1684027512yes—
862C22C2×#1451976611yescharacteristic
863C22C2×#1451977211yescharacteristic
864C22#1684032311yescharacteristic
865C22#1684032711yescharacteristic
866C22#1684035212yes—
867C22D4×C22⋊D6112yes—
868C22#1684039912yes—
869C22#1684040012yes—
870C22#1684040312yes—
871C22#1684040812yes—
872C22#1684043512yes—
873C22#1684043912yes—
874C22#1684044112yes—
875C4—44no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—1224no—
880C4—4882no—
881C4—2442no—
882C4—2442no—
883C4—2442no—
884C2—28no—
885C2—2448no—
886C2C2×#1683965211yescharacteristic
887C2#2144832011yescharacteristic
888C2#2144847611yescharacteristic
889C2#2144866612yes—
890C2#2144879612yes—
891C2#2144914811yescharacteristic
892C2#2144917211yescharacteristic
893C2#2144995212yes—
894C2#2145007212yes—
895C2#2145009211yescharacteristic
896C2#2145070811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×#385D61
hypocenterC61#13991
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#16839652C2semidirect
5. C2×C22⋊C4×Dic61C2semidirect
6. #21444067C2semidirect
7. #21444061C2semidirect
8. #21444055C2semidirect
9. #21444042C2semidirect
10. #21444041C2semidirect
11. C2×C61×#385C2semidirect
24. C22×C4×Dic61C22semidirect
25. C22×C4×Dic61C22semidirect
28. #16839617C4semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
37. C22×C4⋊C4×C61C22semidirect
41. C2×#95×C61C22semidirect
86. C2×#11758198C2×C4semidirect
87. C2×#11758198C2×C4semidirect
387. C22×C61#388semidirect
438. C2×#385D61semidirect
463. C22×C4⋊C4C2×D61semidirect
489. C2×#95C2×D61semidirect
490. C61#13991semidirect
851. C22#16839652semidirect

Maximal subgroups

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

subgroupindex
C23×#117581982
C2×#168396522
C2×#168396172
C2×C22⋊C4×Dic612
#214440672
#214440612
#214440552
#214440422
#214440412
C2×C61×#3852
#1399161