Finite Group Databasebeta

← #29602829

Subgroups — #29602829

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
1C2×#16839656C212yesmaximal, complemented
2C2×#16839635C211yesmaximal, characteristic, complemented
3C2×#16839618C211yesmaximal, characteristic
4C2×#16839618C211yesmaximal, characteristic
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6#21444066C212yesmaximal, complemented
7#21444062C212yesmaximal, complemented
8#21444056C212yesmaximal, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C23×C22⋊C4×C61C211yesmaximal, characteristic
12C22×#11758196C2211yescharacteristic, complemented
13C22×#11758196C2211yescharacteristic, complemented
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2212yes—
22C22×C4×Dic61C2212yescomplemented
23#16839656—28no—
24#16839635—24no—
25#16839618—24no—
26#16839618C418yescomplemented
27C4×C22⋊Dic61—24no—
28C2×#14519684C2211yescharacteristic, complemented
29C2×#14519684C2211yescharacteristic, complemented
30C2×#14519684C2212yescomplemented
31C2×#14519684C2212yescomplemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C26×C61C2211yescharacteristic
36C24×C4×C61C2211yescharacteristic
37C24×C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61—24no—
39C22×C22⋊C4×C61—28no—
40C22×C22⋊C4×C61C2212yes—
41C22×C22⋊C4×C61C2212yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2312yes—
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2312yes—
48C2×#11758196—22no—
49C2×#11758196—22no—
50C2×#11758196—24no—
51C2×#11758196—42no—
52C2×C22⋊Dic61—22no—
53C2×C22⋊Dic61—22no—
54C2×C22⋊Dic61—24no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61—24no—
57C2×C22⋊Dic61—22no—
58C2×C22⋊Dic61—22no—
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61—42no—
69C2×C22⋊Dic61—42no—
70C2×C22⋊Dic61—42no—
71C2×C22⋊Dic61C2×C414yes—
72C2×C22⋊Dic61C2×C414yes—
73C2×C22⋊Dic61C2×C418yescomplemented
74C2×C22⋊Dic61C2×C418yescomplemented
75C2×C22⋊Dic61D414yes—
76C2×C4×Dic61—24no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61—42no—
79#14519684—22no—
80#14519684—22no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—42no—
85#14519684—42no—
86C25×C61—24no—
87C25×C61—22no—
88C25×C61—24no—
89C25×C61—22no—
90C25×C61—22no—
91C25×C61—22no—
92C25×C61—22no—
93C25×C61—22no—
94C25×C61—42no—
95C25×C61—42no—
96C25×C61C2×C414yes—
97C25×C61C2312yes—
98C25×C61C2311yescharacteristic
99C23×C4×C61—22no—
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—24no—
103C23×C4×C61—24no—
104C23×C4×C61—22no—
105C23×C4×C61—22no—
106C23×C4×C61—42no—
107C23×C4×C61—42no—
108C23×C4×C61D414yes—
109C23×C4×C61C2311yescharacteristic
110C23×C4×C61C2312yes—
111C23×C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—232no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—24no—
116C2×C22⋊C4×C61—24no—
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61D418yes—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—28no—
124C24×C61—28no—
125C24×C61—216no—
126C24×C61—216no—
127C24×C61—28no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—22no—
134C24×C61—22no—
135C24×C61—22no—
136C24×C61—22no—
137C24×C61—22no—
138C24×C61—22no—
139C24×C61—22no—
140C24×C61—28no—
141C24×C61—28no—
142C24×C61—48no—
143C24×C61—48no—
144C24×C61—48no—
145C24×C61—48no—
146C24×C61—48no—
147C24×C61—48no—
148C24×C61—48no—
149C24×C61—48no—
150C24×C61—48no—
151C24×C61—44no—
152C24×C61—44no—
153C24×C61—48no—
154C24×C61—44no—
155C24×C61—44no—
156C24×C61—44no—
157C24×C61—44no—
158C24×C61C22×C414yes—
159C24×C61C22×C412yes—
160C24×C61C2×D414yes—
161C24×C61C2×D412yes—
162C24×C61C2×D412yes—
163C24×C61#4114yes—
164C24×C61#4112yes—
165C24×C61#4112yes—
166C24×C61#4112yes—
167C24×C61#4112yes—
168C24×C61C2411yescharacteristic
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—28no—
173C22×C4×C61—28no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—28no—
185C22×C4×C61—44no—
186C22×C4×C61—48no—
187C22×C4×C61—48no—
188C22×C4×C61—48no—
189C22×C4×C61—48no—
190C22×C4×C61—44no—
191C22×C4×C61—44no—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D414yes—
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2×D414yes—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—21no—
200C22×Dic61—22no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—22no—
204C22×Dic61—21no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—21no—
217C22×Dic61—22no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61C22×C412yes—
227C22×Dic61C22×C414yes—
228C22×Dic61C22×C412yes—
229C22×Dic61C2×D414yes—
230C22⋊C4×C61—216no—
231C22⋊C4×C61—216no—
232C22⋊Dic61—28no—
233C22⋊Dic61—28no—
234C22⋊Dic61—216no—
235C22⋊Dic61—28no—
236C22⋊Dic61—48no—
237C22⋊Dic61—48no—
238C22⋊Dic61—48no—
239C22⋊Dic61—44no—
240#11758196—44no—
241#11758196—44no—
242C4×Dic61—48no—
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—232no—
260C23×C61—24no—
261C23×C61—24no—
262C23×C61—24no—
263C23×C61—24no—
264C23×C61—24no—
265C23×C61—24no—
266C23×C61—24no—
267C23×C61—24no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—24no—
273C23×C61—24no—
274C23×C61—24no—
275C23×C61—24no—
276C23×C61—24no—
277C23×C61—24no—
278C23×C61—432no—
279C23×C61—432no—
280C23×C61—416no—
281C23×C61—416no—
282C23×C61—416no—
283C23×C61—416no—
284C23×C61—432no—
285C23×C61—416no—
286C23×C61—432no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—416no—
304C23×C61#11714yes—
305C23×C61C4×D418yes—
306C23×C61C4×D414yes—
307C23×C61C4×D414yes—
308C23×C61#12114yes—
309C23×C61#12314yes—
310C23×C61#12414yes—
311C23×C61#12614yes—
312C23×C61C23×C411yescharacteristic
313C23×C61C22×D411yescharacteristic
314C23×C61C22×D412yes—
315C23×C61C22×D411yescharacteristic
316C23×C61C2×#4111yescharacteristic
317C23×C61C2×#4111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61C2×#4112yes—
320C23×C61C2×#4111yescharacteristic
321C23×C61H(5,𝔽2)12yes—
322C23×C61H(5,𝔽2)12yes—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—24no—
326C2×C4×C61—24no—
327C2×C4×C61—22no—
328C2×C4×C61—24no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—24no—
332C2×C4×C61—24no—
333C2×C4×C61—416no—
334C2×C4×C61—416no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61#12014yes—
342C2×Dic61—22no—
343C2×Dic61—24no—
344C2×Dic61—24no—
345C2×Dic61—22no—
346C2×Dic61—24no—
347C2×Dic61—24no—
348C2×Dic61—24no—
349C2×Dic61—24no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—41no—
353C2×Dic61—42no—
354C2×Dic61—41no—
355C2×Dic61—42no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376#13971—611nomaximal, Sylow
377C22×C61—24no—
378C22×C61—24no—
379C22×C61—28no—
380C22×C61—28no—
381C22×C61—24no—
382C22×C61—24no—
383C22×C61—28no—
384C22×C61—24no—
385C22×C61—28no—
386C22×C61—24no—
387C22×C61—28no—
388C22×C61—28no—
389C22×C61—28no—
390C22×C61—464no—
391C22×C61—44no—
392C22×C61—44no—
393C22×C61—44no—
394C22×C61—44no—
395C22×C61—44no—
396C22×C61—44no—
397C22×C61—44no—
398C22×C61—44no—
399C22×C61—44no—
400C22×C61—44no—
401C22×C61—44no—
402C22×C61—44no—
403C22×C61#38818yescomplemented
404C22×C61C2×#11711yescharacteristic
405C22×C61C2×C4×D411yescharacteristic
406C22×C61C2×C4×D411yescharacteristic
407C22×C61C2×C4×D412yes—
408C22×C61#51812yes—
409C22×C61C2×#12011yescharacteristic
410C22×C61C2×#12111yescharacteristic
411C22×C61C2×#12311yescharacteristic
412C22×C61#52511yescharacteristic
413C22×C61#52512yes—
414C22×C61C2×#12411yescharacteristic
415C22×C61C2×#12611yescharacteristic
416C22×C61#53411yescharacteristic
417C22×C61#53511yescharacteristic
418C22×C61#53812yes—
419C22×C61D4212yes—
420C22×C61#54612yes—
421C22×C61#54612yes—
422C22×C61#54612yes—
423C22×C61#54612yes—
424C22×C61#55112yes—
425C22×C61#55112yes—
426C22×C61#55112yes—
427C4×C61—24no—
428C4×C61—42no—
429C4×C61—44no—
430Dic61—42no—
431Dic61—44no—
432Dic61—44no—
433Dic61—42no—
434Dic61—81no—
435Dic61—81no—
436C23×C22⋊C4D6111yescharacteristic
437C2×#388—612no—
438C2×#385—611no—
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×C61—48no—
449C2×C61C2×#38811yescharacteristic
450C2×C61C4×#12011yescharacteristic
451C2×C61#232111yescharacteristic
452C2×C61#234212yes—
453C2×C61#235812yes—
454C2×C61#241011yescharacteristic
455C2×C61#241111yescharacteristic
456C2×C61#241812yes—
457C2×C61#243511yescharacteristic
458C2×C61#248012yes—
459C2×C61#256111yescharacteristic
460C26C2×D6111yescharacteristic
461C24×C4C2×D6111yescharacteristic
462C24×C4C2×D6111yescharacteristic
463C22×C4⋊C4—611no—
464C22×C4⋊C4—611no—
465C22×C22⋊C4—24no—
466C22×C22⋊C4—28no—
467C22×C22⋊C4—611no—
468C22×C22⋊C4—611no—
469C22×C22⋊C4—611no—
470C22×C22⋊C4—612no—
471C22×C22⋊C4—612no—
472C22×C22⋊C4—611no—
473C22×C22⋊C4—612no—
474C22×C22⋊C4—612no—
475C22×C22⋊C4C2×D6112yes—
476C22×C22⋊C4C2×D6112yes—
477C22×C42—612no—
478#388—1228no—
479#385—1224no—
480#379—618no—
481#379—1224no—
482C4×C22⋊C4—1224no—
483C2×#95—612no—
484C2×#95—612no—
485C2×#95—611no—
486C2×#95—612no—
487C2×#95—611no—
488C2×#95—612no—
489C2×#95—612no—
490C61#1397111yescharacteristic, complemented, Sylow
491C25—24no—
492C25—22no—
493C25—24no—
494C25—22no—
495C25—22no—
496C25—22no—
497C25—22no—
498C25—22no—
499C25—42no—
500C25—42no—
501C25C4×D6114yes—
502C25C22×D6112yes—
503C25C22×D6111yescharacteristic
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—42no—
512C23×C4—42no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—612no—
516C23×C4—612no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4C22⋊D6114yes—
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6112yes—
522C23×C4C22×D6111yescharacteristic
523C2×C4⋊C4—1222no—
524C2×C4⋊C4—1222no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—2442no—
527C2×C22⋊C4—232no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—614no—
534C2×C22⋊C4—614no—
535C2×C22⋊C4—618no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—618no—
538C2×C22⋊C4—1224no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—1222no—
541C2×C22⋊C4—1222no—
542C2×C22⋊C4—1222no—
543C2×C22⋊C4—1222no—
544C2×C22⋊C4—1222no—
545C2×C22⋊C4—1224no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4—1224no—
548C2×C22⋊C4—1224no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1222no—
552C2×C22⋊C4—1224no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4—2442no—
555C2×C22⋊C4—2442no—
556C2×C22⋊C4—2442no—
557C2×C22⋊C4C22⋊D6118yes—
558C2×C42—1224no—
559C2×C42—1224no—
560C2×C42—2442no—
561#95—1224no—
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—28no—
573C24—216no—
574C24—28no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—216no—
588C24—28no—
589C24—28no—
590C24—28no—
591C24—48no—
592C24—48no—
593C24—48no—
594C24—48no—
595C24—48no—
596C24—48no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—44no—
601C24—44no—
602C24—48no—
603C24—44no—
604C24—44no—
605C24—44no—
606C24—44no—
607C24C2×C4×D6114yes—
608C24C2×C4×D6112yes—
609C24#1175822214yes—
610C24#1175822212yes—
611C24D4×D6112yes—
612C24#1175822412yes—
613C24#1175822412yes—
614C24#1175822412yes—
615C24C2×C22⋊D6114yes—
616C24C2×C22⋊D6112yes—
617C24C23×D6111yescharacteristic
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—28no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—614no—
642C22×C4—612no—
643C22×C4—612no—
644C22×C4—614no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1221no—
649C22×C4—1222no—
650C22×C4—1221no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1221no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1222no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4C2×C22⋊D6114yes—
676C22×C4C2×C22⋊D6112yes—
677C22×C4C2×C22⋊D6112yes—
678C22×C4C2×C22⋊D6114yes—
679C4⋊C4—2444no—
680C4⋊C4—2444no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—1228no—
684C22⋊C4—12216no—
685C22⋊C4—1228no—
686C22⋊C4—1228no—
687C22⋊C4—2448no—
688C22⋊C4—2448no—
689C22⋊C4—2448no—
690C22⋊C4—2444no—
691C42—2448no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—232no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—432no—
728C23—432no—
729C23—416no—
730C23—432no—
731C23—432no—
732C23—416no—
733C23—416no—
734C23—416no—
735C23—416no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—416no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23#1451973314yes—
754C23#1451973714yes—
755C23C4×C22⋊D6118yes—
756C23C4×C22⋊D6114yes—
757C23#1451974914yes—
758C23#1451975914yes—
759C23#1451976414yes—
760C23#1451977014yes—
761C23C22×C4×D6111yescharacteristic
762C23C2×D4×D6111yescharacteristic
763C23C22×C22⋊D6111yescharacteristic
764C23C22×C22⋊D6112yes—
765C23C2×#1175822411yescharacteristic
766C23C2×#1175822411yescharacteristic
767C23C2×#1175822411yescharacteristic
768C23C2×#1175822211yescharacteristic
769C23C2×#1175822212yes—
770C23#1451982212yes—
771C23#1451982212yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—1224no—
791C2×C4—1222no—
792C2×C4—1224no—
793C2×C4—1222no—
794C2×C4—1224no—
795C2×C4—1224no—
796C2×C4—1224no—
797C2×C4—1224no—
798C2×C4—1224no—
799C2×C4—1224no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2441no—
811C2×C4—2442no—
812C2×C4—2442no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4#1451974614yes—
825C22—24no—
826C22—28no—
827C22—28no—
828C22—28no—
829C22—24no—
830C22—28no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22#1683965618yescomplemented
852C22C2×#1451973311yescharacteristic
853C22C2×#1451973711yescharacteristic
854C22C2×C4×C22⋊D6111yescharacteristic
855C22C2×C4×C22⋊D6112yes—
856C22#1684023512yes—
857C22C2×#1451974611yescharacteristic
858C22C2×#1451974911yescharacteristic
859C22C2×#1451975911yescharacteristic
860C22#1684027312yes—
861C22#1684027311yescharacteristic
862C22C2×#1451976411yescharacteristic
863C22C2×#1451977011yescharacteristic
864C22#1684032111yescharacteristic
865C22#1684032911yescharacteristic
866C22#1684035012yes—
867C22D4×C22⋊D6112yes—
868C22#1684040212yes—
869C22#1684040612yes—
870C22#1684040612yes—
871C22#1684040612yes—
872C22#1684043812yes—
873C22#1684043812yes—
874C22#1684043812yes—
875C4—24no—
876C4—42no—
877C4—44no—
878C4—4881no—
879C4—4881no—
880C4—2442no—
881C4—2444no—
882C4—2444no—
883C4—2442no—
884C2—28no—
885C2—48no—
886C2C2×#1683965611yescharacteristic
887C2C4×#1451974611yescharacteristic
888C2#2144847711yescharacteristic
889C2#2144866412yes—
890C2#2144879812yes—
891C2#2144919311yescharacteristic
892C2#2144920411yescharacteristic
893C2#2144928112yes—
894C2#2144946611yescharacteristic
895C2#2145005912yes—
896C2#2145097711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC23×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC26×C61C22
hypercenterC23×C22⋊C4D61
hypocenterC61#13971
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839656C2semidirect
2. C2×#16839635C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. #21444066C2semidirect
7. #21444062C2semidirect
8. #21444056C2semidirect
9. #21444042C2semidirect
10. #21444042C2semidirect
12. C22×#11758196C22semidirect
13. C22×#11758196C22semidirect
22. C22×C4×Dic61C22semidirect
26. #16839618C4semidirect
28. C2×#14519684C22semidirect
29. C2×#14519684C22semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
73. C2×C22⋊Dic61C2×C4semidirect
74. C2×C22⋊Dic61C2×C4semidirect
403. C22×C61#388semidirect
490. C61#13971semidirect
851. C22#16839656semidirect

Maximal subgroups

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

subgroupindex
C2×#168396562
C2×#168396352
C2×#168396182
C2×C4×C22⋊Dic612
#214440662
#214440622
#214440562
#214440422
C23×C22⋊C4×C612
#1397161