Finite Group Databasebeta

← #29603138

Subgroups — #29603138

Order 15616.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839642C211yesmaximal, characteristic
2C2×#16839642C211yesmaximal, characteristic
3C2×#16839637C211yesmaximal, characteristic, complemented
4C2×#16839625C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444087C212yesmaximal, complemented
8#21444064C212yesmaximal, complemented
9#21444056C212yesmaximal, complemented
10#21444048C212yesmaximal, complemented
11C22×#123×C61C211yesmaximal, characteristic
12C24×Dic61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2212yes—
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C4×Dic61C2212yes—
21#16839642—24no—
22#16839642—24no—
23#16839637—24no—
24#16839625—24no—
25C22⋊C4×Dic61—24no—
26C2×#14519684—24no—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C23×D4×C61C2211yescharacteristic
37C24×C4×C61C2211yescharacteristic
38C2×#123×C61—24no—
39C2×#123×C61—24no—
40C2×#123×C61C418yescomplemented
41C22×C4⋊C4×C61C2212yes—
42C22×C22⋊C4×C61C2212yes—
43C22×C22⋊C4×C61C2211yescharacteristic
44C23×Dic61—22no—
45C23×Dic61—22no—
46C23×Dic61—22no—
47C23×Dic61—24no—
48C23×Dic61—24no—
49C23×Dic61—22no—
50C23×Dic61—22no—
51C23×Dic61—42no—
52C23×Dic61—42no—
53C23×Dic61D414yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C2×C4⋊Dic61—24no—
61C2×C4⋊Dic61—24no—
62C2×C4⋊Dic61—42no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—24no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—24no—
72C2×C22⋊Dic61—24no—
73C2×C22⋊Dic61—42no—
74C2×C22⋊Dic61—42no—
75C2×C22⋊Dic61D414yes—
76C2×C4×Dic61—24no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61—42no—
79#14519684—24no—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684—24no—
86#14519684—22no—
87#14519684—22no—
88C25×C61C2311yescharacteristic
89C25×C61C2311yescharacteristic
90C22×D4×C61—22no—
91C22×D4×C61—22no—
92C22×D4×C61—22no—
93C22×D4×C61—22no—
94C22×D4×C61—22no—
95C22×D4×C61—22no—
96C22×D4×C61C2×C414yes—
97C23×C4×C61—22no—
98C23×C4×C61—22no—
99C23×C4×C61—22no—
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—22no—
103C23×C4×C61C2×C414yes—
104C23×C4×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107#123×C61—232no—
108C2×C4⋊C4×C61—24no—
109C2×C4⋊C4×C61—24no—
110C2×C4⋊C4×C61C2×C418yescomplemented
111C2×C22⋊C4×C61—24no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61C2×C414yes—
114C2×C22⋊C4×C61C2×C418yescomplemented
115C2×C22⋊C4×C61D414yes—
116C2×C22⋊C4×C61D414yes—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—21no—
126C24×C61—21no—
127C24×C61—22no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61C22×C412yes—
132C24×C61C22×C412yes—
133C24×C61C2×D412yes—
134C24×C61C2×D412yes—
135C24×C61C2×D412yes—
136C24×C61C2×D412yes—
137C24×C61#4112yes—
138C24×C61#4112yes—
139C24×C61C2411yescharacteristic
140C2×D4×C61—28no—
141C2×D4×C61—28no—
142C2×D4×C61—28no—
143C2×D4×C61—44no—
144C2×D4×C61—44no—
145C2×D4×C61—44no—
146C2×D4×C61—44no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—28no—
152C22×C4×C61—28no—
153C22×C4×C61—28no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—44no—
167C22×C4×C61—44no—
168C22×C4×C61—44no—
169C22×C4×C61—44no—
170C22×C4×C61C22×C414yes—
171C22×C4×C61C22×C412yes—
172C22×C4×C61C22×C414yes—
173C22×C4×C61C2×D414yes—
174C22×C4×C61C2×D414yes—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—28no—
179C22×Dic61—28no—
180C22×Dic61—21no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—21no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—28no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—44no—
208C22×Dic61—48no—
209C22×Dic61—48no—
210C22×Dic61—48no—
211C22×Dic61—48no—
212C22×Dic61—44no—
213C22×Dic61—44no—
214C22×Dic61C2×D412yes—
215C22×Dic61C2×D414yes—
216C22×Dic61C2×D412yes—
217C22×Dic61#4114yes—
218C22×Dic61#4114yes—
219C4⋊C4×C61—216no—
220C22⋊C4×C61—216no—
221C22⋊C4×C61C22⋊C4116yescomplemented
222C22⋊Dic61—28no—
223C22⋊Dic61—48no—
224C22⋊Dic61—44no—
225C22⋊Dic61—44no—
226C22⋊Dic61—44no—
227C4⋊Dic61—48no—
228C4×Dic61—48no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—42no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C2×C22⋊C414yes—
269C23×C61C4×D414yes—
270C23×C61C4×D414yes—
271C23×C61#12114yes—
272C23×C61#12114yes—
273C23×C61#12414yes—
274C23×C61#12714yes—
275C23×C61C23×C411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61C22×D411yescharacteristic
279C23×C61C22×D411yescharacteristic
280C23×C61C2×#4111yescharacteristic
281C23×C61C2×#4111yescharacteristic
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C612−1+412yes—
286D4×C61—416no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—22no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—41no—
307C2×C4×C61—416no—
308C2×C4×C61C2×C22⋊C418yes—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—24no—
317C2×Dic61—22no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—416no—
323C2×Dic61—416no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61#12314yescomplemented
345#13996—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61—42no—
357C22×C61—44no—
358C22×C61—44no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—82no—
364C22×C61—82no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61#39018yes—
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61C2×C4×D411yescharacteristic
371C22×C61C4×#4112yes—
372C22×C61#52012yes—
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61C2×#12311yescharacteristic
376C22×C61#52511yescharacteristic
377C22×C61C2×#12411yescharacteristic
378C22×C61#52912yes—
379C22×C61C2×#12711yescharacteristic
380C22×C61#53411yescharacteristic
381C22×C61#53611yescharacteristic
382C22×C61#53912yes—
383C22×C61#54612yes—
384C22×C61#54612yes—
385C22×C61#54612yes—
386C22×C61#54712yes—
387C22×C61#54712yes—
388C22×C61#54712yes—
389C22×C61#55112yes—
390C22×C61#55212yes—
391C4×C61—28no—
392C4×C61—44no—
393C4×C61—42no—
394Dic61—24no—
395Dic61—42no—
396Dic61—44no—
397Dic61—44no—
398Dic61—81no—
399Dic61—81no—
400C22×#123D6111yescharacteristic
401C2×#386—611no—
402C2×#386—611no—
403C2×#385—611no—
404C2×#381—611no—
405C2×C4×C22⋊C4—611no—
406C22×#95—611no—
407#1445—612no—
408#1439—612no—
409#1437—612no—
410C4⋊#95—612no—
411C2×C61—28no—
412C2×C61—82no—
413C2×C61C2×#39011yescharacteristic
414C2×C61C4×#12311yescharacteristic
415C2×C61#232211yescharacteristic
416C2×C61#233912yes—
417C2×C61#235912yes—
418C2×C61#241211yescharacteristic
419C2×C61#241311yescharacteristic
420C2×C61#242512yes—
421C2×C61#248812yes—
422C2×C61#250111yescharacteristic
423C2×C61#253911yescharacteristic
424C23×D4C2×D6111yescharacteristic
425C24×C4—611no—
426C24×C4—611no—
427C24×C4C2×D6111yescharacteristic
428C2×#123—24no—
429C2×#123—24no—
430C2×#123Dic6118yescomplemented
431C22×C4⋊C4—612no—
432C22×C4⋊C4C2×D6112yes—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—612no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4C2×D6112yes—
439C22×C22⋊C4C2×D6111yescharacteristic
440C22×C42—612no—
441#386—1224no—
442#386—1224no—
443#385—1224no—
444#381—1224no—
445C4×C22⋊C4—1224no—
446C2×#95—611no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—612no—
454C2×#95—611no—
455C2×#95—1224no—
456C61#1399611yescharacteristic, complemented, Sylow
457C25C22×D6111yescharacteristic
458C25C22×D6111yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×Dic6114yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—611no—
473C23×C4—612no—
474C23×C4—612no—
475C23×C4—611no—
476C23×C4—614no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—1224no—
480C23×C4—1224no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—2442no—
487C23×C4—2442no—
488C23×C4C2×Dic6114yes—
489C23×C4C22×D6112yes—
490C23×C4C22×D6111yescharacteristic
491C23×C4C22×D6112yes—
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4—2442no—
498C2×C4⋊C4C2×Dic6118yescomplemented
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—614no—
502C2×C22⋊C4—1222no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1222no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—2442no—
513C2×C22⋊C4—2442no—
514C2×C22⋊C4C2×Dic6114yes—
515C2×C22⋊C4C2×Dic6118yescomplemented
516C2×C22⋊C4C22⋊D6114yes—
517C2×C22⋊C4C22⋊D6114yes—
518C2×C42—1224no—
519C2×C42—1224no—
520C2×C42—2442no—
521#95—1224no—
522#95—1224no—
523#95—1224no—
524#95—1224no—
525#95—1222no—
526#95—1224no—
527#95—1222no—
528#95—1224no—
529#95—1224no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24D4×D6112yes—
545C24D4×D6112yes—
546C24#1175822412yes—
547C24#1175822412yes—
548C24C22×Dic6112yes—
549C24C22×Dic6112yes—
550C24C2×C22⋊D6112yes—
551C24C2×C22⋊D6112yes—
552C24C23×D6111yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—612no—
584C22×C4—614no—
585C22×C4—614no—
586C22×C4—612no—
587C22×C4—614no—
588C22×C4—1228no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1228no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1221no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1228no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—2444no—
621C22×C4—2448no—
622C22×C4—2448no—
623C22×C4—2448no—
624C22×C4—2448no—
625C22×C4—2444no—
626C22×C4—2444no—
627C22×C4C22×Dic6114yes—
628C22×C4C22×Dic6112yes—
629C22×C4C22×Dic6114yes—
630C22×C4C2×C22⋊D6114yes—
631C22×C4C2×C22⋊D6114yes—
632C4⋊C4—216no—
633C4⋊C4—2448no—
634C22⋊C4—216no—
635C22⋊C4—1228no—
636C22⋊C4—2444no—
637C22⋊C4—2448no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C22⋊C4C22⋊Dic61116yescomplemented
641C42—2448no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—42no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊Dic6114yes—
682C23D4×Dic6114yes—
683C23D4×Dic6114yes—
684C23#1451974814yes—
685C23#1451974814yes—
686C23#1451976414yes—
687C23#1451977314yes—
688C23C23×Dic6111yescharacteristic
689C23C2×D4×D6111yescharacteristic
690C23C2×D4×D6111yescharacteristic
691C23C22×C22⋊D6111yescharacteristic
692C23C22×C22⋊D6111yescharacteristic
693C23#41×D6112yes—
694C23#41×D6112yes—
695C23C2×#1175822411yescharacteristic
696C23C2×#1175822411yescharacteristic
697C23#1451982312yes—
698C23#1451982412yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—416no—
721C2×C4—614no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1224no—
725C2×C4—1224no—
726C2×C4—1224no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1224no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—24416no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—24416no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4C2×C22⋊Dic6118yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—42no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22#1683966518yes—
780C22C22×C22⋊Dic6111yescharacteristic
781C22C2×D4×Dic6111yescharacteristic
782C22C2×D4×Dic6111yescharacteristic
783C22#41×Dic6112yes—
784C22#1684024512yes—
785C22C2×#1451974811yescharacteristic
786C22C2×#1451974811yescharacteristic
787C22#123×D6111yescharacteristic
788C22#1684027011yescharacteristic
789C22C2×#1451976411yescharacteristic
790C22#1684028912yes—
791C22C2×#1451977311yescharacteristic
792C22#1684032311yescharacteristic
793C22#1684033411yescharacteristic
794C22#1684035612yes—
795C22#1684040012yes—
796C22#1684040012yes—
797C22#1684040412yes—
798C22#1684041012yes—
799C22#1684041112yes—
800C22#1684041112yes—
801C22#1684043512yes—
802C22#1684044912yes—
803C4—28no—
804C4—44no—
805C4—42no—
806C4—1224no—
807C4—4881no—
808C4—4881no—
809C4—2444no—
810C4—2442no—
811C4—2444no—
812C2—28no—
813C2—82no—
814C2C2×#1683966511yescharacteristic
815C2#123×Dic6111yescharacteristic
816C2#2144849111yescharacteristic
817C2#2144864912yes—
818C2#2144881512yes—
819C2#2144921111yescharacteristic
820C2#2144922211yescharacteristic
821C2#2144936612yes—
822C2#2145014912yes—
823C2#2145028811yescharacteristic
824C2#2145074911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×#123×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC22×#123D61
hypocenterC61#13996
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C2×#16839637C2semidirect
4. C2×#16839625C2semidirect
5. C2×C22⋊C4×Dic61C2semidirect
6. C22×#14519684C2semidirect
7. #21444087C2semidirect
8. #21444064C2semidirect
9. #21444056C2semidirect
10. #21444048C2semidirect
40. C2×#123×C61C4semidirect
110. C2×C4⋊C4×C61C2×C4semidirect
114. C2×C22⋊C4×C61C2×C4semidirect
221. C22⋊C4×C61C22⋊C4semidirect
344. C2×Dic61#123semidirect
430. C2×#123Dic61semidirect
456. C61#13996semidirect
498. C2×C4⋊C4C2×Dic61semidirect
515. C2×C22⋊C4C2×Dic61semidirect
640. C22⋊C4C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396422
C2×#168396372
C2×#168396252
C2×C22⋊C4×Dic612
C22×#145196842
#214440872
#214440642
#214440562
#214440482
C22×#123×C612
#1399661