Finite Group Databasebeta

← #29601515

Subgroups — #29601515

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal
3C2×#16839609C212yesmaximal, complemented
4C2×#16839609C211yesmaximal, characteristic, complemented
5C2×#95×D61C211yesmaximal, characteristic, complemented
6#21444055C212yesmaximal, complemented
7#21444053C212yesmaximal, complemented
8#21444040C211yesmaximal, characteristic, complemented
9#21444040C211yesmaximal, characteristic, complemented
10C4×#14519684C211yesmaximal, characteristic, complemented
11C61×#1434C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C23×C4×D61C2211yescharacteristic
16C2×C4×D244—28no—
17C2×C4×D244C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25C22×C4×Dic61C2212yes—
26#16839640C4116yescomplemented
27#16839609—28no—
28#16839609—24no—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35#95×D61—24no—
36C22×C42×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C24×D61C2311yescharacteristic
42C24×D61C2311yescharacteristic
43C22×D244—24no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244C2×C414yes—
47C22×D244C2×C418yes—
48C23×Dic61C2312yes—
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2312yes—
52C22×C4×D61—24no—
53C22×C4×D61—24no—
54C22×C4×D61—24no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—24no—
62C22×C4×D61—42no—
63C22×C4×D61—42no—
64C22×C4×D61—42no—
65C22×C4×D61—42no—
66C22×C4×D61C2×C414yes—
67C22×C4×D61C2×C414yescomplemented
68C22×C4×D61C2×C418yescomplemented
69C4×D244—232no—
70C2×C4⋊Dic61—24no—
71C2×C4⋊Dic61C2×C414yescomplemented
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—24no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198C2×C414yes—
80C2×#11758198C2×C414yescomplemented
81C2×#11758198C2×C418yescomplemented
82C2×#11758198C2×C418yescomplemented
83C2×#11758198C2×C418yescomplemented
84C2×#11758198D418yes—
85C2×C4×Dic61—24no—
86C2×C4×Dic61—24no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61—24no—
89C2×C4×Dic61—42no—
90C2×C4×Dic61—42no—
91#14519684—22no—
92#14519684—24no—
93#14519684—24no—
94#14519684—42no—
95#14519684C2×C418yescomplemented
96#14519684D414yescomplemented
97C23×C4×C61C2312yes—
98C23×C4×C61C2312yes—
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C2×C42×C61—24no—
103C2×C42×C61C2×C414yescomplemented
104#95×C61—22no—
105#95×C61—24no—
106#95×C61—22no—
107#95×C61C2×C418yescomplemented
108C24×C61C2411yescharacteristic
109C23×D61—21no—
110C23×D61—21no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—22no—
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61C22×C412yes—
125C23×D61C22×C414yes—
126C23×D61C22×C412yes—
127C23×D61C22×C414yes—
128C23×D61C2×D414yes—
129C23×D61#4112yes—
130C23×D61#4112yes—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C22×C414yes—
153C22×C4×C61C22×C414yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C2×D414yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61#4112yes—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61C22×C412yes—
178C22×Dic61C22×C414yes—
179C22×Dic61C22×C412yes—
180C22×Dic61C22×C414yes—
181C22×Dic61C2×D414yes—
182C22×Dic61C2×D414yes—
183C22×Dic61#4114yes—
184C2×D244—28no—
185C2×D244—28no—
186C2×D244—216no—
187C2×D244—216no—
188C2×D244C42116yescomplemented
189C2×C4×D61—28no—
190C2×C4×D61—216no—
191C2×C4×D61—28no—
192C2×C4×D61—28no—
193C2×C4×D61—28no—
194C2×C4×D61—216no—
195C2×C4×D61—44no—
196C2×C4×D61—44no—
197C2×C4×D61—48no—
198C2×C4×D61—48no—
199C2×C4×D61—48no—
200C2×C4×D61—48no—
201C2×C4×D61—48no—
202C2×C4×D61—48no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C42×C61—28no—
207#11758198—216no—
208#11758198—28no—
209#11758198—216no—
210#11758198—48no—
211#11758198C22⋊C4116yescomplemented
212C4⋊Dic61—28no—
213C4×Dic61—48no—
214C4×Dic61—48no—
215C23×C61C23×C411yescharacteristic
216C23×C61C23×C412yes—
217C23×C61C22×D412yes—
218C23×C61C22×D411yescharacteristic
219C23×C61C2×#4111yescharacteristic
220C23×C61C2×#4111yescharacteristic
221C23×C61C2×#4111yescharacteristic
222C23×C61C2×#4112yes—
223C23×C61H(5,𝔽2)12yes—
224C23×C61H(5,𝔽2)11yescharacteristic
225C23×C612−1+411yescharacteristic
226C22×D61—22no—
227C22×D61—24no—
228C22×D61—22no—
229C22×D61—24no—
230C22×D61—22no—
231C22×D61—24no—
232C22×D61—22no—
233C22×D61—24no—
234C22×D61—24no—
235C22×D61—22no—
236C22×D61—24no—
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—22no—
240C22×D61—24no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—24no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—24no—
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—22no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—24no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—41no—
260C22×D61—42no—
261C22×D61—41no—
262C22×D61—42no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—42no—
266C22×D61C2×C4214yes—
267C22×D61C2×C4214yes—
268C22×D61C2×C22⋊C414yes—
269C22×D61#11714yes—
270C22×D61C4×D418yes—
271C22×D61C4×D418yes—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61C2×C4214yes—
299C2×C4×C61C2×C22⋊C414yes—
300C2×C4×C61C4×D414yes—
301C2×Dic61—22no—
302C2×Dic61—24no—
303C2×Dic61—22no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—22no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61C2×C22⋊C414yes—
324C2×Dic61C4×D418yescomplemented
325D244—232no—
326C4×D61—416no—
327C4×D61—432no—
328C4×D61—416no—
329#13813—611nomaximal, Sylow
330C22×C61C22×C4211yescharacteristic
331C22×C61C22×C22⋊C411yescharacteristic
332C22×C61C2×#11711yescharacteristic
333C22×C61C2×C4×D412yes—
334C22×C61C2×C4×D412yes—
335C22×C61C2×C4×D412yes—
336C22×C61C2×C4×D411yescharacteristic
337C22×C61C4×#4111yescharacteristic
338C22×C61C4×#4112yes—
339C22×C61#51811yescharacteristic
340C22×C61#51812yes—
341C22×C61#52011yescharacteristic
342C22×C61#52012yes—
343C22×C61D4212yes—
344C22×C61#54612yes—
345C22×C61#54612yes—
346C22×C61#54611yescharacteristic
347C22×C61#54712yes—
348C22×C61#54811yescharacteristic
349C22×C61#55112yes—
350C22×C61#55211yescharacteristic
351C22×C61#55312yes—
352C22×C61#55311yescharacteristic
353C2×D61—24no—
354C2×D61—24no—
355C2×D61—24no—
356C2×D61—24no—
357C2×D61—28no—
358C2×D61—28no—
359C2×D61—28no—
360C2×D61—28no—
361C2×D61—24no—
362C2×D61—24no—
363C2×D61—24no—
364C2×D61—24no—
365C2×D61—24no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61C4×C22⋊C418yescomplemented
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—44no—
379C4×C61—44no—
380Dic61—24no—
381Dic61—28no—
382Dic61—42no—
383Dic61—44no—
384C22×C4×D4—611no—
385C2×#386—612no—
386C2×C4×C22⋊C4—612no—
387C2×C4×C22⋊C4—611no—
388C22×#95—611no—
389#1437—612no—
390#1436—612no—
391#1434D6111yescharacteristic, complemented
392C22⋊#95—611no—
393C22⋊#95—611no—
394C4×#95—611no—
395C2×C61C2×C4×C22⋊C411yescharacteristic
396C2×C61C42×D411yescharacteristic
397C2×C61#227511yescharacteristic
398C2×C61D4×C22⋊C411yescharacteristic
399C2×C61#233911yescharacteristic
400C2×C61#235211yescharacteristic
401C2×C61#235311yescharacteristic
402C2×C61#235812yes—
403C2×C61#235912yes—
404C2×C61#236112yes—
405C2×C61#236412yes—
406D61—28no—
407D61—44no—
408C23×D4—611no—
409C24×C4—611no—
410C24×C4—611no—
411C24×C4—612no—
412C2×C4×D4—618no—
413C2×C4×D4—1228no—
414C22×C4⋊C4—611no—
415C22×C22⋊C4—611no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4—612no—
420C22×C42—612no—
421C22×C42—612no—
422C22×C42C2×D6111yescharacteristic
423#386—6116no—
424C4×C22⋊C4—1224no—
425C4×C22⋊C4—1228no—
426C2×#95—612no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95—612no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95—1224no—
433C2×#95C2×D6111yescharacteristic
434C2×#95C2×D6111yescharacteristic
435C2×#95C2×D6112yes—
436C2×#95C2×D6112yes—
437C61#1381311yescharacteristic, complemented, Sylow
438C25—611no—
439C25—611no—
440C22×D4—614no—
441C22×D4—618no—
442C22×D4—1224no—
443C22×D4—1222no—
444C22×D4—1222no—
445C23×C4—611no—
446C23×C4—612no—
447C23×C4—612no—
448C23×C4—611no—
449C23×C4—614no—
450C23×C4—614no—
451C23×C4—618no—
452C23×C4—1224no—
453C23×C4—1224no—
454C23×C4—1224no—
455C23×C4—1224no—
456C23×C4—1224no—
457C23×C4—1224no—
458C23×C4—1222no—
459C23×C4—1222no—
460C23×C4—1222no—
461C23×C4—1222no—
462C23×C4—2442no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4—2442no—
466C23×C4C22×D6112yes—
467C23×C4C22×D6112yes—
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C4×D4—12232no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—1224no—
474C2×C22⋊C4—614no—
475C2×C22⋊C4—618no—
476C2×C22⋊C4—614no—
477C2×C22⋊C4—618no—
478C2×C22⋊C4—618no—
479C2×C22⋊C4—618no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C22⋊C4—2442no—
486C2×C22⋊C4—2442no—
487C2×C42—24no—
488C2×C42—1224no—
489C2×C42—1224no—
490C2×C42—1224no—
491C2×C42—1224no—
492C2×C42—2442no—
493C2×C42—2442no—
494C2×C42C4×D6114yescomplemented
495#95—22no—
496#95—24no—
497#95—22no—
498#95—618no—
499#95—614no—
500#95—1224no—
501#95—1224no—
502#95—1222no—
503#95—2442no—
504#95C4×D6118yescomplemented
505C24—612no—
506C24—614no—
507C24—614no—
508C24—612no—
509C24—612no—
510C24—614no—
511C24—612no—
512C24—1221no—
513C24—1222no—
514C24—1221no—
515C24—1222no—
516C24—1221no—
517C24—1221no—
518C24—1221no—
519C24—1222no—
520C24—1222no—
521C24—1221no—
522C24—1221no—
523C24—1221no—
524C24—1221no—
525C24—1222no—
526C24—1221no—
527C24C23×D6111yescharacteristic
528C2×D4—6116no—
529C2×D4—1228no—
530C2×D4—1228no—
531C2×D4—12216no—
532C2×D4—12216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—614no—
554C22×C4—612no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—614no—
558C22×C4—614no—
559C22×C4—612no—
560C22×C4—1228no—
561C22×C4—12216no—
562C22×C4—1228no—
563C22×C4—12216no—
564C22×C4—1222no—
565C22×C4—1221no—
566C22×C4—1222no—
567C22×C4—1221no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1221no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1228no—
582C22×C4—1228no—
583C22×C4—2444no—
584C22×C4—2444no—
585C22×C4—2448no—
586C22×C4—2448no—
587C22×C4—2448no—
588C22×C4—2448no—
589C22×C4—2448no—
590C22×C4—2448no—
591C22×C4—2448no—
592C22×C4—2448no—
593C22×C4—2448no—
594C22×C4C2×C4×D6114yes—
595C22×C4C2×C4×D6114yes—
596C22×C4C2×C4×D6114yes—
597C22×C4C2×C4×D6112yes—
598C22×C4C2×C4×D6112yes—
599C22×C4C2×C4×D6112yes—
600C22×C4D4×D6114yes—
601C22×C4D4×D6112yes—
602C22×C4#1175822612yes—
603C4⋊C4—1228no—
604C22⋊C4—6116no—
605C22⋊C4—12216no—
606C22⋊C4—12216no—
607C22⋊C4—1228no—
608C22⋊C4—2448no—
609C42—28no—
610C42—2448no—
611C42—2448no—
612C23—614no—
613C23—614no—
614C23—614no—
615C23—618no—
616C23—618no—
617C23—614no—
618C23—1222no—
619C23—1224no—
620C23—1222no—
621C23—1224no—
622C23—1222no—
623C23—1222no—
624C23—1224no—
625C23—1222no—
626C23—1224no—
627C23—1222no—
628C23—1224no—
629C23—1224no—
630C23—1224no—
631C23—1224no—
632C23—1222no—
633C23—1224no—
634C23—1222no—
635C23—1224no—
636C23—1222no—
637C23—1222no—
638C23—1224no—
639C23—1224no—
640C23—1224no—
641C23—1222no—
642C23—1222no—
643C23—1224no—
644C23—1224no—
645C23—1222no—
646C23—1222no—
647C23—1224no—
648C23—2441no—
649C23—2442no—
650C23—2441no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23—2441no—
655C23—2442no—
656C23—2441no—
657C23—2442no—
658C23C22×C4×D6111yescharacteristic
659C23C22×C4×D6112yes—
660C23C2×D4×D6112yes—
661C23C2×D4×D6111yescharacteristic
662C23#41×D6111yescharacteristic
663C23#41×D6111yescharacteristic
664C23#41×D6112yes—
665C23C2×#1175822611yescharacteristic
666C23#1451982312yes—
667C23#1451982311yescharacteristic
668C23#1451982411yescharacteristic
669D4—12232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—614no—
697C2×C4—618no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1224no—
701C2×C4—1222no—
702C2×C4—1224no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1224no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1222no—
709C2×C4—1224no—
710C2×C4—1222no—
711C2×C4—1224no—
712C2×C4—1224no—
713C2×C4—1222no—
714C2×C4—24416no—
715C2×C4—24416no—
716C2×C4—24432no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4C42×D6114yes—
724C2×C4C22⋊C4×D6114yes—
725C2×C4#1451973914yes—
726C22—618no—
727C22—1224no—
728C22—1224no—
729C22—1228no—
730C22—1228no—
731C22—1228no—
732C22—1228no—
733C22—1224no—
734C22—1224no—
735C22—1224no—
736C22—1224no—
737C22—1224no—
738C22—1224no—
739C22—1224no—
740C22—2442no—
741C22—2442no—
742C22—2444no—
743C22—2444no—
744C22—2444no—
745C22—2444no—
746C22—2442no—
747C22—2442no—
748C22C2×C42×D6111yescharacteristic
749C22C2×C22⋊C4×D6111yescharacteristic
750C22#117×D6111yescharacteristic
751C22C4×D4×D6112yes—
752C22C4×D4×D6112yes—
753C22C4×D4×D6112yes—
754C22C2×#1451973911yescharacteristic
755C22#1684023011yescharacteristic
756C22C4×#1175822612yes—
757C22#1684023611yescharacteristic
758C22#1684023612yes—
759C22#1684024211yescharacteristic
760C22#1684024212yes—
761C22#1684039612yes—
762C22#1684040312yes—
763C22#1684040412yes—
764C22#1684040511yescharacteristic
765C22#1684041012yes—
766C22#1684042011yescharacteristic
767C22#1684043712yes—
768C22#1684045011yescharacteristic
769C22#1684046312yes—
770C22#1684046511yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—44no—
775C4—44no—
776C4—1228no—
777C4—1224no—
778C4—2444no—
779C4—2442no—
780C2—1228no—
781C2—2444no—
782C2C4×C22⋊C4×D6111yescharacteristic
783C2C4×#1451973911yescharacteristic
784C2#2144818111yescharacteristic
785C2#2144863911yescharacteristic
786C2#2144864311yescharacteristic
787C2#2144874511yescharacteristic
788C2#2144875211yescharacteristic
789C2#2144879712yes—
790C2#2144881812yes—
791C2#2144883212yes—
792C2#2144886512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#13813
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16839609C2semidirect
4. C2×#16839609C2semidirect
5. C2×#95×D61C2semidirect
6. #21444055C2semidirect
7. #21444053C2semidirect
8. #21444040C2semidirect
9. #21444040C2semidirect
10. C4×#14519684C2semidirect
11. C61×#1434C2semidirect
17. C2×C4×D244C4semidirect
26. #16839640C4semidirect
67. C22×C4×D61C2×C4semidirect
68. C22×C4×D61C2×C4semidirect
71. C2×C4⋊Dic61C2×C4semidirect
80. C2×#11758198C2×C4semidirect
81. C2×#11758198C2×C4semidirect
82. C2×#11758198C2×C4semidirect
83. C2×#11758198C2×C4semidirect
95. #14519684C2×C4semidirect
96. #14519684D4semidirect
103. C2×C42×C61C2×C4semidirect
107. #95×C61C2×C4semidirect
188. C2×D244C42semidirect
211. #11758198C22⋊C4semidirect
324. C2×Dic61C4×D4semidirect
374. C2×D61C4×C22⋊C4semidirect
391. #1434D61semidirect
437. C61#13813semidirect
494. C2×C42C4×D61semidirect
504. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C2×#168396402
C2×#168396092
C2×#95×D612
#214440552
#214440532
#214440402
C4×#145196842
C61×#14342
#1381361