Finite Group Databasebeta

← #29602058

Subgroups — #29602058

Order 15616.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C212yesmaximal, complemented
2C2×#16839625C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
4#21444064C212yesmaximal, complemented
5#21444060C212yesmaximal
6#21444051C212yesmaximal, complemented
7#21444049C211yesmaximal, characteristic, complemented
8#21444046C211yesmaximal, characteristic, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C22×C4×D4×C61C211yesmaximal, characteristic
12C22×C4⋊Dic61C2212yes—
13C22×C22⋊Dic61C2212yes—
14C22×C22⋊Dic61C2212yes—
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C4×Dic61C2212yes—
18#16839655—28no—
19#16839625—24no—
20C4×C22⋊Dic61—24no—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C23×D4×C61C2211yescharacteristic
32C24×C4×C61C2211yescharacteristic
33C24×C4×C61C2211yescharacteristic
34C2×C4×D4×C61—28no—
35C2×C4×D4×C61C418yescomplemented
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C2×C4⋊Dic61—24no—
45C2×C4⋊Dic61—24no—
46C2×C4⋊Dic61—42no—
47C2×C22⋊Dic61—24no—
48C2×C22⋊Dic61—24no—
49C2×C22⋊Dic61—24no—
50C2×C22⋊Dic61—24no—
51C2×C22⋊Dic61—24no—
52C2×C22⋊Dic61—24no—
53C2×C22⋊Dic61—24no—
54C2×C22⋊Dic61—24no—
55C2×C22⋊Dic61—42no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—42no—
58C2×C22⋊Dic61—42no—
59C2×C4×Dic61—24no—
60C2×C4×Dic61—24no—
61C2×C4×Dic61—42no—
62#14519684—22no—
63#14519684—22no—
64#14519684—24no—
65#14519684—24no—
66#14519684—24no—
67#14519684—24no—
68#14519684—22no—
69#14519684—24no—
70#14519684—42no—
71#14519684D414yescomplemented
72C25×C61C2311yescharacteristic
73C25×C61C2311yescharacteristic
74C22×D4×C61—24no—
75C22×D4×C61—24no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61C2×C414yes—
79C23×C4×C61—24no—
80C23×C4×C61—22no—
81C23×C4×C61—22no—
82C23×C4×C61—24no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—42no—
86C23×C4×C61—42no—
87C23×C4×C61C2×C414yes—
88C23×C4×C61C2×C414yes—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C4×D4×C61—232no—
95C2×C4⋊C4×C61—24no—
96C2×C4⋊C4×C61C2×C414yes—
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61C2×C414yes—
99C2×C22⋊C4×C61C2×C414yes—
100C2×C22⋊C4×C61D418yes—
101C2×C42×C61—24no—
102C2×C42×C61C2×C414yes—
103C24×C61—22no—
104C24×C61—21no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—21no—
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—21no—
121C24×C61C22×C412yes—
122C24×C61C22×C412yes—
123C24×C61C2×D414yes—
124C24×C61#4114yes—
125C24×C61C2411yescharacteristic
126C2×D4×C61—216no—
127C2×D4×C61—216no—
128C2×D4×C61—28no—
129C2×D4×C61—28no—
130C2×D4×C61—28no—
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—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—28no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—28no—
147C22×C4×C61—28no—
148C22×C4×C61—28no—
149C22×C4×C61—44no—
150C22×C4×C61—44no—
151C22×C4×C61—48no—
152C22×C4×C61—48no—
153C22×C4×C61—48no—
154C22×C4×C61—48no—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D414yes—
161C22×C4×C61C2×D414yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C22×C4×C61#4112yes—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61C2×D414yes—
193C22×Dic61#4114yes—
194C4⋊C4×C61—28no—
195C22⋊C4×C61—28no—
196C22⋊C4×C61C22⋊C4116yescomplemented
197C42×C61—28no—
198C22⋊Dic61—216no—
199C22⋊Dic61—48no—
200C22⋊Dic61—48no—
201C22⋊Dic61—48no—
202C4⋊Dic61—48no—
203C4×Dic61—48no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61C2×C22⋊C414yes—
249C23×C61#11714yes—
250C23×C61C23×C411yescharacteristic
251C23×C61C22×D412yes—
252C23×C61C22×D411yescharacteristic
253C23×C61C2×#4112yes—
254C23×C61C2×#4111yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61C2×#4111yescharacteristic
257C23×C61C2×#4112yes—
258C23×C61H(5,𝔽2)12yes—
259C23×C61H(5,𝔽2)11yescharacteristic
260C23×C612−1+411yescharacteristic
261D4×C61—232no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—24no—
271C2×C4×C61—24no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—416no—
282C2×C4×C61—416no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61C2×C22⋊C414yes—
286C2×C4×C61C2×C22⋊C414yes—
287C2×C4×C61#11714yes—
288C2×C4×C61C4×D414yes—
289C2×Dic61—24no—
290C2×Dic61—24no—
291C2×Dic61—24no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—42no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317#13886—611nomaximal, Sylow
318C22×C61—24no—
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—24no—
322C22×C61—24no—
323C22×C61—24no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61—44no—
336C22×C61—44no—
337C22×C61—44no—
338C22×C61—44no—
339C22×C61—42no—
340C22×C61C22×C22⋊C411yescharacteristic
341C22×C61C2×#11711yescharacteristic
342C22×C61C2×#11711yescharacteristic
343C22×C61C2×C4×D411yescharacteristic
344C22×C61C4×#4111yescharacteristic
345C22×C61#51811yescharacteristic
346C22×C61#52011yescharacteristic
347C22×C61#52512yes—
348C22×C61#52512yes—
349C22×C61#52512yes—
350C22×C61#52912yes—
351C22×C61#53812yes—
352C22×C61#53912yes—
353C22×C61D4212yes—
354C22×C61#54612yes—
355C22×C61#54612yes—
356C22×C61#54712yes—
357C22×C61#54711yescharacteristic
358C22×C61#55011yescharacteristic
359C22×C61#55312yes—
360C22×C61#55511yescharacteristic
361C22×C61#55611yescharacteristic
362C22×C61#55912yes—
363C4×C61—24no—
364C4×C61—24no—
365C4×C61—24no—
366C4×C61—24no—
367C4×C61—42no—
368Dic61—44no—
369Dic61—44no—
370Dic61—82no—
371Dic61—82no—
372C22×C4×D4D6111yescharacteristic
373C2×#388—612no—
374C2×#381—611no—
375C2×C4×C22⋊C4—611no—
376#1439—612no—
377#1438—612no—
378#1436—612no—
379C4⋊#95—611no—
380#1434—611no—
381C22⋊#95—611no—
382C22⋊#95—611no—
383C2×C61—44no—
384C2×C61—44no—
385C2×C61#228011yescharacteristic
386C2×C61#229011yescharacteristic
387C2×C61#231811yescharacteristic
388C2×C61D4×C22⋊C411yescharacteristic
389C2×C61#233911yescharacteristic
390C2×C61#235411yescharacteristic
391C2×C61#235711yescharacteristic
392C2×C61#245512yes—
393C2×C61#245612yes—
394C2×C61#245912yes—
395C2×C61#246612yes—
396C23×D4C2×D6111yescharacteristic
397C24×C4C2×D6111yescharacteristic
398C24×C4C2×D6111yescharacteristic
399C2×C4×D4—28no—
400C2×C4×D4Dic6118yescomplemented
401C22×C4⋊C4—612no—
402C22×C4⋊C4C2×D6111yescharacteristic
403C22×C22⋊C4—612no—
404C22×C22⋊C4—612no—
405C22×C22⋊C4—612no—
406C22×C22⋊C4—612no—
407C22×C22⋊C4C2×D6111yescharacteristic
408C22×C22⋊C4C2×D6111yescharacteristic
409C22×C42—612no—
410C22×C42C2×D6111yescharacteristic
411#388—1228no—
412#381—1224no—
413C4×C22⋊C4—1224no—
414C2×#95—611no—
415C2×#95—611no—
416C2×#95—611no—
417C2×#95—611no—
418C2×#95—612no—
419C2×#95—612no—
420C2×#95—612no—
421C2×#95—612no—
422C2×#95—612no—
423C2×#95—612no—
424C61#1388611yescharacteristic, complemented, Sylow
425C25C22×D6111yescharacteristic
426C25C22×D6111yescharacteristic
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4C2×Dic6114yes—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—612no—
441C23×C4—612no—
442C23×C4—612no—
443C23×C4—612no—
444C23×C4C2×Dic6114yes—
445C23×C4C2×Dic6114yes—
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C23×C4C22×D6111yescharacteristic
449C23×C4C22×D6111yescharacteristic
450C23×C4C22×D6111yescharacteristic
451C4×D4—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—1224no—
454C2×C4⋊C4—1224no—
455C2×C4⋊C4—2442no—
456C2×C4⋊C4C2×Dic6114yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—1224no—
459C2×C22⋊C4—1224no—
460C2×C22⋊C4—1224no—
461C2×C22⋊C4—1224no—
462C2×C22⋊C4—1224no—
463C2×C22⋊C4—1224no—
464C2×C22⋊C4—1224no—
465C2×C22⋊C4—1224no—
466C2×C22⋊C4—2442no—
467C2×C22⋊C4—2442no—
468C2×C22⋊C4—2442no—
469C2×C22⋊C4—2442no—
470C2×C22⋊C4C2×Dic6114yes—
471C2×C22⋊C4C2×Dic6114yes—
472C2×C22⋊C4C22⋊D6118yes—
473C2×C42—24no—
474C2×C42—1224no—
475C2×C42—1224no—
476C2×C42—2442no—
477C2×C42C2×Dic6114yes—
478#95—614no—
479#95—1224no—
480#95—1224no—
481#95—1224no—
482#95—1222no—
483#95—1222no—
484#95—1222no—
485#95—1224no—
486#95—1224no—
487#95—2442no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24#1175822214yes—
507C24C22×Dic6112yes—
508C24C22×Dic6112yes—
509C24C2×C22⋊D6114yes—
510C24C23×D6111yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—614no—
541C22×C4—614no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4#1175822212yes—
569C22×C4#1175822212yes—
570C22×C4D4×D6112yes—
571C22×C4#1175822412yes—
572C22×C4C22×Dic6112yes—
573C22×C4C22×Dic6112yes—
574C22×C4C22×Dic6112yes—
575C22×C4C22×Dic6112yes—
576C22×C4C22×Dic6112yes—
577C22×C4C2×C22⋊D6114yes—
578C22×C4C2×C22⋊D6114yes—
579C4⋊C4—28no—
580C4⋊C4—2448no—
581C22⋊C4—28no—
582C22⋊C4—12216no—
583C22⋊C4—2448no—
584C22⋊C4—2448no—
585C22⋊C4—2448no—
586C22⋊C4C22⋊Dic61116yescomplemented
587C42—28no—
588C42—2448no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C22⋊Dic6114yes—
634C23#1451973614yes—
635C23C23×Dic6111yescharacteristic
636C23C2×D4×D6111yescharacteristic
637C23C22×C22⋊D6112yes—
638C23#41×D6112yes—
639C23C2×#1175822411yescharacteristic
640C23C2×#1175822211yescharacteristic
641C23C2×#1175822211yescharacteristic
642C23C2×#1175822212yes—
643C23#1451982212yes—
644C23#1451982311yescharacteristic
645C23#1451982411yescharacteristic
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—1224no—
671C2×C4—1224no—
672C2×C4—1224no—
673C2×C4—1224no—
674C2×C4—1224no—
675C2×C4—1224no—
676C2×C4—2442no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4C2×C22⋊Dic6114yes—
699C2×C4C2×C22⋊Dic6114yes—
700C2×C4#1451973614yes—
701C2×C4D4×Dic6114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—44no—
710C22—44no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22C22×C22⋊Dic6111yescharacteristic
725C22C2×#1451973611yescharacteristic
726C22C2×#1451973611yescharacteristic
727C22C2×D4×Dic6111yescharacteristic
728C22#41×Dic6111yescharacteristic
729C22#1684023711yescharacteristic
730C22#1684024511yescharacteristic
731C22#1684027112yes—
732C22#1684027312yes—
733C22#1684027312yes—
734C22#1684029212yes—
735C22#1684034512yes—
736C22#1684035412yes—
737C22D4×C22⋊D6112yes—
738C22#1684040012yes—
739C22#1684040612yes—
740C22#1684041112yes—
741C22#1684041711yescharacteristic
742C22#1684043311yescharacteristic
743C22#1684046212yes—
744C22#1684047711yescharacteristic
745C22#1684048211yescharacteristic
746C22#1684049512yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—4882no—
753C4—4882no—
754C4—2444no—
755C4—2444no—
756C2—44no—
757C2—44no—
758C2#2144820211yescharacteristic
759C2#2144826411yescharacteristic
760C2#2144845211yescharacteristic
761C2D4×C22⋊Dic6111yescharacteristic
762C2#2144864911yescharacteristic
763C2#2144876811yescharacteristic
764C2#2144879211yescharacteristic
765C2#2144969612yes—
766C2#2144971112yes—
767C2#2144975012yes—
768C2#2144984912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×C4×D4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC22×C4×D4D61
hypocenterC61#13886
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16839655C2semidirect
2. C2×#16839625C2semidirect
3. C2×C4×C22⋊Dic61C2semidirect
4. #21444064C2semidirect
6. #21444051C2semidirect
7. #21444049C2semidirect
8. #21444046C2semidirect
9. #21444042C2semidirect
10. #21444042C2semidirect
35. C2×C4×D4×C61C4semidirect
71. #14519684D4semidirect
196. C22⋊C4×C61C22⋊C4semidirect
400. C2×C4×D4Dic61semidirect
424. C61#13886semidirect
586. C22⋊C4C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×#168396252
C2×C4×C22⋊Dic612
#214440642
#214440602
#214440512
#214440492
#214440462
#214440422
C22×C4×D4×C612
#1388661