Finite Group Databasebeta

← #29602791

Subgroups — #29602791

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519760C211yesmaximal, characteristic
2C22×#14519737C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C22×#14519684C211yesmaximal, characteristic, complemented
5#21444070C212yesmaximal, complemented
6#21444067C212yesmaximal, complemented
7#21444050C212yesmaximal, complemented
8#21444041C211yesmaximal, characteristic, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C61×#381C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×#14519760—24no—
17C2×#14519760—24no—
18C2×#14519760C418yescomplemented
19C2×#14519737—24no—
20C2×#14519737—24no—
21C2×#14519737—24no—
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2212yes—
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2212yes—
27C22×#11758198C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839639—24no—
30C2×#14519684—24no—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C61×#381—24no—
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61C2×C414yes—
50C22×C22⋊D61D414yes—
51C22×C22⋊D61D414yes—
52C23×Dic61—22no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—24no—
56C23×Dic61—24no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—42no—
60C23×Dic61—42no—
61C23×Dic61D414yes—
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—24no—
71C22×C4×D61—42no—
72#14519760—232no—
73#14519737—232no—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—24no—
78C2×#11758196—24no—
79C2×#11758196C2×C418yescomplemented
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61C2×C414yescomplemented
83C2×#11758198—22no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—42no—
91C2×#11758198C2×C418yescomplemented
92C2×C4×Dic61—22no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95#14519684—24no—
96#14519684—24no—
97#14519684—24no—
98#14519684—24no—
99#14519684—24no—
100#14519684—42no—
101#14519684—42no—
102C25×C61C2311yescharacteristic
103C23×C4×C61—22no—
104C23×C4×C61—22no—
105C23×C4×C61—22no—
106C23×C4×C61—22no—
107C23×C4×C61—22no—
108C23×C4×C61—22no—
109C23×C4×C61C2×C414yescomplemented
110C23×C4×C61C2312yes—
111C23×C4×C61C2312yes—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61D414yes—
120#95×C61—24no—
121#95×C61—24no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61C22×C412yes—
127C24×C61C2×D412yes—
128C24×C61C2×D412yes—
129C24×C61C2×D412yes—
130C24×C61C2×D412yes—
131C24×C61#4112yes—
132C24×C61#4112yes—
133C24×C61C2411yescharacteristic
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—22no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61C22×C412yes—
143C23×D61C2×D412yes—
144C23×D61C2×D412yes—
145C22×C4×C61—28no—
146C22×C4×C61—28no—
147C22×C4×C61—28no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—44no—
170C22×C4×C61—44no—
171C22×C4×C61—44no—
172C22×C4×C61—44no—
173C22×C4×C61C22×C414yes—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×D412yes—
176C2×C22⋊D61—28no—
177C2×C22⋊D61—28no—
178C2×C22⋊D61—28no—
179C2×C22⋊D61—28no—
180C2×C22⋊D61—28no—
181C2×C22⋊D61—28no—
182C2×C22⋊D61C22⋊C4116yes—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—22no—
190C22×Dic61—28no—
191C22×Dic61—28no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—28no—
209C22×Dic61—44no—
210C22×Dic61—48no—
211C22×Dic61—48no—
212C22×Dic61—48no—
213C22×Dic61—48no—
214C22×Dic61—44no—
215C22×Dic61—44no—
216C22×Dic61C22×C414yes—
217C22×Dic61C22×C412yes—
218C22×Dic61C2×D412yes—
219C22×Dic61C2×D412yes—
220C22×Dic61C2×D412yes—
221C22×Dic61C2×D412yes—
222C22×Dic61#4114yes—
223C22×Dic61#4114yes—
224C2×C4×D61—28no—
225C2×C4×D61—48no—
226C2×C4×D61—48no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C22⋊C4×C61—28no—
230C22⋊C4×C61—44no—
231C22⋊Dic61—28no—
232#11758198—28no—
233#11758198—216no—
234#11758198—48no—
235#11758196—28no—
236#11758196—216no—
237C4×Dic61—28no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—24no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61—24no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—24no—
251C23×C61—24no—
252C23×C61—24no—
253C23×C61—24no—
254C23×C61C2×C22⋊C414yes—
255C23×C61C4×D414yes—
256C23×C61C4×D414yes—
257C23×C61#12014yes—
258C23×C61#12114yes—
259C23×C61#12114yes—
260C23×C61#12314yes—
261C23×C61C23×C411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C22×D411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4111yescharacteristic
268C23×C61C2×#4112yes—
269C23×C61C2×#4112yes—
270C23×C61H(5,𝔽2)12yes—
271C23×C612−1+412yes—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—24no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—42no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61C2×C22⋊C414yes—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—416no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C22⋊D61—232no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—24no—
333C2×Dic61—24no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—24no—
337C2×Dic61—22no—
338C2×Dic61—24no—
339C2×Dic61—24no—
340C2×Dic61—416no—
341C2×Dic61—416no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C2×C22⋊C414yes—
353C2×Dic61#12314yescomplemented
354C4×D61—416no—
355#13968—611nomaximal, Sylow
356C22×C61—24no—
357C22×C61—28no—
358C22×C61—28no—
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—28no—
362C22×C61—28no—
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61#38618yes—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C2×C4×D411yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61C4×#4112yes—
371C22×C61#52012yes—
372C22×C61C2×#12011yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61C2×#12311yescharacteristic
376C22×C61C2×#12311yescharacteristic
377C22×C61#52511yescharacteristic
378C22×C61#52912yes—
379C22×C61#53411yescharacteristic
380C22×C61#53611yescharacteristic
381C22×C61#53912yes—
382C22×C61#54612yes—
383C22×C61#54612yes—
384C22×C61#54612yes—
385C22×C61#54712yes—
386C22×C61#54712yes—
387C22×C61#54712yes—
388C22×C61#55112yes—
389C22×C61#55212yes—
390C2×D61—28no—
391C2×D61—24no—
392C2×D61—42no—
393C2×D61—44no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—44no—
397C2×D61—44no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—44no—
404C4×C61—82no—
405Dic61—24no—
406Dic61—24no—
407Dic61—44no—
408Dic61—42no—
409Dic61—44no—
410C22×#123—611no—
411C22×C4×D4—611no—
412C2×#386—611no—
413C2×#381D6111yescharacteristic, complemented
414C22×#95—611no—
415#1441—612no—
416#1440—612no—
417#1436—612no—
418C22⋊#95—612no—
419C22⋊#95—611no—
420C22⋊#95—611no—
421C2×C61—28no—
422C2×C61C2×#38611yescharacteristic
423C2×C61C4×#12311yescharacteristic
424C2×C61#232211yescharacteristic
425C2×C61#233912yes—
426C2×C61#235912yes—
427C2×C61#240511yescharacteristic
428C2×C61#240611yescharacteristic
429C2×C61#241912yes—
430C2×C61#242512yes—
431C2×C61#248611yescharacteristic
432C2×C61#253411yescharacteristic
433D61—44no—
434C23×D4—611no—
435C24×C4—611no—
436C24×C4—611no—
437C24×C4—611no—
438C24×C4C2×D6111yescharacteristic
439C2×#123—618no—
440C2×#123—1224no—
441C2×#123—1224no—
442C2×C4×D4—1224no—
443C2×C4×D4—1224no—
444C2×C4×D4—1224no—
445C22×C4⋊C4—612no—
446C22×C4⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—612no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—612no—
451C22×C22⋊C4C2×D6111yescharacteristic
452C22×C22⋊C4C2×D6111yescharacteristic
453C22×C42—611no—
454#386—1224no—
455#381—24no—
456C2×#95—612no—
457C2×#95—612no—
458C2×#95—612no—
459C2×#95—612no—
460C2×#95—612no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—1224no—
464C2×#95C2×D6112yes—
465C2×#95C2×D6112yes—
466C61#1396811yescharacteristic, complemented, Sylow
467C25—611no—
468C25C22×D6111yescharacteristic
469C22×D4—614no—
470C22×D4—614no—
471C22×D4—614no—
472C22×D4—1222no—
473C22×D4—1222no—
474C22×D4—1222no—
475C22×D4—1222no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—612no—
485C23×C4—611no—
486C23×C4—612no—
487C23×C4—614no—
488C23×C4—1222no—
489C23×C4—1224no—
490C23×C4—1222no—
491C23×C4—1224no—
492C23×C4—1224no—
493C23×C4—1222no—
494C23×C4—1222no—
495C23×C4—1222no—
496C23×C4—1222no—
497C23×C4—1222no—
498C23×C4—1222no—
499C23×C4—2442no—
500C23×C4—2442no—
501C23×C4—2442no—
502C23×C4C4×D6114yescomplemented
503C23×C4C22×D6112yes—
504C23×C4C22×D6112yes—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507#123—12232no—
508C4×D4—12232no—
509C2×C4⋊C4—618no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1224no—
513C2×C4⋊C4—1224no—
514C2×C4⋊C4—1222no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—618no—
522C2×C22⋊C4—1222no—
523C2×C22⋊C4—1222no—
524C2×C22⋊C4—1224no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—1224no—
531C2×C22⋊C4—2442no—
532C2×C22⋊C4C22⋊D6114yes—
533C2×C42—1222no—
534C2×C42—1222no—
535C2×C42—1222no—
536#95—24no—
537#95—24no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541#95—1224no—
542#95—1224no—
543#95—2442no—
544#95—2442no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—612no—
550C24—612no—
551C24—612no—
552C24—1221no—
553C24—1221no—
554C24—1222no—
555C24—1222no—
556C24—1221no—
557C24—1221no—
558C24—1222no—
559C24—1222no—
560C24C2×C4×D6112yes—
561C24#1175822212yes—
562C24D4×D6112yes—
563C24D4×D6112yes—
564C24D4×D6112yes—
565C24#1175822412yes—
566C24C2×C22⋊D6112yes—
567C24C23×D6111yescharacteristic
568C2×D4—6116no—
569C2×D4—1228no—
570C2×D4—1228no—
571C2×D4—1228no—
572C2×D4—1228no—
573C2×D4—1228no—
574C2×D4—1228no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—614no—
608C22×C4—614no—
609C22×C4—612no—
610C22×C4—614no—
611C22×C4—1228no—
612C22×C4—1228no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1222no—
620C22×C4—1228no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1228no—
638C22×C4—2448no—
639C22×C4—2444no—
640C22×C4—2448no—
641C22×C4—2444no—
642C22×C4—2444no—
643C22×C4—2448no—
644C22×C4—2448no—
645C22×C4—2448no—
646C22×C4—2448no—
647C22×C4—2444no—
648C22×C4—2444no—
649C22×C4C2×C4×D6114yes—
650C22×C4C2×C22⋊D6112yes—
651C22×C4C2×C22⋊D6112yes—
652C4⋊C4—12216no—
653C4⋊C4—1228no—
654C22⋊C4—28no—
655C22⋊C4—44no—
656C22⋊C4—12216no—
657C22⋊C4—1228no—
658C22⋊C4—1228no—
659C22⋊C4—2448no—
660C42—1228no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—614no—
678C23—1222no—
679C23—1222no—
680C23—1224no—
681C23—1224no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1224no—
687C23—1224no—
688C23—1224no—
689C23—1224no—
690C23—2441no—
691C23—2441no—
692C23—2442no—
693C23—2441no—
694C23—2441no—
695C23—2442no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23C22⋊C4×D6114yes—
701C23#1451973714yes—
702C23C4×C22⋊D6114yes—
703C23#1451974514yes—
704C23#1451974814yes—
705C23#1451975014yes—
706C23#1451975914yes—
707C23C22×C4×D6111yescharacteristic
708C23C2×D4×D6111yescharacteristic
709C23C2×D4×D6111yescharacteristic
710C23C2×D4×D6111yescharacteristic
711C23C22×C22⋊D6111yescharacteristic
712C23#41×D6112yes—
713C23#41×D6112yes—
714C23C2×#1175822411yescharacteristic
715C23C2×#1175822211yescharacteristic
716C23#1451982312yes—
717C23#1451982412yes—
718D4—12232no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—416no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—614no—
745C2×C4—614no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—1224no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1224no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—1224no—
765C2×C4—24416no—
766C2×C4—24416no—
767C2×C4—24416no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2442no—
778C22—24no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—1224no—
789C22—1228no—
790C22—2442no—
791C22—2444no—
792C22—2444no—
793C22—2442no—
794C22—2442no—
795C22—2444no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22#1683963818yes—
800C22C2×C22⋊C4×D6111yescharacteristic
801C22C2×#1451973711yescharacteristic
802C22C2×C4×C22⋊D6111yescharacteristic
803C22#1684023012yes—
804C22#1684024212yes—
805C22C2×#1451974511yescharacteristic
806C22C2×#1451974811yescharacteristic
807C22C2×#1451975011yescharacteristic
808C22#123×D6111yescharacteristic
809C22C2×#1451975911yescharacteristic
810C22#1684027011yescharacteristic
811C22#1684028912yes—
812C22#1684032311yescharacteristic
813C22#1684033411yescharacteristic
814C22#1684035612yes—
815C22#1684040012yes—
816C22#1684040412yes—
817C22#1684040412yes—
818C22#1684041012yes—
819C22#1684041012yes—
820C22#1684041112yes—
821C22#1684043612yes—
822C22#1684044512yes—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—1224no—
828C4—1224no—
829C4—2442no—
830C4—2444no—
831C4—2444no—
832C2—28no—
833C2—2444no—
834C2C2×#1683963811yescharacteristic
835C2#2144833611yescharacteristic
836C2#2144848511yescharacteristic
837C2#2144864312yes—
838C2#2144881112yes—
839C2#2144914311yescharacteristic
840C2#2144915111yescharacteristic
841C2#2144930012yes—
842C2#2144936612yes—
843C2#2145012611yescharacteristic
844C2#2145071411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#381C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#381D61
hypocenterC61#13968
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. C22×#14519684C2semidirect
5. #21444070C2semidirect
6. #21444067C2semidirect
7. #21444050C2semidirect
8. #21444041C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C2×C61×#381C2semidirect
18. C2×#14519760C4semidirect
79. C2×#11758196C2×C4semidirect
82. C2×C22⋊Dic61C2×C4semidirect
91. C2×#11758198C2×C4semidirect
109. C23×C4×C61C2×C4semidirect
353. C2×Dic61#123semidirect
413. C2×#381D61semidirect
466. C61#13968semidirect
502. C23×C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197602
C22×#145197372
C2×#168396392
C22×#145196842
#214440702
#214440672
#214440502
#214440412
#214440402
C2×C61×#3812
#1396861