Finite Group Databasebeta

← #29601918

Subgroups — #29601918

Order 15616.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16839638C212yesmaximal
4C2×#16839622C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6#21444070C212yesmaximal, complemented
7#21444062C212yesmaximal, complemented
8#21444048C211yesmaximal, characteristic, complemented
9#21444048C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C61×#380C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×C4×C22⋊D61—24no—
16C2×C4×C22⋊D61—24no—
17C2×C4×C22⋊D61C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758196C2211yescharacteristic
22C2×C4⋊C4×D61—24no—
23C2×C4⋊C4×D61—24no—
24C2×C4⋊C4×D61—24no—
25C22×C22⋊Dic61C2212yes—
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2212yes—
28C22×#11758198C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839638—28no—
31#16839622—24no—
32#16839619—24no—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C2×#14519684C2212yes—
39C24×C4×C61C2211yescharacteristic
40C22×C4⋊C4×C61C2211yescharacteristic
41C22×C4⋊C4×C61C2211yescharacteristic
42C22×C22⋊C4×C61C2212yes—
43C61×#380—24no—
44C2×#95×C61C2212yes—
45C24×D61C2311yescharacteristic
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61C2×C414yes—
51C22×C22⋊D61D414yes—
52C22×C22⋊D61Q814yes—
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—24no—
63C22×C4×D61—24no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—42no—
68C22×C4×D61—42no—
69C22×C4×D61C2×C414yes—
70C22×C4×D61D414yes—
71C22×C4×D61D414yes—
72C4×C22⋊D61—232no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61D414yescomplemented
79C2×#11758196—24no—
80C2×#11758196—24no—
81C2×#11758196—24no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196C2×C414yescomplemented
85C4⋊C4×D61—232no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—24no—
89C2×C22⋊Dic61—24no—
90C2×C22⋊Dic61—42no—
91C2×C22⋊Dic61C2×C414yescomplemented
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—24no—
97C2×#11758198C2×C414yes—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61C2×C414yescomplemented
101#14519684—24no—
102#14519684—24no—
103#14519684—24no—
104#14519684—24no—
105#14519684—42no—
106#14519684—42no—
107C25×C61C2311yescharacteristic
108C23×C4×C61—22no—
109C23×C4×C61—22no—
110C23×C4×C61—22no—
111C23×C4×C61—22no—
112C23×C4×C61—22no—
113C23×C4×C61—22no—
114C23×C4×C61C2×C414yescomplemented
115C23×C4×C61C2312yes—
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2312yes—
118C23×C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61—22no—
120C2×C4⋊C4×C61—22no—
121C2×C4⋊C4×C61—22no—
122C2×C4⋊C4×C61—22no—
123C2×C4⋊C4×C61—22no—
124C2×C4⋊C4×C61D414yescomplemented
125C2×C22⋊C4×C61—24no—
126C2×C22⋊C4×C61—24no—
127C2×C22⋊C4×C61—42no—
128#95×C61—24no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61C22×C412yes—
142C24×C61C2×D412yes—
143C24×C61C2×Q812yes—
144C24×C61C2411yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61C22×C412yes—
154C23×D61C2×D412yes—
155C23×D61C2×D412yes—
156C23×D61C2×D412yes—
157C23×D61C2×Q812yes—
158C23×D61#4112yes—
159C23×D61#4112yes—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—22no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—28no—
173C22×C4×C61—28no—
174C22×C4×C61—28no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—44no—
183C22×C4×C61—44no—
184C22×C4×C61—44no—
185C22×C4×C61—44no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D414yes—
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2×D412yes—
193C22×C4×C61#4112yes—
194C22×C4×C61#4112yes—
195C2×C22⋊D61—28no—
196C2×C22⋊D61—28no—
197C2×C22⋊D61—28no—
198C2×C22⋊D61—28no—
199C2×C22⋊D61—28no—
200C2×C22⋊D61—28no—
201C2×C22⋊D61C4⋊C4116yescomplemented
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61C22×C412yes—
230C22×Dic61C22×C412yes—
231C22×Dic61C22×C412yes—
232C22×Dic61C2×D414yes—
233C22×Dic61C2×D412yes—
234C22×Dic61C2×D412yes—
235C22×Dic61C2×D412yes—
236C22×Dic61C2×Q812yes—
237C2×C4×D61—28no—
238C2×C4×D61—28no—
239C2×C4×D61—28no—
240C2×C4×D61—28no—
241C2×C4×D61—28no—
242C2×C4×D61—28no—
243C2×C4×D61—216no—
244C2×C4×D61—48no—
245C2×C4×D61—48no—
246C2×C4×D61—48no—
247C2×C4×D61—48no—
248C2×C4×D61—48no—
249C2×C4×D61—48no—
250C2×C4×D61C22⋊C4116yescomplemented
251C4⋊C4×C61—28no—
252C4⋊C4×C61—44no—
253C22⋊C4×C61—48no—
254C22⋊Dic61—28no—
255C22⋊Dic61—48no—
256#11758198—28no—
257#11758198—48no—
258C4⋊Dic61—28no—
259C4⋊Dic61—44no—
260#11758196—216no—
261#11758196—28no—
262C4×Dic61—28no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61C2×C4⋊C414yescomplemented
298C23×C61C23×C411yescharacteristic
299C23×C61C22×D411yescharacteristic
300C23×C61C22×D411yescharacteristic
301C23×C61C22×D411yescharacteristic
302C23×C61C22×D411yescharacteristic
303C23×C61C22×D411yescharacteristic
304C23×C61C22×Q811yescharacteristic
305C23×C61C2×#4111yescharacteristic
306C23×C61C2×#4111yescharacteristic
307C23×C61C2×#4111yescharacteristic
308C23×C61C2×#4111yescharacteristic
309C23×C61H(5,𝔽2)11yescharacteristic
310C23×C61H(5,𝔽2)11yescharacteristic
311C23×C612−1+411yescharacteristic
312C23×C612−1+411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61C2×C22⋊C414yes—
342C22×D61C2×C4⋊C414yes—
343C22×D61#11714yes—
344C22×D61#12114yes—
345C22×D61#12114yes—
346C22×D61C22⋊Q814yes—
347C22×D61C22⋊Q814yes—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—24no—
352C2×C4×C61—24no—
353C2×C4×C61—24no—
354C2×C4×C61—41no—
355C2×C4×C61—42no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61—416no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61C2×C22⋊C414yes—
371C2×C4×C61C4×D414yes—
372C2×C4×C61C4×D414yes—
373C2×C4×C61#12014yes—
374C2×C4×C61#12114yes—
375C2×C4×C61#12114yes—
376C2×C4×C61#12314yes—
377C22⋊D61—232no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—24no—
394C2×Dic61—24no—
395C2×Dic61—24no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—42no—
405C2×Dic61—42no—
406C2×Dic61—42no—
407C2×Dic61—42no—
408C2×Dic61—42no—
409C2×Dic61—42no—
410C2×Dic61—42no—
411C2×Dic61C2×C22⋊C414yes—
412C2×Dic61C2×C4⋊C414yescomplemented
413C4×D61—232no—
414C4×D61—432no—
415#13872—611nomaximal, Sylow
416C22×C61—24no—
417C22×C61—24no—
418C22×C61—24no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61C22×C22⋊C411yescharacteristic
432C22×C61C22×C4⋊C411yescharacteristic
433C22×C61C2×#11711yescharacteristic
434C22×C61C2×C4×D411yescharacteristic
435C22×C61C2×C4×D411yescharacteristic
436C22×C61#52011yescharacteristic
437C22×C61#52011yescharacteristic
438C22×C61C2×#12011yescharacteristic
439C22×C61C2×#12111yescharacteristic
440C22×C61C2×#12111yescharacteristic
441C22×C61C2×#12111yescharacteristic
442C22×C61C2×#12111yescharacteristic
443C22×C61C2×C22⋊Q811yescharacteristic
444C22×C61C2×C22⋊Q811yescharacteristic
445C22×C61C2×#12311yescharacteristic
446C22×C61#53511yescharacteristic
447C22×C61#53611yescharacteristic
448C22×C61#53711yescharacteristic
449C22×C61#53711yescharacteristic
450C22×C61D4211yescharacteristic
451C22×C61D4211yescharacteristic
452C22×C61#54611yescharacteristic
453C22×C61#54611yescharacteristic
454C22×C61#54711yescharacteristic
455C22×C61#54711yescharacteristic
456C22×C61#54811yescharacteristic
457C22×C61#54811yescharacteristic
458C22×C61D4×Q811yescharacteristic
459C22×C61D4×Q811yescharacteristic
460C22×C61#55211yescharacteristic
461C22×C61#55211yescharacteristic
462C22×C61#55311yescharacteristic
463C22×C61#55311yescharacteristic
464C22×C61#55411yescharacteristic
465C22×C61#55411yescharacteristic
466C2×D61—24no—
467C2×D61—24no—
468C2×D61—24no—
469C2×D61—24no—
470C2×D61—24no—
471C2×D61—24no—
472C2×D61—24no—
473C2×D61—24no—
474C2×D61—24no—
475C2×D61—24no—
476C2×D61—24no—
477C2×D61—24no—
478C2×D61—24no—
479C2×D61—24no—
480C2×D61#38018yescomplemented
481C4×C61—44no—
482C4×C61—42no—
483C4×C61—82no—
484C4×C61#38618yescomplemented
485Dic61—24no—
486Dic61—24no—
487Dic61—42no—
488Dic61—44no—
489Dic61—82no—
490C22×C4×D4—611no—
491C23×C4⋊C4—611no—
492C2×#386—612no—
493C2×#380—611no—
494C2×#380—611no—
495C2×#380D6111yescharacteristic, complemented
496#1441—612no—
497#1439—612no—
498C4⋊#95—611no—
499C4⋊#95—611no—
500C22⋊#95—612no—
501C2×C61—44no—
502C2×C61C2×#38011yescharacteristic
503C2×C61C2×#38611yescharacteristic
504C2×C61#231111yescharacteristic
505C2×C61D4×C4⋊C411yescharacteristic
506C2×C61D4×C4⋊C411yescharacteristic
507C2×C61#235211yescharacteristic
508C2×C61#235211yescharacteristic
509C2×C61#240811yescharacteristic
510C2×C61#240911yescharacteristic
511C2×C61#241611yescharacteristic
512C2×C61#241611yescharacteristic
513C2×C61#241711yescharacteristic
514C2×C61#241711yescharacteristic
515C2×C61#248611yescharacteristic
516C2×C61#248711yescharacteristic
517D61—28no—
518C23×D4—611no—
519C24×C4—611no—
520C24×C4—612no—
521C24×C4C2×D6111yescharacteristic
522C2×C4×D4—618no—
523C2×C4×D4—1224no—
524C2×C4×D4—1224no—
525C22×C4⋊C4—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—612no—
528C22×C4⋊C4—611no—
529C22×C4⋊C4—1224no—
530C22×C4⋊C4—1224no—
531C22×C4⋊C4—1224no—
532C22×C4⋊C4C2×D6111yescharacteristic
533C22×C4⋊C4C2×D6111yescharacteristic
534C22×C22⋊C4—611no—
535C22×C22⋊C4—611no—
536C22×C22⋊C4—612no—
537C22×C22⋊C4—612no—
538C22×C22⋊C4C2×D6112yes—
539C22×C42—611no—
540#386—1228no—
541#380—24no—
542#380—1224no—
543#380—1224no—
544C2×#95—612no—
545C2×#95—612no—
546C2×#95—612no—
547C2×#95—612no—
548C2×#95—612no—
549C2×#95—612no—
550C2×#95C2×D6112yes—
551C61#1387211yescharacteristic, complemented, Sylow
552C25—611no—
553C25C22×D6111yescharacteristic
554C22×D4—614no—
555C22×D4—614no—
556C22×D4—614no—
557C22×D4—1222no—
558C22×D4—1222no—
559C22×D4—1222no—
560C22×D4—1222no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—614no—
570C23×C4—614no—
571C23×C4—614no—
572C23×C4—611no—
573C23×C4—612no—
574C23×C4—612no—
575C23×C4—1224no—
576C23×C4—1224no—
577C23×C4—1224no—
578C23×C4—1224no—
579C23×C4—1222no—
580C23×C4—1222no—
581C23×C4—1222no—
582C23×C4—1222no—
583C23×C4—1224no—
584C23×C4—2442no—
585C23×C4—2442no—
586C23×C4C4×D6114yescomplemented
587C23×C4C22×D6112yes—
588C23×C4C22×D6111yescharacteristic
589C23×C4C22×D6112yes—
590C23×C4C22×D6111yescharacteristic
591C4×D4—12232no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—614no—
598C2×C4⋊C4—614no—
599C2×C4⋊C4—12232no—
600C2×C4⋊C4—1224no—
601C2×C4⋊C4—1224no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1224no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4C22⋊D6114yescomplemented
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—42no—
614C2×C22⋊C4—614no—
615C2×C22⋊C4—614no—
616C2×C22⋊C4—1222no—
617C2×C22⋊C4—1222no—
618C2×C22⋊C4—1222no—
619C2×C22⋊C4—1222no—
620C2×C22⋊C4—1224no—
621C2×C22⋊C4—1224no—
622C2×C22⋊C4—1224no—
623C2×C22⋊C4—1224no—
624C2×C22⋊C4—1224no—
625C2×C22⋊C4—2442no—
626C2×C42—614no—
627C2×C42—1222no—
628C2×C42—1222no—
629#95—24no—
630#95—1224no—
631#95—1224no—
632#95—1224no—
633#95—1224no—
634#95—2442no—
635#95—2442no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—612no—
649C24—612no—
650C24—612no—
651C24—612no—
652C24—612no—
653C24—612no—
654C24—612no—
655C24—1221no—
656C24—1221no—
657C24—1221no—
658C24—1221no—
659C24—1221no—
660C24—1221no—
661C24—1221no—
662C24—1221no—
663C24C2×C4×D6112yes—
664C24D4×D6112yes—
665C24Q8×D6112yes—
666C24C23×D6111yescharacteristic
667C2×D4—6116no—
668C2×D4—1228no—
669C2×D4—1228no—
670C2×D4—1228no—
671C2×D4—1228no—
672C2×D4—1228no—
673C2×D4—1228no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—6116no—
707C22×C4—612no—
708C22×C4—614no—
709C22×C4—12216no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1228no—
719C22×C4—1228no—
720C22×C4—1228no—
721C22×C4—1228no—
722C22×C4—1228no—
723C22×C4—1228no—
724C22×C4—1222no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1222no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1221no—
731C22×C4—1222no—
732C22×C4—1221no—
733C22×C4—1222no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1222no—
737C22×C4—1222no—
738C22×C4—1222no—
739C22×C4—1222no—
740C22×C4—1222no—
741C22×C4—1222no—
742C22×C4—1222no—
743C22×C4—2448no—
744C22×C4—2448no—
745C22×C4—2448no—
746C22×C4—2448no—
747C22×C4—2448no—
748C22×C4—2448no—
749C22×C4C2×C4×D6112yes—
750C22×C4C2×C4×D6112yes—
751C22×C4#1175822212yes—
752C22×C4D4×D6112yes—
753C22×C4D4×D6112yes—
754C22×C4D4×D6112yes—
755C22×C4#1175822412yes—
756C22×C4C2×C22⋊D6114yes—
757C22×C4C2×C22⋊D6112yes—
758C4⋊C4—28no—
759C4⋊C4—44no—
760C4⋊C4—1228no—
761C4⋊C4—12216no—
762C4⋊C4—1228no—
763C4⋊C4—2444no—
764C22⋊C4—48no—
765C22⋊C4—1228no—
766C22⋊C4—1228no—
767C22⋊C4—2448no—
768C22⋊C4—2448no—
769C42—1228no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—614no—
805C23—614no—
806C23—614no—
807C23—614no—
808C23—614no—
809C23—614no—
810C23—614no—
811C23—1222no—
812C23—1222no—
813C23—1222no—
814C23—1222no—
815C23—1222no—
816C23—1222no—
817C23—1222no—
818C23—1222no—
819C23—1222no—
820C23—1222no—
821C23—1222no—
822C23—1222no—
823C23—1222no—
824C23—1222no—
825C23—1222no—
826C23—1222no—
827C23—1222no—
828C23—1222no—
829C23—1222no—
830C23—1222no—
831C23—1222no—
832C23—1222no—
833C23—1222no—
834C23—1222no—
835C23—1222no—
836C23—1222no—
837C23—1222no—
838C23—1222no—
839C23C4⋊C4×D6114yescomplemented
840C23C22×C4×D6111yescharacteristic
841C23C2×D4×D6111yescharacteristic
842C23C2×D4×D6111yescharacteristic
843C23C2×D4×D6111yescharacteristic
844C23C2×D4×D6111yescharacteristic
845C23C22×C22⋊D6111yescharacteristic
846C23C2×Q8×D6111yescharacteristic
847C23#41×D6111yescharacteristic
848C23#41×D6111yescharacteristic
849C23C2×#1175822411yescharacteristic
850C23C2×#1175822211yescharacteristic
851C23#1451982211yescharacteristic
852C23#1451982311yescharacteristic
853C23#1451982411yescharacteristic
854C23#1451982511yescharacteristic
855D4—12232no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—416no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—614no—
879C2×C4—614no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—12232no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1224no—
897C2×C4—1224no—
898C2×C4—1224no—
899C2×C4—24432no—
900C2×C4—2442no—
901C2×C4—2442no—
902C2×C4—2442no—
903C2×C4—2442no—
904C2×C4—2442no—
905C2×C4—2442no—
906C2×C4—2442no—
907C2×C4—2442no—
908C2×C4—2441no—
909C2×C4—2442no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2442no—
914C2×C4—2442no—
915C2×C4C22⋊C4×D6114yes—
916C2×C4#1451973714yes—
917C2×C4C4×C22⋊D6114yes—
918C2×C4#1451974514yes—
919C2×C4#1451974814yes—
920C2×C4#1451975014yes—
921C2×C4#1451975914yes—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—618no—
938C22—1224no—
939C22—1224no—
940C22—1224no—
941C22—1224no—
942C22—1224no—
943C22—1224no—
944C22—1224no—
945C22—1224no—
946C22—1224no—
947C22—1224no—
948C22—1224no—
949C22—1224no—
950C22—1224no—
951C22—1224no—
952C22C2×C22⋊C4×D6111yescharacteristic
953C22C2×C4⋊C4×D6111yescharacteristic
954C22#117×D6111yescharacteristic
955C22C2×#1451973711yescharacteristic
956C22C2×C4×C22⋊D6111yescharacteristic
957C22#1684024211yescharacteristic
958C22#1684024311yescharacteristic
959C22C2×#1451974511yescharacteristic
960C22#121×D6111yescharacteristic
961C22#121×D6111yescharacteristic
962C22C2×#1451974811yescharacteristic
963C22C2×#1451975011yescharacteristic
964C22C22⋊Q8×D6111yescharacteristic
965C22C22⋊Q8×D6111yescharacteristic
966C22C2×#1451975911yescharacteristic
967C22#1684032811yescharacteristic
968C22#1684033511yescharacteristic
969C22#1684034111yescharacteristic
970C22#1684034211yescharacteristic
971C22D4×C22⋊D6111yescharacteristic
972C22#1684039611yescharacteristic
973C22#1684040011yescharacteristic
974C22#1684040911yescharacteristic
975C22#1684041211yescharacteristic
976C22#1684041311yescharacteristic
977C22#1684041911yescharacteristic
978C22#1684042211yescharacteristic
979C22#1684042511yescharacteristic
980C22Q8×C22⋊D6111yescharacteristic
981C22#1684044611yescharacteristic
982C22#1684045111yescharacteristic
983C22#1684045611yescharacteristic
984C22#1684045911yescharacteristic
985C22#1684046711yescharacteristic
986C22#1684047011yescharacteristic
987C4—42no—
988C4—44no—
989C4—82no—
990C4—1224no—
991C4—1224no—
992C4—4882no—
993C4—2444no—
994C4—2442no—
995C4#1683963818yescomplemented
996C2—44no—
997C2—1228no—
998C2#380×D6111yescharacteristic
999C2C2×#1683963811yescharacteristic
1000C2#2144840811yescharacteristic
1001C2#2144871511yescharacteristic
1002C2C4⋊C4×C22⋊D6111yescharacteristic
1003C2#2144874111yescharacteristic
1004C2#2144874911yescharacteristic
1005C2#2144917111yescharacteristic
1006C2#2144918011yescharacteristic
1007C2#2144925511yescharacteristic
1008C2#2144926111yescharacteristic
1009C2#2144926611yescharacteristic
1010C2#2144927211yescharacteristic
1011C2#2145012311yescharacteristic
1012C2#2145013211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#380C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#380D61
hypocenterC61#13872
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
4. C2×#16839622C2semidirect
5. C2×#16839619C2semidirect
6. #21444070C2semidirect
7. #21444062C2semidirect
8. #21444048C2semidirect
9. #21444048C2semidirect
10. #21444040C2semidirect
11. C2×C61×#380C2semidirect
17. C2×C4×C22⋊D61C4semidirect
78. C2×C4⋊Dic61D4semidirect
84. C2×#11758196C2×C4semidirect
91. C2×C22⋊Dic61C2×C4semidirect
100. C2×C4×Dic61C2×C4semidirect
114. C23×C4×C61C2×C4semidirect
124. C2×C4⋊C4×C61D4semidirect
201. C2×C22⋊D61C4⋊C4semidirect
250. C2×C4×D61C22⋊C4semidirect
297. C23×C61C2×C4⋊C4semidirect
412. C2×Dic61C2×C4⋊C4semidirect
480. C2×D61#380semidirect
484. C4×C61#386semidirect
495. C2×#380D61semidirect
551. C61#13872semidirect
586. C23×C4C4×D61semidirect
610. C2×C4⋊C4C22⋊D61semidirect
839. C23C4⋊C4×D61semidirect
995. C4#16839638semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C22×C4⋊C4×D612
C2×#168396382
C2×#168396222
C2×#168396192
#214440702
#214440622
#214440482
#214440402
C2×C61×#3802
#1387261