Finite Group Databasebeta

← #29601915

Subgroups — #29601915

Order 15616.

2950 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16839638C212yesmaximal
4C2×#16839621C211yesmaximal, characteristic, complemented
5C2×#16839620C212yesmaximal, complemented
6#21444073C211yesmaximal, characteristic, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444047C212yesmaximal, complemented
10#21444040C212yesmaximal, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C23×C4×D61C2211yescharacteristic
16C2×#14519737—24no—
17C2×#14519737—24no—
18C2×#14519737C418yescomplemented
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2212yes—
23C2×C4⋊C4×D61—28no—
24C2×C4⋊C4×D61—24no—
25C22×C22⋊Dic61C2212yes—
26C22×#11758198C2212yes—
27C22×#11758198C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29#16839638—28no—
30#16839621—24no—
31#16839620—28no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2212yes—
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61C2×C414yes—
49C22×C22⋊D61D414yes—
50C22×C22⋊D61Q814yes—
51C23×Dic61—22no—
52C23×Dic61—22no—
53C23×Dic61—24no—
54C23×Dic61—24no—
55C23×Dic61C2×C414yescomplemented
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C22×C4×D61—24no—
62C22×C4×D61—24no—
63C22×C4×D61—24no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—42no—
69C22×C4×D61—42no—
70C22×C4×D61C2×C414yes—
71C22×C4×D61D414yes—
72C22×C4×D61D414yes—
73#14519737—232no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—24no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196—24no—
79C2×#11758196—24no—
80C2×#11758196—24no—
81C2×#11758196—24no—
82C2×#11758196—24no—
83C2×#11758196C2×C414yescomplemented
84C2×#11758196D418yescomplemented
85C4⋊C4×D61—232no—
86C2×C22⋊Dic61—24no—
87C2×C22⋊Dic61—24no—
88C2×C22⋊Dic61—42no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198—24no—
94C2×#11758198C2×C414yes—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2×C414yescomplemented
98#14519684—24no—
99#14519684—22no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103#14519684—42no—
104C25×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2312yes—
108C23×C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61—24no—
110C2×C4⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—42no—
116C2×C22⋊C4×C61C2×C414yescomplemented
117#95×C61—22no—
118#95×C61—42no—
119C24×C61—21no—
120C24×C61—21no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—22no—
126C24×C61—22no—
127C24×C61C22×C412yes—
128C24×C61C2×D412yes—
129C24×C61C2×Q812yes—
130C24×C61C2411yescharacteristic
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61C22×C412yes—
136C23×D61C2×D412yes—
137C23×D61C2×D412yes—
138C23×D61C2×D412yes—
139C23×D61C2×Q812yes—
140C23×D61#4112yes—
141C23×D61#4112yes—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
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×C61C22×C412yes—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D414yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C2×C22⋊D61—28no—
167C2×C22⋊D61—28no—
168C2×C22⋊D61—28no—
169C2×C22⋊D61—28no—
170C2×C22⋊D61—28no—
171C2×C22⋊D61—28no—
172C2×C22⋊D61C4⋊C4116yescomplemented
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—28no—
188C22×Dic61—216no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—44no—
197C22×Dic61—48no—
198C22×Dic61—44no—
199C22×Dic61C22×C412yes—
200C22×Dic61C22×C412yes—
201C22×Dic61C22×C412yes—
202C22×Dic61C2×D414yes—
203C22×Dic61C2×D412yes—
204C22×Dic61C2×D412yes—
205C22×Dic61C2×D412yes—
206C22×Dic61C2×D414yes—
207C22×Dic61C2×Q812yes—
208C22×Dic61#4114yes—
209C2×C4×D61—216no—
210C2×C4×D61—28no—
211C2×C4×D61—216no—
212C2×C4×D61—28no—
213C2×C4×D61—216no—
214C2×C4×D61—48no—
215C2×C4×D61—48no—
216C2×C4×D61—48no—
217C2×C4×D61—48no—
218C2×C4×D61—48no—
219C2×C4×D61—48no—
220C2×C4×D61C22⋊C4116yescomplemented
221C4⋊C4×C61—28no—
222C22⋊C4×C61—28no—
223C22⋊C4×C61—48no—
224C22⋊Dic61—48no—
225#11758198—28no—
226#11758198—48no—
227C4⋊Dic61—28no—
228#11758196—28no—
229#11758196—216no—
230#11758196—48no—
231C4×Dic61—28no—
232C23×C61—22no—
233C23×C61—22no—
234C23×C61—24no—
235C23×C61—24no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—41no—
245C23×C61—42no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—42no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61C2×C4⋊C414yescomplemented
255C23×C61C23×C411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C23×C61C22×D411yescharacteristic
258C23×C61C22×D411yescharacteristic
259C23×C61C22×D412yes—
260C23×C61C22×Q811yescharacteristic
261C23×C61C2×#4111yescharacteristic
262C23×C61C2×#4111yescharacteristic
263C23×C61C2×#4112yes—
264C23×C61H(5,𝔽2)12yes—
265C23×C612−1+412yes—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—22no—
269C22×D61—24no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61C2×C22⋊C414yes—
283C22×D61C2×C4⋊C414yes—
284C22×D61#11714yes—
285C22×D61#12114yes—
286C22×D61#12114yes—
287C22×D61C22⋊Q814yes—
288C22×D61C22⋊Q814yes—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61C2×C22⋊C414yes—
313C22⋊D61—232no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—41no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—41no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—416no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61C2×C22⋊C414yes—
341C2×Dic61C2×C4⋊C414yescomplemented
342C2×Dic61C4×D418yes—
343C2×Dic61#12014yes—
344C2×Dic61#12118yes—
345C2×Dic61#12314yes—
346C4×D61—232no—
347C4×D61—432no—
348#13872—611nomaximal, Sylow
349C22×C61—28no—
350C22×C61—24no—
351C22×C61—42no—
352C22×C61—44no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—44no—
356C22×C61—44no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61C22×C22⋊C411yescharacteristic
361C22×C61C22×C4⋊C411yescharacteristic
362C22×C61C2×#11711yescharacteristic
363C22×C61C2×C4×D412yes—
364C22×C61#52012yes—
365C22×C61C2×#12011yescharacteristic
366C22×C61C2×#12111yescharacteristic
367C22×C61C2×#12111yescharacteristic
368C22×C61C2×#12112yes—
369C22×C61C2×C22⋊Q811yescharacteristic
370C22×C61C2×C22⋊Q811yescharacteristic
371C22×C61C2×#12311yescharacteristic
372C22×C61#53511yescharacteristic
373C22×C61#53611yescharacteristic
374C22×C61#53712yes—
375C22×C61D4212yes—
376C22×C61#54612yes—
377C22×C61#54712yes—
378C22×C61#54812yes—
379C22×C61D4×Q812yes—
380C22×C61#55212yes—
381C22×C61#55312yes—
382C22×C61#55412yes—
383C2×D61—24no—
384C2×D61—28no—
385C2×D61—28no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—28no—
389C2×D61—28no—
390C2×D61—24no—
391C2×D61—24no—
392C2×D61—24no—
393C2×D61#38018yescomplemented
394C4×C61—24no—
395C4×C61—42no—
396C4×C61—44no—
397C4×C61—82no—
398Dic61—24no—
399Dic61—44no—
400Dic61—42no—
401Dic61—82no—
402Dic61#38618yescomplemented
403C22×C4×D4—611no—
404C23×C4⋊C4—611no—
405C2×#386—612no—
406C2×#380—611no—
407C2×#380—612no—
408#1441—611no—
409#1441—611no—
410#1439—611no—
411#1439D6111yescharacteristic, complemented
412C4⋊#95—612no—
413C22⋊#95—612no—
414C2×C61—44no—
415C2×C61C2×#38011yescharacteristic
416C2×C61C2×#38611yescharacteristic
417C2×C61#231111yescharacteristic
418C2×C61D4×C4⋊C412yes—
419C2×C61#235212yes—
420C2×C61#240811yescharacteristic
421C2×C61#240911yescharacteristic
422C2×C61#241612yes—
423C2×C61#241712yes—
424C2×C61#248611yescharacteristic
425C2×C61#248711yescharacteristic
426D61—28no—
427C23×D4—611no—
428C24×C4—611no—
429C24×C4—611no—
430C24×C4—612no—
431C2×C4×D4—618no—
432C2×C4×D4—1224no—
433C2×C4×D4—1224no—
434C22×C4⋊C4—612no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—612no—
437C22×C4⋊C4—611no—
438C22×C4⋊C4—1228no—
439C22×C4⋊C4—1224no—
440C22×C4⋊C4C2×D6111yescharacteristic
441C22×C22⋊C4—611no—
442C22×C22⋊C4—612no—
443C22×C22⋊C4—612no—
444C22×C22⋊C4C2×D6112yes—
445C22×C22⋊C4C2×D6111yescharacteristic
446C22×C42—611no—
447#386—1228no—
448#380—1224no—
449#380—1228no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—612no—
454C2×#95—611no—
455C2×#95—612no—
456C2×#95C2×D6111yescharacteristic
457C2×#95C2×D6112yes—
458C61#1387211yescharacteristic, complemented, Sylow
459C25—611no—
460C25C22×D6111yescharacteristic
461C22×D4—614no—
462C22×D4—614no—
463C22×D4—614no—
464C22×D4—1222no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1222no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—614no—
471C23×C4—614no—
472C23×C4—614no—
473C23×C4—614no—
474C23×C4—612no—
475C23×C4—611no—
476C23×C4—612no—
477C23×C4—1224no—
478C23×C4—1224no—
479C23×C4—1224no—
480C23×C4—1224no—
481C23×C4—1224no—
482C23×C4—1224no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1224no—
486C23×C4—1224no—
487C23×C4—1224no—
488C23×C4—2442no—
489C23×C4—2442no—
490C23×C4C22×D6112yes—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6112yes—
493C23×C4C22×D6111yescharacteristic
494C4×D4—12232no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—618no—
499C2×C4⋊C4—12232no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1224no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—1224no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—2442no—
523C2×C22⋊C4C4×D6114yescomplemented
524C2×C42—614no—
525C2×C42—1222no—
526C2×C42—1222no—
527#95—22no—
528#95—42no—
529#95—1224no—
530#95—1224no—
531#95—1224no—
532#95—1224no—
533#95—1222no—
534#95—2442no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24—612no—
544C24—612no—
545C24—612no—
546C24—612no—
547C24—612no—
548C24—612no—
549C24—612no—
550C24—1222no—
551C24—1222no—
552C24—1222no—
553C24—1222no—
554C24C2×C4×D6112yes—
555C24D4×D6112yes—
556C24Q8×D6112yes—
557C24C23×D6111yescharacteristic
558C2×D4—6116no—
559C2×D4—1228no—
560C2×D4—1228no—
561C2×D4—1228no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—1228no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—614no—
588C22×C4—614no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—6116no—
593C22×C4—612no—
594C22×C4—614no—
595C22×C4—1228no—
596C22×C4—12216no—
597C22×C4—12216no—
598C22×C4—1228no—
599C22×C4—12216no—
600C22×C4—1228no—
601C22×C4—12216no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—2448no—
624C22×C4—2448no—
625C22×C4—2448no—
626C22×C4—2448no—
627C22×C4—2448no—
628C22×C4—2448no—
629C22×C4—2444no—
630C22×C4—2448no—
631C22×C4—2444no—
632C22×C4C2×C4×D6112yes—
633C22×C4C2×C4×D6112yes—
634C22×C4D4×D6114yes—
635C22×C4D4×D6112yes—
636C22×C4D4×D6112yes—
637C4⋊C4—28no—
638C4⋊C4—12216no—
639C4⋊C4—1228no—
640C4⋊C4—1228no—
641C4⋊C4—2448no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—1228no—
645C22⋊C4—2448no—
646C22⋊C4—2448no—
647C42—1228no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—42no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—614no—
671C23—614no—
672C23—614no—
673C23—614no—
674C23—614no—
675C23—614no—
676C23—614no—
677C23—1224no—
678C23—1224no—
679C23—1224no—
680C23—1224no—
681C23—1224no—
682C23—1222no—
683C23—1224no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23—1224no—
688C23—1224no—
689C23—1224no—
690C23—1224no—
691C23—1224no—
692C23—1224no—
693C23C4⋊C4×D6114yescomplemented
694C23C22×C4×D6111yescharacteristic
695C23C2×D4×D6111yescharacteristic
696C23C2×D4×D6111yescharacteristic
697C23C2×D4×D6111yescharacteristic
698C23C2×D4×D6112yes—
699C23C2×Q8×D6111yescharacteristic
700C23#41×D6111yescharacteristic
701C23#41×D6112yes—
702C23#41×D6111yescharacteristic
703C23#1451982212yes—
704C23#1451982412yes—
705D4—12232no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—614no—
730C2×C4—618no—
731C2×C4—614no—
732C2×C4—618no—
733C2×C4—614no—
734C2×C4—614no—
735C2×C4—12232no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—24432no—
748C2×C4—24416no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2441no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2441no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4C22⋊C4×D6114yes—
764C22—28no—
765C22—24no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—618no—
776C22—1228no—
777C22—1228no—
778C22—1224no—
779C22—1228no—
780C22—1228no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—1224no—
785C22—1224no—
786C22C2×C22⋊C4×D6111yescharacteristic
787C22C2×C4⋊C4×D6111yescharacteristic
788C22#117×D6111yescharacteristic
789C22C4×D4×D6112yes—
790C22#1684024112yes—
791C22#120×D6111yescharacteristic
792C22#121×D6111yescharacteristic
793C22#121×D6112yes—
794C22#121×D6111yescharacteristic
795C22C22⋊Q8×D6111yescharacteristic
796C22C22⋊Q8×D6111yescharacteristic
797C22#123×D6111yescharacteristic
798C22#1684032511yescharacteristic
799C22#1684033211yescharacteristic
800C22#1684034112yes—
801C22#1684039412yes—
802C22#1684040112yes—
803C22#1684041012yes—
804C22#1684042012yes—
805C22#1684042512yes—
806C22#1684044812yes—
807C22#1684045712yes—
808C22#1684046612yes—
809C4—24no—
810C4—44no—
811C4—42no—
812C4—82no—
813C4—618no—
814C4—1224no—
815C4—4882no—
816C4—2442no—
817C4—2444no—
818C2—44no—
819C2—1228no—
820C2#380×D6111yescharacteristic
821C2#386×D6111yescharacteristic
822C2#2144840911yescharacteristic
823C2#2144871712yes—
824C2#2144874712yes—
825C2#2144916811yescharacteristic
826C2#2144917711yescharacteristic
827C2#2144925212yes—
828C2#2144926312yes—
829C2#2145012011yescharacteristic
830C2#2145012911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#13872
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
4. C2×#16839621C2semidirect
5. C2×#16839620C2semidirect
6. #21444073C2semidirect
7. #21444069C2semidirect
8. #21444064C2semidirect
9. #21444047C2semidirect
10. #21444040C2semidirect
11. C61×#1439C2semidirect
18. C2×#14519737C4semidirect
55. C23×Dic61C2×C4semidirect
83. C2×#11758196C2×C4semidirect
84. C2×#11758196D4semidirect
97. C2×C4×Dic61C2×C4semidirect
116. C2×C22⋊C4×C61C2×C4semidirect
172. C2×C22⋊D61C4⋊C4semidirect
220. C2×C4×D61C22⋊C4semidirect
254. C23×C61C2×C4⋊C4semidirect
341. C2×Dic61C2×C4⋊C4semidirect
393. C2×D61#380semidirect
402. Dic61#386semidirect
411. #1439D61semidirect
458. C61#13872semidirect
523. C2×C22⋊C4C4×D61semidirect
693. C23C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×C4⋊C4×D612
C2×#168396382
C2×#168396212
C2×#168396202
#214440732
#214440692
#214440642
#214440472
#214440402
C61×#14392
#1387261