Finite Group Databasebeta

← #29602400

Subgroups — #29602400

Order 15616.

4166 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D61C211yesmaximal, characteristic
2C2×#16839669C211yesmaximal, characteristic, complemented
3C2×#16839668C211yesmaximal, characteristic, complemented
4C2×#16839667C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic
6C2×C4×#11758198C211yesmaximal, characteristic
7#21444089C214yesmaximal, complemented
8#21444040C214yesmaximal
9C2×C61×#391C211yesmaximal, characteristic, complemented
10C23×Dic122C2212yes—
11C23×Dic122C2211yescharacteristic
12C22×Q8×D61—24no—
13C22×Q8×D61—24no—
14C22×Q8×D61—24no—
15C22×Q8×D61—24no—
16C22×Q8×D61—24no—
17C22×Q8×D61—24no—
18C22×Q8×D61C418yescomplemented
19C23×C4×D61C2212yes—
20C23×C4×D61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25#16839669—24no—
26#16839668—24no—
27#16839667—24no—
28#16839619—24no—
29C4×#11758198—24no—
30C2×#14519684C2214yes—
31C2×#14519684C2214yes—
32C2×#14519684C2214yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C23×Q8×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C61×#391—24no—
39C2×#95×C61C2214yes—
40C24×D61C2311yescharacteristic
41C22×Dic122—24no—
42C22×Dic122—24no—
43C22×Dic122—22no—
44C22×Dic122—22no—
45C22×Dic122—22no—
46C22×Dic122—22no—
47C22×Dic122—24no—
48C22×Dic122—24no—
49C22×Dic122—24no—
50C22×Dic122—24no—
51C22×Dic122C2×C418yes—
52C22×Dic122C2×C414yes—
53C22×Dic122D414yes—
54C22×Dic122D414yes—
55C2×Q8×D61—232no—
56C2×Q8×D61—232no—
57C2×Q8×D61—232no—
58C2×Q8×D61—232no—
59C2×Q8×D61—232no—
60C2×Q8×D61—232no—
61C2×Q8×D61—232no—
62C23×Dic61C2312yes—
63C23×Dic61C2312yes—
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—24no—
73C22×C4×D61—22no—
74C22×C4×D61—24no—
75C22×C4×D61—24no—
76C22×C4×D61C2×C418yes—
77C22×C4×D61C2×C414yes—
78C22×C4×D61D414yes—
79C22×C4×D61D414yes—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—28no—
87C2×#11758198Q818yescomplemented
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91#14519684—28no—
92#14519684—24no—
93#14519684—24no—
94#14519684—28no—
95#14519684—28no—
96C22×Q8×C61—22no—
97C22×Q8×C61—22no—
98C22×Q8×C61—22no—
99C22×Q8×C61—22no—
100C22×Q8×C61C2×C414yes—
101C22×Q8×C61D414yes—
102C22×Q8×C61D414yes—
103C23×C4×C61C2312yes—
104C23×C4×C61C2312yes—
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—22no—
110C2×C42×C61—22no—
111C2×C42×C61—22no—
112C2×C42×C61—22no—
113#95×C61—28no—
114C24×C61C2411yescharacteristic
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61C22×C412yes—
122C23×D61C2×D412yes—
123C23×D61C2×D412yes—
124C23×D61C2×Q814yes—
125C23×D61#4114yes—
126C2×Q8×C61—28no—
127C2×Q8×C61—28no—
128C2×Q8×C61—28no—
129C2×Q8×C61—28no—
130C2×Q8×C61—28no—
131C2×Q8×C61—28no—
132C2×Q8×C61C22⋊C4116yescomplemented
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
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—24no—
147C22×C4×C61—24no—
148C22×C4×C61C22×C414yes—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2×D414yes—
151C22×C4×C61C2×D414yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×Q814yescomplemented
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—22no—
165C22×Dic61—21no—
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—24no—
177C22×Dic61—24no—
178C22×Dic61C22×C412yes—
179C22×Dic61C22×C414yes—
180C22×Dic61C2×D414yes—
181C22×Dic61C2×D414yes—
182C22×Dic61C2×D412yes—
183C22×Dic61C2×D412yes—
184C22×Dic61C2×Q814yescomplemented
185Q8×D61—2256no—
186C2×C4×D61—216no—
187C2×C4×D61—216no—
188C2×C4×D61—216no—
189C2×C4×D61—216no—
190C2×C4×D61—216no—
191C2×C4×D61—216no—
192C2×C4×D61—28no—
193C2×C4×D61—28no—
194C2×C4×D61—28no—
195C2×C4×D61—28no—
196C2×C4×D61—28no—
197C2×C4×D61—28no—
198C2×C4×D61—216no—
199C2×C4×D61C22⋊C4116yes—
200C2×Dic122—216no—
201C2×Dic122—216no—
202C2×Dic122—216no—
203C2×Dic122—216no—
204C2×Dic122—216no—
205C2×Dic122—28no—
206C2×Dic122—28no—
207C2×Dic122—28no—
208C2×Dic122—28no—
209C2×Dic122—28no—
210C2×Dic122—28no—
211C2×Dic122—216no—
212C2×Dic122—216no—
213C2×Dic122C22⋊C4116yescomplemented
214C4⋊C4×C61—44no—
215C42×C61—44no—
216#11758198—216no—
217#11758198—48no—
218C4⋊Dic61—44no—
219C4×Dic61—44no—
220C23×C61C23×C411yescharacteristic
221C23×C61C22×D411yescharacteristic
222C23×C61C22×D411yescharacteristic
223C23×C61C22×D411yescharacteristic
224C23×C61C22×D411yescharacteristic
225C23×C61C22×D411yescharacteristic
226C23×C61C22×D411yescharacteristic
227C23×C61C22×Q812yes—
228C23×C61C2×#4112yes—
229C23×C612−1+412yes—
230C23×C612−1+412yes—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—24no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—24no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—24no—
242C22×D61—24no—
243C22×D61—24no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61C2×C22⋊C414yes—
250C22×D61C4×Q818yes—
251C22×D61C22⋊Q818yes—
252C22×D61#12414yes—
253C22×D61C4⋊Q814yes—
254Q8×C61—232no—
255C2×C4×C61—24no—
256C2×C4×C61—24no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—24no—
260C2×C4×C61—24no—
261C2×C4×C61—24no—
262C2×C4×C61—24no—
263C2×C4×C61—24no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—44no—
272C2×C4×C61—44no—
273C2×C4×C61C2×C22⋊C418yes—
274C2×C4×C61C2×C22⋊C414yes—
275C2×C4×C61C2×C22⋊C414yes—
276C2×C4×C61C2×C22⋊C414yes—
277C2×C4×C61#12014yes—
278C2×C4×C61#12014yes—
279C2×C4×C61#12014yes—
280C2×C4×C61#12014yes—
281C2×Dic61—24no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—24no—
285C2×Dic61—22no—
286C2×Dic61—24no—
287C2×Dic61—22no—
288C2×Dic61—24no—
289C2×Dic61—22no—
290C2×Dic61—24no—
291C2×Dic61—22no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—44no—
304C2×Dic61—44no—
305C2×Dic61C2×C22⋊C414yes—
306C2×Dic61C2×C22⋊C418yes—
307C4×D61—264no—
308C4×D61—232no—
309Dic122—264no—
310Dic122—232no—
311#13922—611nomaximal, Sylow
312C22×C61C22×C22⋊C411yescharacteristic
313C22×C61C22×C22⋊C411yescharacteristic
314C22×C61C22×C22⋊C411yescharacteristic
315C22×C61C2×C4×Q812yes—
316C22×C61#51912yes—
317C22×C61C2×#12011yescharacteristic
318C22×C61C2×#12011yescharacteristic
319C22×C61C2×#12011yescharacteristic
320C22×C61C2×#12011yescharacteristic
321C22×C61C2×C22⋊Q812yes—
322C22×C61C2×#12411yescharacteristic
323C22×C61C2×C4⋊Q811yescharacteristic
324C22×C61#53611yescharacteristic
325C22×C61#53612yes—
326C22×C61#53611yescharacteristic
327C22×C61#54812yes—
328C22×C61#54812yes—
329C22×C61#54812yes—
330C22×C61#54812yes—
331C22×C61D4×Q812yes—
332C22×C61D4×Q812yes—
333C22×C61D4×Q812yes—
334C22×C61D4×Q812yes—
335C2×D61—24no—
336C2×D61—28no—
337C2×D61—28no—
338C2×D61—28no—
339C2×D61—28no—
340C2×D61—24no—
341C2×D61—24no—
342C2×D61—24no—
343C2×D61—24no—
344C2×D61—24no—
345C2×D61#39118yescomplemented
346C4×C61—28no—
347C4×C61—44no—
348C4×C61—82no—
349C4×C61#37918yes—
350Dic61—24no—
351Dic61—28no—
352Dic61—44no—
353Dic61—82no—
354C24×Q8—611no—
355C2×#391—611no—
356C2×#391—611no—
357C2×#391—611no—
358C2×#391D6111yescharacteristic, complemented
359C2×#380—611no—
360C2×C4×C22⋊C4—611no—
361#1446—614no—
362C22⋊#95—614no—
363C2×C61C2×#37911yescharacteristic
364C2×C61C2×#39111yescharacteristic
365C2×C61#231011yescharacteristic
366C2×C61Q8×C22⋊C412yes—
367C2×C61Q8×C22⋊C412yes—
368C2×C61#240912yes—
369C2×C61#240912yes—
370C2×C61#243411yescharacteristic
371C2×C61#243411yescharacteristic
372C2×C61#243611yescharacteristic
373C2×C61#243611yescharacteristic
374D61—28no—
375C23×Q8—618no—
376C23×Q8—611no—
377C23×Q8—612no—
378C23×Q8—1224no—
379C23×Q8—1224no—
380C23×Q8—1224no—
381C23×Q8—1224no—
382C23×Q8—1224no—
383C23×Q8—1224no—
384C23×Q8C2×D6111yescharacteristic
385C24×C4—611no—
386C24×C4—612no—
387C22×C4⋊C4—611no—
388C22×C4⋊C4C2×D6111yescharacteristic
389C22×C22⋊C4—612no—
390C22×C22⋊C4—612no—
391C22×C42—611no—
392C22×C42C2×D6111yescharacteristic
393#391—24no—
394#391—1224no—
395#391—1224no—
396#391—1224no—
397#380—1224no—
398C4×C22⋊C4—1224no—
399C2×#95—614no—
400C2×#95—614no—
401C2×#95—614no—
402C2×#95—612no—
403C2×#95—612no—
404C2×#95C2×D6114yes—
405C61#1392211yescharacteristic, complemented, Sylow
406C25—611no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—614no—
412C22×Q8—618no—
413C22×Q8—614no—
414C22×Q8—614no—
415C22×Q8—1224no—
416C22×Q8—1224no—
417C22×Q8—1224no—
418C22×Q8—1224no—
419C22×Q8—12232no—
420C22×Q8—12232no—
421C22×Q8—12232no—
422C22×Q8—12232no—
423C22×Q8—12232no—
424C22×Q8—12232no—
425C22×Q8—12232no—
426C22×Q8—1224no—
427C22×Q8—1222no—
428C22×Q8—1222no—
429C22×Q8—1222no—
430C22×Q8—1224no—
431C22×Q8—1222no—
432C22×Q8C4×D6114yes—
433C22×Q8D24414yes—
434C22×Q8C22⋊D6114yes—
435C23×C4—611no—
436C23×C4—612no—
437C23×C4—614no—
438C23×C4—614no—
439C23×C4—614no—
440C23×C4—612no—
441C23×C4—618no—
442C23×C4—612no—
443C23×C4—1224no—
444C23×C4—1224no—
445C23×C4—1224no—
446C23×C4—1224no—
447C23×C4—1224no—
448C23×C4—1222no—
449C23×C4—1222no—
450C23×C4—1222no—
451C23×C4—1224no—
452C23×C4—1222no—
453C23×C4C22×D6112yes—
454C23×C4C22×D6112yes—
455C23×C4C22×D6112yes—
456C23×C4C22×D6111yescharacteristic
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—1222no—
461C2×C4⋊C4—1222no—
462C2×C4⋊C4—1222no—
463C2×C22⋊C4—618no—
464C2×C22⋊C4—1224no—
465C2×C22⋊C4—1224no—
466C2×C22⋊C4—1224no—
467C2×C22⋊C4—1228no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—1222no—
472C2×C42—1222no—
473C2×C42—1222no—
474#95—28no—
475#95—1224no—
476#95—1224no—
477#95—1228no—
478#95—1228no—
479#95—1228no—
480C24—612no—
481C24—612no—
482C24—612no—
483C24—614no—
484C24—614no—
485C24—1221no—
486C24—1221no—
487C24—1221no—
488C24—1221no—
489C24—1222no—
490C24—1222no—
491C24C23×D6111yescharacteristic
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—28no—
497C2×Q8—28no—
498C2×Q8—6116no—
499C2×Q8—12216no—
500C2×Q8—12216no—
501C2×Q8—12216no—
502C2×Q8—12216no—
503C2×Q8—12216no—
504C2×Q8—12216no—
505C2×Q8—122256no—
506C2×Q8—1228no—
507C2×Q8—12216no—
508C2×Q8—1228no—
509C2×Q8—1228no—
510C2×Q8—1228no—
511C2×Q8—1228no—
512C2×Q8—1228no—
513C2×Q8#11758198116yescomplemented
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—612no—
530C22×C4—614no—
531C22×C4—612no—
532C22×C4—612no—
533C22×C4—614no—
534C22×C4—614no—
535C22×C4—6116no—
536C22×C4—614no—
537C22×C4—12216no—
538C22×C4—12216no—
539C22×C4—12216no—
540C22×C4—12216no—
541C22×C4—12216no—
542C22×C4—12216no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1222no—
549C22×C4—1221no—
550C22×C4—1222no—
551C22×C4—1228no—
552C22×C4—12216no—
553C22×C4—1228no—
554C22×C4—1228no—
555C22×C4—1228no—
556C22×C4—1228no—
557C22×C4—1228no—
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—1224no—
568C22×C4—1224no—
569C22×C4C2×C4×D6114yes—
570C22×C4C2×C4×D6112yes—
571C22×C4C2×D24414yes—
572C22×C4C2×D24412yes—
573C22×C4D4×D6112yes—
574C22×C4D4×D6112yes—
575C22×C4D4×D6112yes—
576C22×C4D4×D6112yes—
577C22×C4Q8×D6114yescomplemented
578C22×C4C2×C22⋊D6114yes—
579C22×C4C2×C22⋊D6112yes—
580C4⋊C4—44no—
581C4⋊C4—2444no—
582C22⋊C4—12216no—
583C22⋊C4—2448no—
584C42—44no—
585C42—2444no—
586C23—614no—
587C23—618no—
588C23—618no—
589C23—614no—
590C23—614no—
591C23—1222no—
592C23—1222no—
593C23—1224no—
594C23—1222no—
595C23—1222no—
596C23—1222no—
597C23—1222no—
598C23—1222no—
599C23—1224no—
600C23—1222no—
601C23—1224no—
602C23—1224no—
603C23—1224no—
604C23—1224no—
605C23—1224no—
606C23—1224no—
607C23—1224no—
608C23—1224no—
609C23C22×C4×D6111yescharacteristic
610C23C2×D4×D6111yescharacteristic
611C23C2×D4×D6111yescharacteristic
612C23C2×D4×D6111yescharacteristic
613C23C2×D4×D6111yescharacteristic
614C23C22×C22⋊D6111yescharacteristic
615C23C22×D24411yescharacteristic
616C23C2×Q8×D6112yes—
617C23#41×D6112yes—
618C23#1451982412yes—
619C23#1451982512yes—
620Q8—232no—
621Q8—12264no—
622Q8—12232no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—614no—
642C2×C4—618no—
643C2×C4—12264no—
644C2×C4—1224no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1224no—
648C2×C4—1222no—
649C2×C4—1224no—
650C2×C4—1222no—
651C2×C4—1224no—
652C2×C4—1222no—
653C2×C4—1224no—
654C2×C4—1222no—
655C2×C4—1224no—
656C2×C4—12232no—
657C2×C4—1224no—
658C2×C4—1224no—
659C2×C4—1224no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2444no—
664C2×C4—2444no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4C22⋊C4×D6114yes—
670C2×C4C22⋊C4×D6114yes—
671C2×C4C2×#1175819818yes—
672C2×C4C2×#1175819814yes—
673C2×C4#1451974514yes—
674C2×C4#1451974514yes—
675C2×C4#1451974714yes—
676C2×C4#1451974714yes—
677C22—618no—
678C22—1224no—
679C22—1224no—
680C22—1228no—
681C22—1228no—
682C22—1224no—
683C22—1228no—
684C22—1228no—
685C22—1224no—
686C22—1224no—
687C22—1224no—
688C22C2×C22⋊C4×D6111yescharacteristic
689C22C2×C22⋊C4×D6111yescharacteristic
690C22C22×#1175819811yescharacteristic
691C22C4×Q8×D6112yes—
692C22#1684023812yes—
693C22C2×#1451974511yescharacteristic
694C22C2×#1451974511yescharacteristic
695C22C2×#1451974711yescharacteristic
696C22C2×#1451974711yescharacteristic
697C22C22⋊Q8×D6112yes—
698C22#124×D6111yescharacteristic
699C22C4⋊Q8×D6111yescharacteristic
700C22#1684033211yescharacteristic
701C22#1684033512yes—
702C22#1684033711yescharacteristic
703C22#1684041912yes—
704C22#1684042012yes—
705C22#1684042212yes—
706C22#1684042412yes—
707C22#1684042512yes—
708C22Q8×C22⋊D6112yes—
709C22#1684042712yes—
710C22Q8×D24412yes—
711C4—28no—
712C4—44no—
713C4—82no—
714C4—1224no—
715C4—1228no—
716C4—4882no—
717C4—2444no—
718C4#1683961718yes—
719C2—1228no—
720C2C2×#1683961711yescharacteristic
721C2#391×D6111yescharacteristic
722C2#2144840211yescharacteristic
723C2Q8×#1175819812yes—
724C2#2144865312yes—
725C2#2144918012yes—
726C2#2144918212yes—
727C2#2144946011yescharacteristic
728C2#2144946211yescharacteristic
729C2#2144947411yescharacteristic
730C2#2144947611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#391C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#391D61
hypocenterC61#13922
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#16839669C2semidirect
3. C2×#16839668C2semidirect
4. C2×#16839667C2semidirect
7. #21444089C2semidirect
9. C2×C61×#391C2semidirect
18. C22×Q8×D61C4semidirect
87. C2×#11758198Q8semidirect
132. C2×Q8×C61C22⋊C4semidirect
158. C22×C4×C61C2×Q8semidirect
184. C22×Dic61C2×Q8semidirect
213. C2×Dic122C22⋊C4semidirect
345. C2×D61#391semidirect
358. C2×#391D61semidirect
405. C61#13922semidirect
513. C2×Q8#11758198semidirect
577. C22×C4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C23×Q8×D612
C2×#168396692
C2×#168396682
C2×#168396672
C2×#168396192
C2×C4×#117581982
#214440892
#214440402
C2×C61×#3912
#1392261