Finite Group Databasebeta

← #29681190

Subgroups — #29681190

Order 15616.

1914 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D61C211yesmaximal, characteristic, complemented
2C2×#16840269C211yesmaximal, characteristic
3C2×#16839779C211yesmaximal, characteristic, complemented
4#21448198C211yesmaximal, characteristic, complemented
5#21446118C218yesmaximal, complemented
6#21445530C211yesmaximal, characteristic, complemented
7#21445529C211yesmaximal, characteristic, complemented
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C23×C4×D61C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758189—21no—
12C2×M16×D61—24no—
13C2×M16×D61—24no—
14C2×M16×D61—22no—
15C2×M16×D61C2214yescomplemented
16C22×C8×D61—21no—
17#16840269—22no—
18#16840269—21no—
19#16840269—21no—
20#16840269C412yescomplemented
21#16840269C412yescomplemented
22#16840269C2214yes—
23C2×#14519758—21no—
24C2×#14519753C412yescomplemented
25C2×#14519748C412yescomplemented
26C2×#14519745—21no—
27C2×C4×C22⋊D61—22no—
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839779—24no—
31C2×#14519704C2214yescomplemented
32#16839623—21no—
33#16839619—22no—
34#16839617—21no—
35C4×#11758198C2214yescomplemented
36#16839523C2214yescomplemented
37#16839522C2214yescomplemented
38C22×#41×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#421—24no—
42C2×#104×C61C2214yescomplemented
43C24×D61D411yescharacteristic
44C22×C22⋊D61—22no—
45C23×Dic61D411yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—22no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D412yes—
54C22×C4×D61D412yes—
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61C2312yes—
58C2×#11758194—22no—
59C2×#11758194—21no—
60C2×#11758194D414yescomplemented
61C2×#11758194C2312yes—
62C2×#11758189—28no—
63C2×#11758189—24no—
64M16×D61—216no—
65M16×D61—28no—
66M16×D61—28no—
67C22×#92418—21no—
68C2×C8×D61—28no—
69C2×C8×D61—24no—
70#14519758—22no—
71#14519758—22no—
72#14519758—24no—
73#14519753—22no—
74#14519753—22no—
75#14519753C2×C414yes—
76#14519753C2×C414yes—
77#14519748—22no—
78#14519748—22no—
79#14519748C2×C414yes—
80#14519748C2×C414yes—
81#14519745—22no—
82#14519745—22no—
83#14519745—24no—
84C4×C22⋊D61—24no—
85C4×C22⋊D61—24no—
86C4×C22⋊D61—24no—
87C4×C22⋊D61—24no—
88#14519736—21no—
89#14519736—21no—
90#14519736—22no—
91#14519736—22no—
92#14519736C2×C412yes—
93#14519736C2312yes—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2×C412yes—
96C2×#11758196—22no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—22no—
101C2×#11758198—24no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2312yes—
104#14519704—28no—
105#14519684—24no—
106C2×#41×C61—21no—
107C2×#41×C61—21no—
108C2×#41×C61—22no—
109C2×#41×C61—22no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61C2×C412yes—
113C2×#41×C61C2312yes—
114C22×Q8×C61C2×C411yescharacteristic
115C22×D4×C61—21no—
116C22×D4×C61C2×C411yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C2×M16×C61—22no—
120C2×M16×C61—21no—
121C2×M16×C61D414yescomplemented
122C2×M16×C61C2312yes—
123C22×C8×C61—21no—
124#117×C61—22no—
125#117×C61—22no—
126C2×C4⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61C2312yes—
129#104×C61—28no—
130C24×C61—21no—
131C24×C61C2×D411yescharacteristic
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—44no—
135C23×D61C22⋊C411yescharacteristic
136C23×D61C22⋊C412yes—
137C23×D61C22⋊C411yescharacteristic
138C23×D61C2×D412yes—
139#41×C61—24no—
140#41×C61—24no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—42no—
146#41×C61—42no—
147#41×C61—42no—
148#41×C61—42no—
149C2×Q8×C61—21no—
150C2×Q8×C61—22no—
151C2×Q8×C61—22no—
152C2×Q8×C61C22×C412yes—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—21no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61C22×C412yes—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D412yes—
174C22×C4×C61#4112yes—
175C22×C4×C61#4112yes—
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C2×C22⋊D61—48no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61C22⋊C412yes—
185C22×Dic61C22⋊C411yescharacteristic
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C2×D412yes—
188C2×C4×D61—24no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—24no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—24no—
196C2×C4×D61—22no—
197C2×C4×D61—24no—
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61C22⋊C412yes—
207C2×C4×D61C22⋊C412yes—
208C2×C4×D61C22⋊C412yes—
209C2×C4×D61C22⋊C412yes—
210C2×C4×D61C22×C412yes—
211C2×C4×D61C22×C412yes—
212C2×C4×D61C2×D412yes—
213C2×C4×D61C2×D412yes—
214M16×C61—24no—
215M16×C61—22no—
216M16×C61C2×D414yescomplemented
217C2×C8×C61—24no—
218C2×C8×C61—22no—
219C4⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C42×C61—22no—
222C42×C61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—24no—
226C22⋊Dic61—24no—
227C22⋊Dic61—42no—
228#11758198—24no—
229#11758198—24no—
230#11758198—48no—
231C4⋊Dic61—22no—
232C4⋊Dic61—42no—
233C4⋊Dic61C22×C414yes—
234#11758196—24no—
235#11758196—24no—
236C4×Dic61—22no—
237C4×Dic61—22no—
238C4×Dic61—22no—
239C4×Dic61—22no—
240#11758194—24no—
241#11758194—22no—
242#11758194C2×D414yescomplemented
243C2×#92418—24no—
244C2×#92418—22no—
245#11758189—216no—
246C8×D61—216no—
247C23×C61—22no—
248C23×C61—42no—
249C23×C61—44no—
250C23×C61—42no—
251C23×C61C2×C22⋊C411yescharacteristic
252C23×C61C2×C22⋊C411yescharacteristic
253C23×C61#12112yes—
254C23×C61#12112yes—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—24no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—24no—
261C22×D61—22no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—48no—
268C22×D61—48no—
269C22×D61C2×C22⋊C412yes—
270C22×D61C2×C22⋊C412yes—
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—42no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—42no—
277D4×C61—42no—
278D4×C61—44no—
279D4×C61—42no—
280C2×C4×C61—22no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—44no—
285C2×C4×C61—44no—
286C2×C4×C61—42no—
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C4×D412yes—
290C2×C4×C61C4×D412yes—
291C2×C4×C61C4×D412yes—
292C2×C4×C61C4×D412yes—
293C2×C4×C61#12012yes—
294C2×C4×C61#12012yes—
295C2×C4×C61#12112yes—
296C2×C4×C61#12112yes—
297C2×C4×C61#12312yes—
298C2×C4×C61#12312yes—
299C2×C4×C61C23×C411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C22⋊D61—48no—
306C22⋊D61—48no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—44no—
314C2×Dic61—44no—
315C2×Dic61—42no—
316C2×Dic61C2×C22⋊C412yes—
317C2×Dic61C2×C22⋊C412yes—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—24no—
327C4×D61—24no—
328C4×D61—24no—
329C4×D61—24no—
330C8×C61—24no—
331#92418—24no—
332#20902—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—44no—
339C22×C61—42no—
340C22×C61—84no—
341C22×C61#38612yes—
342C22×C61#38612yes—
343C22×C61C22×C22⋊C411yescharacteristic
344C22×C61C2×#12111yescharacteristic
345C22×C61C2×#12111yescharacteristic
346C2×D61—28no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—44no—
353C2×D61—44no—
354C2×D61—48no—
355C2×D61—44no—
356C2×D61#42114yescomplemented
357C4×C61—42no—
358C4×C61—82no—
359C4×C61#38612yes—
360C4×C61#38612yes—
361C4×C61C2×C4×D411yescharacteristic
362C4×C61C2×C4×D411yescharacteristic
363C4×C61C2×#12011yescharacteristic
364C4×C61C2×#12311yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—44no—
368Dic61—82no—
369C23×M16—611no—
370C2×#525—611no—
371C2×#421—611no—
372C2×#421D6111yescharacteristic, complemented
373#2280—611no—
374#1871—618no—
375#1733—611no—
376#1733—611no—
377C2×C61—21no—
378C2×C61—21no—
379C2×C61—22no—
380C2×C61—22no—
381C2×C61—82no—
382C2×C61C2×#38611yescharacteristic
383C2×C61C2×#42112yes—
384D61—24no—
385D61—42no—
386C22×#41C2×D6111yescharacteristic
387C24×C4—611no—
388C22×M16—611no—
389C22×M16—614no—
390C22×M16—1221no—
391C22×M16—1224no—
392C22×M16—1222no—
393C22×M16—1224no—
394C22×M16C2×D6111yescharacteristic
395C23×C8—1221no—
396#525—612no—
397#525—612no—
398#525—614no—
399#525—1221no—
400#525—1221no—
401#525—1222no—
402C2×#123—1221no—
403C2×C22⋊Q8—612no—
404C2×#121—612no—
405C2×#120—1221no—
406C2×C4×D4—1222no—
407C2×#117—611no—
408C2×#117—611no—
409C2×#117C2×D6111yescharacteristic
410#421—24no—
411#421—1224no—
412C2×#104—614no—
413C2×#104C2×D6114yescomplemented
414#381—1221no—
415#380—1222no—
416#379—1221no—
417C4×C22⋊C4—614no—
418#339—614no—
419#339—614no—
420C61#2090211yescharacteristic, complemented, Sylow
421C25—611no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41C4×D6112yes—
429C2×#41C22×D6112yes—
430C22×Q8C4×D6111yescharacteristic
431C22×D4—21no—
432C22×D4—1222no—
433C22×D4C4×D6111yescharacteristic
434C23×C4—21no—
435C23×C4—611no—
436C23×C4—612no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—612no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—612no—
443C23×C4—612no—
444C23×C4—1222no—
445C23×C4—1222no—
446C23×C4—1222no—
447C23×C4—1222no—
448C23×C4C22×D6111yescharacteristic
449C2×M16—21no—
450C2×M16—22no—
451C2×M16—614no—
452C2×M16—612no—
453C2×M16—1224no—
454C2×M16—1228no—
455C2×M16—1228no—
456C2×M16—12216no—
457C2×M16—1221no—
458C2×M16—1222no—
459C2×M16—1228no—
460C2×M16C22⋊D6114yescomplemented
461C2×M16C22×D6112yes—
462C22×C8—21no—
463C22×C8—1224no—
464C22×C8—1228no—
465C22×C8—1221no—
466#123—1224no—
467#123—1222no—
468#123—1222no—
469C22⋊Q8—614no—
470C22⋊Q8—614no—
471C22⋊Q8—1222no—
472C22⋊Q8—1222no—
473#121—614no—
474#121—614no—
475#121—1222no—
476#121—1222no—
477#120—1224no—
478#120—1222no—
479#120—1222no—
480C4×D4—1224no—
481C4×D4—1224no—
482C4×D4—1224no—
483C4×D4—1224no—
484#117—22no—
485#117—22no—
486#117—612no—
487#117—612no—
488#117—1221no—
489#117—1221no—
490#117—1222no—
491#117—1222no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—612no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4—1221no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1221no—
502C2×C42—612no—
503C2×C42—1221no—
504C2×C42C22×D6112yes—
505#104—28no—
506#104—1228no—
507#95—1224no—
508C24—21no—
509C24—611no—
510C24—612no—
511C24—612no—
512C24—611no—
513C24—1222no—
514C24—1222no—
515C24—2444no—
516C24D4×D6111yescharacteristic
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—24no—
522#41—24no—
523#41—42no—
524#41—42no—
525#41—42no—
526#41—42no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8C2×C4×D6112yes—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—1224no—
539C2×D4—1224no—
540C2×D4—2448no—
541C2×D4C2×C4×D6112yes—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1224no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1224no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1224no—
574C22×C4—1222no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4C2×C4×D6111yescharacteristic
583C22×C4C2×C4×D6111yescharacteristic
584C22×C4#1175822212yes—
585C22×C4D4×D6112yes—
586C22×C4D4×D6111yescharacteristic
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4#1175822412yes—
590C22×C4C2×C22⋊D6112yes—
591C22×C4C23×D6111yescharacteristic
592M16—22no—
593M16—24no—
594M16—614no—
595M16—12216no—
596M16—1222no—
597M16—1224no—
598M16C2×C22⋊D6114yescomplemented
599C2×C8—22no—
600C2×C8—24no—
601C2×C8—12216no—
602C2×C8—1222no—
603C2×C8—1224no—
604C4⋊C4—42no—
605C4⋊C4—614no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1222no—
609C4⋊C4—2442no—
610C22⋊C4—42no—
611C22⋊C4—1224no—
612C22⋊C4—1224no—
613C22⋊C4—1224no—
614C22⋊C4—1224no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—2448no—
618C22⋊C4—2442no—
619C42—22no—
620C42—22no—
621C42—1222no—
622C42—1222no—
623C42—1222no—
624C42—1222no—
625C23—22no—
626C23—42no—
627C23—44no—
628C23—42no—
629C23—612no—
630C23—612no—
631C23—1224no—
632C23—1224no—
633C23—1224no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1224no—
638C23—1222no—
639C23—2442no—
640C23—2442no—
641C23—2442no—
642C23—2448no—
643C23—2448no—
644C23C22⋊C4×D6111yescharacteristic
645C23C22⋊C4×D6111yescharacteristic
646C23#1451974812yes—
647C23#1451975012yes—
648C23C2×D4×D6111yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652D4—22no—
653D4—22no—
654D4—42no—
655D4—42no—
656D4—44no—
657D4—42no—
658D4—2448no—
659D4—2448no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—42no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1224no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1224no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—1224no—
686C2×C4—1224no—
687C2×C4—2444no—
688C2×C4—2442no—
689C2×C4—2444no—
690C2×C4C22⋊C4×D6111yescharacteristic
691C2×C4C22⋊C4×D6111yescharacteristic
692C2×C4#1451973712yes—
693C2×C4#1451973712yes—
694C2×C4C4×C22⋊D6112yes—
695C2×C4C4×C22⋊D6112yes—
696C2×C4#1451974512yes—
697C2×C4#1451974512yes—
698C2×C4#1451974812yes—
699C2×C4#1451975012yes—
700C2×C4#1451975912yes—
701C2×C4#1451975912yes—
702C2×C4C22×C4×D6111yescharacteristic
703C2×C4C2×D4×D6111yescharacteristic
704C2×C4C2×D4×D6111yescharacteristic
705C2×C4C22×C22⋊D6111yescharacteristic
706C2×C4C2×#1175822411yescharacteristic
707C2×C4C2×#1175822211yescharacteristic
708C8—24no—
709C8—1224no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—42no—
717C22—84no—
718C22—614no—
719C22—1228no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—1222no—
725C22—2444no—
726C22—2444no—
727C22—2448no—
728C22—2444no—
729C22#1683963812yes—
730C22#1683963812yes—
731C22C2×C22⋊C4×D6111yescharacteristic
732C22C2×#1451974811yescharacteristic
733C22C2×#1451975011yescharacteristic
734C4—42no—
735C4—82no—
736C4—1222no—
737C4—1222no—
738C4—4882no—
739C4—2444no—
740C4#1683963812yes—
741C4#1683963812yes—
742C4C2×#1451973711yescharacteristic
743C4C2×C4×C22⋊D6111yescharacteristic
744C4C2×#1451974511yescharacteristic
745C4C2×#1451975911yescharacteristic
746C2—21no—
747C2—21no—
748C2—22no—
749C2—22no—
750C2—82no—
751C2—1224no—
752C2—2442no—
753C2C2×#1683963811yescharacteristic
754C2#421×D6112yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840269C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61#20902
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C22×M16×D61C2semidirect
3. C2×#16839779C2semidirect
4. #21448198C2semidirect
5. #21446118C2semidirect
6. #21445530C2semidirect
7. #21445529C2semidirect
8. C2×C61×#421C2semidirect
15. C2×M16×D61C22semidirect
20. #16840269C4semidirect
21. #16840269C4semidirect
24. C2×#14519753C4semidirect
25. C2×#14519748C4semidirect
31. C2×#14519704C22semidirect
35. C4×#11758198C22semidirect
36. #16839523C22semidirect
37. #16839522C22semidirect
42. C2×#104×C61C22semidirect
60. C2×#11758194D4semidirect
121. C2×M16×C61D4semidirect
216. M16×C61C2×D4semidirect
242. #11758194C2×D4semidirect
356. C2×D61#421semidirect
372. C2×#421D61semidirect
413. C2×#104C2×D61semidirect
420. C61#20902semidirect
460. C2×M16C22⋊D61semidirect
598. M16C2×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
C2×#168402692
C2×#168397792
#214481982
#214461182
#214455302
#214455292
C2×C61×#4212
#2090261