Finite Group Databasebeta

← #30615601

Subgroups — #30615601

Order 15616.

2258 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊#6923C211yesmaximal, characteristic, complemented
2C2×#16840753C212yesmaximal, complemented
3D61⋊#407C211yesmaximal, characteristic, complemented
4#21461806C214yesmaximal, complemented
5#21461804C214yesmaximal, complemented
6#21461508C212yesmaximal, complemented
7#525×D61C211yesmaximal, characteristic
8C24×#6923—21no—
9C2×D61⋊M16C2212yes—
10C22×C4⋊#6923—28no—
11C22×C4⋊#6923—22no—
12C22×C4⋊#6923—21no—
13C22×C4⋊#6923C2214yes—
14C22×C4⋊#6923C2212yes—
15#16840753—28no—
16C2×#14519840C2214yescomplemented
17C2×#14519839C2214yescomplemented
18#16840734—21no—
19#16840733—22no—
20#16840732—21no—
21D61⋊(C22⋊C8)C2214yes—
22#16840635C2218yescomplemented
23C2×#41×D61C2211yescharacteristic
24C23×C4×D61C2211yescharacteristic
25#16840275C412yescomplemented
26#16840274C411yescharacteristic, complemented
27#16840273C411yescharacteristic, complemented
28#16840272C412yescomplemented
29#16840271—22no—
30#16840270—21no—
31#16840269C411yescharacteristic, complemented
32#16840268—21no—
33#123×D61—21no—
34C22⋊Q8×D61C2212yes—
35#121×D61C2212yes—
36#120×D61—21no—
37C4×D4×D61—22no—
38#117×D61C2211yescharacteristic
39C61×#525C411yescharacteristic, complemented
40C23×#6923—28no—
41C23×#6923—24no—
42C23×#6923—22no—
43C23×#6923—48no—
44C2×#11758213—22no—
45D61⋊M16—24no—
46D61⋊M16—24no—
47C2×#11758217—22no—
48C2×D61⋊C8C2314yes—
49C2×C4⋊#6923—28no—
50C2×C4⋊#6923—216no—
51C2×C4⋊#6923—24no—
52C2×C4⋊#6923—22no—
53C2×C4⋊#6923—24no—
54C2×C4⋊#6923—216no—
55C2×C4⋊#6923D418yescomplemented
56C2×C4⋊#6923C2314yes—
57#14519840—28no—
58#14519839—28no—
59#14519834—24no—
60C22⋊#92420—24no—
61C24×D61D411yescharacteristic
62C2×#11758226C2×C411yescharacteristic, complemented
63C2×#11758222—21no—
64C2×#11758222C2×C411yescharacteristic, complemented
65C2×#11758224—21no—
66C2×#11758224C2×C411yescharacteristic, complemented
67#41×D61—24no—
68#41×D61—24no—
69C2×Q8×D61C2311yescharacteristic
70C2×D4×D61—22no—
71C2×D4×D61—21no—
72C2×D4×D61C2311yescharacteristic
73C23×Dic61D411yescharacteristic
74C22×C4×D61—24no—
75C22×C4×D61—24no—
76C22×C4×D61—21no—
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C412yes—
79C22×C4×D61D412yes—
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D412yes—
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2312yes—
84C22×C4×D61C2311yescharacteristic
85#14519762—22no—
86#14519761—21no—
87#14519760—21no—
88#14519759—22no—
89#14519758—21no—
90#14519757C2×C412yescomplemented
91#14519756C2×C412yescomplemented
92#14519755—22no—
93#14519754—22no—
94#14519753C2×C412yescomplemented
95#14519752C2×C412yescomplemented
96#14519751C2×C412yescomplemented
97#14519750—22no—
98#14519749—22no—
99#14519748C2×C412yescomplemented
100#14519747—21no—
101#14519747—22no—
102#14519746—21no—
103#14519745—21no—
104#14519745—22no—
105C4×D244—22no—
106D4×Dic61—22no—
107#14519739—22no—
108C4×C22⋊D61—22no—
109C4×C22⋊D61—22no—
110#14519737—22no—
111#14519737—22no—
112#14519736C2×C411yescharacteristic, complemented
113#14519735C2×C412yescomplemented
114#14519734—21no—
115#14519733—21no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61C2312yes—
118C22⋊C4×D61—21no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C42×D61—21no—
122C2×#41×C61C2×C411yescharacteristic, complemented
123C23×C4×C61C2×C411yescharacteristic
124#123×C61—21no—
125C22⋊Q8×C61C2×C412yescomplemented
126#121×C61C2×C412yescomplemented
127#120×C61—21no—
128C4×D4×C61—22no—
129#117×C61C2×C411yescharacteristic, complemented
130C24×C61C22⋊C411yescharacteristic
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—24no—
134C23×D61—24no—
135C23×D61—21no—
136C23×D61C22⋊C411yescharacteristic
137C23×D61C22⋊C412yes—
138C23×D61C2×D411yescharacteristic
139C23×D61C2×D412yes—
140C22×#6923—216no—
141C22×#6923—28no—
142C22×#6923—24no—
143C22×#6923—432no—
144C22×#6923—48no—
145C22×#6923—48no—
146C22×#6923—48no—
147#41×C61—24no—
148C2×Q8×C61C22×C411yescharacteristic, complemented
149C2×D4×C61—21no—
150C2×D4×C61—22no—
151C2×D4×C61C22×C411yescharacteristic, complemented
152C22×C4×C61—24no—
153C22×C4×C61—21no—
154C22×C4×C61C22⋊C412yes—
155C22×C4×C61C22⋊C411yescharacteristic
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C411yescharacteristic
158C2×C22⋊D61—21no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—21no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—21no—
163C22×Dic61—24no—
164C22×Dic61—21no—
165C22×Dic61C22⋊C412yes—
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C2×D412yes—
168C22×Dic61C2×D411yescharacteristic
169#11758226—24no—
170Q8×D61—22no—
171Q8×D61—22no—
172#11758224—24no—
173#11758224—44no—
174D4×D61—22no—
175D4×D61—22no—
176D4×D61—42no—
177D4×D61—42no—
178D4×D61—44no—
179D4×D61—44no—
180#11758222—24no—
181#11758222—44no—
182C2×D244—21no—
183C2×D244—22no—
184C2×D244C22×C411yescharacteristic, complemented
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—28no—
190C2×C4×D61—24no—
191C2×C4×D61—28no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—21no—
196C2×C4×D61—22no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61C22⋊C412yes—
202C2×C4×D61C22⋊C412yes—
203C2×C4×D61C22⋊C412yes—
204C2×C4×D61C22×C412yes—
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2×D412yes—
208C2×C4×D61C2×D414yes—
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61#4114yes—
212C2×C4×D61C2411yescharacteristic
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic, complemented
215#11758217—44no—
216C2×#92420—24no—
217C4⋊#6923—216no—
218C4⋊#6923—28no—
219C4⋊#6923—24no—
220C4⋊#6923C2×D418yes—
221#11758213—44no—
222D61⋊C8—24no—
223D61⋊C8—24no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61C22×C412yescomplemented
226C22⋊C4×C61—21no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C42×C61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238C4⋊Dic61—22no—
239C4⋊Dic61C22×C412yescomplemented
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243C4×Dic61—21no—
244C4×Dic61—22no—
245C23×C61—22no—
246C23×C61—24no—
247C23×C61—21no—
248C23×C61C2×C22⋊C411yescharacteristic
249C23×C61C2×C22⋊C412yes—
250C22×D61—28no—
251C22×D61—216no—
252C22×D61—28no—
253C22×D61—22no—
254C22×D61—24no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—21no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61C2×C22⋊C411yescharacteristic
270C22×D61C2×C22⋊C412yes—
271C22×D61#12012yes—
272C22×D61#12312yes—
273C22×D61AGL(1,ℤ/8)14yes—
274C22×D61#13714yes—
275C22×D61C22×D411yescharacteristic
276C2×#6923—28no—
277C2×#6923—416no—
278C2×#6923—432no—
279C2×#6923—48no—
280Q8×C61—22no—
281D4×C61—22no—
282D4×C61—42no—
283D4×C61—44no—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—42no—
290C2×C4×C61C2×C22⋊C412yes—
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C4×D414yes—
293C2×C4×C61C23×C411yescharacteristic
294C22⋊D61—42no—
295C22⋊D61—44no—
296C22⋊D61—42no—
297C22⋊D61—44no—
298C22⋊D61—42no—
299C2×Dic61—22no—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—42no—
305C2×Dic61C2×C22⋊C412yes—
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61#12114yes—
308C2×Dic61C22×D411yescharacteristic
309D244—22no—
310D244—42no—
311D244—44no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—24no—
315C4×D61—24no—
316C4×D61—24no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—42no—
322C4×D61—42no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61C4×D414yes—
326C4×D61#12012yes—
327C4×D61#12114yes—
328C4×D61#12312yes—
329C4×D61C22×D412yes—
330C4×D61C2×#4112yes—
331Dic122—22no—
332Dic122—42no—
333#92420—44no—
334#20909—611nomaximal, Sylow
335C22×C61—28no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61#38612yes—
342C22×C61#41714yescomplemented
343C22×C61C22×C22⋊C411yescharacteristic
344C2×D61—216no—
345C2×D61—28no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—24no—
350C2×D61—24no—
351C2×D61—24no—
352C2×D61—22no—
353C2×D61—24no—
354C2×D61—22no—
355C2×D61—24no—
356C2×D61—42no—
357C2×D61—41no—
358C2×D61—82no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61#38612yes—
362C2×D61#41714yescomplemented
363C2×D61C2×#12011yescharacteristic
364C2×D61C2×#12311yescharacteristic
365C2×D61C2×AGL(1,ℤ/8)12yes—
366C2×D61C2×#13712yes—
367#6923—48no—
368C4×C61—22no—
369C4×C61—42no—
370C4×C61—41no—
371C4×C61#38612yes—
372C4×C61C2×C4×D412yes—
373Dic61—22no—
374Dic61—42no—
375Dic61—41no—
376Dic61#38612yes—
377Dic61C2×#12112yes—
378C2×#525—611no—
379C23×C4⋊C4—611no—
380C2×#417—612no—
381C2×#407—611no—
382#1874—614no—
383#1872—614no—
384#1736—612no—
385C2×C61—22no—
386C2×C61—24no—
387C2×C61—81no—
388C2×C61C2×#38611yescharacteristic
389C2×C61C2×#41712yes—
390D61—22no—
391D61—24no—
392D61—81no—
393D61#300311yescharacteristic
394D61#300411yescharacteristic
395D61#309212yes—
396C22×#41—611no—
397C24×C4—611no—
398C24×C4—1221no—
399C22×M16—612no—
400#525—611no—
401#525—611no—
402#525—612no—
403#525—612no—
404#525—611no—
405#525—1222no—
406#525—1221no—
407#525—1221no—
408#525#692311yescharacteristic, complemented
409C2×#123—1221no—
410C2×C22⋊Q8—612no—
411C2×#121—612no—
412C2×#120—1221no—
413C2×C4×D4—1222no—
414C2×#117—611no—
415C22×C4⋊C4—612no—
416C22×C4⋊C4—614no—
417C22×C4⋊C4—1228no—
418C22×C4⋊C4—1222no—
419C22×C4⋊C4—1221no—
420#417—1228no—
421C2×#103—614no—
422C2×#102—614no—
423#407—1221no—
424#407—1222no—
425#407—1221no—
426C2×C22⋊C8—614no—
427#340—618no—
428C61#2090911yescharacteristic, complemented, Sylow
429C25—611no—
430C2×#41—611no—
431C2×#41—611no—
432C2×#41—611no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1224no—
436C2×#41—1224no—
437C2×#41C2×#692311yescharacteristic, complemented
438C22×Q8—611no—
439C22×D4—611no—
440C22×D4—1222no—
441C22×D4—1221no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—612no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—612no—
448C23×C4—612no—
449C23×C4—612no—
450C23×C4—611no—
451C23×C4—1224no—
452C23×C4—1224no—
453C23×C4—1221no—
454C23×C4—1222no—
455C23×C4—1224no—
456C23×C4—1228no—
457C23×C4—2448no—
458C23×C4C2×#692311yescharacteristic
459C2×M16—1222no—
460C2×M16—1224no—
461C2×M16—1224no—
462C2×M16—1222no—
463C22×C8—614no—
464#123—21no—
465#123—1222no—
466#123—1221no—
467#123—1222no—
468#123—1221no—
469#123—1221no—
470C22⋊Q8—612no—
471C22⋊Q8—612no—
472C22⋊Q8—612no—
473C22⋊Q8—1222no—
474C22⋊Q8—1222no—
475C22⋊Q8C2×#692312yescomplemented
476#121—612no—
477#121—612no—
478#121—612no—
479#121—1222no—
480#121—1222no—
481#121C2×#692312yescomplemented
482#120—21no—
483#120—1221no—
484#120—1222no—
485#120—1222no—
486#120—1221no—
487#120—1221no—
488C4×D4—22no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496#117—611no—
497#117—612no—
498#117—1221no—
499#117—1221no—
500#117C2×#692311yescharacteristic, complemented
501C2×C4⋊C4—614no—
502C2×C4⋊C4—618no—
503C2×C4⋊C4—612no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—12216no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4—12216no—
510C2×C4⋊C4—1228no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1222no—
514C2×C42—1221no—
515#103—1228no—
516#102—1228no—
517C22⋊C8—1224no—
518C22⋊C8—1224no—
519C24—611no—
520C24—612no—
521C24—612no—
522C24—611no—
523C24—1222no—
524C24—1222no—
525C24—1224no—
526C24—1224no—
527C24—1221no—
528C24C22⋊#692311yescharacteristic
529#41—24no—
530#41—1224no—
531#41—1224no—
532#41—1224no—
533#41—2444no—
534#41—2444no—
535C2×Q8—611no—
536C2×Q8—1221no—
537C2×Q8—1222no—
538C2×Q8—1222no—
539C2×Q8C22×#692311yescharacteristic, complemented
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—611no—
543C2×D4—1222no—
544C2×D4—1221no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1221no—
548C2×D4—1222no—
549C2×D4—1221no—
550C2×D4—1222no—
551C2×D4—1221no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4—2444no—
555C2×D4—2444no—
556C2×D4C22×#692311yescharacteristic, complemented
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—614no—
563C22×C4—614no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—611no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1228no—
579C22×C4—1224no—
580C22×C4—1228no—
581C22×C4—1224no—
582C22×C4—1221no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1224no—
588C22×C4—1221no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1228no—
592C22×C4—12216no—
593C22×C4—1221no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2448no—
597C22×C4—2448no—
598C22×C4—2448no—
599C22×C4—24432no—
600C22×C4C22⋊#692312yes—
601C22×C4C22⋊#692311yescharacteristic
602C22×C4C22×#692312yes—
603C22×C4C22×#692311yescharacteristic
604M16—2444no—
605M16—2444no—
606C2×C8—1224no—
607C2×C8—1224no—
608C2×C8—1224no—
609C4⋊C4—22no—
610C4⋊C4—618no—
611C4⋊C4—612no—
612C4⋊C4—1222no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1228no—
616C4⋊C4—1224no—
617C4⋊C4—12216no—
618C4⋊C4—1222no—
619C4⋊C4C22×#692312yescomplemented
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1221no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C42—21no—
632C42—1222no—
633C42—1221no—
634C23—22no—
635C23—24no—
636C23—21no—
637C23—611no—
638C23—612no—
639C23—612no—
640C23—614no—
641C23—614no—
642C23—612no—
643C23—611no—
644C23—1222no—
645C23—1222no—
646C23—1224no—
647C23—1222no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—1224no—
652C23—1224no—
653C23—1228no—
654C23—1228no—
655C23—12216no—
656C23—1222no—
657C23—1224no—
658C23—1221no—
659C23—2441no—
660C23—2441no—
661C23—2442no—
662C23—2442no—
663C23C2×C22⋊#692311yescharacteristic
664C23C2×C22⋊#692312yes—
665Q8—22no—
666Q8—1222no—
667Q8—2442no—
668D4—22no—
669D4—42no—
670D4—44no—
671D4—1222no—
672D4—2444no—
673D4—2442no—
674D4—2442no—
675D4—2444no—
676D4—2442no—
677D4—2442no—
678D4—2444no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—42no—
685C2×C4—614no—
686C2×C4—611no—
687C2×C4—611no—
688C2×C4—612no—
689C2×C4—614no—
690C2×C4—612no—
691C2×C4—614no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1224no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1228no—
706C2×C4—1222no—
707C2×C4—1221no—
708C2×C4—2442no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2448no—
715C2×C4—24416no—
716C2×C4—24432no—
717C2×C4—2442no—
718C2×C4C2×C22⋊#692312yes—
719C2×C4C2×C22⋊#692311yescharacteristic
720C2×C4D4×#692314yes—
721C2×C4C23×#692311yescharacteristic
722C8—2444no—
723C22—28no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—42no—
728C22—41no—
729C22—612no—
730C22—612no—
731C22—611no—
732C22—611no—
733C22—614no—
734C22—612no—
735C22—1222no—
736C22—1224no—
737C22—1224no—
738C22—1222no—
739C22—1224no—
740C22—1224no—
741C22—1224no—
742C22—1228no—
743C22—12216no—
744C22—1222no—
745C22—1222no—
746C22—1222no—
747C22—4881no—
748C22—4882no—
749C22—4881no—
750C22—2442no—
751C22—2441no—
752C22#1684071012yes—
753C22#1684075314yescomplemented
754C22C22×C22⋊#692311yescharacteristic
755C4—22no—
756C4—42no—
757C4—41no—
758C4—612no—
759C4—612no—
760C4—1222no—
761C4—2448no—
762C4—2442no—
763C4—2441no—
764C4#1684071012yes—
765C4C2×D4×#692312yes—
766C2—22no—
767C2—24no—
768C2—81no—
769C2—611no—
770C2—612no—
771C2—611no—
772C2—1224no—
773C2—1222no—
774C2—4881no—
775C2C2×#1684071011yescharacteristic
776C2C2×#1684075312yes—
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#525C4
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC2×C4×D61C24
hypercenter#525#6923
hypocenterC61#20909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊#6923C2semidirect
2. C2×#16840753C2semidirect
3. D61⋊#407C2semidirect
4. #21461806C2semidirect
5. #21461804C2semidirect
6. #21461508C2semidirect
16. C2×#14519840C22semidirect
17. C2×#14519839C22semidirect
22. #16840635C22semidirect
25. #16840275C4semidirect
26. #16840274C4semidirect
27. #16840273C4semidirect
28. #16840272C4semidirect
31. #16840269C4semidirect
39. C61×#525C4semidirect
55. C2×C4⋊#6923D4semidirect
62. C2×#11758226C2×C4semidirect
64. C2×#11758222C2×C4semidirect
66. C2×#11758224C2×C4semidirect
90. #14519757C2×C4semidirect
91. #14519756C2×C4semidirect
94. #14519753C2×C4semidirect
95. #14519752C2×C4semidirect
96. #14519751C2×C4semidirect
99. #14519748C2×C4semidirect
112. #14519736C2×C4semidirect
113. #14519735C2×C4semidirect
122. C2×#41×C61C2×C4semidirect
125. C22⋊Q8×C61C2×C4semidirect
126. #121×C61C2×C4semidirect
129. #117×C61C2×C4semidirect
148. C2×Q8×C61C22×C4semidirect
151. C2×D4×C61C22×C4semidirect
184. C2×D244C22×C4semidirect
214. C2×Dic122C22×C4semidirect
225. C4⋊C4×C61C22×C4semidirect
239. C4⋊Dic61C22×C4semidirect
342. C22×C61#417semidirect
362. C2×D61#417semidirect
408. #525#6923semidirect
428. C61#20909semidirect
437. C2×#41C2×#6923semidirect
475. C22⋊Q8C2×#6923semidirect
481. #121C2×#6923semidirect
500. #117C2×#6923semidirect
539. C2×Q8C22×#6923semidirect
556. C2×D4C22×#6923semidirect
619. C4⋊C4C22×#6923semidirect
753. C22#16840753semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊#69232
C2×#168407532
D61⋊#4072
#214618062
#214618042
#214615082
#525×D612
#2090961