Finite Group Databasebeta

← #29852654

Subgroups — #29852654

Order 15616.

2834 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
2#21454108C212yesmaximal, complemented
3#21454103C211yesmaximal, characteristic, complemented
4#21454098C211yesmaximal, characteristic
5#21451634C211yesmaximal, characteristic, complemented
6#21451601C212yesmaximal, complemented
7#21451563C211yesmaximal, characteristic, complemented
8#21450076C214yesmaximal, complemented
9#21449956C214yesmaximal, complemented
10#21449625C214yesmaximal, complemented
11#21449551C214yesmaximal, complemented
12#21448484C212yesmaximal, complemented
13#21448422C211yesmaximal, characteristic, complemented
14C4×#14519745C212yesmaximal, complemented
15C2×C61×#539C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519758C2212yes—
20C2×#14519753C2212yes—
21C2×#14519748C2212yes—
22C2×#14519745C2212yes—
23C2×C4×C22⋊D61C2214yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C2×C4⋊C4×D61—28no—
28C2×C4⋊C4×D61C2214yes—
29C2×C4⋊C4×D61C2214yes—
30#16839701C2214yescomplemented
31#16839700C2212yescomplemented
32#16839698C2214yescomplemented
33#16839695C2214yescomplemented
34#16839693C2212yescomplemented
35#16839692C2214yescomplemented
36#16839687C2214yescomplemented
37#16839685C2214yescomplemented
38#16839681C2212yescomplemented
39#16839676C2212yescomplemented
40#16839657C2214yescomplemented
41#16839656C2214yescomplemented
42#16839648C2214yescomplemented
43#16839648C2214yescomplemented
44#16839646C2214yescomplemented
45#16839642C2212yes—
46#16839642C2212yes—
47#16839638C2214yes—
48#16839638C2214yes—
49#16839638C2214yes—
50#16839638C2214yes—
51#16839635C2214yescomplemented
52#16839634C2212yes—
53#16839634C2212yes—
54#16839633C2214yes—
55#16839633C2214yes—
56#16839633C2214yes—
57#16839633C2214yes—
58#16839625C2212yes—
59#16839623C2212yes—
60#16839622C2211yescharacteristic
61#16839622C2211yescharacteristic
62#16839619C2212yes—
63#16839619C2212yes—
64#16839617C2212yes—
65C4×#11758198C2214yes—
66C4×C22⋊Dic61C2212yes—
67C61×#539—28no—
68C2×#126×C61C2212yescomplemented
69C2×#125×C61C2212yescomplemented
70C2×#123×C61C2212yes—
71C2×#123×C61C2212yescomplemented
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2212yescomplemented
74C2×#121×C61C2211yescharacteristic
75C2×C4×D4×C61C2212yes—
76C22×C4⋊C4×C61C2211yescharacteristic
77C24×D61C2311yescharacteristic
78C22×C22⋊D61C2314yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61—24no—
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—44no—
88C22×C4×D61—44no—
89C22×C4×D61C2314yes—
90C22×C4×D61C2314yes—
91C22×C4×D61C2312yes—
92C22×C4×D61C2312yes—
93#14519758—28no—
94#14519753—44no—
95#14519748—44no—
96#14519745—28no—
97C4×C22⋊D61—48no—
98C2×C4⋊Dic61—24no—
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2312yes—
101C2×C4⋊Dic61C2312yes—
102C2×#11758196—24no—
103C2×#11758196—24no—
104C2×#11758196C2312yes—
105C2×#11758196C2314yes—
106C2×#11758196C2312yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C4⋊C4×D61—216no—
111C4⋊C4×D61—216no—
112C2×C22⋊Dic61C2314yes—
113C2×C22⋊Dic61C2312yes—
114C2×C22⋊Dic61C2312yes—
115C2×C22⋊Dic61C2314yes—
116C2×C22⋊Dic61C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×C4×Dic61C2314yes—
121#14519684C2314yes—
122#14519684C2312yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2312yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61C2312yes—
134C22×D4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2312yes—
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139#126×C61—28no—
140#125×C61—28no—
141#123×C61—28no—
142#123×C61—28no—
143C22⋊Q8×C61—24no—
144C22⋊Q8×C61—28no—
145#121×C61—24no—
146C4×D4×C61—28no—
147C2×C4⋊C4×C61D418yescomplemented
148C2×C4⋊C4×C61C2312yes—
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2312yes—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2312yes—
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2312yes—
155C2×C4⋊C4×C61C2312yes—
156C2×C22⋊C4×C61C2312yes—
157C2×C22⋊C4×C61C2312yes—
158C2×C22⋊C4×C61C2312yes—
159C2×C22⋊C4×C61C2312yes—
160C2×C22⋊C4×C61C2312yes—
161C2×C42×C61C2312yes—
162C24×C61C2412yes—
163C24×C61C2411yescharacteristic
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—24no—
167C23×D61—24no—
168C23×D61#4114yes—
169C23×D61C2412yes—
170C2×Q8×C61—22no—
171C2×Q8×C61—42no—
172C2×D4×C61—24no—
173C2×D4×C61—24no—
174C2×D4×C61—24no—
175C2×D4×C61—22no—
176C2×D4×C61—42no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—24no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—44no—
183C22×C4×C61C2×D414yes—
184C22×C4×C61C2×D414yes—
185C22×C4×C61C2×D414yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2411yescharacteristic
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—28no—
194C2×C22⋊D61—28no—
195C2×C22⋊D61—28no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61#4114yes—
203C22×Dic61C2412yes—
204C22×Dic61C2412yes—
205C22×Dic61C2414yes—
206C22×Dic61C2414yes—
207C22×Dic61C2412yes—
208C2×C4×D61—232no—
209C2×C4×D61—28no—
210C2×C4×D61—28no—
211C2×C4×D61—28no—
212C2×C4×D61—28no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—28no—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61—42no—
219C2×C4×D61—44no—
220C2×C4×D61—42no—
221C2×C4×D61—416no—
222C2×C4×D61—416no—
223C4⋊C4×C61—24no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61C2×D418yes—
230C4⋊C4×C61C2×D418yes—
231C22⋊C4×C61—24no—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—24no—
235C22⋊C4×C61—24no—
236C42×C61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239C22⋊Dic61—28no—
240C22⋊Dic61—44no—
241C22⋊Dic61—44no—
242#11758198—28no—
243#11758198—28no—
244#11758198—28no—
245C4⋊Dic61—28no—
246C4⋊Dic61—42no—
247C4⋊Dic61—42no—
248#11758196—28no—
249#11758196—24no—
250#11758196—24no—
251#11758196—28no—
252#11758196—44no—
253#11758196—44no—
254C4×Dic61—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—24no—
261C23×C61—24no—
262C23×C61C22×D412yes—
263C23×C61C2×#4112yes—
264C23×C61C2×#4112yes—
265C23×C61C2511yescharacteristic
266C22×D61—28no—
267C22×D61—28no—
268C22×D61—216no—
269C22×D61—28no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—216no—
275C22×D61C2×#4114yes—
276C22×D61H(5,𝔽2)14yes—
277C22×D612−1+414yes—
278Q8×C61—82no—
279D4×C61—48no—
280D4×C61—82no—
281C2×C4×C61—28no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—44no—
295C2×C4×C61—44no—
296C2×C4×C61—84no—
297C2×C4×C61C22×D414yes—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D414yes—
301C22⋊D61—416no—
302C2×Dic61—28no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—22no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—44no—
317C2×Dic61—44no—
318C2×Dic61C2×#4114yes—
319C4×D61—232no—
320C4×D61—416no—
321C4×D61—48no—
322C4×D61—48no—
323#34989—611nomaximal, Sylow
324C22×C61—24no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—24no—
328C22×C61—42no—
329C22×C61—44no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—44no—
333C22×C61#52514yes—
334C22×C61C23×D411yescharacteristic
335C22×C61C22×#4111yescharacteristic
336C22×C61C22×#4111yescharacteristic
337C22×C61C2×H(5,𝔽2)12yes—
338C22×C61C2×2−1+412yes—
339C2×D61—232no—
340C2×D61—24no—
341C2×D61—24no—
342C2×D61—24no—
343C2×D61—24no—
344C2×D61—24no—
345C2×D61—24no—
346C2×D61#53918yescomplemented
347C4×C61—24no—
348C4×C61—24no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354Dic61—24no—
355Dic61—44no—
356Dic61—42no—
357Dic61—42no—
358Dic61—44no—
359C2×#539D6111yescharacteristic, complemented
360C23×C4⋊C4—611no—
361#2849—612no—
362#2848—611no—
363#2847—611no—
364#2627—611no—
365#2623—612no—
366#2618—611no—
367#2481—614no—
368#2473—614no—
369#2449—614no—
370#2443—614no—
371#2322—612no—
372#2313—611no—
373C4×#120—612no—
374C2×C61—24no—
375C2×C61—82no—
376C2×C61C2×#52511yescharacteristic
377C2×C61C2×#53912yes—
378C2×C61#348411yescharacteristic
379C2×C61#348611yescharacteristic
380C2×C61#349212yes—
381D61—28no—
382C24×C4—611no—
383C24×C4—611no—
384C24×C4—611no—
385#539—28no—
386C2×#126C2×D6112yescomplemented
387C2×#125C2×D6112yescomplemented
388C2×#123—612no—
389C2×#123C2×D6112yes—
390C2×#123C2×D6112yescomplemented
391C2×C22⋊Q8—612no—
392C2×C22⋊Q8C2×D6111yescharacteristic
393C2×C22⋊Q8C2×D6112yescomplemented
394C2×#121—612no—
395C2×#121C2×D6111yescharacteristic
396C2×#120—612no—
397C2×C4×D4—614no—
398C2×C4×D4C2×D6112yes—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—614no—
403C22×C4⋊C4—614no—
404C22×C4⋊C4—1228no—
405C22×C4⋊C4C2×D6111yescharacteristic
406#400—612no—
407#400—614no—
408#399—614no—
409#398—614no—
410#398—612no—
411#398—614no—
412#397—614no—
413#396—614no—
414#395—612no—
415#394—612no—
416#389—614no—
417#388—614no—
418#387—614no—
419#387—614no—
420#387—614no—
421#386—612no—
422#386—612no—
423#386—614no—
424#386—614no—
425#386—614no—
426#386—614no—
427#385—614no—
428#385—614no—
429#385—614no—
430#385—614no—
431#385—614no—
432#385—612no—
433#385—612no—
434#381—612no—
435#381—612no—
436#380—611no—
437#380—611no—
438#380—612no—
439#380—612no—
440#379—612no—
441C4×C22⋊C4—612no—
442C4×C22⋊C4—614no—
443C61#3498911yescharacteristic, complemented, Sylow
444C25—611no—
445C22×Q8C22×D6111yescharacteristic
446C22×D4—614no—
447C22×D4C22×D6112yes—
448C22×D4C22×D6111yescharacteristic
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—614no—
453C23×C4—614no—
454C23×C4—612no—
455C23×C4—612no—
456C23×C4—1224no—
457C23×C4—1224no—
458C23×C4—1224no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4—2444no—
462C23×C4—2444no—
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6112yes—
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467#126—28no—
468#125—28no—
469#123—28no—
470#123—28no—
471#123—1228no—
472C22⋊Q8—24no—
473C22⋊Q8—28no—
474C22⋊Q8—2444no—
475#121—24no—
476#121—2444no—
477#120—1228no—
478C4×D4—28no—
479C4×D4—2448no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—612no—
482C2×C4⋊C4—612no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—614no—
486C2×C4⋊C4—612no—
487C2×C4⋊C4—612no—
488C2×C4⋊C4—614no—
489C2×C4⋊C4—1224no—
490C2×C4⋊C4—1224no—
491C2×C4⋊C4—1224no—
492C2×C4⋊C4—12216no—
493C2×C4⋊C4—12216no—
494C2×C4⋊C4C22⋊D6118yescomplemented
495C2×C4⋊C4C22×D6112yes—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6112yes—
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C4⋊C4C22×D6112yes—
500C2×C4⋊C4C22×D6112yes—
501C2×C4⋊C4C22×D6112yes—
502C2×C4⋊C4C22×D6112yes—
503C2×C22⋊C4—612no—
504C2×C22⋊C4—612no—
505C2×C22⋊C4—614no—
506C2×C22⋊C4—614no—
507C2×C22⋊C4—614no—
508C2×C22⋊C4—614no—
509C2×C22⋊C4—614no—
510C2×C22⋊C4—614no—
511C2×C22⋊C4C22×D6112yes—
512C2×C22⋊C4C22×D6112yes—
513C2×C22⋊C4C22×D6112yes—
514C2×C22⋊C4C22×D6112yes—
515C2×C22⋊C4C22×D6112yes—
516C2×C42—614no—
517C2×C42C22×D6112yes—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—612no—
522#95—614no—
523#95—612no—
524#95—614no—
525#95—614no—
526#95—614no—
527#95—614no—
528#95—614no—
529C24—612no—
530C24—614no—
531C24—1224no—
532C24—1224no—
533C24—1222no—
534C24—1222no—
535C24C23×D6112yes—
536C24C23×D6111yescharacteristic
537C2×Q8—22no—
538C2×Q8—42no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—42no—
544C2×D4—1228no—
545C2×D4—1228no—
546C2×D4—1228no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—44no—
553C22×C4—614no—
554C22×C4—612no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—1228no—
560C22×C4—1228no—
561C22×C4—12232no—
562C22×C4—1228no—
563C22×C4—1224no—
564C22×C4—1224no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1228no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1228no—
571C22×C4—1224no—
572C22×C4—1224no—
573C22×C4—2444no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—24416no—
577C22×C4—24416no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4C2×C22⋊D6114yes—
581C22×C4C2×C22⋊D6114yes—
582C22×C4C2×C22⋊D6114yes—
583C22×C4C23×D6112yes—
584C22×C4C23×D6112yes—
585C22×C4C23×D6112yes—
586C22×C4C23×D6112yes—
587C22×C4C23×D6112yes—
588C22×C4C23×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—1228no—
597C4⋊C4—1228no—
598C4⋊C4—1224no—
599C4⋊C4—1224no—
600C4⋊C4—1228no—
601C4⋊C4—2444no—
602C4⋊C4—2444no—
603C4⋊C4—2442no—
604C4⋊C4—2442no—
605C4⋊C4C2×C22⋊D6118yes—
606C4⋊C4C2×C22⋊D6118yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—1228no—
613C22⋊C4—1228no—
614C22⋊C4—1228no—
615C22⋊C4—1228no—
616C22⋊C4—1224no—
617C22⋊C4—1224no—
618C22⋊C4—2444no—
619C22⋊C4—2444no—
620C42—24no—
621C42—2444no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—614no—
630C23—614no—
631C23—614no—
632C23—12216no—
633C23—1228no—
634C23—1228no—
635C23—12216no—
636C23—1228no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23C22×C22⋊D6112yes—
642C23#41×D6112yes—
643C23#41×D6112yes—
644C23C24×D6111yescharacteristic
645Q8—82no—
646D4—48no—
647D4—82no—
648D4—24416no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—84no—
665C2×C4—614no—
666C2×C4—12232no—
667C2×C4—1228no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1224no—
673C2×C4—1224no—
674C2×C4—1224no—
675C2×C4—1224no—
676C2×C4—1222no—
677C2×C4—1224no—
678C2×C4—1222no—
679C2×C4—1224no—
680C2×C4—1224no—
681C2×C4—24416no—
682C2×C4—2448no—
683C2×C4—2448no—
684C2×C4—2444no—
685C2×C4—2444no—
686C2×C4C22×C22⋊D6114yes—
687C2×C4C22×C22⋊D6114yes—
688C2×C4C22×C22⋊D6112yes—
689C2×C4C22×C22⋊D6112yes—
690C22—22no—
691C22—24no—
692C22—24no—
693C22—22no—
694C22—42no—
695C22—44no—
696C22—42no—
697C22—44no—
698C22—42no—
699C22—618no—
700C22—12232no—
701C22—1224no—
702C22—1224no—
703C22—1224no—
704C22—1224no—
705C22—1224no—
706C22—1224no—
707C22#1684026914yes—
708C22C23×C22⋊D6111yescharacteristic
709C22C2×#41×D6111yescharacteristic
710C22C2×#41×D6111yescharacteristic
711C22H(5,𝔽2)×D6112yes—
712C222−1+4×D6112yes—
713C4—24no—
714C4—24no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—1224no—
721C4—2444no—
722C4—2444no—
723C4—2442no—
724C4—2442no—
725C2—24no—
726C2—82no—
727C2—1228no—
728C2C2×#1684026911yescharacteristic
729C2#539×D6112yes—
730C2#2145945011yescharacteristic
731C2#2145946711yescharacteristic
732C2#2145952412yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC2×C61×#539C2
prime radical#21454098C2
hypercenterC2×#539D61
hypocenterC61#34989
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D61C2semidirect
2. #21454108C2semidirect
3. #21454103C2semidirect
5. #21451634C2semidirect
6. #21451601C2semidirect
7. #21451563C2semidirect
8. #21450076C2semidirect
9. #21449956C2semidirect
10. #21449625C2semidirect
11. #21449551C2semidirect
12. #21448484C2semidirect
13. #21448422C2semidirect
14. C4×#14519745C2semidirect
15. C2×C61×#539C2semidirect
30. #16839701C22semidirect
31. #16839700C22semidirect
32. #16839698C22semidirect
33. #16839695C22semidirect
34. #16839693C22semidirect
35. #16839692C22semidirect
36. #16839687C22semidirect
37. #16839685C22semidirect
38. #16839681C22semidirect
39. #16839676C22semidirect
40. #16839657C22semidirect
41. #16839656C22semidirect
42. #16839648C22semidirect
43. #16839648C22semidirect
44. #16839646C22semidirect
51. #16839635C22semidirect
68. C2×#126×C61C22semidirect
69. C2×#125×C61C22semidirect
71. C2×#123×C61C22semidirect
73. C2×C22⋊Q8×C61C22semidirect
147. C2×C4⋊C4×C61D4semidirect
346. C2×D61#539semidirect
359. C2×#539D61semidirect
386. C2×#126C2×D61semidirect
387. C2×#125C2×D61semidirect
390. C2×#123C2×D61semidirect
393. C2×C22⋊Q8C2×D61semidirect
443. C61#34989semidirect
494. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
#214541082
#214541032
#214540982
#214516342
#214516012
#214515632
#214500762
#214499562
#214496252
#214495512
#214484842
#214484222
C4×#145197452
C2×C61×#5392
#3498961