Finite Group Databasebeta

← #29732239

Subgroups — #29732239

Order 15616.

1164 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic
2C2×#16840001C211yesmaximal, characteristic, complemented
3#21454153C211yesmaximal, characteristic, complemented
4#21447159C211yesmaximal, characteristic, complemented
5#21447058C211yesmaximal, characteristic, complemented
6#21446968C211yesmaximal, characteristic, complemented
7#21446911C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic
9#21446242C211yesmaximal, characteristic, complemented
10#21446157C211yesmaximal, characteristic, complemented
11#21446155C211yesmaximal, characteristic, complemented
12#21446084C211yesmaximal, characteristic, complemented
13#21446064C211yesmaximal, characteristic, complemented
14C2×#16839516C211yesmaximal, characteristic, complemented
15C2×C61×#465C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16840293—24no—
19#16840293—24no—
20C2×#14519770—21no—
21C2×#14519768C2211yescharacteristic
22C2×#14519764C2211yescharacteristic
23C2×#14519758—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×D4×Dic61—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4×Dic61C2211yescharacteristic
30#16840001—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38#16839669C2211yescharacteristic
39#16839669C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839658C2211yescharacteristic
42#16839643—21no—
43#16839643—21no—
44#16839634—21no—
45#16839623—21no—
46#16839622C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#465—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C23×Dic61D411yescharacteristic
66C23×Dic61D411yescharacteristic
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—41no—
70C22×#92418—22no—
71C22×#92418—22no—
72C22×#92418—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519770—28no—
76#14519768—22no—
77#14519768—22no—
78#14519764—22no—
79#14519764—22no—
80#14519758—28no—
81#14519756—22no—
82#14519756D414yes—
83#14519742—22no—
84#14519742—22no—
85D4×Dic61—28no—
86D4×Dic61—22no—
87D4×Dic61—22no—
88#14519733—28no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110#14519710—22no—
111#14519702—22no—
112#14519702—41no—
113#14519701—22no—
114#14519700—22no—
115#14519698—22no—
116#14519698—41no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×SD16×C61—41no—
131C22×C8×C61—22no—
132C22×C8×C61—22no—
133C22×C8×C61—41no—
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—22no—
138#121×C61—22no—
139#121×C61D414yes—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145#106×C61—22no—
146#103×C61—22no—
147#102×C61—22no—
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61C2×D412yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2411yescharacteristic
176C22×Dic61—24no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—41no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122C2×D412yes—
199SD16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—44no—
206C2×C8×C61#4112yes—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—42no—
214C22⋊Dic61—24no—
215C22⋊Dic61—24no—
216C22⋊Dic61—24no—
217C22⋊Dic61—24no—
218C22⋊Dic61—42no—
219#11758202—44no—
220C4⋊Dic61—24no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61C2×D412yes—
227#11758196—24no—
228#11758196—24no—
229#11758196—24no—
230#11758196—42no—
231#11758196—42no—
232C4×Dic61—24no—
233C4×Dic61—22no—
234C4×Dic61—22no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—44no—
245C2×#92418#4112yes—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61#12012yes—
258C23×C61#13512yes—
259C23×C61#13712yes—
260C23×C61C22×D411yescharacteristic
261Q8×C61—41no—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
265D4×C61—22no—
266D4×C61—22no—
267D4×C61—48no—
268D4×C61—41no—
269D4×C61—41no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61#12012yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—44no—
306C2×Dic61—48no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—44no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61#13512yes—
319Dic122—22no—
320Dic122—22no—
321Dic122—41no—
322Dic122—41no—
323C8×C61—22no—
324C8×C61—41no—
325#92418—22no—
326#92418—41no—
327#25499—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61#45214yes—
342C22×C61C2×#12011yescharacteristic
343C22×C61#53211yescharacteristic
344C22×C61#53711yescharacteristic
345C22×C61C2×#13511yescharacteristic
346C22×C61C2×#13511yescharacteristic
347C22×C61C2×#13711yescharacteristic
348C22×C61#57511yescharacteristic
349C4×C61—22no—
350C4×C61—42no—
351C4×C61—81no—
352C4×C61—81no—
353C4×C61#54611yescharacteristic
354C4×C61#54611yescharacteristic
355C4×C61#54711yescharacteristic
356C4×C61#54711yescharacteristic
357Dic61—22no—
358Dic61—42no—
359Dic61—41no—
360Dic61—41no—
361Dic61—41no—
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365C2×#529—611no—
366C2×#467—611no—
367C2×#465D6111yescharacteristic
368#2855—611no—
369#2059—611no—
370#2042—611no—
371#2026—611no—
372#2015—611no—
373#1893—611no—
374#1892—611no—
375#1878—611no—
376#1877—611no—
377#1865—611no—
378#1862—611no—
379C2×#336—611no—
380C2×C61—24no—
381C2×C61—82no—
382C2×C61#243011yescharacteristic
383C2×C61C2×#45211yescharacteristic
384C2×C61#300211yescharacteristic
385C2×C61#316811yescharacteristic
386C2×C61#318111yescharacteristic
387C2×C61#324811yescharacteristic
388C2×C61#325011yescharacteristic
389C22×Q16—611no—
390C22×SD16C2×D6111yescharacteristic
391C23×C8—611no—
392C23×C8C2×D6111yescharacteristic
393#529—1224no—
394#529—1224no—
395C2×#126—1221no—
396C2×#125—611no—
397C2×#124—611no—
398C2×#123—1221no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8C2×D6111yescharacteristic
401C2×#121C2×D6111yescharacteristic
402C2×C4×Q8—611no—
403C2×C4×D4—611no—
404C2×C4×D4—1221no—
405C2×#117—1221no—
406C22×C42—611no—
407#467—1224no—
408#465—24no—
409C2×#107—611no—
410C2×#106C2×D6111yescharacteristic
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103C2×D6111yescharacteristic
416C2×#102—611no—
417C2×#102—611no—
418C2×#102C2×D6111yescharacteristic
419#391—611no—
420#391—611no—
421#389—611no—
422#389—611no—
423#387—1221no—
424#387—1221no—
425#385—1221no—
426#381—1221no—
427#380—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435#336—611no—
436C61#2549911yescharacteristic, complemented, Sylow
437C22×Q8—611no—
438C22×Q8C22×D6111yescharacteristic
439C22×D4—21no—
440C22×D4C22×D6111yescharacteristic
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C2×Q16—1222no—
446C2×Q16—1222no—
447C2×Q16—2441no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—41no—
451C22×C8—22no—
452C22×C8—22no—
453C22×C8—41no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—1222no—
457C22×C8—1222no—
458C22×C8—2441no—
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461#126—1228no—
462#125—1222no—
463#125—1222no—
464#124—1222no—
465#124—1222no—
466#123—1228no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—614no—
470C22⋊Q8—1222no—
471#121—22no—
472#121C22⋊D6114yes—
473C4×Q8—1222no—
474C4×Q8—1222no—
475C4×D4—1222no—
476C4×D4—1228no—
477C4×D4—1222no—
478#117—1228no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C42—611no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1222no—
504C2×C42—1222no—
505#107—1222no—
506#106—22no—
507#103—22no—
508#103—1222no—
509#103—1222no—
510#103—1222no—
511#103—2441no—
512#102—22no—
513#102—1222no—
514#102—2441no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522C24—21no—
523C24D4×D6111yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—612no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4C2×C22⋊D6112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1222no—
557C22×C4—1224no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—2442no—
567C22×C4—2441no—
568C22×C4—2442no—
569C22×C4D4×D6112yes—
570C22×C4D4×D6111yescharacteristic
571C22×C4C2×C22⋊D6112yes—
572C22×C4C23×D6111yescharacteristic
573Q16—2444no—
574SD16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—44no—
581C2×C8—612no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—2444no—
588C2×C8#1175822412yes—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—612no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1221no—
598C4⋊C4—1224no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—2442no—
604C4⋊C4—2442no—
605C4⋊C4C2×C22⋊D6112yes—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—1224no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C22⋊C4—2442no—
613C42—1224no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1222no—
619C42—1222no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23#1451974512yes—
632C23#1451979812yes—
633C23#1451980612yes—
634C23C2×D4×D6111yescharacteristic
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—1222no—
640Q8—1222no—
641Q8—2441no—
642Q8—2441no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—612no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—2444no—
678C2×C4—2448no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2444no—
690C2×C4#1451974512yes—
691C2×C4C2×D4×D6111yescharacteristic
692C2×C4C22×C22⋊D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822411yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982411yescharacteristic
697C8—22no—
698C8—41no—
699C8—1222no—
700C8—2441no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1683992114yes—
715C22C2×#1451974511yescharacteristic
716C22#1684030711yescharacteristic
717C22#1684033911yescharacteristic
718C22#135×D6111yescharacteristic
719C22C2×#1451979811yescharacteristic
720C22C2×#1451980611yescharacteristic
721C22#1684055911yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—1222no—
727C4—4881no—
728C4—4881no—
729C4—2441no—
730C4—2441no—
731C4—2441no—
732C4—2442no—
733C4—2442no—
734C4#1684040111yescharacteristic
735C4#1684040611yescharacteristic
736C4#1684041111yescharacteristic
737C4#1684041211yescharacteristic
738C2—24no—
739C2—82no—
740C2#2144942511yescharacteristic
741C2C2×#1683992111yescharacteristic
742C2#2145503311yescharacteristic
743C2#2145638211yescharacteristic
744C2#2145652111yescharacteristic
745C2#2145714911yescharacteristic
746C2#2145716711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#465D61
hypocenterC61#25499
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#16840001C2semidirect
3. #21454153C2semidirect
4. #21447159C2semidirect
5. #21447058C2semidirect
6. #21446968C2semidirect
7. #21446911C2semidirect
9. #21446242C2semidirect
10. #21446157C2semidirect
11. #21446155C2semidirect
12. #21446084C2semidirect
13. #21446064C2semidirect
14. C2×#16839516C2semidirect
436. C61#25499semidirect

Maximal subgroups

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

subgroupindex
C2×#168402932
C2×#168400012
#214541532
#214471592
#214470582
#214469682
#214469112
#214462482
#214462422
#214461572
#214461552
#214460842
#214460642
C2×#168395162
C2×C61×#4652
#2549961