Finite Group Databasebeta

← #29714039

Subgroups — #29714039

Order 15616.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840453C211yesmaximal, characteristic
2C2×#16840069C211yesmaximal, characteristic, complemented
3#21450724C211yesmaximal, characteristic
4#21447020C211yesmaximal, characteristic, complemented
5#21447013C211yesmaximal, characteristic, complemented
6#21446826C211yesmaximal, characteristic, complemented
7#21446826C211yesmaximal, characteristic, complemented
8#21446784C211yesmaximal, characteristic, complemented
9#21446613C211yesmaximal, characteristic
10#21446128C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13#21446005C211yesmaximal, characteristic, complemented
14#21445834C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
16#16840453—24no—
17#16840453—24no—
18C2×#14519771—21no—
19C2×#14519769C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519762—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×#14519753C2211yescharacteristic
25C2×#14519753C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519734—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840069—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42#16839692—21no—
43#16839679—21no—
44#16839653—21no—
45#16839653—21no—
46#16839628C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×Q16×C61C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C4×Q16×C61—24no—
59C2×#107×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C22×D244D411yescharacteristic
64C22×C4×D61—21no—
65C22×C4×D61C2311yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519771—28no—
70#14519769—22no—
71#14519769D414yes—
72#14519767—28no—
73#14519762—28no—
74#14519753—22no—
75#14519753—22no—
76#14519753—22no—
77#14519753—22no—
78#14519753—22no—
79#14519753—22no—
80#14519753—41no—
81#14519753—41no—
82C4×D244—22no—
83C4×D244—22no—
84#14519735—22no—
85#14519735—22no—
86#14519734—28no—
87C2×C4⋊Dic61D411yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—22no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198D411yescharacteristic
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111#14519710—22no—
112#14519708—22no—
113C4⋊#92418—22no—
114#14519701—22no—
115#14519701—22no—
116#14519701—41no—
117#14519701—41no—
118#14519689—22no—
119#14519689—22no—
120#14519689—41no—
121#14519689—41no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C22×Q8×C61C2311yescharacteristic
127C22×Q8×C61C2311yescharacteristic
128C2×Q16×C61—22no—
129C2×Q16×C61—22no—
130C2×Q16×C61—22no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C4×Q8×C61—22no—
134C4×Q8×C61—22no—
135C4×Q8×C61—22no—
136C4×Q8×C61D414yes—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C42×C61—21no—
142C2×C42×C61—21no—
143C2×C42×C61C2311yescharacteristic
144#107×C61—22no—
145#103×C61—22no—
146#103×C61—22no—
147C4×C8×C61—22no—
148C23×D61C2×D411yescharacteristic
149C23×D61C2×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×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C2×D412yes—
161C2×Q8×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—41no—
178C2×C4×D61—24no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193Q16×C61—28no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61#4112yes—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61C2×D412yes—
206C42×C61—24no—
207C42×C61—42no—
208C42×C61C2×D412yes—
209C42×C61C2×D412yes—
210#11758198—24no—
211#11758198—24no—
212#11758198—24no—
213#11758198—22no—
214#11758198—22no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219C4⋊Dic61—22no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61C2×D412yes—
227C4⋊Dic61C2×D412yes—
228#11758196—24no—
229#11758196—24no—
230#11758196—24no—
231#11758196—24no—
232#11758196—24no—
233#11758196—42no—
234#11758196—42no—
235C4×Dic61—24no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C23×C61C22×D411yescharacteristic
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61#13512yes—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—41no—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61#12012yes—
282C2×C4×C61#12012yes—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C612−1+411yescharacteristic
289C2×Dic61—21no—
290C2×Dic61—22no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307D244—44no—
308C4×D61—48no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C8×C61—22no—
318C8×C61—41no—
319#92418—41no—
320#92418—41no—
321#24127—611nomaximal, Sylow
322C22×C61C2×#12011yescharacteristic
323C22×C61#54611yescharacteristic
324C22×C61#54711yescharacteristic
325C22×C61C2×#13511yescharacteristic
326C22×C61#57511yescharacteristic
327C22×C61#57811yescharacteristic
328C22×C61#57811yescharacteristic
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—41no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—42no—
348C4×C61—81no—
349C4×C61#52511yescharacteristic
350C4×C61#53711yescharacteristic
351C4×C61#54811yescharacteristic
352C4×C61#55011yescharacteristic
353Dic61—41no—
354Dic61—41no—
355Dic61—42no—
356Dic61—42no—
357Dic61—81no—
358Dic61—81no—
359C2×#552—611no—
360C2×#479—611no—
361C2×C4×Q16D6111yescharacteristic, complemented
362#2536—611no—
363#2036—611no—
364#2035—611no—
365#2001—611no—
366#2001—611no—
367#1991—611no—
368#1954—611no—
369#1873—611no—
370#1872—611no—
371#1854—611no—
372#1852—611no—
373#1805—611no—
374C2×C61#240711yescharacteristic
375C2×C61#300211yescharacteristic
376C2×C61#301111yescharacteristic
377C2×C61#330011yescharacteristic
378C2×C61#332711yescharacteristic
379C2×C61#333611yescharacteristic
380C2×C61#335211yescharacteristic
381D61—42no—
382D61—81no—
383C22×Q16C2×D6111yescharacteristic
384#552—1224no—
385#552—1224no—
386C2×#126—1221no—
387C2×#125—611no—
388C2×#125—1221no—
389C2×#123—1221no—
390C2×C22⋊Q8—611no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—611no—
394C2×C4×Q8C2×D6111yescharacteristic
395C2×C4×Q8C2×D6111yescharacteristic
396C2×C4×D4—611no—
397C2×#117—611no—
398C2×#117—1221no—
399C22×C4⋊C4—611no—
400#479—1224no—
401C4×Q16—24no—
402C2×#107—611no—
403C2×#107C2×D6111yescharacteristic
404C2×#106—611no—
405C2×C4⋊C8—611no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#103C2×D6111yescharacteristic
411C2×#103C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C4×C8C2×D6111yescharacteristic
417#398—1221no—
418#394—1221no—
419#388—1221no—
420#388—1221no—
421#382—611no—
422#380—611no—
423#380—611no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430C61#2412711yescharacteristic, complemented, Sylow
431C22×Q8C22×D6111yescharacteristic
432C22×Q8C22×D6111yescharacteristic
433C22×D4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—1221no—
437C2×Q16—22no—
438C2×Q16—22no—
439C2×Q16—22no—
440C22×C8—611no—
441C22×C8—611no—
442C22×C8C22×D6111yescharacteristic
443C22×C8C22×D6111yescharacteristic
444#126—1228no—
445#125—614no—
446#125—1228no—
447#125—1222no—
448#123—1228no—
449C22⋊Q8—1222no—
450C22⋊Q8—1222no—
451C22⋊Q8—1222no—
452C22⋊Q8—1222no—
453C22⋊Q8—1222no—
454C22⋊Q8—1222no—
455C22⋊Q8—2441no—
456C22⋊Q8—2441no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8C22⋊D6114yes—
461C4×D4—1222no—
462C4×D4—1222no—
463#117—1228no—
464#117—1222no—
465#117—1222no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—1221no—
496C2×C42C22×D6111yescharacteristic
497#107—22no—
498#107—1222no—
499#106—1222no—
500C4⋊C8—1222no—
501#103—22no—
502#103—22no—
503#103—1222no—
504#103—1222no—
505#103—2441no—
506#103—2441no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—2441no—
510C22⋊C8—2441no—
511C4×C8—22no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—611no—
517C24—611no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8#1175822212yes—
529C2×Q8C2×C22⋊D6112yes—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—2441no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—1224no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4D4×D6111yescharacteristic
559C22×C4D4×D6111yescharacteristic
560C22×C4C23×D6111yescharacteristic
561Q16—28no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8#1175822212yes—
574C4⋊C4—21no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1224no—
582C4⋊C4—1224no—
583C4⋊C4—1224no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1222no—
587C4⋊C4—1224no—
588C4⋊C4—1224no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4C2×C22⋊D6112yes—
596C22⋊C4—1224no—
597C22⋊C4—1224no—
598C22⋊C4—1224no—
599C22⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C22⋊C4—2442no—
605C42—24no—
606C42—42no—
607C42—1224no—
608C42D4×D6112yes—
609C42C2×C22⋊D6112yes—
610C23—612no—
611C23—1221no—
612C23—1221no—
613C23—1221no—
614C23—1221no—
615C23—1221no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23C2×D4×D6111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—2444no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—1221no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—2448no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4#1451974512yes—
678C2×C4#1451974512yes—
679C2×C4C2×D4×D6111yescharacteristic
680C2×C4C22×C22⋊D6111yescharacteristic
681C2×C4C2×#1175822211yescharacteristic
682C2×C4C2×#1175822211yescharacteristic
683C2×C4#1451982311yescharacteristic
684C2×C4#1451982411yescharacteristic
685C8—22no—
686C8—41no—
687C8—2441no—
688C8—2441no—
689C22—1222no—
690C22—1222no—
691C22—1222no—
692C22—2441no—
693C22—2441no—
694C22—2441no—
695C22—2441no—
696C22—2441no—
697C22—2441no—
698C22—2441no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22C2×#1451974511yescharacteristic
704C22#1684040811yescharacteristic
705C22#1684041711yescharacteristic
706C22#135×D6111yescharacteristic
707C22#1684055911yescharacteristic
708C22#1684057511yescharacteristic
709C22#1684057511yescharacteristic
710C4—22no—
711C4—22no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—81no—
716C4—4881no—
717C4—4881no—
718C4—2442no—
719C4—2442no—
720C4—2441no—
721C4—2441no—
722C4#1684027311yescharacteristic
723C4#1684034011yescharacteristic
724C4#1684042111yescharacteristic
725C4#1684043311yescharacteristic
726C2—4881no—
727C2—2442no—
728C2#2144916411yescharacteristic
729C2#2145503311yescharacteristic
730C2#2145511011yescharacteristic
731C2#2145771111yescharacteristic
732C2#2145809211yescharacteristic
733C2#2145818911yescharacteristic
734C2#2145839511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×Q16×C61C2
socleC23×C61C22×D4
prime radicalC22×D244D4
hypercenterC2×C4×Q16D61
hypocenterC61#24127
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#16840069C2semidirect
4. #21447020C2semidirect
5. #21447013C2semidirect
6. #21446826C2semidirect
7. #21446826C2semidirect
8. #21446784C2semidirect
10. #21446128C2semidirect
11. #21446123C2semidirect
12. #21446015C2semidirect
13. #21446005C2semidirect
14. #21445834C2semidirect
15. C2×C4×Q16×C61C2semidirect
361. C2×C4×Q16D61semidirect
430. C61#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#168404532
C2×#168400692
#214507242
#214470202
#214470132
#214468262
#214467842
#214466132
#214461282
#214461232
#214460152
#214460052
#214458342
C2×C4×Q16×C612
#2412761