Finite Group Databasebeta

← #29714032

Subgroups — #29714032

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×#16840454C211yesmaximal, characteristic
2C2×#16840071C211yesmaximal, characteristic, complemented
3C2×Q16×Dic61C211yesmaximal, characteristic, complemented
4#21450726C211yesmaximal, characteristic
5#21447021C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21446826C211yesmaximal, characteristic, complemented
8#21446782C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic
10#21446128C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446021C211yesmaximal, characteristic, complemented
13#21446009C211yesmaximal, characteristic, complemented
14#21445832C211yesmaximal, characteristic, complemented
15C61×#2001C211yesmaximal, characteristic, complemented
16#16840454—24no—
17#16840454—24no—
18C2×#14519772—21no—
19C2×#14519768—21no—
20C2×#14519768C2211yescharacteristic
21C2×#14519761—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30#16840071—24no—
31Q16×Dic61—24no—
32C2×#14519711C2211yescharacteristic
33C2×#14519711C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839695—21no—
45#16839678—21no—
46#16839656—21no—
47#16839652—21no—
48#16839627C2211yescharacteristic
49#16839622C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×C22⋊D61D411yescharacteristic
64C23×Dic61—21no—
65C22×C4×D61C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519772—28no—
69#14519768—28no—
70#14519768—22no—
71#14519768D414yes—
72#14519761—28no—
73#14519753—22no—
74#14519753—22no—
75#14519753—22no—
76#14519753—41no—
77Q8×Dic61—22no—
78Q8×Dic61—22no—
79Q8×Dic61—22no—
80Q8×Dic61D414yes—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519735—22no—
84#14519735—22no—
85#14519733—28no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61D411yescharacteristic
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198D411yescharacteristic
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111#14519711—22no—
112#14519711—22no—
113#14519708—22no—
114#14519706—22no—
115#14519701—22no—
116#14519701—22no—
117#14519701—22no—
118#14519701—41no—
119C22⋊#92418—41no—
120#14519689—22no—
121#14519689—41no—
122C8×Dic61—22no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×Q8×C61C2311yescharacteristic
128C22×Q8×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C2×Q16×C61—22no—
131C2×Q16×C61—22no—
132C2×Q16×C61—22no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61—41no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145#103×C61—22no—
146#103×C61—41no—
147C22⋊C8×C61—22no—
148C24×C61C2×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×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×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—41no—
177C22×Dic61—24no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—42no—
183C22×Dic61—42no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
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—
206C22⋊C4×C61—24no—
207C22⋊C4×C61—42no—
208C22⋊Dic61—22no—
209C22⋊Dic61—42no—
210#11758198—24no—
211#11758198—24no—
212#11758198—22no—
213#11758198—42no—
214#11758198—42no—
215C4⋊Dic61—24no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—24no—
219C4⋊Dic61—24no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—42no—
225C4⋊Dic61C2×D412yes—
226C4⋊Dic61C2×D412yes—
227#11758196—24no—
228#11758196—24no—
229#11758196—22no—
230#11758196—42no—
231C4×Dic61—24no—
232C4×Dic61—24no—
233C4×Dic61—42no—
234C4×Dic61C2×D412yes—
235C4×Dic61C2×D412yes—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61#13512yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
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—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—41no—
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—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C612−1+411yescharacteristic
290C22⋊D61—44no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—48no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61#12012yes—
312C2×Dic61#12012yes—
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×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61C2×#12011yescharacteristic
330C22×C61#54611yescharacteristic
331C22×C61#54711yescharacteristic
332C22×C61C2×#13511yescharacteristic
333C22×C61#57511yescharacteristic
334C22×C61#57811yescharacteristic
335C22×C61#57811yescharacteristic
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C4×C61—41no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—81no—
348C4×C61#52511yescharacteristic
349C4×C61#53711yescharacteristic
350C4×C61#54811yescharacteristic
351C4×C61#55011yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—41no—
355Dic61—42no—
356Dic61—42no—
357Dic61—81no—
358Dic61—81no—
359C2×#552—611no—
360C2×#479—611no—
361C2×C4×Q16—611no—
362#2536—611no—
363#2036—611no—
364#2035—611no—
365#2001—611no—
366#2001D6111yescharacteristic, complemented
367#1991—611no—
368#1954—611no—
369#1873—611no—
370#1872—611no—
371#1854—611no—
372#1852—611no—
373#1805—611no—
374C2×C61—42no—
375C2×C61#240711yescharacteristic
376C2×C61#300211yescharacteristic
377C2×C61#301111yescharacteristic
378C2×C61#330011yescharacteristic
379C2×C61#332711yescharacteristic
380C2×C61#333611yescharacteristic
381C2×C61#335211yescharacteristic
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⋊Q8C2×D6111yescharacteristic
393C2×C22⋊Q8C2×D6111yescharacteristic
394C2×C4×Q8—611no—
395C2×C4×Q8—611no—
396C2×C4×D4—611no—
397C2×#117—611no—
398C2×#117—1221no—
399C22×C4⋊C4—611no—
400#479—1224no—
401C4×Q16—1224no—
402C2×#107—611no—
403C2×#107—611no—
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⋊C8C2×D6111yescharacteristic
416C2×C4×C8—611no—
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#340C2×D6111yescharacteristic
430C61#2412711yescharacteristic, complemented, Sylow
431C22×Q8C22×D6111yescharacteristic
432C22×Q8C22×D6111yescharacteristic
433C22×D4—611no—
434C23×C4—611no—
435C23×C4—1221no—
436C23×C4C22×D6111yescharacteristic
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—1222no—
447#125—1228no—
448#123—1228no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—41no—
453C22⋊Q8—1222no—
454C22⋊Q8—1222no—
455C22⋊Q8—1222no—
456C22⋊Q8—2441no—
457C4×Q8—614no—
458C4×Q8—1222no—
459C4×Q8—1222no—
460C4×Q8—1222no—
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—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C42—611no—
494C2×C42—1221no—
495C2×C42—1221no—
496C2×C42—1221no—
497#107—1222no—
498#107—1222no—
499#106—1222no—
500C4⋊C8—1222no—
501#103—22no—
502#103—41no—
503#103—1222no—
504#103—1222no—
505#103—1222no—
506#103—2441no—
507C22⋊C8—22no—
508C22⋊C8—1222no—
509C22⋊C8—2441no—
510C22⋊C8—2441no—
511C4×C8—1222no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—611no—
517C24D4×D6111yescharacteristic
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×Q8D4×D6112yes—
529C2×Q8#1175822412yes—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—2441no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—1224no—
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—1221no—
557C22×C4—2442no—
558C22×C4—2442no—
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#1175822412yes—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1222no—
582C4⋊C4—1224no—
583C4⋊C4—1224no—
584C4⋊C4—1224no—
585C4⋊C4—1224no—
586C4⋊C4—1224no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4D4×D6112yes—
596C22⋊C4—24no—
597C22⋊C4—42no—
598C22⋊C4—1222no—
599C22⋊C4—1224no—
600C22⋊C4—1224no—
601C22⋊C4—1222no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C22⋊C4—2442no—
605C42—612no—
606C42—612no—
607C42—1224no—
608C42—1224no—
609C42—2442no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23#1451980012yes—
624C23C2×D4×D6111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—2444no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
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—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1222no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2448no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4C2×D4×D6111yescharacteristic
680C2×C4C2×D4×D6111yescharacteristic
681C2×C4C2×#1175822411yescharacteristic
682C2×C4C2×#1175822411yescharacteristic
683C2×C4#1451982211yescharacteristic
684C2×C4#1451982411yescharacteristic
685C8—22no—
686C8—41no—
687C8—2441no—
688C8—2441no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—2441no—
697C22—2441no—
698C22—2441no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22#120×D6111yescharacteristic
704C22#1684039911yescharacteristic
705C22#1684041211yescharacteristic
706C22C2×#1451980011yescharacteristic
707C22#1684056111yescharacteristic
708C22#1684057611yescharacteristic
709C22#1684057811yescharacteristic
710C4—42no—
711C4—41no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—1222no—
716C4—1222no—
717C4—4881no—
718C4—4881no—
719C4—2442no—
720C4—2442no—
721C4—2441no—
722C4#1684026811yescharacteristic
723C4#1684033911yescharacteristic
724C4#1684041811yescharacteristic
725C4#1684043211yescharacteristic
726C2—42no—
727C2—4881no—
728C2#2144915711yescharacteristic
729C2#2145504211yescharacteristic
730C2#2145511111yescharacteristic
731C2#2145771011yescharacteristic
732C2#2145808011yescharacteristic
733C2#2145819011yescharacteristic
734C2#2145838911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2001C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2001D61
hypocenterC61#24127
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#16840071C2semidirect
3. C2×Q16×Dic61C2semidirect
5. #21447021C2semidirect
6. #21447012C2semidirect
7. #21446826C2semidirect
8. #21446782C2semidirect
10. #21446128C2semidirect
11. #21446127C2semidirect
12. #21446021C2semidirect
13. #21446009C2semidirect
14. #21445832C2semidirect
15. C61×#2001C2semidirect
366. #2001D61semidirect
430. C61#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#168404542
C2×#168400712
C2×Q16×Dic612
#214507262
#214470212
#214470122
#214468262
#214467822
#214466112
#214461282
#214461272
#214460212
#214460092
#214458322
C61×#20012
#2412761