Finite Group Databasebeta

← #29718382

Subgroups — #29718382

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840099C211yesmaximal, characteristic, complemented
2C2×#102×D61C211yesmaximal, characteristic
3#21449469C211yesmaximal, characteristic
4#21448695C211yesmaximal, characteristic, complemented
5#21447202C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447059C211yesmaximal, characteristic, complemented
8#21446750C211yesmaximal, characteristic, complemented
9#21446749C211yesmaximal, characteristic, complemented
10#21446437C211yesmaximal, characteristic, complemented
11#21446436C211yesmaximal, characteristic, complemented
12#21446241C211yesmaximal, characteristic, complemented
13#21445995C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic
15C61×#2067C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×#14519764C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22#16840099—24no—
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519706C2211yescharacteristic, complemented
25C2×#14519702C2211yescharacteristic, complemented
26C2×#14519702C2211yescharacteristic, complemented
27C2×#14519700C2211yescharacteristic, complemented
28C2×#14519700C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35#102×D61—24no—
36C2×#14519689C2211yescharacteristic
37#16839678—21no—
38#16839678—21no—
39#16839663C2211yescharacteristic
40#16839661C2211yescharacteristic, complemented
41#16839649—21no—
42#16839643—21no—
43#16839619—21no—
44#16839619C2211yescharacteristic
45#16839617—21no—
46#16839617—21no—
47C4⋊C4×Dic61C2211yescharacteristic, complemented
48C4×C4⋊Dic61C2211yescharacteristic, complemented
49C4×#11758198C2211yescharacteristic
50#16839609—21no—
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C2×#107×C61C2211yescharacteristic, complemented
55C2×C4⋊C8×C61C2211yescharacteristic, complemented
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#389C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×Dic122C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—41no—
70C2×D4×D61—41no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—22no—
76C2×C8×D61—41no—
77C2×C8×D61—41no—
78#14519765—22no—
79#14519765—41no—
80#14519764—22no—
81#14519764—41no—
82#14519757—22no—
83#14519757—22no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61D414yes—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104#14519710—22no—
105#14519706—41no—
106#14519702—22no—
107#14519702—41no—
108#14519700—22no—
109#14519700—41no—
110#14519699—22no—
111#14519699—41no—
112#14519698—22no—
113#14519698—22no—
114#14519697—22no—
115#14519697—22no—
116#14519689—22no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684D411yescharacteristic
122#14519684D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#107×C61—22no—
134C4⋊C8×C61—41no—
135#102×C61—22no—
136#102×C61—41no—
137#95×C61—21no—
138C24×C61—21no—
139C23×D61—21no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61#4112yes—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169D4×D61—28no—
170D4×D61—44no—
171D4×D61—44no—
172D4×D61—44no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244#4112yes—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—24no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61C2×D412yes—
187C2×C4×D61#4112yes—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—81no—
206C4⋊C4×C61C2×D412yes—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C42×C61—21no—
210C42×C61—21no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213#11758198—22no—
214#11758198—22no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—81no—
220#11758198—81no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—42no—
225C4⋊Dic61—81no—
226C4⋊Dic61C2×D412yes—
227#11758196—24no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—81no—
231C4×Dic61—81no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C8×D61—44no—
239C23×C61—22no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C22×D411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—22no—
252C22×D61—48no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—84no—
260C22×D61—84no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61#12112yes—
266C22×D61#13512yes—
267C22×D61#13712yes—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—41no—
271D4×C61—41no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
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—41no—
286C2×C4×C61—41no—
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C22⋊D61—48no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
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#12112yes—
312D244—22no—
313D244—22no—
314D244—41no—
315D244—41no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—84no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324Dic122—41no—
325C8×C61—41no—
326C8×C61—41no—
327#92418—41no—
328#92418—41no—
329#24479—611nomaximal, Sylow
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61C2×#12111yescharacteristic
338C22×C61#54611yescharacteristic
339C22×C61#54611yescharacteristic
340C22×C61C2×#13511yescharacteristic
341C22×C61C2×#13711yescharacteristic
342C22×C61#57611yescharacteristic
343C22×C61#57611yescharacteristic
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—816no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61#46414yes—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61#52511yescharacteristic
365C4×C61#53511yescharacteristic
366C4×C61#55111yescharacteristic
367C4×C61#55111yescharacteristic
368Dic61—22no—
369Dic61—42no—
370Dic61—41no—
371Dic61—41no—
372Dic61—81no—
373Dic61—81no—
374C2×#484—611no—
375C22×#102—611no—
376#2435—611no—
377#2345—611no—
378#2067—611no—
379#2067D6111yescharacteristic, complemented
380#2042—611no—
381#2042—611no—
382#1983—611no—
383#1983—611no—
384#1925—611no—
385#1925—611no—
386#1892—611no—
387#1850—611no—
388#1786—611no—
389C2×C61—82no—
390C2×C61#241111yescharacteristic
391C2×C61C2×#46411yescharacteristic
392C2×C61#304111yescharacteristic
393C2×C61#329711yescharacteristic
394C2×C61#329711yescharacteristic
395C2×C61#331411yescharacteristic
396C2×C61#331411yescharacteristic
397D61—24no—
398D61—82no—
399C23×D4—611no—
400C23×C8—611no—
401C2×#124—611no—
402C2×#124—611no—
403C2×C22⋊Q8—611no—
404C22×C4⋊C4—611no—
405#484—1224no—
406C2×#107—611no—
407C2×#107C2×D6111yescharacteristic, complemented
408C2×C4⋊C8—611no—
409C2×C4⋊C8C2×D6111yescharacteristic, complemented
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—1224no—
421C2×#102C2×D6111yescharacteristic
422C2×#102C2×D6111yescharacteristic
423C2×C22⋊C8—611no—
424#394—1221no—
425#394—1221no—
426#390—611no—
427#390C2×D6111yescharacteristic
428#389—611no—
429#389C2×D6111yescharacteristic, complemented
430#387—1221no—
431#387—1221no—
432#380—611no—
433#380—1221no—
434#379—1221no—
435#379—1221no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—611no—
438C4×C22⋊C4—611no—
439C4×C22⋊C4—1221no—
440#340—611no—
441#340C2×D6111yescharacteristic, complemented
442#336—611no—
443#336—611no—
444C61#2447911yescharacteristic, complemented, Sylow
445C25—1221no—
446C22×Q8—611no—
447C22×D4—611no—
448C22×D4—1222no—
449C22×D4—1222no—
450C22×D4—1221no—
451C22×D4—1222no—
452C22×D4—1222no—
453C22×D4—2441no—
454C22×D4—2441no—
455C22×D4C22×D6111yescharacteristic
456C23×C4—611no—
457C23×C4—1221no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—1222no—
461C22×C8—2441no—
462C22×C8—2441no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465#124—1222no—
466#124—1222no—
467#124—2441no—
468#124—2441no—
469C22⋊Q8—1222no—
470C22⋊Q8—1222no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—1222no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
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×C22⋊C4—1221no—
494C2×C42—611no—
495C2×C42—1221no—
496C2×C42—1221no—
497C2×C42C22×D6111yescharacteristic
498#107—22no—
499#107—1222no—
500C4⋊C8—41no—
501C4⋊C8—2441no—
502#103—1222no—
503#103—1222no—
504#103—2441no—
505#103—2441no—
506#102—22no—
507#102—41no—
508#102—1222no—
509#102—1222no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—2441no—
514C22⋊C8—1222no—
515#95—21no—
516#95—611no—
517#95—611no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522C24—21no—
523C24—611no—
524C24—1221no—
525C24—4881no—
526C24—4881no—
527C24—2442no—
528C24—2442no—
529C24—2442no—
530C24—2442no—
531C24—2442no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—612no—
544C2×D4—1228no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—2442no—
551C2×D4—2444no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4—2442no—
555C2×D4—2442no—
556C2×D4#1175822612yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—611no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—1224no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—4881no—
574C22×C4—4881no—
575C22×C4D4×D6111yescharacteristic
576C22×C4D4×D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—2444no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—81no—
597C4⋊C4—612no—
598C4⋊C4—1224no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—4881no—
603C4⋊C4—2442no—
604C4⋊C4D4×D6112yes—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C42—21no—
618C42—21no—
619C42—1221no—
620C42—1221no—
621C42—4881no—
622C42—4881no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—612no—
631C23—612no—
632C23—612no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1222no—
638C23—4884no—
639C23—4884no—
640C23—4884no—
641C23—4884no—
642C23—4884no—
643C23—4884no—
644C23—2448no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23C2×D4×D6111yescharacteristic
652Q8—2441no—
653Q8—2441no—
654Q8—2441no—
655Q8—2441no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—1222no—
661D4—1222no—
662D4—2448no—
663D4—2441no—
664D4—2441no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—612no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—4884no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4C2×D4×D6111yescharacteristic
704C2×C4#41×D6111yescharacteristic
705C2×C4#41×D6111yescharacteristic
706C2×C4C2×#1175822611yescharacteristic
707C2×C4#1451982211yescharacteristic
708C2×C4#1451982311yescharacteristic
709C8—41no—
710C8—41no—
711C8—2441no—
712C8—2441no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—614no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—48816no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22#121×D6111yescharacteristic
736C22#1684040111yescharacteristic
737C22#1684040311yescharacteristic
738C22#135×D6111yescharacteristic
739C22#137×D6111yescharacteristic
740C22#1684056311yescharacteristic
741C22#1684056611yescharacteristic
742C4—41no—
743C4—42no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—1222no—
748C4—4881no—
749C4—4881no—
750C4—2441no—
751C4—2442no—
752C4—2441no—
753C4#1684027511yescharacteristic
754C4#1684032811yescharacteristic
755C4#1684043711yescharacteristic
756C4#1684043911yescharacteristic
757C2—82no—
758C2—1224no—
759C2—4882no—
760C2#2144919911yescharacteristic
761C2#464×D6111yescharacteristic
762C2#2145531711yescharacteristic
763C2#2145766411yescharacteristic
764C2#2145766611yescharacteristic
765C2#2145789511yescharacteristic
766C2#2145789711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2067C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2067D61
hypocenterC61#24479
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#16840099C2semidirect
4. #21448695C2semidirect
5. #21447202C2semidirect
6. #21447060C2semidirect
7. #21447059C2semidirect
8. #21446750C2semidirect
9. #21446749C2semidirect
10. #21446437C2semidirect
11. #21446436C2semidirect
12. #21446241C2semidirect
13. #21445995C2semidirect
15. C61×#2067C2semidirect
23. C2×#14519710C22semidirect
24. C2×#14519706C22semidirect
25. C2×#14519702C22semidirect
26. C2×#14519702C22semidirect
27. C2×#14519700C22semidirect
28. C2×#14519700C22semidirect
40. #16839661C22semidirect
47. C4⋊C4×Dic61C22semidirect
48. C4×C4⋊Dic61C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839516C22semidirect
54. C2×#107×C61C22semidirect
55. C2×C4⋊C8×C61C22semidirect
59. C61×#389C22semidirect
60. C61×#340C22semidirect
379. #2067D61semidirect
407. C2×#107C2×D61semidirect
409. C2×C4⋊C8C2×D61semidirect
429. #389C2×D61semidirect
441. #340C2×D61semidirect
444. C61#24479semidirect

Maximal subgroups

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

subgroupindex
C2×#168400992
C2×#102×D612
#214494692
#214486952
#214472022
#214470602
#214470592
#214467502
#214467492
#214464372
#214464362
#214462412
#214459952
#214457482
C61×#20672
#2447961