Finite Group Databasebeta

← #29716381

Subgroups — #29716381

Order 15616.

1330 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×D4×Dic122C211yesmaximal, characteristic, complemented
2C2×#16840040C211yesmaximal, characteristic, complemented
3C2×D8×Dic61C211yesmaximal, characteristic
4#21450739C211yesmaximal, characteristic, complemented
5#21447148C211yesmaximal, characteristic, complemented
6#21447146C211yesmaximal, characteristic, complemented
7#21446955C211yesmaximal, characteristic, complemented
8#21446953C211yesmaximal, characteristic, complemented
9#21446778C211yesmaximal, characteristic, complemented
10#21446753C211yesmaximal, characteristic, complemented
11#21446169C211yesmaximal, characteristic
12#21446068C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445817C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic
16C23×Dic122—21no—
17D4×Dic122—24no—
18D4×Dic122—24no—
19C2×#14519777C2211yescharacteristic
20C2×#14519776C2211yescharacteristic
21C2×#14519776C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519754—21no—
24C2×#14519754—21no—
25C2×#14519754—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×D4×Dic61C2211yescharacteristic
29C2×D4×Dic61C2211yescharacteristic
30#16840040—24no—
31D8×Dic61—24no—
32C2×#14519711C2211yescharacteristic
33C2×#14519711C2211yescharacteristic
34C2×#14519710C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839685—21no—
42#16839685—21no—
43#16839665C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839631C2211yescharacteristic
47#16839620—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×D8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—28no—
64C22×Dic122—21no—
65C22×Dic122—21no—
66C22×Dic122—21no—
67C22×Dic122—44no—
68C22×Dic122—44no—
69C22×Dic122D411yescharacteristic
70C23×Dic61—21no—
71C23×Dic61—21no—
72C23×Dic61—21no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519777—22no—
76#14519777—22no—
77#14519776—22no—
78#14519776—22no—
79#14519776—22no—
80#14519776D414yes—
81#14519756—28no—
82#14519754—28no—
83#14519754—28no—
84#14519754—44no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90D4×Dic61—22no—
91D4×Dic61—22no—
92D4×Dic61D414yes—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61D411yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196D411yescharacteristic
106C2×#11758196D411yescharacteristic
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519711—22no—
115#14519711—22no—
116#14519710—22no—
117#14519706—22no—
118#14519698—22no—
119#14519698—22no—
120#14519698—22no—
121#14519698—22no—
122C8×Dic61—22no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C2×D8×C61—22no—
129C2×D8×C61—22no—
130C2×D8×C61Q814yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C4×D4×C61—22no—
134C4×D4×C61—22no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61C2311yescharacteristic
141#102×C61—22no—
142#102×C61—22no—
143C24×C61—21no—
144C24×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61C2×D412yes—
154C2×D4×C61C2×Q812yes—
155C2×D4×C61C2×Q812yescomplemented
156C2×D4×C61#4112yes—
157C22×C4×C61—24no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C22×Dic61—24no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—24no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—42no—
172C22×Dic61—42no—
173C22×Dic61—42no—
174C22×Dic61—42no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61—42no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C2×Dic122—22no—
183C2×Dic122—22no—
184C2×Dic122—24no—
185C2×Dic122—24no—
186C2×Dic122—24no—
187C2×Dic122—432no—
188C2×Dic122—42no—
189C2×Dic122—42no—
190C2×Dic122—42no—
191C2×Dic122—42no—
192C2×Dic122—42no—
193C2×Dic122—42no—
194C2×Dic122D814yescomplemented
195D8×C61—28no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×Q812yescomplemented
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C2×D412yes—
206C22⋊C4×C61—24no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—81no—
209C42×C61—21no—
210C42×C61—21no—
211C22⋊Dic61—24no—
212C22⋊Dic61—24no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—81no—
216C4⋊Dic61—24no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—22no—
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—22no—
231#11758196—42no—
232#11758196—42no—
233#11758196—81no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61C2×D412yes—
237C4×Dic61C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C22×D411yescharacteristic
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—41no—
265D4×C61—41no—
266D4×C61C22⋊Q814yescomplemented
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—48no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61C2×D812yes—
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C22×Q811yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C612−1+411yescharacteristic
285C2×C4×C612−1+411yescharacteristic
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—48no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—48no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—84no—
308C2×Dic61#12012yes—
309C2×Dic61#12012yes—
310C2×Dic61C2×D812yes—
311C2×Dic61C2×D812yes—
312C2×Dic61AGL(1,ℤ/8)12yes—
313Dic122—28no—
314Dic122—48no—
315Dic122—48no—
316Dic122—48no—
317C8×C61—22no—
318C8×C61—41no—
319#92418—41no—
320#92418—41no—
321#24326—611nomaximal, Sylow
322C22×C61—24no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61C2×#12011yescharacteristic
337C22×C61#54811yescharacteristic
338C22×C61D4×Q811yescharacteristic
339C22×C61C22×D811yescharacteristic
340C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C61#57711yescharacteristic
342C22×C61#57811yescharacteristic
343C4×C61—22no—
344C4×C61—42no—
345C4×C61—41no—
346C4×C61—81no—
347C4×C61C2×C22⋊Q811yescharacteristic
348C4×C61#53611yescharacteristic
349C4×C61#54811yescharacteristic
350C4×C61D4×Q811yescharacteristic
351Dic61—22no—
352Dic61—22no—
353Dic61—42no—
354Dic61—42no—
355Dic61—41no—
356Dic61—81no—
357Dic61—81no—
358Dic61#44714yes—
359C2×D4×Q8—611no—
360C2×#474—611no—
361C2×C4×D8—611no—
362#2538—611no—
363#2057—611no—
364#2057—611no—
365#2023—611no—
366#2023—611no—
367#1990—611no—
368#1984—611no—
369#1879—611no—
370#1879D6111yescharacteristic
371#1862—611no—
372#1862—611no—
373#1802—611no—
374C2×C61—44no—
375C2×C61—82no—
376C2×C61#240911yescharacteristic
377C2×C61C2×#44711yescharacteristic
378C2×C61#301311yescharacteristic
379C2×C61#335811yescharacteristic
380C2×C61#336711yescharacteristic
381C2×C61Q8×D811yescharacteristic
382C2×C61#338411yescharacteristic
383C23×Q8—1221no—
384C22×D8C2×D6111yescharacteristic
385D4×Q8—1224no—
386D4×Q8—1224no—
387C2×C4⋊Q8—611no—
388C2×C4⋊Q8—611no—
389C2×C4⋊Q8—611no—
390C2×C22⋊Q8—1221no—
391C2×C22⋊Q8—1221no—
392C2×C22⋊Q8—1221no—
393C2×C22⋊Q8—1221no—
394C2×C4×Q8—611no—
395C2×C4×D4—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4C2×D6111yescharacteristic
399#474—1224no—
400C4×D8—1224no—
401C2×#107—611no—
402C2×#107—611no—
403C2×#107—611no—
404C2×C4⋊C8—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102—611no—
409C2×#102C2×D6111yescharacteristic
410C2×#102C2×D6111yescharacteristic
411C2×C4×C8—611no—
412#396—1221no—
413#396—1221no—
414#390—611no—
415#390C2×D6111yescharacteristic
416#389—611no—
417#389—611no—
418#384—611no—
419#380—1221no—
420#340—611no—
421#340—611no—
422#340—611no—
423#340—611no—
424#340—611no—
425#340C2×D6111yescharacteristic
426#336—611no—
427#336—611no—
428#336—611no—
429#336C2×D6111yescharacteristic
430C61#2432611yescharacteristic, complemented, Sylow
431C22×Q8—611no—
432C22×Q8—1221no—
433C22×Q8—1221no—
434C22×Q8—1228no—
435C22×Q8—1221no—
436C22×Q8—2444no—
437C22×Q8—2444no—
438C22×D4C22×D6111yescharacteristic
439C22×D4C22×D6111yescharacteristic
440C23×C4—21no—
441C23×C4—1221no—
442C23×C4—1221no—
443C23×C4—1221no—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8Dic12214yescomplemented
447C22×C8—611no—
448C22×C8—611no—
449C22×C8C22×D6111yescharacteristic
450C22×C8C22×D6111yescharacteristic
451C4⋊Q8—614no—
452C4⋊Q8—1222no—
453C4⋊Q8—1222no—
454C4⋊Q8—1222no—
455C4⋊Q8—1222no—
456C4⋊Q8—1222no—
457C22⋊Q8—1228no—
458C22⋊Q8—1228no—
459C22⋊Q8—1228no—
460C22⋊Q8—2444no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—614no—
466C4×D4—1222no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42C22×D6111yescharacteristic
498#107—1222no—
499#107—1222no—
500#107—1222no—
501C4⋊C8—1222no—
502#102—22no—
503#102—22no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102—1222no—
508C4×C8—1222no—
509#95—1221no—
510#95—1221no—
511C24—21no—
512C24—21no—
513C2×Q8—614no—
514C2×Q8—1222no—
515C2×Q8—1222no—
516C2×Q8—1224no—
517C2×Q8—1224no—
518C2×Q8—1224no—
519C2×Q8—2442no—
520C2×Q8—2442no—
521C2×Q8—2442no—
522C2×Q8—2442no—
523C2×Q8—2442no—
524C2×Q8—24432no—
525C2×Q8—2442no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4C2×Dic12212yes—
535C2×D4C2×Dic12212yescomplemented
536C2×D4D4×D6112yes—
537C2×D4#1175822412yes—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—1224no—
548C22×C4—1224no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—2442no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4D4×D6111yescharacteristic
561C22×C4D4×D6111yescharacteristic
562C22×C4C23×D6111yescharacteristic
563D8—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8C2×Dic12212yescomplemented
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4—1222no—
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—4881no—
594C4⋊C4—2442no—
595C4⋊C4—2442no—
596C4⋊C4—2442no—
597C4⋊C4D4×D6112yes—
598C22⋊C4—24no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—4881no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C42—21no—
607C42—21no—
608C42—612no—
609C42—612no—
610C42—1221no—
611C42—1221no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23C2×D4×D6111yescharacteristic
627Q8—1228no—
628Q8—2448no—
629Q8—2448no—
630Q8—2448no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4#1451975414yescomplemented
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—48no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—612no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—4884no—
666C2×C4—2448no—
667C2×C4—2448no—
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—2441no—
678C2×C4D8×D6112yes—
679C2×C4C2×D4×D6111yescharacteristic
680C2×C4C2×D4×D6111yescharacteristic
681C2×C4C22×Dic12211yescharacteristic
682C2×C4C2×#1175822411yescharacteristic
683C2×C4#1451982411yescharacteristic
684C2×C4#1451982411yescharacteristic
685C8—22no—
686C8—41no—
687C8—2441no—
688C8—2441no—
689C22—24no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22#120×D6111yescharacteristic
704C22#1684041811yescharacteristic
705C22D4×Dic12211yescharacteristic
706C22C2×D8×D6111yescharacteristic
707C22AGL(1,ℤ/8)×D6111yescharacteristic
708C22#1684057211yescharacteristic
709C22#1684057611yescharacteristic
710C4—22no—
711C4—41no—
712C4—42no—
713C4—81no—
714C4—614no—
715C4—1222no—
716C4—1222no—
717C4—4881no—
718C4—4881no—
719C4—2441no—
720C4—2442no—
721C4—2442no—
722C4C2×#1451975411yescharacteristic
723C4#1684033411yescharacteristic
724C4#1684041811yescharacteristic
725C4D4×Dic12211yescharacteristic
726C2—44no—
727C2—82no—
728C2#2144918111yescharacteristic
729C2#447×D6111yescharacteristic
730C2#2145513211yescharacteristic
731C2#2145844911yescharacteristic
732C2#2145853211yescharacteristic
733C2D8×Dic12211yescharacteristic
734C2#2145871911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
hypercenter#1879D61
hypocenterC61#24326
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic122C2semidirect
2. C2×#16840040C2semidirect
4. #21450739C2semidirect
5. #21447148C2semidirect
6. #21447146C2semidirect
7. #21446955C2semidirect
8. #21446953C2semidirect
9. #21446778C2semidirect
10. #21446753C2semidirect
12. #21446068C2semidirect
13. #21446066C2semidirect
14. #21445817C2semidirect
130. C2×D8×C61Q8semidirect
155. C2×D4×C61C2×Q8semidirect
194. C2×Dic122D8semidirect
201. C2×C8×C61C2×Q8semidirect
266. D4×C61C22⋊Q8semidirect
430. C61#24326semidirect
446. C2×D8Dic122semidirect
535. C2×D4C2×Dic122semidirect
575. C2×C8C2×Dic122semidirect
638. D4#14519754semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1222
C2×#168400402
C2×D8×Dic612
#214507392
#214471482
#214471462
#214469552
#214469532
#214467782
#214467532
#214461692
#214460682
#214460662
#214458172
C61×#18792
#2432661