Finite Group Databasebeta

← #29737184

Subgroups — #29737184

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840050C211yesmaximal, characteristic, complemented
2#21449515C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic61C211yesmaximal, characteristic
4#21447350C211yesmaximal, characteristic, complemented
5#21447191C211yesmaximal, characteristic, complemented
6#21447189C211yesmaximal, characteristic, complemented
7#21446953C211yesmaximal, characteristic, complemented
8#21446082C211yesmaximal, characteristic, complemented
9#21446078C211yesmaximal, characteristic, complemented
10#21446012C211yesmaximal, characteristic, complemented
11#21445997C211yesmaximal, characteristic, complemented
12#21445844C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic
15C22×#102×C61C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic, complemented
17C2×#14519756—21no—
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C22×C22⋊Dic61—21no—
21#16840050—24no—
22C2×#14519709C2211yescharacteristic, complemented
23C2×#14519709C2211yescharacteristic, complemented
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26C2×#14519706C2211yescharacteristic, complemented
27C2×#14519706C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33#16839695—21no—
34#16839682—21no—
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839661C2211yescharacteristic, complemented
38#16839658C2211yescharacteristic, complemented
39#16839642—21no—
40#16839642—21no—
41#16839635—21no—
42#16839631C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839618—21no—
46C4×C22⋊Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C23×D4×C61C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C2×#102×C61—24no—
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C22×Dic122—21no—
62C23×Dic61—21no—
63C23×Dic61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519776—22no—
67#14519776—41no—
68#14519756—44no—
69D4×Dic61—22no—
70D4×Dic61—22no—
71D4×Dic61—41no—
72D4×Dic61—41no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—44no—
91C2×C22⋊Dic61D411yescharacteristic
92C2×C22⋊Dic61D411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519709—22no—
96#14519709—41no—
97#14519708—22no—
98#14519708—41no—
99#14519706—22no—
100#14519706—41no—
101#14519698—22no—
102#14519698—22no—
103#14519698—41no—
104#14519698—41no—
105C22⋊#92418—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684D411yescharacteristic
111#14519684D411yescharacteristic
112C25×C61—21no—
113C22×D4×C61—22no—
114C22×D4×C61—22no—
115C22×D4×C61—21no—
116C22×D4×C61—22no—
117C22×D4×C61—41no—
118C22×D4×C61—41no—
119C22×D4×C61Q814yescomplemented
120C22×D4×C61C2311yescharacteristic
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61—22no—
125C22×C8×C61—22no—
126C22×C8×C61—41no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—41no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134#102×C61—22no—
135#102×C61—22no—
136#102×C61—22no—
137#102×C61D414yes—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—81no—
146C24×C61—81no—
147C24×C61C2×D411yescharacteristic
148C2×D4×C61—28no—
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—44no—
159C2×D4×C61—44no—
160C2×D4×C61—44no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61C2×D412yes—
164C2×D4×C61C2×Q812yes—
165C2×D4×C61C2×Q812yes—
166C2×D4×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—81no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×Q812yes—
178C22×C4×C61#4112yes—
179C22×C4×C61C2411yescharacteristic
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61—81no—
189C22×Dic61—81no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C2×Dic122—42no—
195C2×Dic122—42no—
196C2×Dic122—81no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—44no—
203C2×C8×C61C2×D412yes—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61C2×D412yes—
209C22⋊Dic61—22no—
210C22⋊Dic61—42no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—42no—
216C22⋊Dic61—81no—
217C22⋊Dic61—81no—
218C22⋊Dic61SD1614yes—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—42no—
228#11758196—42no—
229#11758196—42no—
230#11758196—42no—
231#11758196—81no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
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—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—48no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—48no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61C22⋊Q812yes—
268C23×C61C2×SD1612yes—
269C23×C61AGL(1,ℤ/8)12yes—
270C23×C61C22×D411yescharacteristic
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—48no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61C22⋊Q814yescomplemented
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—84no—
293C2×C4×C61C22⋊Q812yes—
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C22×Q811yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—84no—
323C2×Dic61—84no—
324C2×Dic61C2×SD1612yes—
325C2×Dic61C2×SD1612yes—
326Dic122—84no—
327C8×C61—22no—
328C8×C61—41no—
329#92418—41no—
330#92418—41no—
331#25958—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—24no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—816no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61#47614yescomplemented
354C22×C61C2×C22⋊Q811yescharacteristic
355C22×C61D4211yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61C22×SD1611yescharacteristic
358C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C61#57611yescharacteristic
360C22×C61#57711yescharacteristic
361C4×C61—22no—
362C4×C61—42no—
363C4×C61—81no—
364C4×C61C2×C22⋊Q811yescharacteristic
365C4×C61#54311yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#55111yescharacteristic
368Dic61—22no—
369Dic61—22no—
370Dic61—41no—
371Dic61—41no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375Dic61—81no—
376C2×#476—611no—
377C22×#102D6111yescharacteristic
378#2440—611no—
379D4×C22⋊C4—611no—
380#2094—611no—
381#2065—611no—
382#2065—611no—
383#2023—611no—
384#1864—611no—
385#1864—611no—
386#1853—611no—
387#1850—611no—
388#1807—611no—
389#1802—611no—
390#1786—611no—
391C2×C61—24no—
392C2×C61—44no—
393C2×C61—82no—
394C2×C61#243711yescharacteristic
395C2×C61C2×#47611yescharacteristic
396C2×C61#308111yescharacteristic
397C2×C61#326411yescharacteristic
398C2×C61D4×SD1611yescharacteristic
399C2×C61#329511yescharacteristic
400C2×C61#330611yescharacteristic
401C23×D4C2×D6111yescharacteristic
402C23×C8C2×D6111yescharacteristic
403C2×C4⋊Q8—611no—
404C2×C22⋊Q8—1221no—
405C2×C4×D4—611no—
406C2×C4×D4—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408C22×C22⋊C4—1221no—
409#476—1224no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#106—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×#102—24no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102C2×D6111yescharacteristic
422C2×#102C2×D6111yescharacteristic
423C2×#102C2×D6111yescharacteristic
424C2×#102C2×D6111yescharacteristic
425C2×C22⋊C8—611no—
426#398—1221no—
427#395—1221no—
428#390—611no—
429#390—611no—
430#389—611no—
431#389—611no—
432#386—1221no—
433#386—1221no—
434#385—1221no—
435#384—611no—
436#380—611no—
437#380—611no—
438#379—1221no—
439C4×C22⋊C4—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2595811yescharacteristic, complemented, Sylow
447C25—21no—
448C22×Q8—1221no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—21no—
452C22×D4—22no—
453C22×D4—41no—
454C22×D4—41no—
455C22×D4Dic12214yescomplemented
456C22×D4C22×D6111yescharacteristic
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—41no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C4⋊Q8—1222no—
470C4⋊Q8—2441no—
471C22⋊Q8—2444no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—2441no—
475C4×D4—2441no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—611no—
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⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—2444no—
501C2×C42—611no—
502C2×C42—611no—
503#106—1222no—
504#106—1222no—
505#106—2441no—
506#106—2441no—
507C4⋊C8—1222no—
508C4⋊C8—2441no—
509#102—22no—
510#102—22no—
511#102—22no—
512#102—1222no—
513#102—1222no—
514#102—2441no—
515#102—2441no—
516#102C22⋊D6114yes—
517C22⋊C8—1222no—
518#95—611no—
519#95—611no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24D4×D6111yescharacteristic
534C2×Q8—4881no—
535C2×Q8—2442no—
536C2×Q8—2442no—
537C2×D4—28no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×Dic12212yes—
553C2×D4C2×Dic12212yes—
554C2×D4#1175822212yes—
555C2×D4C2×C22⋊D6112yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—4881no—
574C22×C4—4881no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4C2×Dic12212yes—
580C22×C4D4×D6111yescharacteristic
581C22×C4#1175822412yes—
582C22×C4C23×D6111yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8C2×C22⋊D6112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4—2442no—
613C4⋊C4C2×C22⋊D6112yes—
614C22⋊C4—614no—
615C22⋊C4—1222no—
616C22⋊C4—4881no—
617C22⋊C4—4881no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#1451975412yes—
654C23SD16×D6112yes—
655C23#1451980112yes—
656C23C2×D4×D6111yescharacteristic
657Q8—4884no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1451975614yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—4884no—
693C2×C4—4884no—
694C2×C4—2441no—
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×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4#1451975412yes—
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4C22×Dic12211yescharacteristic
709C2×C4C2×#1175822411yescharacteristic
710C2×C4C2×#1175822211yescharacteristic
711C2×C4#1451982211yescharacteristic
712C2×C4#1451982211yescharacteristic
713C8—22no—
714C8—41no—
715C8—2441no—
716C8—2441no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1684005014yescomplemented
739C22C2×#1451975411yescharacteristic
740C22D4×C22⋊D6111yescharacteristic
741C22#1684040211yescharacteristic
742C22C2×SD16×D6111yescharacteristic
743C22C2×#1451980111yescharacteristic
744C22#1684056311yescharacteristic
745C22#1684056811yescharacteristic
746C4—22no—
747C4—42no—
748C4—81no—
749C4—1222no—
750C4—1222no—
751C4—4881no—
752C4—4881no—
753C4—4881no—
754C4—4881no—
755C4—2441no—
756C4—2441no—
757C4C2×#1451975611yescharacteristic
758C4#1684038811yescharacteristic
759C4#1684040611yescharacteristic
760C4#1684043811yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#2144948011yescharacteristic
765C2C2×#1684005011yescharacteristic
766C2#2145564611yescharacteristic
767C2#2145729911yescharacteristic
768C2SD16×C22⋊D6111yescharacteristic
769C2#2145763911yescharacteristic
770C2#2145777611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterC22×#102D61
hypocenterC61#25958
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#16840050C2semidirect
2. #21449515C2semidirect
4. #21447350C2semidirect
5. #21447191C2semidirect
6. #21447189C2semidirect
7. #21446953C2semidirect
8. #21446082C2semidirect
9. #21446078C2semidirect
10. #21446012C2semidirect
11. #21445997C2semidirect
12. #21445844C2semidirect
13. #21445817C2semidirect
16. C2×#14519776C22semidirect
22. C2×#14519709C22semidirect
23. C2×#14519709C22semidirect
24. C2×#14519708C22semidirect
25. C2×#14519708C22semidirect
26. C2×#14519706C22semidirect
27. C2×#14519706C22semidirect
37. #16839661C22semidirect
38. #16839658C22semidirect
42. #16839631C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
119. C22×D4×C61Q8semidirect
279. D4×C61C22⋊Q8semidirect
353. C22×C61#476semidirect
446. C61#25958semidirect
455. C22×D4Dic122semidirect
666. D4#14519756semidirect
738. C22#16840050semidirect

Maximal subgroups

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

subgroupindex
C2×#168400502
#214495152
D4×C22⋊Dic612
#214473502
#214471912
#214471892
#214469532
#214460822
#214460782
#214460122
#214459972
#214458442
#214458172
#214457502
C22×#102×C612
#2595861