Finite Group Databasebeta

← #29737197

Subgroups — #29737197

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×#16840051C211yesmaximal, characteristic, complemented
2C22×#14519699C211yesmaximal, characteristic
3#21449522C211yesmaximal, characteristic, complemented
4#21448639C211yesmaximal, characteristic
5#21447349C211yesmaximal, characteristic, complemented
6#21447194C211yesmaximal, characteristic, complemented
7#21447188C211yesmaximal, characteristic, complemented
8#21446954C211yesmaximal, characteristic, complemented
9#21446081C211yesmaximal, characteristic, complemented
10#21446077C211yesmaximal, characteristic, complemented
11#21446011C211yesmaximal, characteristic, complemented
12#21445997C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic
15C61×#1807C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C2×#14519776C2211yescharacteristic, complemented
18C2×#14519754—21no—
19C2×#14519739C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23#16840051—24no—
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26C2×#14519706C2211yescharacteristic, complemented
27C2×#14519706C2211yescharacteristic, complemented
28C2×#14519699—24no—
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38#16839696—21no—
39#16839683—21no—
40#16839663C2211yescharacteristic
41#16839663C2211yescharacteristic
42#16839661C2211yescharacteristic, complemented
43#16839658C2211yescharacteristic, complemented
44#16839640—21no—
45#16839640—21no—
46#16839634—21no—
47#16839631C2211yescharacteristic, complemented
48#16839617—21no—
49C4×C22⋊Dic61C2211yescharacteristic
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×C8×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic, complemented
56C2×#106×C61C2211yescharacteristic, complemented
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×Dic122—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—21no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244Q814yescomplemented
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519776—22no—
78#14519776—41no—
79#14519754—44no—
80#14519739—22no—
81#14519739—22no—
82#14519739—41no—
83#14519739—41no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61D411yescharacteristic
95C2×C22⋊Dic61D411yescharacteristic
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C22⋊C4×D61—44no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519708—22no—
106#14519708—41no—
107#14519706—22no—
108#14519706—41no—
109#14519699—22no—
110#14519699—22no—
111#14519699—22no—
112#14519699D414yes—
113#14519697—22no—
114#14519697—22no—
115#14519697—41no—
116#14519697—41no—
117C22⋊#92418—22no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C22×C8×C61—22no—
124C22×C8×C61—22no—
125C22×C8×C61—41no—
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134#106×C61—22no—
135#106×C61—41no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—81no—
147C23×D61—81no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×Q812yes—
158C22×C4×C61#4112yes—
159C22×C4×C61C2411yescharacteristic
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—42no—
163C22×Dic61—42no—
164C22×Dic61—81no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—28no—
177C2×D244—24no—
178C2×D244—21no—
179C2×D244—44no—
180C2×D244—44no—
181C2×D244—44no—
182C2×D244—42no—
183C2×D244—42no—
184C2×D244C2×D412yes—
185C2×D244C2×Q812yes—
186C2×D244C2×Q812yes—
187C2×D244#4112yes—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
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—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊Dic61—22no—
215C22⋊Dic61SD1614yes—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—42no—
220#11758198—81no—
221#11758198—81no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61—42no—
227C4⋊Dic61C2×D412yes—
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×C61C22⋊Q812yes—
247C23×C61C2×SD1612yes—
248C23×C61AGL(1,ℤ/8)12yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—48no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—48no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61—84no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
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×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C22⋊Q812yes—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×Q811yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—84no—
313C2×Dic61C2×SD1612yes—
314C2×Dic61C2×SD1612yes—
315D244—22no—
316D244—22no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—48no—
321D244—41no—
322D244—41no—
323D244C22⋊Q814yescomplemented
324C4×D61—84no—
325C4×D61—84no—
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#47614yescomplemented
339C22×C61C2×C22⋊Q811yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61C22×SD1611yescharacteristic
343C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—24no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—816no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C4×C61—22no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61—81no—
366C4×C61C2×C22⋊Q811yescharacteristic
367C4×C61#54311yescharacteristic
368C4×C61#54611yescharacteristic
369C4×C61#55111yescharacteristic
370Dic61—22no—
371Dic61—22no—
372Dic61—41no—
373Dic61—42no—
374Dic61—41no—
375Dic61—81no—
376C2×#476—611no—
377C22×#102—611no—
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#1807D6111yescharacteristic, complemented
389#1802—611no—
390#1786—611no—
391C2×C61—24no—
392C2×C61#243711yescharacteristic
393C2×C61C2×#47611yescharacteristic
394C2×C61#308111yescharacteristic
395C2×C61#326411yescharacteristic
396C2×C61D4×SD1611yescharacteristic
397C2×C61#329511yescharacteristic
398C2×C61#330611yescharacteristic
399D61—44no—
400D61—82no—
401C23×D4—611no—
402C23×C8C2×D6111yescharacteristic
403C2×C4⋊Q8—611no—
404C2×C22⋊Q8—1221no—
405C2×C4×D4—611no—
406C2×C4×D4—611no—
407C22×C4⋊C4—611no—
408C22×C22⋊C4—1221no—
409#476—1224no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106C2×D6111yescharacteristic, complemented
413C2×#106C2×D6111yescharacteristic, complemented
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—1224no—
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#380C2×D6111yescharacteristic
437#380C2×D6111yescharacteristic
438#379—1221no—
439C4×C22⋊C4—611no—
440#340—611no—
441#340—611no—
442#340C2×D6111yescharacteristic, complemented
443#340C2×D6111yescharacteristic, complemented
444#336—611no—
445#336—611no—
446C61#2595811yescharacteristic, complemented, Sylow
447C25—1221no—
448C22×Q8—1221no—
449C22×D4—614no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1221no—
456C22×D4—2441no—
457C22×D4—2441no—
458C23×C4—1221no—
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—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1222no—
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⋊C4—2441no—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
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—22no—
504#106—41no—
505#106—1222no—
506#106—2441no—
507C4⋊C8—1222no—
508C4⋊C8—2441no—
509#102—614no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—2441no—
516#102—2441no—
517C22⋊C8—1222no—
518#95—21no—
519#95—21no—
520#95—611no—
521#95—611no—
522#95—1221no—
523#95—1221no—
524C24—1221no—
525C24—1224no—
526C24—1221no—
527C24—4881no—
528C24—4881no—
529C24—2442no—
530C24—2442no—
531C24—2442no—
532C24—2442no—
533C24D4×D6111yescharacteristic
534C2×Q8—4881no—
535C2×Q8—2442no—
536C2×Q8—2442no—
537C2×D4—612no—
538C2×D4—612no—
539C2×D4—612no—
540C2×D4—612no—
541C2×D4—1228no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1224no—
551C2×D4—2444no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4—2442no—
555C2×D4—2442no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—4881no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4#1175822212yes—
580C22×C4D4×D6111yescharacteristic
581C22×C4Q8×D6112yes—
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×C8D4×D6112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—612no—
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⋊C4—2442no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—614no—
617C22⋊C4—1222no—
618C22⋊C4—4881no—
619C22⋊C4—4881no—
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—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—4884no—
637C23—4884no—
638C23—4884no—
639C23—4884no—
640C23—4884no—
641C23—2448no—
642C23—2441no—
643C23—2441no—
644C23—2448no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23#1451975512yes—
654C23SD16×D6112yes—
655C23#1451980412yes—
656C23C2×D4×D6111yescharacteristic
657Q8—4884no—
658D4—614no—
659D4—1222no—
660D4—1222no—
661D4—1222no—
662D4—1222no—
663D4—1222no—
664D4—2448no—
665D4—2441no—
666D4—2441no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1221no—
698C2×C4—4884no—
699C2×C4—4884no—
700C2×C4—4884no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4#1451975512yes—
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4C2×Q8×D6111yescharacteristic
709C2×C4#41×D6111yescharacteristic
710C2×C4C2×#1175822211yescharacteristic
711C2×C4#1451982211yescharacteristic
712C2×C4#1451982311yescharacteristic
713C8—22no—
714C8—41no—
715C8—2441no—
716C8—2441no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—1224no—
724C22—48816no—
725C22—4881no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22#1684005114yescomplemented
739C22C2×#1451975511yescharacteristic
740C22#1684039611yescharacteristic
741C22#1684040111yescharacteristic
742C22C2×SD16×D6111yescharacteristic
743C22C2×#1451980411yescharacteristic
744C22#1684056411yescharacteristic
745C22#1684056911yescharacteristic
746C4—22no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—1222no—
752C4—1222no—
753C4—4881no—
754C4—2441no—
755C4—2441no—
756C4—2442no—
757C4C22⋊Q8×D6111yescharacteristic
758C4#1684038711yescharacteristic
759C4#1684040211yescharacteristic
760C4#1684043611yescharacteristic
761C2—24no—
762C2—4882no—
763C2—2444no—
764C2#2144948711yescharacteristic
765C2C2×#1684005111yescharacteristic
766C2#2145565311yescharacteristic
767C2#2145729611yescharacteristic
768C2#2145751211yescharacteristic
769C2#2145763811yescharacteristic
770C2#2145778611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1807C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#1807D61
hypocenterC61#25958
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
1. C2×#16840051C2semidirect
3. #21449522C2semidirect
5. #21447349C2semidirect
6. #21447194C2semidirect
7. #21447188C2semidirect
8. #21446954C2semidirect
9. #21446081C2semidirect
10. #21446077C2semidirect
11. #21446011C2semidirect
12. #21445997C2semidirect
13. #21445818C2semidirect
15. C61×#1807C2semidirect
17. C2×#14519776C22semidirect
24. C2×#14519708C22semidirect
25. C2×#14519708C22semidirect
26. C2×#14519706C22semidirect
27. C2×#14519706C22semidirect
42. #16839661C22semidirect
43. #16839658C22semidirect
47. #16839631C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
55. C2×#106×C61C22semidirect
56. C2×#106×C61C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
69. C22×D244Q8semidirect
323. D244C22⋊Q8semidirect
338. C22×C61#476semidirect
388. #1807D61semidirect
412. C2×#106C2×D61semidirect
413. C2×#106C2×D61semidirect
442. #340C2×D61semidirect
443. #340C2×D61semidirect
446. C61#25958semidirect
738. C22#16840051semidirect

Maximal subgroups

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

subgroupindex
C2×#168400512
C22×#145196992
#214495222
#214486392
#214473492
#214471942
#214471882
#214469542
#214460812
#214460772
#214460112
#214459972
#214458182
#214457492
C61×#18072
#2595861