Finite Group Databasebeta

← #29733136

Subgroups — #29733136

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840446C211yesmaximal, characteristic
2C2×#16840100C211yesmaximal, characteristic, complemented
3#21449271C211yesmaximal, characteristic
4#21447159C211yesmaximal, characteristic, complemented
5#21447020C211yesmaximal, characteristic, complemented
6#21446968C211yesmaximal, characteristic, complemented
7#21446826C211yesmaximal, characteristic, complemented
8#21446162C211yesmaximal, characteristic, complemented
9#21446127C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21446116C211yesmaximal, characteristic
12#21446085C211yesmaximal, characteristic, complemented
13#21446010C211yesmaximal, characteristic, complemented
14#21445539C211yesmaximal, characteristic, complemented
15C2×C61×#470C211yesmaximal, characteristic, complemented
16#16840446—24no—
17#16840446—24no—
18C2×#14519770—21no—
19C2×#14519768C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519759—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C2×#14519735—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840100—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40#16839695—21no—
41#16839684—21no—
42#16839669C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839639—21no—
45#16839620—21no—
46#16839619C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×Q16×C61C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C61×#470—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C22×C22⋊D61D411yescharacteristic
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C22×C4×D61C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519770—28no—
70#14519768—22no—
71#14519768—22no—
72#14519767—28no—
73#14519759—28no—
74#14519753—22no—
75#14519753—22no—
76#14519753—22no—
77#14519753—41no—
78Q8×Dic61—22no—
79Q8×Dic61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82#14519736—22no—
83#14519736D414yes—
84#14519735—28no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61D411yescharacteristic
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198D411yescharacteristic
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111#14519710—22no—
112#14519708—22no—
113#14519701—22no—
114#14519701—22no—
115#14519701—22no—
116#14519701—41no—
117C22⋊#92418—22no—
118#14519689—22no—
119#14519689—41no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C22×Q8×C61C2311yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×Q16×C61—22no—
128C2×Q16×C61—22no—
129C2×Q16×C61—41no—
130C2×M16×C61—22no—
131C2×M16×C61—22no—
132C2×M16×C61—41no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61D414yes—
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#106×C61—22no—
146#103×C61—22no—
147#103×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×C61—21no—
161C2×Q8×C61C2×D412yes—
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×C61C2×D411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—41no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—81no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×C4×D61—24no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196Q16×C61—44no—
197M16×C61—44no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61#4112yes—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61C2×D412yes—
210C22⋊C4×C61—24no—
211C22⋊C4×C61—42no—
212C22⋊Dic61—24no—
213C22⋊Dic61—22no—
214#11758198—24no—
215#11758198—22no—
216#11758198—42no—
217#11758198—81no—
218C4⋊Dic61—24no—
219C4⋊Dic61—24no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61C2×D412yes—
227C4⋊Dic61C2×D412yes—
228C4⋊Dic61#4112yes—
229#11758196—24no—
230#11758196—24no—
231#11758196—24no—
232#11758196—22no—
233#11758196—42no—
234#11758196—81no—
235C4×Dic61—24no—
236C4×Dic61—24no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61#12012yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61#13712yes—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
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×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61#12012yes—
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C612−1+411yescharacteristic
293C22⋊D61—44no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—84no—
316C4×D61—48no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C8×C61—22no—
322C8×C61—41no—
323#92418—41no—
324#92418—41no—
325#25562—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C2×#12011yescharacteristic
334C22×C61#54611yescharacteristic
335C22×C61#54711yescharacteristic
336C22×C61C2×#13711yescharacteristic
337C22×C61#57511yescharacteristic
338C22×C61#57711yescharacteristic
339C22×C61#57811yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—81no—
351C4×C61—81no—
352C4×C61#53211yescharacteristic
353C4×C61#53711yescharacteristic
354C4×C61#54611yescharacteristic
355C4×C61#54711yescharacteristic
356Dic61—41no—
357Dic61—42no—
358Dic61—41no—
359Dic61—41no—
360Dic61—42no—
361Dic61—42no—
362Dic61—81no—
363C2×#552—611no—
364C2×#485—611no—
365C2×#470D6111yescharacteristic, complemented
366#2417—611no—
367#2059—611no—
368#2036—611no—
369#2026—611no—
370#2001—611no—
371#1878—611no—
372#1872—611no—
373#1872—611no—
374#1870—611no—
375#1865—611no—
376#1853—611no—
377#1736—611no—
378C2×C61—42no—
379C2×C61#243011yescharacteristic
380C2×C61#300711yescharacteristic
381C2×C61#301311yescharacteristic
382C2×C61#331211yescharacteristic
383C2×C61#332311yescharacteristic
384C2×C61#334411yescharacteristic
385C2×C61#335211yescharacteristic
386D61—42no—
387C22×Q16C2×D6111yescharacteristic
388C22×M16C2×D6111yescharacteristic
389#552—1224no—
390#552—1224no—
391C2×#126—1221no—
392C2×#125—611no—
393C2×#125—1221no—
394C2×#123—1221no—
395C2×C22⋊Q8—611no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8C2×D6111yescharacteristic
398C2×C22⋊Q8C2×D6111yescharacteristic
399C2×C4×Q8—611no—
400C2×C4×D4—611no—
401C2×#117—611no—
402C2×#117—1221no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405#485—1224no—
406#470—24no—
407C2×#107—611no—
408C2×#106—611no—
409C2×#106C2×D6111yescharacteristic
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#103C2×D6111yescharacteristic
415C2×#103C2×D6111yescharacteristic
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419#398—1221no—
420#396—1221no—
421#391—611no—
422#389—611no—
423#386—1221no—
424#380—611no—
425#380—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#336—611no—
433#336—611no—
434C61#2556211yescharacteristic, complemented, Sylow
435C22×Q8C22×D6111yescharacteristic
436C22×Q8C22×D6111yescharacteristic
437C22×D4—611no—
438C23×C4—611no—
439C23×C4—1221no—
440C23×C4—1221no—
441C23×C4C22×D6111yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—41no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8C22×D6111yescharacteristic
451C22×C8C22×D6111yescharacteristic
452#126—1228no—
453#125—1222no—
454#125—1228no—
455#125—1222no—
456#123—1228no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—1222no—
461C22⋊Q8—1222no—
462C22⋊Q8—1222no—
463C22⋊Q8—2441no—
464C22⋊Q8C22⋊D6114yes—
465C4×Q8—1222no—
466C4×Q8—1222no—
467C4×D4—1222no—
468C4×D4—1222no—
469#117—614no—
470#117—1228no—
471#117—1222no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—2441no—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1221no—
504#107—1222no—
505#106—22no—
506#106—1222no—
507#103—22no—
508#103—22no—
509#103—1222no—
510#103—1222no—
511#103—1222no—
512#103—2441no—
513C22⋊C8—1222no—
514C22⋊C8—1222no—
515C22⋊C8—2441no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—611no—
521C24D4×D6111yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C22⋊D6112yes—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—2441no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—1224no—
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—1221no—
558C22×C4—1221no—
559C22×C4—4881no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4D4×D6112yes—
565C22×C4D4×D6111yescharacteristic
566C22×C4C2×C22⋊D6112yes—
567C22×C4C23×D6111yescharacteristic
568Q16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8#1175822412yes—
582C4⋊C4—21no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—612no—
588C4⋊C4—612no—
589C4⋊C4—612no—
590C4⋊C4—1224no—
591C4⋊C4—1224no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4—1224no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1222no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—4881no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4C2×C22⋊D6112yes—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—1224no—
608C22⋊C4—1222no—
609C22⋊C4—1224no—
610C22⋊C4—1222no—
611C22⋊C4—4881no—
612C22⋊C4—2442no—
613C42—1224no—
614C42—1221no—
615C42—1221no—
616C42—1224no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—612no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23#1451974512yes—
631C23C2×D4×D6111yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640D4—2444no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—1221no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1222no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—4884no—
672C2×C4—2448no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4#1451974512yes—
687C2×C4C2×D4×D6111yescharacteristic
688C2×C4C22×C22⋊D6111yescharacteristic
689C2×C4#41×D6111yescharacteristic
690C2×C4C2×#1175822411yescharacteristic
691C2×C4#1451982211yescharacteristic
692C2×C4#1451982411yescharacteristic
693C8—22no—
694C8—41no—
695C8—2441no—
696C8—2441no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—2441no—
708C22—2441no—
709C22—2441no—
710C22—2441no—
711C22C2×#1451974511yescharacteristic
712C22#1684040111yescharacteristic
713C22#1684041211yescharacteristic
714C22#137×D6111yescharacteristic
715C22#1684056111yescharacteristic
716C22#1684057111yescharacteristic
717C22#1684057811yescharacteristic
718C4—22no—
719C4—42no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—4881no—
724C4—2441no—
725C4—2442no—
726C4—2442no—
727C4—2441no—
728C4—2441no—
729C4—2442no—
730C4#1684030711yescharacteristic
731C4#1684033911yescharacteristic
732C4#1684040611yescharacteristic
733C4#1684041111yescharacteristic
734C2—42no—
735C2—2442no—
736C2#2144942511yescharacteristic
737C2#2145507511yescharacteristic
738C2#2145513311yescharacteristic
739C2#2145786511yescharacteristic
740C2#2145804111yescharacteristic
741C2#2145826911yescharacteristic
742C2#2145838911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#470C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#470D61
hypocenterC61#25562
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#16840100C2semidirect
4. #21447159C2semidirect
5. #21447020C2semidirect
6. #21446968C2semidirect
7. #21446826C2semidirect
8. #21446162C2semidirect
9. #21446127C2semidirect
10. #21446123C2semidirect
12. #21446085C2semidirect
13. #21446010C2semidirect
14. #21445539C2semidirect
15. C2×C61×#470C2semidirect
365. C2×#470D61semidirect
434. C61#25562semidirect

Maximal subgroups

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

subgroupindex
C2×#168404462
C2×#168401002
#214492712
#214471592
#214470202
#214469682
#214468262
#214461622
#214461272
#214461232
#214461162
#214460852
#214460102
#214455392
C2×C61×#4702
#2556261