Finite Group Databasebeta

← #29722346

Subgroups — #29722346

Order 15616.

1032 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840007C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839830C211yesmaximal, characteristic, complemented
4C2×#16839803C211yesmaximal, characteristic, complemented
5#21449255C211yesmaximal, characteristic
6#21449250C211yesmaximal, characteristic, complemented
7#21447209C211yesmaximal, characteristic, complemented
8#21447191C211yesmaximal, characteristic, complemented
9#21447016C211yesmaximal, characteristic, complemented
10#21446701C211yesmaximal, characteristic, complemented
11#21446561C211yesmaximal, characteristic, complemented
12#21446138C211yesmaximal, characteristic, complemented
13#21446125C211yesmaximal, characteristic, complemented
14#21445846C211yesmaximal, characteristic, complemented
15C61×#2033C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519748—21no—
22C2×#14519748C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×#14519735C2211yescharacteristic
25C2×C4⋊C4×D61C2211yescharacteristic
26#16840007—24no—
27#16839989—24no—
28#16839830—24no—
29#16839803—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519710C2211yescharacteristic
32C2×#14519709C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×#14519706C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41#16839691—21no—
42#16839685—21no—
43#16839677—21no—
44#16839676—21no—
45#16839667C2211yescharacteristic
46#16839665C2211yescharacteristic
47#16839661C2211yescharacteristic
48#16839659—21no—
49#16839658C2211yescharacteristic
50#16839655—21no—
51#16839638—21no—
52#16839622C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#107×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189D414yescomplemented
74C22×#92418—22no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519757—22no—
80#14519757—22no—
81#14519756—22no—
82#14519756—41no—
83#14519748—22no—
84#14519748—22no—
85#14519748—44no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88#14519735—22no—
89#14519735—41no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196D411yescharacteristic
99C4⋊C4×D61—22no—
100C4⋊C4×D61—41no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112#14519710—22no—
113#14519710—22no—
114#14519709—22no—
115#14519708D414yescomplemented
116#14519706—22no—
117#14519702—22no—
118#14519702—41no—
119#14519700—22no—
120#14519698—22no—
121#14519689—22no—
122#14519687—22no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128C22×D4×C61—21no—
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133#121×C61—22no—
134#121×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140#107×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143C22⋊C8×C61—22no—
144#95×C61—21no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
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—21no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—81no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—42no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—81no—
188C2×C4×D61C2×D412yes—
189C2×C4×D61#4112yes—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C2×D412yes—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊Dic61—22no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—81no—
216#11758200—44no—
217#11758198—22no—
218#11758198—42no—
219#11758198—42no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61—42no—
227C4⋊Dic61C2×D412yes—
228#11758196—22no—
229#11758196—42no—
230#11758196—42no—
231#11758196—42no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—42no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—44no—
239C2×#92418C2×D412yes—
240C2×#92418C2×D412yes—
241C2×#92418#4112yes—
242#11758189—28no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61AGL(1,ℤ/8)12yes—
257C23×C61C22×D411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61#12112yes—
265D4×C61—41no—
266D4×C61—41no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—84no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C22⋊D61—44no—
293C22⋊D61—84no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
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—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61#12112yes—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—84no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324C8×C61—22no—
325C8×C61—41no—
326#92418—41no—
327#92418#12114yescomplemented
328#24789—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61C2×#12111yescharacteristic
344C22×C61D4211yescharacteristic
345C22×C61#54711yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61#57511yescharacteristic
348C22×C61#57711yescharacteristic
349C22×C61#57811yescharacteristic
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C4×C61—41no—
358C4×C61—42no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61C2×#12111yescharacteristic
362C4×C61#53711yescharacteristic
363C4×C61#54811yescharacteristic
364C4×C61#55311yescharacteristic
365Dic61—22no—
366Dic61—42no—
367Dic61—41no—
368Dic61—41no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#468—611no—
373C2×#465—611no—
374C2×#435—611no—
375C2×#428—611no—
376#2416—611no—
377#2415—611no—
378#2068—611no—
379#2065—611no—
380#2035—611no—
381#2033D6111yescharacteristic, complemented
382#1973—611no—
383#1944—611no—
384#1875—611no—
385#1872—611no—
386#1808—611no—
387C2×C61—42no—
388C2×C61—161no—
389C2×C61#241611yescharacteristic
390C2×C61#305511yescharacteristic
391C2×C61#306311yescharacteristic
392C2×C61#326511yescharacteristic
393C2×C61#326911yescharacteristic
394C2×C61#334311yescharacteristic
395C2×C61#335011yescharacteristic
396D61—42no—
397C22×SD16—611no—
398C22×M16—611no—
399C23×C8—611no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—611no—
402C2×#121—611no—
403C2×#121—1221no—
404C2×#121C2×D6111yescharacteristic
405C2×C4×D4—611no—
406C2×#117—611no—
407C22×C4⋊C4—611no—
408#468—1224no—
409#465—1224no—
410#435—1224no—
411#428—1224no—
412C2×#107—611no—
413C2×#107—611no—
414C2×#107C2×D6111yescharacteristic
415C2×#106—611no—
416C2×#106—611no—
417C2×C4⋊C8—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#102—611no—
422C2×#102C2×D6111yescharacteristic
423C2×#102C2×D6111yescharacteristic
424C2×C22⋊C8—611no—
425C2×C22⋊C8C2×D6111yescharacteristic
426C2×#97—611no—
427#397—1221no—
428#396—1221no—
429#394—1221no—
430#394—1221no—
431#391—611no—
432#390—611no—
433#389—611no—
434#389—611no—
435#389—1221no—
436#388—1221no—
437#386—1221no—
438#380—611no—
439#380C2×D6111yescharacteristic
440#340—611no—
441#340—611no—
442#340—611no—
443#340C2×D6111yescharacteristic
444C61#2478911yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—21no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4C22×D6111yescharacteristic
453C2×SD16—1222no—
454C2×SD16—1222no—
455C2×SD16—1222no—
456C2×M16—614no—
457C2×M16—1222no—
458C2×M16—1222no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—1222no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22⋊Q8—1222no—
467C22⋊Q8—1222no—
468C22⋊Q8—1222no—
469C22⋊Q8—2441no—
470#121—22no—
471#121—41no—
472#121—1222no—
473#121—1222no—
474#121—2444no—
475C4×D4—1222no—
476C4×D4—1222no—
477#117—1222no—
478#117—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—2441no—
490C2×C4⋊C4C22×D6111yescharacteristic
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×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—611no—
505C2×C42—1221no—
506#107—22no—
507#107—1222no—
508#107—1222no—
509#106—614no—
510#106—1222no—
511C4⋊C8—1222no—
512#103—1222no—
513#103—1222no—
514#103—2441no—
515#102—22no—
516#102—41no—
517#102—1222no—
518C22⋊C8—22no—
519C22⋊C8—1222no—
520#97—1222no—
521#95—21no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527C24—21no—
528C24—611no—
529C24D4×D6111yescharacteristic
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—81no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—2441no—
548C2×D4—2442no—
549C2×D4—2442no—
550C2×D4—2442no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
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—1221no—
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—2442no—
575C22×C4—2442no—
576C22×C4D4×D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578SD16—2444no—
579M16—1228no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—612no—
586C2×C8—612no—
587C2×C8—612no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—2444no—
592C2×C8D4×D6112yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—612no—
599C4⋊C4—1222no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—2442no—
606C4⋊C4—2442no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4D4×D6112yes—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—4881no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—1221no—
623C42—1221no—
624C42—2442no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—612no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23#1451980112yes—
646C23C2×D4×D6111yescharacteristic
647Q8—2441no—
648Q8—2441no—
649Q8—2441no—
650Q8—2441no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—84no—
656D4—4884no—
657D4—2444no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—612no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1222no—
688C2×C4—4884no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4#41×D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982411yescharacteristic
706C8—22no—
707C8—41no—
708C8—614no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—2441no—
728C22—2441no—
729C22—2441no—
730C22—2441no—
731C22#121×D6111yescharacteristic
732C22#1684039411yescharacteristic
733C22#1684041011yescharacteristic
734C22C2×#1451980111yescharacteristic
735C22#1684055911yescharacteristic
736C22#1684057211yescharacteristic
737C22#1684057811yescharacteristic
738C4—41no—
739C4—42no—
740C4—81no—
741C4—81no—
742C4—1222no—
743C4—4881no—
744C4—4881no—
745C4—4881no—
746C4—2441no—
747C4—2441no—
748C4—2442no—
749C4#121×D6111yescharacteristic
750C4#1684034111yescharacteristic
751C4#1684042011yescharacteristic
752C4#1684045711yescharacteristic
753C2—42no—
754C2—161no—
755C2—2442no—
756C2#2144925211yescharacteristic
757C2#2145543511yescharacteristic
758C2#2145550511yescharacteristic
759C2#2145731811yescharacteristic
760C2#2145736711yescharacteristic
761C2#2145826311yescharacteristic
762C2#2145836811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2033C2
socleC23×C61C22×D4
prime radical#21449255C2
hypercenter#2033D61
hypocenterC61#24789
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
1. C2×#16840007C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839830C2semidirect
4. C2×#16839803C2semidirect
6. #21449250C2semidirect
7. #21447209C2semidirect
8. #21447191C2semidirect
9. #21447016C2semidirect
10. #21446701C2semidirect
11. #21446561C2semidirect
12. #21446138C2semidirect
13. #21446125C2semidirect
14. #21445846C2semidirect
15. C61×#2033C2semidirect
73. C2×#11758189D4semidirect
115. #14519708D4semidirect
327. #92418#121semidirect
381. #2033D61semidirect
444. C61#24789semidirect

Maximal subgroups

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

subgroupindex
C2×#168400072
C2×#168399892
C2×#168398302
C2×#168398032
#214492552
#214492502
#214472092
#214471912
#214470162
#214467012
#214465612
#214461382
#214461252
#214458462
C61×#20332
#2478961