Finite Group Databasebeta

← #29722416

Subgroups — #29722416

Order 15616.

1026 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×#16840005C211yesmaximal, characteristic, complemented
2C2×#16839838C211yesmaximal, characteristic, complemented
3C2×#16839803C211yesmaximal, characteristic, complemented
4#21449255C211yesmaximal, characteristic
5#21449244C211yesmaximal, characteristic, complemented
6#21447203C211yesmaximal, characteristic, complemented
7#21447196C211yesmaximal, characteristic, complemented
8#21447019C211yesmaximal, characteristic, complemented
9#21447005C211yesmaximal, characteristic, complemented
10#21446675C211yesmaximal, characteristic, complemented
11#21446553C211yesmaximal, characteristic, complemented
12#21446138C211yesmaximal, characteristic, complemented
13#21446123C211yesmaximal, characteristic, complemented
14#21445852C211yesmaximal, characteristic, complemented
15C2×C61×#468C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×#14519753C2211yescharacteristic
18C2×#14519748—21no—
19C2×#14519748C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16840005—24no—
24#16839838—24no—
25#16839803—24no—
26C2×#14519711C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519709C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839688—21no—
39#16839685—21no—
40#16839678—21no—
41#16839676—21no—
42#16839669C2211yescharacteristic
43#16839665C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839661C2211yescharacteristic
46#16839658—21no—
47#16839650—21no—
48#16839638—21no—
49#16839622C2211yescharacteristic
50#16839622C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#468—24no—
60C2×#107×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61D411yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189D414yescomplemented
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519753—22no—
73#14519753—22no—
74#14519748—22no—
75#14519748—22no—
76#14519748—44no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79#14519735—22no—
80#14519735—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196D411yescharacteristic
90C4⋊C4×D61—22no—
91C4⋊C4×D61—41no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61D411yescharacteristic
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103#14519711—22no—
104#14519710—22no—
105#14519709—22no—
106#14519708—22no—
107#14519706—22no—
108#14519701—22no—
109#14519701—41no—
110#14519698—22no—
111#14519698—41no—
112C22⋊#92418—22no—
113#14519689—22no—
114C8×Dic61—22no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C22×Q8×C61C2311yescharacteristic
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61—22no—
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—41no—
135#121×C61—22no—
136#121×C61—41no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142#107×C61D414yescomplemented
143#103×C61—22no—
144#102×C61—22no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C23×D61C2×D411yescharacteristic
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—81no—
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×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—41no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C2×C4×D61C2×D412yes—
195C2×C4×D61#4112yes—
196SD16×C61—44no—
197M16×C61—44no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C2×C8×C61C2×D412yes—
203C2×C8×C61#4112yes—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61C2×D412yes—
208C4⋊C4×C61C2×D412yes—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊Dic61—22no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—42no—
216C22⋊Dic61—81no—
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—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61—42no—
230#11758196—22no—
231#11758196—42no—
232#11758196—42no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—42no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418C2×D412yes—
242#11758189—28no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61C22×D411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61#12112yes—
265Q8×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268Q8×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—41no—
273D4×C61—84no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
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×C61—41no—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C612−1+411yescharacteristic
296C22⋊D61—44no—
297C22⋊D61—84no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
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—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61#12112yes—
318C2×Dic61AGL(1,ℤ/8)12yes—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—84no—
324C8×C61—41no—
325C8×C61#12114yescomplemented
326#92418—22no—
327#92418—41no—
328#24794—611nomaximal, Sylow
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
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—42no—
360C4×C61—81no—
361C4×C61C2×#12111yescharacteristic
362C4×C61#53711yescharacteristic
363C4×C61#54811yescharacteristic
364C4×C61#55311yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—41no—
368Dic61—81no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#468—611no—
373C2×#468D6111yescharacteristic, complemented
374C2×#436—611no—
375C2×#428—611no—
376#2416—611no—
377#2415—611no—
378#2067—611no—
379#2066—611no—
380#2036—611no—
381#2034—611no—
382#1968—611no—
383#1942—611no—
384#1875—611no—
385#1872—611no—
386#1809—611no—
387C2×C61—81no—
388C2×C61—161no—
389C2×C61#241611yescharacteristic
390C2×C61#305511yescharacteristic
391C2×C61#306311yescharacteristic
392C2×C61#327211yescharacteristic
393C2×C61#327711yescharacteristic
394C2×C61#335111yescharacteristic
395C2×C61#335311yescharacteristic
396D61—42no—
397C22×SD16C2×D6111yescharacteristic
398C22×M16—611no—
399C22×M16C2×D6111yescharacteristic
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×#121—611no—
403C2×#121—1221no—
404C2×#121C2×D6111yescharacteristic
405C2×C4×D4—611no—
406C2×#117—611no—
407C22×C4⋊C4—611no—
408#468—24no—
409#468—1224no—
410#436—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×#103C2×D6111yescharacteristic
421C2×#102—611no—
422C2×#102—611no—
423C2×#102C2×D6111yescharacteristic
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C4×C8—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#380—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444C61#2479411yescharacteristic, complemented, Sylow
445C22×Q8C22×D6111yescharacteristic
446C22×D4—21no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4C22×D6111yescharacteristic
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—614no—
460C2×M16—1222no—
461C2×M16—1222no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22⋊Q8—22no—
467C22⋊Q8—41no—
468C22⋊Q8—1222no—
469C22⋊Q8—1222no—
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—21no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1221no—
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×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—611no—
505C2×C42—1221no—
506#107—1222no—
507#107—1222no—
508#107C22⋊D6114yescomplemented
509#106—1222no—
510#106—1222no—
511C4⋊C8—1222no—
512#103—22no—
513#103—1222no—
514#103—2441no—
515#102—22no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—1222no—
520C4×C8—1222no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527C24—21no—
528C24—611no—
529C24D4×D6111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
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—611no—
562C22×C4—612no—
563C22×C4—612no—
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—44no—
579M16—44no—
580M16—1228no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—612no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8D4×D6112yes—
591C2×C8#1175822412yes—
592C2×C8C2×C22⋊D6112yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—1222no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
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⋊C4C2×C22⋊D6112yes—
610C4⋊C4C2×C22⋊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—21no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—612no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23C2×D4×D6111yescharacteristic
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—84no—
656D4—4884no—
657D4—2444no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
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—612no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—4884no—
688C2×C4—2441no—
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×C4C22×C22⋊D6111yescharacteristic
702C2×C4#41×D6111yescharacteristic
703C2×C4C2×#1175822411yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982411yescharacteristic
706C8—41no—
707C8—1222no—
708C8—2441no—
709C8#1451974814yescomplemented
710C22—41no—
711C22—41no—
712C22—41no—
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
732C22D4×C22⋊D6111yescharacteristic
733C22#1684041211yescharacteristic
734C22AGL(1,ℤ/8)×D6111yescharacteristic
735C22#1684056111yescharacteristic
736C22#1684057211yescharacteristic
737C22#1684057811yescharacteristic
738C4—42no—
739C4—42no—
740C4—41no—
741C4—81no—
742C4—1222no—
743C4—1222no—
744C4—4881no—
745C4—4881no—
746C4—4881no—
747C4—4881no—
748C4—2441no—
749C4C2×#1451974811yescharacteristic
750C4#1684034111yescharacteristic
751C4#1684041911yescharacteristic
752C4#1684045911yescharacteristic
753C2—81no—
754C2—161no—
755C2—2442no—
756C2#2144925511yescharacteristic
757C2#2145543311yescharacteristic
758C2#2145550511yescharacteristic
759C2#2145741311yescharacteristic
760C2#2145747011yescharacteristic
761C2#2145838511yescharacteristic
762C2#2145839811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#468C2
socleC23×C61C22×D4
prime radical#21449255C2
hypercenterC2×#468D61
hypocenterC61#24794
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16840005C2semidirect
2. C2×#16839838C2semidirect
3. C2×#16839803C2semidirect
5. #21449244C2semidirect
6. #21447203C2semidirect
7. #21447196C2semidirect
8. #21447019C2semidirect
9. #21447005C2semidirect
10. #21446675C2semidirect
11. #21446553C2semidirect
12. #21446138C2semidirect
13. #21446123C2semidirect
14. #21445852C2semidirect
15. C2×C61×#468C2semidirect
69. C2×#11758189D4semidirect
142. #107×C61D4semidirect
325. C8×C61#121semidirect
373. C2×#468D61semidirect
444. C61#24794semidirect
508. #107C22⋊D61semidirect
709. C8#14519748semidirect

Maximal subgroups

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

subgroupindex
C2×#168400052
C2×#168398382
C2×#168398032
#214492552
#214492442
#214472032
#214471962
#214470192
#214470052
#214466752
#214465532
#214461382
#214461232
#214458522
C2×C61×#4682
#2479461