Finite Group Databasebeta

← #29722437

Subgroups — #29722437

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 762 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×#16839804C211yesmaximal, characteristic, complemented
4#21449271C211yesmaximal, characteristic, complemented
5#21449238C211yesmaximal, characteristic
6#21447212C211yesmaximal, characteristic, complemented
7#21447191C211yesmaximal, characteristic, complemented
8#21447014C211yesmaximal, characteristic, complemented
9#21447000C211yesmaximal, characteristic, complemented
10#21446675C211yesmaximal, characteristic, complemented
11#21446550C211yesmaximal, characteristic, complemented
12#21446137C211yesmaximal, characteristic, complemented
13#21446132C211yesmaximal, characteristic, complemented
14#21445853C211yesmaximal, characteristic, complemented
15C2×C61×#468C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×#14519753C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16840005—24no—
23#16839838—24no—
24#16839804—24no—
25C2×#14519711C2211yescharacteristic
26C2×#14519711C2211yescharacteristic
27C2×#14519709C2211yescharacteristic
28C2×#14519709C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839695—21no—
38#16839684—21no—
39#16839676—21no—
40#16839670—21no—
41#16839669C2211yescharacteristic
42#16839665C2211yescharacteristic
43#16839662—21no—
44#16839658C2211yescharacteristic
45#16839658C2211yescharacteristic
46#16839656—21no—
47#16839639—21no—
48#16839620—21no—
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
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
65C23×Dic61—21no—
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519753—22no—
73#14519753—41no—
74#14519748—22no—
75#14519748—41no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78#14519736—22no—
79#14519736—41no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196D411yescharacteristic
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61D411yescharacteristic
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102#14519711—22no—
103#14519711D414yescomplemented
104#14519709—22no—
105#14519709—22no—
106#14519706—22no—
107#14519701—22no—
108#14519701—41no—
109#14519698—22no—
110#14519698—41no—
111C22⋊#92418—22no—
112#14519689—22no—
113C8×Dic61—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C22×Q8×C61C2311yescharacteristic
121C22×D4×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×SD16×C61—22no—
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×M16×C61—22no—
128C2×M16×C61—22no—
129C2×M16×C61D414yescomplemented
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—22no—
134#121×C61—22no—
135#121×C61—22no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141#107×C61—22no—
142#103×C61—22no—
143#102×C61—22no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61C2×D411yescharacteristic
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×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—21no—
159C2×D4×C61—42no—
160C2×D4×C61—81no—
161C2×D4×C61—81no—
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×C61C2×D411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61#4112yes—
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—81no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61—81no—
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195SD16×C61—44no—
196M16×C61—28no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61C2×D412yes—
200C2×C8×C61C2×D412yes—
201C2×C8×C61C2×D412yes—
202C2×C8×C61#4112yes—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊Dic61—22no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—81no—
215#11758198—22no—
216#11758198—42no—
217#11758198—81no—
218#11758198—81no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61C2×D412yes—
227C4⋊Dic61C2×D412yes—
228#11758196—22no—
229#11758196—42no—
230#11758196—81no—
231#11758196—81no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—42no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241#11758189—44no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61#12112yes—
256C23×C61C22×D411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—84no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
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#12112yes—
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C612−1+411yescharacteristic
295C22⋊D61—44no—
296C22⋊D61—84no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—21no—
303C2×Dic61—22no—
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—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—84no—
318C2×Dic61#13712yes—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C8×C61—22no—
324C8×C61#12114yes—
325#92418—41no—
326#92418—41no—
327#24795—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61C2×#12111yescharacteristic
343C22×C61D4211yescharacteristic
344C22×C61#54711yescharacteristic
345C22×C61C2×#13711yescharacteristic
346C22×C61#57511yescharacteristic
347C22×C61#57611yescharacteristic
348C22×C61#57711yescharacteristic
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C4×C61—22no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61C2×#12111yescharacteristic
361C4×C61#53711yescharacteristic
362C4×C61#54811yescharacteristic
363C4×C61#55311yescharacteristic
364Dic61—22no—
365Dic61—41no—
366Dic61—42no—
367Dic61—42no—
368Dic61—41no—
369Dic61—81no—
370Dic61—81no—
371C2×#468—611no—
372C2×#468D6111yescharacteristic, complemented
373C2×#436—611no—
374C2×#428—611no—
375#2417—611no—
376#2414—611no—
377#2068—611no—
378#2065—611no—
379#2035—611no—
380#2033—611no—
381#1968—611no—
382#1942—611no—
383#1874—611no—
384#1873—611no—
385#1809—611no—
386C2×C61—42no—
387C2×C61—161no—
388C2×C61#241611yescharacteristic
389C2×C61#305611yescharacteristic
390C2×C61#306211yescharacteristic
391C2×C61#327311yescharacteristic
392C2×C61#327811yescharacteristic
393C2×C61#335111yescharacteristic
394C2×C61#335711yescharacteristic
395D61—81no—
396C22×SD16C2×D6111yescharacteristic
397C22×M16—611no—
398C22×M16C2×D6111yescharacteristic
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8C2×D6111yescharacteristic
401C2×#121—611no—
402C2×#121C2×D6111yescharacteristic
403C2×C4×D4—611no—
404C2×#117—611no—
405C22×C4⋊C4—611no—
406#468—24no—
407#468—1224no—
408#436—1224no—
409#428—1224no—
410C2×#107—611no—
411C2×#107—611no—
412C2×#107C2×D6111yescharacteristic
413C2×#106—611no—
414C2×#106—611no—
415C2×C4⋊C8—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103C2×D6111yescharacteristic
419C2×#102—611no—
420C2×#102—611no—
421C2×#102C2×D6111yescharacteristic
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C4×C8—611no—
425#398—1221no—
426#396—1221no—
427#394—1221no—
428#392—1221no—
429#391—611no—
430#390—611no—
431#390—1221no—
432#389—611no—
433#389—611no—
434#388—1221no—
435#386—1221no—
436#380—611no—
437#380—611no—
438#380—1221no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443C61#2479511yescharacteristic, complemented, Sylow
444C22×Q8C22×D6111yescharacteristic
445C22×D4—21no—
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4C22×D6111yescharacteristic
449C23×C4—611no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—1222no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16C22⋊D6114yescomplemented
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—1222no—
468C22⋊Q8—2441no—
469#121—22no—
470#121—22no—
471#121—1222no—
472#121—2441no—
473C4×D4—1222no—
474C4×D4—1222no—
475#117—1222no—
476#117—2441no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—611no—
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—2441no—
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C42—611no—
503C2×C42—1221no—
504#107—22no—
505#107—614no—
506#107—1222no—
507#106—1222no—
508#106—1222no—
509C4⋊C8—1222no—
510#103—22no—
511#103—1222no—
512#103—2441no—
513#102—22no—
514#102—1222no—
515#102—2441no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C4×C8—1222no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525C24—21no—
526C24—611no—
527C24D4×D6111yescharacteristic
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4—81no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—4881no—
546C2×D4—2442no—
547C2×D4—2441no—
548C2×D4—2442no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4D4×D6111yescharacteristic
573C22×C4#1175822412yes—
574C22×C4C2×C22⋊D6112yes—
575C22×C4C23×D6111yescharacteristic
576SD16—44no—
577M16—28no—
578M16—2444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8D4×D6112yes—
588C2×C8#1175822412yes—
589C2×C8C2×C22⋊D6112yes—
590C2×C8C2×C22⋊D6112yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—612no—
597C4⋊C4—612no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1222no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—4881no—
606C4⋊C4—4881no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—4881no—
614C22⋊C4—4881no—
615C22⋊C4—4881no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C42—1221no—
621C42—1221no—
622C42—2442no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23#1451974812yes—
644C23C2×D4×D6111yescharacteristic
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—4884no—
655D4—2444no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
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—612no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1222no—
679C2×C4—1221no—
680C2×C4—1222no—
681C2×C4—1221no—
682C2×C4—4884no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
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#1451974812yes—
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4C22×C22⋊D6111yescharacteristic
700C2×C4C2×#1175822411yescharacteristic
701C2×C4C2×#1175822411yescharacteristic
702C2×C4#1451982311yescharacteristic
703C2×C4#1451982411yescharacteristic
704C8—22no—
705C8—2441no—
706C8—2441no—
707C8#1451974914yes—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22—2441no—
726C22—2441no—
727C22—2441no—
728C22—2441no—
729C22C2×#1451974811yescharacteristic
730C22#1684039611yescharacteristic
731C22#1684041211yescharacteristic
732C22#137×D6111yescharacteristic
733C22#1684056111yescharacteristic
734C22#1684056611yescharacteristic
735C22#1684057211yescharacteristic
736C4—22no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—1222no—
741C4—4881no—
742C4—4881no—
743C4—2442no—
744C4—2442no—
745C4—2441no—
746C4—2441no—
747C4C2×#1451974911yescharacteristic
748C4#1684034011yescharacteristic
749C4#1684041811yescharacteristic
750C4#1684046411yescharacteristic
751C2—42no—
752C2—161no—
753C2—4881no—
754C2#2144926011yescharacteristic
755C2#2145544311yescharacteristic
756C2#2145549311yescharacteristic
757C2#2145742711yescharacteristic
758C2#2145748211yescharacteristic
759C2#2145838511yescharacteristic
760C2#2145844011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#468C2
socleC23×C61C22×D4
prime radical#21449238C2
hypercenterC2×#468D61
hypocenterC61#24795
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×#16839804C2semidirect
4. #21449271C2semidirect
6. #21447212C2semidirect
7. #21447191C2semidirect
8. #21447014C2semidirect
9. #21447000C2semidirect
10. #21446675C2semidirect
11. #21446550C2semidirect
12. #21446137C2semidirect
13. #21446132C2semidirect
14. #21445853C2semidirect
15. C2×C61×#468C2semidirect
103. #14519711D4semidirect
129. C2×M16×C61D4semidirect
372. C2×#468D61semidirect
443. C61#24795semidirect
460. C2×M16C22⋊D61semidirect

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×#168398042
#214492712
#214492382
#214472122
#214471912
#214470142
#214470002
#214466752
#214465502
#214461372
#214461322
#214458532
C2×C61×#4682
#2479561