Finite Group Databasebeta

← #29708652

Subgroups — #29708652

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839797C211yesmaximal, characteristic, complemented
2C2×#16839787C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic
4C2×#102×D61C211yesmaximal, characteristic
5#21448441C211yesmaximal, characteristic, complemented
6#21448398C211yesmaximal, characteristic
7#21447208C211yesmaximal, characteristic, complemented
8#21447207C211yesmaximal, characteristic, complemented
9#21447204C211yesmaximal, characteristic, complemented
10#21447203C211yesmaximal, characteristic, complemented
11#21447192C211yesmaximal, characteristic, complemented
12#21447191C211yesmaximal, characteristic, complemented
13#21447188C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#2065C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839797—24no—
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519709C2211yescharacteristic, complemented
27#16839787—24no—
28C2×C4⋊#92418C2211yescharacteristic, complemented
29C2×#14519706C2211yescharacteristic, complemented
30C2×#14519706C2211yescharacteristic, complemented
31#16839765—24no—
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38#102×D61—24no—
39#16839665C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839663C2211yescharacteristic
42#16839662—21no—
43#16839662—21no—
44#16839661C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839658C2211yescharacteristic, complemented
47#16839636—21no—
48#16839633—21no—
49#16839631—21no—
50#16839626—21no—
51#16839617—21no—
52#16839617—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C2×#106×C61C2211yescharacteristic, complemented
57C2×C4⋊C8×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#389C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C24×D61—21no—
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61Q814yes—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C2×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—22no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61D414yes—
82#14519735—22no—
83#14519735—22no—
84#14519735—22no—
85#14519735D414yes—
86#14519734—22no—
87#14519734—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196D411yescharacteristic
96C2×#11758196D411yescharacteristic
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198D411yescharacteristic
108C2×#11758198D411yescharacteristic
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112#14519710—22no—
113#14519710—22no—
114#14519709—22no—
115C4⋊#92418—22no—
116#14519706—22no—
117#14519706—22no—
118#14519699—22no—
119#14519699—22no—
120#14519698—22no—
121#14519698—22no—
122#14519697—22no—
123#14519697—22no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×D4×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137#106×C61—22no—
138C4⋊C8×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#95×C61—21no—
142C24×C61—21no—
143C23×D61—21no—
144C23×D61—24no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—81no—
148C23×D61—81no—
149C23×D61—81no—
150C23×D61—81no—
151C23×D61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61C2×Q812yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—24no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173D4×D61—28no—
174D4×D61—28no—
175D4×D61—44no—
176D4×D61—44no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244C2×Q812yes—
183C2×C4×D61—42no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61C2×D412yes—
187C2×C4×D61C2×D412yes—
188C2×C4×D61C2×Q812yes—
189C2×C4×D61#4112yes—
190C2×C4×D61#4112yes—
191C2×C4×D61#4112yes—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C2×D412yes—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—81no—
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—81no—
206C22⋊C4×C61—81no—
207C42×C61—21no—
208C42×C61—21no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211#11758198—24no—
212#11758198—22no—
213#11758198—22no—
214#11758198—42no—
215#11758198—81no—
216#11758198—81no—
217#11758198—81no—
218#11758198—81no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—81no—
225C4⋊Dic61C2×D412yes—
226#11758196—22no—
227#11758196—22no—
228#11758196—42no—
229#11758196—81no—
230#11758196—81no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—24no—
234C4×Dic61—42no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C2×D412yes—
241#11758189—44no—
242C8×D61—28no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61C22×D411yescharacteristic
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—48no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—84no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61#12112yes—
270C22×D61#12112yes—
271C22×D61C22⋊Q812yes—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—41no—
275D4×C61—41no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
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×C61—41no—
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×Q811yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C22⋊D61—48no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—22no—
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#12112yes—
314C2×Dic61#12112yes—
315C2×Dic61C22⋊Q812yes—
316D244—22no—
317D244—22no—
318D244—41no—
319D244—41no—
320C4×D61—84no—
321C4×D61#12114yes—
322C4×D61C22⋊Q814yes—
323C4×D61C22⋊Q814yes—
324C4×D61#12614yes—
325C8×C61—22no—
326C8×C61—41no—
327#92418—22no—
328#92418—41no—
329#23612—611nomaximal, Sylow
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61C2×#12111yescharacteristic
338C22×C61C2×#12111yescharacteristic
339C22×C61C2×C22⋊Q811yescharacteristic
340C22×C61#57611yescharacteristic
341C22×C61#57611yescharacteristic
342C22×C61#57711yescharacteristic
343C22×C61#57711yescharacteristic
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—816no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61#39614yes—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61C2×#12111yescharacteristic
365C4×C61C2×C22⋊Q811yescharacteristic
366C4×C61C2×C22⋊Q811yescharacteristic
367C4×C61C2×#12611yescharacteristic
368Dic61—42no—
369Dic61—41no—
370Dic61—41no—
371Dic61—81no—
372Dic61—81no—
373Dic61#39614yes—
374C2×#427—611no—
375C2×#424—611no—
376C2×#418—611no—
377C22×#102—611no—
378#2317—611no—
379#2309—611no—
380#2067—611no—
381#2067—611no—
382#2067—611no—
383#2067—611no—
384#2065—611no—
385#2065—611no—
386#2065—611no—
387#2065D6111yescharacteristic, complemented
388#1736—611no—
389C2×C61—82no—
390C2×C61C2×#39611yescharacteristic
391C2×C61#304511yescharacteristic
392C2×C61#304511yescharacteristic
393C2×C61#305711yescharacteristic
394C2×C61#305811yescharacteristic
395C2×C61#308111yescharacteristic
396C2×C61#308111yescharacteristic
397D61—24no—
398D61—82no—
399C23×D4—611no—
400C22×M16—611no—
401C23×C8—611no—
402C2×#117—611no—
403C2×#117—611no—
404C2×#117—611no—
405C22×C4⋊C4—611no—
406#427—1224no—
407C2×#107—611no—
408C2×#107—611no—
409C2×#106—611no—
410C2×#106C2×D6111yescharacteristic, complemented
411#424—1224no—
412C2×C4⋊C8—611no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8C2×D6111yescharacteristic, complemented
416#418—1224no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—1224no—
424C2×#102C2×D6111yescharacteristic
425C2×#102C2×D6111yescharacteristic
426#390—611no—
427#390—611no—
428#390—611no—
429#390—1221no—
430#390—1221no—
431#390C2×D6111yescharacteristic
432#389—611no—
433#389—611no—
434#389—611no—
435#389C2×D6111yescharacteristic, complemented
436#385—1221no—
437#385—1221no—
438#384—1221no—
439#382—1221no—
440#379—1221no—
441#379—1221no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic, complemented
446C61#2361211yescharacteristic, complemented, Sylow
447C25—1221no—
448C22×D4—614no—
449C22×D4—611no—
450C22×D4—1222no—
451C22×D4—1222no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1221no—
456C22×D4C22×D6111yescharacteristic
457C23×C4—611no—
458C23×C4—1221no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C22×C8—611no—
463C22×C8—614no—
464C22×C8—611no—
465C22×C8—1222no—
466C22×C8—1222no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469#117—614no—
470#117—1222no—
471#117—1222no—
472#117—1222no—
473#117—1222no—
474#117—1222no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
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—1221no—
501C2×C22⋊C4—1221no—
502C2×C42—611no—
503C2×C42—1221no—
504C2×C42—1221no—
505C2×C42C22×D6111yescharacteristic
506#107—1222no—
507#107—1222no—
508#106—22no—
509#106—1222no—
510C4⋊C8—22no—
511C4⋊C8—1222no—
512C4⋊C8—1222no—
513C4⋊C8—1222no—
514#102—22no—
515#102—22no—
516#102—1222no—
517#102—1222no—
518#102—1222no—
519#102—1222no—
520#102—1222no—
521#102—1222no—
522#95—21no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526C24—21no—
527C24—611no—
528C24—1224no—
529C24—1221no—
530C24—4881no—
531C24—4881no—
532C24—4881no—
533C24—4881no—
534C24—2442no—
535C24—2442no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—612no—
542C2×D4—1228no—
543C2×D4—1228no—
544C2×D4—1224no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—2444no—
551C2×D4—2444no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4Q8×D6112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—611no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—2442no—
573C22×C4D4×D6111yescharacteristic
574C22×C4D4×D6111yescharacteristic
575C22×C4C23×D6111yescharacteristic
576M16—2444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—612no—
583C2×C8—1228no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8D4×D6112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—81no—
596C4⋊C4—612no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—4881no—
605C4⋊C4—4881no—
606C4⋊C4—4881no—
607C4⋊C4—2442no—
608C4⋊C4D4×D6112yes—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1224no—
614C22⋊C4—4881no—
615C22⋊C4—4881no—
616C22⋊C4—4881no—
617C22⋊C4—4881no—
618C22⋊C4—4881no—
619C22⋊C4—4881no—
620C22⋊C4—2442no—
621C42—21no—
622C42—21no—
623C42—1224no—
624C42—1221no—
625C42—1221no—
626C42—2442no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—612no—
635C23—612no—
636C23—612no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1222no—
642C23—4884no—
643C23—4884no—
644C23—4884no—
645C23—4884no—
646C23—4884no—
647C23—4884no—
648C23—2448no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23C2×D4×D6111yescharacteristic
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—1222no—
661D4—1222no—
662D4—2448no—
663D4—2441no—
664D4—2441no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—614no—
684C2×C4—614no—
685C2×C4—614no—
686C2×C4—614no—
687C2×C4—1222no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—4884no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4C2×D4×D6111yescharacteristic
704C2×C4C2×D4×D6111yescharacteristic
705C2×C4C2×Q8×D6111yescharacteristic
706C2×C4#41×D6111yescharacteristic
707C2×C4#41×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C8—22no—
710C8—41no—
711C8—1222no—
712C8—2441no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—614no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—48816no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22#121×D6111yescharacteristic
736C22#121×D6111yescharacteristic
737C22C22⋊Q8×D6111yescharacteristic
738C22#1684056611yescharacteristic
739C22#1684056611yescharacteristic
740C22#1684056811yescharacteristic
741C22#1684056911yescharacteristic
742C4—41no—
743C4—41no—
744C4—42no—
745C4—81no—
746C4—81no—
747C4—614no—
748C4—4881no—
749C4—4881no—
750C4—2441no—
751C4—2441no—
752C4—2442no—
753C4#121×D6111yescharacteristic
754C4C22⋊Q8×D6111yescharacteristic
755C4C22⋊Q8×D6111yescharacteristic
756C4#126×D6111yescharacteristic
757C2—82no—
758C2—1224no—
759C2—4882no—
760C2#396×D6111yescharacteristic
761C2#2145535511yescharacteristic
762C2#2145535911yescharacteristic
763C2#2145545311yescharacteristic
764C2#2145546511yescharacteristic
765C2#2145564511yescharacteristic
766C2#2145564911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2065C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2065D61
hypocenterC61#23612
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. C2×#16839797C2semidirect
2. C2×#16839787C2semidirect
5. #21448441C2semidirect
7. #21447208C2semidirect
8. #21447207C2semidirect
9. #21447204C2semidirect
10. #21447203C2semidirect
11. #21447192C2semidirect
12. #21447191C2semidirect
13. #21447188C2semidirect
14. #21445537C2semidirect
15. C61×#2065C2semidirect
24. C2×#14519710C22semidirect
25. C2×#14519710C22semidirect
26. C2×#14519709C22semidirect
28. C2×C4⋊#92418C22semidirect
29. C2×#14519706C22semidirect
30. C2×#14519706C22semidirect
44. #16839661C22semidirect
45. #16839660C22semidirect
46. #16839658C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. C2×#106×C61C22semidirect
57. C2×C4⋊C8×C61C22semidirect
61. C61×#389C22semidirect
62. C61×#340C22semidirect
387. #2065D61semidirect
410. C2×#106C2×D61semidirect
415. C2×C4⋊C8C2×D61semidirect
435. #389C2×D61semidirect
445. #340C2×D61semidirect
446. C61#23612semidirect

Maximal subgroups

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

subgroupindex
C2×#168397972
C2×#168397872
C2×#168397652
C2×#102×D612
#214484412
#214483982
#214472082
#214472072
#214472042
#214472032
#214471922
#214471912
#214471882
#214455372
C61×#20652
#2361261