Finite Group Databasebeta

← D61×#2065 #29708591

Subgroups — D61×#2065 #29708591

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D61C211yesmaximal, characteristic, complemented
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic
4C2×#102×D61C211yesmaximal, characteristic
5#390×D61C211yesmaximal, characteristic
6#389×D61C211yesmaximal, characteristic, complemented
7#21447194C211yesmaximal, characteristic, complemented
8#21447193C211yesmaximal, characteristic, complemented
9#21447192C211yesmaximal, characteristic, complemented
10#21447191C211yesmaximal, characteristic, complemented
11#21447190C211yesmaximal, characteristic, complemented
12#21447189C211yesmaximal, characteristic, complemented
13#21447188C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#2065C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×C4⋊C4×D61—21no—
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24C2×C22⋊C4×D61—21no—
25C2×C42×D61C2211yescharacteristic
26C2×#14519709C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28C2×#14519708C2211yescharacteristic, complemented
29#106×D61—24no—
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519706C2211yescharacteristic, complemented
32C2×#14519706C2211yescharacteristic, complemented
33C4⋊C8×D61—24no—
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40#102×D61—24no—
41#102×D61—24no—
42#16839665C2211yescharacteristic
43#16839664C2211yescharacteristic
44#16839663C2211yescharacteristic
45#16839662—21no—
46#16839662—21no—
47#16839661C2211yescharacteristic, complemented
48#16839660C2211yescharacteristic, complemented
49#16839659—21no—
50#16839658C2211yescharacteristic, complemented
51#16839657—21no—
52#95×D61—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×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61D414yes—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—44no—
101C4⋊C4×D61D414yes—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C22⋊C4×D61—44no—
109C22⋊C4×D61—44no—
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—22no—
114C42×D61—22no—
115#14519709—22no—
116#14519708—22no—
117#14519708—22no—
118C4⋊#92418—22no—
119#14519706—22no—
120#14519706—22no—
121#14519699—22no—
122#14519699—22no—
123#14519698—22no—
124#14519698—22no—
125#14519697—22no—
126#14519697—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C22×D4×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#106×C61—22no—
141C4⋊C8×C61—22no—
142#102×C61—22no—
143#102×C61—22no—
144#95×C61—21no—
145C24×C61—21no—
146C23×D61—21no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—42no—
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61C2×Q812yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176D4×D61—28no—
177D4×D61—28no—
178D4×D61—44no—
179D4×D61—44no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244C2×Q812yes—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—24no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61SD1614yes—
201C2×C4×D61C2×D412yes—
202C2×C4×D61C2×D412yes—
203C2×C4×D61C2×Q812yes—
204C2×C4×D61#4112yes—
205C2×C4×D61#4112yes—
206C2×C4×D61#4112yes—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61C2×D412yes—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61C2×D412yes—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C42×C61—21no—
223C42×C61—21no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198—42no—
229#11758198—42no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—42no—
236C4⋊Dic61C2×D412yes—
237#11758196—24no—
238#11758196—42no—
239#11758196—42no—
240#11758196—42no—
241#11758196—42no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418C2×D412yes—
252C8×D61—28no—
253C8×D61—44no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61C22×D411yescharacteristic
262C22×D61—22no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—48no—
270C22×D61—48no—
271C22×D61—48no—
272C22×D61—84no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61#12112yes—
277C22×D61#12112yes—
278C22×D61C22⋊Q812yes—
279C22×D61C2×SD1612yes—
280C22×D61#13512yes—
281C22×D61AGL(1,ℤ/8)12yes—
282C22×D61AGL(1,ℤ/8)12yes—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—41no—
286D4×C61—41no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61C2×SD1612yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×Q811yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—48no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61#12112yes—
324C2×Dic61#12112yes—
325C2×Dic61C22⋊Q812yes—
326C2×Dic61C2×SD1612yes—
327D244—22no—
328D244—22no—
329D244—41no—
330D244—41no—
331C4×D61—28no—
332C4×D61—48no—
333C4×D61—44no—
334C4×D61—84no—
335C4×D61—84no—
336C4×D61#12114yes—
337C4×D61C22⋊Q814yes—
338C4×D61C22⋊Q814yes—
339C4×D61#12614yes—
340C8×C61—22no—
341C8×C61—41no—
342#92418—22no—
343#92418—41no—
344C2×#2065—611nomaximal, Sylow
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61C2×#12111yescharacteristic
353C22×C61C2×#12111yescharacteristic
354C22×C61C2×C22⋊Q811yescharacteristic
355C22×C61C22×SD1611yescharacteristic
356C22×C61C2×#13511yescharacteristic
357C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—816no—
367C2×D61#39614yes—
368C2×D61#46014yes—
369C2×D61#46314yes—
370C2×D61#46514yes—
371C2×D61#46914yes—
372C2×D61#47614yes—
373C2×D61#47814yes—
374C4×C61—22no—
375C4×C61—42no—
376C4×C61—41no—
377C4×C61—81no—
378C4×C61—81no—
379C4×C61C2×#12111yescharacteristic
380C4×C61C2×C22⋊Q811yescharacteristic
381C4×C61C2×C22⋊Q811yescharacteristic
382C4×C61C2×#12611yescharacteristic
383Dic61—22no—
384Dic61—42no—
385Dic61—41no—
386Dic61—81no—
387Dic61—81no—
388Dic61#39614yes—
389C22×#106—611no—
390C22×C4⋊C8—611no—
391C22×#102—611no—
392C22×#102—611no—
393C2×#390—611no—
394C2×#389—611no—
395#2065—611no—
396#2065—611no—
397#2065—611no—
398#2065—611no—
399#2065—611no—
400#2065—611no—
401#2065—611no—
402#2065D6111yescharacteristic, direct product factor
403C2×#340—611no—
404C2×C61—82no—
405C2×C61C2×#39611yescharacteristic
406C2×C61C2×#46311yescharacteristic
407C2×C61C2×#46011yescharacteristic
408C2×C61C2×#46511yescharacteristic
409C2×C61C2×#46911yescharacteristic
410C2×C61C2×#47611yescharacteristic
411C2×C61C2×#47811yescharacteristic
412D61—82no—
413D61#206518yesdirect product factor
414C23×D4—611no—
415C23×C8—611no—
416C23×C8—611no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—1221no—
421C22×C22⋊C4—1221no—
422C22×C22⋊C4—1221no—
423C22×C42—611no—
424C2×#106—611no—
425C2×#106—611no—
426C2×#106—611no—
427C2×#106—1224no—
428C2×#106C2×D6111yescharacteristic, complemented
429C2×C4⋊C8—611no—
430C2×C4⋊C8—611no—
431C2×C4⋊C8—611no—
432C2×C4⋊C8—1224no—
433C2×C4⋊C8C2×D6111yescharacteristic, complemented
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—1224no—
441C2×#102—1224no—
442C2×#102C2×D6111yescharacteristic
443C2×#102C2×D6111yescharacteristic
444#390—611no—
445#390—611no—
446#390—611no—
447#390—1221no—
448#390—1221no—
449#390C2×D6111yescharacteristic
450#389—611no—
451#389—611no—
452#389—611no—
453#389—1221no—
454#389—1221no—
455#389C2×D6111yescharacteristic, complemented
456C2×#95—1221no—
457#340—611no—
458#340—611no—
459#340—611no—
460#340C2×D6111yescharacteristic, complemented
461C61C2×#206511yescharacteristic, complemented, Sylow
462C25—1221no—
463C22×D4—614no—
464C22×D4—611no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—1222no—
469C22×D4—1222no—
470C22×D4—1221no—
471C22×D4C22×D6111yescharacteristic
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C22×C8—611no—
479C22×C8—614no—
480C22×C8—611no—
481C22×C8—1222no—
482C22×C8—1222no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—1222no—
486C22×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488C2×C4⋊C4—21no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—614no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4—1222no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—2444no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—2444no—
517C2×C22⋊C4—2444no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—1222no—
522C2×C42—1222no—
523C2×C42C22×D6111yescharacteristic
524#106—22no—
525#106—1222no—
526#106—1222no—
527#106—1222no—
528C4⋊C8—22no—
529C4⋊C8—1222no—
530C4⋊C8—1222no—
531C4⋊C8—1222no—
532#102—22no—
533#102—22no—
534#102—1222no—
535#102—1222no—
536#102—1222no—
537#102—1222no—
538#102—1222no—
539#102—1222no—
540#95—21no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544C24—21no—
545C24—611no—
546C24—1224no—
547C24—1221no—
548C24—2442no—
549C24—2442no—
550C24—2442no—
551C24—2442no—
552C24—2442no—
553C24—2442no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—612no—
560C2×D4—1228no—
561C2×D4—1228no—
562C2×D4—1224no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—2444no—
569C2×D4—2444no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4Q8×D6112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—611no—
584C22×C4—614no—
585C22×C4—611no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1224no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4D4×D6111yescharacteristic
604C22×C4D4×D6111yescharacteristic
605C22×C4C23×D6111yescharacteristic
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—612no—
612C2×C8—1228no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—2444no—
619C2×C8D4×D6112yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4—612no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—2442no—
634C4⋊C4—2442no—
635C4⋊C4—2442no—
636C4⋊C4—2442no—
637C4⋊C4—2442no—
638C4⋊C4D4×D6112yes—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C22⋊C4—2442no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C42—21no—
648C42—21no—
649C42—1222no—
650C42—1222no—
651C42—1221no—
652C42—1221no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—612no—
661C23—612no—
662C23—612no—
663C23—612no—
664C23—612no—
665C23—612no—
666C23—612no—
667C23—1222no—
668C23—4884no—
669C23—4884no—
670C23—4884no—
671C23—4884no—
672C23—2448no—
673C23—2448no—
674C23—2448no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23C2×D4×D6111yescharacteristic
682D4—22no—
683D4—22no—
684D4—41no—
685D4—41no—
686D4—1222no—
687D4—1222no—
688D4—2448no—
689D4—2441no—
690D4—2441no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—614no—
709C2×C4—614no—
710C2×C4—614no—
711C2×C4—614no—
712C2×C4—612no—
713C2×C4—1228no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1222no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—4884no—
721C2×C4—4884no—
722C2×C4—2444no—
723C2×C4—2448no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4SD16×D6112yes—
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×Q8×D6111yescharacteristic
736C2×C4#41×D6111yescharacteristic
737C2×C4#41×D6111yescharacteristic
738C2×C4#41×D6111yescharacteristic
739C8—22no—
740C8—41no—
741C8—1222no—
742C8—2441no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—614no—
751C22—614no—
752C22—614no—
753C22—614no—
754C22—614no—
755C22—614no—
756C22—614no—
757C22—48816no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22#121×D6111yescharacteristic
766C22#121×D6111yescharacteristic
767C22C22⋊Q8×D6111yescharacteristic
768C22C2×SD16×D6111yescharacteristic
769C22#135×D6111yescharacteristic
770C22AGL(1,ℤ/8)×D6111yescharacteristic
771C22AGL(1,ℤ/8)×D6111yescharacteristic
772C4—22no—
773C4—41no—
774C4—42no—
775C4—81no—
776C4—81no—
777C4—614no—
778C4—1222no—
779C4—4881no—
780C4—4881no—
781C4—2441no—
782C4—2442no—
783C4#121×D6111yescharacteristic
784C4C22⋊Q8×D6111yescharacteristic
785C4C22⋊Q8×D6111yescharacteristic
786C4#126×D6111yescharacteristic
787C2—82no—
788C2—618no—
789C2—4882no—
790C2#396×D6111yescharacteristic
791C2#463×D6111yescharacteristic
792C2#460×D6111yescharacteristic
793C2#465×D6111yescharacteristic
794C2#469×D6111yescharacteristic
795C2#476×D6111yescharacteristic
796C2#478×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2065C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2065D61
hypocenterC61C2×#2065
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×#106×D61C2semidirect
2. C2×C4⋊C8×D61C2semidirect
6. #389×D61C2semidirect
7. #21447194C2semidirect
8. #21447193C2semidirect
9. #21447192C2semidirect
10. #21447191C2semidirect
11. #21447190C2semidirect
12. #21447189C2semidirect
13. #21447188C2semidirect
14. #340×D61C2semidirect
15. C61×#2065C2semidirect
26. C2×#14519709C22semidirect
27. C2×#14519708C22semidirect
28. C2×#14519708C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519706C22semidirect
32. C2×#14519706C22semidirect
47. #16839661C22semidirect
48. #16839660C22semidirect
50. #16839658C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. C2×#106×C61C22semidirect
57. C2×C4⋊C8×C61C22semidirect
61. C61×#389C22semidirect
62. C61×#340C22semidirect
402. #2065D61direct (N × H)
413. D61#2065direct (N × H)
428. C2×#106C2×D61semidirect
433. C2×C4⋊C8C2×D61semidirect
455. #389C2×D61semidirect
460. #340C2×D61semidirect
461. C61C2×#2065semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D612
C2×C4⋊C8×D612
C2×#102×D612
#390×D612
#389×D612
#214471942
#214471932
#214471922
#214471912
#214471902
#214471892
#214471882
#340×D612
C61×#20652
C2×#206561