Finite Group Databasebeta

← #30623930

Subgroups — #30623930

Order 15616.

1410 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462429C211yesmaximal, characteristic, complemented
2#21462418C211yesmaximal, characteristic, complemented
3#21462079C212yesmaximal, complemented
4#21462077C212yesmaximal, complemented
5#21462074C212yesmaximal, complemented
6#21462073C212yesmaximal, complemented
7C2×#16840663C212yesmaximal, complemented
8D61⋊AΣL(1,𝔽16)C212yesmaximal, complemented
9#21459451C211yesmaximal, characteristic
10#16840840—21no—
11#16840829—21no—
12#16840749—21no—
13#16840749C2212yescomplemented
14#16840748—21no—
15D61⋊#100C2212yescomplemented
16C2×#14519837—21no—
17C2×#14519837C2212yescomplemented
18#16840742C2212yescomplemented
19#16840741—21no—
20D61⋊#99—21no—
21D61⋊#99C2212yescomplemented
22C2×#14519835—21no—
23C2×#14519835C2212yescomplemented
24#16840664C2214yescomplemented
25#16840663C2214yescomplemented
26#16840663C2214yescomplemented
27#16840662C2214yescomplemented
28C2×#14519822C2211yescharacteristic
29C22×D4×D61C411yescharacteristic, complemented
30#16840404—21no—
31#16840404—21no—
32#16840401—21no—
33#16840401—21no—
34#16840396—21no—
35#16840396—21no—
36#16840394—21no—
37#16840394—21no—
38#16840327C411yescharacteristic, complemented
39#16840327C2211yescharacteristic
40#16840323C411yescharacteristic, complemented
41#16840323C2211yescharacteristic
42#16840321C2211yescharacteristic
43#16840270C411yescharacteristic, complemented
44#16840270C2211yescharacteristic
45C2×#14519747C2211yescharacteristic
46C2×#14519745C411yescharacteristic, complemented
47#120×D61C411yescharacteristic, complemented
48#120×D61C2211yescharacteristic
49#16840235C411yescharacteristic, complemented
50C61×#534C411yescharacteristic, complemented
51#14519864—44no—
52D61⋊M16—22no—
53C2×#11758217—22no—
54C2×#11758217—22no—
55D4×#6923—44no—
56#14519856—22no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59#14519838—22no—
60#14519837—22no—
61#14519837—22no—
62#14519837C2314yes—
63#14519836—22no—
64#14519835—22no—
65#14519835—22no—
66#14519835C2314yes—
67C24×D61C2×C411yescharacteristic, complemented
68C24×D61C2×C411yescharacteristic, complemented
69#14519822—44no—
70C2×#11758222D411yescharacteristic
71C2×#11758222D411yescharacteristic
72C2×#11758224C2×C411yescharacteristic
73C2×#11758224D411yescharacteristic
74C2×#11758224D411yescharacteristic
75C2×#11758224C2311yescharacteristic
76C22×D244—21no—
77C22×D244C2×C411yescharacteristic, complemented
78C22×C22⋊D61—21no—
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic, complemented
81C22×C22⋊D61D411yescharacteristic
82C22×C22⋊D61D411yescharacteristic
83C22×C22⋊D61C2311yescharacteristic
84C2×D4×D61—21no—
85C2×D4×D61—21no—
86C2×D4×D61—21no—
87C2×D4×D61—21no—
88C2×D4×D61—21no—
89C2×D4×D61—21no—
90C2×D4×D61—44no—
91C2×D4×D61C2×C411yescharacteristic
92C2×D4×D61D411yescharacteristic
93C2×D4×D61D411yescharacteristic
94C2×D4×D61C2311yescharacteristic
95C22×C4×D61C2×C411yescharacteristic, complemented
96#14519773—21no—
97#14519773—21no—
98#14519763—21no—
99#14519763—21no—
100#14519762—21no—
101#14519762—21no—
102#14519760C2×C411yescharacteristic, complemented
103#14519760C2311yescharacteristic
104#14519758—21no—
105#14519755—21no—
106#14519755—21no—
107#14519752—21no—
108#14519752—21no—
109#14519750—21no—
110#14519750—21no—
111#14519750—21no—
112#14519750—21no—
113#14519750—21no—
114#14519750—21no—
115#14519749—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519747—21no—
120#14519747—21no—
121#14519747—21no—
122#14519747—21no—
123#14519747—21no—
124#14519747—21no—
125#14519747C2×C411yescharacteristic, complemented
126#14519747C2×C411yescharacteristic, complemented
127#14519747C2311yescharacteristic
128#14519747C2311yescharacteristic
129#14519746C2×C411yescharacteristic, complemented
130#14519746C2311yescharacteristic
131#14519745—21no—
132#14519745—21no—
133#14519745—21no—
134#14519745—21no—
135#14519745—21no—
136#14519745C2×C411yescharacteristic, complemented
137#14519745C2×C411yescharacteristic, complemented
138#14519745C2×C411yescharacteristic, complemented
139#14519745C2×C411yescharacteristic, complemented
140#14519739—21no—
141#14519739—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144#14519737—21no—
145#14519737—21no—
146#14519737—21no—
147#14519737—21no—
148#14519733C2×C411yescharacteristic, complemented
149#14519733C2×C411yescharacteristic, complemented
150C2×C22⋊Dic61C2×C411yescharacteristic, complemented
151C2×#11758198—21no—
152C2×#11758198—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61C2×C411yescharacteristic, complemented
156C22⋊C4×D61C2×C411yescharacteristic, complemented
157C22×D4×C61C2×C411yescharacteristic
158C22×D4×C61C2×C411yescharacteristic, complemented
159#123×C61—21no—
160#123×C61C2×C411yescharacteristic, complemented
161#123×C61C2×C411yescharacteristic, complemented
162#121×C61—21no—
163#121×C61—21no—
164#120×C61—21no—
165#120×C61C2×C411yescharacteristic, complemented
166#120×C61C2×C411yescharacteristic, complemented
167C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
168C24×C61C22⋊C411yescharacteristic
169C24×C61C22×C411yescharacteristic
170C24×C61C22×C411yescharacteristic
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—82no—
178C23×D61—82no—
179C23×D61C22⋊C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C23×D61C22×C411yescharacteristic
182C23×D61C22×C411yescharacteristic
183C23×D61C2×D411yescharacteristic
184C23×D61C2×D411yescharacteristic
185C22×#6923—42no—
186C22×#6923—42no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61C22⋊C411yescharacteristic
194C2×D4×C61C22⋊C411yescharacteristic
195C2×D4×C61C22×C411yescharacteristic
196C2×D4×C61C22×C411yescharacteristic
197C22×C4×C61—21no—
198C22×C4×C61C22⋊C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C2×C22⋊D61—24no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—82no—
214C2×C22⋊D61C22⋊C411yescharacteristic
215C2×C22⋊D61C22⋊C411yescharacteristic
216C2×C22⋊D61C22⋊C411yescharacteristic
217C2×C22⋊D61C22⋊C411yescharacteristic
218C2×C22⋊D61C22⋊C411yescharacteristic
219C2×C22⋊D61C22⋊C411yescharacteristic
220C2×C22⋊D61C22×C411yescharacteristic
221C2×C22⋊D61C2×D411yescharacteristic
222C2×C22⋊D61C2×D411yescharacteristic
223C2×C22⋊D61C2×D411yescharacteristic
224C2×C22⋊D61C2×D411yescharacteristic
225C2×C22⋊D61C2411yescharacteristic
226C22×Dic61—21no—
227C22×Dic61C22⋊C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758224—24no—
232#11758224—42no—
233#11758224—42no—
234#11758224—42no—
235D4×D61—24no—
236D4×D61—42no—
237D4×D61—42no—
238D4×D61—42no—
239D4×D61—44no—
240D4×D61—44no—
241D4×D61—44no—
242D4×D61—44no—
243D4×D61—82no—
244D4×D61—82no—
245#11758222—42no—
246#11758222—42no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—42no—
254C2×D244—82no—
255C2×D244C22⋊C411yescharacteristic
256C2×D244C2×D411yescharacteristic
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—42no—
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×Dic122C22⋊C411yescharacteristic
267C2×Dic122C2×D411yescharacteristic
268C22⋊#6923—24no—
269C22⋊#6923—42no—
270C22⋊#6923—42no—
271#11758217—24no—
272#11758217—42no—
273#11758217—42no—
274C2×#92420—42no—
275C2×#92420—42no—
276C4⋊#6923—42no—
277C4×#6923—42no—
278#11758213—42no—
279D61⋊C8—42no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61C22×C411yescharacteristic
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61C22×C411yescharacteristic
293C22⋊Dic61C22×C411yescharacteristic
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C23×C61—22no—
313C23×C61—21no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—81no—
317C23×C61—81no—
318C23×C61—81no—
319C23×C61C2×C22⋊C411yescharacteristic
320C23×C61C2×C22⋊C411yescharacteristic
321C23×C61C2×C22⋊C411yescharacteristic
322C23×C61C2×C22⋊C411yescharacteristic
323C23×C61C23×C411yescharacteristic
324C22×D61—21no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—21no—
329C22×D61—41no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—41no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—41no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61—81no—
344C22×D61—81no—
345C22×D61—81no—
346C22×D61—81no—
347C22×D61—81no—
348C22×D61—81no—
349C22×D61—81no—
350C22×D61—84no—
351C22×D61—84no—
352C22×D61—84no—
353C22×D61—84no—
354C22×D61C2×C22⋊C411yescharacteristic
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61C22×D411yescharacteristic
358C2×#6923—44no—
359C2×#6923—162no—
360C2×#6923—162no—
361D4×C61—22no—
362D4×C61—22no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—42no—
366D4×C61—42no—
367D4×C61—81no—
368D4×C61—81no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—81no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C22⋊D61—22no—
378C22⋊D61—22no—
379C22⋊D61—22no—
380C22⋊D61—22no—
381C22⋊D61—22no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—42no—
389C22⋊D61—42no—
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C22⋊D61—81no—
395C22⋊D61—81no—
396C22⋊D61#9914yes—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—41no—
403C2×Dic61—81no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C22×D411yescharacteristic
408D244—22no—
409D244—41no—
410D244—42no—
411D244—42no—
412D244—42no—
413D244—42no—
414D244—81no—
415D244—81no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—42no—
421C4×D61—42no—
422C4×D61—81no—
423C4×D61—81no—
424Dic122—22no—
425Dic122—41no—
426#92420—44no—
427#33348—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—82no—
441C22×C61—82no—
442C22×C61—161no—
443C22×C61C2×#9912yes—
444C22×C61C22×C22⋊C411yescharacteristic
445C2×D61—22no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—42no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—42no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—82no—
461C2×D61—82no—
462C2×D61—84no—
463C2×D61—82no—
464C2×D61—84no—
465C2×D61—84no—
466C2×D61—84no—
467C2×D61—82no—
468C2×D61—161no—
469C2×D61C2×#9912yes—
470#6923—84no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—41no—
474C4×C61—41no—
475C4×C61—41no—
476Dic61—21no—
477Dic61—21no—
478Dic61—21no—
479Dic61—41no—
480Dic61—41no—
481Dic61C2×#9912yes—
482#3484—611no—
483#2888—611no—
484#2883—611no—
485#2122—612no—
486#2121—612no—
487#2121—612no—
488#2120—612no—
489C2×AΣL(1,𝔽16)—612no—
490C2×AΣL(1,𝔽16)—612no—
491C2×C61—21no—
492C2×C61—22no—
493C2×C61—41no—
494C2×C61—41no—
495C2×C61—41no—
496C2×C61—41no—
497C2×C61—81no—
498C2×C61C22×#9911yescharacteristic
499D61—22no—
500D61—41no—
501D61—42no—
502D61—41no—
503D61—41no—
504D61—81no—
505C2×H(5,𝔽2)—611no—
506C23×D4—611no—
507#568—1221no—
508#546—1221no—
509#546—1221no—
510#546—1221no—
511#546—1221no—
512D42—1221no—
513D42—1221no—
514D42—1221no—
515D42—1221no—
516#535—611no—
517#535—611no—
518#534—611no—
519#534—611no—
520#534—611no—
521#534#692311yescharacteristic, complemented
522#525—611no—
523#525—611no—
524C2×#120—611no—
525C2×#120—611no—
526C2×#120—611no—
527C2×#120—611no—
528#518—611no—
529#518—1221no—
530#413—612no—
531#413—1221no—
532#413—1221no—
533C2×#100—612no—
534C2×#100—612no—
535C2×#100—1221no—
536#410—612no—
537#410—1221no—
538C2×#99—612no—
539C2×#99—612no—
540C2×#99—1221no—
541C2×#99—1221no—
542#352—614no—
543AΣL(1,𝔽16)—614no—
544AΣL(1,𝔽16)—614no—
545AΣL(1,𝔽16)—614no—
546C61#3334811yescharacteristic, complemented, Sylow
547C25—611no—
548C25—611no—
549H(5,𝔽2)—2444no—
550C2×#41—611no—
551C2×#41—611no—
552C2×#41—611no—
553C2×#41—611no—
554C2×#41—611no—
555C2×#41—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4—611no—
560C22×D4—611no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—611no—
566C22×D4—1221no—
567C22×D4—1221no—
568C22×D4—1221no—
569C22×D4—1221no—
570C22×D4—1221no—
571C22×D4—1221no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—2444no—
575C22×D4C2×#692311yescharacteristic
576C22×D4C2×#692311yescharacteristic, complemented
577C23×C4—611no—
578#131—2444no—
579C2×M16—1222no—
580C2×M16—1222no—
581C2×M16—1222no—
582#127—1221no—
583#127—1221no—
584#124—1221no—
585#124—1221no—
586#123—21no—
587#123—611no—
588#123—611no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123C2×#692311yescharacteristic, complemented
593#123C2×#692311yescharacteristic, complemented
594C22⋊Q8—1221no—
595C22⋊Q8—1221no—
596#121—21no—
597#121—21no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121—1221no—
606#121—1221no—
607#121—1221no—
608#121—1221no—
609#121—1221no—
610#120—21no—
611#120—611no—
612#120—611no—
613#120—611no—
614#120—611no—
615#120—611no—
616#120—611no—
617#120—611no—
618#120—611no—
619#120—611no—
620#120—611no—
621#120—1221no—
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628#120—1221no—
629#120—1221no—
630#120—1221no—
631#120—1221no—
632#120C2×#692311yescharacteristic, complemented
633#120C2×#692311yescharacteristic, complemented
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—2444no—
643#117—611no—
644#117—611no—
645#117—1222no—
646C2×C22⋊C4—611no—
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1222no—
654C2×C22⋊C4—1222no—
655C2×C22⋊C4C2×#692311yescharacteristic, complemented
656#101—1222no—
657#100—614no—
658#100—1222no—
659#100—1222no—
660#99—614no—
661#99—1222no—
662#99—1222no—
663#99—1222no—
664C24—611no—
665C24—611no—
666C24—611no—
667C24—611no—
668C24—611no—
669C24—611no—
670C24—1221no—
671C24—1221no—
672C24—1221no—
673C24—1221no—
674C24—4882no—
675C24—4882no—
676C24—2442no—
677C24—2442no—
678C24C22⋊#692311yescharacteristic
679C24C22×#692311yescharacteristic
680C24C22×#692311yescharacteristic
681#41—1224no—
682#41—2442no—
683#41—2442no—
684#41—2442no—
685#41—2442no—
686#41—2442no—
687C2×Q8—611no—
688C2×Q8—611no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—611no—
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—611no—
701C2×D4—611no—
702C2×D4—611no—
703C2×D4—611no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1224no—
718C2×D4—1224no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—4882no—
726C2×D4—4882no—
727C2×D4—4882no—
728C2×D4—4882no—
729C2×D4—2442no—
730C2×D4—2442no—
731C2×D4—2442no—
732C2×D4—2442no—
733C2×D4—2442no—
734C2×D4—2442no—
735C2×D4—2444no—
736C2×D4—2442no—
737C2×D4—2444no—
738C2×D4—2444no—
739C2×D4—2444no—
740C2×D4—2442no—
741C2×D4C22⋊#692311yescharacteristic
742C2×D4C22⋊#692311yescharacteristic
743C2×D4C22×#692311yescharacteristic
744C2×D4C22×#692311yescharacteristic
745C22×C4—21no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—2442no—
760C22×C4—2442no—
761C22×C4—2442no—
762C22×C4C22⋊#692311yescharacteristic
763C22×C4C22×#692311yescharacteristic
764M16—1224no—
765M16—2442no—
766M16—2442no—
767M16—2442no—
768C2×C8—2442no—
769C2×C8—2442no—
770C2×C8—2442no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—2442no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1224no—
801C22⋊C4—2442no—
802C22⋊C4—2442no—
803C22⋊C4C22×#692311yescharacteristic
804C22⋊C4C22×#692311yescharacteristic
805C42—1221no—
806C42—1221no—
807C42—2442no—
808C23—22no—
809C23—21no—
810C23—41no—
811C23—41no—
812C23—81no—
813C23—81no—
814C23—81no—
815C23—611no—
816C23—611no—
817C23—611no—
818C23—611no—
819C23—1222no—
820C23—1222no—
821C23—1222no—
822C23—1221no—
823C23—1221no—
824C23—4881no—
825C23—4881no—
826C23—4881no—
827C23—4881no—
828C23—4881no—
829C23—4881no—
830C23—4881no—
831C23—4881no—
832C23—4881no—
833C23—4884no—
834C23—4884no—
835C23—4884no—
836C23—4884no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23—2441no—
841C23—2442no—
842C23—2442no—
843C23—2442no—
844C23—2442no—
845C23—2442no—
846C23—2442no—
847C23—2442no—
848C23—2442no—
849C23C2×C22⋊#692311yescharacteristic
850C23C2×C22⋊#692311yescharacteristic
851C23C2×C22⋊#692311yescharacteristic
852C23C2×C22⋊#692311yescharacteristic
853C23C23×#692311yescharacteristic
854Q8—1222no—
855Q8—2441no—
856D4—22no—
857D4—22no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—42no—
862D4—81no—
863D4—81no—
864D4—614no—
865D4—1222no—
866D4—1222no—
867D4—1222no—
868D4—1222no—
869D4—1222no—
870D4—1222no—
871D4—4881no—
872D4—4881no—
873D4—4881no—
874D4—4881no—
875D4—4881no—
876D4—4881no—
877D4—2441no—
878D4—2442no—
879D4—2442no—
880D4—2442no—
881D4—2442no—
882D4—2442no—
883D4—2441no—
884D4—2441no—
885D4—2441no—
886D4—2441no—
887D4—2441no—
888D4—2441no—
889D4—2442no—
890D4—2442no—
891D4—2442no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—9762no—
910C2×C4—9762no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2442no—
917C2×C4—2442no—
918C2×C4—2441no—
919C2×C4—2444no—
920C2×C4C2×C22⋊#692311yescharacteristic
921C2×C4C2×C22⋊#692311yescharacteristic
922C8—2444no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—82no—
936C22—82no—
937C22—161no—
938C22—612no—
939C22—1222no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—9761no—
944C22—4884no—
945C22—4882no—
946C22—4882no—
947C22—4882no—
948C22—4882no—
949C22—4884no—
950C22—4884no—
951C22—4884no—
952C22—2441no—
953C22—2441no—
954C22—2441no—
955C22—2441no—
956C22—2441no—
957C22—2441no—
958C22—2441no—
959C22—2442no—
960C22—2442no—
961C22—2441no—
962C22—2441no—
963C22D61⋊#9912yes—
964C22C22×C22⋊#692311yescharacteristic
965C4—21no—
966C4—21no—
967C4—41no—
968C4—41no—
969C4—41no—
970C4—612no—
971C4—1221no—
972C4—1221no—
973C4—1221no—
974C4—4884no—
975C4—2441no—
976C4—2441no—
977C2—21no—
978C2—22no—
979C2—41no—
980C2—41no—
981C2—41no—
982C2—41no—
983C2—81no—
984C2—1222no—
985C2—4881no—
986C2—2441no—
987C2—2441no—
988C2—2441no—
989C2—2442no—
990C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#534C4
socleC2×C61C22×#99
prime radical#21459451C2
cosocleC2×C22⋊D61C24
hypercenter#534#6923
hypocenterC61#33348
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #21462429C2semidirect
2. #21462418C2semidirect
3. #21462079C2semidirect
4. #21462077C2semidirect
5. #21462074C2semidirect
6. #21462073C2semidirect
7. C2×#16840663C2semidirect
8. D61⋊AΣL(1,𝔽16)C2semidirect
13. #16840749C22semidirect
15. D61⋊#100C22semidirect
17. C2×#14519837C22semidirect
18. #16840742C22semidirect
21. D61⋊#99C22semidirect
23. C2×#14519835C22semidirect
24. #16840664C22semidirect
25. #16840663C22semidirect
26. #16840663C22semidirect
27. #16840662C22semidirect
29. C22×D4×D61C4semidirect
38. #16840327C4semidirect
40. #16840323C4semidirect
43. #16840270C4semidirect
46. C2×#14519745C4semidirect
47. #120×D61C4semidirect
49. #16840235C4semidirect
50. C61×#534C4semidirect
67. C24×D61C2×C4semidirect
68. C24×D61C2×C4semidirect
77. C22×D244C2×C4semidirect
80. C22×C22⋊D61C2×C4semidirect
95. C22×C4×D61C2×C4semidirect
102. #14519760C2×C4semidirect
125. #14519747C2×C4semidirect
126. #14519747C2×C4semidirect
129. #14519746C2×C4semidirect
136. #14519745C2×C4semidirect
137. #14519745C2×C4semidirect
138. #14519745C2×C4semidirect
139. #14519745C2×C4semidirect
148. #14519733C2×C4semidirect
149. #14519733C2×C4semidirect
150. C2×C22⋊Dic61C2×C4semidirect
155. C22⋊C4×D61C2×C4semidirect
156. C22⋊C4×D61C2×C4semidirect
158. C22×D4×C61C2×C4semidirect
160. #123×C61C2×C4semidirect
161. #123×C61C2×C4semidirect
165. #120×C61C2×C4semidirect
166. #120×C61C2×C4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
521. #534#6923semidirect
546. C61#33348semidirect
576. C22×D4C2×#6923semidirect
592. #123C2×#6923semidirect
593. #123C2×#6923semidirect
632. #120C2×#6923semidirect
633. #120C2×#6923semidirect
655. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624292
#214624182
#214620792
#214620772
#214620742
#214620732
C2×#168406632
D61⋊AΣL(1,𝔽16)2
#214594512
#3334861