Finite Group Databasebeta

← #30623927

Subgroups — #30623927

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#21462076C212yesmaximal, complemented
5#21462075C212yesmaximal, complemented
6#21462071C212yesmaximal, complemented
7D61⋊AΣL(1,𝔽16)C212yesmaximal, complemented
8C2×#16840662C212yesmaximal, complemented
9#21459448C211yesmaximal, 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#16840665C2214yescomplemented
25#16840663C2214yescomplemented
26#16840662C2214yescomplemented
27#16840662C2214yescomplemented
28C2×#14519822C2211yescharacteristic
29C23×C22⋊D61C411yescharacteristic, complemented
30#16840402—21no—
31#16840402—21no—
32#16840399—21no—
33#16840399—21no—
34D4×C22⋊D61—21no—
35D4×C22⋊D61—21no—
36#16840394—21no—
37#16840394—21no—
38#16840327C411yescharacteristic, complemented
39#16840327C2211yescharacteristic
40#16840324C2211yescharacteristic
41#16840322C411yescharacteristic, complemented
42#16840322C2211yescharacteristic
43#16840321C411yescharacteristic, complemented
44#16840268C411yescharacteristic, complemented
45#16840268C2211yescharacteristic
46C2×#14519746C2211yescharacteristic
47#120×D61C411yescharacteristic, complemented
48#120×D61C2211yescharacteristic
49#16840235C411yescharacteristic, complemented
50C2×#120×C61C411yescharacteristic, 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
68#14519822—44no—
69C2×#11758222D411yescharacteristic
70C2×#11758222D411yescharacteristic
71C2×#11758224C2×C411yescharacteristic
72C2×#11758224D411yescharacteristic
73C2×#11758224D411yescharacteristic
74C2×#11758224C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C22⋊D61—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61—44no—
81C22×C22⋊D61C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic, complemented
83C22×C22⋊D61C2×C411yescharacteristic, complemented
84C22×C22⋊D61C2×C411yescharacteristic, complemented
85C22×C22⋊D61D411yescharacteristic
86C22×C22⋊D61D411yescharacteristic
87C22×C22⋊D61C2311yescharacteristic
88C2×D4×D61—21no—
89C2×D4×D61—21no—
90C2×D4×D61C2×C411yescharacteristic
91C2×D4×D61D411yescharacteristic
92C2×D4×D61D411yescharacteristic
93C2×D4×D61C2311yescharacteristic
94C23×Dic61C2×C411yescharacteristic, complemented
95#14519773—21no—
96#14519773—21no—
97#14519763—21no—
98#14519763—21no—
99#14519761—21no—
100#14519761C2×C411yescharacteristic, complemented
101#14519761C2311yescharacteristic
102#14519760—21no—
103#14519759—21no—
104#14519759—21no—
105#14519758C2×C411yescharacteristic, complemented
106#14519758C2×C411yescharacteristic, complemented
107#14519754—21no—
108#14519754—21no—
109#14519751—21no—
110#14519751—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#14519749—21no—
120#14519749—21no—
121#14519748—21no—
122#14519748—21no—
123#14519747—21no—
124#14519747—21no—
125#14519747—21no—
126#14519747C2×C411yescharacteristic, complemented
127#14519747C2311yescharacteristic
128#14519746—21no—
129#14519746—21no—
130#14519746—21no—
131#14519746C2×C411yescharacteristic, complemented
132#14519746C2×C411yescharacteristic, complemented
133#14519746C2311yescharacteristic
134#14519746C2311yescharacteristic
135#14519745—21no—
136#14519745—21no—
137#14519745—21no—
138#14519745—21no—
139#14519745C2×C411yescharacteristic, complemented
140#14519745C2×C411yescharacteristic, complemented
141D4×Dic61—21no—
142D4×Dic61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145#14519737—21no—
146#14519737—21no—
147#14519737—21no—
148#14519737—21no—
149#14519733C2×C411yescharacteristic, complemented
150#14519733C2×C411yescharacteristic, complemented
151C2×C22⋊Dic61—21no—
152C2×C22⋊Dic61C2×C411yescharacteristic, complemented
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61C2×C411yescharacteristic, complemented
156C22⋊C4×D61C2×C411yescharacteristic, complemented
157C25×C61C2×C411yescharacteristic, complemented
158C22×D4×C61—21no—
159C22×D4×C61C2×C411yescharacteristic
160#120×C61—21no—
161#120×C61—21no—
162#120×C61C2×C411yescharacteristic, complemented
163#120×C61C2×C411yescharacteristic, complemented
164#120×C61C2×C411yescharacteristic, complemented
165#120×C61C2×C411yescharacteristic, complemented
166C2×C22⋊C4×C61—21no—
167C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—42no—
171C24×C61—82no—
172C24×C61C22⋊C411yescharacteristic
173C24×C61C22×C411yescharacteristic
174C24×C61C22×C411yescharacteristic
175C24×C61C22×C411yescharacteristic
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—42no—
179C23×D61—82no—
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—82no—
193C2×D4×C61C22⋊C411yescharacteristic
194C2×D4×C61C22⋊C411yescharacteristic
195C2×D4×C61C22×C411yescharacteristic
196C2×D4×C61C22×C411yescharacteristic
197C22×C4×C61—21no—
198C22×C4×C61C22⋊C411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—21no—
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—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—42no—
215C2×C22⋊D61—42no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61C22⋊C411yescharacteristic
224C2×C22⋊D61C22⋊C411yescharacteristic
225C2×C22⋊D61C22⋊C411yescharacteristic
226C2×C22⋊D61C22⋊C411yescharacteristic
227C2×C22⋊D61C22⋊C411yescharacteristic
228C2×C22⋊D61C22⋊C411yescharacteristic
229C2×C22⋊D61C22×C411yescharacteristic
230C2×C22⋊D61C2×D411yescharacteristic
231C2×C22⋊D61C2×D411yescharacteristic
232C2×C22⋊D61C2×D411yescharacteristic
233C2×C22⋊D61C2×D411yescharacteristic
234C2×C22⋊D61C2411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—42no—
239C22×Dic61C22⋊C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758224—24no—
245#11758224—42no—
246#11758224—42no—
247#11758224—42no—
248D4×D61—24no—
249D4×D61—42no—
250D4×D61—42no—
251D4×D61—42no—
252D4×D61—82no—
253D4×D61—82no—
254#11758222—42no—
255#11758222—42no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244C22⋊C411yescharacteristic
259C2×D244C2×D411yescharacteristic
260C2×C4×D61—21no—
261C2×C4×D61—21no—
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—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61C22×C411yescharacteristic
286C22⋊C4×C61C22×C411yescharacteristic
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61C22×C411yescharacteristic
295C22⋊Dic61C22×C411yescharacteristic
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—41no—
322C23×C61—42no—
323C23×C61—81no—
324C23×C61—81no—
325C23×C61—81no—
326C23×C61—81no—
327C23×C61—81no—
328C23×C61—84no—
329C23×C61—84no—
330C23×C61C2×C22⋊C411yescharacteristic
331C23×C61C2×C22⋊C411yescharacteristic
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C23×C411yescharacteristic
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—21no—
339C22×D61—41no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—41no—
345C22×D61—81no—
346C22×D61—81no—
347C22×D61—81no—
348C22×D61—81no—
349C22×D61—81no—
350C22×D61—81no—
351C22×D61—81no—
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—41no—
372C2×C4×C61—81no—
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C22⋊D61—22no—
376C22⋊D61—22no—
377C22⋊D61—22no—
378C22⋊D61—22no—
379C22⋊D61—22no—
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—41no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—42no—
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—81no—
395C22⋊D61—81no—
396C22⋊D61—81no—
397C22⋊D61—81no—
398C22⋊D61#9914yes—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—41no—
406C2×Dic61—42no—
407C2×Dic61—42no—
408C2×Dic61—41no—
409C2×Dic61—81no—
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C22×D411yescharacteristic
414D244—22no—
415D244—41no—
416D244—81no—
417D244—81no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—81no—
423C4×D61—81no—
424Dic122—22no—
425Dic122—41no—
426#92420—44no—
427#33348—611nomaximal, Sylow
428C22×C61—22no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—82no—
446C22×C61—84no—
447C22×C61—84no—
448C22×C61—82no—
449C22×C61—161no—
450C22×C61C2×#9912yes—
451C22×C61C22×C22⋊C411yescharacteristic
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—82no—
463C2×D61—82no—
464C2×D61—84no—
465C2×D61—82no—
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—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—41no—
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—42no—
495C2×C61—41no—
496C2×C61—41no—
497C2×C61—41no—
498C2×C61—81no—
499C2×C61C22×#9911yescharacteristic
500D61—22no—
501D61—41no—
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—611no—
522#525—611no—
523#525—611no—
524C2×#120—611no—
525C2×#120—611no—
526C2×#120—611no—
527C2×#120#692311yescharacteristic, complemented
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—
548C25C2×#692311yescharacteristic, complemented
549H(5,𝔽2)—2444no—
550C2×#41—611no—
551C2×#41—611no—
552C2×#41—611no—
553C2×#41—611no—
554C2×#41—611no—
555C2×#41—611no—
556C22×D4—21no—
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—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C22×D4—1221no—
570C22×D4—1221no—
571C22×D4—1221no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—2444no—
576C22×D4C2×#692311yescharacteristic
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—611no—
587#123—611no—
588#123—611no—
589#123—611no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8—1221no—
596#121—1221no—
597#121—1221no—
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—21no—
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—1221no—
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#120C2×#692311yescharacteristic, complemented
631#120C2×#692311yescharacteristic, complemented
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—21no—
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—611no—
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—21no—
665C24—21no—
666C24—42no—
667C24—82no—
668C24—611no—
669C24—611no—
670C24—611no—
671C24—611no—
672C24—611no—
673C24—1221no—
674C24—1221no—
675C24—4882no—
676C24—2442no—
677C24C22⋊#692311yescharacteristic
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—82no—
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—1224no—
714C2×D4—1224no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
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—2442no—
729C2×D4—2442no—
730C2×D4—2442no—
731C2×D4—2442no—
732C2×D4—2442no—
733C2×D4—2442no—
734C2×D4—2444no—
735C2×D4—2442no—
736C2×D4—2444no—
737C2×D4—2444no—
738C2×D4—2444no—
739C2×D4—2442no—
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—611no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—2442no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4C22⋊#692311yescharacteristic
764M16—1224no—
765M16—2442no—
766M16—2442no—
767M16—2442no—
768C2×C8—2442no—
769C2×C8—2442no—
770C2×C8—2442no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
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—21no—
809C23—22no—
810C23—21no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—41no—
818C23—42no—
819C23—81no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—84no—
825C23—84no—
826C23—611no—
827C23—611no—
828C23—611no—
829C23—611no—
830C23—1222no—
831C23—1222no—
832C23—1222no—
833C23—1221no—
834C23—4881no—
835C23—4884no—
836C23—4884no—
837C23—4881no—
838C23—4881no—
839C23—4881no—
840C23—4881no—
841C23—4881no—
842C23—4881no—
843C23—2441no—
844C23—2441no—
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—2441no—
880D4—2441no—
881D4—2441no—
882D4—2441no—
883D4—2441no—
884D4—2441no—
885D4—2442no—
886D4—2442no—
887D4—2442no—
888D4—2442no—
889D4—2442no—
890D4—2442no—
891D4—2442no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—41no—
895C2×C4—81no—
896C2×C4—611no—
897C2×C4—611no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—9762no—
909C2×C4—9762no—
910C2×C4—4881no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2442no—
916C2×C4—2441no—
917C2×C4—2442no—
918C2×C4—2444no—
919C2×C4—2441no—
920C2×C4C2×C22⋊#692311yescharacteristic
921C2×C4C2×C22⋊#692311yescharacteristic
922C8—2444no—
923C22—22no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—82no—
941C22—84no—
942C22—84no—
943C22—82no—
944C22—161no—
945C22—612no—
946C22—1221no—
947C22—1221no—
948C22—1221no—
949C22—9761no—
950C22—4882no—
951C22—4884no—
952C22—4882no—
953C22—4882no—
954C22—4882no—
955C22—4884no—
956C22—2441no—
957C22—2441no—
958C22—2441no—
959C22—2441no—
960C22—2441no—
961C22—2441no—
962C22—2441no—
963C22D61⋊#9912yes—
964C22C22×C22⋊#692311yescharacteristic
965C4—21no—
966C4—21no—
967C4—41no—
968C4—41no—
969C4—612no—
970C4—1221no—
971C4—1221no—
972C4—1221no—
973C4—4884no—
974C4—2441no—
975C4—2441no—
976C4—2441no—
977C2—21no—
978C2—22no—
979C2—42no—
980C2—41no—
981C2—41no—
982C2—41no—
983C2—41no—
984C2—81no—
985C2—1222no—
986C2—4881no—
987C2—2441no—
988C2—2441no—
989C2—2441no—
990C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#120×C61C4
socleC2×C61C22×#99
prime radical#21459448C2
cosocleC2×C22⋊D61C24
hypercenterC2×#120#6923
hypocenterC61#33348
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #21462429C2semidirect
2. #21462418C2semidirect
3. #21462079C2semidirect
4. #21462076C2semidirect
5. #21462075C2semidirect
6. #21462071C2semidirect
7. D61⋊AΣL(1,𝔽16)C2semidirect
8. C2×#16840662C2semidirect
13. #16840749C22semidirect
15. D61⋊#100C22semidirect
17. C2×#14519837C22semidirect
18. #16840742C22semidirect
21. D61⋊#99C22semidirect
23. C2×#14519835C22semidirect
24. #16840665C22semidirect
25. #16840663C22semidirect
26. #16840662C22semidirect
27. #16840662C22semidirect
29. C23×C22⋊D61C4semidirect
38. #16840327C4semidirect
41. #16840322C4semidirect
43. #16840321C4semidirect
44. #16840268C4semidirect
47. #120×D61C4semidirect
49. #16840235C4semidirect
50. C2×#120×C61C4semidirect
67. C24×D61C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
83. C22×C22⋊D61C2×C4semidirect
84. C22×C22⋊D61C2×C4semidirect
94. C23×Dic61C2×C4semidirect
100. #14519761C2×C4semidirect
105. #14519758C2×C4semidirect
106. #14519758C2×C4semidirect
126. #14519747C2×C4semidirect
131. #14519746C2×C4semidirect
132. #14519746C2×C4semidirect
139. #14519745C2×C4semidirect
140. #14519745C2×C4semidirect
149. #14519733C2×C4semidirect
150. #14519733C2×C4semidirect
152. C2×C22⋊Dic61C2×C4semidirect
155. C22⋊C4×D61C2×C4semidirect
156. C22⋊C4×D61C2×C4semidirect
157. C25×C61C2×C4semidirect
162. #120×C61C2×C4semidirect
163. #120×C61C2×C4semidirect
164. #120×C61C2×C4semidirect
165. #120×C61C2×C4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
527. C2×#120#6923semidirect
546. C61#33348semidirect
548. C25C2×#6923semidirect
630. #120C2×#6923semidirect
631. #120C2×#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
#214620762
#214620752
#214620712
D61⋊AΣL(1,𝔽16)2
C2×#168406622
#214594482
#3334861