Finite Group Databasebeta

← D61⋊#2121 #30623908

Subgroups — D61⋊#2121 #30623908

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#100C211yesmaximal, characteristic, complemented
2C2×D61⋊#99C211yesmaximal, characteristic, complemented
3#21462077C212yesmaximal, complemented
4#21462076C212yesmaximal, complemented
5#21462075C212yesmaximal, complemented
6#21462074C212yesmaximal, complemented
7D61⋊#352C212yesmaximal, complemented
8D61⋊AΣL(1,𝔽16)C212yesmaximal, complemented
9#534×D61C211yesmaximal, characteristic
10C2×D61⋊M16—21no—
11C22×C22⋊#6923—21no—
12D61⋊#100—21no—
13D61⋊#100—21no—
14D61⋊#100C2212yes—
15D61⋊#100C2212yescomplemented
16C2×#14519837—21no—
17C2×#14519837C2212yescomplemented
18C2×#14519836—21no—
19D61⋊#99—21no—
20D61⋊#99—21no—
21D61⋊#99C2212yes—
22D61⋊#99C2212yescomplemented
23C2×#14519835C2212yescomplemented
24#16840665C2214yescomplemented
25#16840664C2214yescomplemented
26#16840663C2214yescomplemented
27#16840662C2214yescomplemented
28C22×D4×D61C411yescharacteristic, complemented
29C22×D4×D61C2211yescharacteristic
30#16840324C2211yescharacteristic
31#16840323—21no—
32#16840323C411yescharacteristic, complemented
33#16840323C2211yescharacteristic
34#16840322—21no—
35#16840322C411yescharacteristic, complemented
36#16840322C2211yescharacteristic
37#16840321C411yescharacteristic, complemented
38#16840321C2211yescharacteristic
39#16840320—21no—
40#16840320—21no—
41#123×D61—21no—
42#123×D61C411yescharacteristic, complemented
43#123×D61C2211yescharacteristic
44#121×D61—21no—
45#121×D61—21no—
46#120×D61—21no—
47#120×D61C411yescharacteristic, complemented
48#120×D61C2211yescharacteristic
49C2×C22⋊C4×D61C411yescharacteristic, complemented
50C61×#534C411yescharacteristic, complemented
51C23×#6923—41no—
52C2×#11758213—41no—
53D61⋊M16—22no—
54D61⋊M16—22no—
55D61⋊M16—41no—
56D61⋊M16—41no—
57C2×#11758217—22no—
58C2×D61⋊C8—41no—
59C2×C22⋊#6923—22no—
60C2×C22⋊#6923—22no—
61C2×C22⋊#6923—22no—
62C2×C22⋊#6923—41no—
63C2×C22⋊#6923—41no—
64C2×C22⋊#6923—41no—
65#14519837—22no—
66#14519837—22no—
67#14519837—22no—
68#14519837C2314yes—
69#14519836—22no—
70#14519836—22no—
71#14519835—22no—
72#14519835C2314yes—
73C24×D61C2×C411yescharacteristic
74C24×D61C2×C411yescharacteristic, complemented
75C24×D61D411yescharacteristic
76C22×D244C2×C411yescharacteristic, complemented
77C22×D244D411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic, complemented
79C22×C22⋊D61C2×C411yescharacteristic, complemented
80C22×C22⋊D61D411yescharacteristic
81C22×C22⋊D61C2311yescharacteristic
82C2×D4×D61—21no—
83C2×D4×D61—21no—
84C2×D4×D61—21no—
85C2×D4×D61—21no—
86C2×D4×D61—21no—
87C2×D4×D61—21no—
88C2×D4×D61—41no—
89C2×D4×D61—41no—
90C2×D4×D61—41no—
91C2×D4×D61—41no—
92C2×D4×D61—41no—
93C2×D4×D61—41no—
94C2×D4×D61—41no—
95C2×D4×D61—41no—
96C2×D4×D61C2×C411yescharacteristic
97C2×D4×D61C2×C411yescharacteristic
98C2×D4×D61D411yescharacteristic
99C2×D4×D61D411yescharacteristic
100C2×D4×D61D411yescharacteristic
101C2×D4×D61D411yescharacteristic
102C2×D4×D61C2311yescharacteristic
103C2×D4×D61C2311yescharacteristic
104C22×C4×D61—21no—
105C22×C4×D61C2×C411yescharacteristic, complemented
106C22×C4×D61D411yescharacteristic
107#14519762—21no—
108#14519762—21no—
109#14519762—21no—
110#14519762—21no—
111#14519761—21no—
112#14519761C2×C411yescharacteristic, complemented
113#14519761C2311yescharacteristic
114#14519760—21no—
115#14519760C2×C411yescharacteristic, complemented
116#14519760C2311yescharacteristic
117#14519759—21no—
118#14519759—21no—
119#14519759—21no—
120#14519759—21no—
121#14519758—21no—
122#14519758C2×C411yescharacteristic, complemented
123#14519758C2×C411yescharacteristic, complemented
124#14519752—21no—
125#14519752—21no—
126#14519751—21no—
127#14519751—21no—
128#14519750—21no—
129#14519750—21no—
130#14519750—21no—
131#14519750—21no—
132#14519749—21no—
133#14519749—21no—
134#14519749—21no—
135#14519749—21no—
136#14519748—21no—
137#14519748—21no—
138#14519747—21no—
139#14519747—21no—
140#14519747—21no—
141#14519747—21no—
142#14519747—21no—
143#14519747C2×C411yescharacteristic, complemented
144#14519747C2311yescharacteristic
145#14519746—21no—
146#14519746C2×C411yescharacteristic, complemented
147#14519746C2311yescharacteristic
148#14519745—21no—
149#14519745—21no—
150#14519745—21no—
151#14519745—21no—
152#14519745—21no—
153#14519745C2×C411yescharacteristic, complemented
154#14519745C2×C411yescharacteristic, complemented
155C4⋊C4×D61—21no—
156C4⋊C4×D61—21no—
157C2×C22⋊Dic61C2×C411yescharacteristic, complemented
158C2×#11758198—21no—
159C22⋊C4×D61—21no—
160C22⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61C2×C411yescharacteristic, complemented
166C22⋊C4×D61C2×C411yescharacteristic, complemented
167C22⋊C4×D61C2×C411yescharacteristic, complemented
168C22⋊C4×D61C2×C411yescharacteristic, complemented
169C22×D4×C61C2×C411yescharacteristic
170C22×D4×C61C2×C411yescharacteristic, complemented
171#123×C61—21no—
172#123×C61C2×C411yescharacteristic, complemented
173#123×C61C2×C411yescharacteristic, complemented
174#121×C61—21no—
175#121×C61—21no—
176#120×C61—21no—
177#120×C61C2×C411yescharacteristic, complemented
178#120×C61C2×C411yescharacteristic, complemented
179C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
180C24×C61C22⋊C411yescharacteristic
181C24×C61C22×C411yescharacteristic
182C24×C61C22×C411yescharacteristic, complemented
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—41no—
194C23×D61—41no—
195C23×D61—82no—
196C23×D61—82no—
197C23×D61—82no—
198C23×D61C22⋊C411yescharacteristic
199C23×D61C22⋊C411yescharacteristic
200C23×D61C22⋊C411yescharacteristic
201C23×D61C22⋊C411yescharacteristic
202C23×D61C22⋊C411yescharacteristic
203C23×D61C22⋊C411yescharacteristic
204C23×D61C22×C411yescharacteristic
205C23×D61C22×C411yescharacteristic
206C23×D61C22×C411yescharacteristic, complemented
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C22×#6923—42no—
211C22×#6923—42no—
212C22×#6923—42no—
213C22×#6923—84no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—41no—
219C2×D4×C61—41no—
220C2×D4×C61—41no—
221C2×D4×C61—41no—
222C2×D4×C61C22⋊C411yescharacteristic
223C2×D4×C61C22⋊C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C22×C4×C61—21no—
227C22×C4×C61C22⋊C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic, complemented
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—41no—
238C2×C22⋊D61—41no—
239C2×C22⋊D61—41no—
240C2×C22⋊D61—41no—
241C2×C22⋊D61—41no—
242C2×C22⋊D61—41no—
243C2×C22⋊D61—41no—
244C2×C22⋊D61—41no—
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22×C411yescharacteristic
248C2×C22⋊D61C2×D411yescharacteristic
249C2×C22⋊D61C2×D411yescharacteristic
250C2×C22⋊D61C2×D411yescharacteristic
251C2×C22⋊D61C2×D411yescharacteristic
252C2×C22⋊D61C2411yescharacteristic
253C22×Dic61—21no—
254C22×Dic61C22×C411yescharacteristic, complemented
255C22×Dic61C2×D411yescharacteristic
256D4×D61—41no—
257D4×D61—41no—
258D4×D61—41no—
259D4×D61—41no—
260D4×D61—41no—
261D4×D61—41no—
262D4×D61—41no—
263D4×D61—41no—
264D4×D61—41no—
265D4×D61—41no—
266D4×D61—41no—
267D4×D61—41no—
268D4×D61—41no—
269D4×D61—41no—
270D4×D61—41no—
271D4×D61—41no—
272D4×D61—42no—
273D4×D61—42no—
274D4×D61—42no—
275D4×D61—42no—
276D4×D61—42no—
277D4×D61—42no—
278D4×D61—41no—
279D4×D61—41no—
280D4×D61—41no—
281D4×D61—41no—
282D4×D61—82no—
283D4×D61—82no—
284C2×D244—21no—
285C2×D244—21no—
286C2×D244—21no—
287C2×D244—21no—
288C2×D244—41no—
289C2×D244—41no—
290C2×D244—41no—
291C2×D244—41no—
292C2×D244C22⋊C411yescharacteristic
293C2×D244C22⋊C411yescharacteristic
294C2×D244C2×D411yescharacteristic
295C2×D244C2×D411yescharacteristic
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—21no—
300C2×C4×D61—21no—
301C2×C4×D61—21no—
302C2×C4×D61—21no—
303C2×C4×D61—21no—
304C2×C4×D61—21no—
305C2×C4×D61—21no—
306C2×C4×D61—41no—
307C2×C4×D61—41no—
308C2×C4×D61—82no—
309C2×C4×D61C22⋊C411yescharacteristic
310C2×C4×D61C22⋊C411yescharacteristic
311C2×C4×D61C2×D411yescharacteristic
312C2×C4×D61C2×D411yescharacteristic
313C22⋊#6923—24no—
314C22⋊#6923—42no—
315C22⋊#6923—42no—
316C22⋊#6923—42no—
317#11758217—24no—
318#11758217—42no—
319C2×#92420—42no—
320#11758213—42no—
321#11758213—42no—
322D61⋊C8—42no—
323D61⋊C8—42no—
324C4⋊C4×C61—21no—
325C4⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61—21no—
331C22⋊C4×C61C22×C411yescharacteristic, complemented
332C22⋊C4×C61C22×C411yescharacteristic, complemented
333C22⋊Dic61—21no—
334C22⋊Dic61—21no—
335C22⋊Dic61—21no—
336C22⋊Dic61—21no—
337C22⋊Dic61—21no—
338C22⋊Dic61C22×C411yescharacteristic, complemented
339C22⋊Dic61C22×C411yescharacteristic, complemented
340#11758198—21no—
341#11758198—21no—
342#11758198—21no—
343#11758198—21no—
344#11758198—21no—
345#11758198—21no—
346#11758198—21no—
347#11758198—21no—
348#11758198—21no—
349#11758198—21no—
350#11758198—21no—
351#11758198—21no—
352C4⋊Dic61—21no—
353C4⋊Dic61—21no—
354#11758196—21no—
355#11758196—21no—
356#11758196—21no—
357#11758196—21no—
358C23×C61—21no—
359C23×C61—21no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—21no—
363C23×C61—41no—
364C23×C61—81no—
365C23×C61—81no—
366C23×C61—81no—
367C23×C61C2×C22⋊C411yescharacteristic
368C23×C61C2×C22⋊C411yescharacteristic
369C23×C61C2×C22⋊C411yescharacteristic
370C23×C61C2×C22⋊C411yescharacteristic
371C23×C61C23×C411yescharacteristic
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—21no—
389C22×D61—21no—
390C22×D61—21no—
391C22×D61—21no—
392C22×D61—21no—
393C22×D61—42no—
394C22×D61—44no—
395C22×D61—42no—
396C22×D61—42no—
397C22×D61—42no—
398C22×D61—42no—
399C22×D61—42no—
400C22×D61—42no—
401C22×D61—42no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—82no—
406C22×D61—82no—
407C22×D61—82no—
408C22×D61—81no—
409C22×D61—81no—
410C22×D61—81no—
411C22×D61—82no—
412C22×D61—82no—
413C22×D61—82no—
414C22×D61—82no—
415C22×D61—81no—
416C22×D61—81no—
417C22×D61—81no—
418C22×D61—81no—
419C22×D61—81no—
420C22×D61—81no—
421C22×D61—84no—
422C22×D61—84no—
423C22×D61#9911yescharacteristic
424C22×D61#9911yescharacteristic
425C22×D61#9911yescharacteristic
426C22×D61#9911yescharacteristic
427C22×D61C2×C22⋊C411yescharacteristic
428C22×D61C2×C22⋊C411yescharacteristic
429C22×D61C2×C22⋊C411yescharacteristic
430C22×D61C2×C22⋊C411yescharacteristic
431C22×D61C2×C22⋊C411yescharacteristic
432C22×D61C22×D411yescharacteristic
433C2×#6923—44no—
434C2×#6923—84no—
435C2×#6923—84no—
436C2×#6923—84no—
437D4×C61—41no—
438D4×C61—41no—
439D4×C61—41no—
440D4×C61—41no—
441D4×C61—42no—
442D4×C61—41no—
443D4×C61—41no—
444D4×C61—81no—
445D4×C61—81no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—41no—
452C2×C4×C61—81no—
453C2×C4×C61C2×C22⋊C411yescharacteristic
454C2×C4×C61C2×C22⋊C411yescharacteristic
455C22⋊D61—41no—
456C22⋊D61—41no—
457C22⋊D61—41no—
458C22⋊D61—41no—
459C22⋊D61—41no—
460C22⋊D61—41no—
461C22⋊D61—41no—
462C22⋊D61—41no—
463C22⋊D61—42no—
464C22⋊D61—42no—
465C22⋊D61—41no—
466C22⋊D61—41no—
467C22⋊D61—41no—
468C22⋊D61—41no—
469C22⋊D61—81no—
470C22⋊D61—81no—
471C22⋊D61—81no—
472C22⋊D61—81no—
473C2×Dic61—21no—
474C2×Dic61—21no—
475C2×Dic61—21no—
476C2×Dic61—21no—
477C2×Dic61—21no—
478C2×Dic61—41no—
479C2×Dic61—81no—
480C2×Dic61C2×C22⋊C411yescharacteristic
481C2×Dic61C22×D411yescharacteristic
482D244—41no—
483D244—41no—
484D244—41no—
485D244—41no—
486D244—42no—
487D244—41no—
488D244—41no—
489D244—81no—
490D244—81no—
491C4×D61—21no—
492C4×D61—21no—
493C4×D61—21no—
494C4×D61—21no—
495C4×D61—21no—
496C4×D61—21no—
497C4×D61—21no—
498C4×D61—21no—
499C4×D61—42no—
500C4×D61—42no—
501C4×D61—42no—
502C4×D61—41no—
503C4×D61—41no—
504C4×D61—81no—
505C4×D61—81no—
506#92420—44no—
507C2×#2121—611nomaximal, Sylow
508C22×C61—21no—
509C22×C61—21no—
510C22×C61—21no—
511C22×C61—21no—
512C22×C61—41no—
513C22×C61—41no—
514C22×C61—41no—
515C22×C61—41no—
516C22×C61—41no—
517C22×C61—42no—
518C22×C61—41no—
519C22×C61—41no—
520C22×C61—41no—
521C22×C61—81no—
522C22×C61—81no—
523C22×C61—81no—
524C22×C61—82no—
525C22×C61C2×#9911yescharacteristic
526C22×C61C2×#9911yescharacteristic
527C22×C61C22×C22⋊C411yescharacteristic
528C2×D61—22no—
529C2×D61—22no—
530C2×D61—22no—
531C2×D61—21no—
532C2×D61—21no—
533C2×D61—21no—
534C2×D61—21no—
535C2×D61—41no—
536C2×D61—41no—
537C2×D61—41no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—41no—
548C2×D61—41no—
549C2×D61—41no—
550C2×D61—41no—
551C2×D61—41no—
552C2×D61—41no—
553C2×D61—41no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61—81no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—82no—
563C2×D61—81no—
564C2×D61—81no—
565C2×D61—81no—
566C2×D61—84no—
567C2×D61—82no—
568C2×D61—82no—
569C2×D61C2×#9911yescharacteristic
570C2×D61C2×#9911yescharacteristic
571C2×D61C2×#9911yescharacteristic
572C2×D61C2×#9911yescharacteristic
573#6923—84no—
574C4×C61—21no—
575C4×C61—21no—
576C4×C61—41no—
577C4×C61—41no—
578C4×C61—41no—
579Dic61—21no—
580Dic61—21no—
581Dic61—41no—
582Dic61—41no—
583Dic61—41no—
584C2×#534—611no—
585C22×#100—611no—
586C22×#99—611no—
587#2121—612no—
588#2121—612no—
589#2121—612no—
590#2121—612no—
591C2×#352—612no—
592C2×AΣL(1,𝔽16)—612no—
593C2×C61—21no—
594C2×C61—21no—
595C2×C61—21no—
596C2×C61—41no—
597C2×C61—41no—
598C2×C61—41no—
599C2×C61—41no—
600C2×C61—81no—
601C2×C61C22×#9911yescharacteristic
602D61—21no—
603D61—21no—
604D61—21no—
605D61—41no—
606D61—41no—
607D61—41no—
608D61—41no—
609D61—81no—
610D61#212112yescomplemented
611C23×D4—611no—
612C23×D4—611no—
613C22×M16—1221no—
614#534—611no—
615#534—611no—
616#534—611no—
617#534—611no—
618#534—611no—
619#534—611no—
620#534—611no—
621#534—1221no—
622#534—1221no—
623#534—1221no—
624#534—1221no—
625#534#692311yescharacteristic, complemented
626C2×#123—611no—
627C2×#123—611no—
628C2×#123—1221no—
629C2×#121—1221no—
630C2×#121—1221no—
631C2×#120—611no—
632C2×#120—611no—
633C2×#120—1221no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—1221no—
636C2×#100—612no—
637C2×#100—612no—
638C2×#100—612no—
639C2×#100—1221no—
640C2×#100—1221no—
641C2×#100—1221no—
642C2×#99—612no—
643C2×#99—612no—
644C2×#99—612no—
645C2×#99—1221no—
646C2×#99—1221no—
647C2×#99—1221no—
648#352—614no—
649#352—614no—
650AΣL(1,𝔽16)—614no—
651AΣL(1,𝔽16)—614no—
652C61C2×#212111yescharacteristic, complemented, Sylow
653C25—611no—
654C25—611no—
655C25—611no—
656C22×D4—611no—
657C22×D4—611no—
658C22×D4—611no—
659C22×D4—611no—
660C22×D4—611no—
661C22×D4—611no—
662C22×D4—611no—
663C22×D4—611no—
664C22×D4—611no—
665C22×D4—611no—
666C22×D4—611no—
667C22×D4—611no—
668C22×D4—611no—
669C22×D4—611no—
670C22×D4—1221no—
671C22×D4—1221no—
672C22×D4—1221no—
673C22×D4—1221no—
674C22×D4—1221no—
675C22×D4—1221no—
676C22×D4—2441no—
677C22×D4—2441no—
678C22×D4—2441no—
679C22×D4—2441no—
680C22×D4—2441no—
681C22×D4—2441no—
682C22×D4—2441no—
683C22×D4—2441no—
684C22×D4C2×#692311yescharacteristic
685C22×D4C2×#692311yescharacteristic, complemented
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—1221no—
689C23×C4—2441no—
690C2×M16—1222no—
691C2×M16—1222no—
692C2×M16—1222no—
693C2×M16—2441no—
694C2×M16—2441no—
695C2×M16—2441no—
696C22×C8—2441no—
697#123—21no—
698#123—611no—
699#123—611no—
700#123—611no—
701#123—611no—
702#123—611no—
703#123—611no—
704#123—1221no—
705#123—1221no—
706#123—1221no—
707#123—1221no—
708#123—1221no—
709#123—1221no—
710#123—1221no—
711#123—1221no—
712#123—1221no—
713#123—1221no—
714#123—1221no—
715#123C2×#692311yescharacteristic, complemented
716#123C2×#692311yescharacteristic, complemented
717#121—21no—
718#121—21no—
719#121—1221no—
720#121—1221no—
721#121—1221no—
722#121—1221no—
723#121—1221no—
724#121—1221no—
725#121—1221no—
726#121—1221no—
727#121—1221no—
728#121—1221no—
729#121—1221no—
730#121—1221no—
731#121—1221no—
732#121—1221no—
733#120—21no—
734#120—611no—
735#120—611no—
736#120—611no—
737#120—611no—
738#120—611no—
739#120—611no—
740#120—1221no—
741#120—1221no—
742#120—1221no—
743#120—1221no—
744#120—1221no—
745#120—1221no—
746#120—1221no—
747#120—1221no—
748#120—1221no—
749#120—1221no—
750#120—1221no—
751#120C2×#692311yescharacteristic, complemented
752#120C2×#692311yescharacteristic, complemented
753C2×C4⋊C4—1221no—
754C2×C4⋊C4—1221no—
755C2×C22⋊C4—611no—
756C2×C22⋊C4—611no—
757C2×C22⋊C4—611no—
758C2×C22⋊C4—611no—
759C2×C22⋊C4—611no—
760C2×C22⋊C4—1221no—
761C2×C22⋊C4—1221no—
762C2×C22⋊C4—1221no—
763C2×C22⋊C4—1221no—
764C2×C22⋊C4—1221no—
765C2×C22⋊C4—1221no—
766C2×C22⋊C4—1221no—
767C2×C22⋊C4—1222no—
768C2×C22⋊C4—1222no—
769C2×C22⋊C4—1222no—
770C2×C22⋊C4—2441no—
771C2×C22⋊C4—2441no—
772C2×C22⋊C4—2441no—
773C2×C22⋊C4C2×#692311yescharacteristic, complemented
774#100—614no—
775#100—1222no—
776#100—1222no—
777#100—1222no—
778#99—614no—
779#99—1222no—
780#99—1222no—
781#99—1222no—
782C24—611no—
783C24—611no—
784C24—611no—
785C24—611no—
786C24—611no—
787C24—611no—
788C24—611no—
789C24—611no—
790C24—611no—
791C24—611no—
792C24—611no—
793C24—611no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24—1221no—
804C24—4882no—
805C24—4882no—
806C24—4882no—
807C24—2441no—
808C24—2441no—
809C24C22⋊#692311yescharacteristic
810C24C22×#692311yescharacteristic
811C24C22×#692311yescharacteristic, complemented
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—611no—
821C2×D4—611no—
822C2×D4—611no—
823C2×D4—611no—
824C2×D4—611no—
825C2×D4—611no—
826C2×D4—611no—
827C2×D4—611no—
828C2×D4—611no—
829C2×D4—611no—
830C2×D4—611no—
831C2×D4—611no—
832C2×D4—1221no—
833C2×D4—1221no—
834C2×D4—1221no—
835C2×D4—1221no—
836C2×D4—1221no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1221no—
840C2×D4—1221no—
841C2×D4—1221no—
842C2×D4—1221no—
843C2×D4—1221no—
844C2×D4—4882no—
845C2×D4—4882no—
846C2×D4—2441no—
847C2×D4—2441no—
848C2×D4—2441no—
849C2×D4—2441no—
850C2×D4—2441no—
851C2×D4—2441no—
852C2×D4—2441no—
853C2×D4—2441no—
854C2×D4—2441no—
855C2×D4—2441no—
856C2×D4—2441no—
857C2×D4—2441no—
858C2×D4—2441no—
859C2×D4—2441no—
860C2×D4—2441no—
861C2×D4—2441no—
862C2×D4—2441no—
863C2×D4—2441no—
864C2×D4—2441no—
865C2×D4—2441no—
866C2×D4—2441no—
867C2×D4—2441no—
868C2×D4—2441no—
869C2×D4—2441no—
870C2×D4—2441no—
871C2×D4—2441no—
872C2×D4—2441no—
873C2×D4—2441no—
874C2×D4—2442no—
875C2×D4—2442no—
876C2×D4—2442no—
877C2×D4—2442no—
878C2×D4—2442no—
879C2×D4—2442no—
880C2×D4—2441no—
881C2×D4—2441no—
882C2×D4—2441no—
883C2×D4—2441no—
884C2×D4C22⋊#692311yescharacteristic
885C2×D4C22⋊#692311yescharacteristic
886C2×D4C22×#692311yescharacteristic
887C2×D4C22×#692311yescharacteristic
888C22×C4—21no—
889C22×C4—611no—
890C22×C4—611no—
891C22×C4—611no—
892C22×C4—611no—
893C22×C4—611no—
894C22×C4—611no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—4882no—
907C22×C4—4884no—
908C22×C4—2441no—
909C22×C4—2441no—
910C22×C4—2442no—
911C22×C4—2442no—
912C22×C4—2442no—
913C22×C4C22⋊#692311yescharacteristic
914C22×C4C22×#692311yescharacteristic, complemented
915M16—1224no—
916M16—2442no—
917M16—2442no—
918M16—2442no—
919C2×C8—2442no—
920C2×C8—2442no—
921C2×C8—2442no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—1221no—
925C4⋊C4—1221no—
926C4⋊C4—1221no—
927C4⋊C4—1221no—
928C4⋊C4—1221no—
929C4⋊C4—1221no—
930C22⋊C4—21no—
931C22⋊C4—21no—
932C22⋊C4—21no—
933C22⋊C4—21no—
934C22⋊C4—21no—
935C22⋊C4—611no—
936C22⋊C4—611no—
937C22⋊C4—1221no—
938C22⋊C4—1221no—
939C22⋊C4—1221no—
940C22⋊C4—1221no—
941C22⋊C4—1221no—
942C22⋊C4—1221no—
943C22⋊C4—1221no—
944C22⋊C4—1221no—
945C22⋊C4—1221no—
946C22⋊C4—1221no—
947C22⋊C4—1221no—
948C22⋊C4—1221no—
949C22⋊C4—1221no—
950C22⋊C4—1221no—
951C22⋊C4—1221no—
952C22⋊C4—1221no—
953C22⋊C4—1221no—
954C22⋊C4—1224no—
955C22⋊C4—2442no—
956C22⋊C4—2442no—
957C22⋊C4—2442no—
958C22⋊C4C22×#692311yescharacteristic, complemented
959C22⋊C4C22×#692311yescharacteristic, complemented
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—41no—
966C23—81no—
967C23—81no—
968C23—81no—
969C23—611no—
970C23—611no—
971C23—611no—
972C23—611no—
973C23—611no—
974C23—611no—
975C23—611no—
976C23—611no—
977C23—611no—
978C23—611no—
979C23—1221no—
980C23—1221no—
981C23—1221no—
982C23—1221no—
983C23—1221no—
984C23—1221no—
985C23—1221no—
986C23—1221no—
987C23—1221no—
988C23—1221no—
989C23—1221no—
990C23—1221no—
991C23—1221no—
992C23—1221no—
993C23—1221no—
994C23—1221no—
995C23—1221no—
996C23—1221no—
997C23—1221no—
998C23—1221no—
999C23—1221no—
1000C23—4882no—
1001C23—4881no—
1002C23—4881no—
1003C23—4881no—
1004C23—4881no—
1005C23—4881no—
1006C23—4881no—
1007C23—4881no—
1008C23—4881no—
1009C23—4881no—
1010C23—4882no—
1011C23—4882no—
1012C23—4882no—
1013C23—4884no—
1014C23—4884no—
1015C23—4882no—
1016C23—4882no—
1017C23—4882no—
1018C23—2441no—
1019C23—2441no—
1020C23—2441no—
1021C23—2442no—
1022C23—2442no—
1023C23—2442no—
1024C23—2442no—
1025C23—2442no—
1026C23—2442no—
1027C23—2442no—
1028C23—2442no—
1029C23—2444no—
1030C23C2×C22⋊#692311yescharacteristic
1031C23C2×C22⋊#692311yescharacteristic
1032C23C2×C22⋊#692311yescharacteristic
1033C23C2×C22⋊#692311yescharacteristic
1034C23C23×#692311yescharacteristic
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—42no—
1040D4—41no—
1041D4—41no—
1042D4—81no—
1043D4—81no—
1044D4—4881no—
1045D4—4881no—
1046D4—4881no—
1047D4—4881no—
1048D4—4881no—
1049D4—4881no—
1050D4—2441no—
1051D4—2441no—
1052D4—2441no—
1053D4—2441no—
1054D4—2441no—
1055D4—2441no—
1056D4—2442no—
1057D4—2441no—
1058D4—2441no—
1059D4—2441no—
1060D4—2441no—
1061D4—2441no—
1062D4—2441no—
1063D4—2441no—
1064D4—2441no—
1065D4—2442no—
1066D4—2441no—
1067D4—2441no—
1068D4—2442no—
1069D4—2441no—
1070D4—2441no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—41no—
1077C2×C4—81no—
1078C2×C4—611no—
1079C2×C4—611no—
1080C2×C4—1221no—
1081C2×C4—1221no—
1082C2×C4—1221no—
1083C2×C4—1221no—
1084C2×C4—1221no—
1085C2×C4—1221no—
1086C2×C4—1221no—
1087C2×C4—1221no—
1088C2×C4—1221no—
1089C2×C4—1221no—
1090C2×C4—1221no—
1091C2×C4—1221no—
1092C2×C4—1221no—
1093C2×C4—4881no—
1094C2×C4—4881no—
1095C2×C4—4884no—
1096C2×C4—4884no—
1097C2×C4—4884no—
1098C2×C4—4881no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2442no—
1102C2×C4—2442no—
1103C2×C4—2442no—
1104C2×C4—2444no—
1105C2×C4—2441no—
1106C2×C4C2×C22⋊#692311yescharacteristic
1107C2×C4C2×C22⋊#692311yescharacteristic
1108C8—2444no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—41no—
1117C22—41no—
1118C22—42no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—82no—
1126C22—611no—
1127C22—611no—
1128C22—611no—
1129C22—611no—
1130C22—1222no—
1131C22—1222no—
1132C22—1222no—
1133C22—1221no—
1134C22—1221no—
1135C22—1221no—
1136C22—1221no—
1137C22—4881no—
1138C22—4881no—
1139C22—4881no—
1140C22—4881no—
1141C22—4881no—
1142C22—4881no—
1143C22—4881no—
1144C22—4881no—
1145C22—4881no—
1146C22—4881no—
1147C22—4881no—
1148C22—4882no—
1149C22—4882no—
1150C22—4882no—
1151C22—4884no—
1152C22—2441no—
1153C22—2441no—
1154C22—2441no—
1155C22—2441no—
1156C22—2441no—
1157C22—2441no—
1158C22—2441no—
1159C22—2441no—
1160C22—2441no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22—2442no—
1168C22—2442no—
1169C22—2442no—
1170C22—2441no—
1171C22D61⋊#9911yescharacteristic
1172C22D61⋊#9911yescharacteristic
1173C22C22×C22⋊#692311yescharacteristic
1174C4—21no—
1175C4—21no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—1221no—
1180C4—1221no—
1181C4—4884no—
1182C4—2441no—
1183C4—2441no—
1184C4—2441no—
1185C2—21no—
1186C2—21no—
1187C2—21no—
1188C2—41no—
1189C2—41no—
1190C2—41no—
1191C2—41no—
1192C2—81no—
1193C2—612no—
1194C2—1221no—
1195C2—1221no—
1196C2—1221no—
1197C2—4881no—
1198C2—2441no—
1199C2—2441no—
1200C2—2441no—
1201C2—2441no—
1202C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#534C4
socleC2×C61C22×#99
prime radical#534×D61C2
cosocleC2×C22⋊D61C24
hypercenter#534#6923
hypocenterC61C2×#2121
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. C2×D61⋊#100C2semidirect
2. C2×D61⋊#99C2semidirect
3. #21462077C2semidirect
4. #21462076C2semidirect
5. #21462075C2semidirect
6. #21462074C2semidirect
7. D61⋊#352C2semidirect
8. D61⋊AΣL(1,𝔽16)C2semidirect
15. D61⋊#100C22semidirect
17. C2×#14519837C22semidirect
22. D61⋊#99C22semidirect
23. C2×#14519835C22semidirect
24. #16840665C22semidirect
25. #16840664C22semidirect
26. #16840663C22semidirect
27. #16840662C22semidirect
28. C22×D4×D61C4semidirect
32. #16840323C4semidirect
35. #16840322C4semidirect
37. #16840321C4semidirect
42. #123×D61C4semidirect
47. #120×D61C4semidirect
49. C2×C22⋊C4×D61C4semidirect
50. C61×#534C4semidirect
74. C24×D61C2×C4semidirect
76. C22×D244C2×C4semidirect
78. C22×C22⋊D61C2×C4semidirect
79. C22×C22⋊D61C2×C4semidirect
105. C22×C4×D61C2×C4semidirect
112. #14519761C2×C4semidirect
115. #14519760C2×C4semidirect
122. #14519758C2×C4semidirect
123. #14519758C2×C4semidirect
143. #14519747C2×C4semidirect
146. #14519746C2×C4semidirect
153. #14519745C2×C4semidirect
154. #14519745C2×C4semidirect
157. C2×C22⋊Dic61C2×C4semidirect
165. C22⋊C4×D61C2×C4semidirect
166. C22⋊C4×D61C2×C4semidirect
167. C22⋊C4×D61C2×C4semidirect
168. C22⋊C4×D61C2×C4semidirect
170. C22×D4×C61C2×C4semidirect
172. #123×C61C2×C4semidirect
173. #123×C61C2×C4semidirect
177. #120×C61C2×C4semidirect
178. #120×C61C2×C4semidirect
179. C2×C22⋊C4×C61C2×C4semidirect
182. C24×C61C22×C4semidirect
206. C23×D61C22×C4semidirect
228. C22×C4×C61C22×C4semidirect
254. C22×Dic61C22×C4semidirect
331. C22⋊C4×C61C22×C4semidirect
332. C22⋊C4×C61C22×C4semidirect
338. C22⋊Dic61C22×C4semidirect
339. C22⋊Dic61C22×C4semidirect
610. D61#2121semidirect
625. #534#6923semidirect
652. C61C2×#2121semidirect
685. C22×D4C2×#6923semidirect
715. #123C2×#6923semidirect
716. #123C2×#6923semidirect
751. #120C2×#6923semidirect
752. #120C2×#6923semidirect
773. C2×C22⋊C4C2×#6923semidirect
811. C24C22×#6923semidirect
914. C22×C4C22×#6923semidirect
958. C22⋊C4C22×#6923semidirect
959. C22⋊C4C22×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1002
C2×D61⋊#992
#214620772
#214620762
#214620752
#214620742
D61⋊#3522
D61⋊AΣL(1,𝔽16)2
#534×D612
C2×#212161