Finite Group Databasebeta

← D61⋊#2120 #30623903

Subgroups — D61⋊#2120 #30623903

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#413C211yesmaximal, characteristic, complemented
2D61⋊#410C211yesmaximal, characteristic, complemented
3#21462073C212yesmaximal, complemented
4#21462072C212yesmaximal, complemented
5#21462071C212yesmaximal, complemented
6#21462070C212yesmaximal, complemented
7D61⋊#352C212yesmaximal, complemented
8D61⋊AΣL(1,𝔽16)C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C2×D61⋊M16—21no—
11C2×#14519856—21no—
12#16840749—21no—
13#16840749C2212yescomplemented
14#16840748—21no—
15#16840748C2212yescomplemented
16D61⋊#101—21no—
17D61⋊#100C2212yes—
18#16840743—21no—
19#16840742C2212yescomplemented
20#16840741—21no—
21#16840741C2212yescomplemented
22D61⋊#99—21no—
23D61⋊#99C2212yes—
24#16840665C2214yescomplemented
25#16840664C2214yescomplemented
26#16840663C2214yescomplemented
27#16840662C2214yescomplemented
28C2×#41×D61C2211yescharacteristic
29C23×C4×D61C411yescharacteristic, complemented
30#16840275—21no—
31#16840274C2211yescharacteristic
32#16840273C2211yescharacteristic
33#16840272—21no—
34#16840271—21no—
35#16840271—21no—
36#16840270C411yescharacteristic, complemented
37#16840270C2211yescharacteristic
38#16840269C411yescharacteristic, complemented
39#16840268C411yescharacteristic, complemented
40#16840268C2211yescharacteristic
41#123×D61C411yescharacteristic, complemented
42#123×D61C2211yescharacteristic
43C22⋊Q8×D61—21no—
44#121×D61—21no—
45#120×D61C411yescharacteristic, complemented
46#120×D61C2211yescharacteristic
47C4×D4×D61—21no—
48C4×D4×D61—21no—
49#117×D61C411yescharacteristic, complemented
50C61×#525C411yescharacteristic, complemented
51C2×#11758213—41no—
52D61⋊M16—22no—
53D61⋊M16—22no—
54D61⋊M16—41no—
55D61⋊M16—41no—
56C2×#11758217—22no—
57C2×D61⋊C8—41no—
58#14519856—22no—
59#14519856—22no—
60#14519856—41no—
61#14519856—41no—
62C2×C4⋊#6923—41no—
63C2×C22⋊#6923—22no—
64C2×C4×#6923—41no—
65#14519838—22no—
66#14519838—22no—
67#14519837—22no—
68#14519837C2314yes—
69#14519836—22no—
70#14519836—22no—
71#14519835—22no—
72#14519835C2314yes—
73C24×D61C2×C411yescharacteristic
74C2×#11758226D411yescharacteristic
75C2×#11758222D411yescharacteristic
76C2×#11758222D411yescharacteristic
77C2×#11758222C2311yescharacteristic
78C2×#11758224C2×C411yescharacteristic
79C2×#11758224D411yescharacteristic
80C2×#11758224C2311yescharacteristic
81#41×D61—41no—
82#41×D61—41no—
83#41×D61—41no—
84#41×D61—41no—
85C2×Q8×D61D411yescharacteristic
86C2×D4×D61—21no—
87C2×D4×D61—21no—
88C2×D4×D61C2×C411yescharacteristic
89C2×D4×D61D411yescharacteristic
90C2×D4×D61C2311yescharacteristic
91C23×Dic61C2×C411yescharacteristic, complemented
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61—41no—
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2×C411yescharacteristic
102C22×C4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61C2×C411yescharacteristic, complemented
104C22×C4×D61D411yescharacteristic
105C22×C4×D61D411yescharacteristic
106#14519762—21no—
107#14519762—21no—
108#14519761C2×C411yescharacteristic, complemented
109#14519761C2311yescharacteristic
110#14519760C2×C411yescharacteristic, complemented
111#14519760C2311yescharacteristic
112#14519759—21no—
113#14519759—21no—
114#14519758C2×C411yescharacteristic
115#14519758C2×C411yescharacteristic, complemented
116#14519757—21no—
117#14519756—21no—
118#14519755—21no—
119#14519755—21no—
120#14519754—21no—
121#14519754—21no—
122#14519753—21no—
123#14519752—21no—
124#14519751—21no—
125#14519750—21no—
126#14519750—21no—
127#14519749—21no—
128#14519749—21no—
129#14519748—21no—
130#14519747—21no—
131#14519747—21no—
132#14519747C2×C411yescharacteristic, complemented
133#14519747C2311yescharacteristic
134#14519746C2×C411yescharacteristic, complemented
135#14519746C2311yescharacteristic
136#14519745—21no—
137#14519745—21no—
138#14519745C2×C411yescharacteristic
139#14519745C2×C411yescharacteristic, complemented
140C4×D244—21no—
141C4×D244—21no—
142D4×Dic61—21no—
143D4×Dic61—21no—
144#14519739—21no—
145#14519739—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519736C2×C411yescharacteristic, complemented
155#14519735—21no—
156#14519734—21no—
157#14519733C2×C411yescharacteristic, complemented
158#14519733C2×C411yescharacteristic, complemented
159C4⋊C4×D61—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—21no—
166C22⋊C4×D61C2×C411yescharacteristic
167C22⋊C4×D61C2×C411yescharacteristic
168C42×D61—21no—
169C2×#41×C61C2×C411yescharacteristic
170C23×C4×C61C2×C411yescharacteristic, complemented
171#123×C61C2×C411yescharacteristic
172#123×C61C2×C411yescharacteristic, complemented
173C22⋊Q8×C61—21no—
174#121×C61—21no—
175#120×C61C2×C411yescharacteristic
176#120×C61C2×C411yescharacteristic, complemented
177C4×D4×C61—21no—
178C4×D4×C61—21no—
179#117×C61C2×C411yescharacteristic, complemented
180C24×C61C22×C411yescharacteristic
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—41no—
184C23×D61—41no—
185C23×D61—44no—
186C23×D61C22⋊C411yescharacteristic
187C23×D61C22×C411yescharacteristic
188C23×D61C22×C411yescharacteristic
189C23×D61C2×D411yescharacteristic
190C22×#6923—42no—
191#41×C61—41no—
192#41×C61—41no—
193C2×Q8×C61C22⋊C411yescharacteristic
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61C22⋊C411yescharacteristic
197C2×D4×C61C22×C411yescharacteristic
198C2×D4×C61C22×C411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—41no—
202C22×C4×C61—41no—
203C22×C4×C61C22⋊C411yescharacteristic
204C22×C4×C61C22⋊C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61C22⋊C411yescharacteristic
212C2×C22⋊D61C22⋊C411yescharacteristic
213C2×C22⋊D61C22×C411yescharacteristic
214C2×C22⋊D61C2×D411yescharacteristic
215C2×C22⋊D61C2×D411yescharacteristic
216C2×C22⋊D61C2411yescharacteristic
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—41no—
220C22×Dic61—41no—
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758226—41no—
226#11758226—41no—
227Q8×D61—41no—
228Q8×D61—41no—
229#11758224—41no—
230#11758224—41no—
231#11758224—41no—
232#11758224—41no—
233#11758224—41no—
234#11758224—41no—
235D4×D61—41no—
236D4×D61—41no—
237D4×D61—41no—
238D4×D61—41no—
239D4×D61—41no—
240D4×D61—41no—
241D4×D61—44no—
242D4×D61—44no—
243#11758222—41no—
244#11758222—41no—
245#11758222—41no—
246#11758222—41no—
247#11758222—41no—
248#11758222—41no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244C22⋊C411yescharacteristic
252C2×D244C2×D411yescharacteristic
253C2×D244C2×D411yescharacteristic
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61—42no—
277C2×C4×D61—42no—
278C2×C4×D61—42no—
279C2×C4×D61—42no—
280C2×C4×D61—41no—
281C2×C4×D61—41no—
282C2×C4×D61—41no—
283C2×C4×D61—41no—
284C2×C4×D61—41no—
285C2×C4×D61—41no—
286C2×C4×D61—41no—
287C2×C4×D61—41no—
288C2×C4×D61—41no—
289C2×C4×D61—41no—
290C2×C4×D61C22⋊C411yescharacteristic
291C2×C4×D61C22⋊C411yescharacteristic
292C2×C4×D61C22⋊C411yescharacteristic
293C2×C4×D61C22⋊C411yescharacteristic
294C2×C4×D61C22⋊C411yescharacteristic
295C2×C4×D61C22⋊C411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×C4×D61C2×D411yescharacteristic
299C2×C4×D61C2×D411yescharacteristic
300C2×Dic122C22⋊C411yescharacteristic
301C2×Dic122C2×D411yescharacteristic
302C2×Dic122C2×D411yescharacteristic
303C22⋊#6923—24no—
304C22⋊#6923—42no—
305#11758217—24no—
306#11758217—42no—
307C2×#92420—42no—
308C4⋊#6923—42no—
309C4⋊#6923—42no—
310C4×#6923—42no—
311C4×#6923—42no—
312#11758213—42no—
313#11758213—42no—
314D61⋊C8—42no—
315D61⋊C8—42no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61—21no—
318C4⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61C22×C411yescharacteristic
324C22⋊C4×C61C22×C411yescharacteristic
325C42×C61—21no—
326C22⋊Dic61—21no—
327C22⋊Dic61—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330C22⋊Dic61C22×C411yescharacteristic
331C22⋊Dic61C22×C411yescharacteristic
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—21no—
339#11758198—21no—
340#11758198—21no—
341#11758198—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196—21no—
349#11758196—21no—
350#11758196—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61—21no—
354C23×C61—21no—
355C23×C61—41no—
356C23×C61—42no—
357C23×C61C2×C22⋊C411yescharacteristic
358C23×C61C2×C22⋊C411yescharacteristic
359C23×C61C23×C411yescharacteristic
360C22×D61—24no—
361C22×D61—21no—
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—21no—
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—42no—
369C22×D61—42no—
370C22×D61—42no—
371C22×D61—42no—
372C22×D61—42no—
373C22×D61—42no—
374C22×D61—42no—
375C22×D61—42no—
376C22×D61—44no—
377C22×D61—44no—
378C22×D61—44no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—44no—
383C22×D61C2×C22⋊C411yescharacteristic
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C22×D411yescharacteristic
387C2×#6923—44no—
388C2×#6923—84no—
389Q8×C61—41no—
390D4×C61—41no—
391D4×C61—41no—
392D4×C61—41no—
393D4×C61—42no—
394D4×C61—42no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—42no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61C2×C22⋊C411yescharacteristic
409C2×C4×C61C2×C22⋊C411yescharacteristic
410C2×C4×C61C2×C22⋊C411yescharacteristic
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C22⋊D61—41no—
413C22⋊D61—41no—
414C22⋊D61—41no—
415C22⋊D61—41no—
416C22⋊D61—41no—
417C22⋊D61—41no—
418C22⋊D61—42no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C22⋊D61—42no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—42no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C22×D411yescharacteristic
439D244—41no—
440D244—41no—
441D244—41no—
442D244—42no—
443D244—42no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—21no—
457C4×D61—21no—
458C4×D61—21no—
459C4×D61—21no—
460C4×D61—21no—
461C4×D61—21no—
462C4×D61—42no—
463C4×D61—42no—
464C4×D61—42no—
465C4×D61—42no—
466C4×D61—42no—
467C4×D61—41no—
468C4×D61—41no—
469C4×D61—41no—
470C4×D61—41no—
471C4×D61—41no—
472C4×D61—41no—
473C4×D61#9911yescharacteristic
474C4×D61#9911yescharacteristic
475C4×D61#9911yescharacteristic
476C4×D61#9911yescharacteristic
477Dic122—41no—
478Dic122—41no—
479Dic122—41no—
480#92420—44no—
481C2×#2120—611nomaximal, Sylow
482C22×C61—22no—
483C22×C61—21no—
484C22×C61—21no—
485C22×C61—21no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—41no—
493C22×C61C22×C22⋊C411yescharacteristic
494C2×D61—22no—
495C2×D61—22no—
496C2×D61—21no—
497C2×D61—21no—
498C2×D61—21no—
499C2×D61—44no—
500C2×D61—42no—
501C2×D61—41no—
502C2×D61—48no—
503C2×D61—42no—
504C2×D61—41no—
505C2×D61—42no—
506C2×D61—42no—
507C2×D61—44no—
508C2×D61—42no—
509C2×D61—41no—
510C2×D61—41no—
511C2×D61—41no—
512C2×D61—42no—
513C2×D61—81no—
514C2×D61—81no—
515C2×D61C2×#9911yescharacteristic
516C2×D61C2×#9911yescharacteristic
517#6923—84no—
518C4×C61—21no—
519C4×C61—21no—
520C4×C61—21no—
521C4×C61—41no—
522C4×C61—41no—
523C4×C61—41no—
524C4×C61C2×#9911yescharacteristic
525C4×C61C2×#9911yescharacteristic
526Dic61—21no—
527Dic61—21no—
528Dic61—21no—
529Dic61—41no—
530Dic61—41no—
531Dic61—41no—
532Dic61C2×#9911yescharacteristic
533Dic61C2×#9911yescharacteristic
534C2×#525—611no—
535C2×#413—611no—
536C2×#410—611no—
537#2120—612no—
538#2120—612no—
539#2120—612no—
540#2120—612no—
541C2×#352—612no—
542C2×AΣL(1,𝔽16)—612no—
543C2×C61—21no—
544C2×C61—42no—
545C2×C61—41no—
546C2×C61—41no—
547C2×C61—41no—
548C2×C61C22×#9911yescharacteristic
549D61—21no—
550D61—41no—
551D61—42no—
552D61—41no—
553D61—41no—
554D61#212012yescomplemented
555C22×#41—611no—
556C24×C4—611no—
557C22×M16—1221no—
558#525—611no—
559#525—611no—
560#525—611no—
561#525—611no—
562#525—611no—
563#525—611no—
564#525—611no—
565#525—1221no—
566#525—1221no—
567#525—1221no—
568#525—1221no—
569#525#692311yescharacteristic, complemented
570C2×#123—611no—
571C2×#123—611no—
572C2×C22⋊Q8—1221no—
573C2×#121—1221no—
574C2×#120—611no—
575C2×#120—611no—
576C2×C4×D4—1221no—
577C2×C4×D4—1221no—
578C2×#117—611no—
579C2×#117—1221no—
580#413—612no—
581#413—612no—
582#413—1221no—
583#413—1221no—
584C2×#101—1221no—
585C2×#100—612no—
586#410—612no—
587#410—612no—
588#410—1221no—
589#410—1221no—
590C2×#99—612no—
591C2×#99—1221no—
592#352—614no—
593#352—614no—
594AΣL(1,𝔽16)—614no—
595AΣL(1,𝔽16)—614no—
596C61C2×#212011yescharacteristic, complemented, Sylow
597C25—611no—
598C2×#41—611no—
599C2×#41—611no—
600C2×#41—611no—
601C2×#41—611no—
602C2×#41—611no—
603C2×#41—611no—
604C2×#41—611no—
605C2×#41—2441no—
606C2×#41—2441no—
607C2×#41—2441no—
608C2×#41—2441no—
609C2×#41C2×#692311yescharacteristic
610C22×Q8—611no—
611C22×D4—611no—
612C22×D4—611no—
613C22×D4—611no—
614C22×D4—1221no—
615C22×D4—1221no—
616C23×C4—611no—
617C23×C4—611no—
618C23×C4—611no—
619C23×C4—611no—
620C23×C4—611no—
621C23×C4—611no—
622C23×C4—611no—
623C23×C4—1221no—
624C23×C4—1221no—
625C23×C4—1221no—
626C23×C4—1221no—
627C23×C4—2441no—
628C23×C4—2441no—
629C23×C4—2441no—
630C23×C4—2441no—
631C23×C4C2×#692311yescharacteristic, complemented
632C2×M16—1222no—
633C2×M16—1222no—
634C2×M16—1222no—
635C2×M16—2441no—
636C2×M16—2441no—
637C2×M16—2441no—
638C22×C8—2441no—
639#123—611no—
640#123—611no—
641#123—611no—
642#123—611no—
643#123—611no—
644#123—611no—
645#123—1221no—
646#123—1221no—
647#123—1221no—
648#123—1221no—
649#123C2×#692311yescharacteristic
650#123C2×#692311yescharacteristic, complemented
651C22⋊Q8—21no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658C22⋊Q8—1221no—
659#121—21no—
660#121—1221no—
661#121—1221no—
662#121—1221no—
663#121—1221no—
664#121—1221no—
665#121—1221no—
666#121—1221no—
667#120—611no—
668#120—611no—
669#120—611no—
670#120—611no—
671#120—611no—
672#120—611no—
673#120—1221no—
674#120—1221no—
675#120—1221no—
676#120—1221no—
677#120C2×#692311yescharacteristic
678#120C2×#692311yescharacteristic, complemented
679C4×D4—21no—
680C4×D4—21no—
681C4×D4—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690C4×D4—1221no—
691C4×D4—1221no—
692C4×D4—1221no—
693C4×D4—1221no—
694C4×D4—1221no—
695#117—611no—
696#117—611no—
697#117—611no—
698#117—1221no—
699#117—1221no—
700#117—1222no—
701#117—1222no—
702#117—2441no—
703#117—2441no—
704#117C2×#692311yescharacteristic, complemented
705C2×C4⋊C4—1221no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4—2441no—
709C2×C22⋊C4—611no—
710C2×C22⋊C4—611no—
711C2×C22⋊C4—1221no—
712C2×C22⋊C4—1221no—
713C2×C22⋊C4—1221no—
714C2×C22⋊C4—1221no—
715C2×C22⋊C4—1222no—
716C2×C42—1221no—
717C2×C42—2441no—
718#101—1222no—
719#101—1222no—
720#100—614no—
721#100—1222no—
722#99—614no—
723#99—1222no—
724#99—1222no—
725#99—1222no—
726C24—611no—
727C24—611no—
728C24—611no—
729C24—611no—
730C24—1221no—
731C24—1221no—
732C24—2441no—
733C24—2441no—
734C24—2444no—
735C24C22×#692311yescharacteristic
736#41—41no—
737#41—41no—
738#41—2441no—
739#41—2441no—
740#41—2441no—
741#41—2441no—
742#41—2441no—
743#41—2441no—
744#41—2441no—
745#41—2441no—
746#41—2441no—
747#41—2441no—
748#41—2441no—
749#41—2441no—
750#41—2441no—
751#41—2441no—
752C2×Q8—611no—
753C2×Q8—611no—
754C2×Q8—611no—
755C2×Q8—2441no—
756C2×Q8—2441no—
757C2×Q8C22⋊#692311yescharacteristic
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—611no—
761C2×D4—611no—
762C2×D4—611no—
763C2×D4—611no—
764C2×D4—611no—
765C2×D4—611no—
766C2×D4—611no—
767C2×D4—611no—
768C2×D4—611no—
769C2×D4—1221no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—2441no—
776C2×D4—2441no—
777C2×D4—2441no—
778C2×D4—2441no—
779C2×D4—2441no—
780C2×D4—2441no—
781C2×D4—2444no—
782C2×D4—2444no—
783C2×D4C22⋊#692311yescharacteristic
784C2×D4C22×#692311yescharacteristic
785C2×D4C22×#692311yescharacteristic
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—2441no—
827C22×C4—2441no—
828C22×C4—2441no—
829C22×C4—2441no—
830C22×C4—2441no—
831C22×C4—2441no—
832C22×C4—2442no—
833C22×C4—2442no—
834C22×C4—2442no—
835C22×C4—2442no—
836C22×C4—2442no—
837C22×C4—2442no—
838C22×C4—2441no—
839C22×C4—2441no—
840C22×C4—2441no—
841C22×C4—2441no—
842C22×C4—2441no—
843C22×C4—2441no—
844C22×C4—2442no—
845C22×C4C22⋊#692311yescharacteristic
846C22×C4C22⋊#692311yescharacteristic
847C22×C4C22×#692311yescharacteristic
848C22×C4C22×#692311yescharacteristic
849M16—1224no—
850M16—2442no—
851M16—2442no—
852M16—2442no—
853C2×C8—2442no—
854C2×C8—2442no—
855C2×C8—2442no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4—1221no—
868C4⋊C4—2442no—
869C4⋊C4—2442no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—611no—
875C22⋊C4—611no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—1221no—
886C22⋊C4—1221no—
887C22⋊C4—1221no—
888C22⋊C4—1221no—
889C22⋊C4—1221no—
890C22⋊C4—1224no—
891C22⋊C4—2442no—
892C22⋊C4C22×#692311yescharacteristic
893C22⋊C4C22×#692311yescharacteristic
894C42—21no—
895C42—1221no—
896C42—1221no—
897C42—1221no—
898C42—2442no—
899C42—2442no—
900C23—21no—
901C23—41no—
902C23—42no—
903C23—611no—
904C23—611no—
905C23—611no—
906C23—611no—
907C23—1221no—
908C23—1221no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1224no—
914C23—1221no—
915C23—2441no—
916C23—2442no—
917C23—2441no—
918C23—2441no—
919C23—2442no—
920C23—2442no—
921C23—2442no—
922C23—2442no—
923C23—2442no—
924C23—2442no—
925C23—2442no—
926C23—2444no—
927C23—2444no—
928C23—2444no—
929C23—2444no—
930C23C2×C22⋊#692311yescharacteristic
931C23C2×C22⋊#692311yescharacteristic
932C23C23×#692311yescharacteristic
933Q8—41no—
934Q8—2441no—
935Q8—2441no—
936Q8—2441no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—42no—
941D4—42no—
942D4—2441no—
943D4—2441no—
944D4—2441no—
945D4—2442no—
946D4—2442no—
947D4—2441no—
948D4—2441no—
949D4—2441no—
950D4—2441no—
951D4—2441no—
952D4—2441no—
953D4—2442no—
954D4—2442no—
955D4—2442no—
956D4—2442no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—611no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—611no—
977C2×C4—611no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1221no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—1221no—
987C2×C4—1221no—
988C2×C4—1221no—
989C2×C4—1221no—
990C2×C4—1221no—
991C2×C4—1221no—
992C2×C4—1221no—
993C2×C4—1221no—
994C2×C4—1221no—
995C2×C4—1221no—
996C2×C4—1221no—
997C2×C4—1221no—
998C2×C4—1221no—
999C2×C4—1221no—
1000C2×C4—1221no—
1001C2×C4—1221no—
1002C2×C4—1221no—
1003C2×C4—1221no—
1004C2×C4—1221no—
1005C2×C4—4884no—
1006C2×C4—2442no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2442no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2442no—
1013C2×C4—2442no—
1014C2×C4—2442no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2442no—
1018C2×C4—2444no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4C2×C22⋊#692311yescharacteristic
1023C2×C4C2×C22⋊#692311yescharacteristic
1024C2×C4C2×C22⋊#692311yescharacteristic
1025C2×C4C2×C22⋊#692311yescharacteristic
1026C8—2444no—
1027C22—22no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—41no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22—42no—
1036C22—42no—
1037C22—41no—
1038C22—611no—
1039C22—611no—
1040C22—1222no—
1041C22—1222no—
1042C22—1221no—
1043C22—1221no—
1044C22—1221no—
1045C22—4881no—
1046C22—4881no—
1047C22—2441no—
1048C22—2441no—
1049C22—2441no—
1050C22—2441no—
1051C22—2442no—
1052C22—2442no—
1053C22—2442no—
1054C22—2444no—
1055C22—2442no—
1056C22—2444no—
1057C22—2442no—
1058C22—2442no—
1059C22—2448no—
1060C22—2441no—
1061C22C22×C22⋊#692311yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—611no—
1069C4—611no—
1070C4—1221no—
1071C4—1221no—
1072C4—1221no—
1073C4—4884no—
1074C4—2441no—
1075C4—2441no—
1076C4—2441no—
1077C4D61⋊#9911yescharacteristic
1078C4D61⋊#9911yescharacteristic
1079C2—21no—
1080C2—42no—
1081C2—41no—
1082C2—41no—
1083C2—41no—
1084C2—612no—
1085C2—1221no—
1086C2—2441no—
1087C2—2441no—
1088C2—2442no—
1089C2—2441no—
1090C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#525C4
socleC2×C61C22×#99
prime radical#525×D61C2
cosocleC2×C22⋊D61C24
hypercenter#525#6923
hypocenterC61C2×#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #525

Complements

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

NH ≅ G/Ntype
1. D61⋊#413C2semidirect
2. D61⋊#410C2semidirect
3. #21462073C2semidirect
4. #21462072C2semidirect
5. #21462071C2semidirect
6. #21462070C2semidirect
7. D61⋊#352C2semidirect
8. D61⋊AΣL(1,𝔽16)C2semidirect
13. #16840749C22semidirect
15. #16840748C22semidirect
19. #16840742C22semidirect
21. #16840741C22semidirect
24. #16840665C22semidirect
25. #16840664C22semidirect
26. #16840663C22semidirect
27. #16840662C22semidirect
29. C23×C4×D61C4semidirect
36. #16840270C4semidirect
38. #16840269C4semidirect
39. #16840268C4semidirect
41. #123×D61C4semidirect
45. #120×D61C4semidirect
49. #117×D61C4semidirect
50. C61×#525C4semidirect
91. C23×Dic61C2×C4semidirect
102. C22×C4×D61C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
108. #14519761C2×C4semidirect
110. #14519760C2×C4semidirect
115. #14519758C2×C4semidirect
132. #14519747C2×C4semidirect
134. #14519746C2×C4semidirect
139. #14519745C2×C4semidirect
154. #14519736C2×C4semidirect
157. #14519733C2×C4semidirect
158. #14519733C2×C4semidirect
170. C23×C4×C61C2×C4semidirect
172. #123×C61C2×C4semidirect
176. #120×C61C2×C4semidirect
179. #117×C61C2×C4semidirect
554. D61#2120semidirect
569. #525#6923semidirect
596. C61C2×#2120semidirect
631. C23×C4C2×#6923semidirect
650. #123C2×#6923semidirect
678. #120C2×#6923semidirect
704. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4132
D61⋊#4102
#214620732
#214620722
#214620712
#214620702
D61⋊#3522
D61⋊AΣL(1,𝔽16)2
#525×D612
C2×#212061