Finite Group Databasebeta

← D61⋊#1468 #30610042

Subgroups — D61⋊#1468 #30610042

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic, complemented
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#21461087C212yesmaximal, complemented
4#21461086C212yesmaximal, complemented
5#21461085C212yesmaximal, complemented
6#21461084C212yesmaximal, complemented
7D61⋊#324C212yesmaximal, complemented
8D61⋊#323C212yesmaximal, complemented
9C2×#123×D61C211yesmaximal, characteristic
10C2×D61⋊M16—21no—
11C22×D61⋊C8—21no—
12#16840734—21no—
13#16840733—21no—
14#16840733C2212yescomplemented
15#16840732C2212yescomplemented
16C2×#14519834—21no—
17D61⋊(C22⋊C8)—21no—
18D61⋊(C22⋊C8)—21no—
19D61⋊(C22⋊C8)—21no—
20D61⋊(C22⋊C8)C2212yes—
21D61⋊(C22⋊C8)C2212yes—
22D61⋊(C22⋊C8)C2212yescomplemented
23C2×C22⋊#92420C2212yescomplemented
24#16840608C2214yescomplemented
25#16840607C2214yescomplemented
26#16840606C2214yescomplemented
27#16840605C2214yescomplemented
28C22×D4×D61C411yescharacteristic
29C23×C4×D61C2211yescharacteristic
30C2×#14519762C411yescharacteristic
31C2×#14519762C2211yescharacteristic
32C2×#14519761C2211yescharacteristic
33C2×#14519760C411yescharacteristic
34C2×#14519759C411yescharacteristic
35C2×#14519759C2211yescharacteristic
36C2×#14519758C2211yescharacteristic
37#123×D61—21no—
38#123×D61—21no—
39#123×D61—21no—
40#123×D61—21no—
41#123×D61—21no—
42#123×D61—21no—
43#123×D61—21no—
44#123×D61—21no—
45C2×C4⋊C4×D61C411yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C22⋊C4×D61C411yescharacteristic
48C2×C22⋊C4×D61C411yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×#123×C61C411yescharacteristic
51C2×#11758213—22no—
52D61⋊M16—44no—
53C2×#11758217—22no—
54C2×D61⋊C8—22no—
55C2×D61⋊C8—22no—
56C2×D61⋊C8—22no—
57C2×D61⋊C8—44no—
58C22×#92420—22no—
59#14519834—22no—
60#14519834—22no—
61#14519834—22no—
62#14519834—22no—
63C22⋊#92420—22no—
64C22⋊#92420—22no—
65C22⋊#92420C2314yes—
66C22⋊#92420C2314yes—
67C24×D61C2×C411yescharacteristic
68C24×D61C2×C411yescharacteristic
69C22×D244C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C2×D4×D61—21no—
73C2×D4×D61—21no—
74C2×D4×D61—21no—
75C2×D4×D61—21no—
76C2×D4×D61—44no—
77C23×Dic61C2311yescharacteristic
78C22×C4×D61—44no—
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61C2311yescharacteristic
93C22×C4×D61C2311yescharacteristic
94#14519762—21no—
95#14519762—21no—
96#14519762—21no—
97#14519762—21no—
98#14519762—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519761—21no—
103#14519761—21no—
104#14519761—21no—
105#14519761—21no—
106#14519760—21no—
107#14519760—21no—
108#14519760—21no—
109#14519760—21no—
110#14519759—21no—
111#14519759—21no—
112#14519759—21no—
113#14519759—21no—
114#14519759—21no—
115#14519759—21no—
116#14519759—21no—
117#14519759—21no—
118#14519758—21no—
119#14519758—21no—
120#14519758—21no—
121#14519758—21no—
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2311yescharacteristic
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C2×C22⋊Dic61C2×C411yescharacteristic
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×C22⋊Dic61C2311yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2311yescharacteristic
145C22⋊C4×D61—21no—
146C22⋊C4×D61—21no—
147C22⋊C4×D61—21no—
148C22⋊C4×D61—21no—
149C22⋊C4×D61—21no—
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22×D4×C61C2×C411yescharacteristic
158C23×C4×C61C2×C411yescharacteristic
159#123×C61—21no—
160#123×C61—21no—
161#123×C61—21no—
162#123×C61—21no—
163C2×C4⋊C4×C61C2×C411yescharacteristic
164C2×C4⋊C4×C61C2×C411yescharacteristic
165C2×C22⋊C4×C61C2×C411yescharacteristic
166C2×C22⋊C4×C61C2×C411yescharacteristic
167C2×C22⋊C4×C61C2×C411yescharacteristic
168C24×C61C22×C411yescharacteristic
169C24×C61C22×C411yescharacteristic
170C23×D61—24no—
171C23×D61—24no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—24no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—42no—
178C23×D61C22⋊C411yescharacteristic
179C23×D61C22⋊C411yescharacteristic
180C23×D61C22⋊C411yescharacteristic
181C23×D61C22⋊C411yescharacteristic
182C23×D61C22×C411yescharacteristic
183C23×D61C22×C411yescharacteristic
184C23×D61C22×C411yescharacteristic
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—42no—
188C22×C4×C61—42no—
189C22×C4×C61C22⋊C411yescharacteristic
190C22×C4×C61C22⋊C411yescharacteristic
191C22×C4×C61C22⋊C411yescharacteristic
192C22×C4×C61C22⋊C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C22×Dic61—42no—
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C22×C411yescharacteristic
208C22×Dic61C22×C411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2411yescharacteristic
214D4×D61—44no—
215D4×D61—44no—
216D4×D61—44no—
217D4×D61—44no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—42no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—24no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61C22⋊C411yescharacteristic
243C2×C4×D61C22⋊C411yescharacteristic
244C2×C4×D61C22⋊C411yescharacteristic
245C2×C4×D61C22⋊C411yescharacteristic
246C2×C4×D61C22⋊C411yescharacteristic
247C2×C4×D61C22⋊C411yescharacteristic
248C2×C4×D61C22⋊C411yescharacteristic
249C2×C4×D61C22⋊C411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258#11758217—44no—
259C2×#92420—24no—
260C2×#92420—24no—
261C2×#92420—44no—
262#11758213—44no—
263D61⋊C8—44no—
264D61⋊C8—44no—
265D61⋊C8—44no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—21no—
309C23×C61—22no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61C2×C22⋊C411yescharacteristic
314C23×C61C2×C22⋊C411yescharacteristic
315C23×C61C23×C411yescharacteristic
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—21no—
330C22×D61—22no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—416no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—88no—
344C22×D61#9914yes—
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
347C22×D61C2×C22⋊C411yescharacteristic
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61#13114yes—
350D4×C61—42no—
351D4×C61—42no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—22no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C22⋊D61—42no—
369C22⋊D61—42no—
370C22⋊D61—42no—
371C22⋊D61—42no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—22no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C22×D411yescharacteristic
387C2×Dic61C22×D411yescharacteristic
388D244—42no—
389D244—42no—
390C4×D61—22no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—41no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—42no—
407C4×D61—42no—
408C4×D61—42no—
409C4×D61—42no—
410C4×D61—42no—
411C4×D61—42no—
412#92420—44no—
413#92420—44no—
414C2×#1468—611nomaximal, Sylow
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—44no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—82no—
427C22×C61C2×#9912yes—
428C22×C61C22×C22⋊C411yescharacteristic
429C22×C61C2×#13112yes—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—28no—
435C2×D61—28no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—44no—
440C2×D61—44no—
441C2×D61—44no—
442C2×D61—44no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—84no—
447C2×D61—84no—
448C2×D61—82no—
449C2×D61#40812yes—
450C2×D61#40812yes—
451C2×D61C2×#9912yes—
452C2×D61C2×#9912yes—
453C2×D61#41312yes—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61—41no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—41no—
466Dic61—41no—
467Dic61—41no—
468C22×#123—611no—
469C2×#407—611no—
470C22×C22⋊C8—611no—
471#1468—612no—
472#1468—612no—
473#1468—612no—
474#1468—612no—
475C2×#324—612no—
476C2×#323—612no—
477C2×C61—22no—
478C2×C61—22no—
479C2×C61—41no—
480C2×C61—81no—
481C2×C61C2×#40811yescharacteristic
482C2×C61C22×#9911yescharacteristic
483C2×C61C2×#41311yescharacteristic
484D61—22no—
485D61—22no—
486D61—41no—
487D61—81no—
488D61#146814yescomplemented
489C23×D4—611no—
490C24×C4—611no—
491C22×M16—1221no—
492C23×C8—1221no—
493C2×#123—611no—
494C2×#123—611no—
495C2×#123—611no—
496C2×#123—611no—
497C2×#123—611no—
498C2×#123—611no—
499C2×#123—611no—
500C2×#123—1221no—
501C2×#123—1221no—
502C2×#123—1221no—
503C2×#123—1221no—
504C2×#123—1221no—
505C2×#123—1221no—
506C2×#123—1221no—
507C2×#123—1221no—
508C2×#123#692311yescharacteristic
509C22×C4⋊C4—611no—
510C22×C4⋊C4—611no—
511C22×C22⋊C4—611no—
512C22×C22⋊C4—611no—
513C22×C22⋊C4—611no—
514#407—612no—
515#407—612no—
516#407—1221no—
517#407—1221no—
518C2×C22⋊C8—612no—
519C2×C22⋊C8—612no—
520C2×C22⋊C8—612no—
521C2×C22⋊C8—612no—
522C2×C22⋊C8—1221no—
523C2×C22⋊C8—1221no—
524C2×C22⋊C8—1221no—
525C2×C22⋊C8—1221no—
526#324—614no—
527#324—614no—
528#323—614no—
529#323—614no—
530C61C2×#146811yescharacteristic, complemented, Sylow
531C25—611no—
532C25—611no—
533C22×D4—611no—
534C22×D4—611no—
535C22×D4—611no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—2444no—
541C22×D4C2×#692311yescharacteristic
542C23×C4—611no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—2444no—
559C23×C4C2×#692311yescharacteristic
560C2×M16—1222no—
561C2×M16—1222no—
562C2×M16—2444no—
563C22×C8—1222no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—1222no—
567C22×C8—2444no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—1221no—
573#123—1221no—
574#123—1221no—
575#123—1221no—
576#123—1221no—
577#123—1221no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4C2×#692311yescharacteristic
615C2×C4⋊C4C2×#692311yescharacteristic
616C2×C22⋊C4—611no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4C2×#692311yescharacteristic
638C2×C22⋊C4C2×#692311yescharacteristic
639C2×C22⋊C4C2×#692311yescharacteristic
640C22⋊C8—614no—
641C22⋊C8—614no—
642C22⋊C8—1222no—
643C22⋊C8—1222no—
644C22⋊C8—1222no—
645C22⋊C8—1222no—
646C22⋊C8—1222no—
647C22⋊C8—1222no—
648C24—611no—
649C24—611no—
650C24—611no—
651C24—611no—
652C24—611no—
653C24—611no—
654C24—611no—
655C24—1224no—
656C24—1224no—
657C24—1224no—
658C24—1221no—
659C24—1221no—
660C24—2442no—
661C24—2442no—
662C24—2442no—
663C24C22×#692311yescharacteristic
664C24C22×#692311yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—42no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—2442no—
675C2×D4—2444no—
676C2×D4—2444no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2442no—
680C2×D4—2442no—
681C22×C4—42no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—1224no—
708C22×C4—1224no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1224no—
716C22×C4—2442no—
717C22×C4—2442no—
718C22×C4—2442no—
719C22×C4—2442no—
720C22×C4—2442no—
721C22×C4—2442no—
722C22×C4—2442no—
723C22×C4—2442no—
724C22×C4—2442no—
725C22×C4—2442no—
726C22×C4—2442no—
727C22×C4—2442no—
728C22×C4—2442no—
729C22×C4C22⋊#692311yescharacteristic
730C22×C4C22⋊#692311yescharacteristic
731C22×C4C22⋊#692311yescharacteristic
732C22×C4C22⋊#692311yescharacteristic
733C22×C4C22×#692311yescharacteristic
734C22×C4C22×#692311yescharacteristic
735C22×C4C22×#692311yescharacteristic
736C22×C4C22×#692311yescharacteristic
737C22×C4C22×#692311yescharacteristic
738M16—2444no—
739M16—2444no—
740C2×C8—1224no—
741C2×C8—1224no—
742C2×C8—2444no—
743C2×C8—2444no—
744C2×C8—2444no—
745C2×C8—2444no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C23—22no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—611no—
794C23—614no—
795C23—611no—
796C23—611no—
797C23—614no—
798C23—611no—
799C23—1222no—
800C23—1222no—
801C23—1222no—
802C23—1222no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—1222no—
810C23—1222no—
811C23—1222no—
812C23—1222no—
813C23—1221no—
814C23—4888no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2442no—
821C23—2442no—
822C23—2442no—
823C23—2442no—
824C23—24416no—
825C23—2442no—
826C23—2442no—
827C23C2×C22⋊#692311yescharacteristic
828C23C2×C22⋊#692311yescharacteristic
829C23C23×#692311yescharacteristic
830D4—42no—
831D4—42no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4—2442no—
836D4—2442no—
837D4—2442no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1222no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2442no—
877C2×C4—2442no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4C2×C22⋊#692311yescharacteristic
889C2×C4C2×C22⋊#692311yescharacteristic
890C2×C4C2×C22⋊#692311yescharacteristic
891C2×C4C2×C22⋊#692311yescharacteristic
892C8—2444no—
893C8—2444no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—44no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—82no—
906C22—612no—
907C22—612no—
908C22—612no—
909C22—612no—
910C22—612no—
911C22—1228no—
912C22—1228no—
913C22—1221no—
914C22—1221no—
915C22—1221no—
916C22—1221no—
917C22—1221no—
918C22—1221no—
919C22—1221no—
920C22—4882no—
921C22—4884no—
922C22—4884no—
923C22—2444no—
924C22—2444no—
925C22—2444no—
926C22—2444no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22D61⋊#9912yes—
931C22C22×C22⋊#692311yescharacteristic
932C22D61⋊#13112yes—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—1221no—
941C4—1221no—
942C4—1221no—
943C4—1221no—
944C4—2441no—
945C4—2441no—
946C4—2441no—
947C2—22no—
948C2—22no—
949C2—41no—
950C2—81no—
951C2—614no—
952C2—1222no—
953C2—1222no—
954C2—4881no—
955C2—2441no—
956C2D61⋊#40811yescharacteristic
957C2C2×D61⋊#9911yescharacteristic
958C2D61⋊#41311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61C2×#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. D61⋊#407C2semidirect
2. C2×D61⋊(C22⋊C8)C2semidirect
3. #21461087C2semidirect
4. #21461086C2semidirect
5. #21461085C2semidirect
6. #21461084C2semidirect
7. D61⋊#324C2semidirect
8. D61⋊#323C2semidirect
14. #16840733C22semidirect
15. #16840732C22semidirect
22. D61⋊(C22⋊C8)C22semidirect
23. C2×C22⋊#92420C22semidirect
24. #16840608C22semidirect
25. #16840607C22semidirect
26. #16840606C22semidirect
27. #16840605C22semidirect
488. D61#1468semidirect
530. C61C2×#1468semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×D61⋊(C22⋊C8)2
#214610872
#214610862
#214610852
#214610842
D61⋊#3242
D61⋊#3232
C2×#123×D612
C2×#146861