Finite Group Databasebeta

← D61⋊#1465 #30609955

Subgroups — D61⋊#1465 #30609955

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C212yesmaximal, complemented
2#21461077C212yesmaximal, complemented
3#21461076C212yesmaximal, complemented
4#21461075C212yesmaximal, complemented
5#21461074C212yesmaximal, complemented
6D61⋊#324C212yesmaximal, complemented
7D61⋊#323C212yesmaximal, complemented
8C2×C4×D4×D61C211yesmaximal, characteristic
9C2×D61⋊M16—22no—
10#16840734—22no—
11#16840733—22no—
12#16840733C2214yescomplemented
13#16840732C2214yescomplemented
14D61⋊(C22⋊C8)—22no—
15D61⋊(C22⋊C8)C2214yes—
16#16840608C2214yescomplemented
17#16840607C2214yescomplemented
18#16840606C2214yescomplemented
19#16840605C2214yescomplemented
20C22×D4×D61C411yescharacteristic
21C23×C4×D61C411yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×#14519739C411yescharacteristic
26C2×C4×C22⋊D61C411yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737C411yescharacteristic
29C2×#14519737C2211yescharacteristic
30C4×D4×D61—22no—
31C4×D4×D61—22no—
32C4×D4×D61—22no—
33C4×D4×D61—22no—
34C2×C4⋊C4×D61C2211yescharacteristic
35C2×C22⋊C4×D61C411yescharacteristic
36C2×C22⋊C4×D61C2211yescharacteristic
37C2×C42×D61C411yescharacteristic
38C2×C4×D4×C61C411yescharacteristic
39C2×#11758213—24no—
40D61⋊M16—48no—
41C2×#11758217—24no—
42C2×D61⋊C8—24no—
43#14519834—24no—
44#14519834—24no—
45C22⋊#92420—24no—
46C22⋊#92420C2318yes—
47C24×D61C2×C411yescharacteristic
48C24×D61C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61C2×C411yescharacteristic
51C22×C22⋊D61C2×C411yescharacteristic
52C2×D4×D61—22no—
53C2×D4×D61—22no—
54C2×D4×D61—24no—
55C2×D4×D61—24no—
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61—44no—
63C22×C4×D61—44no—
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61D412yes—
72C22×C4×D61D412yes—
73C22×C4×D61D412yes—
74C22×C4×D61D412yes—
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C4×D244—22no—
78C4×D244—22no—
79D4×Dic61—22no—
80D4×Dic61—22no—
81#14519739—22no—
82#14519739—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87#14519737—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2311yescharacteristic
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2311yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2311yescharacteristic
102C22⋊C4×D61—22no—
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C42×D61—21no—
110C42×D61—21no—
111C42×D61—21no—
112C42×D61—21no—
113C22×D4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C23×C4×C61C2×C411yescharacteristic
116C4×D4×C61—22no—
117C4×D4×C61—22no—
118C2×C4⋊C4×C61C2×C411yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2×C411yescharacteristic
121C2×C42×C61C2×C411yescharacteristic
122C24×C61C22×C411yescharacteristic
123C24×C61C22×C411yescharacteristic
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—42no—
130C23×D61—42no—
131C23×D61—42no—
132C23×D61—42no—
133C23×D61C22⋊C412yes—
134C23×D61C22⋊C412yes—
135C23×D61M1614yescomplemented
136C23×D61C22×C411yescharacteristic
137C23×D61C22×C411yescharacteristic
138C23×D61C22×C411yescharacteristic
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61C22⋊C412yes—
147C22×C4×C61C22⋊C412yes—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C2×D412yes—
168C22×Dic61C2×D412yes—
169C22×Dic61C2411yescharacteristic
170D4×D61—216no—
171D4×D61—216no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—22no—
178C2×C4×D61—24no—
179C2×C4×D61—28no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—42no—
189C2×C4×D61—44no—
190C2×C4×D61—44no—
191C2×C4×D61—42no—
192C2×C4×D61—44no—
193C2×C4×D61—42no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—44no—
197C2×C4×D61—44no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C412yes—
206C2×C4×D61C22⋊C412yes—
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61M1614yescomplemented
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×D412yes—
211C2×C4×D61C2×D412yes—
212C2×C4×D61C2×D412yes—
213#11758217—48no—
214C2×#92420—28no—
215#11758213—48no—
216D61⋊C8—48no—
217C4⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C42×C61—21no—
221C42×C61—21no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228C4⋊Dic61—22no—
229#11758196—22no—
230#11758196—22no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61C2×C22⋊C412yes—
246C23×C61C2×M1612yescomplemented
247C23×C61C23×C411yescharacteristic
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—24no—
259C22×D61—24no—
260C22×D61—42no—
261C22×D61—41no—
262C22×D61—42no—
263C22×D61—41no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—48no—
267C22×D61—48no—
268C22×D61—48no—
269C22×D61—48no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61C2×C22⋊C412yes—
275C22×D61C2×C22⋊C411yescharacteristic
276C22×D61C2×C22⋊C411yescharacteristic
277C22×D61C2×M1612yes—
278C22×D61C2×M1612yes—
279C22×D61C2×M1612yescomplemented
280D4×C61—28no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—42no—
288C2×C4×C61—41no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×M1612yescomplemented
297C22⋊D61—28no—
298C22⋊D61—28no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—42no—
306C2×Dic61—41no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×M1612yescomplemented
314C2×Dic61C22×D412yes—
315D244—28no—
316C4×D61—24no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—22no—
320C4×D61—24no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—24no—
324C4×D61—42no—
325C4×D61—42no—
326C4×D61—42no—
327C4×D61—42no—
328C4×D61—42no—
329C4×D61—42no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61—42no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61#9914yes—
336#92420—48no—
337C2×#1465—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61C22×C22⋊C411yescharacteristic
351C22×C61C22×M1611yescharacteristic
352C22×C61C22×M1611yescharacteristic
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—24no—
356C2×D61—24no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—48no—
362C2×D61—48no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—48no—
369C2×D61—48no—
370C2×D61—42no—
371C2×D61#40712yes—
372C2×D61#40712yes—
373C2×D61C2×#9912yes—
374C2×D61#41312yes—
375C4×C61—22no—
376C4×C61—21no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61C2×#9912yes—
381Dic61—22no—
382Dic61—22no—
383Dic61—21no—
384Dic61—41no—
385Dic61—41no—
386Dic61C2×#9912yes—
387C22×C4×D4—611no—
388C2×#407—612no—
389#1465—612no—
390#1465—612no—
391#1465—612no—
392#1465—612no—
393C2×#324—612no—
394C2×#323—612no—
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—42no—
398C2×C61—42no—
399C2×C61C2×#40711yescharacteristic
400C2×C61C22×#9911yescharacteristic
401C2×C61C2×#41311yescharacteristic
402D61—22no—
403D61—42no—
404D61—42no—
405D61#146514yescomplemented
406C23×D4—611no—
407C24×C4—611no—
408C24×C4—611no—
409C22×M16—1222no—
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—1222no—
418C2×C4×D4—1222no—
419C2×C4×D4—1222no—
420C2×C4×D4—1222no—
421C2×C4×D4#692311yescharacteristic
422C22×C4⋊C4—611no—
423C22×C22⋊C4—611no—
424C22×C22⋊C4—611no—
425C22×C42—611no—
426#407—614no—
427#407—614no—
428#407—1222no—
429#407—1222no—
430C2×C22⋊C8—614no—
431C2×C22⋊C8—1222no—
432#324—614no—
433#324—614no—
434#323—614no—
435#323—614no—
436C61C2×#146511yescharacteristic, complemented, Sylow
437C25—611no—
438C25—611no—
439C22×D4—611no—
440C22×D4—611no—
441C22×D4—611no—
442C22×D4—1224no—
443C22×D4—1222no—
444C22×D4—1222no—
445C22×D4—1224no—
446C22×D4C2×#692311yescharacteristic
447C23×C4—611no—
448C23×C4—612no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—612no—
452C23×C4—612no—
453C23×C4—612no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4—2444no—
467C23×C4—2444no—
468C23×C4C2×#692311yescharacteristic
469C23×C4C2×#692311yescharacteristic
470C2×M16—1224no—
471C2×M16—1224no—
472C2×M16—2448no—
473C22×C8—1224no—
474C4×D4—22no—
475C4×D4—22no—
476C4×D4—1222no—
477C4×D4—1222no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—1222no—
484C4×D4—1222no—
485C4×D4—1222no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—1222no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4C2×#692311yescharacteristic
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—1222no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4C2×#692311yescharacteristic
507C2×C22⋊C4C2×#692311yescharacteristic
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1221no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42—1221no—
515C2×C42C2×#692311yescharacteristic
516C22⋊C8—618no—
517C22⋊C8—1224no—
518C22⋊C8—1224no—
519C22⋊C8—1224no—
520C24—611no—
521C24—612no—
522C24—612no—
523C24—614no—
524C24—611no—
525C24—611no—
526C24—1221no—
527C24—1221no—
528C24—1222no—
529C24—1222no—
530C24—1222no—
531C24—2442no—
532C24—2442no—
533C24—2442no—
534C24—2442no—
535C24C22×#692311yescharacteristic
536C24C22×#692311yescharacteristic
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—12216no—
545C2×D4—12216no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—612no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—614no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—1228no—
574C22×C4—1224no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1222no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—2442no—
589C22×C4—2444no—
590C22×C4—2442no—
591C22×C4—2444no—
592C22×C4—2444no—
593C22×C4—2442no—
594C22×C4—2444no—
595C22×C4—2442no—
596C22×C4—2444no—
597C22×C4—2444no—
598C22×C4—2444no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4C22⋊#692312yes—
605C22×C4C22⋊#692312yes—
606C22×C4C22×#692311yescharacteristic
607C22×C4C22×#692311yescharacteristic
608C22×C4C22×#692311yescharacteristic
609C22×C4C22×#692311yescharacteristic
610C22×C4C22×#692311yescharacteristic
611M16—2448no—
612M16—2448no—
613C2×C8—1228no—
614C2×C8—2448no—
615C4⋊C4—22no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C42—21no—
628C42—21no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C42—1221no—
633C42—1221no—
634C42—1221no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—611no—
644C23—611no—
645C23—612no—
646C23—612no—
647C23—612no—
648C23—612no—
649C23—1222no—
650C23—1222no—
651C23—1224no—
652C23—1224no—
653C23—1224no—
654C23—1224no—
655C23—1224no—
656C23—1224no—
657C23—1221no—
658C23—1221no—
659C23—1221no—
660C23—1221no—
661C23—2441no—
662C23—2442no—
663C23—2441no—
664C23—2442no—
665C23—2441no—
666C23—2441no—
667C23—2442no—
668C23—2442no—
669C23—2448no—
670C23—2442no—
671C23—2448no—
672C23—2448no—
673C23—2448no—
674C23—2442no—
675C23C2×C22⋊#692312yes—
676C23D61⋊M1612yescomplemented
677C23C23×#692311yescharacteristic
678D4—28no—
679D4—1228no—
680D4—1228no—
681D4—1228no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—611no—
695C2×C4—614no—
696C2×C4—611no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—1224no—
700C2×C4—1222no—
701C2×C4—1224no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1224no—
706C2×C4—1222no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1224no—
710C2×C4—1222no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2441no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4C2×C22⋊#692311yescharacteristic
731C2×C4C2×C22⋊#692312yes—
732C2×C4C2×C22⋊#692311yescharacteristic
733C2×C4D61⋊M1612yescomplemented
734C8—2448no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—612no—
748C22—612no—
749C22—612no—
750C22—612no—
751C22—1224no—
752C22—1224no—
753C22—1221no—
754C22—1221no—
755C22—1222no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22—2448no—
764C22—2448no—
765C22—2448no—
766C22—2448no—
767C22—2441no—
768C22—2441no—
769C22C22×C22⋊#692311yescharacteristic
770C22C2×D61⋊M1611yescharacteristic
771C22C2×D61⋊M1611yescharacteristic
772C4—22no—
773C4—21no—
774C4—22no—
775C4—41no—
776C4—41no—
777C4—612no—
778C4—1222no—
779C4—1222no—
780C4—1221no—
781C4—2441no—
782C4—2441no—
783C4D61⋊#9912yes—
784C2—21no—
785C2—21no—
786C2—42no—
787C2—42no—
788C2—614no—
789C2—1222no—
790C2—2442no—
791C2—2442no—
792C2D61⋊#40711yescharacteristic
793C2C2×D61⋊#9911yescharacteristic
794C2D61⋊#41311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1465
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. D61⋊#407C2semidirect
2. #21461077C2semidirect
3. #21461076C2semidirect
4. #21461075C2semidirect
5. #21461074C2semidirect
6. D61⋊#324C2semidirect
7. D61⋊#323C2semidirect
12. #16840733C22semidirect
13. #16840732C22semidirect
16. #16840608C22semidirect
17. #16840607C22semidirect
18. #16840606C22semidirect
19. #16840605C22semidirect
135. C23×D61M16semidirect
208. C2×C4×D61M16semidirect
246. C23×C61C2×M16semidirect
279. C22×D61C2×M16semidirect
296. C2×C4×C61C2×M16semidirect
313. C2×Dic61C2×M16semidirect
405. D61#1465semidirect
436. C61C2×#1465semidirect
676. C23D61⋊M16semidirect
733. C2×C4D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214610772
#214610762
#214610752
#214610742
D61⋊#3242
D61⋊#3232
C2×C4×D4×D612
C2×#146561