Finite Group Databasebeta

← C2×D61⋊#352 #30623900

Subgroups — C2×D61⋊#352 #30623900

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#100C211yesmaximal, characteristic
2C2×D61⋊#99C211yesmaximal, characteristic
3C2×#16840665C212yesmaximal, complemented
4D61⋊#352C218yesmaximal, direct product factor
5C2×#16840664C212yesmaximal, complemented
6C2×#123×D61C211yesmaximal, characteristic
7C2×D61⋊M16—21no—
8C22×C22⋊#6923—21no—
9D61⋊#100—22no—
10D61⋊#100C2214yes—
11C2×#14519837—21no—
12C2×#14519837C2212yes—
13C2×#14519836—21no—
14D61⋊#99—22no—
15D61⋊#99C2214yes—
16C2×#14519835C2212yes—
17#16840665C2218yescomplemented
18#16840664C2218yescomplemented
19C22×D4×D61C2211yescharacteristic
20C23×C4×D61C411yescharacteristic, complemented
21C2×#14519762—21no—
22C2×#14519761C2211yescharacteristic
23C2×#14519760C2211yescharacteristic
24C2×#14519759—21no—
25C2×#14519758C411yescharacteristic, complemented
26#123×D61—22no—
27#123×D61—22no—
28#123×D61C414yescomplemented
29#123×D61C2214yes—
30C2×C4⋊C4×D61—21no—
31C2×C22⋊C4×D61—21no—
32C2×C22⋊C4×D61C411yescharacteristic, complemented
33C2×#123×C61C411yescharacteristic, complemented
34C23×#6923—41no—
35C2×#11758213—41no—
36D61⋊M16—24no—
37D61⋊M16—42no—
38C2×#11758217—22no—
39C2×D61⋊C8—41no—
40C2×C22⋊#6923—22no—
41C2×C22⋊#6923—24no—
42C2×C22⋊#6923—42no—
43C2×C22⋊#6923—41no—
44#14519837—24no—
45#14519837—22no—
46#14519837C2314yes—
47#14519836—24no—
48#14519835—22no—
49#14519835C2314yes—
50C24×D61C2×C411yescharacteristic
51C24×D61D411yescharacteristic
52C22×D244D411yescharacteristic
53C22×C22⋊D61D411yescharacteristic
54C22×C22⋊D61C2311yescharacteristic
55C2×D4×D61—41no—
56C2×D4×D61—42no—
57C2×D4×D61—41no—
58C2×D4×D61C2×C412yes—
59C2×D4×D61D412yes—
60C2×D4×D61D412yes—
61C2×D4×D61C2312yes—
62C23×Dic61C2×C411yescharacteristic, complemented
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—22no—
66C22×C4×D61—21no—
67C22×C4×D61—42no—
68C22×C4×D61—41no—
69C22×C4×D61—41no—
70C22×C4×D61C2×C414yescomplemented
71C22×C4×D61D411yescharacteristic
72#14519762—24no—
73#14519762—24no—
74#14519761—21no—
75#14519761—21no—
76#14519761C2×C412yescomplemented
77#14519761C2312yes—
78#14519760—21no—
79#14519760—21no—
80#14519760C2×C412yescomplemented
81#14519760C2312yes—
82#14519759—24no—
83#14519759—24no—
84#14519758—22no—
85#14519758C2×C414yescomplemented
86C2×C4⋊Dic61—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C4⋊C4×D61—24no—
90C4⋊C4×D61—24no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61C2×C411yescharacteristic, complemented
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C22⋊C4×D61—24no—
97C22⋊C4×D61—22no—
98C22⋊C4×D61—24no—
99C22⋊C4×D61C2×C414yescomplemented
100C22×D4×C61C2×C411yescharacteristic
101C23×C4×C61C2×C411yescharacteristic, complemented
102#123×C61—22no—
103#123×C61C2×C414yescomplemented
104C2×C4⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
107C24×C61C22⋊C411yescharacteristic
108C24×C61C22×C411yescharacteristic
109C23×D61—22no—
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—22no—
115C23×D61—44no—
116C23×D61—44no—
117C23×D61C22⋊C411yescharacteristic
118C23×D61C22⋊C412yes—
119C23×D61C22⋊C411yescharacteristic
120C23×D61C22⋊C412yes—
121C23×D61C22×C412yes—
122C23×D61C2×D412yes—
123C23×D61C2×D411yescharacteristic
124C22×#6923—42no—
125C22×#6923—44no—
126C22×#6923—84no—
127C2×D4×C61—41no—
128C2×D4×C61—41no—
129C2×D4×C61C22⋊C412yes—
130C2×D4×C61C22×C412yes—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22×C412yescomplemented
138C2×C22⋊D61—41no—
139C2×C22⋊D61—41no—
140C2×C22⋊D61—41no—
141C2×C22⋊D61—41no—
142C2×C22⋊D61C22⋊C412yes—
143C2×C22⋊D61C22×C411yescharacteristic
144C2×C22⋊D61C2×D411yescharacteristic
145C2×C22⋊D61C2×D411yescharacteristic
146C2×C22⋊D61C2×D412yes—
147C2×C22⋊D61C2411yescharacteristic
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—41no—
152C22×Dic61—41no—
153C22×Dic61C22×C412yescomplemented
154C22×Dic61C2×D411yescharacteristic
155D4×D61—42no—
156D4×D61—42no—
157D4×D61—42no—
158D4×D61—42no—
159D4×D61—42no—
160D4×D61—42no—
161D4×D61—42no—
162D4×D61—42no—
163C2×D244—41no—
164C2×D244—41no—
165C2×D244C22⋊C412yes—
166C2×D244C2×D412yes—
167C2×C4×D61—21no—
168C2×C4×D61—22no—
169C2×C4×D61—21no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—24no—
173C2×C4×D61—44no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—44no—
177C2×C4×D61—44no—
178C2×C4×D61—41no—
179C2×C4×D61—42no—
180C2×C4×D61—41no—
181C2×C4×D61—44no—
182C2×C4×D61—44no—
183C2×C4×D61C22⋊C412yes—
184C2×C4×D61C2×D412yes—
185C22⋊#6923—24no—
186C22⋊#6923—42no—
187C22⋊#6923—44no—
188#11758217—24no—
189#11758217—42no—
190C2×#92420—42no—
191#11758213—44no—
192D61⋊C8—44no—
193C4⋊C4×C61—24no—
194C22⋊C4×C61—24no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61C22×C412yescomplemented
197C22⋊Dic61—24no—
198C22⋊Dic61—21no—
199C22⋊Dic61C22×C412yescomplemented
200#11758198—22no—
201#11758198—22no—
202#11758198—24no—
203#11758198—22no—
204#11758198—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207#11758196—24no—
208#11758196—22no—
209#11758196—22no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61C2×C22⋊C411yescharacteristic
217C23×C61C2×C22⋊C412yes—
218C23×C61C2×C22⋊C411yescharacteristic
219C23×C61C23×C411yescharacteristic
220C22×D61—24no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—44no—
234C22×D61—48no—
235C22×D61—44no—
236C22×D61—44no—
237C22×D61—44no—
238C22×D61—44no—
239C22×D61—44no—
240C22×D61—44no—
241C22×D61—42no—
242C22×D61—42no—
243C22×D61—84no—
244C22×D61—82no—
245C22×D61#9911yescharacteristic
246C22×D61#9912yes—
247C22×D61#9911yescharacteristic
248C22×D61C2×C22⋊C412yes—
249C22×D61C2×C22⋊C411yescharacteristic
250C22×D61C2×C22⋊C412yes—
251C22×D61C22×D411yescharacteristic
252C2×#6923—44no—
253C2×#6923—84no—
254C2×#6923—88no—
255D4×C61—42no—
256D4×C61—42no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—42no—
266C2×C4×C61C2×C22⋊C412yes—
267C22⋊D61—42no—
268C22⋊D61—41no—
269C22⋊D61—42no—
270C22⋊D61—41no—
271C22⋊D61—41no—
272C22⋊D61—41no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—42no—
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C22×D411yescharacteristic
284D244—42no—
285D244—42no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—48no—
291C4×D61—48no—
292C4×D61—44no—
293C4×D61—44no—
294#92420—44no—
295C22×#352—611nomaximal, Sylow
296C22×C61—22no—
297C22×C61—21no—
298C22×C61—21no—
299C22×C61—22no—
300C22×C61—41no—
301C22×C61—42no—
302C22×C61—41no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—81no—
307C22×C61C2×#9911yescharacteristic
308C22×C61C2×#9911yescharacteristic
309C22×C61C22×C22⋊C411yescharacteristic
310C2×D61—22no—
311C2×D61—24no—
312C2×D61—24no—
313C2×D61—22no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—44no—
317C2×D61—44no—
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—44no—
322C2×D61—44no—
323C2×D61—44no—
324C2×D61—44no—
325C2×D61—42no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—82no—
329C2×D61—82no—
330C2×D61—81no—
331C2×D61#35214yescomplemented
332C2×D61C2×#9912yes—
333C2×D61C2×#9912yes—
334#6923—84no—
335C4×C61—22no—
336C4×C61—42no—
337C4×C61—42no—
338Dic61—21no—
339Dic61—21no—
340Dic61—42no—
341Dic61—42no—
342C22×#123—611no—
343C22×#100—611no—
344C22×#99—611no—
345C2×#352—612no—
346C2×#352—618no—
347C2×#352—612no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61—41no—
351C2×C61—41no—
352C2×C61—42no—
353C2×C61C2×#35212yescomplemented
354C2×C61C22×#9911yescharacteristic
355D61—22no—
356D61—41no—
357D61—42no—
358D61—41no—
359D61C2×#35214yescomplemented
360C23×D4—611no—
361C24×C4—611no—
362C22×M16—1221no—
363C2×#123—611no—
364C2×#123—611no—
365C2×#123—614no—
366C2×#123—614no—
367C2×#123—611no—
368C2×#123—1221no—
369C2×#123—1221no—
370C2×#123—1222no—
371C2×#123—1222no—
372C2×#123#692311yescharacteristic, complemented
373C22×C4⋊C4—1221no—
374C22×C22⋊C4—611no—
375C22×C22⋊C4—1221no—
376C22×C22⋊C4—1221no—
377C2×#100—612no—
378C2×#100—614no—
379C2×#100—1221no—
380C2×#100—1222no—
381C2×#99—612no—
382C2×#99—614no—
383C2×#99—1222no—
384C2×#99—1221no—
385#352—618no—
386#352—618no—
387C61C22×#35211yescharacteristic, complemented, Sylow
388C25—611no—
389C25—611no—
390C22×D4—611no—
391C22×D4—611no—
392C22×D4—612no—
393C22×D4—612no—
394C22×D4—612no—
395C22×D4—612no—
396C22×D4—611no—
397C22×D4—2441no—
398C22×D4—2442no—
399C22×D4—2441no—
400C22×D4C2×#692311yescharacteristic
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—614no—
404C23×C4—1221no—
405C23×C4—1221no—
406C23×C4—1222no—
407C23×C4—1221no—
408C23×C4—2442no—
409C23×C4—2441no—
410C23×C4—2441no—
411C23×C4—2441no—
412C23×C4C2×#692311yescharacteristic, complemented
413C2×M16—1222no—
414C2×M16—1224no—
415C2×M16—2442no—
416C2×M16—2441no—
417C22×C8—2441no—
418#123—22no—
419#123—614no—
420#123—612no—
421#123—612no—
422#123—612no—
423#123—612no—
424#123—1224no—
425#123—1224no—
426#123—1221no—
427#123—1221no—
428#123—1224no—
429#123—1224no—
430#123—1221no—
431#123—1221no—
432#123—1222no—
433#123C2×#692314yescomplemented
434C2×C4⋊C4—21no—
435C2×C4⋊C4—1224no—
436C2×C4⋊C4—1224no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—614no—
443C2×C22⋊C4—1222no—
444C2×C22⋊C4—1224no—
445C2×C22⋊C4—1224no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1224no—
451C2×C22⋊C4—1222no—
452C2×C22⋊C4—2441no—
453C2×C22⋊C4—2442no—
454C2×C22⋊C4C2×#692311yescharacteristic, complemented
455#100—614no—
456#100—1224no—
457#100—1222no—
458#99—614no—
459#99—1222no—
460#99—1224no—
461C24—611no—
462C24—612no—
463C24—612no—
464C24—612no—
465C24—611no—
466C24—611no—
467C24—612no—
468C24—1221no—
469C24—1222no—
470C24—1222no—
471C24—1221no—
472C24—1221no—
473C24—1221no—
474C24—2444no—
475C24—2444no—
476C24C22⋊#692311yescharacteristic
477C24C22×#692311yescharacteristic
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—611no—
481C2×D4—611no—
482C2×D4—612no—
483C2×D4—612no—
484C2×D4—611no—
485C2×D4—611no—
486C2×D4—612no—
487C2×D4—612no—
488C2×D4—2441no—
489C2×D4—2441no—
490C2×D4—2442no—
491C2×D4—2442no—
492C2×D4—2442no—
493C2×D4—2442no—
494C2×D4—2442no—
495C2×D4—2442no—
496C2×D4—2442no—
497C2×D4—2442no—
498C2×D4—2441no—
499C2×D4—2441no—
500C2×D4—2441no—
501C2×D4—2441no—
502C2×D4C22⋊#692312yes—
503C2×D4C22×#692312yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—611no—
510C22×C4—612no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—1221no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1224no—
517C22×C4—1224no—
518C22×C4—1224no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—4884no—
523C22×C4—2442no—
524C22×C4—2441no—
525C22×C4—2441no—
526C22×C4—2444no—
527C22×C4—2444no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4—2444no—
531C22×C4—2444no—
532C22×C4—2444no—
533C22×C4—2444no—
534C22×C4—2442no—
535C22×C4—2441no—
536C22×C4—2441no—
537C22×C4C22⋊#692311yescharacteristic
538C22×C4C22×#692312yescomplemented
539M16—1224no—
540M16—2444no—
541M16—2442no—
542C2×C8—2444no—
543C2×C8—2442no—
544C4⋊C4—24no—
545C4⋊C4—1222no—
546C4⋊C4—1222no—
547C4⋊C4—1222no—
548C4⋊C4—1222no—
549C4⋊C4—1224no—
550C22⋊C4—24no—
551C22⋊C4—21no—
552C22⋊C4—612no—
553C22⋊C4—1224no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—1222no—
558C22⋊C4—1221no—
559C22⋊C4—1224no—
560C22⋊C4—1224no—
561C22⋊C4—2444no—
562C22⋊C4—2442no—
563C22⋊C4C22×#692312yescomplemented
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—42no—
569C23—42no—
570C23—611no—
571C23—612no—
572C23—611no—
573C23—612no—
574C23—611no—
575C23—612no—
576C23—611no—
577C23—1224no—
578C23—1222no—
579C23—1222no—
580C23—1222no—
581C23—1222no—
582C23—1222no—
583C23—1222no—
584C23—1222no—
585C23—1222no—
586C23—1221no—
587C23—1221no—
588C23—1221no—
589C23—1221no—
590C23—4882no—
591C23—4884no—
592C23—2442no—
593C23—2442no—
594C23—2444no—
595C23—2444no—
596C23—2444no—
597C23—2444no—
598C23—2444no—
599C23—2444no—
600C23—2448no—
601C23—2444no—
602C23C2×C22⋊#692312yes—
603C23C2×C22⋊#692311yescharacteristic
604C23C2×C22⋊#692311yescharacteristic
605C23C23×#692311yescharacteristic
606D4—42no—
607D4—42no—
608D4—2442no—
609D4—2442no—
610D4—2441no—
611D4—2441no—
612D4—2442no—
613D4—2441no—
614D4—2441no—
615D4—2442no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—611no—
626C2×C4—611no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—4888no—
636C2×C4—4884no—
637C2×C4—2444no—
638C2×C4—2444no—
639C2×C4—2448no—
640C2×C4—2448no—
641C2×C4—2444no—
642C2×C4—2442no—
643C2×C4—2442no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2442no—
647C2×C4C2×C22⋊#692312yes—
648C8—2444no—
649C22—22no—
650C22—21no—
651C22—21no—
652C22—22no—
653C22—41no—
654C22—42no—
655C22—41no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—81no—
660C22—614no—
661C22—612no—
662C22—612no—
663C22—1224no—
664C22—1224no—
665C22—1222no—
666C22—1221no—
667C22—1222no—
668C22—1221no—
669C22—4881no—
670C22—4882no—
671C22—4882no—
672C22—2441no—
673C22—2441no—
674C22—2442no—
675C22—2442no—
676C22—2444no—
677C22—2444no—
678C22—2444no—
679C22—2444no—
680C22—2444no—
681C22—2444no—
682C22—2442no—
683C22—2442no—
684C22D61⋊#9911yescharacteristic
685C22D61⋊#9911yescharacteristic
686C22C22×C22⋊#692311yescharacteristic
687C4—22no—
688C4—42no—
689C4—42no—
690C4—1221no—
691C4—1221no—
692C4—4884no—
693C4—2442no—
694C4—2442no—
695C2—21no—
696C2—21no—
697C2—41no—
698C2—41no—
699C2—42no—
700C2—614no—
701C2—1222no—
702C2—2441no—
703C2—2441no—
704C2—2442no—
705C2D61⋊#35212yesdirect product factor
706C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C2×#99
prime radicalC22×D4×D61C22
cosocleC2×C22⋊D61C24
hypercenterC2×#123#6923
hypocenterC61C22×#352
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. C2×#16840665C2semidirect
4. D61⋊#352C2direct (N × H)
5. C2×#16840664C2semidirect
17. #16840665C22semidirect
18. #16840664C22semidirect
20. C23×C4×D61C4semidirect
25. C2×#14519758C4semidirect
28. #123×D61C4semidirect
32. C2×C22⋊C4×D61C4semidirect
33. C2×#123×C61C4semidirect
62. C23×Dic61C2×C4semidirect
70. C22×C4×D61C2×C4semidirect
76. #14519761C2×C4semidirect
80. #14519760C2×C4semidirect
85. #14519758C2×C4semidirect
92. C2×C22⋊Dic61C2×C4semidirect
99. C22⋊C4×D61C2×C4semidirect
101. C23×C4×C61C2×C4semidirect
103. #123×C61C2×C4semidirect
106. C2×C22⋊C4×C61C2×C4semidirect
137. C22×C4×C61C22×C4semidirect
153. C22×Dic61C22×C4semidirect
196. C22⋊C4×C61C22×C4semidirect
199. C22⋊Dic61C22×C4semidirect
331. C2×D61#352semidirect
353. C2×C61C2×#352semidirect
359. D61C2×#352semidirect
372. C2×#123#6923semidirect
387. C61C22×#352semidirect
412. C23×C4C2×#6923semidirect
433. #123C2×#6923semidirect
454. C2×C22⋊C4C2×#6923semidirect
538. C22×C4C22×#6923semidirect
563. C22⋊C4C22×#6923semidirect
705. C2D61⋊#352direct (N × H)

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
C2×#168406652
D61⋊#3522
C2×#168406642
C2×#123×D612
C22×#35261