Finite Group Databasebeta

← C2×D61⋊#327 #30610894

Subgroups — C2×D61⋊#327 #30610894

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2C22×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3C2×#16840614C212yesmaximal, complemented
4D61⋊#327C218yesmaximal, direct product factor
5C2×#16840613C212yesmaximal, complemented
6C2×#121×D61C211yesmaximal, characteristic
7C24×#6923—21no—
8C22×D61⋊C8—21no—
9C2×#14519834C2212yescomplemented
10D61⋊(C22⋊C8)—22no—
11D61⋊(C22⋊C8)C2214yescomplemented
12C2×C22⋊#92420—21no—
13C2×(C2×#6923)⋊C4—22no—
14C2×(C2×#6923)⋊C4—21no—
15C2×(C2×#6923)⋊C4C2212yescomplemented
16C2×(C2×#6923)⋊C4C2214yescomplemented
17#16840614C2218yescomplemented
18#16840613C2218yescomplemented
19C22×D4×D61—21no—
20C22×D4×D61C411yescharacteristic, complemented
21C23×C4×D61C2211yescharacteristic
22C2×#14519752C2211yescharacteristic
23C2×#14519751C411yescharacteristic, complemented
24C2×#14519750—21no—
25C2×#14519749—21no—
26C2×#14519748C2211yescharacteristic
27#121×D61—22no—
28#121×D61—22no—
29#121×D61C414yescomplemented
30#121×D61C2214yes—
31C2×C4⋊C4×D61C411yescharacteristic, complemented
32C2×C22⋊C4×D61—21no—
33C2×#121×C61C411yescharacteristic, complemented
34C23×#6923—28no—
35C23×#6923—24no—
36C23×#6923—22no—
37C23×#6923—44no—
38C23×#6923—44no—
39C2×D61⋊C8—24no—
40C2×D61⋊C8—44no—
41C22×#92420—22no—
42#14519834—22no—
43#14519834C2314yescomplemented
44C22⋊#92420—24no—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—24no—
47(C2×#6923)⋊C4C2314yescomplemented
48C24×D61—21no—
49C24×D61D411yescharacteristic
50C22×D244—21no—
51C22×D244C2×C411yescharacteristic, complemented
52C22×C22⋊D61—21no—
53C22×C22⋊D61—21no—
54C22×C22⋊D61—21no—
55C2×D4×D61—24no—
56C2×D4×D61—24no—
57C2×D4×D61—22no—
58C2×D4×D61—44no—
59C2×D4×D61—44no—
60C2×D4×D61—44no—
61C2×D4×D61C2×C414yescomplemented
62C23×Dic61D411yescharacteristic
63C22×C4×D61—21no—
64C22×C4×D61—44no—
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C412yes—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D412yes—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D412yes—
71C22×C4×D61C2312yes—
72C22×C4×D61C2311yescharacteristic
73#14519752—21no—
74#14519752—21no—
75#14519752C2×C412yescomplemented
76#14519752C2312yes—
77#14519751—22no—
78#14519751C2×C414yescomplemented
79#14519750—24no—
80#14519750—24no—
81#14519749—24no—
82#14519749—24no—
83#14519748—21no—
84#14519748—21no—
85#14519748C2×C412yescomplemented
86#14519748C2312yes—
87C2×C4⋊Dic61C2×C411yescharacteristic, complemented
88C2×#11758196—21no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61C2×C414yescomplemented
91C2×C22⋊Dic61—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C22⋊C4×D61—24no—
95C22⋊C4×D61—24no—
96C22×D4×C61—21no—
97C22×D4×C61C2×C411yescharacteristic, complemented
98C23×C4×C61C2×C411yescharacteristic
99#121×C61—22no—
100#121×C61C2×C414yescomplemented
101C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
102C2×C22⋊C4×C61—21no—
103C24×C61—21no—
104C24×C61C22⋊C411yescharacteristic
105C23×D61—24no—
106C23×D61—24no—
107C23×D61—21no—
108C23×D61—24no—
109C23×D61—44no—
110C23×D61—44no—
111C23×D61—44no—
112C23×D61C22⋊C412yes—
113C23×D61C22⋊C411yescharacteristic
114C23×D61D814yes—
115C23×D61SD1614yes—
116C23×D61C2×D412yes—
117C23×D61C2×D411yescharacteristic
118C22×#6923—28no—
119C22×#6923—216no—
120C22×#6923—24no—
121C22×#6923—44no—
122C22×#6923—432no—
123C22×#6923—48no—
124C22×#6923—44no—
125C22×#6923—48no—
126C2×D4×C61—24no—
127C2×D4×C61—21no—
128C2×D4×C61—42no—
129C2×D4×C61—44no—
130C2×D4×C61C22×C412yescomplemented
131C22×C4×C61—21no—
132C22×C4×C61—42no—
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22⋊C412yes—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C412yes—
137C2×C22⋊D61—24no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—24no—
141C2×C22⋊D61—44no—
142C2×C22⋊D61—44no—
143C2×C22⋊D61—42no—
144C2×C22⋊D61—42no—
145C22×Dic61—21no—
146C22×Dic61—42no—
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C412yes—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D412yes—
151D4×D61—48no—
152D4×D61—48no—
153D4×D61—416no—
154D4×D61—48no—
155D4×D61—48no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—21no—
159C2×D244—42no—
160C2×D244—42no—
161C2×D244—42no—
162C2×D244C22×C412yescomplemented
163C2×C4×D61—24no—
164C2×C4×D61—24no—
165C2×C4×D61—24no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61—44no—
169C2×C4×D61—44no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—44no—
173C2×C4×D61C22⋊C412yes—
174C2×C4×D61C22⋊C412yes—
175C2×C4×D61C22⋊C412yes—
176C2×C4×D61C22×C412yes—
177C2×C4×D61C22×C411yescharacteristic
178C2×C4×D61C2×D412yes—
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2411yescharacteristic
183C2×#92420—24no—
184C2×#92420—44no—
185D61⋊C8—48no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61C22×C412yescomplemented
188C22⋊C4×C61—24no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191#11758198—24no—
192#11758198—22no—
193#11758198—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61C22×C412yescomplemented
196#11758196—24no—
197C23×C61—22no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61#10214yes—
204C23×C61C2×C22⋊C412yes—
205C23×C61C2×C22⋊C411yescharacteristic
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—216no—
209C22×D61—216no—
210C22×D61—24no—
211C22×D61—24no—
212C22×D61—24no—
213C22×D61—24no—
214C22×D61—22no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—48no—
219C22×D61—48no—
220C22×D61—48no—
221C22×D61—816no—
222C22×D61#9914yes—
223C22×D61#10218yes—
224C22×D61#10214yes—
225C22×D61#10414yes—
226C22×D61C2×C22⋊C411yescharacteristic
227C22×D61C2×C22⋊C412yes—
228C22×D61C2×D812yes—
229C22×D61C2×D814yes—
230C22×D61C2×SD1612yes—
231C22×D61C2×SD1614yes—
232C22×D61C22×D411yescharacteristic
233C2×#6923—28no—
234C2×#6923—44no—
235C2×#6923—416no—
236C2×#6923—432no—
237C2×#6923—44no—
238D4×C61—42no—
239D4×C61—42no—
240D4×C61—48no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C23×C411yescharacteristic
250C22⋊D61—48no—
251C22⋊D61—48no—
252C22⋊D61—42no—
253C22⋊D61—42no—
254C22⋊D61—44no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C22×D411yescharacteristic
264D244—42no—
265D244—42no—
266D244—42no—
267D244—42no—
268D244—44no—
269C4×D61—24no—
270C4×D61—24no—
271C4×D61—24no—
272C4×D61—24no—
273C4×D61—42no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—42no—
278C4×D61—41no—
279C4×D61—48no—
280#92420—44no—
281C22×#327—611nomaximal, Sylow
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—28no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—84no—
289C22×C61C2×#9912yes—
290C22×C61C2×#10214yes—
291C22×C61C2×#10212yes—
292C22×C61C2×#10412yes—
293C22×C61C22×C22⋊C411yescharacteristic
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—24no—
299C2×D61—24no—
300C2×D61—28no—
301C2×D61—216no—
302C2×D61—28no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—84no—
307C2×D61—816no—
308C2×D61#327116yescomplemented
309C2×D61C2×#9914yes—
310C2×D61C2×#10212yes—
311C2×D61C2×#10214yes—
312C2×D61C2×#10414yes—
313C2×D61C22×D811yescharacteristic
314C2×D61C22×SD1611yescharacteristic
315#6923—48no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—22no—
319C4×C61—42no—
320Dic61—21no—
321Dic61—21no—
322Dic61—22no—
323Dic61—42no—
324C22×#121—611no—
325C22×C22⋊C8—611no—
326C22×#95—611no—
327C2×#327—612no—
328C2×#327—618no—
329C2×#327—612no—
330C2×C61—24no—
331C2×C61—82no—
332C2×C61C2×#32714yescomplemented
333C2×C61C22×#9911yescharacteristic
334C2×C61C22×#10211yescharacteristic
335C2×C61C22×#10411yescharacteristic
336D61—21no—
337D61—21no—
338D61—22no—
339D61—82no—
340D61C2×#32718yescomplemented
341C23×D4—611no—
342C23×D4—1221no—
343C24×C4—611no—
344C24×C4—1221no—
345C23×C8—1221no—
346C2×#121—611no—
347C2×#121—611no—
348C2×#121—614no—
349C2×#121—614no—
350C2×#121—611no—
351C2×#121—1221no—
352C2×#121—1222no—
353C2×#121—1222no—
354C2×#121—1221no—
355C2×#121#692311yescharacteristic, complemented
356C22×C4⋊C4—611no—
357C22×C22⋊C4—1221no—
358C2×C22⋊C8—614no—
359C2×C22⋊C8—612no—
360C2×C22⋊C8—1221no—
361C2×C22⋊C8—1222no—
362C2×#95—612no—
363C2×#95—614no—
364C2×#95—1221no—
365C2×#95—1222no—
366#327—618no—
367#327—618no—
368C61C22×#32711yescharacteristic, complemented, Sylow
369C25—611no—
370C25—1221no—
371C22×D4—21no—
372C22×D4—614no—
373C22×D4—611no—
374C22×D4—1221no—
375C22×D4—1222no—
376C22×D4—1221no—
377C22×D4—1224no—
378C22×D4—1224no—
379C22×D4—1221no—
380C22×D4—1221no—
381C22×D4—2444no—
382C22×D4—2444no—
383C22×D4—2444no—
384C22×D4C2×#692311yescharacteristic, complemented
385C23×C4—611no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—612no—
390C23×C4—612no—
391C23×C4—612no—
392C23×C4—611no—
393C23×C4—612no—
394C23×C4—1221no—
395C23×C4—1224no—
396C23×C4—1222no—
397C23×C4—1228no—
398C23×C4—2444no—
399C23×C4—2444no—
400C23×C4—2444no—
401C23×C4C2×#692311yescharacteristic
402C22×C8—1222no—
403C22×C8—1224no—
404C22×C8—2444no—
405#121—22no—
406#121—612no—
407#121—612no—
408#121—614no—
409#121—612no—
410#121—612no—
411#121—1224no—
412#121—1224no—
413#121—1221no—
414#121—1221no—
415#121—1221no—
416#121—1221no—
417#121—1224no—
418#121—1224no—
419#121—1222no—
420#121C2×#692314yescomplemented
421C2×C4⋊C4—611no—
422C2×C4⋊C4—614no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4C2×#692311yescharacteristic, complemented
426C2×C22⋊C4—21no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4—1224no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C22⋊C8—614no—
433C22⋊C8—1224no—
434C22⋊C8—1222no—
435#95—614no—
436#95—1222no—
437#95—1224no—
438C24—21no—
439C24—611no—
440C24—614no—
441C24—614no—
442C24—612no—
443C24—612no—
444C24—611no—
445C24—1224no—
446C24—1224no—
447C24—1224no—
448C24—1221no—
449C24—2444no—
450C24—2444no—
451C24—2444no—
452C24C22⋊#692311yescharacteristic
453C2×D4—24no—
454C2×D4—21no—
455C2×D4—42no—
456C2×D4—44no—
457C2×D4—612no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1224no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1224no—
464C2×D4—1221no—
465C2×D4—2442no—
466C2×D4—2442no—
467C2×D4—2442no—
468C2×D4—2448no—
469C2×D4—2448no—
470C2×D4—2444no—
471C2×D4—24416no—
472C2×D4—2448no—
473C2×D4—2448no—
474C2×D4—2442no—
475C2×D4—2442no—
476C2×D4—2444no—
477C2×D4C22×#692312yescomplemented
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—611no—
489C22×C4—612no—
490C22×C4—611no—
491C22×C4—612no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—1224no—
495C22×C4—1224no—
496C22×C4—1224no—
497C22×C4—1224no—
498C22×C4—12216no—
499C22×C4—1228no—
500C22×C4—1221no—
501C22×C4—2442no—
502C22×C4—2442no—
503C22×C4—2444no—
504C22×C4—2444no—
505C22×C4—2444no—
506C22×C4—2444no—
507C22×C4—2444no—
508C22×C4—2442no—
509C22×C4—2448no—
510C22×C4—2444no—
511C22×C4—2448no—
512C22×C4—24432no—
513C22×C4—2444no—
514C22×C4C22⋊#692311yescharacteristic
515C22×C4C22⋊#692312yes—
516C22×C4C22×#692311yescharacteristic
517C22×C4C22×#692312yes—
518C2×C8—1224no—
519C2×C8—2448no—
520C2×C8—2444no—
521C4⋊C4—21no—
522C4⋊C4—612no—
523C4⋊C4—1224no—
524C4⋊C4—1221no—
525C4⋊C4C22×#692312yescomplemented
526C22⋊C4—24no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1224no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—614no—
539C23—614no—
540C23—614no—
541C23—612no—
542C23—618no—
543C23—614no—
544C23—612no—
545C23—614no—
546C23—612no—
547C23—611no—
548C23—611no—
549C23—1224no—
550C23—1224no—
551C23—1224no—
552C23—12216no—
553C23—1224no—
554C23—12216no—
555C23—1222no—
556C23—1222no—
557C23—1222no—
558C23—48816no—
559C23—2448no—
560C23—2448no—
561C23—2448no—
562C23—2442no—
563C23—2442no—
564C23—2442no—
565C23#1451983914yes—
566C23C2×C22⋊#692312yes—
567C23C2×C22⋊#692311yescharacteristic
568D4—42no—
569D4—42no—
570D4—48no—
571D4—2442no—
572D4—2442no—
573D4—2442no—
574D4—2442no—
575D4—2444no—
576D4—2448no—
577D4—2442no—
578D4—2442no—
579D4—2444no—
580D4—2448no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—611no—
588C2×C4—612no—
589C2×C4—611no—
590C2×C4—1224no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1228no—
597C2×C4—1222no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2448no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2444no—
608C2×C4—24432no—
609C2×C4—2444no—
610C2×C4—24416no—
611C2×C4—2442no—
612C2×C4C2×C22⋊#692312yes—
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C23×#692311yescharacteristic
615C8—2444no—
616C22—22no—
617C22—22no—
618C22—28no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—84no—
623C22—614no—
624C22—614no—
625C22—614no—
626C22—6116no—
627C22—611no—
628C22—611no—
629C22—612no—
630C22—1228no—
631C22—12216no—
632C22—1228no—
633C22—1221no—
634C22—1221no—
635C22—1221no—
636C22—1221no—
637C22—1224no—
638C22—1224no—
639C22—48816no—
640C22—4884no—
641C22—2442no—
642C22—2442no—
643C22—2442no—
644C22D61⋊#9912yes—
645C22C2×#1451983914yes—
646C22C2×#1451983912yes—
647C22D61⋊#10412yes—
648C22C22×C22⋊#692311yescharacteristic
649C4—22no—
650C4—21no—
651C4—21no—
652C4—42no—
653C4—1221no—
654C4—1221no—
655C4—1222no—
656C4—2448no—
657C4—2442no—
658C2—24no—
659C2—82no—
660C2—618no—
661C2—1221no—
662C2—1221no—
663C2—1222no—
664C2—4882no—
665C2D61⋊#32714yesdirect product factor
666C2C2×D61⋊#9911yescharacteristic
667C2C22×#1451983911yescharacteristic
668C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×D61C2
cosocleC2×C4×D61C24
hypercenterC2×#121#6923
hypocenterC61C22×#327
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊(C22⋊C8)C2semidirect
2. C22×(C2×#6923)⋊C4C2semidirect
3. C2×#16840614C2semidirect
4. D61⋊#327C2direct (N × H)
5. C2×#16840613C2semidirect
9. C2×#14519834C22semidirect
11. D61⋊(C22⋊C8)C22semidirect
15. C2×(C2×#6923)⋊C4C22semidirect
16. C2×(C2×#6923)⋊C4C22semidirect
17. #16840614C22semidirect
18. #16840613C22semidirect
20. C22×D4×D61C4semidirect
23. C2×#14519751C4semidirect
29. #121×D61C4semidirect
31. C2×C4⋊C4×D61C4semidirect
33. C2×#121×C61C4semidirect
43. #14519834C23semidirect
47. (C2×#6923)⋊C4C23semidirect
51. C22×D244C2×C4semidirect
61. C2×D4×D61C2×C4semidirect
75. #14519752C2×C4semidirect
78. #14519751C2×C4semidirect
85. #14519748C2×C4semidirect
87. C2×C4⋊Dic61C2×C4semidirect
90. C4⋊C4×D61C2×C4semidirect
97. C22×D4×C61C2×C4semidirect
100. #121×C61C2×C4semidirect
101. C2×C4⋊C4×C61C2×C4semidirect
130. C2×D4×C61C22×C4semidirect
162. C2×D244C22×C4semidirect
187. C4⋊C4×C61C22×C4semidirect
195. C4⋊Dic61C22×C4semidirect
308. C2×D61#327semidirect
332. C2×C61C2×#327semidirect
340. D61C2×#327semidirect
355. C2×#121#6923semidirect
368. C61C22×#327semidirect
384. C22×D4C2×#6923semidirect
420. #121C2×#6923semidirect
425. C2×C4⋊C4C2×#6923semidirect
477. C2×D4C22×#6923semidirect
525. C4⋊C4C22×#6923semidirect
665. C2D61⋊#327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
C22×(C2×#6923)⋊C42
C2×#168406142
D61⋊#3272
C2×#168406132
C2×#121×D612
C22×#32761