Finite Group Databasebeta

← D61⋊#1827 #30615115

Subgroups — D61⋊#1827 #30615115

Order 15616.

1354 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#413C211yesmaximal, characteristic
2D61⋊#410C211yesmaximal, characteristic
3#21461729C214yesmaximal, complemented
4#21461728C214yesmaximal, complemented
5C2×#16840633C212yesmaximal, complemented
6#21461489C212yesmaximal, complemented
7C4×#41×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519856C2212yes—
10#16840749—22no—
11#16840748C2214yes—
12D61⋊#101—21no—
13D61⋊#100—21no—
14#16840743—21no—
15#16840742—21no—
16#16840741C2214yes—
17D61⋊#99—22no—
18#16840633C2214yescomplemented
19#16840633C2214yescomplemented
20#16840629C2218yescomplemented
21C2×#41×D61C2211yescharacteristic
22#41×Dic61C411yescharacteristic, complemented
23C4×#11758226—21no—
24C4×#11758222C411yescharacteristic, complemented
25C4×#11758222C2212yes—
26#16840230C411yescharacteristic, complemented
27#16840230C2212yes—
28C4×#11758224—21no—
29C4×#11758224—22no—
30C4×Q8×D61—21no—
31C4×D4×D61—21no—
32C4×D4×D61—22no—
33#117×D61C412yescomplemented
34#117×D61C2211yescharacteristic
35C2×C42×D61C412yescomplemented
36C2×C42×D61C2211yescharacteristic
37C4×#41×C61C411yescharacteristic, complemented
38C2×#11758213—22no—
39D61⋊M16—22no—
40D61⋊M16—22no—
41D61⋊M16—22no—
42D61⋊M16C2314yes—
43C2×#11758217—22no—
44C2×D61⋊C8—22no—
45#14519856—22no—
46#14519856—22no—
47#14519856—22no—
48#14519856C2314yes—
49C2×C4⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923—22no—
52#14519838—24no—
53#14519837—24no—
54#14519836—24no—
55#14519835—24no—
56C2×#11758226D411yescharacteristic
57C2×#11758222C2×C411yescharacteristic
58C2×#11758222C2312yes—
59C2×#11758224D411yescharacteristic
60C2×#11758224D412yes—
61#41×D61—22no—
62#41×D61—22no—
63#41×D61—22no—
64#41×D61—22no—
65C2×Q8×D61D411yescharacteristic
66C2×D4×D61D412yes—
67C2×D4×D61D411yescharacteristic
68C22×C4×D61—22no—
69C22×C4×D61—21no—
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2311yescharacteristic
72Q8×Dic61—21no—
73C4×Dic122—21no—
74C4×Dic122—22no—
75#14519742—21no—
76#14519742—22no—
77C4×D244—21no—
78C4×D244—22no—
79D4×Dic61—21no—
80D4×Dic61—22no—
81#14519739—21no—
82#14519739—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86#14519737—22no—
87#14519737—22no—
88#14519737—22no—
89#14519736C2×C411yescharacteristic
90#14519736C2×C412yescomplemented
91#14519735—22no—
92#14519735—21no—
93#14519734C2×C412yescomplemented
94#14519734C2×C412yescomplemented
95#14519734C2312yes—
96#14519733—22no—
97#14519733—21no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—21no—
100C22⋊C4×D61—22no—
101C22⋊C4×D61—21no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C412yescomplemented
106C42×D61—22no—
107C42×D61—22no—
108C42×D61—21no—
109C42×D61—21no—
110C42×D61C2×C411yescharacteristic
111C42×D61C2×C412yes—
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C412yescomplemented
114C42×D61C2×C412yescomplemented
115C42×D61C2311yescharacteristic
116C42×D61C2311yescharacteristic
117C2×#41×C61C2×C411yescharacteristic
118C4×Q8×C61—21no—
119C4×D4×C61—21no—
120C4×D4×C61—22no—
121#117×C61C2×C411yescharacteristic
122#117×C61C2×C412yescomplemented
123C2×C42×C61C2×C411yescharacteristic
124C2×C42×C61C2×C412yescomplemented
125C23×D61C22⋊C412yes—
126C23×D61C2×D411yescharacteristic
127C22×#6923—42no—
128#41×C61—22no—
129#41×C61—22no—
130C2×Q8×C61C22⋊C411yescharacteristic
131C2×D4×C61C22⋊C412yes—
132C2×D4×C61C22⋊C411yescharacteristic
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61C22×C412yes—
136C22×C4×C61C22×C411yescharacteristic
137C2×C22⋊D61C22⋊C412yes—
138C2×C22⋊D61C2×D412yes—
139C2×C22⋊D61C2×D412yes—
140C22×Dic61—21no—
141C22×Dic61—22no—
142C22×Dic61C22⋊C412yes—
143C22×Dic61C2×D411yescharacteristic
144#11758226—22no—
145#11758226—22no—
146Q8×D61—22no—
147Q8×D61—22no—
148#11758224—24no—
149#11758224—24no—
150#11758224—22no—
151#11758224—22no—
152D4×D61—24no—
153D4×D61—24no—
154D4×D61—22no—
155D4×D61—22no—
156#11758222—22no—
157#11758222—22no—
158#11758222—24no—
159#11758222—24no—
160C2×D244C22⋊C411yescharacteristic
161C2×D244C2×D412yes—
162C2×C4×D61—21no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—44no—
174C2×C4×D61—48no—
175C2×C4×D61C22⋊C412yes—
176C2×C4×D61C22⋊C412yes—
177C2×C4×D61C22×C412yes—
178C2×C4×D61C22×C411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61#4112yes—
182C2×C4×D61#4112yes—
183C2×C4×D61#4112yes—
184C2×C4×D61#4112yes—
185C2×C4×D61C2411yescharacteristic
186C2×Dic122C22⋊C411yescharacteristic
187C2×Dic122C2×D412yes—
188C22⋊#6923—24no—
189C22⋊#6923—42no—
190#11758217—24no—
191#11758217—42no—
192C2×#92420—42no—
193C4⋊#6923—24no—
194C4⋊#6923—42no—
195C4×#6923—24no—
196C4×#6923—42no—
197#11758213—24no—
198#11758213—42no—
199D61⋊C8—24no—
200D61⋊C8—42no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—22no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—22no—
205C42×C61—21no—
206C42×C61—22no—
207C42×C61C22×C411yescharacteristic
208C42×C61C22×C411yescharacteristic
209C42×C61C22×C412yes—
210C22⋊Dic61—21no—
211C22⋊Dic61—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215C4⋊Dic61—21no—
216C4⋊Dic61—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220C4×Dic61—21no—
221C4×Dic61—22no—
222C4×Dic61—21no—
223C4×Dic61—22no—
224C4×Dic61—21no—
225C4×Dic61—22no—
226C4×Dic61—22no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61C22×C411yescharacteristic
230C4×Dic61C22×C412yes—
231C4×Dic61C22×C411yescharacteristic
232C23×C61C2×C22⋊C412yes—
233C23×C61C2×C22⋊C411yescharacteristic
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—42no—
237C22×D61—44no—
238C22×D61C2×C22⋊C411yescharacteristic
239C22×D61C2×C22⋊C412yes—
240C22×D61#12312yes—
241C22×D61#12312yes—
242C22×D61C22×D411yescharacteristic
243C2×#6923—44no—
244C2×#6923—84no—
245Q8×C61—22no—
246D4×C61—24no—
247D4×C61—22no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—42no—
254C2×C4×C61—44no—
255C2×C4×C61C2×C22⋊C412yes—
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61#11712yes—
258C2×C4×C61#11712yes—
259C2×C4×C61C23×C411yescharacteristic
260C22⋊D61—24no—
261C22⋊D61—24no—
262C22⋊D61—24no—
263C2×Dic61—21no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—21no—
267C2×Dic61—22no—
268C2×Dic61—42no—
269C2×Dic61—44no—
270C2×Dic61C2×C22⋊C412yes—
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61#12312yes—
273C2×Dic61#12312yes—
274C2×Dic61C22×D411yescharacteristic
275D244—24no—
276D244—22no—
277C4×D61—24no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—42no—
285C4×D61—44no—
286C4×D61—42no—
287C4×D61—44no—
288C4×D61—44no—
289C4×D61—42no—
290C4×D61#11711yescharacteristic
291C4×D61#11711yescharacteristic
292C4×D61#11711yescharacteristic
293C4×D61#11711yescharacteristic
294C4×D61#12312yes—
295C4×D61#12312yes—
296C4×D61#12312yes—
297C4×D61#12312yes—
298C4×D61C2×#4112yes—
299C4×D61C2×#4112yes—
300Dic122—22no—
301Dic122—24no—
302#92420—44no—
303C2×#1827—611nomaximal, Sylow
304C22×C61—22no—
305C22×C61—41no—
306C22×C61—42no—
307C22×C61#38112yes—
308C22×C61C22×C22⋊C411yescharacteristic
309C2×D61—22no—
310C2×D61—24no—
311C2×D61—22no—
312C2×D61—41no—
313C2×D61—42no—
314C2×D61—44no—
315C2×D61—44no—
316C2×D61—42no—
317C2×D61#38111yescharacteristic
318C2×D61#38111yescharacteristic
319C2×D61C2×#12312yes—
320#6923—84no—
321C4×C61—22no—
322C4×C61—22no—
323C4×C61—41no—
324C4×C61—42no—
325C4×C61#38112yes—
326C4×C61C2×#11711yescharacteristic
327C4×C61C2×#11711yescharacteristic
328Dic61—22no—
329Dic61—22no—
330Dic61—41no—
331Dic61—42no—
332Dic61#38111yescharacteristic
333Dic61#38111yescharacteristic
334Dic61C2×#12312yes—
335C2×C4×#41—611no—
336C2×#413—611no—
337C2×#410—611no—
338#1827—614no—
339#1827—614no—
340C2×#339—612no—
341C2×H(3,ℤ/4)—612no—
342C2×C61—21no—
343C2×C61—22no—
344C2×C61—42no—
345C2×C61C2×#38111yescharacteristic
346D61—22no—
347D61—21no—
348D61—42no—
349D61#182712yescomplemented
350C22×#41—611no—
351C22×M16—612no—
352C4×#41—611no—
353C4×#41—611no—
354C4×#41—612no—
355C4×#41—611no—
356C4×#41—612no—
357C4×#41—1221no—
358C4×#41—1222no—
359C4×#41—1221no—
360C4×#41#692311yescharacteristic, complemented
361C2×C4×Q8—1221no—
362C2×C4×D4—1222no—
363C2×C4×D4—1221no—
364C2×#117—611no—
365C2×#117—612no—
366C2×#117—612no—
367C22×C42—611no—
368C22×C42—612no—
369#413—614no—
370#413—1222no—
371C2×#101—1221no—
372C2×#100—1221no—
373#410—614no—
374#410—1221no—
375#410—1221no—
376C2×#99—1222no—
377#339—614no—
378#339—614no—
379H(3,ℤ/4)—618no—
380C61C2×#182711yescharacteristic, complemented, Sylow
381C2×#41—611no—
382C2×#41—611no—
383C2×#41—612no—
384C2×#41—611no—
385C2×#41—612no—
386C2×#41—1222no—
387C2×#41—1222no—
388C2×#41—1222no—
389C2×#41—1222no—
390C2×#41C2×#692311yescharacteristic
391C22×Q8—611no—
392C22×D4—612no—
393C22×D4—611no—
394C23×C4—611no—
395C23×C4—612no—
396C23×C4—1221no—
397C23×C4—1222no—
398C2×M16—614no—
399C2×M16—1222no—
400C2×M16—1222no—
401C2×M16—1222no—
402C2×M16—1222no—
403C2×M16—1222no—
404C22×C8—1222no—
405C4×Q8—21no—
406C4×Q8—1221no—
407C4×Q8—1222no—
408C4×Q8—1221no—
409C4×Q8—1222no—
410C4×Q8—1221no—
411C4×D4—21no—
412C4×D4—22no—
413C4×D4—1221no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1221no—
419C4×D4—1222no—
420C4×D4—1222no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1221no—
425#117—611no—
426#117—612no—
427#117—612no—
428#117—612no—
429#117—612no—
430#117—614no—
431#117—1221no—
432#117—1222no—
433#117—1221no—
434#117—1222no—
435#117—1222no—
436#117—1222no—
437#117—1222no—
438#117C2×#692311yescharacteristic
439#117C2×#692312yescomplemented
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1222no—
442C2×C4⋊C4—1222no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1222no—
445C2×C22⋊C4—1222no—
446C2×C42—611no—
447C2×C42—612no—
448C2×C42—611no—
449C2×C42—612no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—612no—
453C2×C42—612no—
454C2×C42—611no—
455C2×C42—1221no—
456C2×C42—1222no—
457C2×C42—1221no—
458C2×C42—1222no—
459C2×C42—1221no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42C2×#692311yescharacteristic
463C2×C42C2×#692312yescomplemented
464#101—1224no—
465#100—1224no—
466#99—1224no—
467#99—1224no—
468C24—611no—
469C24—612no—
470#41—22no—
471#41—22no—
472#41—1224no—
473#41—1224no—
474#41—1224no—
475#41—1224no—
476#41—1222no—
477#41—1222no—
478#41—1222no—
479#41—1222no—
480#41—1222no—
481#41—1222no—
482C2×Q8—612no—
483C2×Q8—611no—
484C2×Q8—1222no—
485C2×Q8—1222no—
486C2×Q8C22⋊#692311yescharacteristic
487C2×D4—612no—
488C2×D4—612no—
489C2×D4—612no—
490C2×D4—612no—
491C2×D4—611no—
492C2×D4—1222no—
493C2×D4—1222no—
494C2×D4—1224no—
495C2×D4—1224no—
496C2×D4C22⋊#692312yes—
497C2×D4C22⋊#692311yescharacteristic
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—612no—
504C22×C4—612no—
505C22×C4—612no—
506C22×C4—612no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—612no—
510C22×C4—612no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—1221no—
521C22×C4—1222no—
522C22×C4—1221no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1221no—
526C22×C4—2444no—
527C22×C4—2448no—
528C22×C4—2442no—
529C22×C4C22×#692312yes—
530C22×C4C22×#692311yescharacteristic
531M16—1224no—
532M16—1224no—
533M16—2442no—
534M16—2442no—
535C2×C8—1224no—
536C2×C8—2442no—
537C2×C8—2442no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—1222no—
541C4⋊C4—1222no—
542C4⋊C4—1222no—
543C4⋊C4—1224no—
544C4⋊C4—1222no—
545C4⋊C4—1221no—
546C4⋊C4—2442no—
547C22⋊C4—21no—
548C22⋊C4—22no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—1222no—
553C22⋊C4—1221no—
554C22⋊C4—1224no—
555C22⋊C4—2442no—
556C42—21no—
557C42—22no—
558C42—611no—
559C42—611no—
560C42—612no—
561C42—1221no—
562C42—1221no—
563C42—1222no—
564C42—1221no—
565C42—1222no—
566C42—1221no—
567C42—1222no—
568C42—1224no—
569C42—1222no—
570C42—1221no—
571C42—2442no—
572C42C22×#692311yescharacteristic
573C42C22×#692311yescharacteristic
574C42C22×#692312yes—
575C23—612no—
576C23—611no—
577C23—612no—
578C23—611no—
579C23—612no—
580C23—1222no—
581C23—1222no—
582C23—2442no—
583C23—2444no—
584C23C2×C22⋊#692312yes—
585C23C2×C22⋊#692311yescharacteristic
586Q8—22no—
587Q8—1224no—
588Q8—1222no—
589D4—24no—
590D4—22no—
591D4—1224no—
592D4—1224no—
593D4—1224no—
594D4—1224no—
595D4—1222no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—612no—
608C2×C4—612no—
609C2×C4—612no—
610C2×C4—612no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—612no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1224no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1221no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1222no—
630C2×C4—4884no—
631C2×C4—2442no—
632C2×C4—2444no—
633C2×C4—2442no—
634C2×C4—2444no—
635C2×C4—2442no—
636C2×C4—2444no—
637C2×C4—2442no—
638C2×C4—2444no—
639C2×C4—2444no—
640C2×C4C2×C22⋊#692312yes—
641C2×C4C2×C22⋊#692311yescharacteristic
642C2×C4#1451985612yes—
643C2×C4#1451985612yes—
644C2×C4C23×#692311yescharacteristic
645C8—2444no—
646C22—22no—
647C22—41no—
648C22—42no—
649C22—611no—
650C22—611no—
651C22—612no—
652C22—1222no—
653C22—1224no—
654C22—1222no—
655C22—2441no—
656C22—2442no—
657C22—2442no—
658C22—2444no—
659C22—2444no—
660C22#1684070512yes—
661C22C22×C22⋊#692311yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—42no—
666C4—612no—
667C4—611no—
668C4—611no—
669C4—1222no—
670C4—1222no—
671C4—4884no—
672C4—2441no—
673C4—2442no—
674C4#1684070512yes—
675C4C2×#1451985611yescharacteristic
676C4C2×#1451985611yescharacteristic
677C2—21no—
678C2—22no—
679C2—42no—
680C2—612no—
681C2—1222no—
682C2—1221no—
683C2—2442no—
684C2C2×#1684070511yescharacteristic
subgroupG/H
centerC4C2×#14519856
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC2×C61C2×#381
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61C2×#1827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ #117 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
3. #21461729C2semidirect
4. #21461728C2semidirect
5. C2×#16840633C2semidirect
6. #21461489C2semidirect
18. #16840633C22semidirect
19. #16840633C22semidirect
20. #16840629C22semidirect
22. #41×Dic61C4semidirect
24. C4×#11758222C4semidirect
26. #16840230C4semidirect
33. #117×D61C4semidirect
35. C2×C42×D61C4semidirect
37. C4×#41×C61C4semidirect
90. #14519736C2×C4semidirect
93. #14519734C2×C4semidirect
94. #14519734C2×C4semidirect
105. C2×C4×Dic61C2×C4semidirect
113. C42×D61C2×C4semidirect
114. C42×D61C2×C4semidirect
122. #117×C61C2×C4semidirect
124. C2×C42×C61C2×C4semidirect
349. D61#1827semidirect
360. C4×#41#6923semidirect
380. C61C2×#1827semidirect
439. #117C2×#6923semidirect
463. C2×C42C2×#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
#214617292
#214617282
C2×#168406332
#214614892
C4×#41×D612
C2×#182761