Finite Group Databasebeta

← D61⋊#2133 #30624008

Subgroups — D61⋊#2133 #30624008

Order 15616.

1198 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#101C212yesmaximal, complemented
2#21462117C212yesmaximal, complemented
3#21462116C212yesmaximal, complemented
4#21462115C212yesmaximal, complemented
5#21462114C212yesmaximal, complemented
6D61⋊#356C212yesmaximal, complemented
7D61⋊#355C212yesmaximal, complemented
8#536×D61C211yesmaximal, characteristic
9C2×D61⋊M16—22no—
10D61⋊#101—22no—
11D61⋊#101—22no—
12D61⋊#101C2214yes—
13D61⋊#101C2214yescomplemented
14C2×#14519838—22no—
15C2×#14519838C2214yescomplemented
16#16840673C2214yescomplemented
17#16840672C2214yescomplemented
18#16840671C2214yescomplemented
19#16840670C2214yescomplemented
20C2×#41×D61C411yescharacteristic
21C22×Q8×D61C2211yescharacteristic
22#16840338C2211yescharacteristic
23#16840337C411yescharacteristic
24#16840337C2211yescharacteristic
25#16840336C411yescharacteristic
26#16840335—22no—
27#16840334—22no—
28#16840333C2211yescharacteristic
29#16840332C411yescharacteristic
30#16840332C2211yescharacteristic
31C4⋊Q8×D61C411yescharacteristic
32C4⋊Q8×D61C2211yescharacteristic
33#124×D61C411yescharacteristic
34#124×D61C2211yescharacteristic
35#123×D61—22no—
36C22⋊Q8×D61—22no—
37#117×D61C411yescharacteristic
38C61×#536C411yescharacteristic
39C2×#11758213—42no—
40D61⋊M16—24no—
41D61⋊M16—24no—
42D61⋊M16—42no—
43D61⋊M16—42no—
44C2×#11758217—24no—
45C2×D61⋊C8—42no—
46#14519838—24no—
47#14519838—24no—
48#14519838—24no—
49#14519838C2318yes—
50C2×#11758226C2×C411yescharacteristic
51C2×#11758222—21no—
52C2×#11758222C2×C411yescharacteristic
53C2×#11758224—21no—
54C2×#11758224C2×C411yescharacteristic
55#41×D61—42no—
56#41×D61—42no—
57C22×Dic122D412yes—
58C22×Dic122C2311yescharacteristic
59C2×Q8×D61—42no—
60C2×Q8×D61—42no—
61C2×Q8×D61C2×C411yescharacteristic
62C2×Q8×D61C2×C411yescharacteristic
63C2×Q8×D61C2×C411yescharacteristic
64C2×Q8×D61D412yes—
65C2×Q8×D61D412yes—
66C2×Q8×D61C2311yescharacteristic
67C2×Q8×D61C2311yescharacteristic
68C2×D4×D61—21no—
69C2×D4×D61C2×C411yescharacteristic
70C22×C4×D61—21no—
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61D412yes—
73#14519777C2×C411yescharacteristic
74#14519777C2311yescharacteristic
75#14519776—22no—
76#14519776—22no—
77#14519775C2×C411yescharacteristic
78#14519775C2×C411yescharacteristic
79#14519775C2×C411yescharacteristic
80#14519775C2311yescharacteristic
81#14519766C2×C411yescharacteristic
82#14519766C2×C411yescharacteristic
83#14519765C2×C411yescharacteristic
84#14519765C2311yescharacteristic
85#14519764C2×C411yescharacteristic
86#14519764C2311yescharacteristic
87#14519763—22no—
88#14519763—22no—
89#14519762—22no—
90#14519762—22no—
91#14519761—22no—
92#14519760—22no—
93#14519759—22no—
94#14519759—22no—
95#14519758—22no—
96#14519757—22no—
97#14519756—22no—
98#14519755—22no—
99#14519755—22no—
100#14519754—22no—
101#14519754—22no—
102#14519753—22no—
103#14519736C2×C411yescharacteristic
104#14519735—21no—
105#14519734C2×C411yescharacteristic
106#14519734C2×C411yescharacteristic
107#14519733—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C22⋊C4×D61—21no—
112C22⋊C4×D61—22no—
113C22⋊C4×D61—22no—
114C42×D61C2×C411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C2×#41×C61C2×C411yescharacteristic
117C22×Q8×C61C2×C411yescharacteristic
118C4⋊Q8×C61C2×C411yescharacteristic
119C4⋊Q8×C61C2×C411yescharacteristic
120#124×C61C2×C411yescharacteristic
121#124×C61C2×C411yescharacteristic
122#123×C61—22no—
123C22⋊Q8×C61—22no—
124#117×C61C2×C411yescharacteristic
125C23×D61—21no—
126C23×D61C22⋊C411yescharacteristic
127#41×C61—42no—
128C2×Q8×C61—42no—
129C2×Q8×C61C22⋊C412yes—
130C2×Q8×C61C22×C411yescharacteristic
131C2×Q8×C61C22×C411yescharacteristic
132C2×Q8×C61C22×C411yescharacteristic
133C2×D4×C61—21no—
134C2×D4×C61C22×C411yescharacteristic
135C22×C4×C61—21no—
136C22×C4×C61C22⋊C412yes—
137C22×C4×C61C22×C411yescharacteristic
138C2×C22⋊D61—21no—
139C2×C22⋊D61—21no—
140C2×C22⋊D61—21no—
141C22×Dic61—21no—
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C2×D412yes—
144#11758226—42no—
145Q8×D61—41no—
146Q8×D61—41no—
147Q8×D61—42no—
148Q8×D61—42no—
149Q8×D61—42no—
150Q8×D61—42no—
151Q8×D61—42no—
152Q8×D61—41no—
153Q8×D61—42no—
154Q8×D61—41no—
155Q8×D61—41no—
156Q8×D61—41no—
157#11758224—42no—
158#11758224—44no—
159D4×D61—41no—
160D4×D61—41no—
161D4×D61—42no—
162D4×D61—42no—
163#11758222—44no—
164#11758222—42no—
165C2×D244—21no—
166C2×D244C22×C411yescharacteristic
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61C22⋊C411yescharacteristic
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C412yes—
183C2×C4×D61C22⋊C412yes—
184C2×C4×D61C22×C411yescharacteristic
185C2×C4×D61C22×C411yescharacteristic
186C2×C4×D61C2×D412yes—
187C2×C4×D61C2×D412yes—
188C2×Dic122—21no—
189C2×Dic122—42no—
190C2×Dic122—42no—
191C2×Dic122—42no—
192C2×Dic122C22⋊C412yes—
193C2×Dic122C22⋊C412yes—
194C2×Dic122C22×C411yescharacteristic
195C2×Dic122C22×C411yescharacteristic
196C2×Dic122C2×D412yes—
197C2×Dic122C2×D412yes—
198C2×Dic122C2×D412yes—
199C2×Dic122C2411yescharacteristic
200#11758217—28no—
201#11758217—44no—
202C2×#92420—44no—
203#11758213—44no—
204#11758213—44no—
205D61⋊C8—44no—
206D61⋊C8—44no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—22no—
210C22⋊C4×C61—21no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C42×C61C22×C411yescharacteristic
214C42×C61C22×C411yescharacteristic
215C22⋊Dic61—21no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218#11758198—21no—
219#11758198—21no—
220#11758198—22no—
221#11758198—22no—
222#11758198—22no—
223#11758198—22no—
224C4⋊Dic61—21no—
225C4⋊Dic61—22no—
226C4⋊Dic61—22no—
227#11758196—22no—
228#11758196—22no—
229#11758196—21no—
230#11758196—21no—
231#11758196—22no—
232#11758196—22no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61C22×C411yescharacteristic
236C4×Dic61C22×C411yescharacteristic
237C23×C61—21no—
238C23×C61C2×C22⋊C411yescharacteristic
239C22×D61—21no—
240C22×D61—42no—
241C22×D61—44no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61#9912yes—
245C22×D61#9912yes—
246C22×D61C2×C22⋊C411yescharacteristic
247C22×D61C2×C22⋊C411yescharacteristic
248Q8×C61—42no—
249Q8×C61—41no—
250Q8×C61—41no—
251Q8×C61—41no—
252D4×C61—41no—
253D4×C61—42no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—42no—
261C2×C4×C61C2×C22⋊C412yes—
262C2×C4×C61C2×C22⋊C412yes—
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C23×C411yescharacteristic
265C22⋊D61—42no—
266C22⋊D61—42no—
267C22⋊D61—42no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—42no—
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277C2×Dic61C2×C22⋊C412yes—
278C2×Dic61C22×D412yes—
279D244—41no—
280D244—42no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—21no—
286C4×D61—21no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—21no—
293C4×D61—21no—
294C4×D61—22no—
295C4×D61—42no—
296C4×D61—42no—
297C4×D61—42no—
298C4×D61—42no—
299C4×D61—41no—
300C4×D61—41no—
301Dic122—42no—
302Dic122—42no—
303Dic122—41no—
304Dic122—42no—
305Dic122—42no—
306Dic122—42no—
307Dic122—41no—
308Dic122—42no—
309Dic122—41no—
310#92420—48no—
311C2×#2133—611nomaximal, Sylow
312C22×C61—41no—
313C22×C61—42no—
314C22×C61—41no—
315C22×C61C2×#9912yes—
316C22×C61C22×C22⋊C411yescharacteristic
317C2×D61—22no—
318C2×D61—24no—
319C2×D61—42no—
320C2×D61—41no—
321C2×D61—42no—
322C2×D61—41no—
323C2×D61—82no—
324C2×D61—82no—
325C2×D61C2×#9911yescharacteristic
326C2×D61C2×#9912yes—
327C2×D61C2×#9911yescharacteristic
328C4×C61—21no—
329C4×C61—21no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61—41no—
335Dic61—22no—
336Dic61—21no—
337Dic61—21no—
338Dic61—22no—
339Dic61—41no—
340Dic61—41no—
341Dic61—41no—
342C2×#536—611no—
343C22×#101—612no—
344#2133—612no—
345#2133—612no—
346#2133—612no—
347#2133—612no—
348C2×#356—612no—
349C2×#355—612no—
350C2×C61—21no—
351C2×C61—22no—
352C2×C61—81no—
353C2×C61C22×#9911yescharacteristic
354D61—21no—
355D61—22no—
356D61—81no—
357D61#213312yescomplemented
358C22×#41—611no—
359C23×Q8—611no—
360C22×M16—1222no—
361#536—611no—
362#536—611no—
363#536—611no—
364#536—611no—
365#536—611no—
366#536—611no—
367#536—611no—
368#536—1222no—
369#536—1222no—
370#536#692311yescharacteristic
371C2×C4⋊Q8—611no—
372C2×C4⋊Q8—611no—
373C2×#124—611no—
374C2×#124—611no—
375C2×#123—1222no—
376C2×C22⋊Q8—1222no—
377C2×#117—611no—
378C2×#101—614no—
379C2×#101—614no—
380C2×#101—614no—
381C2×#101—1222no—
382C2×#101—1222no—
383C2×#101—1222no—
384#356—614no—
385#356—614no—
386#355—614no—
387#355—614no—
388C61C2×#213311yescharacteristic, complemented, Sylow
389C2×#41—611no—
390C2×#41—611no—
391C2×#41—611no—
392C2×#41—1221no—
393C2×#41—1221no—
394C2×#41—2442no—
395C2×#41—2442no—
396C2×#41C2×#692311yescharacteristic
397C22×Q8—612no—
398C22×Q8—612no—
399C22×Q8—611no—
400C22×Q8—611no—
401C22×Q8—611no—
402C22×Q8—611no—
403C22×Q8—612no—
404C22×Q8—611no—
405C22×Q8—611no—
406C22×Q8—2442no—
407C22×Q8—2442no—
408C22×Q8C2×#692311yescharacteristic
409C22×D4—611no—
410C22×D4—1221no—
411C23×C4—612no—
412C23×C4—611no—
413C23×C4—1221no—
414C2×M16—1224no—
415C2×M16—1224no—
416C2×M16—1224no—
417C2×M16—2442no—
418C2×M16—2442no—
419C2×M16—2442no—
420C22×C8—2442no—
421C4⋊Q8—611no—
422C4⋊Q8—611no—
423C4⋊Q8—611no—
424C4⋊Q8—611no—
425C4⋊Q8—611no—
426C4⋊Q8—611no—
427C4⋊Q8—1222no—
428C4⋊Q8—1222no—
429C4⋊Q8C2×#692311yescharacteristic
430C4⋊Q8C2×#692311yescharacteristic
431#124—611no—
432#124—611no—
433#124—611no—
434#124—611no—
435#124—611no—
436#124—611no—
437#124—1222no—
438#124—1222no—
439#124C2×#692311yescharacteristic
440#124C2×#692311yescharacteristic
441#123—22no—
442#123—1222no—
443#123—1222no—
444#123—1222no—
445#123—1222no—
446#123—1222no—
447#123—1222no—
448#123—1222no—
449C22⋊Q8—22no—
450C22⋊Q8—1222no—
451C22⋊Q8—1222no—
452C22⋊Q8—1222no—
453C22⋊Q8—1222no—
454C22⋊Q8—1222no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457#117—611no—
458#117—611no—
459#117—611no—
460#117—1221no—
461#117—1221no—
462#117C2×#692311yescharacteristic
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1222no—
465C2×C4⋊C4—1222no—
466C2×C22⋊C4—1222no—
467C2×C22⋊C4—1222no—
468C2×C22⋊C4—1221no—
469C2×C42—611no—
470C2×C42—611no—
471#101—618no—
472#101—1224no—
473#101—1224no—
474#101—1224no—
475C24—611no—
476C24—1221no—
477#41—42no—
478#41—2442no—
479#41—2444no—
480#41—2444no—
481#41—2442no—
482#41—2442no—
483C2×Q8—42no—
484C2×Q8—612no—
485C2×Q8—612no—
486C2×Q8—612no—
487C2×Q8—612no—
488C2×Q8—612no—
489C2×Q8—611no—
490C2×Q8—611no—
491C2×Q8—611no—
492C2×Q8—1221no—
493C2×Q8—2442no—
494C2×Q8—2442no—
495C2×Q8—2442no—
496C2×Q8—2441no—
497C2×Q8—2442no—
498C2×Q8—2442no—
499C2×Q8—2442no—
500C2×Q8—2441no—
501C2×Q8—2442no—
502C2×Q8—2442no—
503C2×Q8—2441no—
504C2×Q8—2441no—
505C2×Q8—2442no—
506C2×Q8—2441no—
507C2×Q8—2441no—
508C2×Q8C22⋊#692312yes—
509C2×Q8C22×#692311yescharacteristic
510C2×Q8C22×#692311yescharacteristic
511C2×Q8C22×#692311yescharacteristic
512C2×D4—21no—
513C2×D4—611no—
514C2×D4—1221no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4—1221no—
518C2×D4—2441no—
519C2×D4—2441no—
520C2×D4—2442no—
521C2×D4—2442no—
522C2×D4C22×#692311yescharacteristic
523C22×C4—21no—
524C22×C4—611no—
525C22×C4—612no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—612no—
531C22×C4—612no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—1221no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—2442no—
547C22×C4—2442no—
548C22×C4C22⋊#692312yes—
549C22×C4C22×#692311yescharacteristic
550M16—1228no—
551M16—2444no—
552M16—2444no—
553M16—2444no—
554C2×C8—2444no—
555C2×C8—2444no—
556C2×C8—2444no—
557C4⋊C4—21no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1222no—
563C4⋊C4—1222no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C4⋊C4—1221no—
569C22⋊C4—21no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1221no—
575C22⋊C4—1221no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C22⋊C4—1221no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C42—611no—
582C42—611no—
583C42—1221no—
584C42—1221no—
585C42C22×#692311yescharacteristic
586C42C22×#692311yescharacteristic
587C23—21no—
588C23—612no—
589C23—611no—
590C23—612no—
591C23—611no—
592C23—1221no—
593C23—2441no—
594C23—2441no—
595C23—2442no—
596C23—2444no—
597C23C2×C22⋊#692311yescharacteristic
598Q8—42no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—2442no—
603Q8—2442no—
604Q8—2442no—
605Q8—2442no—
606Q8—2442no—
607Q8—2441no—
608Q8—2441no—
609Q8—2441no—
610Q8—2442no—
611D4—41no—
612D4—42no—
613D4—2441no—
614D4—2442no—
615D4—2442no—
616D4—2442no—
617D4—2442no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—42no—
625C2×C4—611no—
626C2×C4—612no—
627C2×C4—611no—
628C2×C4—612no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—2442no—
650C2×C4—2442no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2442no—
654C2×C4—2442no—
655C2×C4—2442no—
656C2×C4C2×C22⋊#692312yes—
657C2×C4C2×C22⋊#692312yes—
658C2×C4C2×C22⋊#692311yescharacteristic
659C2×C4C23×#692311yescharacteristic
660C8—2448no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—611no—
665C22—611no—
666C22—612no—
667C22—1222no—
668C22—1224no—
669C22—4882no—
670C22—4882no—
671C22—2441no—
672C22—2442no—
673C22—2442no—
674C22—2441no—
675C22D61⋊#9912yes—
676C22C22×C22⋊#692311yescharacteristic
677C4—21no—
678C4—22no—
679C4—22no—
680C4—21no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—1222no—
685C4—1221no—
686C4—1221no—
687C4—1222no—
688C4—2441no—
689C4—2441no—
690C4—2441no—
691C2—21no—
692C2—22no—
693C2—81no—
694C2—612no—
695C2—1221no—
696C2—1222no—
697C2—4881no—
698C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#536C4
socleC2×C61C22×#99
prime radicalC2×#41×D61C4
cosocleC2×Dic122C24
hypercenter#536#6923
hypocenterC61C2×#2133
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊#101C2semidirect
2. #21462117C2semidirect
3. #21462116C2semidirect
4. #21462115C2semidirect
5. #21462114C2semidirect
6. D61⋊#356C2semidirect
7. D61⋊#355C2semidirect
13. D61⋊#101C22semidirect
15. C2×#14519838C22semidirect
16. #16840673C22semidirect
17. #16840672C22semidirect
18. #16840671C22semidirect
19. #16840670C22semidirect
357. D61#2133semidirect
388. C61C2×#2133semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1012
#214621172
#214621162
#214621152
#214621142
D61⋊#3562
D61⋊#3552
#536×D612
C2×#213361