Finite Group Databasebeta

← D61×#1918 #29682137

Subgroups — D61×#1918 #29682137

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D61C211yesmaximal, characteristic
2#389×D61C211yesmaximal, characteristic
3C4×C4⋊C4×D61C211yesmaximal, characteristic
4#21446393C211yesmaximal, characteristic, complemented
5#21446392C211yesmaximal, characteristic, complemented
6#21446391C211yesmaximal, characteristic, complemented
7#21446390C211yesmaximal, characteristic, complemented
8#21446389C211yesmaximal, characteristic, complemented
9#21446388C211yesmaximal, characteristic, complemented
10#21446387C211yesmaximal, characteristic, complemented
11#340×D61C211yesmaximal, characteristic
12#340×D61C211yesmaximal, characteristic
13#340×D61C211yesmaximal, characteristic
14#336×D61C211yesmaximal, characteristic
15C61×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4⋊C4×D61—21no—
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C42×D61—21no—
24C2×C42×D61C2211yescharacteristic
25C2×#14519711C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28#107×D61C418yescomplemented
29#16839661C2211yescharacteristic
30#16839660C2211yescharacteristic
31#16839659—21no—
32#16839658C2211yescharacteristic
33#16839657—21no—
34C4⋊C4×Dic61C2211yescharacteristic
35C4⋊C4×Dic61C2211yescharacteristic
36C4×#11758196—21no—
37C4×C4⋊Dic61C2211yescharacteristic
38#16839613—21no—
39#95×D61—21no—
40#95×D61—21no—
41#16839525C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C2×C8×D61—22no—
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61C2×C414yes—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—44no—
92C4⋊C4×D61C2×C414yes—
93C4⋊C4×D61C2×C414yes—
94C4⋊C4×D61Q814yes—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61D411yescharacteristic
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C42×D61—22no—
102C42×D61—22no—
103C42×D61—44no—
104#14519711C2×C414yescomplemented
105#14519710C2×C414yescomplemented
106#14519710C2×C414yescomplemented
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#107×C61C2×C414yescomplemented
123#95×C61—21no—
124#95×C61—21no—
125C23×D61C2×D411yescharacteristic
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—24no—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61D814yes—
158C2×C4×D61C22×C412yes—
159C2×C4×D61C2×Q812yes—
160C2×C4×D61#4112yes—
161C2×C4×D61#4112yes—
162C2×C4×D61#4112yes—
163C2×C4×D61#4112yes—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C22×C412yes—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—42no—
176C4⋊C4×C61C22×C412yes—
177C4⋊C4×C61C22×C412yes—
178C4⋊C4×C61C2×Q812yes—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—42no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—42no—
188C4⋊Dic61C22×C412yes—
189C4⋊Dic61C22×C412yes—
190C4⋊Dic61C2×Q812yes—
191#11758196—24no—
192#11758196—24no—
193#11758196—24no—
194#11758196—42no—
195#11758196—42no—
196#11758196—42no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—42no—
202C4×Dic61—42no—
203C4×Dic61—42no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C22×C412yes—
210C8×D61—28no—
211C8×D61—44no—
212C23×C61C22×D411yescharacteristic
213C22×D61C4×D412yes—
214C22×D61C22⋊Q812yes—
215C22×D61#12312yes—
216C22×D61C2×D812yes—
217C22×D61#13512yes—
218C22×D61#13712yes—
219C22×D61#13712yes—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61C2×D812yes—
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×Q811yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61C4×D412yes—
262C2×Dic61C22⋊Q812yes—
263C2×Dic61#12312yes—
264C2×Dic61C2×D812yes—
265C4×D61—28no—
266C4×D61—48no—
267C4×D61—48no—
268C4×D61—48no—
269C4×D61—44no—
270C4×D61—84no—
271C4×D61#11714yes—
272C4×D61C4×Q814yes—
273C4×D61#12514yes—
274C4×D61#12614yes—
275C8×C61—22no—
276C8×C61—41no—
277#92418—22no—
278#92418—41no—
279C2×#1918—611nomaximal, Sylow
280C22×C61C2×C4×D411yescharacteristic
281C22×C61C2×C22⋊Q811yescharacteristic
282C22×C61C2×#12311yescharacteristic
283C22×C61C22×D811yescharacteristic
284C22×C61C2×#13511yescharacteristic
285C22×C61C2×#13711yescharacteristic
286C22×C61C2×#13711yescharacteristic
287C2×D61#38714yes—
288C2×D61C4×D814yes—
289C2×D61#44114yes—
290C2×D61#47414yes—
291C2×D61#47914yes—
292C2×D61#48014yes—
293C2×D61#48514yes—
294C4×C61—22no—
295C4×C61—41no—
296C4×C61—42no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61—81no—
300C4×C61C2×#11711yescharacteristic
301C4×C61C2×C4×Q811yescharacteristic
302C4×C61C2×#12511yescharacteristic
303C4×C61C2×#12611yescharacteristic
304Dic61—22no—
305Dic61—41no—
306Dic61—42no—
307Dic61—42no—
308Dic61—42no—
309Dic61—81no—
310Dic61#38714yes—
311C22×#107—611no—
312C2×#389—611no—
313C2×C4×C4⋊C4—611no—
314#1918—611no—
315#1918—611no—
316#1918—611no—
317#1918—611no—
318#1918—611no—
319#1918—611no—
320#1918—611no—
321#1918D6111yescharacteristic, direct product factor
322C2×#340—611no—
323C2×#340—611no—
324C2×#340—611no—
325C2×#336—611no—
326C2×C61C2×#38711yescharacteristic
327C2×C61C2×C4×D811yescharacteristic
328C2×C61C2×#44111yescharacteristic
329C2×C61C2×#47411yescharacteristic
330C2×C61C2×#47911yescharacteristic
331C2×C61C2×#48011yescharacteristic
332C2×C61C2×#48511yescharacteristic
333D61#191818yesdirect product factor
334C23×C8—611no—
335C23×C8—611no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—611no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4—611no—
340C22×C4⋊C4—1221no—
341C22×C42—611no—
342C22×C42—1221no—
343C2×#107—611no—
344C2×#107—611no—
345C2×#107—611no—
346C2×#107—618no—
347C2×#107C2×D6111yescharacteristic
348#389—611no—
349#389—611no—
350#389—611no—
351#389—1221no—
352#389—1221no—
353#389C2×D6111yescharacteristic
354C4×C4⋊C4—611no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—1221no—
358C4×C4⋊C4—1221no—
359C4×C4⋊C4C2×D6111yescharacteristic
360C2×#95—1221no—
361C2×#95—1221no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340C2×D6111yescharacteristic
372#340C2×D6111yescharacteristic
373#340C2×D6111yescharacteristic
374#336—611no—
375#336—611no—
376#336—611no—
377#336C2×D6111yescharacteristic
378C61C2×#191811yescharacteristic, complemented, Sylow
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—1221no—
383C23×C4—1221no—
384C23×C4—1221no—
385C23×C4—1221no—
386C22×C8—611no—
387C22×C8—614no—
388C22×C8—611no—
389C22×C8—1222no—
390C22×C8—1222no—
391C22×C8—1222no—
392C22×C8—1222no—
393C22×C8—1222no—
394C22×C8C22×D6111yescharacteristic
395C22×C8C22×D6111yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—614no—
401C2×C4⋊C4—614no—
402C2×C4⋊C4—614no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—2444no—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C42—21no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1222no—
426C2×C42—1222no—
427C2×C42—1221no—
428C2×C42—1221no—
429C2×C42—1221no—
430C2×C42—2444no—
431C2×C42C22×D6111yescharacteristic
432#107—614no—
433#107—614no—
434#107—614no—
435#107C4×D6114yescomplemented
436#95—21no—
437#95—21no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444C24—611no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—611no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—611no—
457C22×C4—614no—
458C22×C4—611no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1224no—
463C22×C4—1224no—
464C22×C4—1224no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2442no—
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4C23×D6111yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—612no—
489C2×C8—1228no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—2444no—
496C2×C8C2×C4×D6112yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—612no—
504C4⋊C4—612no—
505C4⋊C4—612no—
506C4⋊C4—1224no—
507C4⋊C4—1224no—
508C4⋊C4—1224no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—2442no—
515C4⋊C4—2442no—
516C4⋊C4—2442no—
517C4⋊C4—2442no—
518C4⋊C4C2×C4×D6112yes—
519C4⋊C4C2×C4×D6112yes—
520C4⋊C4Q8×D6112yes—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—1222no—
525C42—1222no—
526C42—1221no—
527C42—1221no—
528C42—2442no—
529C42—2442no—
530C42—2442no—
531C23—612no—
532C23—612no—
533C23—612no—
534C23—612no—
535C23—612no—
536C23—612no—
537C23—612no—
538C23C2×D4×D6111yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—612no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—614no—
560C2×C4—614no—
561C2×C4—614no—
562C2×C4—614no—
563C2×C4—612no—
564C2×C4—1228no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—4884no—
574C2×C4—2444no—
575C2×C4—2448no—
576C2×C4—2448no—
577C2×C4—2448no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4D8×D6112yes—
588C2×C4C22×C4×D6111yescharacteristic
589C2×C4C2×Q8×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C8—22no—
595C8—41no—
596C8—1222no—
597C8—2441no—
598C22—614no—
599C22—614no—
600C22—614no—
601C22—614no—
602C22—614no—
603C22—614no—
604C22—614no—
605C22C4×D4×D6111yescharacteristic
606C22C22⋊Q8×D6111yescharacteristic
607C22#123×D6111yescharacteristic
608C22C2×D8×D6111yescharacteristic
609C22#135×D6111yescharacteristic
610C22#137×D6111yescharacteristic
611C22#137×D6111yescharacteristic
612C4—22no—
613C4—41no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—81no—
618C4—614no—
619C4—1222no—
620C4—4881no—
621C4—2441no—
622C4—2442no—
623C4—2442no—
624C4—2442no—
625C4#117×D6111yescharacteristic
626C4C4×Q8×D6111yescharacteristic
627C4#125×D6111yescharacteristic
628C4#126×D6111yescharacteristic
629C2—618no—
630C2#387×D6111yescharacteristic
631C2C4×D8×D6111yescharacteristic
632C2#441×D6111yescharacteristic
633C2#474×D6111yescharacteristic
634C2#479×D6111yescharacteristic
635C2#480×D6111yescharacteristic
636C2#485×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1918C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1918D61
hypocenterC61C2×#1918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #21446393C2semidirect
5. #21446392C2semidirect
6. #21446391C2semidirect
7. #21446390C2semidirect
8. #21446389C2semidirect
9. #21446388C2semidirect
10. #21446387C2semidirect
15. C61×#1918C2semidirect
28. #107×D61C4semidirect
104. #14519711C2×C4semidirect
105. #14519710C2×C4semidirect
106. #14519710C2×C4semidirect
122. #107×C61C2×C4semidirect
321. #1918D61direct (N × H)
333. D61#1918direct (N × H)
378. C61C2×#1918semidirect
435. #107C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D612
#389×D612
C4×C4⋊C4×D612
#214463932
#214463922
#214463912
#214463902
#214463892
#214463882
#214463872
#340×D612
#336×D612
C61×#19182
C2×#191861