Finite Group Databasebeta

← D61×#1436 #29601134

Subgroups — D61×#1436 #29601134

Order 15616.

3550 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C22×C42×D61C211yesmaximal, characteristic
3C2×#95×D61C212yesmaximal
4C2×#95×D61C211yesmaximal, characteristic
5C2×#95×D61C212yesmaximal
6#21444054C211yesmaximal, characteristic, complemented
7#21444053C212yesmaximal, complemented
8#21444052C211yesmaximal, characteristic, complemented
9#21444051C211yesmaximal, characteristic, complemented
10#21444050C212yesmaximal, complemented
11C61×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C23×C4×D61C2212yes—
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C2×C4⋊C4×D61—24no—
21C2×C4⋊C4×D61—24no—
22C2×C4⋊C4×D61C418yescomplemented
23C22×C4×Dic61C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25C2×C42×D61—24no—
26C2×C42×D61—28no—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35#95×D61—24no—
36#95×D61—28no—
37#95×D61C4116yescomplemented
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2312yes—
49C22×C4×D61—24no—
50C22×C4×D61—24no—
51C22×C4×D61—24no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—24no—
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—24no—
61C22×C4×D61—24no—
62C22×C4×D61—24no—
63C22×C4×D61—24no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61C2×C414yes—
69C22×C4×D61C2×C418yes—
70C22×C4×D61C2×C414yes—
71C22×C4×D61C2×C418yes—
72C22×C4×D61C2×C414yes—
73C22×C4×D61C2×C418yes—
74C22×C4×D61D414yes—
75C22×C4×D61D414yes—
76C22×C4×D61D418yes—
77C22×C4×D61Q818yes—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61C2×C414yescomplemented
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—22no—
85C2×#11758196C2×C414yescomplemented
86C2×#11758196C2×C414yescomplemented
87C4⋊C4×D61—232no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—24no—
90C2×C4×Dic61—24no—
91C2×C4×Dic61—24no—
92C2×C4×Dic61—24no—
93C42×D61—232no—
94#14519684—22no—
95#14519684—24no—
96#14519684—24no—
97#14519684—24no—
98#14519684—24no—
99#14519684C2×C418yescomplemented
100#14519684C2×C418yescomplemented
101#14519684C2×C418yescomplemented
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2312yes—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61C2×C414yescomplemented
110C2×C42×C61—22no—
111C2×C42×C61—24no—
112#95×C61—22no—
113#95×C61—24no—
114#95×C61C2×C418yescomplemented
115C24×C61C2411yescharacteristic
116C23×D61C22×C412yes—
117C23×D61C22×C414yes—
118C23×D61C2×D412yes—
119C23×D61C2×D412yes—
120C23×D61C2×D414yes—
121C23×D61C2×Q814yes—
122C23×D61#4114yes—
123C23×D61#4114yes—
124C23×D61#4114yes—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61C22×C414yes—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C414yes—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C22×C412yes—
149C22×C4×C61C22×C414yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D414yes—
153C22×C4×C61C2×Q814yes—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61C22×C414yes—
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C414yes—
176C22×Dic61C22×C412yes—
177C22×Dic61C22×C412yes—
178C22×Dic61C22×C414yes—
179C22×Dic61C2×D412yes—
180C22×Dic61C2×D412yes—
181C22×Dic61C2×D414yes—
182C22×Dic61C2×Q814yes—
183C2×C4×D61—28no—
184C2×C4×D61—28no—
185C2×C4×D61—216no—
186C2×C4×D61—216no—
187C2×C4×D61—216no—
188C2×C4×D61—216no—
189C2×C4×D61—216no—
190C2×C4×D61—216no—
191C2×C4×D61—28no—
192C2×C4×D61—216no—
193C2×C4×D61—216no—
194C2×C4×D61—216no—
195C2×C4×D61—216no—
196C2×C4×D61—28no—
197C2×C4×D61—28no—
198C2×C4×D61—216no—
199C2×C4×D61—216no—
200C2×C4×D61—216no—
201C2×C4×D61—216no—
202C2×C4×D61—44no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C2×C4×D61—44no—
206C2×C4×D61—48no—
207C2×C4×D61—48no—
208C2×C4×D61—48no—
209C2×C4×D61C42116yescomplemented
210C2×C4×D61C22⋊C4116yes—
211C2×C4×D61C4⋊C4132yescomplemented
212C4⋊C4×C61—28no—
213C42×C61—28no—
214C4⋊Dic61—28no—
215#11758196—28no—
216#11758196—28no—
217C4×Dic61—28no—
218C4×Dic61—216no—
219C23×C61C23×C411yescharacteristic
220C23×C61C23×C412yes—
221C23×C61C22×D411yescharacteristic
222C23×C61C22×D411yescharacteristic
223C23×C61C22×D412yes—
224C23×C61C22×Q812yes—
225C23×C61C2×#4112yes—
226C23×C61C2×#4112yes—
227C23×C61C2×#4112yes—
228C22×D61C2×C4214yes—
229C22×D61C2×C22⋊C414yes—
230C22×D61C2×C4⋊C418yes—
231C22×D61#11714yes—
232C22×D61#11718yes—
233C22×D61C4×D418yes—
234C22×D61C4×D418yes—
235C22×D61C4×D418yes—
236C22×D61C4×D418yes—
237C22×D61C4×Q818yes—
238C22×D61C4×Q818yes—
239C22×D61#12014yes—
240C22×D61#12118yes—
241C22×D61C22⋊Q818yes—
242C22×D61C22⋊Q818yes—
243C22×D61#12318yes—
244C22×D61#12314yes—
245C22×D61#12414yes—
246C22×D61#12518yes—
247C22×D61#12618yes—
248C22×D61C4⋊Q814yes—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—24no—
252C2×C4×C61—24no—
253C2×C4×C61—24no—
254C2×C4×C61—24no—
255C2×C4×C61—24no—
256C2×C4×C61—24no—
257C2×C4×C61—22no—
258C2×C4×C61—24no—
259C2×C4×C61—24no—
260C2×C4×C61—24no—
261C2×C4×C61—24no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—24no—
265C2×C4×C61—24no—
266C2×C4×C61—24no—
267C2×C4×C61—24no—
268C2×C4×C61—41no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—41no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61C2×C4214yescomplemented
276C2×C4×C61C2×C22⋊C414yes—
277C2×C4×C61C2×C4⋊C418yescomplemented
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—24no—
281C2×Dic61—24no—
282C2×Dic61—24no—
283C2×Dic61—24no—
284C2×Dic61—24no—
285C2×Dic61—24no—
286C2×Dic61—22no—
287C2×Dic61—24no—
288C2×Dic61—24no—
289C2×Dic61—24no—
290C2×Dic61—24no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—24no—
297C2×Dic61—41no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—41no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61C2×C4214yescomplemented
305C2×Dic61C2×C22⋊C414yes—
306C2×Dic61C2×C4⋊C418yescomplemented
307C4×D61—232no—
308C4×D61—264no—
309C4×D61—232no—
310C4×D61—416no—
311C4×D61—432no—
312C2×#1436—611nomaximal, Sylow
313C22×C61C22×C4211yescharacteristic
314C22×C61C22×C22⋊C411yescharacteristic
315C22×C61C22×C4⋊C412yes—
316C22×C61C2×#11711yescharacteristic
317C22×C61C2×#11712yes—
318C22×C61C2×C4×D412yes—
319C22×C61C2×C4×D412yes—
320C22×C61C2×C4×D412yes—
321C22×C61C2×C4×D412yes—
322C22×C61C2×C4×Q812yes—
323C22×C61C2×C4×Q812yes—
324C22×C61C2×#12011yescharacteristic
325C22×C61C2×#12112yes—
326C22×C61C2×C22⋊Q812yes—
327C22×C61C2×C22⋊Q812yes—
328C22×C61C2×#12312yes—
329C22×C61C2×#12311yescharacteristic
330C22×C61C2×#12411yescharacteristic
331C22×C61C2×#12512yes—
332C22×C61C2×#12612yes—
333C22×C61C2×C4⋊Q811yescharacteristic
334C2×D61C4×C22⋊C418yes—
335C2×D61C4×C4⋊C4116yes—
336C2×D61#385116yes—
337C2×D61#38618yes—
338C2×D61#387116yes—
339C2×D61#387116yes—
340C2×D61#388116yes—
341C2×D61#389116yes—
342C2×D61#39118yes—
343C4×C61—24no—
344C4×C61—28no—
345C4×C61—24no—
346C4×C61—42no—
347C4×C61—44no—
348Dic61—24no—
349Dic61—28no—
350Dic61—24no—
351Dic61—42no—
352Dic61—44no—
353C23×C4⋊C4—611no—
354C23×C42—611no—
355C22×#95—612no—
356C22×#95—611no—
357C22×#95—612no—
358#1436—611no—
359#1436—612no—
360#1436—612no—
361#1436—611no—
362#1436—611no—
363#1436D6111yescharacteristic, direct product factor
364C2×C61C2×C4×C22⋊C411yescharacteristic
365C2×C61C2×C4×C4⋊C412yes—
366C2×C61C2×#38512yes—
367C2×C61C2×#38611yescharacteristic
368C2×C61C2×#38712yes—
369C2×C61C2×#38712yes—
370C2×C61C2×#38812yes—
371C2×C61C2×#38912yes—
372C2×C61C2×#39111yescharacteristic
373D61#1436116yesdirect product factor
374C24×C4—611no—
375C24×C4—612no—
376C24×C4—611no—
377C24×C4—611no—
378C24×C4—612no—
379C22×C4⋊C4—611no—
380C22×C4⋊C4—611no—
381C22×C4⋊C4—611no—
382C22×C4⋊C4—618no—
383C22×C4⋊C4—1224no—
384C22×C4⋊C4—1224no—
385C22×C4⋊C4C2×D6111yescharacteristic
386C22×C42—612no—
387C22×C42—611no—
388C22×C42—1224no—
389C22×C42—1228no—
390C22×C42C2×D6111yescharacteristic
391C2×#95—612no—
392C2×#95—612no—
393C2×#95—612no—
394C2×#95—6116no—
395C2×#95—612no—
396C2×#95—612no—
397C2×#95—612no—
398C2×#95—612no—
399C2×#95—611no—
400C2×#95—1224no—
401C2×#95—1228no—
402C2×#95C2×D6112yes—
403C2×#95C2×D6111yescharacteristic
404C2×#95C2×D6112yes—
405C61C2×#143611yescharacteristic, complemented, Sylow
406C25—611no—
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—612no—
410C23×C4—614no—
411C23×C4—614no—
412C23×C4—618no—
413C23×C4—618no—
414C23×C4—614no—
415C23×C4—614no—
416C23×C4—618no—
417C23×C4—618no—
418C23×C4—611no—
419C23×C4—612no—
420C23×C4—614no—
421C23×C4—618no—
422C23×C4—1222no—
423C23×C4—1222no—
424C23×C4—1224no—
425C23×C4—1224no—
426C23×C4—1224no—
427C23×C4—1224no—
428C23×C4—1224no—
429C23×C4—1224no—
430C23×C4—1224no—
431C23×C4—1222no—
432C23×C4—1222no—
433C23×C4—1224no—
434C23×C4—1224no—
435C23×C4—1224no—
436C23×C4—1224no—
437C23×C4—1224no—
438C23×C4—1224no—
439C23×C4—1224no—
440C23×C4—1224no—
441C23×C4C22×D6111yescharacteristic
442C23×C4C22×D6112yes—
443C23×C4C22×D6111yescharacteristic
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6112yes—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—614no—
449C2×C4⋊C4—614no—
450C2×C4⋊C4—614no—
451C2×C4⋊C4—12232no—
452C2×C4⋊C4—1222no—
453C2×C4⋊C4—1222no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1222no—
456C2×C4⋊C4—1222no—
457C2×C4⋊C4—1222no—
458C2×C4⋊C4C4×D6114yescomplemented
459C2×C42—22no—
460C2×C42—24no—
461C2×C42—12232no—
462C2×C42—1224no—
463C2×C42—1224no—
464C2×C42—1224no—
465C2×C42—1222no—
466C2×C42—1224no—
467#95—22no—
468#95—24no—
469#95—618no—
470#95—618no—
471#95—618no—
472#95—1224no—
473#95—1224no—
474#95—1224no—
475#95—1222no—
476#95—1224no—
477#95C4×D6118yescomplemented
478C24—612no—
479C24—614no—
480C24—612no—
481C24—612no—
482C24—614no—
483C24—614no—
484C24—614no—
485C24—614no—
486C24—614no—
487C24C23×D6111yescharacteristic
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—614no—
508C22×C4—614no—
509C22×C4—612no—
510C22×C4—612no—
511C22×C4—614no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—614no—
515C22×C4—6116no—
516C22×C4—6116no—
517C22×C4—6132no—
518C22×C4—614no—
519C22×C4—612no—
520C22×C4—1228no—
521C22×C4—12216no—
522C22×C4—1228no—
523C22×C4—1228no—
524C22×C4—12216no—
525C22×C4—12216no—
526C22×C4—12216no—
527C22×C4—12216no—
528C22×C4—12216no—
529C22×C4—12216no—
530C22×C4—12216no—
531C22×C4—12216no—
532C22×C4—1228no—
533C22×C4—12216no—
534C22×C4—1228no—
535C22×C4—12216no—
536C22×C4—12216no—
537C22×C4—12216no—
538C22×C4—12216no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—2444no—
559C22×C4—2448no—
560C22×C4—2448no—
561C22×C4—2444no—
562C22×C4—2448no—
563C22×C4—2448no—
564C22×C4—2448no—
565C22×C4C2×C4×D6114yes—
566C22×C4C2×C4×D6112yes—
567C22×C4C2×C4×D6114yes—
568C22×C4C2×C4×D6112yes—
569C22×C4C2×C4×D6112yes—
570C22×C4C2×C4×D6114yes—
571C22×C4D4×D6112yes—
572C22×C4D4×D6112yes—
573C22×C4D4×D6114yes—
574C22×C4Q8×D6114yes—
575C4⋊C4—28no—
576C4⋊C4—1228no—
577C4⋊C4—1228no—
578C4⋊C4—1228no—
579C42—28no—
580C42—12216no—
581C42—1228no—
582C23—614no—
583C23—614no—
584C23—618no—
585C23—614no—
586C23—618no—
587C23—618no—
588C23—618no—
589C23—618no—
590C23—618no—
591C23—618no—
592C23—618no—
593C23—614no—
594C23—618no—
595C23—618no—
596C23—618no—
597C23—618no—
598C23—614no—
599C23—614no—
600C23—618no—
601C23—618no—
602C23—614no—
603C23C22×C4×D6111yescharacteristic
604C23C22×C4×D6112yes—
605C23C2×D4×D6111yescharacteristic
606C23C2×D4×D6111yescharacteristic
607C23C2×D4×D6112yes—
608C23C2×Q8×D6112yes—
609C23#41×D6112yes—
610C23#41×D6112yes—
611C23#41×D6112yes—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—614no—
639C2×C4—614no—
640C2×C4—618no—
641C2×C4—12264no—
642C2×C4—12232no—
643C2×C4—12232no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1224no—
647C2×C4—1224no—
648C2×C4—1224no—
649C2×C4—1224no—
650C2×C4—1224no—
651C2×C4—1224no—
652C2×C4—1222no—
653C2×C4—1224no—
654C2×C4—1224no—
655C2×C4—1224no—
656C2×C4—1224no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1224no—
660C2×C4—1224no—
661C2×C4—1224no—
662C2×C4—1224no—
663C2×C4—24416no—
664C2×C4—24432no—
665C2×C4—2441no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2441no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4C42×D6114yescomplemented
673C2×C4C22⋊C4×D6114yes—
674C2×C4C4⋊C4×D6118yescomplemented
675C22—6116no—
676C22—618no—
677C22—6116no—
678C22—6116no—
679C22—6116no—
680C22—6116no—
681C22—618no—
682C22—618no—
683C22—6116no—
684C22C2×C42×D6111yescharacteristic
685C22C2×C22⋊C4×D6111yescharacteristic
686C22C2×C4⋊C4×D6112yes—
687C22#117×D6111yescharacteristic
688C22#117×D6112yes—
689C22C4×D4×D6112yes—
690C22C4×D4×D6112yes—
691C22C4×D4×D6112yes—
692C22C4×D4×D6112yes—
693C22C4×Q8×D6112yes—
694C22C4×Q8×D6112yes—
695C22#120×D6111yescharacteristic
696C22#121×D6112yes—
697C22C22⋊Q8×D6112yes—
698C22C22⋊Q8×D6112yes—
699C22#123×D6112yes—
700C22#123×D6111yescharacteristic
701C22#124×D6111yescharacteristic
702C22#125×D6112yes—
703C22#126×D6112yes—
704C22C4⋊Q8×D6111yescharacteristic
705C4—28no—
706C4—24no—
707C4—24no—
708C4—42no—
709C4—44no—
710C4—1228no—
711C4—1224no—
712C4—1224no—
713C4—2442no—
714C4—2444no—
715C2—6116no—
716C2C4×C22⋊C4×D6111yescharacteristic
717C2C4×C4⋊C4×D6112yes—
718C2#385×D6112yes—
719C2#386×D6111yescharacteristic
720C2#387×D6112yes—
721C2#387×D6112yes—
722C2#388×D6112yes—
723C2#389×D6112yes—
724C2#391×D6111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1436D61
hypocenterC61C2×#1436
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #21444054C2semidirect
7. #21444053C2semidirect
8. #21444052C2semidirect
9. #21444051C2semidirect
10. #21444050C2semidirect
11. C61×#1436C2semidirect
22. C2×C4⋊C4×D61C4semidirect
37. #95×D61C4semidirect
80. C2×C4⋊Dic61C2×C4semidirect
85. C2×#11758196C2×C4semidirect
86. C2×#11758196C2×C4semidirect
99. #14519684C2×C4semidirect
100. #14519684C2×C4semidirect
101. #14519684C2×C4semidirect
109. C2×C4⋊C4×C61C2×C4semidirect
114. #95×C61C2×C4semidirect
209. C2×C4×D61C42semidirect
211. C2×C4×D61C4⋊C4semidirect
275. C2×C4×C61C2×C42semidirect
277. C2×C4×C61C2×C4⋊C4semidirect
304. C2×Dic61C2×C42semidirect
306. C2×Dic61C2×C4⋊C4semidirect
363. #1436D61direct (N × H)
373. D61#1436direct (N × H)
405. C61C2×#1436semidirect
458. C2×C4⋊C4C4×D61semidirect
477. #95C4×D61semidirect
672. C2×C4C42×D61semidirect
674. C2×C4C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
C22×C42×D612
C2×#95×D612
#214440542
#214440532
#214440522
#214440512
#214440502
C61×#14362
C2×#143661