Finite Group Databasebeta

← D61×#1441 #29601682

Subgroups — D61×#1441 #29601682

Order 15616.

3246 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic
3C2×#95×D61C212yesmaximal
4C2×#95×D61C212yesmaximal
5C2×#95×D61C211yesmaximal, characteristic
6#21444073C211yesmaximal, characteristic, complemented
7#21444072C211yesmaximal, characteristic, complemented
8#21444071C212yesmaximal, complemented
9#21444070C212yesmaximal, complemented
10#21444069C211yesmaximal, characteristic, complemented
11C61×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2212yes—
15C23×C4×D61C2211yescharacteristic
16C23×C4×D61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2212yes—
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C2×C4⋊C4×D61—28no—
23C2×C4⋊C4×D61—24no—
24C2×C4⋊C4×D61—24no—
25C2×C4⋊C4×D61—24no—
26C2×C4⋊C4×D61C418yescomplemented
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35#95×D61—28no—
36#95×D61—24no—
37#95×D61—28no—
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2212yes—
42C2×#95×C61C2211yescharacteristic
43C24×D61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2312yes—
46C23×Dic61C2312yes—
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—24no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—24no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61—24no—
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×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—24no—
71C22×C4×D61C2×C414yes—
72C22×C4×D61C2×C414yes—
73C22×C4×D61C2×C414yes—
74C22×C4×D61D418yes—
75C22×C4×D61D414yes—
76C22×C4×D61D414yes—
77C22×C4×D61D414yes—
78C22×C4×D61Q818yes—
79C22×C4×D61Q814yes—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—24no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61C2×C414yescomplemented
85C2×#11758196—24no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—24no—
89C2×#11758196—24no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196C2×C414yescomplemented
93C2×#11758196C2×C414yescomplemented
94C4⋊C4×D61—232no—
95C4⋊C4×D61—232no—
96#14519684—24no—
97#14519684—22no—
98#14519684—24no—
99#14519684—24no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103#14519684—24no—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61—24no—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61C2×C414yescomplemented
114#95×C61—24no—
115#95×C61—22no—
116#95×C61—24no—
117C24×C61C2411yescharacteristic
118C23×D61C22×C412yes—
119C23×D61C2×D412yes—
120C23×D61C2×D412yes—
121C23×D61C2×D412yes—
122C23×D61C2×D414yes—
123C23×D61C2×Q812yes—
124C23×D61C2×Q814yes—
125C23×D61#4112yes—
126C23×D61#4112yes—
127C23×D61#4114yes—
128C23×D61#4114yes—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×Q814yes—
159C22×C4×C61C2×Q812yes—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C412yes—
184C22×Dic61C22×C412yes—
185C22×Dic61C2×D414yes—
186C22×Dic61C2×D412yes—
187C22×Dic61C2×D412yes—
188C22×Dic61C2×D412yes—
189C22×Dic61C2×Q814yes—
190C22×Dic61C2×Q812yes—
191C2×C4×D61—28no—
192C2×C4×D61—28no—
193C2×C4×D61—216no—
194C2×C4×D61—28no—
195C2×C4×D61—28no—
196C2×C4×D61—28no—
197C2×C4×D61—216no—
198C2×C4×D61—28no—
199C2×C4×D61—28no—
200C2×C4×D61—28no—
201C2×C4×D61—28no—
202C2×C4×D61—216no—
203C2×C4×D61—216no—
204C2×C4×D61—216no—
205C2×C4×D61—216no—
206C2×C4×D61—216no—
207C2×C4×D61—216no—
208C2×C4×D61—216no—
209C2×C4×D61—44no—
210C2×C4×D61—48no—
211C2×C4×D61—48no—
212C2×C4×D61—48no—
213C2×C4×D61—48no—
214C2×C4×D61—48no—
215C2×C4×D61—48no—
216C2×C4×D61—44no—
217C2×C4×D61—48no—
218C2×C4×D61—48no—
219C2×C4×D61—48no—
220C2×C4×D61C22⋊C4116yes—
221C2×C4×D61C4⋊C4116yescomplemented
222C4⋊C4×C61—28no—
223C4⋊C4×C61—28no—
224C4⋊Dic61—28no—
225C4⋊Dic61—28no—
226#11758196—216no—
227#11758196—28no—
228#11758196—28no—
229C23×C61C23×C411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×D411yescharacteristic
233C23×C61C22×D412yes—
234C23×C61C22×Q811yescharacteristic
235C23×C61C22×Q812yes—
236C23×C61C2×#4111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C23×C61C2×#4112yes—
239C23×C61C2×#4112yes—
240C22×D61C2×C22⋊C414yes—
241C22×D61C2×C4⋊C414yes—
242C22×D61#11714yes—
243C22×D61C4×D418yes—
244C22×D61C4×Q818yes—
245C22×D61#12014yes—
246C22×D61#12114yes—
247C22×D61#12114yes—
248C22×D61#12118yes—
249C22×D61#12118yes—
250C22×D61C22⋊Q814yes—
251C22×D61C22⋊Q814yes—
252C22×D61C22⋊Q818yes—
253C22×D61C22⋊Q818yes—
254C22×D61C22⋊Q818yes—
255C22×D61#12314yes—
256C22×D61#12318yes—
257C22×D61#12414yes—
258C22×D61#12518yes—
259C22×D61#12518yes—
260C22×D61#12618yes—
261C22×D61C4⋊Q818yes—
262C22×D61C4⋊Q814yes—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—24no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—24no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61C2×C22⋊C414yes—
293C2×C4×C61C2×C4⋊C414yescomplemented
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—24no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—24no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—41no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—41no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61C2×C22⋊C414yes—
324C2×Dic61C2×C4⋊C414yescomplemented
325C4×D61—232no—
326C4×D61—232no—
327C4×D61—416no—
328C4×D61—432no—
329C4×D61—432no—
330C2×#1441—611nomaximal, Sylow
331C22×C61C22×C22⋊C411yescharacteristic
332C22×C61C22×C4⋊C411yescharacteristic
333C22×C61C2×#11711yescharacteristic
334C22×C61C2×C4×D412yes—
335C22×C61C2×C4×Q812yes—
336C22×C61C2×#12011yescharacteristic
337C22×C61C2×#12112yes—
338C22×C61C2×#12111yescharacteristic
339C22×C61C2×#12111yescharacteristic
340C22×C61C2×#12112yes—
341C22×C61C2×C22⋊Q812yes—
342C22×C61C2×C22⋊Q811yescharacteristic
343C22×C61C2×C22⋊Q812yes—
344C22×C61C2×C22⋊Q812yes—
345C22×C61C2×C22⋊Q811yescharacteristic
346C22×C61C2×#12312yes—
347C22×C61C2×#12311yescharacteristic
348C22×C61C2×#12411yescharacteristic
349C22×C61C2×#12512yes—
350C22×C61C2×#12512yes—
351C22×C61C2×#12612yes—
352C22×C61C2×C4⋊Q812yes—
353C22×C61C2×C4⋊Q811yescharacteristic
354C2×D61#38018yes—
355C2×D61#38618yes—
356C2×D61#387116yes—
357C2×D61#389116yes—
358C2×D61#39118yes—
359C2×D61#39418yes—
360C2×D61#39518yes—
361C2×D61#396116yes—
362C2×D61#39818yes—
363C2×D61#398116yes—
364C2×D61#40018yes—
365C4×C61—24no—
366C4×C61—24no—
367C4×C61—44no—
368C4×C61—44no—
369C4×C61—42no—
370Dic61—24no—
371Dic61—24no—
372Dic61—44no—
373Dic61—44no—
374Dic61—42no—
375C23×C4⋊C4—611no—
376C23×C4⋊C4—611no—
377C22×#95—611no—
378C22×#95—612no—
379C22×#95—612no—
380#1441—612no—
381#1441—612no—
382#1441—611no—
383#1441—611no—
384#1441—611no—
385#1441D6111yescharacteristic, direct product factor
386C2×C61C2×#38011yescharacteristic
387C2×C61C2×#38611yescharacteristic
388C2×C61C2×#38712yes—
389C2×C61C2×#38912yes—
390C2×C61C2×#39111yescharacteristic
391C2×C61C2×#39411yescharacteristic
392C2×C61C2×#39511yescharacteristic
393C2×C61C2×#39612yes—
394C2×C61C2×#39811yescharacteristic
395C2×C61C2×#39812yes—
396C2×C61C2×#40011yescharacteristic
397D61#1441116yesdirect product factor
398C24×C4—611no—
399C24×C4—611no—
400C24×C4—611no—
401C24×C4—612no—
402C24×C4—612no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—618no—
407C22×C4⋊C4—612no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4—1224no—
410C22×C4⋊C4—1224no—
411C22×C4⋊C4—1224no—
412C22×C4⋊C4—1228no—
413C22×C4⋊C4C2×D6111yescharacteristic
414C22×C4⋊C4C2×D6111yescharacteristic
415C2×#95—612no—
416C2×#95—612no—
417C2×#95—612no—
418C2×#95—612no—
419C2×#95—612no—
420C2×#95—612no—
421C2×#95—612no—
422C2×#95—611no—
423C2×#95—1224no—
424C2×#95—1228no—
425C2×#95—1228no—
426C2×#95C2×D6112yes—
427C2×#95C2×D6112yes—
428C2×#95C2×D6111yescharacteristic
429C61C2×#144111yescharacteristic, complemented, Sylow
430C25—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—614no—
434C23×C4—614no—
435C23×C4—614no—
436C23×C4—614no—
437C23×C4—614no—
438C23×C4—614no—
439C23×C4—611no—
440C23×C4—612no—
441C23×C4—612no—
442C23×C4—614no—
443C23×C4—618no—
444C23×C4—618no—
445C23×C4—1224no—
446C23×C4—1222no—
447C23×C4—1222no—
448C23×C4—1224no—
449C23×C4—1222no—
450C23×C4—1222no—
451C23×C4—1222no—
452C23×C4—1222no—
453C23×C4—1224no—
454C23×C4—1224no—
455C23×C4—1224no—
456C23×C4—1224no—
457C23×C4—1224no—
458C23×C4—1224no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4—1224no—
462C23×C4—1224no—
463C23×C4—1224no—
464C23×C4—1224no—
465C23×C4—1224no—
466C23×C4—1224no—
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6112yes—
469C23×C4C22×D6112yes—
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—12232no—
480C2×C4⋊C4—12232no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1224no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4—1224no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1222no—
492C2×C4⋊C4C4×D6114yescomplemented
493#95—24no—
494#95—22no—
495#95—24no—
496#95—1224no—
497#95—1224no—
498#95—1224no—
499#95—1224no—
500#95—1224no—
501#95—1224no—
502#95—1222no—
503#95—1224no—
504C24—612no—
505C24—612no—
506C24—612no—
507C24—612no—
508C24—614no—
509C24—612no—
510C24—614no—
511C24—612no—
512C24—612no—
513C24—614no—
514C24—614no—
515C24C23×D6111yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—6116no—
545C22×C4—6116no—
546C22×C4—612no—
547C22×C4—614no—
548C22×C4—614no—
549C22×C4—1228no—
550C22×C4—1228no—
551C22×C4—1228no—
552C22×C4—12216no—
553C22×C4—12216no—
554C22×C4—1228no—
555C22×C4—1228no—
556C22×C4—1228no—
557C22×C4—1228no—
558C22×C4—1228no—
559C22×C4—1228no—
560C22×C4—12216no—
561C22×C4—12216no—
562C22×C4—12216no—
563C22×C4—12216no—
564C22×C4—12216no—
565C22×C4—12216no—
566C22×C4—12216no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1222no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—2444no—
590C22×C4—2448no—
591C22×C4—2448no—
592C22×C4—2448no—
593C22×C4—2448no—
594C22×C4—2448no—
595C22×C4—2448no—
596C22×C4—2444no—
597C22×C4—2448no—
598C22×C4—2448no—
599C22×C4—2448no—
600C22×C4C2×C4×D6112yes—
601C22×C4C2×C4×D6112yes—
602C22×C4C2×C4×D6112yes—
603C22×C4D4×D6114yes—
604C22×C4D4×D6112yes—
605C22×C4D4×D6112yes—
606C22×C4D4×D6112yes—
607C22×C4Q8×D6114yes—
608C22×C4Q8×D6112yes—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—1228no—
612C4⋊C4—1228no—
613C4⋊C4—12216no—
614C4⋊C4—1228no—
615C4⋊C4—1228no—
616C23—614no—
617C23—614no—
618C23—614no—
619C23—618no—
620C23—618no—
621C23—614no—
622C23—618no—
623C23—618no—
624C23—614no—
625C23—614no—
626C23—618no—
627C23—614no—
628C23—618no—
629C23—618no—
630C23—614no—
631C23—614no—
632C23—618no—
633C23—614no—
634C23—618no—
635C23—618no—
636C23—618no—
637C23—618no—
638C23—614no—
639C23C22×C4×D6111yescharacteristic
640C23C2×D4×D6111yescharacteristic
641C23C2×D4×D6111yescharacteristic
642C23C2×D4×D6111yescharacteristic
643C23C2×D4×D6112yes—
644C23C2×Q8×D6111yescharacteristic
645C23C2×Q8×D6112yes—
646C23#41×D6111yescharacteristic
647C23#41×D6111yescharacteristic
648C23#41×D6112yes—
649C23#41×D6112yes—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—614no—
680C2×C4—614no—
681C2×C4—12232no—
682C2×C4—12232no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1224no—
686C2×C4—1222no—
687C2×C4—1224no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1224no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—24416no—
702C2×C4—24432no—
703C2×C4—24432no—
704C2×C4—2441no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2441no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4C22⋊C4×D6114yes—
716C2×C4C4⋊C4×D6114yescomplemented
717C22—618no—
718C22—6116no—
719C22—618no—
720C22—618no—
721C22—6116no—
722C22—6116no—
723C22—6116no—
724C22—618no—
725C22—618no—
726C22—618no—
727C22—618no—
728C22C2×C22⋊C4×D6111yescharacteristic
729C22C2×C4⋊C4×D6111yescharacteristic
730C22#117×D6111yescharacteristic
731C22C4×D4×D6112yes—
732C22C4×Q8×D6112yes—
733C22#120×D6111yescharacteristic
734C22#121×D6112yes—
735C22#121×D6112yes—
736C22#121×D6111yescharacteristic
737C22#121×D6111yescharacteristic
738C22C22⋊Q8×D6112yes—
739C22C22⋊Q8×D6111yescharacteristic
740C22C22⋊Q8×D6112yes—
741C22C22⋊Q8×D6112yes—
742C22C22⋊Q8×D6111yescharacteristic
743C22#123×D6111yescharacteristic
744C22#123×D6112yes—
745C22#124×D6111yescharacteristic
746C22#125×D6112yes—
747C22#125×D6112yes—
748C22#126×D6112yes—
749C22C4⋊Q8×D6112yes—
750C22C4⋊Q8×D6111yescharacteristic
751C4—24no—
752C4—24no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—1224no—
757C4—1224no—
758C4—2442no—
759C4—2444no—
760C4—2444no—
761C2—6116no—
762C2#380×D6111yescharacteristic
763C2#386×D6111yescharacteristic
764C2#387×D6112yes—
765C2#389×D6112yes—
766C2#391×D6111yescharacteristic
767C2#394×D6111yescharacteristic
768C2#395×D6111yescharacteristic
769C2#396×D6112yes—
770C2#398×D6112yes—
771C2#398×D6111yescharacteristic
772C2#400×D6111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1441D61
hypocenterC61C2×#1441
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
6. #21444073C2semidirect
7. #21444072C2semidirect
8. #21444071C2semidirect
9. #21444070C2semidirect
10. #21444069C2semidirect
11. C61×#1441C2semidirect
26. C2×C4⋊C4×D61C4semidirect
84. C2×C4⋊Dic61C2×C4semidirect
92. C2×#11758196C2×C4semidirect
93. C2×#11758196C2×C4semidirect
113. C2×C4⋊C4×C61C2×C4semidirect
221. C2×C4×D61C4⋊C4semidirect
293. C2×C4×C61C2×C4⋊C4semidirect
324. C2×Dic61C2×C4⋊C4semidirect
385. #1441D61direct (N × H)
397. D61#1441direct (N × H)
429. C61C2×#1441semidirect
492. C2×C4⋊C4C4×D61semidirect
716. 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
C2×#95×D612
#214440732
#214440722
#214440712
#214440702
#214440692
C61×#14412
C2×#144161