Finite Group Databasebeta

← D61×#1864 #29680930

Subgroups — D61×#1864 #29680930

Order 15616.

1974 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×#106×D61C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic
4C2×#102×D61C211yesmaximal, characteristic
5#389×D61C211yesmaximal, characteristic, complemented
6#21446083C211yesmaximal, characteristic, complemented
7#21446082C211yesmaximal, characteristic, complemented
8#21446081C211yesmaximal, characteristic, complemented
9#21446080C211yesmaximal, characteristic, complemented
10#21446079C211yesmaximal, characteristic, complemented
11#21446078C211yesmaximal, characteristic, complemented
12#21446077C211yesmaximal, characteristic, complemented
13#340×D61C211yesmaximal, characteristic, complemented
14#336×D61C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61—21no—
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×C4×C22⋊D61—21no—
24C2×#14519737—21no—
25C4×D4×D61—24no—
26C4×D4×D61—24no—
27C2×C4⋊C4×D61—21no—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32C2×C42×D61C2211yescharacteristic
33C2×#14519709C2211yescharacteristic, complemented
34C2×#14519708C2211yescharacteristic, complemented
35C2×#14519708C2211yescharacteristic, complemented
36#106×D61—24no—
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43#102×D61—24no—
44#102×D61C418yescomplemented
45#16839661C2211yescharacteristic, complemented
46#16839660C2211yescharacteristic, complemented
47#16839659—21no—
48#16839658C2211yescharacteristic, complemented
49#16839657—21no—
50#95×D61—21no—
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839517C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C2×D4×D61D414yes—
72C2×D4×D61Q814yes—
73C23×Dic61—21no—
74C22×C4×D61—28no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61—44no—
81C22×C4×D61—44no—
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—22no—
88C2×C8×D61—22no—
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61C2×C414yescomplemented
93C4×D244—22no—
94C4×D244—22no—
95D4×Dic61—22no—
96D4×Dic61—22no—
97#14519739—22no—
98#14519739—22no—
99C4×C22⋊D61—28no—
100#14519737—28no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—44no—
115C4⋊C4×D61C2×C414yescomplemented
116C4⋊C4×D61D414yes—
117C2×C22⋊Dic61—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121C2×C4×Dic61D411yescharacteristic
122C2×C4×Dic61D411yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C42×D61—22no—
125C42×D61—22no—
126#14519709—22no—
127#14519708—22no—
128#14519708—22no—
129#14519699—22no—
130#14519699C2×C414yescomplemented
131#14519698—22no—
132#14519698C2×C414yescomplemented
133#14519697—22no—
134#14519697C2×C414yescomplemented
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C4×D4×C61—22no—
143C4×D4×C61—22no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#106×C61—22no—
151#102×C61—22no—
152#102×C61C2×C414yescomplemented
153#95×C61—21no—
154C24×C61—21no—
155C23×D61—21no—
156C23×D61—24no—
157C23×D61—24no—
158C23×D61—24no—
159C23×D61—42no—
160C23×D61—42no—
161C23×D61—42no—
162C23×D61—42no—
163C23×D61C2×D411yescharacteristic
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61C22×C412yes—
168C2×D4×C61C2×D412yes—
169C2×D4×C61C2×Q812yes—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C22×Dic61—24no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191D4×D61—28no—
192D4×D61—28no—
193D4×D61—28no—
194D4×D61C4⋊C4116yescomplemented
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244C22×C412yes—
199C2×D244C2×D412yes—
200C2×D244C2×Q812yes—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—24no—
204C2×C4×D61—24no—
205C2×C4×D61—24no—
206C2×C4×D61—24no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—432no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61SD1614yes—
223C2×C4×D61C22×C412yes—
224C2×C4×D61C2×D412yes—
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2×Q812yes—
227C2×C4×D61#4112yes—
228C2×C4×D61#4112yes—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61C22×C412yescomplemented
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—42no—
240C4⋊C4×C61C22×C412yescomplemented
241C4⋊C4×C61C2×D412yes—
242C22⋊C4×C61—24no—
243C42×C61—21no—
244C42×C61—21no—
245C22⋊Dic61—24no—
246#11758198—24no—
247#11758198—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—42no—
253C4⋊Dic61C22×C412yescomplemented
254C4⋊Dic61C2×D412yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—42no—
258#11758196—42no—
259#11758196—42no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—22no—
263C4×Dic61—22no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418C22×C412yescomplemented
270C8×D61—28no—
271C8×D61—44no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—216no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—48no—
289C22×D61—48no—
290C22×D61—48no—
291C22×D61—48no—
292C22×D61—48no—
293C22×D61—48no—
294C22×D61C4×D412yes—
295C22×D61#12012yes—
296C22×D61C22⋊Q812yes—
297C22×D61C2×SD1612yes—
298C22×D61#13512yes—
299C22×D61AGL(1,ℤ/8)12yes—
300C22×D61AGL(1,ℤ/8)12yes—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61C2×C4⋊C414yescomplemented
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—48no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61C2×SD1612yes—
321C2×C4×C61C23×C411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×Q811yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C22⋊D61—216no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—48no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61C4×D412yes—
344C2×Dic61#12012yes—
345C2×Dic61C22⋊Q812yes—
346C2×Dic61C2×SD1612yes—
347D244—22no—
348D244—22no—
349D244—22no—
350D244C2×C4⋊C414yescomplemented
351C4×D61—28no—
352C4×D61—48no—
353C4×D61—48no—
354C4×D61—48no—
355C4×D61—44no—
356C4×D61—48no—
357C4×D61—84no—
358C4×D61C2×C4⋊C414yes—
359C4×D61C4×D414yes—
360C4×D61C22⋊Q814yes—
361C4×D61#12314yes—
362C8×C61—22no—
363C8×C61—41no—
364#92418—22no—
365#92418—41no—
366C2×#1864—611nomaximal, Sylow
367C22×C61—24no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61C2×C4×D411yescharacteristic
375C22×C61C2×#12011yescharacteristic
376C22×C61C2×C22⋊Q811yescharacteristic
377C22×C61C22×SD1611yescharacteristic
378C22×C61C2×#13511yescharacteristic
379C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
381C2×D61—24no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—432no—
389C2×D61#38514yes—
390C2×D61C4×SD1614yes—
391C2×D61#44214yes—
392C2×D61#44914yes—
393C2×D61#45014yes—
394C2×D61#47614yes—
395C2×D61#47814yes—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61—41no—
400C4×C61—81no—
401C4×C61C22×C4⋊C411yescharacteristic
402C4×C61C2×C4×D411yescharacteristic
403C4×C61C2×C22⋊Q811yescharacteristic
404C4×C61C2×#12311yescharacteristic
405Dic61—22no—
406Dic61—42no—
407Dic61—42no—
408Dic61—41no—
409Dic61—81no—
410Dic61#38514yes—
411C22×C4×D4—611no—
412C22×#106—611no—
413C22×#102—611no—
414C22×#102—611no—
415C2×#389—611no—
416#1864—611no—
417#1864—611no—
418#1864—611no—
419#1864—611no—
420#1864—611no—
421#1864—611no—
422#1864—611no—
423#1864D6111yescharacteristic, direct product factor
424C2×#340—611no—
425C2×#336—611no—
426C2×C61—44no—
427C2×C61C2×#38511yescharacteristic
428C2×C61C2×C4×SD1611yescharacteristic
429C2×C61C2×#44211yescharacteristic
430C2×C61C2×#45011yescharacteristic
431C2×C61C2×#44911yescharacteristic
432C2×C61C2×#47611yescharacteristic
433C2×C61C2×#47811yescharacteristic
434D61—44no—
435D61#186418yesdirect product factor
436C23×D4—611no—
437C24×C4—1221no—
438C23×C8—611no—
439C23×C8—611no—
440C2×C4×D4—611no—
441C2×C4×D4—611no—
442C2×C4×D4—611no—
443C2×C4×D4—1221no—
444C2×C4×D4—1221no—
445C2×C4×D4—1224no—
446C2×C4×D4—1224no—
447C2×C4×D4C2×D6111yescharacteristic
448C22×C4⋊C4—611no—
449C22×C4⋊C4—611no—
450C22×C4⋊C4—611no—
451C22×C4⋊C4—1221no—
452C22×C22⋊C4—1221no—
453C22×C42—611no—
454C2×#106—611no—
455C2×#106—611no—
456C2×#106—611no—
457C2×#106—1224no—
458C2×#106C2×D6111yescharacteristic, complemented
459C2×#102—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#102—618no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—1224no—
467C2×#102C2×D6111yescharacteristic
468C2×#102C2×D6111yescharacteristic
469#389—611no—
470#389—611no—
471#389—611no—
472#389—1221no—
473#389—1221no—
474#389C2×D6111yescharacteristic, complemented
475C2×#95—1221no—
476#340—611no—
477#340—611no—
478#340—611no—
479#340C2×D6111yescharacteristic, complemented
480#336—611no—
481#336—611no—
482#336—611no—
483#336C2×D6111yescharacteristic, complemented
484C61C2×#186411yescharacteristic, complemented, Sylow
485C25—1221no—
486C22×D4—614no—
487C22×D4—614no—
488C22×D4—614no—
489C22×D4—611no—
490C22×D4—1222no—
491C22×D4—1222no—
492C22×D4—1222no—
493C22×D4—1221no—
494C22×D4C22×D6111yescharacteristic
495C23×C4—21no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—1221no—
500C23×C4—1221no—
501C23×C4—1221no—
502C23×C4—1228no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—2444no—
507C23×C4—2444no—
508C22×C8—611no—
509C22×C8—614no—
510C22×C8—611no—
511C22×C8—1222no—
512C22×C8—1222no—
513C22×C8—1222no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8C22×D6111yescharacteristic
517C22×C8C22×D6111yescharacteristic
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1228no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1228no—
526C4×D4—1222no—
527C4×D4—1222no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—614no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—1222no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4—1222no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—2444no—
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1228no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—1222no—
557C2×C42—1222no—
558C2×C42C22×D6111yescharacteristic
559#106—22no—
560#106—1222no—
561#106—1222no—
562#106—1222no—
563#102—22no—
564#102—614no—
565#102—614no—
566#102—614no—
567#102—1222no—
568#102—1222no—
569#102—1222no—
570#102C4×D6114yescomplemented
571#95—21no—
572#95—1221no—
573#95—1221no—
574#95—1221no—
575C24—21no—
576C24—611no—
577C24—1224no—
578C24—1224no—
579C24—1224no—
580C24—1221no—
581C24—2442no—
582C24—2442no—
583C24—2442no—
584C24—2442no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—6116no—
589C2×D4—612no—
590C2×D4—612no—
591C2×D4—612no—
592C2×D4—1228no—
593C2×D4—1228no—
594C2×D4—1228no—
595C2×D4—1224no—
596C2×D4—1224no—
597C2×D4—1224no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4C2×C4×D6112yes—
602C2×D4D4×D6112yes—
603C2×D4Q8×D6112yes—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—611no—
611C22×C4—612no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—611no—
618C22×C4—614no—
619C22×C4—611no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1224no—
628C22×C4—1224no—
629C22×C4—1224no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—24432no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—612no—
656C2×C8—1228no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—2444no—
663C2×C8C2×C4×D6112yescomplemented
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—1224no—
672C4⋊C4—1224no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—2442no—
678C4⋊C4—2442no—
679C4⋊C4—2442no—
680C4⋊C4—2442no—
681C4⋊C4C2×C4×D6112yescomplemented
682C4⋊C4D4×D6112yes—
683C22⋊C4—24no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C42—21no—
688C42—21no—
689C42—1222no—
690C42—1222no—
691C42—1221no—
692C42—1221no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—612no—
701C23—612no—
702C23—612no—
703C23—612no—
704C23—612no—
705C23—612no—
706C23—612no—
707C23—12216no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—2448no—
712C23—2448no—
713C23—2448no—
714C23—2448no—
715C23—2448no—
716C23—2448no—
717C23—2441no—
718C23—2441no—
719C23—2441no—
720C23—2441no—
721C23C2×D4×D6111yescharacteristic
722D4—22no—
723D4—22no—
724D4—22no—
725D4—614no—
726D4—12216no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4C4⋊C4×D6114yescomplemented
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—48no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—614no—
750C2×C4—614no—
751C2×C4—614no—
752C2×C4—614no—
753C2×C4—612no—
754C2×C4—1228no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1222no—
758C2×C4—1221no—
759C2×C4—1222no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—4884no—
763C2×C4—2448no—
764C2×C4—2448no—
765C2×C4—2444no—
766C2×C4—2448no—
767C2×C4—2448no—
768C2×C4—2448no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4SD16×D6112yes—
777C2×C4C22×C4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×Q8×D6111yescharacteristic
781C2×C4#41×D6111yescharacteristic
782C2×C4#41×D6111yescharacteristic
783C8—22no—
784C8—41no—
785C8—1222no—
786C8—2441no—
787C22—24no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—614no—
795C22—614no—
796C22—614no—
797C22—614no—
798C22—614no—
799C22—614no—
800C22—614no—
801C22—1224no—
802C22—24432no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22C4×D4×D6111yescharacteristic
810C22#120×D6111yescharacteristic
811C22C22⋊Q8×D6111yescharacteristic
812C22C2×SD16×D6111yescharacteristic
813C22#135×D6111yescharacteristic
814C22AGL(1,ℤ/8)×D6111yescharacteristic
815C22AGL(1,ℤ/8)×D6111yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—41no—
820C4—81no—
821C4—614no—
822C4—1222no—
823C4—4881no—
824C4—2442no—
825C4—2442no—
826C4—2441no—
827C4C2×C4⋊C4×D6111yescharacteristic
828C4C4×D4×D6111yescharacteristic
829C4C22⋊Q8×D6111yescharacteristic
830C4#123×D6111yescharacteristic
831C2—44no—
832C2—618no—
833C2—2444no—
834C2#385×D6111yescharacteristic
835C2C4×SD16×D6111yescharacteristic
836C2#442×D6111yescharacteristic
837C2#450×D6111yescharacteristic
838C2#449×D6111yescharacteristic
839C2#476×D6111yescharacteristic
840C2#478×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1864C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1864D61
hypocenterC61C2×#1864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#106×D61C2semidirect
5. #389×D61C2semidirect
6. #21446083C2semidirect
7. #21446082C2semidirect
8. #21446081C2semidirect
9. #21446080C2semidirect
10. #21446079C2semidirect
11. #21446078C2semidirect
12. #21446077C2semidirect
13. #340×D61C2semidirect
14. #336×D61C2semidirect
15. C61×#1864C2semidirect
33. C2×#14519709C22semidirect
34. C2×#14519708C22semidirect
35. C2×#14519708C22semidirect
44. #102×D61C4semidirect
45. #16839661C22semidirect
46. #16839660C22semidirect
48. #16839658C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839517C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
58. C2×#106×C61C22semidirect
61. C61×#389C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
92. C2×C8×D61C2×C4semidirect
115. C4⋊C4×D61C2×C4semidirect
130. #14519699C2×C4semidirect
132. #14519698C2×C4semidirect
134. #14519697C2×C4semidirect
152. #102×C61C2×C4semidirect
194. D4×D61C4⋊C4semidirect
234. C2×C8×C61C22×C4semidirect
240. C4⋊C4×C61C22×C4semidirect
253. C4⋊Dic61C22×C4semidirect
269. C2×#92418C22×C4semidirect
304. D4×C61C2×C4⋊C4semidirect
350. D244C2×C4⋊C4semidirect
423. #1864D61direct (N × H)
435. D61#1864direct (N × H)
458. C2×#106C2×D61semidirect
474. #389C2×D61semidirect
479. #340C2×D61semidirect
483. #336C2×D61semidirect
484. C61C2×#1864semidirect
570. #102C4×D61semidirect
663. C2×C8C2×C4×D61semidirect
681. C4⋊C4C2×C4×D61semidirect
730. D4C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×#106×D612
C2×#102×D612
#389×D612
#214460832
#214460822
#214460812
#214460802
#214460792
#214460782
#214460772
#340×D612
#336×D612
C61×#18642
C2×#186461