Finite Group Databasebeta

← D61×#1823 #29679785

Subgroups — D61×#1823 #29679785

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic
3#380×D61C211yesmaximal, characteristic
4#21445906C211yesmaximal, characteristic, complemented
5#21445905C211yesmaximal, characteristic, complemented
6#21445904C214yesmaximal, complemented
7#21445903C211yesmaximal, characteristic, complemented
8#340×D61C214yesmaximal, complemented
9C61×#1823C211yesmaximal, characteristic, complemented
10C23×C4×D61—21no—
11C23×C4×D61C2211yescharacteristic
12C22×C8×D61C2212yes—
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196—21no—
15C2×C4⋊C4×D61—24no—
16C2×C4⋊C4×D61—21no—
17C2×C4⋊C4×D61—21no—
18C2×C4⋊C4×D61C418yescomplemented
19C2×C4⋊C4×D61C2212yes—
20C2×C4⋊C4×D61C2212yes—
21C2×C4⋊C4×D61C2212yes—
22C2×C22⋊C4×D61—21no—
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519689C2212yes—
25C22⋊C8×D61—24no—
26#16839622C2211yescharacteristic
27#16839621—21no—
28#16839620—21no—
29#16839619C2212yes—
30#95×D61—21no—
31#16839525C2214yescomplemented
32#16839524C2214yescomplemented
33#16839524C2214yescomplemented
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C61×#380C2211yescharacteristic
37C61×#340C2214yescomplemented
38C24×D61D411yescharacteristic
39C23×Dic61—21no—
40C23×Dic61D411yescharacteristic
41C22×C4×D61—28no—
42C22×C4×D61—28no—
43C22×C4×D61—22no—
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—44no—
47C22×C4×D61—44no—
48C22×C4×D61C2×C414yes—
49C22×C4×D61D411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D414yes—
52C22×C4×D61C2311yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C22×#92418C2312yes—
55C2×C8×D61—24no—
56C2×C8×D61—28no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61C2×C414yescomplemented
60C2×C4⋊Dic61C2312yes—
61C2×C4⋊Dic61C2312yes—
62C2×#11758196—28no—
63C2×#11758196—22no—
64C2×#11758196—22no—
65C2×#11758196—22no—
66C4⋊C4×D61—28no—
67C4⋊C4×D61—28no—
68C4⋊C4×D61—24no—
69C4⋊C4×D61—24no—
70C4⋊C4×D61—28no—
71C4⋊C4×D61C2×C418yes—
72C4⋊C4×D61C2×C418yescomplemented
73C2×C22⋊Dic61—21no—
74C2×#11758198—22no—
75C22⋊C4×D61—44no—
76C22⋊#92418—22no—
77#14519689—24no—
78#14519684—21no—
79#14519684—22no—
80C23×C4×C61—21no—
81C23×C4×C61C2311yescharacteristic
82C22×C8×C61C2312yes—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61C2×C414yescomplemented
86C2×C4⋊C4×C61C2312yes—
87C2×C4⋊C4×C61C2312yes—
88C2×C22⋊C4×C61—21no—
89C22⋊C8×C61—22no—
90#95×C61—21no—
91C24×C61C2×D411yescharacteristic
92C23×D61—24no—
93C23×D61—24no—
94C23×D61C22⋊C414yes—
95C23×D61D814yes—
96C23×D61SD1614yes—
97C23×D61C2×D411yescharacteristic
98C23×D61C2×D411yescharacteristic
99C22×C4×C61—24no—
100C22×C4×C61—24no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—42no—
104C22×C4×C61—42no—
105C22×C4×C61C22×C412yes—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D412yes—
108C22×C4×C61C2411yescharacteristic
109C22×Dic61—24no—
110C22×Dic61—24no—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—42no—
114C22×Dic61—42no—
115C22×Dic61C22⋊C414yes—
116C22×Dic61C2×D411yescharacteristic
117C22×Dic61C2×D411yescharacteristic
118C2×C4×D61—24no—
119C2×C4×D61—24no—
120C2×C4×D61—24no—
121C2×C4×D61—216no—
122C2×C4×D61—216no—
123C2×C4×D61—28no—
124C2×C4×D61—28no—
125C2×C4×D61—432no—
126C2×C4×D61—44no—
127C2×C4×D61—44no—
128C2×C4×D61—44no—
129C2×C4×D61—44no—
130C2×C4×D61—44no—
131C2×C4×D61—44no—
132C2×C4×D61—44no—
133C2×C4×D61C22⋊C414yes—
134C2×C4×D61C22⋊C414yes—
135C2×C4×D61C22×C412yes—
136C2×C4×D61C22×C412yes—
137C2×C4×D61C2×D412yes—
138C2×C4×D61C2×D412yes—
139C2×C4×D61#4118yes—
140C2×C8×C61—22no—
141C2×C8×C61—24no—
142C4⋊C4×C61—24no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—24no—
145C4⋊C4×C61C22×C414yes—
146C22⋊C4×C61—42no—
147C22⋊Dic61—42no—
148#11758198—44no—
149C4⋊Dic61—24no—
150C4⋊Dic61—22no—
151C4⋊Dic61—24no—
152C4⋊Dic61C22×C414yes—
153#11758196—28no—
154#11758196—28no—
155#11758196—44no—
156C2×#92418—22no—
157C2×#92418—24no—
158C8×D61—48no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61C2×C22⋊C412yes—
162C23×C61C2×D812yes—
163C23×C61C2×SD1612yes—
164C23×C61C22×D411yescharacteristic
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—28no—
168C22×D61—28no—
169C22×D61—216no—
170C22×D61—216no—
171C22×D61#102116yes—
172C22×D61C2×C22⋊C412yes—
173C22×D61C2×C22⋊C412yes—
174C22×D61#12314yes—
175C22×D61C2×D812yes—
176C22×D61C2×D812yes—
177C22×D61C2×SD1612yes—
178C22×D61C2×SD1612yes—
179C22×D61#13714yes—
180C2×C4×C61—22no—
181C2×C4×C61—24no—
182C2×C4×C61—24no—
183C2×C4×C61—24no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—48no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61C2×C22⋊C412yes—
191C2×C4×C61C23×C411yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C2×C4×C61C2×#4114yes—
194C2×Dic61—22no—
195C2×Dic61—28no—
196C2×Dic61—24no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—48no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61C2×C22⋊C412yes—
204C2×Dic61C2×C22⋊C412yes—
205C2×Dic61#12314yes—
206C4×D61—28no—
207C4×D61—24no—
208C4×D61—24no—
209C4×D61—28no—
210C4×D61—416no—
211C4×D61—416no—
212C4×D61—88no—
213C4×D61#11718yes—
214C4×D61#12318yes—
215C8×C61—42no—
216#92418—42no—
217C2×#1823—611nomaximal, Sylow
218C22×C61—24no—
219C22×C61—24no—
220C22×C61—22no—
221C22×C61—22no—
222C22×C61C2×#10214yes—
223C22×C61C22×C22⋊C411yescharacteristic
224C22×C61C2×#12312yes—
225C22×C61C22×D811yescharacteristic
226C22×C61C22×SD1611yescharacteristic
227C22×C61C2×#13712yes—
228C2×D61—24no—
229C2×D61—24no—
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—232no—
233C2×D61#38114yes—
234C2×D61C2×#10214yes—
235C2×D61C2×#10214yes—
236C2×D61#41914yes—
237C2×D61#48018yes—
238C2×D61#48318yes—
239C4×C61—22no—
240C4×C61—44no—
241C4×C61—82no—
242C4×C61C2×#11712yes—
243C4×C61C2×#12312yes—
244Dic61—22no—
245Dic61—44no—
246Dic61—82no—
247Dic61#38114yes—
248C23×C4⋊C4—611no—
249C22×C22⋊C8—611no—
250C2×#380—611no—
251#1823—611no—
252#1823—611no—
253#1823—614no—
254#1823—611no—
255#1823D6111yescharacteristic, direct product factor
256C2×#340—614no—
257C2×C61—24no—
258C2×C61C2×#38111yescharacteristic
259C2×C61C22×#10211yescharacteristic
260C2×C61C2×#41911yescharacteristic
261C2×C61C2×#48012yes—
262C2×C61C2×#48312yes—
263D61—24no—
264D61#182318yesdirect product factor
265C24×C4—611no—
266C24×C4—1221no—
267C23×C8—612no—
268C22×C4⋊C4—611no—
269C22×C4⋊C4—618no—
270C22×C4⋊C4—612no—
271C22×C4⋊C4—612no—
272C22×C4⋊C4—612no—
273C22×C4⋊C4—1221no—
274C22×C4⋊C4—1221no—
275C22×C4⋊C4—1224no—
276C22×C4⋊C4—1221no—
277C22×C4⋊C4C2×D6111yescharacteristic
278C22×C22⋊C4—1221no—
279C2×C22⋊C8—611no—
280C2×C22⋊C8—612no—
281C2×C22⋊C8—1224no—
282C2×C22⋊C8C2×D6111yescharacteristic
283#380—611no—
284#380—612no—
285#380—1221no—
286#380—1221no—
287#380C2×D6111yescharacteristic
288C2×#95—1221no—
289#340—614no—
290#340—614no—
291#340—614no—
292#340C2×D6114yescomplemented
293C61C2×#182311yescharacteristic, complemented, Sylow
294C25—611no—
295C23×C4—21no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—614no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—614no—
302C23×C4—611no—
303C23×C4—1228no—
304C23×C4—1222no—
305C23×C4—1222no—
306C23×C4—1228no—
307C23×C4—1222no—
308C23×C4—1221no—
309C23×C4—2444no—
310C23×C4—2444no—
311C23×C4C22×D6111yescharacteristic
312C22×C8—612no—
313C22×C8—1224no—
314C22×C8—1228no—
315C22×C8C22×D6112yes—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—614no—
319C2×C4⋊C4—612no—
320C2×C4⋊C4—618no—
321C2×C4⋊C4—618no—
322C2×C4⋊C4—612no—
323C2×C4⋊C4—1224no—
324C2×C4⋊C4—1224no—
325C2×C4⋊C4—1228no—
326C2×C4⋊C4—1228no—
327C2×C4⋊C4—1228no—
328C2×C4⋊C4—1222no—
329C2×C4⋊C4—1222no—
330C2×C4⋊C4—1228no—
331C2×C4⋊C4—1222no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4—1222no—
334C2×C4⋊C4C4×D6114yescomplemented
335C2×C4⋊C4C22×D6112yes—
336C2×C4⋊C4C22×D6112yes—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—2444no—
341C22⋊C8—22no—
342C22⋊C8—1224no—
343C22⋊C8—1222no—
344#95—21no—
345#95—1222no—
346#95—1221no—
347C24—611no—
348C24—611no—
349C24—614no—
350C24—614no—
351C24—614no—
352C24—1224no—
353C24—1224no—
354C24D4×D6111yescharacteristic
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—611no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—618no—
365C22×C4—611no—
366C22×C4—614no—
367C22×C4—612no—
368C22×C4—612no—
369C22×C4—614no—
370C22×C4—614no—
371C22×C4—1224no—
372C22×C4—12216no—
373C22×C4—12216no—
374C22×C4—1224no—
375C22×C4—1228no—
376C22×C4—1228no—
377C22×C4—1224no—
378C22×C4—1224no—
379C22×C4—1222no—
380C22×C4—1224no—
381C22×C4—1222no—
382C22×C4—2444no—
383C22×C4—2444no—
384C22×C4—2444no—
385C22×C4—24432no—
386C22×C4—2444no—
387C22×C4—2444no—
388C22×C4—2444no—
389C22×C4—2444no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4C2×C4×D6112yes—
393C22×C4D4×D6112yes—
394C22×C4D4×D6111yescharacteristic
395C22×C4C23×D6111yescharacteristic
396C2×C8—22no—
397C2×C8—24no—
398C2×C8—1222no—
399C2×C8—1224no—
400C2×C8—2448no—
401C4⋊C4—22no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—614no—
405C4⋊C4—1228no—
406C4⋊C4—1228no—
407C4⋊C4—1222no—
408C4⋊C4—1224no—
409C4⋊C4—1224no—
410C4⋊C4—2444no—
411C4⋊C4C2×C4×D6114yes—
412C22⋊C4—42no—
413C22⋊C4—2444no—
414C22⋊C4—2442no—
415C23—22no—
416C23—22no—
417C23—612no—
418C23—614no—
419C23—612no—
420C23—612no—
421C23—614no—
422C23—612no—
423C23—6116no—
424C23—612no—
425C23—612no—
426C23—1228no—
427C23—12216no—
428C23—12216no—
429C23—1228no—
430C23—1222no—
431C23—1222no—
432C23C22⋊C4×D6112yes—
433C23D8×D6112yes—
434C23SD16×D6112yes—
435C23C2×D4×D6111yescharacteristic
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—612no—
447C2×C4—614no—
448C2×C4—618no—
449C2×C4—618no—
450C2×C4—612no—
451C2×C4—1228no—
452C2×C4—1228no—
453C2×C4—1228no—
454C2×C4—1222no—
455C2×C4—1224no—
456C2×C4—1224no—
457C2×C4—1224no—
458C2×C4—4888no—
459C2×C4—24416no—
460C2×C4—24416no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2448no—
465C2×C4—2442no—
466C2×C4—2442no—
467C2×C4C22⋊C4×D6112yes—
468C2×C4C22×C4×D6111yescharacteristic
469C2×C4C2×D4×D6111yescharacteristic
470C2×C4#41×D6114yes—
471C8—42no—
472C8—2442no—
473C22—22no—
474C22—24no—
475C22—24no—
476C22—22no—
477C22—614no—
478C22—618no—
479C22—618no—
480C22—614no—
481C22—614no—
482C22—614no—
483C22—12232no—
484C22—1222no—
485C22—1224no—
486C22—1224no—
487C22—1222no—
488C22#102×D6114yes—
489C22C2×C22⋊C4×D6111yescharacteristic
490C22#123×D6112yes—
491C22C2×D8×D6111yescharacteristic
492C22C2×SD16×D6111yescharacteristic
493C22#137×D6112yes—
494C4—22no—
495C4—44no—
496C4—82no—
497C4—614no—
498C4—1222no—
499C4—4882no—
500C4—2444no—
501C4#117×D6112yes—
502C4#123×D6112yes—
503C2—24no—
504C2—618no—
505C2—1224no—
506C2#381×D6111yescharacteristic
507C2C2×#102×D6111yescharacteristic
508C2#419×D6111yescharacteristic
509C2#480×D6112yes—
510C2#483×D6112yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1823C2
socleC23×C61C22×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1823D61
hypocenterC61C2×#1823
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #21445906C2semidirect
5. #21445905C2semidirect
6. #21445904C2semidirect
7. #21445903C2semidirect
8. #340×D61C2semidirect
9. C61×#1823C2semidirect
18. C2×C4⋊C4×D61C4semidirect
31. #16839525C22semidirect
32. #16839524C22semidirect
33. #16839524C22semidirect
37. C61×#340C22semidirect
59. C2×C4⋊Dic61C2×C4semidirect
72. C4⋊C4×D61C2×C4semidirect
85. C2×C4⋊C4×C61C2×C4semidirect
255. #1823D61direct (N × H)
264. D61#1823direct (N × H)
292. #340C2×D61semidirect
293. C61C2×#1823semidirect
334. C2×C4⋊C4C4×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×C22⋊C8×D612
#380×D612
#214459062
#214459052
#214459042
#214459032
#340×D612
C61×#18232
C2×#182361