Finite Group Databasebeta

← D61×#2072 #29708753

Subgroups — D61×#2072 #29708753

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#103×D61C212yesmaximal
2#391×D61C211yesmaximal, characteristic
3#384×D61C211yesmaximal, characteristic
4#21447231C212yesmaximal, complemented
5#21447230C212yesmaximal, complemented
6#21447229C211yesmaximal, characteristic, complemented
7#21447228C211yesmaximal, characteristic, complemented
8#21447227C211yesmaximal, characteristic, complemented
9#340×D61C212yesmaximal
10#336×D61C211yesmaximal, characteristic
11C61×#2072C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2211yescharacteristic
13C22×C8×D61C2212yes—
14C2×C4⋊C4×D61—21no—
15C2×C4⋊C4×D61—21no—
16C2×C4⋊C4×D61C2212yes—
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19C2×#14519702C2212yes—
20C2×#14519701C2212yes—
21C2×#14519700C2212yes—
22#103×D61—28no—
23#16839669C2211yescharacteristic
24#16839668C2211yescharacteristic
25#16839667C2211yescharacteristic
26#16839666—21no—
27#16839666—21no—
28#16839632C2211yescharacteristic
29#16839631—21no—
30#16839631—21no—
31#16839631C2212yes—
32#95×D61—21no—
33#95×D61—21no—
34#16839525C2212yes—
35#16839524C2212yes—
36#16839524C2212yes—
37#16839517C2211yescharacteristic
38#16839516C2212yes—
39C2×#103×C61C2212yes—
40C61×#391C2211yescharacteristic
41C61×#384C2211yescharacteristic
42C61×#340C2212yes—
43C61×#336C2211yescharacteristic
44C22×Dic122—21no—
45C22×Dic122C2311yescharacteristic
46C2×Q8×D61—22no—
47C2×Q8×D61—24no—
48C2×Q8×D61—24no—
49C2×Q8×D61D414yes—
50C22×C4×D61—21no—
51C22×C4×D61—22no—
52C22×C4×D61—21no—
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C22×#92418C2312yes—
57C2×C8×D61—24no—
58C2×C8×D61—24no—
59C2×C8×D61—24no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61C2312yes—
63C2×C4⋊Dic61C2311yescharacteristic
64C2×#11758196—22no—
65C2×#11758196—22no—
66C2×#11758196—22no—
67C2×#11758196—21no—
68C4⋊C4×D61—24no—
69C4⋊C4×D61—24no—
70C4⋊C4×D61—24no—
71C4⋊C4×D61—44no—
72C4⋊C4×D61—44no—
73C2×C4×Dic61D411yescharacteristic
74C2×C4×Dic61D411yescharacteristic
75C2×C4×Dic61C2311yescharacteristic
76C42×D61—24no—
77#14519702—24no—
78#14519701—24no—
79#14519700—24no—
80#14519684—21no—
81#14519684—21no—
82#14519684—21no—
83#14519684—21no—
84#14519684—21no—
85#14519684—21no—
86C22×Q8×C61C2311yescharacteristic
87C22×C8×C61C2312yes—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2312yes—
92C2×C42×C61C2311yescharacteristic
93#103×C61—24no—
94#95×C61—21no—
95#95×C61—21no—
96C23×D61C2×D411yescharacteristic
97C2×Q8×C61—21no—
98C2×Q8×C61—22no—
99C2×Q8×C61—22no—
100C2×Q8×C61C2×D412yes—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2411yescharacteristic
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—22no—
110C22×Dic61C2×D411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112C22×Dic61C2×D411yescharacteristic
113Q8×D61—216no—
114Q8×D61—48no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—24no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—44no—
123C2×C4×D61—42no—
124C2×C4×D61—44no—
125C2×C4×D61—42no—
126C2×C4×D61—44no—
127C2×C4×D61—42no—
128C2×C4×D61SD1614yes—
129C2×C4×D61Q1614yes—
130C2×C4×D61C2×D412yes—
131C2×C4×D61#4114yes—
132C2×C4×D61#4114yes—
133C2×C4×D61#4112yes—
134C2×Dic122—22no—
135C2×Dic122—22no—
136C2×Dic122—21no—
137C2×Dic122—24no—
138C2×Dic122—42no—
139C2×Dic122—42no—
140C2×Dic122C2×D412yes—
141C2×C8×C61—22no—
142C2×C8×C61—22no—
143C2×C8×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—42no—
148C4⋊C4×C61—42no—
149C42×C61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—42no—
154C4⋊Dic61—42no—
155#11758196—44no—
156#11758196—44no—
157#11758196—42no—
158#11758196—44no—
159C4×Dic61—22no—
160C4×Dic61—22no—
161C4×Dic61—22no—
162C2×#92418—22no—
163C2×#92418—22no—
164C2×#92418—22no—
165C8×D61—48no—
166C23×C61C22×D411yescharacteristic
167C22×D61#12112yes—
168C22×D61#12312yes—
169C22×D61#12412yes—
170C22×D61C2×SD1612yes—
171C22×D61C2×Q1612yes—
172C22×D61AGL(1,ℤ/8)12yes—
173C22×D61#13712yes—
174Q8×C61—24no—
175Q8×C61—42no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—22no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—42no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61C2×SD1612yes—
190C2×C4×C61C2×Q1612yes—
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C2×#4112yes—
193C2×C4×C61C2×#4112yes—
194C2×C4×C61C2×#4111yescharacteristic
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—22no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—42no—
203C2×Dic61—41no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61#12112yes—
209C2×Dic61#12312yes—
210C2×Dic61#12412yes—
211C2×Dic61C2×SD1612yes—
212C2×Dic61C2×Q1612yes—
213C4×D61—28no—
214C4×D61—28no—
215C4×D61—48no—
216C4×D61—88no—
217C4×D61—84no—
218C4×D61#12318yes—
219C4×D61#12618yes—
220Dic122—24no—
221Dic122—42no—
222Dic122—48no—
223C8×C61—42no—
224#92418—42no—
225C2×#2072—611nomaximal, Sylow
226C22×C61C2×#12111yescharacteristic
227C22×C61C2×#12311yescharacteristic
228C22×C61C2×#12411yescharacteristic
229C22×C61C22×SD1611yescharacteristic
230C22×C61C22×Q1611yescharacteristic
231C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
232C22×C61C2×#13711yescharacteristic
233C2×D61#39714yes—
234C2×D61#46014yes—
235C2×D61#46214yes—
236C2×D61#48314yes—
237C2×D61#48414yes—
238C2×D61#48714yes—
239C2×D61#48914yes—
240C4×C61—22no—
241C4×C61—22no—
242C4×C61—42no—
243C4×C61—81no—
244C4×C61—82no—
245C4×C61C2×#12312yes—
246C4×C61C2×#12612yes—
247Dic61—22no—
248Dic61—22no—
249Dic61—42no—
250Dic61—81no—
251Dic61—82no—
252Dic61#39714yes—
253C22×#103—612no—
254C2×#391—611no—
255C2×#384—611no—
256#2072—612no—
257#2072—611no—
258#2072—611no—
259#2072—612no—
260#2072—611no—
261#2072D6111yescharacteristic, direct product factor
262C2×#340—612no—
263C2×#336—611no—
264C2×C61C2×#39711yescharacteristic
265C2×C61C2×#46011yescharacteristic
266C2×C61C2×#46211yescharacteristic
267C2×C61C2×#48311yescharacteristic
268C2×C61C2×#48411yescharacteristic
269C2×C61C2×#48711yescharacteristic
270C2×C61C2×#48911yescharacteristic
271D61#207218yesdirect product factor
272C23×Q8—611no—
273C23×C8—612no—
274C22×C4⋊C4—612no—
275C22×C4⋊C4—611no—
276C22×C4⋊C4—1221no—
277C22×C4⋊C4—1221no—
278C22×C42—611no—
279C2×#103—612no—
280C2×#103—612no—
281C2×#103—612no—
282C2×#103—1228no—
283C2×#103C2×D6112yes—
284#391—611no—
285#391—611no—
286#391—611no—
287#391—1221no—
288#391—1221no—
289#391C2×D6111yescharacteristic
290#384—612no—
291#384—611no—
292#384—1221no—
293#384—1221no—
294#384C2×D6111yescharacteristic
295C2×#95—1221no—
296C2×#95—1221no—
297#340—612no—
298#340—612no—
299#340—612no—
300#340C2×D6112yes—
301#336—612no—
302#336—611no—
303#336C2×D6111yescharacteristic
304C61C2×#207211yescharacteristic, complemented, Sylow
305C22×Q8—614no—
306C22×Q8—611no—
307C22×Q8—1221no—
308C22×Q8—1222no—
309C22×Q8—1224no—
310C22×Q8—1224no—
311C22×Q8C22×D6111yescharacteristic
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—1221no—
316C23×C4—1222no—
317C23×C4—1221no—
318C22×C8—612no—
319C22×C8—1224no—
320C22×C8—1224no—
321C22×C8—1224no—
322C22×C8C22×D6112yes—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—611no—
326C2×C4⋊C4—612no—
327C2×C4⋊C4—1224no—
328C2×C4⋊C4—1224no—
329C2×C4⋊C4—1224no—
330C2×C4⋊C4—1222no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4—1222no—
333C2×C4⋊C4—1222no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—2444no—
337C2×C4⋊C4—2444no—
338C2×C4⋊C4C22×D6111yescharacteristic
339C2×C4⋊C4C22×D6112yes—
340C2×C42—611no—
341C2×C42—611no—
342C2×C42—611no—
343C2×C42—1224no—
344C2×C42C22×D6111yescharacteristic
345#103—24no—
346#103—1224no—
347#103—1224no—
348#103—1224no—
349#95—21no—
350#95—21no—
351#95—1221no—
352#95—1221no—
353#95—1221no—
354#95—1221no—
355#95—1221no—
356#95—1221no—
357C24—611no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—612no—
362C2×Q8—1224no—
363C2×Q8—12216no—
364C2×Q8—1221no—
365C2×Q8—1222no—
366C2×Q8—1222no—
367C2×Q8—2442no—
368C2×Q8—2442no—
369C2×Q8—2448no—
370C2×Q8D4×D6112yes—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—611no—
375C22×C4—612no—
376C22×C4—614no—
377C22×C4—612no—
378C22×C4—614no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—614no—
382C22×C4—614no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1224no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1222no—
391C22×C4—2444no—
392C22×C4—2442no—
393C22×C4—2444no—
394C22×C4—2444no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4D4×D6111yescharacteristic
400C22×C4D4×D6111yescharacteristic
401C22×C4C23×D6111yescharacteristic
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—1222no—
406C2×C8—1222no—
407C2×C8—1222no—
408C2×C8—2448no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—1222no—
415C4⋊C4—1222no—
416C4⋊C4—1222no—
417C4⋊C4—2442no—
418C4⋊C4—2444no—
419C4⋊C4—2442no—
420C4⋊C4—2444no—
421C4⋊C4—2444no—
422C4⋊C4—2442no—
423C42—22no—
424C42—1222no—
425C42—1222no—
426C42—1222no—
427C23—612no—
428C23—612no—
429C23—612no—
430C23—612no—
431C23—612no—
432C23—612no—
433C23—612no—
434C23C2×D4×D6111yescharacteristic
435Q8—24no—
436Q8—42no—
437Q8—1224no—
438Q8—2448no—
439Q8—2442no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—612no—
454C2×C4—612no—
455C2×C4—612no—
456C2×C4—618no—
457C2×C4—618no—
458C2×C4—612no—
459C2×C4—612no—
460C2×C4—1228no—
461C2×C4—1228no—
462C2×C4—1221no—
463C2×C4—1221no—
464C2×C4—1221no—
465C2×C4—1221no—
466C2×C4—1222no—
467C2×C4—4884no—
468C2×C4—4888no—
469C2×C4—2448no—
470C2×C4—2442no—
471C2×C4—2441no—
472C2×C4—2442no—
473C2×C4—2442no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4SD16×D6112yes—
479C2×C4Q16×D6112yes—
480C2×C4C2×D4×D6111yescharacteristic
481C2×C4#41×D6112yes—
482C2×C4#41×D6112yes—
483C2×C4#41×D6111yescharacteristic
484C8—42no—
485C8—2442no—
486C22—614no—
487C22—614no—
488C22—614no—
489C22—614no—
490C22—614no—
491C22—614no—
492C22—614no—
493C22#121×D6111yescharacteristic
494C22#123×D6111yescharacteristic
495C22#124×D6111yescharacteristic
496C22C2×SD16×D6111yescharacteristic
497C22C2×Q16×D6111yescharacteristic
498C22AGL(1,ℤ/8)×D6111yescharacteristic
499C22#137×D6111yescharacteristic
500C4—22no—
501C4—22no—
502C4—42no—
503C4—81no—
504C4—82no—
505C4—614no—
506C4—1222no—
507C4—1222no—
508C4—4881no—
509C4—4882no—
510C4—2442no—
511C4#123×D6112yes—
512C4#126×D6112yes—
513C2—618no—
514C2#397×D6111yescharacteristic
515C2#460×D6111yescharacteristic
516C2#462×D6111yescharacteristic
517C2#483×D6111yescharacteristic
518C2#484×D6111yescharacteristic
519C2#487×D6111yescharacteristic
520C2#489×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2072C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2072D61
hypocenterC61C2×#2072
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
4. #21447231C2semidirect
5. #21447230C2semidirect
6. #21447229C2semidirect
7. #21447228C2semidirect
8. #21447227C2semidirect
11. C61×#2072C2semidirect
261. #2072D61direct (N × H)
271. D61#2072direct (N × H)
304. C61C2×#2072semidirect

Maximal subgroups

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

subgroupindex
C2×#103×D612
#391×D612
#384×D612
#214472312
#214472302
#214472292
#214472282
#214472272
#340×D612
#336×D612
C61×#20722
C2×#207261