Finite Group Databasebeta

← D61×#2100 #29709919

Subgroups — D61×#2100 #29709919

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D61C211yesmaximal, characteristic
2#384×D61C211yesmaximal, characteristic
3#21447385C212yesmaximal, complemented
4#21447384C212yesmaximal, complemented
5#21447383C211yesmaximal, characteristic, complemented
6#21447382C211yesmaximal, characteristic, complemented
7#21447381C211yesmaximal, characteristic, complemented
8#340×D61C212yesmaximal
9#340×D61C212yesmaximal
10#336×D61C211yesmaximal, characteristic
11C61×#2100C211yesmaximal, characteristic, complemented
12C22×C8×D61C2212yes—
13C2×C4⋊C4×D61—21no—
14C2×C4⋊C4×D61—21no—
15C2×C4⋊C4×D61—21no—
16C2×C4⋊C4×D61C2212yes—
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839661C2211yescharacteristic
21#16839660C2211yescharacteristic
22#16839659—21no—
23#16839658C2211yescharacteristic
24#16839657—21no—
25#16839632C2211yescharacteristic
26#16839631—21no—
27#16839631—21no—
28#16839631C2212yes—
29#95×D61—21no—
30#16839525C2212yes—
31#16839525C2212yes—
32#16839524C2212yes—
33#16839524C2212yes—
34#16839524C2212yes—
35#16839524C2212yes—
36#16839517C2211yescharacteristic
37#16839516C2212yes—
38C61×#389C2211yescharacteristic
39C61×#384C2211yescharacteristic
40C61×#340C2212yes—
41C61×#340C2212yes—
42C61×#336C2211yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61—22no—
45C22×C4×D61—21no—
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61C2311yescharacteristic
49C22×#92418C2312yes—
50C2×C8×D61—24no—
51C2×C8×D61—24no—
52C2×C8×D61—24no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61C2312yes—
57C2×C4⋊Dic61C2311yescharacteristic
58C2×C4⋊Dic61C2311yescharacteristic
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196—22no—
62C2×#11758196—22no—
63C2×#11758196—21no—
64C2×#11758196—22no—
65C2×#11758196—21no—
66C4⋊C4×D61—22no—
67C4⋊C4×D61—24no—
68C4⋊C4×D61—28no—
69C4⋊C4×D61—44no—
70C4⋊C4×D61—44no—
71C4⋊C4×D61—44no—
72C4⋊C4×D61Q814yes—
73C2×C4×Dic61D411yescharacteristic
74C2×C4×Dic61D411yescharacteristic
75C2×C4×Dic61C2311yescharacteristic
76C42×D61—24no—
77#14519684—21no—
78#14519684—21no—
79#14519684—21no—
80C22×C8×C61C2312yes—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61C2312yes—
85C2×C4⋊C4×C61C2311yescharacteristic
86C2×C4⋊C4×C61C2311yescharacteristic
87C2×C42×C61C2311yescharacteristic
88#95×C61—21no—
89C23×D61C2×D411yescharacteristic
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2411yescharacteristic
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61C2×D411yescharacteristic
100C22×Dic61C2×D411yescharacteristic
101C22×Dic61C2×D411yescharacteristic
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—24no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—44no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—44no—
114C2×C4×D61—44no—
115C2×C4×D61SD1614yes—
116C2×C4×D61Q1614yes—
117C2×C4×D61C2×Q812yes—
118C2×C4×D61#4114yes—
119C2×C4×D61#4114yes—
120C2×C4×D61#4112yes—
121C2×C8×C61—22no—
122C2×C8×C61—22no—
123C2×C8×C61—22no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—24no—
127C4⋊C4×C61—42no—
128C4⋊C4×C61—42no—
129C4⋊C4×C61—42no—
130C4⋊C4×C61C2×Q812yes—
131C42×C61—22no—
132C4⋊Dic61—21no—
133C4⋊Dic61—22no—
134C4⋊Dic61—24no—
135C4⋊Dic61—42no—
136C4⋊Dic61—42no—
137C4⋊Dic61—42no—
138C4⋊Dic61C2×Q812yes—
139#11758196—24no—
140#11758196—44no—
141#11758196—44no—
142#11758196—42no—
143#11758196—42no—
144#11758196—44no—
145#11758196—42no—
146C4×Dic61—22no—
147C4×Dic61—22no—
148C4×Dic61—22no—
149C2×#92418—22no—
150C2×#92418—22no—
151C2×#92418—22no—
152C8×D61—48no—
153C23×C61C22×D411yescharacteristic
154C22×D61C22⋊Q812yes—
155C22×D61#12312yes—
156C22×D61#12412yes—
157C22×D61C2×SD1612yes—
158C22×D61C2×Q1612yes—
159C22×D61AGL(1,ℤ/8)12yes—
160C22×D61AGL(1,ℤ/8)12yes—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—22no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—41no—
174C2×C4×C61C2×SD1612yes—
175C2×C4×C61C2×Q1612yes—
176C2×C4×C61C22×Q811yescharacteristic
177C2×C4×C61C2×#4112yes—
178C2×C4×C61C2×#4112yes—
179C2×C4×C61C2×#4111yescharacteristic
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—22no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—42no—
189C2×Dic61—41no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—41no—
193C2×Dic61C22⋊Q812yes—
194C2×Dic61#12312yes—
195C2×Dic61#12412yes—
196C2×Dic61C2×SD1612yes—
197C2×Dic61C2×Q1612yes—
198C4×D61—28no—
199C4×D61—28no—
200C4×D61—48no—
201C4×D61—84no—
202C4×D61—88no—
203C4×D61#12518yes—
204C4×D61#12618yes—
205C8×C61—42no—
206#92418—42no—
207C2×#2100—611nomaximal, Sylow
208C22×C61C2×C22⋊Q811yescharacteristic
209C22×C61C2×#12311yescharacteristic
210C22×C61C2×#12411yescharacteristic
211C22×C61C22×SD1611yescharacteristic
212C22×C61C22×Q1611yescharacteristic
213C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
214C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
215C2×D61#40014yes—
216C2×D61#47614yes—
217C2×D61#47714yes—
218C2×D61#48114yes—
219C2×D61#48414yes—
220C2×D61#48714yes—
221C2×D61#49014yes—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—42no—
225C4×C61—81no—
226C4×C61—82no—
227C4×C61C2×#12512yes—
228C4×C61C2×#12612yes—
229Dic61—22no—
230Dic61—22no—
231Dic61—42no—
232Dic61—81no—
233Dic61—82no—
234Dic61#40014yes—
235C2×#389—611no—
236C2×#384—611no—
237#2100—611no—
238#2100—611no—
239#2100—612no—
240#2100—612no—
241#2100—611no—
242#2100D6111yescharacteristic, direct product factor
243C2×#340—612no—
244C2×#340—612no—
245C2×#336—611no—
246C2×C61C2×#40011yescharacteristic
247C2×C61C2×#47611yescharacteristic
248C2×C61C2×#47711yescharacteristic
249C2×C61C2×#48111yescharacteristic
250C2×C61C2×#48411yescharacteristic
251C2×C61C2×#48711yescharacteristic
252C2×C61C2×#49011yescharacteristic
253D61#210018yesdirect product factor
254C23×C8—612no—
255C22×C4⋊C4—611no—
256C22×C4⋊C4—612no—
257C22×C4⋊C4—611no—
258C22×C4⋊C4—1221no—
259C22×C4⋊C4—1221no—
260C22×C4⋊C4—1221no—
261C22×C42—611no—
262#389—611no—
263#389—611no—
264#389—611no—
265#389—1221no—
266#389—1221no—
267#389C2×D6111yescharacteristic
268#384—612no—
269#384—611no—
270#384—1221no—
271#384—1221no—
272#384C2×D6111yescharacteristic
273C2×#95—1221no—
274#340—612no—
275#340—612no—
276#340—612no—
277#340—612no—
278#340—612no—
279#340—612no—
280#340C2×D6112yes—
281#340C2×D6112yes—
282#336—612no—
283#336—611no—
284#336C2×D6111yescharacteristic
285C61C2×#210011yescharacteristic, complemented, Sylow
286C23×C4—611no—
287C23×C4—611no—
288C23×C4—611no—
289C23×C4—1221no—
290C23×C4—1222no—
291C23×C4—1221no—
292C22×C8—612no—
293C22×C8—1224no—
294C22×C8—1224no—
295C22×C8—1224no—
296C22×C8C22×D6112yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—614no—
302C2×C4⋊C4—612no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1222no—
305C2×C4⋊C4—1224no—
306C2×C4⋊C4—1228no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1222no—
311C2×C4⋊C4—1222no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—2444no—
318C2×C4⋊C4—2444no—
319C2×C4⋊C4—2444no—
320C2×C4⋊C4C22×D6112yes—
321C2×C4⋊C4C22×D6111yescharacteristic
322C2×C4⋊C4C22×D6111yescharacteristic
323C2×C42—611no—
324C2×C42—611no—
325C2×C42—611no—
326C2×C42—1224no—
327C2×C42C22×D6111yescharacteristic
328#95—21no—
329#95—1221no—
330#95—1221no—
331#95—1221no—
332C24—611no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—611no—
337C22×C4—612no—
338C22×C4—614no—
339C22×C4—614no—
340C22×C4—612no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—614no—
344C22×C4—614no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1224no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—2442no—
354C22×C4—2444no—
355C22×C4—2442no—
356C22×C4—2444no—
357C22×C4—2444no—
358C22×C4—2442no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4D4×D6111yescharacteristic
362C22×C4D4×D6111yescharacteristic
363C22×C4C23×D6111yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—1222no—
368C2×C8—1222no—
369C2×C8—1222no—
370C2×C8—2448no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—612no—
378C4⋊C4—1224no—
379C4⋊C4—1221no—
380C4⋊C4—1222no—
381C4⋊C4—1224no—
382C4⋊C4—2442no—
383C4⋊C4—2442no—
384C4⋊C4—2442no—
385C4⋊C4—2444no—
386C4⋊C4—2442no—
387C4⋊C4—2442no—
388C4⋊C4—2444no—
389C4⋊C4—2444no—
390C4⋊C4—2442no—
391C4⋊C4Q8×D6112yes—
392C42—22no—
393C42—1222no—
394C42—1222no—
395C42—1222no—
396C23—612no—
397C23—612no—
398C23—612no—
399C23—612no—
400C23—612no—
401C23—612no—
402C23—612no—
403C23C2×D4×D6111yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—612no—
418C2×C4—612no—
419C2×C4—612no—
420C2×C4—618no—
421C2×C4—618no—
422C2×C4—612no—
423C2×C4—612no—
424C2×C4—1228no—
425C2×C4—1228no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1222no—
431C2×C4—4888no—
432C2×C4—4884no—
433C2×C4—2448no—
434C2×C4—2441no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4SD16×D6112yes—
443C2×C4Q16×D6112yes—
444C2×C4C2×Q8×D6111yescharacteristic
445C2×C4#41×D6112yes—
446C2×C4#41×D6112yes—
447C2×C4#41×D6111yescharacteristic
448C8—42no—
449C8—2442no—
450C22—614no—
451C22—614no—
452C22—614no—
453C22—614no—
454C22—614no—
455C22—614no—
456C22—614no—
457C22C22⋊Q8×D6111yescharacteristic
458C22#123×D6111yescharacteristic
459C22#124×D6111yescharacteristic
460C22C2×SD16×D6111yescharacteristic
461C22C2×Q16×D6111yescharacteristic
462C22AGL(1,ℤ/8)×D6111yescharacteristic
463C22AGL(1,ℤ/8)×D6111yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—614no—
470C4—1222no—
471C4—1222no—
472C4—4882no—
473C4—4881no—
474C4—2442no—
475C4#125×D6112yes—
476C4#126×D6112yes—
477C2—618no—
478C2#400×D6111yescharacteristic
479C2#476×D6111yescharacteristic
480C2#477×D6111yescharacteristic
481C2#481×D6111yescharacteristic
482C2#484×D6111yescharacteristic
483C2#487×D6111yescharacteristic
484C2#490×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2100C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2100D61
hypocenterC61C2×#2100
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
3. #21447385C2semidirect
4. #21447384C2semidirect
5. #21447383C2semidirect
6. #21447382C2semidirect
7. #21447381C2semidirect
11. C61×#2100C2semidirect
242. #2100D61direct (N × H)
253. D61#2100direct (N × H)
285. C61C2×#2100semidirect

Maximal subgroups

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

subgroupindex
#389×D612
#384×D612
#214473852
#214473842
#214473832
#214473822
#214473812
#340×D612
#336×D612
C61×#21002
C2×#210061