Finite Group Databasebeta

← D61×#2243 #29835317

Subgroups — D61×#2243 #29835317

Order 15616.

634 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D61C211yesmaximal, characteristic, complemented
2#495×D61C211yesmaximal, characteristic
3#21448058C211yesmaximal, characteristic, complemented
4#21448057C212yesmaximal, complemented
5#21448056C211yesmaximal, characteristic, complemented
6#21448055C211yesmaximal, characteristic, complemented
7#21448054C212yesmaximal, complemented
8#358×D61C212yesmaximal, complemented
9#357×D61C212yesmaximal
10#346×D61C211yesmaximal, characteristic, complemented
11C61×#2243C211yesmaximal, characteristic, complemented
12C2×Q16×D61C2211yescharacteristic
13C2×SD16×D61—21no—
14C2×D8×D61C2211yescharacteristic
15C4⋊Q8×D61—21no—
16#124×D61—21no—
17C2×C16×D61C2212yes—
18#16840167C2211yescharacteristic, complemented
19#16840166—21no—
20#16840166C2212yescomplemented
21#16840165—21no—
22#16840147C2211yescharacteristic
23#16840146C2211yescharacteristic
24#16840145C2211yescharacteristic
25#16840144—21no—
26#16840143—21no—
27#107×D61—21no—
28#107×D61C2212yes—
29C4×C8×D61C2211yescharacteristic
30#16839567C2212yescomplemented
31#16839566C2212yescomplemented
32#16839565C2212yescomplemented
33#16839564C2212yes—
34#16839563C2212yes—
35#16839562C2212yes—
36#16839538C2211yescharacteristic, complemented
37#16839537C2212yescomplemented
38C61×#500C2211yescharacteristic, complemented
39C61×#495C2211yescharacteristic
40C61×#358C2212yescomplemented
41C61×#357C2212yes—
42C61×#346C2211yescharacteristic, complemented
43C2×Q8×D61—21no—
44C2×Q8×D61—41no—
45C2×D4×D61—21no—
46C2×Dic244C2311yescharacteristic
47C2×#11758202—21no—
48Q16×D61—24no—
49C2×#11758190—21no—
50C2×#11758200—21no—
51C2×#11758201—21no—
52SD16×D61—44no—
53C2×D488C2311yescharacteristic
54C2×#11758199—21no—
55D8×D61—24no—
56C2×C8×D61D411yescharacteristic
57C2×C8×D61C2311yescharacteristic
58#14519777—21no—
59#14519776—22no—
60#14519776—41no—
61#14519775—41no—
62#14519766—21no—
63#14519765—21no—
64#14519764—21no—
65#14519763—41no—
66#14519763—41no—
67C4⋊C4×D61—22no—
68C4⋊C4×D61—41no—
69C22⋊C4×D61—41no—
70C22⋊C4×D61—41no—
71C42×D61D411yescharacteristic
72C2×#11758185C2312yes—
73C16×D61—24no—
74#14519711—21no—
75#14519711C2312yes—
76#14519710—22no—
77#14519710—22no—
78C4×#92418D411yescharacteristic
79C8×Dic61D411yescharacteristic
80C8×Dic61C2311yescharacteristic
81C2×Q16×C61C2311yescharacteristic
82C2×SD16×C61—21no—
83C2×D8×C61C2311yescharacteristic
84C4⋊Q8×C61—21no—
85#124×C61—21no—
86C2×C16×C61C2312yes—
87#107×C61—21no—
88#107×C61C2312yes—
89C4×C8×C61C2311yescharacteristic
90C23×D61—41no—
91C2×Q8×C61—21no—
92C2×Q8×C61—41no—
93C2×D4×C61—21no—
94C2×C22⋊D61—41no—
95Q8×D61—42no—
96Q8×D61—42no—
97Q8×D61—84no—
98D4×D61—42no—
99D4×D61—42no—
100C2×D244—21no—
101C2×C4×D61—41no—
102C2×C4×D61—42no—
103C2×C4×D61D811yescharacteristic
104C2×C4×D61D811yescharacteristic
105C2×C4×D61C2×D411yescharacteristic
106C2×Dic122—21no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—42no—
110Q16×C61—22no—
111SD16×C61—42no—
112D8×C61—22no—
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2411yescharacteristic
115C4⋊C4×C61—22no—
116C4⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C42×C61C2×D411yescharacteristic
120C22⋊Dic61—41no—
121C22⋊Dic61—41no—
122#11758202—42no—
123#11758201—42no—
124#11758200—42no—
125#11758199—42no—
126#11758198—41no—
127#11758198—41no—
128#11758198—41no—
129#11758198—41no—
130C4⋊Dic61—22no—
131C4⋊Dic61—41no—
132#11758196—42no—
133#11758196—42no—
134C4×Dic61D811yescharacteristic
135C4×Dic61D811yescharacteristic
136C4×Dic61C2×D411yescharacteristic
137C2×#92418C2×D411yescharacteristic
138C2×#92418C2×D411yescharacteristic
139Dic244—22no—
140D488—22no—
141#11758190—42no—
142C8×D61SD1614yes—
143C8×D61#4114yes—
144C16×C61—22no—
145#11758185—22no—
146C23×C61—41no—
147C22×D61—41no—
148C22×D61—82no—
149C22×D61—82no—
150C22×D61—82no—
151C22×D61C2×D811yescharacteristic
152Q8×C61—41no—
153Q8×C61—41no—
154Q8×C61—82no—
155D4×C61—41no—
156D4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C22⋊D61—82no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61C2×D811yescharacteristic
166C2×Dic61C2×D811yescharacteristic
167C2×Dic61C2×D811yescharacteristic
168D244—41no—
169D244—41no—
170C4×D61—22no—
171C4×D61—22no—
172C4×D61—82no—
173C4×D61—84no—
174C4×D61#12412yes—
175C4×D61C2×SD1612yes—
176Dic122—41no—
177Dic122—41no—
178Dic122—84no—
179Dic122—82no—
180Dic122—82no—
181C8×C61C2×SD1612yes—
182C8×C61C2×#4112yes—
183#92418#12412yes—
184#92418C2×SD1612yes—
185C2×#2243—611nomaximal, Sylow
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61C22×D811yescharacteristic
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—164no—
194C2×D61#48612yes—
195C2×D61#50912yes—
196C2×D61#51012yes—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—81no—
200C4×C61—82no—
201C4×C61C2×#12411yescharacteristic
202C4×C61C22×SD1611yescharacteristic
203Dic61—21no—
204Dic61—21no—
205Dic61—81no—
206Dic61—82no—
207Dic61#48612yes—
208C2×#500—611no—
209C2×#495—611no—
210#2243—611no—
211#2243—611no—
212#2243—612no—
213#2243—612no—
214#2243—611no—
215#2243D6111yescharacteristic, direct product factor
216C2×#358—612no—
217C2×#357—612no—
218C2×#346—611no—
219C2×C61—161no—
220C2×C61C2×#48611yescharacteristic
221C2×C61C2×#50911yescharacteristic
222C2×C61C2×#51011yescharacteristic
223D61—161no—
224D61#224314yesdirect product factor
225C22×Q16—611no—
226C22×SD16—1221no—
227C22×D8—611no—
228C2×C4⋊Q8—1221no—
229C2×#124—1221no—
230C22×C16—612no—
231#500—612no—
232#500—611no—
233#500—1221no—
234#500—1221no—
235#500C2×D6111yescharacteristic, complemented
236#495—611no—
237#495—611no—
238#495—611no—
239#495—1221no—
240#495—1221no—
241#495C2×D6111yescharacteristic
242C2×#107—612no—
243C2×#107—1221no—
244C2×C4×C8—611no—
245#358—612no—
246#358—612no—
247#358—612no—
248#358C2×D6112yescomplemented
249#357—612no—
250#357—612no—
251#357—612no—
252#357C2×D6112yes—
253#346—612no—
254#346—611no—
255#346C2×D6111yescharacteristic, complemented
256C61C2×#224311yescharacteristic, complemented, Sylow
257C22×Q8—1221no—
258C22×Q8—2441no—
259C22×D4—1221no—
260C2×Q16—611no—
261C2×Q16—1224no—
262C2×Q16—1221no—
263C2×Q16C22×D6111yescharacteristic
264C2×SD16—21no—
265C2×SD16—1221no—
266C2×SD16—1221no—
267C2×SD16—1221no—
268C2×SD16—2444no—
269C2×D8—611no—
270C2×D8—1224no—
271C2×D8—1221no—
272C2×D8C22×D6111yescharacteristic
273C22×C8—611no—
274C22×C8—611no—
275C4⋊Q8—21no—
276C4⋊Q8—1222no—
277C4⋊Q8—1221no—
278C4⋊Q8—2441no—
279C4⋊Q8—2441no—
280#124—21no—
281#124—1221no—
282#124—1221no—
283#124—1221no—
284#124—2441no—
285#124—2441no—
286C2×C4⋊C4—1222no—
287C2×C4⋊C4—2441no—
288C2×C22⋊C4—2441no—
289C2×C22⋊C4—2441no—
290C2×C42—611no—
291C2×C16—612no—
292C2×C16—1224no—
293C2×C16C22×D6112yes—
294#107—21no—
295#107—612no—
296#107—1222no—
297#107—1222no—
298#107—1221no—
299#107C22×D6112yes—
300C4×C8—611no—
301C4×C8—611no—
302C4×C8—611no—
303C4×C8C22×D6111yescharacteristic
304C24—2441no—
305C2×Q8—21no—
306C2×Q8—41no—
307C2×Q8—1221no—
308C2×Q8—4884no—
309C2×Q8—2441no—
310C2×Q8—2442no—
311C2×Q8—2442no—
312C2×Q8—2442no—
313C2×Q8—2441no—
314C2×D4—21no—
315C2×D4—1221no—
316C2×D4—2442no—
317C2×D4—2442no—
318C2×D4—2441no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—2441no—
323C22×C4—2442no—
324Q16—22no—
325Q16—1222no—
326Q16—2442no—
327SD16—42no—
328SD16—2442no—
329SD16—2442no—
330SD16—2442no—
331D8—22no—
332D8—1222no—
333D8—2442no—
334C2×C8—611no—
335C2×C8—611no—
336C2×C8—614no—
337C2×C8—614no—
338C2×C8D4×D6111yescharacteristic
339C2×C8C23×D6111yescharacteristic
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—1222no—
343C4⋊C4—2442no—
344C4⋊C4—2442no—
345C4⋊C4—2441no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C42—611no—
355C42—611no—
356C42—611no—
357C42D4×D6111yescharacteristic
358C16—22no—
359C16—1222no—
360C23—41no—
361C23—611no—
362C23—4882no—
363C23—4882no—
364C23—4882no—
365C23—2441no—
366Q8—41no—
367Q8—41no—
368Q8—82no—
369Q8—4882no—
370Q8—4882no—
371Q8—4884no—
372Q8—2441no—
373Q8—2441no—
374D4—41no—
375D4—41no—
376D4—4882no—
377D4—2441no—
378D4—2441no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—611no—
382C2×C4—612no—
383C2×C4—612no—
384C2×C4—611no—
385C2×C4—611no—
386C2×C4—1222no—
387C2×C4—1222no—
388C2×C4—4884no—
389C2×C4—4882no—
390C2×C4—2441no—
391C2×C4—2442no—
392C2×C4D8×D6111yescharacteristic
393C2×C4D8×D6111yescharacteristic
394C2×C4C2×D4×D6111yescharacteristic
395C8—612no—
396C8—612no—
397C8SD16×D6112yes—
398C8#41×D6112yes—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—612no—
403C22—612no—
404C22—612no—
405C22—9764no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22C2×D8×D6111yescharacteristic
410C4—21no—
411C4—21no—
412C4—81no—
413C4—82no—
414C4—612no—
415C4—1221no—
416C4—1221no—
417C4—4881no—
418C4—4882no—
419C4#124×D6111yescharacteristic
420C4C2×SD16×D6111yescharacteristic
421C2—161no—
422C2—614no—
423C2—9761no—
424C2#486×D6111yescharacteristic
425C2#509×D6111yescharacteristic
426C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2243C2
socleC22×C61C22×D8
prime radicalC2×D8×D61C22
hypercenter#2243D61
hypocenterC61C2×#2243
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. #500×D61C2semidirect
3. #21448058C2semidirect
4. #21448057C2semidirect
5. #21448056C2semidirect
6. #21448055C2semidirect
7. #21448054C2semidirect
8. #358×D61C2semidirect
10. #346×D61C2semidirect
11. C61×#2243C2semidirect
18. #16840167C22semidirect
20. #16840166C22semidirect
30. #16839567C22semidirect
31. #16839566C22semidirect
32. #16839565C22semidirect
36. #16839538C22semidirect
37. #16839537C22semidirect
38. C61×#500C22semidirect
40. C61×#358C22semidirect
42. C61×#346C22semidirect
215. #2243D61direct (N × H)
224. D61#2243direct (N × H)
235. #500C2×D61semidirect
248. #358C2×D61semidirect
255. #346C2×D61semidirect
256. C61C2×#2243semidirect

Maximal subgroups

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

subgroupindex
#500×D612
#495×D612
#214480582
#214480572
#214480562
#214480552
#214480542
#358×D612
#357×D612
#346×D612
C61×#22432
C2×#224361