Finite Group Databasebeta

← D61×#2159 #29833043

Subgroups — D61×#2159 #29833043

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D61C211yesmaximal, characteristic
2#427×D61C211yesmaximal, characteristic
3C2×#107×D61C211yesmaximal, characteristic
4#21447608C211yesmaximal, characteristic, complemented
5#21447607C211yesmaximal, characteristic, complemented
6#21447606C212yesmaximal, complemented
7#21447605C211yesmaximal, characteristic, complemented
8#21447604C212yesmaximal, complemented
9#367×D61C212yesmaximal, complemented
10#366×D61C212yesmaximal, complemented
11C61×#2159C211yesmaximal, characteristic, complemented
12C22×C8×D61C2211yescharacteristic
13#117×D61—21no—
14C2×C4⋊C4×D61—21no—
15C2×#14519717C2211yescharacteristic
16C2×#14519716C2212yes—
17M32×D61C418yescomplemented
18C2×C16×D61C2212yes—
19#16839800C2211yescharacteristic
20#16839799C2211yescharacteristic
21#16839799C2211yescharacteristic
22#16839798—21no—
23#16839797—21no—
24C2×#14519711C2211yescharacteristic
25C2×#14519710—21no—
26#107×D61—21no—
27#107×D61—21no—
28#107×D61C2212yes—
29#107×D61C2212yes—
30#107×D61C2211yescharacteristic
31#107×D61C2211yescharacteristic
32#106×D61—21no—
33#16839590C2212yescomplemented
34#16839589C2212yescomplemented
35#16839589C2212yescomplemented
36#16839588C2212yescomplemented
37#16839587C2212yescomplemented
38#16839587C2212yescomplemented
39C2×M32×C61C2211yescharacteristic
40C61×#427C2211yescharacteristic
41C2×#107×C61C2211yescharacteristic
42C61×#367C2212yescomplemented
43C61×#366C2212yescomplemented
44C22×C4×D61—41no—
45C22×C4×D61D411yescharacteristic
46C22×#92418D411yescharacteristic
47C2×C8×D61C2×C414yes—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61D411yescharacteristic
50C2×C8×D61Q814yes—
51C2×C8×D61C2311yescharacteristic
52C2×C8×D61C2311yescharacteristic
53#14519736—21no—
54#14519735—21no—
55#14519735—21no—
56#14519734—41no—
57#14519733—41no—
58C2×C4⋊Dic61—21no—
59C2×#11758196—41no—
60C4⋊C4×D61—22no—
61C4⋊C4×D61—22no—
62C4⋊C4×D61—21no—
63C4⋊C4×D61—21no—
64C4⋊C4×D61—41no—
65C4⋊C4×D61—41no—
66C22⋊C4×D61—41no—
67C42×D61—41no—
68#14519717C2×C414yescomplemented
69#14519716C2×C418yescomplemented
70C2×#11758185C2312yes—
71C16×D61C2×C418yescomplemented
72#14519711—21no—
73#14519711C2312yes—
74#14519711C2311yescharacteristic
75#14519711C2311yescharacteristic
76#14519710—22no—
77#14519710—22no—
78#14519710—21no—
79#14519710—21no—
80#14519709—21no—
81#14519708—21no—
82#14519708—21no—
83C22×C8×C61C2311yescharacteristic
84#117×C61—21no—
85C2×C4⋊C4×C61—21no—
86M32×C61C2×C414yescomplemented
87C2×C16×C61C2312yes—
88#107×C61—21no—
89#107×C61C2311yescharacteristic
90#107×C61C2312yes—
91#107×C61C2311yescharacteristic
92#106×C61—21no—
93C23×D61D811yescharacteristic
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×Dic61—41no—
97C22×Dic61D811yescharacteristic
98C2×C4×D61—42no—
99C2×C4×D61—42no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—84no—
103C2×C4×D61C4⋊C414yes—
104C2×C4×D61D811yescharacteristic
105C2×C4×D61D811yescharacteristic
106C2×C4×D61Q1614yes—
107C2×C4×D61C2×D411yescharacteristic
108C2×C4×D61C2×D411yescharacteristic
109C2×C8×C61C22×C412yes—
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×Q812yes—
112C2×C8×C61C2411yescharacteristic
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61—41no—
119C22⋊Dic61—41no—
120#11758198—41no—
121#11758198—41no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—22no—
125C4⋊Dic61—41no—
126#11758196—42no—
127#11758196—42no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—41no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C2×#92418C4⋊C414yes—
134C2×#92418C2×D411yescharacteristic
135C2×#92418C2×D411yescharacteristic
136C8×D61C4⋊C414yes—
137C8×D61C4⋊C414yes—
138C8×D61C22×C412yes—
139C8×D61C22×C412yes—
140C8×D61C2×Q812yes—
141C8×D61C2×Q812yes—
142C16×C61C22×C414yescomplemented
143#11758185C22×C414yescomplemented
144C23×C61C2×D811yescharacteristic
145C22×D61—22no—
146C22×D61—22no—
147C22×D61#10714yes—
148C22×D61C2×D811yescharacteristic
149C22×D61C2×D811yescharacteristic
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—82no—
154C2×C4×C61C2×C4⋊C412yes—
155C2×C4×C61C2×D811yescharacteristic
156C2×C4×C61C2×Q1612yes—
157C2×C4×C61C22×D411yescharacteristic
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—82no—
162C2×Dic61#10714yes—
163C2×Dic61C2×D811yescharacteristic
164C2×Dic61C2×D811yescharacteristic
165C4×D61—84no—
166C4×D61—82no—
167C4×D61—84no—
168C4×D61—82no—
169C4×D61#10714yes—
170C4×D61#10714yes—
171C4×D61C2×C4⋊C412yes—
172C4×D61C2×C4⋊C412yes—
173C4×D61C2×Q1612yes—
174C4×D61C2×Q1612yes—
175C8×C61C2×C4⋊C412yes—
176C8×C61C23×C411yescharacteristic
177C8×C61C22×Q811yescharacteristic
178#92418C2×C4⋊C412yes—
179#92418C2×C4⋊C412yes—
180C2×#2159—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61C2×#10712yes—
184C22×C61C22×D811yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—28no—
188C2×D61C2×#10712yes—
189C2×D61C2×#10712yes—
190C2×D61#50912yes—
191C2×D61#51012yes—
192C4×C61—82no—
193C4×C61—81no—
194C4×C61—81no—
195C4×C61C2×#10712yes—
196C4×C61C22×C4⋊C411yescharacteristic
197C4×C61C22×Q1611yescharacteristic
198Dic61—82no—
199Dic61—81no—
200Dic61—81no—
201Dic61C2×#10712yes—
202Dic61C2×#10712yes—
203C22×M32—611no—
204C2×#427—611no—
205C22×#107—611no—
206#2159—611no—
207#2159—611no—
208#2159—611no—
209#2159—612no—
210#2159—612no—
211#2159D6111yescharacteristic, direct product factor
212C2×#367—612no—
213C2×#366—612no—
214C2×C61—22no—
215C2×C61C22×#10711yescharacteristic
216C2×C61C2×#50911yescharacteristic
217C2×C61C2×#51011yescharacteristic
218D61—22no—
219D61#215914yesdirect product factor
220C23×C8—611no—
221C2×#117—1221no—
222C22×C4⋊C4—1221no—
223C2×M32—611no—
224C2×M32—618no—
225C2×M32—612no—
226C2×M32C2×D6111yescharacteristic
227C22×C16—612no—
228#427—611no—
229#427—611no—
230#427—611no—
231#427—1221no—
232#427—1221no—
233#427C2×D6111yescharacteristic
234C2×#107—611no—
235C2×#107—612no—
236C2×#107—612no—
237C2×#107—611no—
238C2×#107—611no—
239C2×#107—1221no—
240C2×#107—1221no—
241C2×#107—1221no—
242C2×#107C2×D6111yescharacteristic
243C2×#106—1221no—
244#367—612no—
245#367—612no—
246#367—612no—
247#367C2×D6112yescomplemented
248#366—612no—
249#366—612no—
250#366—612no—
251#366C2×D6112yescomplemented
252C61C2×#215911yescharacteristic, complemented, Sylow
253C23×C4—611no—
254C23×C4—2441no—
255C22×C8—611no—
256C22×C8—614no—
257C22×C8—611no—
258C22×C8—611no—
259C22×C8—614no—
260C22×C8—611no—
261C22×C8—611no—
262C22×C8C22×D6111yescharacteristic
263#117—21no—
264#117—1221no—
265#117—1221no—
266#117—1221no—
267#117—2441no—
268#117—2441no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4—1222no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—2441no—
276C2×C4⋊C4—2441no—
277C2×C4⋊C4—2441no—
278C2×C22⋊C4—2441no—
279C2×C42—2441no—
280M32—614no—
281M32—618no—
282M32C4×D6114yescomplemented
283C2×C16—612no—
284C2×C16—618no—
285C2×C16C22×D6112yes—
286#107—21no—
287#107—611no—
288#107—612no—
289#107—611no—
290#107—1222no—
291#107—1222no—
292#107—1221no—
293#107—1221no—
294#107—1221no—
295#107C22×D6111yescharacteristic
296#107C22×D6112yes—
297#107C22×D6111yescharacteristic
298#106—21no—
299#106—1221no—
300#106—1221no—
301#106—1221no—
302C24—611no—
303C22×C4—41no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—614no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—614no—
311C22×C4—4884no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2441no—
317C22×C4D4×D6111yescharacteristic
318C2×C8—611no—
319C2×C8—611no—
320C2×C8—614no—
321C2×C8—612no—
322C2×C8—612no—
323C2×C8—612no—
324C2×C8—612no—
325C2×C8—614no—
326C2×C8—614no—
327C2×C8C2×C4×D6112yes—
328C2×C8D4×D6111yescharacteristic
329C2×C8Q8×D6112yes—
330C2×C8C23×D6111yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C4⋊C4—1222no—
338C4⋊C4—2442no—
339C4⋊C4—2442no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C22⋊C4—41no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—41no—
348C42—2441no—
349C42—2441no—
350C42—2441no—
351C16—614no—
352C16C2×C4×D6114yescomplemented
353C23—611no—
354C23—611no—
355C23—614no—
356C23—1222no—
357C23—1222no—
358C23D8×D6111yescharacteristic
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—614no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—612no—
369C2×C4—612no—
370C2×C4—614no—
371C2×C4—614no—
372C2×C4—4884no—
373C2×C4—4882no—
374C2×C4—4882no—
375C2×C4—4884no—
376C2×C4—4882no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4C4⋊C4×D6112yes—
381C2×C4D8×D6111yescharacteristic
382C2×C4Q16×D6112yes—
383C2×C4C2×D4×D6111yescharacteristic
384C8—612no—
385C8—612no—
386C8C4⋊C4×D6112yes—
387C8C22×C4×D6111yescharacteristic
388C8C2×Q8×D6111yescharacteristic
389C22—21no—
390C22—21no—
391C22—612no—
392C22—612no—
393C22—612no—
394C22—612no—
395C22—1228no—
396C22—1221no—
397C22—1221no—
398C22#107×D6112yes—
399C22C2×D8×D6111yescharacteristic
400C4—81no—
401C4—82no—
402C4—81no—
403C4—612no—
404C4—612no—
405C4—4881no—
406C4—4882no—
407C4—4881no—
408C4#107×D6112yes—
409C4C2×C4⋊C4×D6111yescharacteristic
410C4C2×Q16×D6111yescharacteristic
411C2—22no—
412C2—614no—
413C2—1222no—
414C2C2×#107×D6111yescharacteristic
415C2#509×D6111yescharacteristic
416C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC61×#2159C2
socleC22×C61C22×D8
prime radicalC23×D61D8
cosocleC2×C8×C61C24
hypercenter#2159D61
hypocenterC61C2×#2159
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
4. #21447608C2semidirect
5. #21447607C2semidirect
6. #21447606C2semidirect
7. #21447605C2semidirect
8. #21447604C2semidirect
9. #367×D61C2semidirect
10. #366×D61C2semidirect
11. C61×#2159C2semidirect
17. M32×D61C4semidirect
33. #16839590C22semidirect
34. #16839589C22semidirect
35. #16839589C22semidirect
36. #16839588C22semidirect
37. #16839587C22semidirect
38. #16839587C22semidirect
42. C61×#367C22semidirect
43. C61×#366C22semidirect
68. #14519717C2×C4semidirect
69. #14519716C2×C4semidirect
71. C16×D61C2×C4semidirect
86. M32×C61C2×C4semidirect
142. C16×C61C22×C4semidirect
143. #11758185C22×C4semidirect
211. #2159D61direct (N × H)
219. D61#2159direct (N × H)
247. #367C2×D61semidirect
251. #366C2×D61semidirect
252. C61C2×#2159semidirect
282. M32C4×D61semidirect
352. C16C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
#427×D612
C2×#107×D612
#214476082
#214476072
#214476062
#214476052
#214476042
#367×D612
#366×D612
C61×#21592
C2×#215961