Finite Group Databasebeta

← D61×#2255 #29835506

Subgroups — D61×#2255 #29835506

Order 15616.

518 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D61C211yesmaximal, characteristic
2#499×D61C211yesmaximal, characteristic
3#21448106C211yesmaximal, characteristic, complemented
4#21448105C211yesmaximal, characteristic, complemented
5#21448104C212yesmaximal, complemented
6#21448103C212yesmaximal, complemented
7#21448102C211yesmaximal, characteristic, complemented
8#367×D61C212yesmaximal
9#366×D61C212yesmaximal
10#346×D61C211yesmaximal, characteristic
11C61×#2255C211yesmaximal, characteristic, complemented
12C4⋊Q8×D61—21no—
13#125×D61—21no—
14C2×C16×D61C2212yes—
15#16840167C2211yescharacteristic
16#16840166—21no—
17#16840166C2212yes—
18#16840165—21no—
19#16840164C2211yescharacteristic
20#16840163C2211yescharacteristic
21#16840163C2211yescharacteristic
22#16840162—21no—
23#16840161—21no—
24#107×D61—21no—
25#107×D61C2211yescharacteristic
26#107×D61C2212yes—
27#107×D61C2211yescharacteristic
28#106×D61—21no—
29C4×C8×D61C2211yescharacteristic
30#16839590C2212yes—
31#16839589C2212yes—
32#16839589C2212yes—
33#16839588C2212yes—
34#16839587C2212yes—
35#16839587C2212yes—
36#16839538C2211yescharacteristic
37#16839537C2212yes—
38C61×#500C2211yescharacteristic
39C61×#499C2211yescharacteristic
40C61×#367C2212yes—
41C61×#366C2212yes—
42C61×#346C2211yescharacteristic
43C2×Q8×D61—41no—
44C2×C8×D61D411yescharacteristic
45C2×C8×D61C2311yescharacteristic
46#14519777—21no—
47#14519776—22no—
48#14519776—41no—
49#14519775—41no—
50#14519769—21no—
51#14519768—21no—
52#14519768—21no—
53#14519767—41no—
54#14519767—41no—
55C4⋊C4×D61—21no—
56C4⋊C4×D61—21no—
57C4⋊C4×D61—22no—
58C4⋊C4×D61—41no—
59C4⋊C4×D61—41no—
60C4⋊C4×D61—41no—
61C42×D61D411yescharacteristic
62C2×#11758185C2312yes—
63C16×D61Q818yescomplemented
64#14519711—21no—
65#14519711C2311yescharacteristic
66#14519711C2312yes—
67#14519711C2311yescharacteristic
68#14519710—22no—
69#14519710—21no—
70#14519710—21no—
71#14519710—22no—
72#14519709—21no—
73#14519708—21no—
74#14519708—21no—
75C4×#92418D411yescharacteristic
76C8×Dic61D411yescharacteristic
77C8×Dic61C2311yescharacteristic
78C4⋊Q8×C61—21no—
79#125×C61—21no—
80C2×C16×C61C2312yes—
81#107×C61—21no—
82#107×C61C2311yescharacteristic
83#107×C61C2312yes—
84#107×C61C2311yescharacteristic
85#106×C61—21no—
86C4×C8×C61C2311yescharacteristic
87C2×Q8×C61—41no—
88Q8×D61—84no—
89C2×C4×D61—42no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61D811yescharacteristic
93C2×C4×D61D811yescharacteristic
94C2×C4×D61C2×D411yescharacteristic
95C2×Dic122—41no—
96C2×Dic122—42no—
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2411yescharacteristic
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61C2×D411yescharacteristic
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112#11758196—41no—
113#11758196—41no—
114#11758196—41no—
115#11758196—41no—
116#11758196—42no—
117#11758196—41no—
118#11758196—41no—
119#11758196—42no—
120C4×Dic61D811yescharacteristic
121C4×Dic61D811yescharacteristic
122C4×Dic61C2×D411yescharacteristic
123C2×#92418C2×D411yescharacteristic
124C2×#92418C2×D411yescharacteristic
125C8×D61Q1614yes—
126C8×D61C2×Q814yes—
127C16×C61C2×Q814yescomplemented
128#11758185C2×Q814yescomplemented
129C22×D61C2×D811yescharacteristic
130Q8×C61—82no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61C2×D811yescharacteristic
135C2×C4×C61C2×D811yescharacteristic
136C2×C4×C61C22×D411yescharacteristic
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61C2×D811yescharacteristic
141C2×Dic61C2×D811yescharacteristic
142C2×Dic61C2×D811yescharacteristic
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—82no—
146C4×D61—84no—
147C4×D61—82no—
148C4×D61C4⋊Q812yes—
149C4×D61C2×Q1612yes—
150Dic122—84no—
151Dic122—82no—
152C8×C61C2×Q1612yes—
153C8×C61C22×Q812yes—
154#92418C4⋊Q812yes—
155#92418C2×Q1612yes—
156C2×#2255—611nomaximal, Sylow
157C22×C61C22×D811yescharacteristic
158C2×D61#50012yes—
159C2×D61#50912yes—
160C2×D61#51012yes—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—82no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61C2×C4⋊Q811yescharacteristic
167C4×C61C22×Q1611yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—82no—
171Dic61—81no—
172Dic61—81no—
173Dic61#50012yes—
174C2×#500—611no—
175C2×#499—611no—
176#2255—611no—
177#2255—611no—
178#2255—612no—
179#2255—612no—
180#2255—611no—
181#2255D6111yescharacteristic, direct product factor
182C2×#367—612no—
183C2×#366—612no—
184C2×#346—611no—
185C2×C61C2×#50011yescharacteristic
186C2×C61C2×#50911yescharacteristic
187C2×C61C2×#51011yescharacteristic
188D61#225514yesdirect product factor
189C2×C4⋊Q8—1221no—
190C2×#125—1221no—
191C22×C16—612no—
192#500—612no—
193#500—611no—
194#500—1221no—
195#500—1221no—
196#500C2×D6111yescharacteristic
197#499—611no—
198#499—611no—
199#499—611no—
200#499—1221no—
201#499—1221no—
202#499C2×D6111yescharacteristic
203C2×#107—611no—
204C2×#107—611no—
205C2×#107—612no—
206C2×#107—1221no—
207C2×#106—1221no—
208C2×C4×C8—611no—
209#367—612no—
210#367—612no—
211#367—612no—
212#367C2×D6112yes—
213#366—612no—
214#366—612no—
215#366—612no—
216#366C2×D6112yes—
217#346—612no—
218#346—611no—
219#346C2×D6111yescharacteristic
220C61C2×#225511yescharacteristic, complemented, Sylow
221C22×Q8—2441no—
222C22×C8—611no—
223C22×C8—611no—
224C4⋊Q8—21no—
225C4⋊Q8—1222no—
226C4⋊Q8—1221no—
227C4⋊Q8—2441no—
228C4⋊Q8—2441no—
229#125—21no—
230#125—1221no—
231#125—1221no—
232#125—1221no—
233#125—2441no—
234#125—2441no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—2441no—
239C2×C4⋊C4—2441no—
240C2×C4⋊C4—2441no—
241C2×C42—611no—
242C2×C16—612no—
243C2×C16—618no—
244C2×C16C22×D6112yes—
245#107—21no—
246#107—611no—
247#107—612no—
248#107—611no—
249#107—1221no—
250#107—1221no—
251#107—1222no—
252#107—1222no—
253#107—1221no—
254#107C22×D6111yescharacteristic
255#107C22×D6112yes—
256#107C22×D6111yescharacteristic
257#106—21no—
258#106—1221no—
259#106—1221no—
260#106—1221no—
261C4×C8—611no—
262C4×C8—611no—
263C4×C8—611no—
264C4×C8C22×D6111yescharacteristic
265C2×Q8—41no—
266C2×Q8—4884no—
267C2×Q8—2442no—
268C2×Q8—2441no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2442no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—614no—
278C2×C8—614no—
279C2×C8D4×D6111yescharacteristic
280C2×C8C23×D6111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1222no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2442no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2442no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C42—611no—
302C42—611no—
303C42—611no—
304C42D4×D6111yescharacteristic
305C16—614no—
306C16Q8×D6114yescomplemented
307C23—611no—
308Q8—82no—
309Q8—4882no—
310Q8—4884no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—4882no—
322C2×C4—4882no—
323C2×C4—4884no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2442no—
327C2×C4D8×D6111yescharacteristic
328C2×C4D8×D6111yescharacteristic
329C2×C4C2×D4×D6111yescharacteristic
330C8—612no—
331C8—612no—
332C8Q16×D6112yes—
333C8C2×Q8×D6112yes—
334C22—612no—
335C22—612no—
336C22—612no—
337C22C2×D8×D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—82no—
343C4—612no—
344C4—1221no—
345C4—1221no—
346C4—4881no—
347C4—4881no—
348C4—4882no—
349C4C4⋊Q8×D6111yescharacteristic
350C4C2×Q16×D6111yescharacteristic
351C2—614no—
352C2#500×D6111yescharacteristic
353C2#509×D6111yescharacteristic
354C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2255C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenter#2255D61
hypocenterC61C2×#2255
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #21448106C2semidirect
4. #21448105C2semidirect
5. #21448104C2semidirect
6. #21448103C2semidirect
7. #21448102C2semidirect
11. C61×#2255C2semidirect
63. C16×D61Q8semidirect
127. C16×C61C2×Q8semidirect
128. #11758185C2×Q8semidirect
181. #2255D61direct (N × H)
188. D61#2255direct (N × H)
220. C61C2×#2255semidirect
306. C16Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#500×D612
#499×D612
#214481062
#214481052
#214481042
#214481032
#214481022
#367×D612
#366×D612
#346×D612
C61×#22552
C2×#225561