Finite Group Databasebeta

← D61×#1412 #29600356

Subgroups — D61×#1412 #29600356

Order 15616.

390 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#490×D61C211yesmaximal, characteristic
2#353×D61C212yesmaximal
3#21443990C211yesmaximal, characteristic, complemented
4#21443989C212yesmaximal, complemented
5C61×#1412C211yesmaximal, characteristic, complemented
6#127×D61C2211yescharacteristic
7#125×D61C411yescharacteristic, complemented
8#16840128C411yescharacteristic, complemented
9#16840127C411yescharacteristic, complemented
10#16840126C2211yescharacteristic
11#16840125—22no—
12#102×D61—22no—
13#99×D61—22no—
14#97×D61C411yescharacteristic, complemented
15#16839555C2212yes—
16#16839554—22no—
17C61×#490C2211yescharacteristic
18C61×#353C2212yes—
19C2×D4×D61—41no—
20C2×D4×D61D412yes—
21C2×C8×D61—21no—
22#14519774C2×C411yescharacteristic
23#14519773—41no—
24#14519773D412yes—
25#14519769C2×C411yescharacteristic, complemented
26#14519768—21no—
27#14519767—41no—
28C4⋊C4×D61—21no—
29C4⋊C4×D61—41no—
30C22⋊C4×D61—42no—
31C42×D61C2×C411yescharacteristic
32#14519699—22no—
33#14519698—22no—
34#14519697—22no—
35#14519692—22no—
36#14519691—42no—
37#14519688C2×C411yescharacteristic, complemented
38#14519687—21no—
39#127×C61C2311yescharacteristic
40#125×C61C2×C411yescharacteristic, complemented
41#102×C61—22no—
42#99×C61—22no—
43#97×C61C2×C411yescharacteristic, complemented
44C23×D61—22no—
45C2×D4×C61—41no—
46C2×D4×C61C2×D412yes—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—42no—
49D4×D61—42no—
50D4×D61—42no—
51D4×D61—84no—
52C2×D244—41no—
53C2×D244C22⋊C412yes—
54C2×C4×D61—21no—
55C2×C4×D61—41no—
56C2×C4×D61—82no—
57C2×C4×D61C22⋊C411yescharacteristic
58C2×C8×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—41no—
61C22⋊C4×C61—42no—
62C42×C61C22×C411yescharacteristic
63C22⋊Dic61—42no—
64#11758198—82no—
65C4⋊Dic61—21no—
66C4⋊Dic61—41no—
67#11758196—41no—
68#11758196—41no—
69#11758196—41no—
70C4×Dic61—21no—
71C4×Dic61C22⋊C411yescharacteristic
72C2×#92418—21no—
73C8×D61—41no—
74C8×D61—41no—
75C23×C61—22no—
76C22×D61—22no—
77C22×D61—42no—
78C22×D61—42no—
79C22×D61—84no—
80C22×D61#9911yescharacteristic
81D4×C61—42no—
82D4×C61—82no—
83C2×C4×C61—21no—
84C2×C4×C61—41no—
85C2×C4×C61—82no—
86C2×C4×C61C2×C22⋊C411yescharacteristic
87C22⋊D61—82no—
88C22⋊D61—84no—
89C2×Dic61—21no—
90C2×Dic61—41no—
91C2×Dic61—82no—
92C2×Dic61#9911yescharacteristic
93D244—42no—
94D244—82no—
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—42no—
98C4×D61—82no—
99C4×D61—164no—
100C8×C61—41no—
101#92418—41no—
102C2×#1412—611nomaximal, Sylow
103C22×C61—42no—
104C22×C61—82no—
105C22×C61C2×#9911yescharacteristic
106C2×D61—22no—
107C2×D61—42no—
108C2×D61—84no—
109C2×D61—82no—
110C2×D61—162no—
111C2×D61#35411yescharacteristic
112C2×D61#35411yescharacteristic
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—81no—
116C4×C61—162no—
117Dic61—21no—
118Dic61—41no—
119Dic61—81no—
120Dic61—162no—
121C2×#490—611no—
122C2×#353—612no—
123#1412—611no—
124#1412—612no—
125#1412D6111yescharacteristic, direct product factor
126C2×C61—21no—
127C2×C61—82no—
128C2×C61C2×#35411yescharacteristic
129D61—21no—
130D61—82no—
131D61#141212yesdirect product factor
132C2×#127—611no—
133C2×#125—611no—
134#490—611no—
135#490—611no—
136#490—611no—
137#490—1222no—
138#490C2×D6111yescharacteristic
139C2×#102—1222no—
140C2×#99—1222no—
141C2×#97—611no—
142#353—612no—
143#353—1222no—
144#353C2×D6112yes—
145C61C2×#141211yescharacteristic, complemented, Sylow
146C22×D4—612no—
147C22×D4—2441no—
148C22×C8—1221no—
149#127—612no—
150#127—611no—
151#127—2441no—
152#127C22×D6111yescharacteristic
153#125—611no—
154#125—1221no—
155#125—2441no—
156#125C4×D6111yescharacteristic, complemented
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—2441no—
159C2×C22⋊C4—2442no—
160C2×C42—611no—
161#102—22no—
162#102—1222no—
163#102—1222no—
164#102—1222no—
165#99—22no—
166#99—1222no—
167#99—2442no—
168#97—611no—
169#97—1221no—
170#97C4×D6111yescharacteristic, complemented
171C24—1222no—
172C2×D4—41no—
173C2×D4—612no—
174C2×D4—1222no—
175C2×D4—4884no—
176C2×D4—2441no—
177C2×D4—2442no—
178C2×D4—2442no—
179C2×D4—2442no—
180C2×D4D4×D6112yes—
181C22×C4—611no—
182C22×C4—1221no—
183C22×C4—4882no—
184C22×C4—2441no—
185C2×C8—21no—
186C2×C8—1221no—
187C2×C8—2441no—
188C2×C8—2441no—
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—1221no—
192C4⋊C4—2441no—
193C4⋊C4—2441no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C22⋊C4—42no—
197C22⋊C4—4882no—
198C22⋊C4—2442no—
199C42—611no—
200C42—1221no—
201C42C2×C4×D6111yescharacteristic
202C23—22no—
203C23—611no—
204C23—1222no—
205C23—4884no—
206C23—2442no—
207C23—2442no—
208D4—42no—
209D4—82no—
210D4—4882no—
211D4—4882no—
212D4—4884no—
213D4—2442no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—82no—
217C2×C4—611no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—9764no—
222C2×C4—4882no—
223C2×C4—4882no—
224C2×C4—2442no—
225C2×C4—2441no—
226C2×C4C22⋊C4×D6111yescharacteristic
227C8—41no—
228C8—2441no—
229C22—42no—
230C22—82no—
231C22—611no—
232C22—611no—
233C22—1222no—
234C22—9762no—
235C22—4882no—
236C22—4884no—
237C22—2442no—
238C22#99×D6111yescharacteristic
239C4—21no—
240C4—41no—
241C4—81no—
242C4—162no—
243C4—1221no—
244C4—9762no—
245C4—4881no—
246C4—2441no—
247C2—21no—
248C2—82no—
249C2—612no—
250C2—1221no—
251C2—4882no—
252C2#354×D6111yescharacteristic
subgroupG/H
centerC2#354×D61
commutatorC42×C61C22×C4
Frattini#127C22×D61
FittingC61×#1412C2
socleC2×C61C2×#354
prime radical#127×D61C22
cosocle#127×C61C23
hypercenter#1412D61
hypocenterC61C2×#1412
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #21443990C2semidirect
4. #21443989C2semidirect
5. C61×#1412C2semidirect
7. #125×D61C4semidirect
8. #16840128C4semidirect
9. #16840127C4semidirect
14. #97×D61C4semidirect
25. #14519769C2×C4semidirect
37. #14519688C2×C4semidirect
40. #125×C61C2×C4semidirect
43. #97×C61C2×C4semidirect
125. #1412D61direct (N × H)
131. D61#1412direct (N × H)
145. C61C2×#1412semidirect
156. #125C4×D61semidirect
170. #97C4×D61semidirect

Maximal subgroups

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

subgroupindex
#490×D612
#353×D612
#214439902
#214439892
C61×#14122
C2×#141261