Finite Group Databasebeta

← D61×#1410 #29600336

Subgroups — D61×#1410 #29600336

Order 15616.

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

normal subgroups only

This group has 450 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#492×D61C211yesmaximal, characteristic
2#356×D61C212yesmaximal, complemented
3#21443986C211yesmaximal, characteristic, complemented
4#21443985C212yesmaximal, complemented
5C61×#1410C211yesmaximal, characteristic, complemented
6C2×SD16×D61—22no—
7C4⋊Q8×D61C2211yescharacteristic
8#127×D61C411yescharacteristic
9#16840136C2211yescharacteristic
10#16840135C411yescharacteristic
11#16840134C411yescharacteristic
12#16840133—22no—
13#101×D61—22no—
14C4×C8×D61C411yescharacteristic
15#16839561C2212yescomplemented
16#16839560—22no—
17C61×#492C2211yescharacteristic
18C61×#356C2212yescomplemented
19C2×Q8×D61D412yes—
20C2×D4×D61—21no—
21C2×D4×D61—41no—
22C2×#11758190—22no—
23C2×#11758200—22no—
24C2×#11758201—22no—
25SD16×D61—44no—
26SD16×D61—44no—
27M16×D61—42no—
28C2×C8×D61—21no—
29#14519777C2×C411yescharacteristic
30#14519776—41no—
31#14519775D412yes—
32#14519774C2×C411yescharacteristic
33#14519773—21no—
34#14519773—41no—
35C4⋊C4×D61—41no—
36C42×D61C2×C411yescharacteristic
37#14519696—22no—
38#14519695—42no—
39C4×#92418C2×C411yescharacteristic
40C8×Dic61—21no—
41C2×SD16×C61—22no—
42C4⋊Q8×C61C2311yescharacteristic
43#127×C61C2×C411yescharacteristic
44#101×C61—22no—
45C4×C8×C61C2×C411yescharacteristic
46C23×D61—41no—
47C2×Q8×C61C2×D412yes—
48C2×D4×C61—21no—
49C2×D4×C61—41no—
50C2×C22⋊D61—42no—
51C2×C22⋊D61—41no—
52Q8×D61—42no—
53Q8×D61—42no—
54D4×D61—42no—
55D4×D61—42no—
56D4×D61—84no—
57C2×D244—21no—
58C2×D244—41no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×Dic122—22no—
63C2×Dic122C22⋊C412yes—
64SD16×C61—44no—
65M16×C61—42no—
66C2×C8×C61—21no—
67C4⋊C4×C61—41no—
68C42×C61C22×C411yescharacteristic
69#11758201—44no—
70#11758200—44no—
71C4⋊Dic61—41no—
72#11758196—42no—
73C4×Dic61—21no—
74C4×Dic61C22⋊C411yescharacteristic
75#11758194—42no—
76C2×#92418—21no—
77#11758190—44no—
78#11758189—82no—
79C8×D61—22no—
80C8×D61—22no—
81C8×D61—82no—
82C23×C61—41no—
83C22×D61—41no—
84C22×D61—84no—
85C22×D61—81no—
86C22×D61—81no—
87C22×D61#9911yescharacteristic
88Q8×C61—42no—
89D4×C61—42no—
90D4×C61—82no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C22⋊D61—82no—
95C22⋊D61—84no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61#9911yescharacteristic
99D244—42no—
100D244—82no—
101C4×D61—24no—
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—42no—
105C4×D61—42no—
106Dic122—42no—
107Dic122—82no—
108C8×C61—22no—
109C8×C61—82no—
110#92418—22no—
111#92418—82no—
112C2×#1410—611nomaximal, Sylow
113C22×C61—82no—
114C22×C61—81no—
115C22×C61C2×#9911yescharacteristic
116C2×D61—22no—
117C2×D61—82no—
118C2×D61—81no—
119C2×D61—162no—
120C2×D61—162no—
121C2×D61#35311yescharacteristic
122C2×D61#35311yescharacteristic
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—42no—
126Dic61—22no—
127Dic61—21no—
128Dic61—42no—
129C2×#492—611no—
130C2×#356—612no—
131#1410—611no—
132#1410—612no—
133#1410D6111yescharacteristic, direct product factor
134C2×C61—21no—
135C2×C61—161no—
136C2×C61C2×#35311yescharacteristic
137D61—21no—
138D61—161no—
139D61#141012yesdirect product factor
140C22×SD16—1222no—
141C2×C4⋊Q8—611no—
142C2×#127—611no—
143#492—611no—
144#492—611no—
145#492—611no—
146#492—1222no—
147#492C2×D6111yescharacteristic
148C2×#101—1222no—
149C2×C4×C8—611no—
150#356—612no—
151#356—1222no—
152#356C2×D6112yescomplemented
153C61C2×#141011yescharacteristic, complemented, Sylow
154C22×Q8—612no—
155C22×D4—1221no—
156C22×D4—2441no—
157C2×SD16—22no—
158C2×SD16—1222no—
159C2×SD16—1222no—
160C2×SD16—1222no—
161C2×SD16—2444no—
162C2×SD16—2444no—
163C2×M16—2442no—
164C22×C8—1221no—
165C4⋊Q8—612no—
166C4⋊Q8—611no—
167C4⋊Q8—2441no—
168C4⋊Q8C22×D6111yescharacteristic
169#127—611no—
170#127—1221no—
171#127—2441no—
172#127C4×D6111yescharacteristic
173C2×C4⋊C4—2441no—
174C2×C42—611no—
175#101—22no—
176#101—1222no—
177#101—2442no—
178C4×C8—611no—
179C4×C8—1221no—
180C4×C8C4×D6111yescharacteristic
181C24—2441no—
182C2×Q8—612no—
183C2×Q8—1222no—
184C2×Q8—2442no—
185C2×Q8—2442no—
186C2×Q8D4×D6112yes—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—1221no—
190C2×D4—4884no—
191C2×D4—2441no—
192C2×D4—2441no—
193C2×D4—2442no—
194C2×D4—2442no—
195C2×D4—2442no—
196C22×C4—611no—
197C22×C4—1221no—
198C22×C4—1222no—
199SD16—44no—
200SD16—2444no—
201SD16—2444no—
202SD16—2444no—
203M16—42no—
204M16—4882no—
205M16—2442no—
206C2×C8—21no—
207C2×C8—1222no—
208C2×C8—1222no—
209C2×C8—1221no—
210C2×C8—4882no—
211C4⋊C4—41no—
212C4⋊C4—2442no—
213C4⋊C4—2441no—
214C42—611no—
215C42—1221no—
216C42C2×C4×D6111yescharacteristic
217C23—41no—
218C23—611no—
219C23—4881no—
220C23—4881no—
221C23—4884no—
222C23—2441no—
223Q8—42no—
224Q8—4882no—
225Q8—2442no—
226D4—42no—
227D4—82no—
228D4—4882no—
229D4—4884no—
230D4—4882no—
231D4—2442no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—611no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1224no—
238C2×C4—1221no—
239C2×C4—1222no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4C22⋊C4×D6111yescharacteristic
243C8—22no—
244C8—82no—
245C8—1222no—
246C8—4882no—
247C22—82no—
248C22—81no—
249C22—611no—
250C22—611no—
251C22—1222no—
252C22—9762no—
253C22—9762no—
254C22—4882no—
255C22—4881no—
256C22#99×D6111yescharacteristic
257C4—22no—
258C4—21no—
259C4—42no—
260C4—1222no—
261C4—1221no—
262C4—2442no—
263C2—21no—
264C2—161no—
265C2—612no—
266C2—1221no—
267C2—9761no—
268C2#353×D6111yescharacteristic
subgroupG/H
centerC2#353×D61
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#1410C2
socleC2×C61C2×#353
prime radical#127×D61C4
cosocleC4⋊Q8×C61C23
hypercenter#1410D61
hypocenterC61C2×#1410
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1410

Complements

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

NH ≅ G/Ntype
2. #356×D61C2semidirect
3. #21443986C2semidirect
4. #21443985C2semidirect
5. C61×#1410C2semidirect
15. #16839561C22semidirect
18. C61×#356C22semidirect
133. #1410D61direct (N × H)
139. D61#1410direct (N × H)
152. #356C2×D61semidirect
153. C61C2×#1410semidirect

Maximal subgroups

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

subgroupindex
#492×D612
#356×D612
#214439862
#214439852
C61×#14102
C2×#141061