Finite Group Databasebeta

← D61×#1359 #29591225

Subgroups — D61×#1359 #29591225

Order 15616.

442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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#364×D61C212yesmaximal, complemented
3#21443860C211yesmaximal, characteristic, complemented
4#21443859C212yesmaximal, complemented
5C61×#1359C211yesmaximal, characteristic, complemented
6C2×SD16×D61—22no—
7C4⋊Q8×D61C411yescharacteristic
8#127×D61C411yescharacteristic
9M32×D61—22no—
10#16840136C411yescharacteristic
11#16840135C2211yescharacteristic
12#16840134C411yescharacteristic
13#16840133—22no—
14C4×C8×D61C2211yescharacteristic
15#16839583C2212yescomplemented
16#16839582—22no—
17C61×#492C2211yescharacteristic
18C61×#364C2212yescomplemented
19C2×Q8×D61—21no—
20C2×D4×D61—21no—
21C2×D4×D61—41no—
22C2×#11758190—22no—
23C2×#11758200—22no—
24C2×#11758201—22no—
25SD16×D61—42no—
26SD16×D61—42no—
27SD16×D61—42no—
28SD16×D61—42no—
29C2×C8×D61D412yes—
30#14519777C2×C411yescharacteristic
31#14519776—41no—
32#14519775—21no—
33#14519774C2×C411yescharacteristic
34#14519773—21no—
35#14519773—41no—
36C4⋊C4×D61—41no—
37C42×D61C2×C411yescharacteristic
38#14519717—22no—
39#14519716—42no—
40C16×D61—42no—
41C4×#92418C2×C411yescharacteristic
42C8×Dic61D412yes—
43C2×SD16×C61—22no—
44C4⋊Q8×C61C2×C411yescharacteristic
45#127×C61C2×C411yescharacteristic
46M32×C61—22no—
47C4×C8×C61C2311yescharacteristic
48C23×D61—41no—
49C2×Q8×C61—21no—
50C2×D4×C61—21no—
51C2×D4×C61—41no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—41no—
54Q8×D61—42no—
55Q8×D61—42no—
56D4×D61—42no—
57D4×D61—42no—
58D4×D61—84no—
59C2×D244—21no—
60C2×D244—41no—
61C2×C4×D61—21no—
62C2×C4×D61—41no—
63C2×C4×D61C22⋊C411yescharacteristic
64C2×Dic122—21no—
65C2×Dic122—41no—
66SD16×C61—42no—
67SD16×C61—42no—
68C2×C8×C61C2×D412yes—
69C4⋊C4×C61—41no—
70C42×C61C22×C411yescharacteristic
71#11758201—42no—
72#11758201—42no—
73#11758200—42no—
74#11758200—42no—
75C4⋊Dic61—41no—
76#11758196—42no—
77C4×Dic61—21no—
78C4×Dic61C22⋊C411yescharacteristic
79C2×#92418C22⋊C412yes—
80#11758190—42no—
81#11758190—42no—
82C8×D61D812yes—
83C8×D61D812yes—
84C8×D61SD1612yes—
85C8×D61SD1612yes—
86C16×C61—42no—
87#11758185—42no—
88C23×C61—41no—
89C22×D61—41no—
90C22×D61—84no—
91C22×D61—81no—
92C22×D61—81no—
93C22×D61#10011yescharacteristic
94Q8×C61—42no—
95D4×C61—42no—
96D4×C61—82no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C22⋊D61—84no—
101C22⋊D61—82no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61#10011yescharacteristic
105D244—42no—
106D244—82no—
107C4×D61—24no—
108C4×D61—81no—
109C4×D61—81no—
110C4×D61#10212yes—
111C4×D61#10212yes—
112Dic122—42no—
113Dic122—82no—
114C8×C61C2×D812yes—
115C8×C61C2×SD1612yes—
116#92418#10212yes—
117#92418#10212yes—
118C2×#1359—611nomaximal, Sylow
119C22×C61—82no—
120C22×C61—81no—
121C22×C61C2×#10011yescharacteristic
122C2×D61—22no—
123C2×D61—82no—
124C2×D61—81no—
125C2×D61—162no—
126C2×D61—162no—
127C2×D61#33111yescharacteristic
128C2×D61#33111yescharacteristic
129C4×C61—22no—
130C4×C61—81no—
131C4×C61C2×#10212yes—
132Dic61—22no—
133Dic61—81no—
134Dic61#33112yes—
135C2×#492—611no—
136C2×#364—612no—
137#1359—611no—
138#1359—612no—
139#1359D6111yescharacteristic, direct product factor
140C2×C61—21no—
141C2×C61—161no—
142C2×C61C2×#33111yescharacteristic
143D61—21no—
144D61—161no—
145D61#135912yesdirect product factor
146C22×SD16—1222no—
147C2×C4⋊Q8—611no—
148C2×#127—611no—
149C2×M32—1222no—
150#492—611no—
151#492—611no—
152#492—611no—
153#492—1222no—
154#492C2×D6111yescharacteristic
155C2×C4×C8—611no—
156#364—612no—
157#364—1222no—
158#364C2×D6112yescomplemented
159C61C2×#135911yescharacteristic, complemented, Sylow
160C22×Q8—1221no—
161C22×D4—1221no—
162C22×D4—2441no—
163C2×SD16—22no—
164C2×SD16—1222no—
165C2×SD16—1222no—
166C2×SD16—1222no—
167C2×SD16—2442no—
168C2×SD16—2442no—
169C2×SD16—2442no—
170C2×SD16—2442no—
171C22×C8—612no—
172C4⋊Q8—611no—
173C4⋊Q8—1221no—
174C4⋊Q8—2441no—
175C4⋊Q8C4×D6111yescharacteristic
176#127—611no—
177#127—1221no—
178#127—2441no—
179#127C4×D6111yescharacteristic
180C2×C4⋊C4—2441no—
181C2×C42—611no—
182M32—22no—
183M32—1222no—
184M32—2442no—
185C2×C16—2442no—
186C4×C8—612no—
187C4×C8—611no—
188C4×C8C22×D6111yescharacteristic
189C24—2441no—
190C2×Q8—21no—
191C2×Q8—1221no—
192C2×Q8—2441no—
193C2×Q8—2442no—
194C2×Q8—2442no—
195C2×D4—21no—
196C2×D4—41no—
197C2×D4—1221no—
198C2×D4—4884no—
199C2×D4—2441no—
200C2×D4—2442no—
201C2×D4—2442no—
202C2×D4—2441no—
203C2×D4—2442no—
204C22×C4—611no—
205C22×C4—1221no—
206C22×C4—2441no—
207SD16—42no—
208SD16—42no—
209SD16—2442no—
210SD16—2442no—
211SD16—2442no—
212SD16—2442no—
213SD16—2442no—
214SD16—2442no—
215C2×C8—612no—
216C2×C8—612no—
217C2×C8—612no—
218C2×C8—612no—
219C2×C8—612no—
220C2×C8D4×D6112yes—
221C4⋊C4—41no—
222C4⋊C4—2441no—
223C4⋊C4—2442no—
224C42—611no—
225C42—1221no—
226C42C2×C4×D6111yescharacteristic
227C16—42no—
228C16—2442no—
229C23—41no—
230C23—611no—
231C23—4881no—
232C23—4881no—
233C23—4884no—
234C23—2441no—
235Q8—42no—
236Q8—4882no—
237Q8—2442no—
238D4—42no—
239D4—82no—
240D4—4882no—
241D4—4882no—
242D4—4884no—
243D4—2442no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—611no—
247C2×C4—612no—
248C2×C4—612no—
249C2×C4—1224no—
250C2×C4—1221no—
251C2×C4—4881no—
252C2×C4—4881no—
253C2×C4—2441no—
254C2×C4C22⋊C4×D6111yescharacteristic
255C8—612no—
256C8—612no—
257C8D8×D6112yes—
258C8SD16×D6112yes—
259C22—82no—
260C22—81no—
261C22—611no—
262C22—611no—
263C22—1222no—
264C22—9762no—
265C22—9762no—
266C22—4882no—
267C22—4881no—
268C22#100×D6111yescharacteristic
269C4—22no—
270C4—81no—
271C4—612no—
272C4—1222no—
273C4—4881no—
274C4#102×D6112yes—
275C2—21no—
276C2—161no—
277C2—612no—
278C2—1221no—
279C2—9761no—
280C2#331×D6111yescharacteristic
subgroupG/H
centerC2#331×D61
commutatorC42×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1359C2
socleC2×C61C2×#331
prime radical#127×D61C4
cosocleC4×C8×C61C23
hypercenter#1359D61
hypocenterC61C2×#1359
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1359

Complements

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

NH ≅ G/Ntype
2. #364×D61C2semidirect
3. #21443860C2semidirect
4. #21443859C2semidirect
5. C61×#1359C2semidirect
15. #16839583C22semidirect
18. C61×#364C22semidirect
139. #1359D61direct (N × H)
145. D61#1359direct (N × H)
158. #364C2×D61semidirect
159. C61C2×#1359semidirect

Maximal subgroups

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

subgroupindex
#492×D612
#364×D612
#214438602
#214438592
C61×#13592
C2×#135961