Finite Group Databasebeta

← D61×#1408 #29600316

Subgroups — D61×#1408 #29600316

Order 15616.

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

normal subgroups only

This group has 526 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#493×D61C211yesmaximal, characteristic
2#353×D61C212yesmaximal, complemented
3#21443982C211yesmaximal, characteristic, complemented
4#21443981C212yesmaximal, complemented
5C61×#1408C211yesmaximal, characteristic, complemented
6C2×D8×D61—22no—
7#127×D61C411yescharacteristic, complemented
8#127×D61C2211yescharacteristic
9#16840139C411yescharacteristic, complemented
10#16840138C411yescharacteristic, complemented
11#16840138C2211yescharacteristic
12#16840137—22no—
13#99×D61—22no—
14C4×C8×D61C411yescharacteristic, complemented
15#16839555C2212yescomplemented
16#16839554—22no—
17C61×#493C2211yescharacteristic
18C61×#353C2212yescomplemented
19C2×D4×D61—21no—
20C2×D4×D61—41no—
21C2×D4×D61—41no—
22C2×D4×D61D412yes—
23C2×D488—22no—
24C2×#11758199—22no—
25C2×#11758199—22no—
26D8×D61—44no—
27D8×D61—44no—
28C2×C8×D61—21no—
29#14519774C2×C411yescharacteristic
30#14519774C2×C411yescharacteristic, complemented
31#14519773—21no—
32#14519773—41no—
33#14519773—41no—
34#14519773D412yes—
35C22⋊C4×D61—42no—
36C42×D61C2×C411yescharacteristic
37#14519692—22no—
38#14519691—42no—
39C4×#92418C2×C411yescharacteristic, complemented
40C8×Dic61—21no—
41C2×D8×C61—22no—
42#127×C61C2×C411yescharacteristic, complemented
43#127×C61C2311yescharacteristic
44#99×C61—22no—
45C4×C8×C61C2×C411yescharacteristic, complemented
46C23×D61—22no—
47C23×D61—41no—
48C2×D4×C61—21no—
49C2×D4×C61—41no—
50C2×D4×C61—41no—
51C2×D4×C61C2×D412yes—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—42no—
54C2×C22⋊D61—42no—
55C2×C22⋊D61—41no—
56D4×D61—42no—
57D4×D61—42no—
58D4×D61—42no—
59D4×D61—42no—
60D4×D61—84no—
61D4×D61—84no—
62C2×D244—21no—
63C2×D244—41no—
64C2×D244—41no—
65C2×D244C22⋊C412yes—
66C2×C4×D61—21no—
67C2×C4×D61—82no—
68C2×C4×D61C22⋊C411yescharacteristic
69D8×C61—44no—
70C2×C8×C61—21no—
71C22⋊C4×C61—42no—
72C42×C61C22×C411yescharacteristic
73C22⋊Dic61—42no—
74#11758199—44no—
75#11758199—44no—
76#11758198—82no—
77C4×Dic61—21no—
78C4×Dic61C22⋊C411yescharacteristic
79C2×#92418—21no—
80D488—44no—
81C8×D61—22no—
82C8×D61—22no—
83C23×C61—22no—
84C23×C61—41no—
85C22×D61—22no—
86C22×D61—42no—
87C22×D61—42no—
88C22×D61—41no—
89C22×D61—84no—
90C22×D61—84no—
91C22×D61—81no—
92C22×D61—81no—
93C22×D61#9911yescharacteristic
94D4×C61—42no—
95D4×C61—42no—
96D4×C61—82no—
97D4×C61—82no—
98C2×C4×C61—21no—
99C2×C4×C61—82no—
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C22⋊D61—82no—
102C22⋊D61—82no—
103C22⋊D61—84no—
104C22⋊D61—84no—
105C2×Dic61—21no—
106C2×Dic61—82no—
107C2×Dic61#9911yescharacteristic
108D244—42no—
109D244—42no—
110D244—82no—
111D244—82no—
112C4×D61—24no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—164no—
116C8×C61—22no—
117#92418—22no—
118C2×#1408—611nomaximal, Sylow
119C22×C61—42no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61—81no—
123C22×C61C2×#9911yescharacteristic
124C2×D61—22no—
125C2×D61—42no—
126C2×D61—84no—
127C2×D61—82no—
128C2×D61—82no—
129C2×D61—81no—
130C2×D61—162no—
131C2×D61—162no—
132C2×D61—162no—
133C2×D61#35311yescharacteristic
134C2×D61#35311yescharacteristic
135C4×C61—22no—
136C4×C61—21no—
137C4×C61—162no—
138Dic61—22no—
139Dic61—21no—
140Dic61—162no—
141C2×#493—611no—
142C2×#353—612no—
143#1408—611no—
144#1408—612no—
145#1408D6111yescharacteristic, direct product factor
146C2×C61—21no—
147C2×C61—82no—
148C2×C61—161no—
149C2×C61C2×#35311yescharacteristic
150D61—21no—
151D61—82no—
152D61—161no—
153D61#140812yesdirect product factor
154C22×D8—1222no—
155C2×#127—611no—
156C2×#127—611no—
157#493—611no—
158#493—611no—
159#493—611no—
160#493—1222no—
161#493C2×D6111yescharacteristic
162C2×#99—1222no—
163C2×C4×C8—611no—
164#353—612no—
165#353—1222no—
166#353C2×D6112yescomplemented
167C61C2×#140811yescharacteristic, complemented, Sylow
168C22×D4—612no—
169C22×D4—1221no—
170C22×D4—2441no—
171C22×D4—2441no—
172C2×D8—22no—
173C2×D8—1222no—
174C2×D8—1222no—
175C2×D8—1222no—
176C2×D8—2444no—
177C2×D8—2444no—
178C22×C8—1221no—
179#127—612no—
180#127—611no—
181#127—611no—
182#127—1221no—
183#127—2441no—
184#127—2441no—
185#127C4×D6111yescharacteristic, complemented
186#127C22×D6111yescharacteristic
187C2×C22⋊C4—2442no—
188C2×C42—611no—
189#99—22no—
190#99—1222no—
191#99—2442no—
192C4×C8—611no—
193C4×C8—1221no—
194C4×C8C4×D6111yescharacteristic, complemented
195C24—1222no—
196C24—2441no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4—612no—
201C2×D4—1222no—
202C2×D4—1221no—
203C2×D4—4884no—
204C2×D4—4884no—
205C2×D4—2441no—
206C2×D4—2441no—
207C2×D4—2441no—
208C2×D4—2442no—
209C2×D4—2442no—
210C2×D4—2442no—
211C2×D4—2442no—
212C2×D4—2442no—
213C2×D4—2442no—
214C2×D4D4×D6112yes—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—4882no—
218D8—44no—
219D8—2444no—
220D8—2444no—
221D8—2444no—
222C2×C8—21no—
223C2×C8—1222no—
224C2×C8—1222no—
225C2×C8—1221no—
226C22⋊C4—42no—
227C22⋊C4—4882no—
228C22⋊C4—2442no—
229C42—611no—
230C42—1221no—
231C42C2×C4×D6111yescharacteristic
232C23—22no—
233C23—41no—
234C23—611no—
235C23—1222no—
236C23—4881no—
237C23—4881no—
238C23—4884no—
239C23—4884no—
240C23—2442no—
241C23—2442no—
242C23—2441no—
243D4—42no—
244D4—42no—
245D4—82no—
246D4—82no—
247D4—4882no—
248D4—4882no—
249D4—4882no—
250D4—4884no—
251D4—4884no—
252D4—4882no—
253D4—2442no—
254D4—2442no—
255C2×C4—21no—
256C2×C4—82no—
257C2×C4—611no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1224no—
261C2×C4—1221no—
262C2×C4—9764no—
263C2×C4—4882no—
264C2×C4C22⋊C4×D6111yescharacteristic
265C8—22no—
266C8—1222no—
267C22—42no—
268C22—82no—
269C22—82no—
270C22—81no—
271C22—611no—
272C22—611no—
273C22—1222no—
274C22—9762no—
275C22—9762no—
276C22—9762no—
277C22—4882no—
278C22—4882no—
279C22—4884no—
280C22—4881no—
281C22—2442no—
282C22#99×D6111yescharacteristic
283C4—22no—
284C4—21no—
285C4—162no—
286C4—1222no—
287C4—1221no—
288C4—9762no—
289C2—21no—
290C2—82no—
291C2—161no—
292C2—612no—
293C2—1221no—
294C2—9761no—
295C2—4882no—
296C2#353×D6111yescharacteristic
subgroupG/H
centerC2#353×D61
commutatorC42×C61C22×C4
Frattini#127C22×D61
FittingC61×#1408C2
socleC2×C61C2×#353
prime radical#493×D61C2
cosocle#127×C61C23
hypercenter#1408D61
hypocenterC61C2×#1408
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1408

Complements

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

NH ≅ G/Ntype
2. #353×D61C2semidirect
3. #21443982C2semidirect
4. #21443981C2semidirect
5. C61×#1408C2semidirect
7. #127×D61C4semidirect
9. #16840139C4semidirect
10. #16840138C4semidirect
14. C4×C8×D61C4semidirect
15. #16839555C22semidirect
18. C61×#353C22semidirect
30. #14519774C2×C4semidirect
39. C4×#92418C2×C4semidirect
42. #127×C61C2×C4semidirect
45. C4×C8×C61C2×C4semidirect
145. #1408D61direct (N × H)
153. D61#1408direct (N × H)
166. #353C2×D61semidirect
167. C61C2×#1408semidirect
185. #127C4×D61semidirect
194. C4×C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#493×D612
#353×D612
#214439822
#214439812
C61×#14082
C2×#140861