Finite Group Databasebeta

← #30594577

Subgroups — #30594577

Order 15616.

402 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D61⋊(C22⋊C16)C211yesmaximal, characteristic
2#21461696C211yesmaximal, characteristic
3#340×D61C211yesmaximal, characteristic
4C2×D61⋊C16—21no—
5C2×#14519846C412yescomplemented
6#16840704—21no—
7#16840657C412yescomplemented
8C22⋊#11758187—21no—
9#16840636—21no—
10C22×C8×D61C2211yescharacteristic
11C2×C4⋊C4×D61—21no—
12#16839525C411yescharacteristic, complemented
13#16839524—21no—
14C61×#340C411yescharacteristic, complemented
15C2×C4⋊#6923—22no—
16C2×C22⋊#6923—41no—
17D61⋊C16—42no—
18C2×#11758187—22no—
19#14519846—42no—
20(C2×#6923)⋊C4—41no—
21C22×C4×D61—41no—
22C22×C4×D61D411yescharacteristic
23C22×#92418D411yescharacteristic
24C2×C8×D61—42no—
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61C2×C411yescharacteristic
27C2×C8×D61D411yescharacteristic
28C2×C8×D61Q811yescharacteristic
29C2×C4⋊Dic61—21no—
30C2×#11758196—41no—
31C4⋊C4×D61—24no—
32C4⋊C4×D61—42no—
33C22×C8×C61C2×C411yescharacteristic
34C2×C4⋊C4×C61—21no—
35C23×D61D811yescharacteristic
36C22×#6923—42no—
37C22×C4×C61—41no—
38C22×C4×C61C22⋊C411yescharacteristic
39C22×Dic61—41no—
40C22×Dic61SD1611yescharacteristic
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61—44no—
44C2×C4×D61—82no—
45C2×C4×D61—81no—
46C2×C4×D61—81no—
47C2×C4×D61C22⋊C411yescharacteristic
48C2×C4×D61C4⋊C411yescharacteristic
49C2×C4×D61SD1611yescharacteristic
50C2×C4×D61Q1611yescharacteristic
51C22⋊#6923—81no—
52C22⋊#6923—81no—
53C4⋊#6923—42no—
54C4⋊#6923—42no—
55C2×C8×C61—41no—
56C2×C8×C61C4211yescharacteristic
57C2×C8×C61C4⋊C411yescharacteristic
58C4⋊C4×C61—22no—
59C4⋊C4×C61—41no—
60C4⋊Dic61—22no—
61C4⋊Dic61—41no—
62#11758196—44no—
63C2×#92418—41no—
64C2×#92418C22⋊C411yescharacteristic
65C2×#92418C4⋊C411yescharacteristic
66C8×D61—22no—
67C8×D61—22no—
68C8×D61—41no—
69C8×D61—41no—
70#11758187—42no—
71C23×C61#10211yescharacteristic
72C22×D61—22no—
73C22×D61—22no—
74C22×D61#10211yescharacteristic
75C22×D61#10711yescharacteristic
76C22×D61D1611yescharacteristic
77C22×D61SD3211yescharacteristic
78C22×D61SD3211yescharacteristic
79C22×D61Q3211yescharacteristic
80C2×#6923—82no—
81C2×#6923—82no—
82C2×#6923—82no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—42no—
86C2×C4×C61—81no—
87C2×C4×C61—81no—
88C2×C4×C61#9511yescharacteristic
89C2×C4×C61#10311yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—42no—
92C2×Dic61—81no—
93C2×Dic61—81no—
94C2×Dic61#10311yescharacteristic
95C2×Dic61#10611yescharacteristic
96C4×D61—22no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—22no—
100C4×D61—84no—
101C4×D61—84no—
102C4×D61#9912yes—
103C4×D61#10412yes—
104C8×C61—21no—
105C8×C61—21no—
106#92418—21no—
107#92418—21no—
108#7258—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61#34011yescharacteristic
112C22×C61#35711yescharacteristic
113C22×C61#35811yescharacteristic
114C2×D61—21no—
115C2×D61—21no—
116C2×D61—22no—
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—22no—
120C2×D61#32712yes—
121C2×D61#35711yescharacteristic
122C2×D61#35811yescharacteristic
123C2×D61#36012yes—
124C2×D61#36611yescharacteristic
125C2×D61#36711yescharacteristic
126#6923—162no—
127C4×C61—21no—
128C4×C61—82no—
129C4×C61#33911yescharacteristic
130C4×C61#34211yescharacteristic
131Dic61—21no—
132Dic61—82no—
133Dic61#32812yes—
134C2×C22⋊C16—611no—
135#1808—611no—
136C2×#340—611no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61#129411yescharacteristic
140C2×C61#138011yescharacteristic
141C2×C61#138611yescharacteristic
142D61—21no—
143D61—21no—
144D61#134712yes—
145D61#134812yes—
146C23×C8—611no—
147C22×C4⋊C4—1221no—
148C22×C16—1221no—
149C2×#107—612no—
150#380—1221no—
151C22⋊C16—612no—
152C22⋊C16—1221no—
153#340—611no—
154#340—1221no—
155#340—1221no—
156#340#692311yescharacteristic, complemented
157C61#725811yescharacteristic, complemented, Sylow
158C23×C4—611no—
159C23×C4—2441no—
160C22×C8—611no—
161C22×C8—611no—
162C22×C8—611no—
163C22×C8—611no—
164C22×C8—611no—
165C22×C8—2442no—
166C22×C8C2×#692311yescharacteristic
167C2×C4⋊C4—21no—
168C2×C4⋊C4—1224no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4—2442no—
172C2×C4⋊C4—2441no—
173C2×C22⋊C4—2441no—
174C2×C16—1222no—
175C2×C16—2442no—
176#107—2442no—
177#95—2441no—
178C24—611no—
179C22×C4—41no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1222no—
186C22×C4—1222no—
187C22×C4—4881no—
188C22×C4—4881no—
189C22×C4—4882no—
190C22×C4—2444no—
191C22×C4—2442no—
192C22×C4—2441no—
193C22×C4C22⋊#692311yescharacteristic
194C2×C8—41no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—1222no—
198C2×C8—1222no—
199C2×C8—2441no—
200C2×C8—2441no—
201C2×C8—2441no—
202C2×C8C4×#692311yescharacteristic
203C2×C8C4⋊#692311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—1222no—
207C4⋊C4—2441no—
208C4⋊C4—2444no—
209C4⋊C4—2442no—
210C4⋊C4—2442no—
211C22⋊C4—4881no—
212C22⋊C4—4881no—
213C16—2442no—
214C23—611no—
215C23—611no—
216C23—611no—
217C23—611no—
218C23—611no—
219C23—611no—
220C23—1222no—
221C23—1222no—
222C23#1451983911yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—611no—
229C2×C4—612no—
230C2×C4—612no—
231C2×C4—611no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—4884no—
238C2×C4—4884no—
239C2×C4—4882no—
240C2×C4—4882no—
241C2×C4—4882no—
242C2×C4—4881no—
243C2×C4—4881no—
244C2×C4—2442no—
245C2×C4(C2×#6923)⋊C411yescharacteristic
246C2×C4#1451984011yescharacteristic
247C8—21no—
248C8—21no—
249C8—1221no—
250C8—1221no—
251C22—21no—
252C22—21no—
253C22—611no—
254C22—611no—
255C22—612no—
256C22—612no—
257C22—611no—
258C22—611no—
259C22—1222no—
260C22—1222no—
261C22—1222no—
262C22—1222no—
263C22—1221no—
264C22—1221no—
265C22#1684063511yescharacteristic
266C22#1684067411yescharacteristic
267C22#1684067511yescharacteristic
268C4—21no—
269C4—82no—
270C4—612no—
271C4—1221no—
272C4—9762no—
273C4—4882no—
274C4#1684063311yescharacteristic
275C4#1684063911yescharacteristic
276C2—21no—
277C2—21no—
278C2—612no—
279C2—612no—
280C2—1221no—
281C2—1221no—
282C2#2146069311yescharacteristic
283C2#2146087611yescharacteristic
284C2#2146089211yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#340C4
socleC22×C61#340
prime radicalC23×D61D8
cosocleC22×C8×D61C22
hypercenter#340#6923
hypocenterC61#7258
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
5. C2×#14519846C4semidirect
7. #16840657C4semidirect
12. #16839525C4semidirect
14. C61×#340C4semidirect
156. #340#6923semidirect
157. C61#7258semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616962
#340×D612
#725861