Finite Group Databasebeta

← #30605652

Subgroups — #30605652

Order 15616.

394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462178C211yesmaximal, characteristic
2#21461378C211yesmaximal, characteristic
3#21460834C214yesmaximal, complemented
4#494×D61C211yesmaximal, characteristic
5#16840766—21no—
6#16840683C2212yes—
7#16840657—21no—
8C4×#11758187—21no—
9#16840626—21no—
10#16840626C2212yes—
11C2×Q16×D61—21no—
12C2×Q16×D61C412yes—
13C4⋊Q8×D61—21no—
14#16840142C411yescharacteristic
15#16840141—21no—
16#16840140—21no—
17#16840140C2212yes—
18C4×C8×D61C2211yescharacteristic
19C61×#494C411yescharacteristic
20C2×#11758213—41no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23C4⋊#92420—41no—
24C2×Q8×D61—22no—
25C2×Dic244—21no—
26C2×Dic244C2×C412yes—
27C2×#11758202—22no—
28C2×#11758202—22no—
29Q16×D61—44no—
30Q16×D61—44no—
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519777—21no—
34#14519776—41no—
35#14519776—41no—
36#14519775—22no—
37C4⋊C4×D61—41no—
38C4⋊C4×D61—41no—
39C42×D61D411yescharacteristic
40C4×#92418D411yescharacteristic
41C8×Dic61D411yescharacteristic
42C8×Dic61C2311yescharacteristic
43C2×Q16×C61—21no—
44C2×Q16×C61C2×C412yes—
45C4⋊Q8×C61—21no—
46C4×C8×C61C2×C411yescharacteristic
47C2×Q8×C61—22no—
48Q8×D61—44no—
49Q8×D61—44no—
50C2×C4×D61—42no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×C4×D61D811yescharacteristic
53C2×C4×D61SD1611yescharacteristic
54C2×Dic122—22no—
55C2×Dic122—42no—
56C2×#92420—42no—
57#11758213—82no—
58Q16×C61—42no—
59Q16×C61—42no—
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22×C411yescharacteristic
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61C22⋊C411yescharacteristic
65#11758202—44no—
66#11758202—44no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61D811yescharacteristic
72C4×Dic61SD1611yescharacteristic
73C4×Dic61C2×D411yescharacteristic
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C2×D411yescharacteristic
76Dic244—42no—
77Dic244—42no—
78C8×D61—22no—
79C8×D61—22no—
80#11758187—42no—
81C22×D61#10211yescharacteristic
82Q8×C61—42no—
83Q8×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61#10211yescharacteristic
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C2×Dic61—42no—
89C2×Dic61#10211yescharacteristic
90C2×Dic61C2×D811yescharacteristic
91C2×Dic61C2×SD1611yescharacteristic
92C4×D61—22no—
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—84no—
96C4×D61SD3212yes—
97C4×D61Q3212yes—
98Dic122—42no—
99Dic122—42no—
100Dic122—84no—
101#92420—82no—
102C8×C61—21no—
103C8×C61—21no—
104#92418#10012yes—
105#92418AGL(1,ℤ/8)12yes—
106#11962—611nomaximal, Sylow
107C22×C61C2×#10211yescharacteristic
108C2×D61—21no—
109C2×D61—21no—
110C2×D61#35812yes—
111C4×C61—82no—
112C4×C61#35812yes—
113C4×C61#36212yes—
114C4×C61C2×#10011yescharacteristic
115C4×C61#41811yescharacteristic
116Dic61—21no—
117Dic61—21no—
118Dic61—82no—
119Dic61C2×SD3211yescharacteristic
120Dic61C2×Q3211yescharacteristic
121C2×#494—611no—
122#2162—611no—
123#1567—611no—
124#1362—614no—
125C2×C61#154511yescharacteristic
126C2×C61C2×#35811yescharacteristic
127C2×C61C2×#36211yescharacteristic
128D61—22no—
129C22×Q16—612no—
130C22×Q16—1221no—
131C2×C4⋊Q8—1221no—
132#494—612no—
133#494—611no—
134#494—1221no—
135#494—1221no—
136#494#692311yescharacteristic
137#423—1221no—
138C2×C4×C8—611no—
139C4⋊C16—612no—
140C22⋊C16—1221no—
141C4×C16—1221no—
142#335—612no—
143#335—1221no—
144C61#1196211yescharacteristic, complemented, Sylow
145C22×Q8—1222no—
146C2×Q16—21no—
147C2×Q16—612no—
148C2×Q16—1222no—
149C2×Q16—1222no—
150C2×Q16—1221no—
151C2×Q16—2444no—
152C2×Q16—2444no—
153C2×Q16C2×#692312yes—
154C2×M16—2441no—
155C22×C8—611no—
156C22×C8—611no—
157C4⋊Q8—21no—
158C4⋊Q8—1222no—
159C4⋊Q8—1221no—
160C4⋊Q8—2441no—
161C4⋊Q8—2441no—
162C2×C4⋊C4—2441no—
163C2×C4⋊C4—2441no—
164C2×C42—611no—
165C2×C16—1222no—
166C4⋊C8—1222no—
167C4⋊C8—2441no—
168C4×C8—611no—
169C4×C8—611no—
170C4×C8—611no—
171C4×C8C2×#692311yescharacteristic
172C2×Q8—22no—
173C2×Q8—1222no—
174C2×Q8—2442no—
175C2×Q8—2444no—
176C2×Q8—2444no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—2442no—
181Q16—42no—
182Q16—42no—
183Q16—2442no—
184Q16—2442no—
185Q16—2444no—
186Q16—2444no—
187M16—4882no—
188C2×C8—611no—
189C2×C8—611no—
190C2×C8—1222no—
191C2×C8—1222no—
192C2×C8—2442no—
193C2×C8C22⋊#692311yescharacteristic
194C2×C8C22×#692311yescharacteristic
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—2442no—
198C4⋊C4—2442no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C42—611no—
202C42—611no—
203C42—611no—
204C42C22⋊#692311yescharacteristic
205C16—2442no—
206C23—611no—
207Q8—42no—
208Q8—42no—
209Q8—4884no—
210Q8—2442no—
211Q8—2442no—
212C2×C4—42no—
213C2×C4—611no—
214C2×C4—612no—
215C2×C4—612no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—4884no—
222C2×C4—2442no—
223C2×C4#1451983911yescharacteristic
224C2×C4#1451983911yescharacteristic
225C2×C4C2×C22⋊#692311yescharacteristic
226C8—21no—
227C8—21no—
228C8—612no—
229C8—612no—
230C8—4882no—
231C22—612no—
232C22—1221no—
233C22—1221no—
234C22C2×#1451983911yescharacteristic
235C4—82no—
236C4—611no—
237C4—611no—
238C4—1221no—
239C4—1221no—
240C4—4882no—
241C4#1684067512yes—
242C4#1684068112yes—
243C4D61⋊#10011yescharacteristic
244C4#1684075411yescharacteristic
245C2—1222no—
246C2#2146132711yescharacteristic
247C2C2×#1684067511yescharacteristic
248C2C2×#1684068111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#494C4
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC8×Dic61C23
hypercenter#494#6923
hypocenterC61#11962
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #21460834C2semidirect
144. C61#11962semidirect

Maximal subgroups

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

subgroupindex
#214621782
#214613782
#214608342
#494×D612
#1196261