Finite Group Databasebeta

← #30605658

Subgroups — #30605658

Order 15616.

382 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462182C211yesmaximal, characteristic
2#21461382C211yesmaximal, characteristic
3#21460834C214yesmaximal, complemented
4#494×D61C211yesmaximal, characteristic
5#16840784—21no—
6#16840683C2212yes—
7#16840657—21no—
8#16840650—21no—
9#16840626C2212yes—
10#16840624—21no—
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×#11758187—22no—
21C4⋊#92420—22no—
22#14519834—41no—
23#14519832—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—
57Q16×C61—42no—
58Q16×C61—42no—
59C2×C8×C61C22⋊C411yescharacteristic
60C2×C8×C61C22×C411yescharacteristic
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C42×C61C22⋊C411yescharacteristic
64#11758202—44no—
65#11758202—44no—
66C4⋊Dic61—41no—
67C4⋊Dic61—41no—
68#11758196—42no—
69#11758196—42no—
70C4×Dic61D811yescharacteristic
71C4×Dic61SD1611yescharacteristic
72C4×Dic61C2×D411yescharacteristic
73C2×#92418C22⋊C411yescharacteristic
74C2×#92418C2×D411yescharacteristic
75Dic244—42no—
76Dic244—42no—
77C8×D61—22no—
78C8×D61—22no—
79#11758187—42no—
80C22×D61#10211yescharacteristic
81Q8×C61—42no—
82Q8×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61#10211yescharacteristic
85C2×C4×C61#10211yescharacteristic
86C2×C4×C61C2×C22⋊C411yescharacteristic
87C2×Dic61—42no—
88C2×Dic61#10211yescharacteristic
89C2×Dic61C2×D811yescharacteristic
90C2×Dic61C2×SD1611yescharacteristic
91C4×D61—22no—
92C4×D61—21no—
93C4×D61—21no—
94C4×D61—22no—
95C4×D61—84no—
96Dic122—42no—
97Dic122—42no—
98Dic122—84no—
99#92420—82no—
100C8×C61—21no—
101C8×C61—21no—
102#92418#10012yes—
103#92418AGL(1,ℤ/8)12yes—
104#11965—611nomaximal, Sylow
105C22×C61C2×#10211yescharacteristic
106C2×D61—21no—
107C2×D61—21no—
108C2×D61#36212yes—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—82no—
112C4×C61C2×#10011yescharacteristic
113C4×C61#41811yescharacteristic
114Dic61—21no—
115Dic61—21no—
116Dic61—82no—
117Dic61#51012yes—
118C2×#494—611no—
119#2163—611no—
120#1568—611no—
121#1362—614no—
122C2×C61#154511yescharacteristic
123C2×C61#214111yescharacteristic
124C2×C61C2×#36211yescharacteristic
125D61—22no—
126C22×Q16—612no—
127C22×Q16—1221no—
128C2×C4⋊Q8—1221no—
129#494—612no—
130#494—611no—
131#494—1221no—
132#494—1221no—
133#494#692311yescharacteristic
134#432—1221no—
135C2×C4×C8—611no—
136C4⋊C16—612no—
137C22⋊C16—1221no—
138#346—1221no—
139#335—612no—
140#334—1221no—
141C61#1196511yescharacteristic, complemented, Sylow
142C22×Q8—1222no—
143C2×Q16—21no—
144C2×Q16—612no—
145C2×Q16—1222no—
146C2×Q16—1222no—
147C2×Q16—1221no—
148C2×Q16—2444no—
149C2×Q16—2444no—
150C2×Q16C2×#692312yes—
151C22×C8—611no—
152C22×C8—611no—
153C4⋊Q8—21no—
154C4⋊Q8—1222no—
155C4⋊Q8—1221no—
156C4⋊Q8—2441no—
157C4⋊Q8—2441no—
158C2×C4⋊C4—2441no—
159C2×C4⋊C4—2441no—
160C2×C42—611no—
161C2×C16—1222no—
162C4⋊C8—1222no—
163C22⋊C8—2441no—
164#97—2441no—
165C4×C8—611no—
166C4×C8—611no—
167C4×C8—611no—
168C4×C8C2×#692311yescharacteristic
169C2×Q8—22no—
170C2×Q8—1222no—
171C2×Q8—2442no—
172C2×Q8—2444no—
173C2×Q8—2444no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—2442no—
178Q16—42no—
179Q16—42no—
180Q16—2442no—
181Q16—2442no—
182Q16—2444no—
183Q16—2444no—
184C2×C8—611no—
185C2×C8—611no—
186C2×C8—1222no—
187C2×C8—1222no—
188C2×C8—2442no—
189C2×C8C22⋊#692311yescharacteristic
190C2×C8C22×#692311yescharacteristic
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C42—611no—
198C42—611no—
199C42—611no—
200C42C22⋊#692311yescharacteristic
201C16—2442no—
202C23—611no—
203Q8—42no—
204Q8—42no—
205Q8—4884no—
206Q8—2442no—
207Q8—2442no—
208C2×C4—42no—
209C2×C4—611no—
210C2×C4—611no—
211C2×C4—611no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—4884no—
217C2×C4—2442no—
218C2×C4#1451983911yescharacteristic
219C2×C4#1451983911yescharacteristic
220C2×C4C2×C22⋊#692311yescharacteristic
221C8—21no—
222C8—21no—
223C8—612no—
224C8—612no—
225C8—4882no—
226C22—612no—
227C22—1221no—
228C22—1221no—
229C22C2×#1451983911yescharacteristic
230C4—21no—
231C4—21no—
232C4—82no—
233C4—612no—
234C4—1221no—
235C4—1221no—
236C4—4882no—
237C4D61⋊#10011yescharacteristic
238C4#1684075411yescharacteristic
239C2—1222no—
240C2#2146132711yescharacteristic
241C2#2146212911yescharacteristic
242C2D61⋊#36211yescharacteristic
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#11965
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
141. C61#11965semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214613822
#214608342
#494×D612
#1196561