Finite Group Databasebeta

← #29567337

Subgroups — #29567337

Order 15616.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#21445890C211yesmaximal, characteristic
2#21444153C211yesmaximal, characteristic
3C61×#1464C211yesmaximal, characteristic
4#16839819—21no—
5C2×C22⋊#92418C411yescharacteristic
6C2×C22⋊#92418C411yescharacteristic
7#16839517—21no—
8#16839517—21no—
9#16839488C412yes—
10#16839486—21no—
11C2×#117×C61C2211yescharacteristic
12C61×#432—21no—
13C61×#324C412yes—
14C61×#323—21no—
15C22×#92418—21no—
16C22×#92418—21no—
17C4⋊#92418—41no—
18C22⋊#92418—22no—
19C22⋊#92418—41no—
20C22⋊#92418—41no—
21#14519688—41no—
22C23×C4×C61C2×C411yescharacteristic
23#117×C61—41no—
24#117×C61—41no—
25C2×C4⋊C4×C61C2×C411yescharacteristic
26C2×C4⋊C4×C61C2×C411yescharacteristic
27C2×C22⋊C4×C61D411yescharacteristic
28C2×C22⋊C4×C61Q811yescharacteristic
29C2×C42×C61D411yescharacteristic
30C2×C42×C61D411yescharacteristic
31C4⋊C8×C61—41no—
32C22⋊C8×C61—22no—
33#97×C61—41no—
34C24×C61C4⋊C411yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61—41no—
38C22×C4×C61—41no—
39C22×C4×C61C4211yescharacteristic
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C4⋊C411yescharacteristic
44C22×C4×C61C4⋊C411yescharacteristic
45C2×C8×C61—42no—
46C4⋊C4×C61—41no—
47C4⋊C4×C61—41no—
48C22⋊C4×C61—41no—
49C22⋊C4×C61—41no—
50C42×C61—21no—
51C42×C61—21no—
52C42×C61—21no—
53C42×C61—21no—
54C2×#92418—42no—
55C2×#92418—41no—
56C2×#92418—41no—
57C2×#92418—41no—
58C2×#92418—41no—
59C2×#92418—41no—
60C2×#92418—41no—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61#9511yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61#9911yescharacteristic
83C2×C4×C61#9911yescharacteristic
84C8×C61—82no—
85#92418—81no—
86#92418—81no—
87#92418—82no—
88#7327—611nomaximal, Sylow
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—81no—
95C22×C61—81no—
96C22×C61#34211yescharacteristic
97C22×C61#34411yescharacteristic
98C22×C61#34411yescharacteristic
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—41no—
103C4×C61—41no—
104C4×C61—41no—
105C4×C61—41no—
106#1818—611no—
107#1464—611no—
108#1464D6111yescharacteristic
109C2×C61—21no—
110C2×C61—21no—
111C2×C61—81no—
112C2×C61#130611yescharacteristic
113C2×C61#139511yescharacteristic
114C2×C61#139511yescharacteristic
115C2×#117C2×D6111yescharacteristic
116#432—21no—
117#432—1221no—
118C2×C22⋊C8—611no—
119C2×C22⋊C8—611no—
120#336—1221no—
121#336—1221no—
122#324—612no—
123#324Dic6112yes—
124#323—21no—
125#323—1221no—
126C61#732711yescharacteristic, complemented, Sylow
127C23×C4C4×D6111yescharacteristic
128C22×C8—1221no—
129C22×C8—1221no—
130#117—41no—
131#117—41no—
132C2×C4⋊C4C4×D6111yescharacteristic
133C2×C4⋊C4C2×Dic6111yescharacteristic
134C2×C22⋊C4Dic12211yescharacteristic
135C2×C22⋊C4C22⋊D6111yescharacteristic
136C2×C42D24411yescharacteristic
137C2×C42C22⋊D6111yescharacteristic
138C4⋊C8—41no—
139C4⋊C8—2441no—
140C22⋊C8—22no—
141C22⋊C8—1222no—
142C22⋊C8—2441no—
143C22⋊C8—2441no—
144#97—41no—
145#97—2441no—
146C24#1175819611yescharacteristic
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4C4×Dic6111yescharacteristic
152C22×C4#1175819611yescharacteristic
153C22×C4C4⋊Dic6111yescharacteristic
154C22×C4#1175819811yescharacteristic
155C22×C4#1175819811yescharacteristic
156C22×C4C22⋊Dic6111yescharacteristic
157C2×C8—42no—
158C2×C8—2442no—
159C2×C8—2441no—
160C2×C8—2441no—
161C2×C8—2441no—
162C2×C8—2441no—
163C2×C8—2441no—
164C2×C8—2441no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C42—21no—
170C42—21no—
171C42—21no—
172C42—21no—
173C23—21no—
174C23—21no—
175C23—21no—
176C23—41no—
177C23—41no—
178C23#1451968411yescharacteristic
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4#1451969111yescharacteristic
195C2×C4#1451969111yescharacteristic
196C8—82no—
197C8—4881no—
198C8—4881no—
199C8—4882no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—81no—
207C22#1683952811yescharacteristic
208C22#1683953311yescharacteristic
209C22#1683953411yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—41no—
216C4—41no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#2144372811yescharacteristic
221C2#2144394711yescharacteristic
222C2#2144394911yescharacteristic
subgroupG/H
centerC22#16839528
commutatorC22×C4×C61C42
FrattiniC2×#117C2×D61
FittingC61×#1464C2
socleC22×C61#342
prime radicalC24×C61C4⋊C4
cosocleC2×#117×C61C22
hypercenter#1464D61
hypocenterC61#7327
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
126. C61#7327semidirect

Maximal subgroups

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

subgroupindex
#214458902
#214441532
C61×#14642
#732761