Finite Group Databasebeta

← #29567395

Subgroups — #29567395

Order 15616.

268 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 43 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#21446624C211yesmaximal, characteristic
2#21443765C211yesmaximal, characteristic, complemented
3C61×#1325C211yesmaximal, characteristic, complemented
4C2×#14519774C411yescharacteristic
5C2×#14519697—21no—
6C2×#14519697—21no—
7C2×C4×#92418C411yescharacteristic
8#16839488—21no—
9C61×#384C2211yescharacteristic
10C61×#324—21no—
11C22×D244—21no—
12C22×D244—41no—
13C22×#92418—21no—
14#14519774—21no—
15#14519774—41no—
16#14519774C812yescomplemented
17#14519697—42no—
18#14519697—42no—
19C22⋊#92418—41no—
20C4×#92418—41no—
21C2×C4⋊C4×C61—41no—
22C2×C4⋊C4×C61D411yescharacteristic
23C2×C4⋊C4×C61D411yescharacteristic
24C2×C42×C61C2×C411yescharacteristic
25C22⋊C8×C61—41no—
26C23×D61—41no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61C22⋊C411yescharacteristic
31C2×D244—22no—
32C2×D244—41no—
33C2×D244—41no—
34C2×D244—41no—
35C2×D244—41no—
36C2×D244—42no—
37C2×D244—42no—
38C2×D244—41no—
39C2×D244—82no—
40C2×D244—82no—
41C2×C8×C61—81no—
42C4⋊C4×C61—41no—
43C4⋊C4×C61—41no—
44C4⋊C4×C61—82no—
45C42×C61—21no—
46C42×C61C2×C811yescharacteristic
47C42×C61M1611yescharacteristic
48C2×#92418—22no—
49C2×#92418—41no—
50C2×#92418—41no—
51C2×#92418—81no—
52C23×C61#9911yescharacteristic
53C22×D61—42no—
54C22×D61—82no—
55C22×D61—82no—
56C22×D61—81no—
57C22×D61—81no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—81no—
67C2×C4×C61—81no—
68C2×C4×C61C22⋊C811yescharacteristic
69C2×C4×C61#10011yescharacteristic
70D244—42no—
71D244—42no—
72D244—81no—
73D244—81no—
74D244—84no—
75D244—84no—
76C8×C61—161no—
77#92418—42no—
78#92418—161no—
79#7354—611nomaximal, Sylow
80C22×C61—21no—
81C22×C61—21no—
82C22×C61#32311yescharacteristic
83C22×C61#35311yescharacteristic
84C22×C61#35511yescharacteristic
85C2×D61—84no—
86C2×D61—82no—
87C2×D61—162no—
88C2×D61—161no—
89C2×D61—161no—
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—81no—
95C4×C61—81no—
96#1957—611no—
97#1325—611no—
98#1325D6111yescharacteristic, complemented
99C2×C61—21no—
100C2×C61—21no—
101C2×C61#131811yescharacteristic
102C2×C61#140811yescharacteristic
103C2×C61#141011yescharacteristic
104D61—162no—
105C2×#127—611no—
106C2×#102—1221no—
107C2×#102—1221no—
108C2×C4×C8—611no—
109#384C2×D6111yescharacteristic
110#324—21no—
111#324—1221no—
112C61#735411yescharacteristic, complemented, Sylow
113C22×D4—1221no—
114C22×D4—2441no—
115C22×C8—1221no—
116#127—612no—
117#127—1221no—
118#127—2441no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4D24411yescharacteristic
121C2×C4⋊C4C22⋊D6111yescharacteristic
122C2×C42C4×D6111yescharacteristic
123#102—2442no—
124#102—2442no—
125C22⋊C8—41no—
126C22⋊C8—2441no—
127C4×C8—2441no—
128C24—2441no—
129C2×D4—1222no—
130C2×D4—4882no—
131C2×D4—4882no—
132C2×D4—2442no—
133C2×D4—2442no—
134C2×D4—2441no—
135C2×D4—2441no—
136C2×D4—2441no—
137C2×D4—2441no—
138C2×D4—2441no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4#1175819811yescharacteristic
143C2×C8—81no—
144C2×C8—1222no—
145C2×C8—4881no—
146C2×C8—2441no—
147C2×C8—2441no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—82no—
151C42—21no—
152C42C8×D6111yescharacteristic
153C42#1175818911yescharacteristic
154C23—4882no—
155C23—4882no—
156C23—4881no—
157C23—4881no—
158C23—2442no—
159C23#1451969111yescharacteristic
160D4—4884no—
161D4—4884no—
162D4—4881no—
163D4—4881no—
164D4—2442no—
165D4—2442no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4#1451968911yescharacteristic
177C2×C4#1451969311yescharacteristic
178C8—161no—
179C8—9761no—
180C8—2442no—
181C22—21no—
182C22—21no—
183C22—9762no—
184C22—9761no—
185C22—9761no—
186C22—4884no—
187C22—4882no—
188C22#1683948511yescharacteristic
189C22#1683955411yescharacteristic
190C22#1683955811yescharacteristic
191C4—22no—
192C4—22no—
193C4—21no—
194C4—21no—
195C4—81no—
196C4—81no—
197C2—21no—
198C2—21no—
199C2—9762no—
200C2#2144375011yescharacteristic
201C2#2144398111yescharacteristic
202C2#2144398511yescharacteristic
subgroupG/H
centerC22#16839554
commutatorC42×C61C2×C8
Frattini#384C2×D61
FittingC61×#1325C2
socleC22×C61#353
prime radicalC2×#14519774C4
cosocleC61×#384C22
hypercenter#1325D61
hypocenterC61#7354
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #21443765C2semidirect
3. C61×#1325C2semidirect
16. #14519774C8semidirect
98. #1325D61semidirect
112. C61#7354semidirect

Maximal subgroups

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

subgroupindex
#214466242
#214437652
C61×#13252
#735461