Finite Group Databasebeta

← #21444178

Subgroups — #21444178

Order 7808.

322 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#14519751C211yesmaximal, characteristic
2#16839726C211yesmaximal, characteristic, complemented
3#16839485C214yesmaximal, complemented
4C2×C22⋊C8×C61C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic
6C22×C22⋊D61C412yes—
7C2×#11758194—21no—
8#14519751—21no—
9#14519751—21no—
10#14519751—21no—
11#14519751—21no—
12C2×C4⋊Dic61C411yescharacteristic
13C2×#11758198C2212yes—
14C22⋊#92418—21no—
15C22⋊#92418C2212yes—
16C23×C4×C61C2211yescharacteristic
17C22×C8×C61—21no—
18C22⋊C8×C61—21no—
19C22⋊C8×C61C2212yes—
20C24×C61C2×C411yescharacteristic
21C23×D61C2×C412yes—
22C22×C4×C61—42no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C2×C22⋊D61—44no—
32C22×Dic61C2×C412yes—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—42no—
36C2×C8×C61—22no—
37C2×C8×C61—42no—
38#11758198—22no—
39#11758198—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42#11758194—42no—
43C2×#92418—22no—
44C23×C61—22no—
45C23×C61—22no—
46C23×C61—41no—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C22⋊C411yescharacteristic
49C23×C61C22×C411yescharacteristic
50C22×D61—22no—
51C22×D61—24no—
52C22×D61—42no—
53C22×D61—42no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—44no—
65C22⋊D61—44no—
66C2×Dic61—22no—
67C2×Dic61—42no—
68D244—42no—
69D244—42no—
70C8×C61—42no—
71#92418—42no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—44no—
80C22×C61#10012yes—
81C22×C61C2×C22⋊C411yescharacteristic
82C22×C61#13112yes—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—42no—
86C2×D61—84no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61#9912yes—
91Dic61—42no—
92#1471—611nomaximal, Sylow
93C2×C61—22no—
94C2×C61—22no—
95C2×C61—41no—
96C2×C61#40811yescharacteristic
97C2×C61C2×#9911yescharacteristic
98C2×C61C2×#10011yescharacteristic
99D61—82no—
100C2×#121—611no—
101#407—611no—
102C2×C22⋊C8D6111yescharacteristic, complemented
103#323—614no—
104C61#147111yescharacteristic, complemented, Sylow
105C22×D4—612no—
106C22×D4—611no—
107C23×C4C2×D6111yescharacteristic
108C2×M16—1221no—
109C22×C8—21no—
110#121—1221no—
111#121—1221no—
112#121—1221no—
113#121—1221no—
114C2×C4⋊C4—611no—
115C2×C22⋊C4—612no—
116C22⋊C8—21no—
117C22⋊C8—612no—
118C22⋊C8—1221no—
119C22⋊C8C2×D6112yes—
120C24—612no—
121C24C4×D6111yescharacteristic
122C2×D4—1222no—
123C2×D4—1222no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—2442no—
127C2×D4—2444no—
128C22×C4—42no—
129C22×C4—612no—
130C22×C4C4×D6111yescharacteristic
131C22×C4D24411yescharacteristic
132C22×C4D24411yescharacteristic
133C22×C4C22⋊D6111yescharacteristic
134C22×C4C22⋊D6111yescharacteristic
135C22×C4C22×D6111yescharacteristic
136M16—2442no—
137C2×C8—22no—
138C2×C8—42no—
139C2×C8—1222no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C23—22no—
145C23—22no—
146C23—41no—
147C23—1224no—
148C23—1222no—
149C23—2442no—
150C23—2442no—
151C23#1175819811yescharacteristic
152C23#1175819811yescharacteristic
153C23C2×C4×D6111yescharacteristic
154D4—2442no—
155D4—2444no—
156D4—2444no—
157D4—2442no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—1222no—
165C2×C4—2442no—
166C2×C4#1175819811yescharacteristic
167C2×C4#1175819811yescharacteristic
168C2×C4C2×D24411yescharacteristic
169C2×C4C2×C22⋊D6111yescharacteristic
170C8—42no—
171C8—2442no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—44no—
180C22—4884no—
181C22—2442no—
182C22—2442no—
183C22—2442no—
184C22#1451969312yes—
185C22C2×#1175819811yescharacteristic
186C22#1451978312yes—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—2442no—
191C4#1451969112yes—
192C2—22no—
193C2—22no—
194C2—41no—
195C2—4882no—
196C2#1683972811yescharacteristic
197C2C2×#1451969111yescharacteristic
198C2C2×#1451969311yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C8D61
hypocenterC61#1471
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839726C2semidirect
3. #16839485C2semidirect
4. C2×C22⋊C8×C61C2semidirect
102. C2×C22⋊C8D61semidirect
104. C61#1471semidirect