Finite Group Databasebeta

← #21461259

Subgroups — #21461259

Order 7808.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#16840704C211yesmaximal, characteristic
3#16840616C214yesmaximal, complemented
4C2×#14519753C211yesmaximal, characteristic
5C2×D61⋊C8—21no—
6C2×C4⋊#6923—21no—
7C2×C22⋊#6923—21no—
8#14519834C2212yes—
9C22⋊#92420—21no—
10(C2×#6923)⋊C4C2212yes—
11C22×C4×D61C2211yescharacteristic
12#14519753—21no—
13#14519753—21no—
14#14519753C412yescomplemented
15#14519753C2212yes—
16C2×C4⋊Dic61C411yescharacteristic, complemented
17C2×#11758196—21no—
18C2×#11758198—21no—
19C22×Q8×C61C411yescharacteristic, complemented
20C23×D61D411yescharacteristic
21C22×#6923—22no—
22C2×Q8×C61—21no—
23C2×Q8×C61—42no—
24C2×Q8×C61C2×C412yes—
25C22×C4×C61—21no—
26C22×C4×C61C2×C411yescharacteristic
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C2×C4×D61—42no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61C2311yescharacteristic
34C22⋊#6923—42no—
35C2×#92420—22no—
36C4⋊#6923—42no—
37D61⋊C8—42no—
38#11758198—22no—
39#11758198—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C412yes—
42#11758196—22no—
43#11758196—22no—
44C23×C61C22⋊C411yescharacteristic
45C22×D61—41no—
46C22×D61—41no—
47C22×D61C22⋊C411yescharacteristic
48C22×D61SD1612yes—
49C22×D61Q1612yes—
50C22×D61C2×D411yescharacteristic
51C2×#6923—42no—
52C2×#6923—42no—
53C2×#6923—42no—
54Q8×C61—42no—
55Q8×C61—42no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—42no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C2×Dic61—22no—
62C2×Dic61—41no—
63C2×Dic61—42no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C4×D61—22no—
67C4×D61—22no—
68C4×D61—41no—
69C4×D61—41no—
70#92420—42no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61#10312yes—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—21no—
78C2×D61—21no—
79C2×D61—42no—
80C2×D61—42no—
81C2×D61#10312yes—
82C2×D61C2×SD1611yescharacteristic
83C2×D61C2×Q1611yescharacteristic
84#6923—82no—
85C4×C61—21no—
86C4×C61—42no—
87C4×C61#9912yes—
88Dic61—21no—
89Dic61—21no—
90Dic61—42no—
91#1520—611nomaximal, Sylow
92C2×C61—22no—
93C2×C61C2×#9911yescharacteristic
94C2×C61C2×#10311yescharacteristic
95C2×C61#42111yescharacteristic
96D61—21no—
97D61—22no—
98D61—21no—
99C2×C22⋊Q8—611no—
100C2×C22⋊C8—611no—
101#380—611no—
102#328—614no—
103C61#152011yescharacteristic, complemented, Sylow
104C22×Q8#692311yescharacteristic, complemented
105C23×C4—611no—
106C22×C8—1221no—
107C22⋊Q8—612no—
108C22⋊Q8—612no—
109C22⋊Q8—1221no—
110C22⋊Q8—1221no—
111C2×C4⋊C4—611no—
112C2×C4⋊C4—1221no—
113C2×C4⋊C4—1221no—
114C2×C22⋊C4—1221no—
115C2×C22⋊C4—1221no—
116C22⋊C8—612no—
117C22⋊C8—1221no—
118#95—612no—
119C24—611no—
120C2×Q8—21no—
121C2×Q8—42no—
122C2×Q8C2×#692312yes—
123C22×C4—21no—
124C22×C4—611no—
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—1221no—
130C22×C4—1222no—
131C22×C4—2442no—
132C22×C4C2×#692311yescharacteristic
133C2×C8—1222no—
134C2×C8—2442no—
135C4⋊C4—612no—
136C4⋊C4—1222no—
137C4⋊C4—1222no—
138C4⋊C4—1221no—
139C4⋊C4—2442no—
140C22⋊C4—1222no—
141C22⋊C4—1222no—
142C22⋊C4—2442no—
143C23—611no—
144C23—611no—
145C23—612no—
146C23—612no—
147C23—2441no—
148C23—2441no—
149C23C22⋊#692311yescharacteristic
150Q8—42no—
151Q8—42no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—611no—
156C2×C4—611no—
157C2×C4—1222no—
158C2×C4—1222no—
159C2×C4—1222no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4—2442no—
167C2×C4C22⋊#692311yescharacteristic
168C2×C4C22×#692311yescharacteristic
169C8—2442no—
170C22—21no—
171C22—21no—
172C22—611no—
173C22—612no—
174C22—611no—
175C22—1221no—
176C22—1221no—
177C22—1221no—
178C22—1221no—
179C22—2442no—
180C22—2442no—
181C22#1451984012yes—
182C22C2×C22⋊#692311yescharacteristic
183C4—21no—
184C4—42no—
185C4—1221no—
186C4—1221no—
187C4—4882no—
188C4—2442no—
189C4#1451983512yes—
190C2—22no—
191C2—1221no—
192C2—1222no—
193C2—1221no—
194C2C2×#1451983511yescharacteristic
195C2C2×#1451984011yescharacteristic
196C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×Q8#6923
hypocenterC61#1520
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #16840616C2semidirect
14. #14519753C4semidirect
16. C2×C4⋊Dic61C4semidirect
19. C22×Q8×C61C4semidirect
103. C61#1520semidirect
104. C22×Q8#6923semidirect