Finite Group Databasebeta

← C2×#15688919 #20245065

Subgroups — C2×#15688919 #20245065

Order 6016.

260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13094013C211yesmaximal, characteristic
2C2×#13093943C211yesmaximal, characteristic, complemented
3#15688919C214yesmaximal, direct product factor
4C2×#101×C47C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic
6C2×#10625329—21no—
7#13094013—21no—
8#13094013—21no—
9#13094013C412yes—
10#13094013C2212yes—
11C2×(C2×D47)⋊C4—21no—
12C2×(C2×D47)⋊C4—21no—
13C2×C4×Dic47C411yescharacteristic
14#13093943—21no—
15#13093943C2212yescomplemented
16C22×Q8×C47C2211yescharacteristic
17C2×M16×C47—21no—
18#101×C47—21no—
19#101×C47C2212yescomplemented
20C23×D47—21no—
21C2×Q8×C47—41no—
22C2×Q8×C47—41no—
23C2×Q8×C47C2×C411yescharacteristic
24C2×Q8×C47D411yescharacteristic
25C2×Q8×C47D411yescharacteristic
26C2×Q8×C47C2311yescharacteristic
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×Dic47—21no—
31C2×D188—21no—
32C2×D188—41no—
33C2×D188—41no—
34C2×D188C2×C412yes—
35M16×C47—22no—
36M16×C47—41no—
37C2×C8×C47—41no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—22no—
42C4×Dic47—21no—
43C4×Dic47C2×C412yes—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47C22⋊C411yescharacteristic
48C22×D47—22no—
49C22×D47—44no—
50C22×D47—41no—
51C22×D47—41no—
52Q8×C47—41no—
53Q8×C47—41no—
54Q8×C47—41no—
55Q8×C47—41no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×Dic47—22no—
69C2×Dic47—42no—
70D188—42no—
71D188—42no—
72C8×C47—42no—
73C47⋊C8—42no—
74C22×C47—22no—
75C22×C47#9911yescharacteristic
76C22×C47#9911yescharacteristic
77C22×C47C2×C22⋊C411yescharacteristic
78C2×D47—44no—
79C2×D47—42no—
80C2×D47—82no—
81C2×D47—82no—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—21no—
88Dic47—42no—
89C2×#355—471nomaximal, Sylow
90C2×C47—21no—
91C2×C47—21no—
92C2×C47#35512yescomplemented
93C2×C47C2×#9911yescharacteristic
94D47—82no—
95C2×#124—471no—
96C2×#101—471no—
97C2×#101D4711yescharacteristic, complemented
98#355—474no—
99C47C2×#35511yescharacteristic, complemented, Sylow
100C22×Q8C2×D4711yescharacteristic
101C22×D4—471no—
102C2×M16—21no—
103C2×M16—941no—
104#124—472no—
105#124—472no—
106#124—941no—
107#124—941no—
108C2×C22⋊C4—941no—
109C2×C22⋊C4—941no—
110C2×C42—471no—
111#101—21no—
112#101—472no—
113#101—941no—
114#101C2×D4712yescomplemented
115C24—941no—
116C2×Q8—41no—
117C2×Q8—41no—
118C2×Q8C4×D4711yescharacteristic
119C2×Q8D18811yescharacteristic
120C2×Q8C22⋊D4711yescharacteristic
121C2×Q8C22×D4711yescharacteristic
122C2×D4—472no—
123C2×D4—941no—
124C2×D4—1881no—
125C2×D4—1881no—
126C22×C4—941no—
127C22×C4C4×D4711yescharacteristic
128C22×C4D18811yescharacteristic
129C22×C4C22⋊D4711yescharacteristic
130M16—22no—
131M16—41no—
132M16—942no—
133M16—1881no—
134C2×C8—41no—
135C2×C8—1881no—
136C22⋊C4—942no—
137C22⋊C4—942no—
138C22⋊C4—942no—
139C22⋊C4—942no—
140C42—472no—
141C42—941no—
142C23—942no—
143C23—1884no—
144C23—1881no—
145C23—1881no—
146C23(C2×D47)⋊C411yescharacteristic
147Q8—41no—
148Q8—41no—
149Q8—41no—
150Q8—41no—
151D4—1882no—
152D4—1882no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—942no—
160C2×C4—1882no—
161C2×C4(C2×D47)⋊C411yescharacteristic
162C2×C4(C2×D47)⋊C411yescharacteristic
163C2×C4(C2×D47)⋊C411yescharacteristic
164C2×C4C2×C4×D4711yescharacteristic
165C2×C4C2×D18811yescharacteristic
166C2×C4C2×C22⋊D4711yescharacteristic
167C8—42no—
168C8—1882no—
169C22—22no—
170C22—3762no—
171C22—3762no—
172C22—1884no—
173C22—1882no—
174C22#1309393811yescharacteristic
175C22#1309393811yescharacteristic
176C22C2×(C2×D47)⋊C411yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—1882no—
184C2—21no—
185C2—21no—
186C2—3762no—
187C2#1568891912yesdirect product factor
188C2C2×#1309393811yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC2×#101×C47C2
socleC22×C47#99
hypercenterC2×#101D47
hypocenterC47C2×#355
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#13093943C2semidirect
3. #15688919C2direct (N × H)
4. C2×#101×C47C2semidirect
15. #13093943C22semidirect
19. #101×C47C22semidirect
92. C2×C47#355semidirect
97. C2×#101D47semidirect
99. C47C2×#355semidirect
114. #101C2×D47semidirect
187. C2#15688919direct (N × H)