Finite Group Databasebeta

← C2×#16839558 #21447496

Subgroups — C2×#16839558 #21447496

Order 7808.

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×#14519766C211yesmaximal, characteristic
2C2×#14519696C211yesmaximal, characteristic, complemented
3#16839558C214yesmaximal, direct product factor
4C2×#101×C61C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic
6C2×#11758194—21no—
7#14519766—21no—
8#14519766—21no—
9#14519766C412yes—
10#14519766C2212yes—
11C2×#11758198—21no—
12C2×#11758198—21no—
13C2×C4×Dic61C411yescharacteristic
14#14519696—21no—
15#14519696C2212yescomplemented
16C22×Q8×C61C2211yescharacteristic
17C2×M16×C61—21no—
18#101×C61—21no—
19#101×C61C2212yescomplemented
20C23×D61—21no—
21C2×Q8×C61—41no—
22C2×Q8×C61—41no—
23C2×Q8×C61C2×C411yescharacteristic
24C2×Q8×C61D411yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×Q8×C61C2311yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×Dic61—21no—
31C2×D244—21no—
32C2×D244—41no—
33C2×D244—41no—
34C2×D244C2×C412yes—
35M16×C61—22no—
36M16×C61—41no—
37C2×C8×C61—41no—
38#11758198—22no—
39#11758198—22no—
40#11758198—22no—
41#11758198—22no—
42C4×Dic61—21no—
43C4×Dic61C2×C412yes—
44#11758194—22no—
45#11758194—41no—
46C2×#92418—41no—
47C23×C61C22⋊C411yescharacteristic
48C22×D61—22no—
49C22×D61—44no—
50C22×D61—41no—
51C22×D61—41no—
52Q8×C61—41no—
53Q8×C61—41no—
54Q8×C61—41no—
55Q8×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22⋊C411yescharacteristic
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—42no—
70D244—42no—
71D244—42no—
72C8×C61—42no—
73#92418—42no—
74C22×C61—22no—
75C22×C61#9911yescharacteristic
76C22×C61#9911yescharacteristic
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—44no—
79C2×D61—42no—
80C2×D61—82no—
81C2×D61—82no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—21no—
88Dic61—42no—
89C2×#355—611nomaximal, Sylow
90C2×C61—21no—
91C2×C61—21no—
92C2×C61#35512yescomplemented
93C2×C61C2×#9911yescharacteristic
94D61—82no—
95C2×#124—611no—
96C2×#101—611no—
97C2×#101D6111yescharacteristic, complemented
98#355—614no—
99C61C2×#35511yescharacteristic, complemented, Sylow
100C22×Q8C2×D6111yescharacteristic
101C22×D4—611no—
102C2×M16—21no—
103C2×M16—1221no—
104#124—612no—
105#124—612no—
106#124—1221no—
107#124—1221no—
108C2×C22⋊C4—1221no—
109C2×C22⋊C4—1221no—
110C2×C42—611no—
111#101—21no—
112#101—612no—
113#101—1221no—
114#101C2×D6112yescomplemented
115C24—1221no—
116C2×Q8—41no—
117C2×Q8—41no—
118C2×Q8C4×D6111yescharacteristic
119C2×Q8D24411yescharacteristic
120C2×Q8C22⋊D6111yescharacteristic
121C2×Q8C22×D6111yescharacteristic
122C2×D4—612no—
123C2×D4—1221no—
124C2×D4—2441no—
125C2×D4—2441no—
126C22×C4—1221no—
127C22×C4C4×D6111yescharacteristic
128C22×C4D24411yescharacteristic
129C22×C4C22⋊D6111yescharacteristic
130M16—22no—
131M16—41no—
132M16—1222no—
133M16—2441no—
134C2×C8—41no—
135C2×C8—2441no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C22⋊C4—1222no—
139C22⋊C4—1222no—
140C42—612no—
141C42—1221no—
142C23—1222no—
143C23—2444no—
144C23—2441no—
145C23—2441no—
146C23#1175819811yescharacteristic
147Q8—41no—
148Q8—41no—
149Q8—41no—
150Q8—41no—
151D4—2442no—
152D4—2442no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—1222no—
160C2×C4—2442no—
161C2×C4#1175819811yescharacteristic
162C2×C4#1175819811yescharacteristic
163C2×C4#1175819811yescharacteristic
164C2×C4C2×C4×D6111yescharacteristic
165C2×C4C2×D24411yescharacteristic
166C2×C4C2×C22⋊D6111yescharacteristic
167C8—42no—
168C8—2442no—
169C22—22no—
170C22—4882no—
171C22—4882no—
172C22—2444no—
173C22—2442no—
174C22#1451969111yescharacteristic
175C22#1451969111yescharacteristic
176C22C2×#1175819811yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—2442no—
184C2—21no—
185C2—21no—
186C2—4882no—
187C2#1683955812yesdirect product factor
188C2C2×#1451969111yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC2×#101×C61C2
socleC22×C61#99
hypercenterC2×#101D61
hypocenterC61C2×#355
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14519696C2semidirect
3. #16839558C2direct (N × H)
4. C2×#101×C61C2semidirect
15. #14519696C22semidirect
19. #101×C61C22semidirect
92. C2×C61#355semidirect
97. C2×#101D61semidirect
99. C61C2×#355semidirect
114. #101C2×D61semidirect
187. C2#16839558direct (N × H)