Finite Group Databasebeta

← C2×#16840129 #21456157

Subgroups — C2×#16840129 #21456157

Order 7808.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519775C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic
3#16840129C218yesmaximal, direct product factor
4C2×#14519702C211yesmaximal, characteristic
5C2×#14519701C211yesmaximal, characteristic
6C2×#14519700C211yesmaximal, characteristic
7C2×#14519687C211yesmaximal, characteristic
8C2×#103×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519775—22no—
12#14519775C2214yes—
13#14519768—22no—
14#14519768C2214yes—
15C2×C4⋊Dic61—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—21no—
18C2×#11758196—21no—
19C2×#11758196—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519702C2214yes—
22#14519701C2214yes—
23#14519700C2214yes—
24#14519687C2214yes—
25C22×Q8×C61C2211yescharacteristic
26C22×C8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#103×C61C2214yes—
29C2×Q8×C61—21no—
30C2×Q8×C61—22no—
31C2×Q8×C61—22no—
32C2×Q8×C61C2312yes—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C22×Dic61D411yescharacteristic
39C22×Dic61D411yescharacteristic
40C2×Dic122—22no—
41C2×Dic122—22no—
42C2×Dic122—21no—
43C2×Dic122C2312yes—
44C2×C8×C61—22no—
45C2×C8×C61C2312yes—
46C4⋊C4×C61—21no—
47C4⋊C4×C61C2312yes—
48C4⋊Dic61—21no—
49C4⋊Dic61—24no—
50C4⋊Dic61C2312yes—
51#11758196—24no—
52#11758196—24no—
53#11758196—24no—
54C4×Dic61D412yes—
55C4×Dic61C2312yes—
56C2×#92418—22no—
57C2×#92418C2312yes—
58C23×C61C2×D411yescharacteristic
59Q8×C61—22no—
60Q8×C61—22no—
61Q8×C61—42no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61#4112yes—
68C2×C4×C61#4112yes—
69C2×C4×C61C2411yescharacteristic
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61C2×D412yes—
77C2×Dic61C2×D412yes—
78Dic122—22no—
79Dic122—22no—
80Dic122—42no—
81C8×C61—22no—
82#92418—22no—
83C22×C61#12412yes—
84C22×C61#13712yes—
85C22×C61#13712yes—
86C22×C61C22×D411yescharacteristic
87C4×C61—42no—
88C4×C61—42no—
89C4×C61#12412yes—
90C4×C61C2×#4111yescharacteristic
91C4×C61C2×#4111yescharacteristic
92Dic61—22no—
93Dic61—22no—
94Dic61—42no—
95Dic61—42no—
96C2×#491—611nomaximal, Sylow
97C2×C61#49114yescomplemented
98C2×C61C2×#12411yescharacteristic
99C2×C61C2×#13711yescharacteristic
100C2×C61C2×#13711yescharacteristic
101C2×C4⋊Q8—611no—
102C2×#125—611no—
103#491—618no—
104C2×#103—611no—
105C2×#103—611no—
106C2×#103—611no—
107C2×#103D6111yescharacteristic
108C2×#97—611no—
109C61C2×#49111yescharacteristic, complemented, Sylow
110C22×Q8—611no—
111C22×Q8C2×D6111yescharacteristic
112C22×C8—611no—
113C22×C8C2×D6111yescharacteristic
114C4⋊Q8—614no—
115C4⋊Q8—1222no—
116#125—614no—
117#125—1222no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—1221no—
120C2×C4⋊C4—1221no—
121C2×C4⋊C4—1221no—
122C2×C4⋊C4—1221no—
123C2×C4⋊C4C2×D6111yescharacteristic
124C2×C42—611no—
125#103—614no—
126#103—614no—
127#103—614no—
128#103C2×D6114yes—
129#97—614no—
130C2×Q8—21no—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—612no—
134C2×Q8—1221no—
135C2×Q8—1222no—
136C2×Q8—1222no—
137C2×Q8C22×D6112yes—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—611no—
141C22×C4—611no—
142C22×C4—1221no—
143C22×C4—1221no—
144C22×C4C22×D6111yescharacteristic
145C2×C8—22no—
146C2×C8—612no—
147C2×C8—1222no—
148C2×C8C22×D6112yes—
149C4⋊C4—21no—
150C4⋊C4—612no—
151C4⋊C4—1224no—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—1224no—
155C4⋊C4—1221no—
156C4⋊C4C22×D6112yes—
157C42—612no—
158C42—612no—
159C23D4×D6111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—42no—
163Q8—1222no—
164Q8—1222no—
165Q8—2442no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—612no—
171C2×C4—612no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4#1175822212yes—
179C2×C4D4×D6111yescharacteristic
180C2×C4#1175822412yes—
181C2×C4C23×D6111yescharacteristic
182C8—22no—
183C8—1222no—
184C22#1451976312yes—
185C22#1451980612yes—
186C22#1451980912yes—
187C22C2×D4×D6111yescharacteristic
188C4—42no—
189C4—42no—
190C4—1222no—
191C4—1222no—
192C4—2442no—
193C4—2442no—
194C4#1451976312yes—
195C4C2×#1175822411yescharacteristic
196C4C2×#1175822211yescharacteristic
197C2#1684012914yesdirect product factor
198C2C2×#1451976311yescharacteristic
199C2C2×#1451980611yescharacteristic
200C2C2×#1451980911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61C2×#491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #16840129C2direct (N × H)
97. C2×C61#491semidirect
109. C61C2×#491semidirect
197. C2#16840129direct (N × H)