Finite Group Databasebeta

← C2×#16840111 #21456128

Subgroups — C2×#16840111 #21456128

Order 7808.

424 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519776C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic
3#16840111C218yesmaximal, direct product factor
4C2×#14519702C211yesmaximal, characteristic
5C2×#14519701C211yesmaximal, characteristic
6C2×#14519700C211yesmaximal, characteristic
7C2×C8×Dic61C211yesmaximal, characteristic
8C2×#103×C61C211yesmaximal, characteristic
9C22×Dic122—21no—
10C22×Dic122C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12#14519776—22no—
13#14519776C2214yes—
14#14519775—22no—
15#14519775C2214yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—21no—
18C2×#11758196—21no—
19C2×#11758196—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519702C2214yes—
22#14519701C2214yes—
23#14519700C2214yes—
24C8×Dic61C2214yes—
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×Dic122—24no—
44C2×Dic122—44no—
45C2×Dic122C2312yes—
46C2×C8×C61—22no—
47C2×C8×C61C2312yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61C2312yes—
50C4⋊Dic61—21no—
51C4⋊Dic61C2312yes—
52#11758196—24no—
53#11758196—24no—
54#11758196—24no—
55C4×Dic61D412yes—
56C4×Dic61C2312yes—
57C2×#92418—22no—
58C2×#92418C2312yes—
59C23×C61C2×D411yescharacteristic
60Q8×C61—22no—
61Q8×C61—22no—
62Q8×C61—42no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4112yes—
69C2×C4×C61#4112yes—
70C2×C4×C61C2411yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—42no—
74C2×Dic61—42no—
75C2×Dic61SD1614yes—
76C2×Dic61Q1614yes—
77C2×Dic61C2×D412yes—
78C2×Dic61C2×D412yes—
79Dic122—22no—
80Dic122—22no—
81Dic122—42no—
82Dic122—48no—
83C8×C61—22no—
84#92418—22no—
85C22×C61#12412yes—
86C22×C61C2×SD1612yes—
87C22×C61C2×Q1612yes—
88C22×C61C22×D411yescharacteristic
89C4×C61—42no—
90C4×C61—42no—
91C4×C61#12412yes—
92C4×C61C2×#4111yescharacteristic
93C4×C61C2×#4111yescharacteristic
94Dic61—42no—
95Dic61—42no—
96Dic61C2×SD1614yes—
97Dic61C2×Q1614yes—
98C2×#487—611nomaximal, Sylow
99C2×C61#48714yescomplemented
100C2×C61C2×#12411yescharacteristic
101C2×C61C22×SD1611yescharacteristic
102C2×C61C22×Q1611yescharacteristic
103C2×C4⋊Q8—611no—
104C2×C4⋊Q8—611no—
105#487—618no—
106C2×#103—611no—
107C2×#103—611no—
108C2×#103—611no—
109C2×#103D6111yescharacteristic
110C2×C4×C8—611no—
111C61C2×#48711yescharacteristic, complemented, Sylow
112C22×Q8—611no—
113C22×Q8—1221no—
114C22×Q8C2×D6111yescharacteristic
115C22×C8—611no—
116C22×C8C2×D6111yescharacteristic
117C4⋊Q8—614no—
118C4⋊Q8—614no—
119C4⋊Q8—1222no—
120C4⋊Q8—1222no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—1221no—
123C2×C4⋊C4—1221no—
124C2×C4⋊C4—1221no—
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C42—611no—
127#103—614no—
128#103—614no—
129#103—614no—
130#103C2×D6114yes—
131C4×C8—614no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—612no—
136C2×Q8—1224no—
137C2×Q8—1221no—
138C2×Q8—1222no—
139C2×Q8—1222no—
140C2×Q8—2444no—
141C2×Q8C22×D6112yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—1221no—
147C22×C4—1221no—
148C22×C4C22×D6111yescharacteristic
149C2×C8—22no—
150C2×C8—612no—
151C2×C8—1222no—
152C2×C8C22×D6112yes—
153C4⋊C4—21no—
154C4⋊C4—612no—
155C4⋊C4—1224no—
156C4⋊C4—1224no—
157C4⋊C4—1224no—
158C4⋊C4—1221no—
159C4⋊C4C22×D6112yes—
160C42—612no—
161C42—612no—
162C23D4×D6111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—42no—
166Q8—1222no—
167Q8—1222no—
168Q8—2448no—
169Q8—2442no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—612no—
175C2×C4—612no—
176C2×C4—614no—
177C2×C4—614no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—2442no—
181C2×C4—2442no—
182C2×C4#1175822212yes—
183C2×C4D4×D6111yescharacteristic
184C2×C4#1175822412yes—
185C2×C4C23×D6111yescharacteristic
186C8—22no—
187C8—1222no—
188C22#1451976312yes—
189C22SD16×D6112yes—
190C22Q16×D6112yes—
191C22C2×D4×D6111yescharacteristic
192C4—42no—
193C4—42no—
194C4—614no—
195C4—614no—
196C4—2442no—
197C4—2442no—
198C4#1451976312yes—
199C4C2×#1175822411yescharacteristic
200C4C2×#1175822211yescharacteristic
201C2#1684011114yesdirect product factor
202C2C2×#1451976311yescharacteristic
203C2C2×SD16×D6111yescharacteristic
204C2C2×Q16×D6111yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61C2×#487
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. #16840111C2direct (N × H)
99. C2×C61#487semidirect
111. C61C2×#487semidirect
201. C2#16840111direct (N × H)