Finite Group Databasebeta

← C2×#16840070 #21455597

Subgroups — C2×#16840070 #21455597

Order 7808.

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

normal subgroups only

This group has 384 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×#14519769C211yesmaximal, characteristic
2C2×C4×Dic122C211yesmaximal, characteristic
3#16840070C218yesmaximal, direct product factor
4C2×#14519711C211yesmaximal, characteristic
5C2×#14519709C211yesmaximal, characteristic
6C2×#14519702C211yesmaximal, characteristic
7C2×#14519702C211yesmaximal, characteristic
8C2×C4⋊C8×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10#14519769—22no—
11#14519769C2214yes—
12C4×Dic122—22no—
13C4×Dic122C2214yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—21no—
18C2×#11758196—21no—
19C2×#11758196—21no—
20C2×C4×Dic61—21no—
21#14519711C2214yes—
22#14519709C2214yes—
23#14519702C2214yes—
24#14519702C2214yes—
25C22×C8×C61C2211yescharacteristic
26C22×C8×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28C4⋊C8×C61C2214yes—
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C2×Dic122—21no—
37C2×Dic122—22no—
38C2×Dic122Q814yes—
39C2×Dic122C2312yes—
40C2×C8×C61—22no—
41C2×C8×C61—22no—
42C2×C8×C61C2312yes—
43C2×C8×C61C2312yes—
44C42×C61D412yes—
45C42×C61C2312yes—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61C2312yes—
50C4⋊Dic61C2312yes—
51C4⋊Dic61C2312yes—
52#11758196—24no—
53#11758196—24no—
54#11758196—24no—
55C4×Dic61—24no—
56C23×C61C2×D411yescharacteristic
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61C2×D412yes—
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×Q812yes—
63C2×C4×C61#4112yes—
64C2×C4×C61C2411yescharacteristic
65C2×Dic61—24no—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—42no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73Dic122—24no—
74Dic122—22no—
75Dic122C2×Q814yes—
76C8×C61—22no—
77C8×C61—22no—
78C22×C61C22⋊Q812yes—
79C22×C61#13512yes—
80C22×C61#13712yes—
81C22×C61C22×D411yescharacteristic
82C4×C61—22no—
83C4×C61—22no—
84C4×C61C22⋊Q812yes—
85C4×C61C22×Q811yescharacteristic
86C4×C61C2×#4111yescharacteristic
87Dic61—24no—
88Dic61—42no—
89Dic61—42no—
90Dic61—42no—
91C2×#479—611nomaximal, Sylow
92C2×C61#47914yescomplemented
93C2×C61C2×C22⋊Q811yescharacteristic
94C2×C61C2×#13511yescharacteristic
95C2×C61C2×#13711yescharacteristic
96C2×#125—611no—
97C2×C4×Q8—611no—
98#479—618no—
99C2×#107—611no—
100C2×#106—611no—
101C2×C4⋊C8D6111yescharacteristic
102C2×#103—611no—
103C2×#103—611no—
104C61C2×#47911yescharacteristic, complemented, Sylow
105C22×Q8—611no—
106C22×C8C2×D6111yescharacteristic
107C22×C8C2×D6111yescharacteristic
108#125—614no—
109#125—1222no—
110C4×Q8—614no—
111C4×Q8—1222no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4—1221no—
117C2×C4⋊C4—1221no—
118C2×C42—1221no—
119C2×C42C2×D6111yescharacteristic
120#107—614no—
121#106—614no—
122C4⋊C8C2×D6114yes—
123#103—614no—
124#103—614no—
125C2×Q8—614no—
126C2×Q8—612no—
127C2×Q8—1221no—
128C2×Q8—1222no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4D24411yescharacteristic
134C22×C4D24411yescharacteristic
135C22×C4C22×D6111yescharacteristic
136C2×C8—22no—
137C2×C8—22no—
138C2×C8C22×D6112yes—
139C2×C8C22×D6112yes—
140C4⋊C4—612no—
141C4⋊C4—612no—
142C4⋊C4—612no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1224no—
147C4⋊C4—1224no—
148C4⋊C4—1224no—
149C42—1224no—
150C42D24412yes—
151C42C22×D6112yes—
152C23C2×D24411yescharacteristic
153Q8—614no—
154Q8—1222no—
155Q8—1224no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—1222no—
159C2×C4—1224no—
160C2×C4—1222no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4C2×D24412yes—
167C2×C4C2×D24412yes—
168C2×C4C2×D24411yescharacteristic
169C2×C4#1175822412yes—
170C2×C4Q8×D6112yes—
171C2×C4C23×D6111yescharacteristic
172C8—22no—
173C8—22no—
174C22#1451975712yes—
175C22#1451979912yes—
176C22#1451981012yes—
177C22C22×D24411yescharacteristic
178C4—22no—
179C4—22no—
180C4—1224no—
181C4—2442no—
182C4—2442no—
183C4—2442no—
184C4#1451975712yes—
185C4C2×Q8×D6111yescharacteristic
186C4C2×#1175822411yescharacteristic
187C2#1684007014yesdirect product factor
188C2C2×#1451975711yescharacteristic
189C2C2×#1451979911yescharacteristic
190C2C2×#1451981011yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C4⋊C8D61
hypocenterC61C2×#479
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #16840070C2direct (N × H)
92. C2×C61#479semidirect
104. C61C2×#479semidirect
187. C2#16840070direct (N × H)