Finite Group Databasebeta

← C2×#16839971 #21455256

Subgroups — C2×#16839971 #21455256

Order 7808.

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

normal subgroups only

This group has 480 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
1C22×Dic244C211yesmaximal, characteristic
2C22×#11758202C211yesmaximal, characteristic
3C2×#14519775C211yesmaximal, characteristic
4C2×#14519742C211yesmaximal, characteristic
5#16839971C218yesmaximal, direct product factor
6C2×#14519706C211yesmaximal, characteristic
7C2×#14519700C211yesmaximal, characteristic
8C2×#103×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10C22×Dic122C2211yescharacteristic
11C2×Dic244—24no—
12C2×Dic244C2214yes—
13C2×#11758202—24no—
14C2×#11758202C2214yes—
15C22×#92418C2211yescharacteristic
16#14519775—22no—
17#14519775C2214yes—
18#14519742—22no—
19#14519742C2214yes—
20C2×#11758196—21no—
21C2×#11758196—21no—
22C2×#11758196—21no—
23C2×C4×Dic61—21no—
24C2×C4×Dic61C2211yescharacteristic
25#14519706C2214yes—
26#14519700C2214yes—
27C22×Q8×C61C2211yescharacteristic
28C22×C8×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30#103×C61C2214yes—
31C2×Q8×C61—21no—
32C2×Q8×C61—22no—
33C2×Q8×C61—22no—
34C2×Q8×C61C2312yes—
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61—21no—
39C22×Dic61—21no—
40C22×Dic61D411yescharacteristic
41C22×Dic61D411yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—22no—
44C2×Dic122—22no—
45C2×Dic122—22no—
46C2×Dic122—21no—
47C2×Dic122D414yes—
48C2×Dic122C2312yes—
49C2×Dic122C2312yes—
50C2×C8×C61—22no—
51C2×C8×C61C2312yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54#11758202—28no—
55#11758196—24no—
56#11758196—24no—
57#11758196—24no—
58C4×Dic61—24no—
59C4×Dic61D412yes—
60C4×Dic61C2312yes—
61C2×#92418—22no—
62C2×#92418C2312yes—
63Dic244—28no—
64C23×C61C2×D411yescharacteristic
65Q8×C61—22no—
66Q8×C61—22no—
67Q8×C61—42no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D412yes—
74C2×C4×C61#4112yes—
75C2×C4×C61C2411yescharacteristic
76C2×Dic61—24no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—42no—
81C2×Dic61Q1614yescomplemented
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D412yes—
84Dic122—24no—
85Dic122—22no—
86Dic122—22no—
87Dic122—22no—
88Dic122—42no—
89Dic122C2×D414yes—
90C8×C61—22no—
91#92418—22no—
92C22×C61#12112yes—
93C22×C61C2×Q1612yes—
94C22×C61#13712yes—
95C22×C61C22×D411yescharacteristic
96C4×C61—42no—
97C4×C61—42no—
98C4×C61#12112yes—
99C4×C61C22×D411yescharacteristic
100C4×C61C2×#4111yescharacteristic
101Dic61—24no—
102Dic61—22no—
103Dic61—42no—
104Dic61C2×Q1614yescomplemented
105C2×#462—611nomaximal, Sylow
106C2×C61#46214yescomplemented
107C2×C61C2×#12111yescharacteristic
108C2×C61C22×Q1611yescharacteristic
109C2×C61C2×#13711yescharacteristic
110C22×Q16—611no—
111C22×Q16—611no—
112C2×C4⋊Q8—611no—
113C2×C4×Q8—611no—
114#462—618no—
115C2×C4⋊C8—611no—
116C2×#103—611no—
117C2×#103D6111yescharacteristic
118C61C2×#46211yescharacteristic, complemented, Sylow
119C22×Q8—611no—
120C22×Q8—611no—
121C22×Q8C2×D6111yescharacteristic
122C2×Q16—614no—
123C2×Q16—614no—
124C2×Q16—1224no—
125C2×Q16—1224no—
126C22×C8—611no—
127C22×C8C2×D6111yescharacteristic
128C4⋊Q8—614no—
129C4⋊Q8—1222no—
130C4×Q8—614no—
131C4×Q8—1222no—
132C2×C4⋊C4—1221no—
133C2×C4⋊C4—1221no—
134C2×C4⋊C4—1221no—
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C42—611no—
137C2×C42—1221no—
138C4⋊C8—614no—
139#103—614no—
140#103C2×D6114yes—
141C2×Q8—21no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—614no—
145C2×Q8—612no—
146C2×Q8—612no—
147C2×Q8—1222no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×Q8—1222no—
151C2×Q8—1222no—
152C2×Q8C22×D6112yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—1221no—
158C22×C4—1221no—
159C22×C4C22×D6111yescharacteristic
160Q16—1228no—
161Q16—1228no—
162C2×C8—22no—
163C2×C8—612no—
164C2×C8—1222no—
165C2×C8C22×D6112yes—
166C4⋊C4—21no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—1224no—
170C4⋊C4C22×D6112yes—
171C42—612no—
172C42—612no—
173C42—1224no—
174C23D4×D6111yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—42no—
178Q8—614no—
179Q8—1222no—
180Q8—1224no—
181Q8—1222no—
182Q8—1222no—
183Q8—2442no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—612no—
189C2×C4—614no—
190C2×C4—612no—
191C2×C4—1222no—
192C2×C4—1224no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—2442no—
196C2×C4#1175822212yes—
197C2×C4D4×D6112yes—
198C2×C4D4×D6111yescharacteristic
199C2×C4C23×D6111yescharacteristic
200C8—22no—
201C8—1222no—
202C22#1451975012yes—
203C22Q16×D6112yes—
204C22#1451980612yes—
205C22C2×D4×D6111yescharacteristic
206C4—42no—
207C4—42no—
208C4—614no—
209C4—1224no—
210C4—1222no—
211C4—2442no—
212C4#1451975012yes—
213C4C2×D4×D6111yescharacteristic
214C4C2×#1175822211yescharacteristic
215C2#1683997114yesdirect product factor
216C2C2×#1451975011yescharacteristic
217C2C2×Q16×D6111yescharacteristic
218C2C2×#1451980611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61C2×#462
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
5. #16839971C2direct (N × H)
81. C2×Dic61Q16semidirect
104. Dic61C2×Q16semidirect
106. C2×C61#462semidirect
118. C61C2×#462semidirect
215. C2#16839971direct (N × H)