Finite Group Databasebeta

← C2×#16840072 #21455599

Subgroups — C2×#16840072 #21455599

Order 7808.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519768C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16840072C218yesmaximal, direct product factor
4C2×#14519710C211yesmaximal, characteristic
5C2×#14519706C211yesmaximal, characteristic
6C2×#14519702C211yesmaximal, characteristic
7C2×#14519700C211yesmaximal, characteristic
8C2×#106×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519768—22no—
12#14519768C2214yes—
13#14519742—22no—
14#14519742C2214yes—
15C2×C4⋊Dic61—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—21no—
18C2×#11758196—21no—
19C2×C4×Dic61—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519710C2214yes—
22#14519706C2214yes—
23#14519702C2214yes—
24#14519700C2214yes—
25C22×C8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#106×C61C2214yes—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61D411yescharacteristic
35C22×Dic61D411yescharacteristic
36C2×Dic122—21no—
37C2×Dic122—22no—
38C2×Dic122Q814yes—
39C2×Dic122C2312yes—
40C2×C8×C61—22no—
41C2×C8×C61C2312yes—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61C2312yes—
45C4⋊C4×C61C2312yes—
46C4⋊Dic61—21no—
47C4⋊Dic61—24no—
48C4⋊Dic61C2312yes—
49#11758196—24no—
50#11758196—24no—
51C4×Dic61—24no—
52C4×Dic61D412yes—
53C4×Dic61C2312yes—
54C2×#92418—22no—
55C2×#92418C2312yes—
56C23×C61C2×D411yescharacteristic
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—42no—
60C2×C4×C61—42no—
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×Dic61C2×D412yes—
72C2×Dic61C2×D412yes—
73Dic122—24no—
74Dic122—22no—
75Dic122C2×Q814yes—
76C8×C61—22no—
77#92418—22no—
78C22×C61C22⋊Q812yes—
79C22×C61#13512yes—
80C22×C61#13712yes—
81C22×C61C22×D411yescharacteristic
82C4×C61—42no—
83C4×C61—42no—
84C4×C61C22⋊Q812yes—
85C4×C61C22×Q811yescharacteristic
86C4×C61C2×#4111yescharacteristic
87Dic61—24no—
88Dic61—22no—
89Dic61—22no—
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×#106D6111yescharacteristic
101C2×C4⋊C8—611no—
102C2×#103—611no—
103C2×#103—611no—
104C61C2×#47911yescharacteristic, complemented, Sylow
105C22×Q8—611no—
106C22×C8—611no—
107C22×C8C2×D6111yescharacteristic
108#125—614no—
109#125—1222no—
110C4×Q8—614no—
111C4×Q8—1222no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—1221no—
114C2×C4⋊C4—1221no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C42—611no—
119C2×C42—1221no—
120#107—614no—
121#106C2×D6114yes—
122C4⋊C8—614no—
123#103—614no—
124#103—614no—
125C2×Q8—614no—
126C2×Q8—612no—
127C2×Q8—1222no—
128C2×Q8—1221no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4C22×D6111yescharacteristic
136C2×C8—22no—
137C2×C8—612no—
138C2×C8—1222no—
139C2×C8C22×D6112yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—612no—
143C4⋊C4—1224no—
144C4⋊C4—1224no—
145C4⋊C4—1224no—
146C4⋊C4—1221no—
147C4⋊C4C22×D6112yes—
148C4⋊C4C22×D6112yes—
149C42—612no—
150C42—612no—
151C42—1224no—
152C23D4×D6111yescharacteristic
153Q8—614no—
154Q8—1222no—
155Q8—1224no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—612no—
161C2×C4—612no—
162C2×C4—1222no—
163C2×C4—1224no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—2442no—
168C2×C4#1175822212yes—
169C2×C4D4×D6111yescharacteristic
170C2×C4Q8×D6112yes—
171C2×C4C23×D6111yescharacteristic
172C8—22no—
173C8—1222no—
174C22#1451975512yes—
175C22#1451979812yes—
176C22#1451980612yes—
177C22C2×D4×D6111yescharacteristic
178C4—42no—
179C4—42no—
180C4—1224no—
181C4—1222no—
182C4—1222no—
183C4—2442no—
184C4#1451975512yes—
185C4C2×Q8×D6111yescharacteristic
186C4C2×#1175822211yescharacteristic
187C2#1684007214yesdirect product factor
188C2C2×#1451975511yescharacteristic
189C2C2×#1451979811yescharacteristic
190C2C2×#1451980611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#106×C61C2
socleC23×C61C2×D4
hypercenterC2×#106D61
hypocenterC61C2×#479
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #16840072C2direct (N × H)
92. C2×C61#479semidirect
104. C61C2×#479semidirect
187. C2#16840072direct (N × H)