Finite Group Databasebeta

← #21461931

Subgroups — #21461931

Order 7808.

256 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 88 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×#14519845C212yesmaximal
2#16840708C211yesmaximal, characteristic
3C4×C4⋊#6923C211yesmaximal, characteristic
4#16840636C212yesmaximal
5C4⋊C8×D61C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C2×C4⋊#6923—21no—
8C2×C4⋊#6923C2212yes—
9C2×C4⋊#6923C2211yescharacteristic
10C2×C4⋊#6923C2211yescharacteristic
11C2×C4×#6923—21no—
12#14519845—24no—
13(C2×#6923)⋊C4—21no—
14C2×C8×D61C2212yes—
15C42×D61C2211yescharacteristic
16C4⋊#92418C411yescharacteristic, complemented
17#14519706C412yescomplemented
18C4⋊C8×C61C411yescharacteristic, complemented
19C22×#6923—21no—
20C22×#6923—21no—
21C22×#6923—22no—
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61C2311yescharacteristic
25C4⋊#6923—22no—
26C4⋊#6923—21no—
27C4⋊#6923—21no—
28C4⋊#6923—22no—
29C4⋊#6923—42no—
30C4⋊#6923—42no—
31C4⋊#6923D412yes—
32C4⋊#6923Q812yes—
33C4×#6923—42no—
34C2×C8×C61C2×C412yes—
35C42×C61C2×C411yescharacteristic
36C4×Dic61C2×C411yescharacteristic
37C4×Dic61Q811yescharacteristic
38C4×Dic61Q811yescharacteristic
39C2×#92418C2×C412yes—
40C8×D61—22no—
41C8×D61—22no—
42C22×D61C2×D411yescharacteristic
43C2×#6923—22no—
44C2×#6923—22no—
45C2×#6923—41no—
46C2×#6923—41no—
47C2×#6923—41no—
48C2×#6923—41no—
49C2×#6923—42no—
50C2×#6923—42no—
51C2×#6923—42no—
52C2×C4×C61C4⋊C411yescharacteristic
53C2×C4×C61C4⋊C411yescharacteristic
54C2×C4×C61C22×C411yescharacteristic
55C2×Dic61C4⋊C411yescharacteristic
56C2×Dic61C4⋊C411yescharacteristic
57C2×Dic61C2×Q811yescharacteristic
58C4×D61—21no—
59C4×D61—21no—
60C4×D61SD1612yes—
61C4×D61SD1612yes—
62C4×D61C2×D411yescharacteristic
63C4×D61C2×Q811yescharacteristic
64C4×D61#4111yescharacteristic
65C4×D61#4111yescharacteristic
66C8×C61—22no—
67#92418—22no—
68C22×C61C2×C4⋊C411yescharacteristic
69C2×D61#12111yescharacteristic
70C2×D61C22⋊Q811yescharacteristic
71C2×D61C2×SD1611yescharacteristic
72C2×D61C2×SD1611yescharacteristic
73C2×D61AGL(1,ℤ/8)11yescharacteristic
74C2×D61#13711yescharacteristic
75#6923—42no—
76#6923—42no—
77#6923—82no—
78C4×C61—21no—
79C4×C61#10612yescomplemented
80C4×C61C4×D411yescharacteristic
81C4×C61C4×Q811yescharacteristic
82Dic61—21no—
83Dic61#10612yescomplemented
84Dic61#12511yescharacteristic
85Dic61C4⋊Q811yescharacteristic
86#1948—611nomaximal, Sylow
87C2×C61#38911yescharacteristic
88C2×C61C2×#10611yescharacteristic
89C2×C61#42811yescharacteristic
90D61#46011yescharacteristic
91D61#46111yescharacteristic
92D61#47511yescharacteristic
93D61#47611yescharacteristic
94C2×#106—612no—
95C2×C4⋊C8—611no—
96#384—611no—
97C4×C4⋊C4—611no—
98#340—612no—
99C61#194811yescharacteristic, complemented, Sylow
100C22×C8—612no—
101C2×C4⋊C4—611no—
102C2×C4⋊C4—611no—
103C2×C4⋊C4—612no—
104C2×C4⋊C4—1221no—
105C2×C4⋊C4—1221no—
106C2×C42—611no—
107C2×C42—1221no—
108#106—1224no—
109C4⋊C8—612no—
110C4⋊C8—611no—
111C4⋊C8#692311yescharacteristic, complemented
112#95—1221no—
113C22×C4—611no—
114C22×C4—611no—
115C22×C4—611no—
116C22×C4—1221no—
117C22×C4—1221no—
118C22×C4—1222no—
119C2×C8—612no—
120C2×C8—1222no—
121C2×C8—1222no—
122C2×C8C2×#692312yes—
123C4⋊C4—612no—
124C4⋊C4—612no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1222no—
128C4⋊C4—1222no—
129C4⋊C4—2442no—
130C4⋊C4—2442no—
131C42—611no—
132C42—611no—
133C42—611no—
134C42—2442no—
135C42C2×#692311yescharacteristic
136C23—611no—
137C2×C4—611no—
138C2×C4—611no—
139C2×C4—612no—
140C2×C4—612no—
141C2×C4—611no—
142C2×C4—611no—
143C2×C4—611no—
144C2×C4—611no—
145C2×C4—611no—
146C2×C4—1221no—
147C2×C4—1221no—
148C2×C4—1222no—
149C2×C4—1222no—
150C2×C4—2442no—
151C2×C4—2442no—
152C2×C4—2442no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4C4⋊#692311yescharacteristic
158C2×C4C4⋊#692311yescharacteristic
159C2×C4C22×#692311yescharacteristic
160C8—22no—
161C8—1222no—
162C22—611no—
163C22—611no—
164C22—611no—
165C22—611no—
166C22—611no—
167C22—611no—
168C22C2×C4⋊#692311yescharacteristic
169C4—21no—
170C4—611no—
171C4—611no—
172C4—612no—
173C4—1221no—
174C4—4882no—
175C4—2442no—
176C4—2442no—
177C4#1451984512yescomplemented
178C4D4×#692311yescharacteristic
179C4Q8×#692311yescharacteristic
180C2—611no—
181C2—611no—
182C2—611no—
183C2—611no—
184C2#1684071311yescharacteristic
185C2C2×#1451984511yescharacteristic
186C2#1684077311yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC4⋊C8#6923
hypocenterC61#1948
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
16. C4⋊#92418C4semidirect
17. #14519706C4semidirect
18. C4⋊C8×C61C4semidirect
79. C4×C61#106semidirect
83. Dic61#106semidirect
99. C61#1948semidirect
111. C4⋊C8#6923semidirect
177. C4#14519845semidirect