Finite Group Databasebeta

← #21461769

Subgroups — #21461769

Order 7808.

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

normal subgroups only

This group has 360 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
1C22×C4⋊#6923C211yesmaximal, characteristic
2C2×#14519845C212yesmaximal, complemented
3#16840704C211yesmaximal, characteristic
4#16840636C212yesmaximal, complemented
5C22⋊C8×D61C211yesmaximal, characteristic
6C23×#6923—21no—
7C2×C4⋊#6923—21no—
8C2×C4⋊#6923—24no—
9C2×C4⋊#6923C2211yescharacteristic
10C2×C4⋊#6923C2211yescharacteristic
11C2×C4⋊#6923C2212yes—
12C2×C22⋊#6923—21no—
13#14519845—24no—
14(C2×#6923)⋊C4—21no—
15C22×C4×D61C2211yescharacteristic
16C2×C8×D61C2212yes—
17C22⋊#92418C411yescharacteristic, complemented
18#14519689C412yescomplemented
19C22⋊C8×C61C411yescharacteristic, complemented
20C23×D61D411yescharacteristic
21C22×#6923—24no—
22C22×#6923—22no—
23C22×#6923—21no—
24C22×#6923—21no—
25C22×#6923—42no—
26C22×#6923—42no—
27C22×C4×C61C2×C411yescharacteristic
28C22×Dic61Q811yescharacteristic
29C2×C4×D61—22no—
30C2×C4×D61—22no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61Q811yescharacteristic
34C2×C4×D61C2311yescharacteristic
35C22⋊#6923—42no—
36C4⋊#6923—24no—
37C4⋊#6923—22no—
38C4⋊#6923—22no—
39C4⋊#6923—22no—
40C4⋊#6923D414yes—
41C2×C8×C61C2×C412yescomplemented
42C2×#92418C2×C412yescomplemented
43C8×D61—22no—
44C8×D61—22no—
45C23×C61C4⋊C411yescharacteristic
46C22×D61—21no—
47C22×D61—21no—
48C22×D61—21no—
49C22×D61—21no—
50C22×D61C4⋊C411yescharacteristic
51C22×D61SD1612yes—
52C22×D61SD1612yes—
53C22×D61C2×D411yescharacteristic
54C2×#6923—24no—
55C2×#6923—48no—
56C2×#6923—42no—
57C2×#6923—42no—
58C2×#6923—41no—
59C2×#6923—41no—
60C2×#6923—41no—
61C2×#6923—41no—
62C2×#6923—41no—
63C2×#6923—41no—
64C2×C4×C61—22no—
65C2×C4×C61C4⋊C411yescharacteristic
66C2×C4×C61C22×C411yescharacteristic
67C2×Dic61—22no—
68C2×Dic61C4⋊C411yescharacteristic
69C2×Dic61C2×Q811yescharacteristic
70C4×D61—21no—
71C4×D61—21no—
72C4×D61—22no—
73C4×D61—22no—
74C4×D61C2×D412yes—
75C4×D61#4112yes—
76C8×C61—22no—
77#92418—22no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61#10612yescomplemented
81C22×C61C2×C4⋊C411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—22no—
85C2×D61—22no—
86C2×D61—22no—
87C2×D61—22no—
88C2×D61#10612yescomplemented
89C2×D61#12011yescharacteristic
90C2×D61#12311yescharacteristic
91C2×D61C2×SD1611yescharacteristic
92C2×D61C2×SD1611yescharacteristic
93C2×D61AGL(1,ℤ/8)11yescharacteristic
94C2×D61#13711yescharacteristic
95#6923—44no—
96#6923—81no—
97#6923—81no—
98C4×C61—21no—
99C4×C61C4×D412yes—
100Dic61—21no—
101Dic61C22⋊Q812yes—
102#1853—611nomaximal, Sylow
103C2×C61—22no—
104C2×C61#38511yescharacteristic
105C2×C61C2×#10611yescharacteristic
106C2×C61#42811yescharacteristic
107D61—22no—
108D61#44811yescharacteristic
109D61#45011yescharacteristic
110D61#48111yescharacteristic
111D61#48311yescharacteristic
112C22×C4⋊C4—611no—
113C2×#106—612no—
114C2×C22⋊C8—611no—
115#380—611no—
116#340—612no—
117C61#185311yescharacteristic, complemented, Sylow
118C23×C4—611no—
119C23×C4—1221no—
120C22×C8—612no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—1224no—
125C2×C4⋊C4—1221no—
126C2×C22⋊C4—1221no—
127#106—1224no—
128C22⋊C8—611no—
129C22⋊C8—612no—
130C22⋊C8#692311yescharacteristic, complemented
131#95—1221no—
132C24—611no—
133C22×C4—611no—
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1222no—
139C22×C4—1222no—
140C22×C4—1222no—
141C22×C4—1224no—
142C22×C4—1221no—
143C22×C4—1221no—
144C22×C4—2442no—
145C22×C4—2442no—
146C22×C4C2×#692311yescharacteristic
147C2×C8—612no—
148C2×C8—1222no—
149C2×C8—1222no—
150C2×C8C2×#692312yescomplemented
151C4⋊C4—614no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1224no—
156C22⋊C4—2442no—
157C23—611no—
158C23—612no—
159C23—612no—
160C23—611no—
161C23—1221no—
162C23—1221no—
163C23—1221no—
164C23—1221no—
165C23C4⋊#692311yescharacteristic
166C2×C4—22no—
167C2×C4—611no—
168C2×C4—612no—
169C2×C4—612no—
170C2×C4—611no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1224no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4—2448no—
186C2×C4C4⋊#692311yescharacteristic
187C2×C4C22×#692311yescharacteristic
188C8—22no—
189C8—1222no—
190C22—21no—
191C22—21no—
192C22—611no—
193C22—611no—
194C22—611no—
195C22—611no—
196C22—611no—
197C22—611no—
198C22—612no—
199C22—1222no—
200C22—1222no—
201C22—1222no—
202C22—1222no—
203C22—1221no—
204C22—1221no—
205C22#1451984512yescomplemented
206C22C2×C4⋊#692311yescharacteristic
207C4—21no—
208C4—612no—
209C4—1221no—
210C4—4881no—
211C4—4881no—
212C4—2444no—
213C4D4×#692312yes—
214C2—22no—
215C2—611no—
216C2—611no—
217C2—611no—
218C2—611no—
219C2—1222no—
220C2#1684070911yescharacteristic
221C2C2×#1451984511yescharacteristic
222C2#1684077311yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC22⋊C8#6923
hypocenterC61#1853
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14519845C2semidirect
4. #16840636C2semidirect
17. C22⋊#92418C4semidirect
18. #14519689C4semidirect
19. C22⋊C8×C61C4semidirect
41. C2×C8×C61C2×C4semidirect
42. C2×#92418C2×C4semidirect
80. C22×C61#106semidirect
88. C2×D61#106semidirect
117. C61#1853semidirect
130. C22⋊C8#6923semidirect
150. C2×C8C2×#6923semidirect
205. C22#14519845semidirect