Finite Group Databasebeta

← #21444753

Subgroups — #21444753

Order 7808.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#16840343C211yesmaximal, characteristic, complemented
2#16839896C212yesmaximal, complemented
3#16839495C212yesmaximal, complemented
4#16839488C211yesmaximal, characteristic, complemented
5C61×#394C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7C2×#11758199—22no—
8#14519757—22no—
9#14519752—22no—
10#14519751—21no—
11#14519751C2212yes—
12#14519698—22no—
13C22⋊#92418C2212yes—
14C22×D4×C61C2211yescharacteristic
15C2×C4⋊C4×C61C2211yescharacteristic
16C2×C22⋊C4×C61—21no—
17C2×C22⋊C4×C61—21no—
18#95×C61C2211yescharacteristic
19C24×C61—21no—
20C2×D4×C61—22no—
21C2×D4×C61—42no—
22C22×C4×C61—21no—
23C22×C4×C61D411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61C2311yescharacteristic
26C2×C22⋊D61—22no—
27#11758222—42no—
28#11758222—42no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244D412yes—
32C2×C4×D61—22no—
33C2×Dic122—21no—
34C4⋊C4×C61—22no—
35C22⋊C4×C61—42no—
36C22⋊C4×C61—42no—
37#11758199—44no—
38#11758198—22no—
39#11758198—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61D412yes—
42C2×#92418—22no—
43C23×C61—22no—
44C23×C61—41no—
45C23×C61—41no—
46C23×C61—41no—
47C23×C61—41no—
48C23×C61—41no—
49C23×C61—41no—
50C23×C61C2×D411yescharacteristic
51C22×D61—22no—
52D4×C61—24no—
53D4×C61—42no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61D812yescomplemented
63C2×C4×C61C2×D412yes—
64C22⋊D61—42no—
65C22⋊D61—42no—
66C2×Dic61—22no—
67D244—42no—
68D244—42no—
69D244—81no—
70C4×D61—44no—
71Dic122—42no—
72#92418—42no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—42no—
76C22×C61—42no—
77C22×C61—42no—
78C22×C61—81no—
79C22×C61—81no—
80C22×C61—81no—
81C22×C61—81no—
82C22×C61#12011yescharacteristic
83C22×C61C2×D811yescharacteristic
84C22×C61AGL(1,ℤ/8)11yescharacteristic
85C2×D61—42no—
86C2×D61—42no—
87C2×D61—42no—
88C4×C61—22no—
89C4×C61—22no—
90C4×C61—41no—
91C4×C61—81no—
92Dic61—42no—
93#1598—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—21no—
96C2×C61—82no—
97C2×C61#44711yescharacteristic
98C2×C61#45411yescharacteristic
99C2×C61B(4,𝔽2)11yescharacteristic
100D61—82no—
101#537—611no—
102#447—612no—
103#394D6111yescharacteristic, complemented
104#327—612no—
105#324—611no—
106C61#159811yescharacteristic, complemented, Sylow
107C2×#41—1221no—
108C22×D4C2×D6111yescharacteristic
109C2×D8—1222no—
110C22⋊Q8—1222no—
111#121—612no—
112#121—1222no—
113#121—1221no—
114C2×C4⋊C4C2×D6111yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—1222no—
118C22⋊C8—612no—
119#95C2×D6111yescharacteristic
120C24—21no—
121#41—2442no—
122#41—2442no—
123C2×Q8—1221no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—612no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4—1222no—
130C22×C4—21no—
131C22×C4—1222no—
132C22×C4C22⋊D6111yescharacteristic
133C22×C4C22⋊D6111yescharacteristic
134C22×C4C22×D6111yescharacteristic
135D8—2444no—
136C2×C8—1222no—
137C4⋊C4—22no—
138C4⋊C4—612no—
139C4⋊C4—1221no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—1222no—
152C23C2×C22⋊D6111yescharacteristic
153Q8—2442no—
154D4—24no—
155D4—42no—
156D4—4881no—
157D4—2442no—
158D4—2442no—
159D4—2442no—
160D4—2442no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—1222no—
170C2×C4—2444no—
171C2×C4#1175819912yescomplemented
172C2×C4D4×D6112yes—
173C8—2442no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—2442no—
184C22—2442no—
185C22—2442no—
186C22#1451974511yescharacteristic
187C22C2×#1175819911yescharacteristic
188C22#1451980211yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—2442no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—4882no—
198C2#1683989511yescharacteristic
199C2#1683993411yescharacteristic
200C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#394C2
socleC22×C61#120
hypercenter#394D61
hypocenterC61#1598
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #16840343C2semidirect
2. #16839896C2semidirect
3. #16839495C2semidirect
4. #16839488C2semidirect
5. C61×#394C2semidirect
62. C2×C4×C61D8semidirect
103. #394D61semidirect
106. C61#1598semidirect
171. C2×C4#11758199semidirect