Finite Group Databasebeta

← #21447223

Subgroups — #21447223

Order 7808.

274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519697C212yesmaximal
2#16839664C211yesmaximal, characteristic
3#16839524C212yesmaximal, complemented
4#16839517C211yesmaximal, characteristic, complemented
5C61×#384C211yesmaximal, characteristic, complemented
6C22×D244C2211yescharacteristic
7C22×#92418C2212yes—
8C2×C4⋊Dic61C2211yescharacteristic
9C2×#11758198—21no—
10C2×#11758198—21no—
11#14519697—24no—
12C2×C4⋊C4×C61—21no—
13C2×C4⋊C4×C61—21no—
14C2×C4⋊C4×C61C2212yes—
15C2×C42×C61C2211yescharacteristic
16C23×D61—21no—
17C22×C4×C61—22no—
18C22×C4×C61D411yescharacteristic
19C22×C4×C61D411yescharacteristic
20C22×C4×C61C2311yescharacteristic
21C22×Dic61—21no—
22C2×D244—22no—
23C2×D244—22no—
24C2×D244—21no—
25C2×D244D412yes—
26C4⋊C4×C61—22no—
27C4⋊C4×C61—22no—
28C4⋊C4×C61—42no—
29C4⋊C4×C61—42no—
30C42×C61—22no—
31#11758198—42no—
32#11758198—42no—
33C4⋊Dic61—22no—
34C2×#92418—22no—
35C2×#92418—22no—
36C2×#92418—22no—
37C23×C61C2×D411yescharacteristic
38C22×D61—22no—
39C22×D61—41no—
40C22×D61—41no—
41C22×D61—41no—
42C22×D61—41no—
43C22×D61—41no—
44C22×D61—41no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—42no—
50C2×C4×C61—42no—
51C2×C4×C61—42no—
52C2×C4×C61D812yes—
53C2×C4×C61SD1612yes—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61#4112yes—
56C2×C4×C61#4112yes—
57C2×C4×C61#4111yescharacteristic
58C2×Dic61—41no—
59C2×Dic61—41no—
60C2×Dic61—41no—
61D244—24no—
62D244—42no—
63#92418—42no—
64C22×C61#12111yescharacteristic
65C22×C61#12311yescharacteristic
66C22×C61#12411yescharacteristic
67C22×C61C2×D811yescharacteristic
68C22×C61C2×SD1611yescharacteristic
69C22×C61AGL(1,ℤ/8)11yescharacteristic
70C22×C61#13711yescharacteristic
71C2×D61—42no—
72C2×D61—42no—
73C2×D61—42no—
74C2×D61—81no—
75C2×D61—81no—
76C2×D61—81no—
77C2×D61—81no—
78C4×C61—22no—
79C4×C61—22no—
80C4×C61—82no—
81C4×C61#12312yes—
82C4×C61#12612yes—
83Dic61—81no—
84#2071—611nomaximal, Sylow
85C2×C61#39711yescharacteristic
86C2×C61#45911yescharacteristic
87C2×C61#46111yescharacteristic
88C2×C61#48011yescharacteristic
89C2×C61#48111yescharacteristic
90C2×C61#48611yescharacteristic
91C2×C61#48911yescharacteristic
92D61—82no—
93C2×#102—612no—
94#390—611no—
95#384D6111yescharacteristic, complemented
96#340—612no—
97#336—611no—
98C61#207111yescharacteristic, complemented, Sylow
99C22×D4—611no—
100C22×C8—612no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4C2×D6112yes—
105C2×C22⋊C4—1221no—
106C2×C22⋊C4—1221no—
107C2×C42C2×D6111yescharacteristic
108#102—1224no—
109C24—1221no—
110C2×D4—612no—
111C2×D4—1222no—
112C2×D4—1221no—
113C2×D4—1222no—
114C22×C4—22no—
115C22×C4—1221no—
116C22×C4C22⋊D6111yescharacteristic
117C22×C4C22⋊D6111yescharacteristic
118C22×C4C22×D6111yescharacteristic
119C2×C8—1222no—
120C2×C8—1222no—
121C2×C8—1222no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—1222no—
127C22⋊C4—2442no—
128C22⋊C4—2442no—
129C42—22no—
130C23—1222no—
131C23—2441no—
132C23—2441no—
133C23—2441no—
134C23—2441no—
135C23—2441no—
136C23—2441no—
137C23C2×C22⋊D6111yescharacteristic
138D4—1224no—
139D4—2442no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4—2441no—
150C2×C4#1175819912yes—
151C2×C4#1175820112yes—
152C2×C4#1175822212yes—
153C2×C4D4×D6111yescharacteristic
154C2×C4#1175822411yescharacteristic
155C2×C4#1175822612yes—
156C8—2442no—
157C22—4881no—
158C22—4881no—
159C22—4881no—
160C22—4881no—
161C22—2442no—
162C22—2442no—
163C22—2442no—
164C22#1451974811yescharacteristic
165C22#1451976011yescharacteristic
166C22#1451976611yescharacteristic
167C22C2×#1175819911yescharacteristic
168C22C2×#1175820111yescharacteristic
169C22#1451980311yescharacteristic
170C22#1451980811yescharacteristic
171C4—22no—
172C4—22no—
173C4—82no—
174C4—4881no—
175C4#1451976212yes—
176C4#1451977212yes—
177C2—4882no—
178C2#1683968811yescharacteristic
179C2#1683995411yescharacteristic
180C2#1683996411yescharacteristic
181C2#1684007511yescharacteristic
182C2#1684008011yescharacteristic
183C2#1684011011yescharacteristic
184C2#1684012411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#384C2
socleC23×C61C2×D4
hypercenter#384D61
hypocenterC61#2071
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #16839524C2semidirect
4. #16839517C2semidirect
5. C61×#384C2semidirect
95. #384D61semidirect
98. C61#2071semidirect