Finite Group Databasebeta

← #21447043

Subgroups — #21447043

Order 7808.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×#14519705C212yesmaximal, complemented
3#16839761C212yesmaximal, complemented
4#16839531C211yesmaximal, characteristic, complemented
5C61×#384C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7C2×#11758194C2212yes—
8#14519757—22no—
9#14519752—22no—
10#14519751—22no—
11#14519705—24no—
12#14519700—22no—
13#14519697—22no—
14C2×C4⋊C4×C61—22no—
15C2×C4⋊C4×C61C2211yescharacteristic
16C2×C4⋊C4×C61C2211yescharacteristic
17C2×C42×C61C2211yescharacteristic
18C22×C4×C61—21no—
19C22×C4×C61—21no—
20C22×C4×C61D412yes—
21C22×C4×C61C2311yescharacteristic
22C2×C22⋊D61—22no—
23#11758222—22no—
24#11758222—22no—
25#11758222—22no—
26#11758222—22no—
27C2×D244—22no—
28C2×D244D412yes—
29C2×C4×D61—22no—
30C2×Dic122D412yes—
31C4⋊C4×C61—22no—
32C4⋊C4×C61—22no—
33C4⋊C4×C61—44no—
34C42×C61—21no—
35C42×C61D412yescomplemented
36#11758198—24no—
37C4⋊Dic61—22no—
38#11758194—22no—
39#11758194—22no—
40C2×#92418—22no—
41C23×C61C2×D411yescharacteristic
42C22×D61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—22no—
46C2×C4×C61—22no—
47C2×C4×C61—42no—
48C2×C4×C61—42no—
49C2×C4×C61—41no—
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D412yes—
52C2×C4×C61#4112yes—
53C2×C4×C61#4111yescharacteristic
54C22⋊D61—42no—
55C22⋊D61—42no—
56C2×Dic61—22no—
57D244—22no—
58D244—22no—
59D244—82no—
60C4×D61—42no—
61C4×D61—42no—
62Dic122—22no—
63Dic122—22no—
64#92418—42no—
65C22×C61—21no—
66C22×C61—21no—
67C22×C61#12011yescharacteristic
68C22×C61#12111yescharacteristic
69C22×C61#12411yescharacteristic
70C2×D61—42no—
71C2×D61—42no—
72C2×D61—42no—
73C4×C61—24no—
74C4×C61—42no—
75C4×C61—81no—
76C4×C61#12112yes—
77C4×C61#12312yes—
78Dic61—42no—
79#2039—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61#39411yescharacteristic
83C2×C61#45311yescharacteristic
84C2×C61#45611yescharacteristic
85D61—82no—
86#537—611no—
87C2×#104—612no—
88#417—612no—
89#384D6111yescharacteristic, complemented
90#343—611no—
91C61#203911yescharacteristic, complemented, Sylow
92C2×#41—612no—
93C2×M16—612no—
94C22⋊Q8—1222no—
95#121—1222no—
96#121—1222no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4C2×D6111yescharacteristic
99C2×C4⋊C4C2×D6111yescharacteristic
100C2×C42C2×D6111yescharacteristic
101#104—1224no—
102#103—1222no—
103#102—1222no—
104#41—1222no—
105#41—1222no—
106#41—1222no—
107#41—1222no—
108C2×Q8—612no—
109C2×D4—612no—
110C2×D4—1222no—
111C2×D4—1222no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—1222no—
115C22×C4C22⋊D6112yes—
116C22×C4C22×D6111yescharacteristic
117M16—1222no—
118M16—1222no—
119C2×C8—1222no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—44no—
123C4⋊C4—1222no—
124C22⋊C4—1224no—
125C42—21no—
126C42D24412yescomplemented
127C23—1222no—
128C23C2×C22⋊D6111yescharacteristic
129Q8—1222no—
130Q8—1222no—
131D4—1222no—
132D4—1222no—
133D4—4882no—
134D4—2442no—
135D4—2442no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—1222no—
144C2×C4—2442no—
145C2×C4—2442no—
146C2×C4C2×D24411yescharacteristic
147C2×C4#1175822211yescharacteristic
148C2×C4D4×D6112yes—
149C2×C4#1175822612yes—
150C8—2442no—
151C22—21no—
152C22—21no—
153C22—2442no—
154C22—2442no—
155C22—2442no—
156C22#1451974511yescharacteristic
157C22#1451975111yescharacteristic
158C22#1451976611yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—2442no—
163C4#1451975212yes—
164C4#1451976212yes—
165C2—21no—
166C2—21no—
167C2—4882no—
168C2#1683967911yescharacteristic
169C2#1683992911yescharacteristic
170C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#384C2
socleC22×C61#120
hypercenter#384D61
hypocenterC61#2039
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839761C2semidirect
4. #16839531C2semidirect
5. C61×#384C2semidirect
35. C42×C61D4semidirect
89. #384D61semidirect
91. C61#2039semidirect
126. C42D244semidirect