Finite Group Databasebeta

← #21447048

Subgroups — #21447048

Order 7808.

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

normal subgroups only

This group has 290 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×#382C211yesmaximal, 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×C61C2211yescharacteristic
15C2×C4⋊C4×C61C2211yescharacteristic
16C2×C42×C61C2211yescharacteristic
17#95×C61—22no—
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—
33C42×C61—21no—
34C42×C61D412yescomplemented
35#11758198—24no—
36C4⋊Dic61—22no—
37#11758194—22no—
38#11758194—22no—
39C2×#92418—22no—
40C23×C61C2×D411yescharacteristic
41C22×D61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61—42no—
47C2×C4×C61—42no—
48C2×C4×C61—41no—
49C2×C4×C61C2×D411yescharacteristic
50C2×C4×C61C2×D412yes—
51C2×C4×C61#4112yes—
52C2×C4×C61#4111yescharacteristic
53C22⋊D61—42no—
54C22⋊D61—42no—
55C2×Dic61—22no—
56D244—22no—
57D244—22no—
58D244—82no—
59C4×D61—42no—
60C4×D61—42no—
61Dic122—22no—
62Dic122—22no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#12011yescharacteristic
67C22×C61#12111yescharacteristic
68C22×C61#12411yescharacteristic
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—42no—
72C4×C61—42no—
73C4×C61—42no—
74C4×C61—81no—
75C4×C61#12112yes—
76C4×C61#12312yes—
77Dic61—42no—
78#2040—611nomaximal, Sylow
79C2×C61—21no—
80C2×C61—21no—
81C2×C61#39411yescharacteristic
82C2×C61#45411yescharacteristic
83C2×C61#45511yescharacteristic
84D61—82no—
85#537—611no—
86C2×#104—612no—
87#417—612no—
88#382D6111yescharacteristic, complemented
89#343—611no—
90C61#204011yescharacteristic, complemented, Sylow
91C2×#41—612no—
92C2×M16—612no—
93C22⋊Q8—1222no—
94#121—1222no—
95#121—1222no—
96C2×C4⋊C4C2×D6111yescharacteristic
97C2×C4⋊C4C2×D6111yescharacteristic
98C2×C42C2×D6111yescharacteristic
99#104—1224no—
100#103—1222no—
101#102—1222no—
102#95—22no—
103#41—1222no—
104#41—1222no—
105#41—1222no—
106#41—1222no—
107C2×Q8—612no—
108C2×D4—612no—
109C2×D4—1222no—
110C2×D4—1222no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—1222no—
114C22×C4C22⋊D6112yes—
115C22×C4C22×D6111yescharacteristic
116M16—1222no—
117M16—1222no—
118C2×C8—1222no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—1222no—
122C22⋊C4—1224no—
123C42—21no—
124C42D24412yescomplemented
125C23—1222no—
126C23C2×C22⋊D6111yescharacteristic
127Q8—1222no—
128Q8—1222no—
129D4—1222no—
130D4—1222no—
131D4—4882no—
132D4—2442no—
133D4—2442no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—1222no—
142C2×C4—2442no—
143C2×C4—2442no—
144C2×C4C2×D24411yescharacteristic
145C2×C4#1175822211yescharacteristic
146C2×C4D4×D6112yes—
147C2×C4#1175822612yes—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—2442no—
152C22—2442no—
153C22—2442no—
154C22#1451974511yescharacteristic
155C22#1451975111yescharacteristic
156C22#1451976611yescharacteristic
157C4—42no—
158C4—42no—
159C4—81no—
160C4—2442no—
161C4#1451975212yes—
162C4#1451976212yes—
163C2—21no—
164C2—21no—
165C2—4882no—
166C2#1683967911yescharacteristic
167C2#1683993411yescharacteristic
168C2#1683993911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#382C2
socleC22×C61#120
hypercenter#382D61
hypocenterC61#2040
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839761C2semidirect
4. #16839531C2semidirect
5. C61×#382C2semidirect
34. C42×C61D4semidirect
88. #382D61semidirect
90. C61#2040semidirect
124. C42D244semidirect