Finite Group Databasebeta

← #21447107

Subgroups — #21447107

Order 7808.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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#16840562C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic, complemented
3C2×#14519703C212yesmaximal, complemented
4#16839744C212yesmaximal, complemented
5C61×#338C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7#14519810—22no—
8#14519805—22no—
9#14519799—22no—
10C2×#11758194C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12#14519706—22no—
13#14519703—22no—
14#14519703—22no—
15#14519695—22no—
16#14519693—22no—
17C2×M16×C61C2212yes—
18C2×M16×C61C2211yescharacteristic
19C22×C4×C61C2311yescharacteristic
20C2×C22⋊D61—22no—
21C22×Dic61—21no—
22#11758222—22no—
23#11758222—22no—
24#11758222—22no—
25#11758222—22no—
26C2×D244D412yes—
27C2×C4×D61—22no—
28C2×Dic122D412yes—
29M16×C61—22no—
30M16×C61—22no—
31M16×C61—22no—
32C2×C8×C61—22no—
33C2×C8×C61D412yes—
34C4×Dic61—21no—
35C4×Dic61D411yescharacteristic
36C4×Dic61D411yescharacteristic
37#11758194—22no—
38C2×#92418—21no—
39Dic244—22no—
40D488—22no—
41#11758190—24no—
42C23×C61#4111yescharacteristic
43C22×D61—22no—
44C2×C4×C61C2×D412yes—
45C2×C4×C61C2×D411yescharacteristic
46C2×C4×C61C2×D411yescharacteristic
47C2×C4×C61#4112yes—
48C22⋊D61—42no—
49C22⋊D61—42no—
50C2×Dic61—21no—
51C2×Dic61—21no—
52C2×Dic61—22no—
53C2×Dic61—42no—
54D244—22no—
55D244—22no—
56C4×D61—42no—
57C4×D61—42no—
58Dic122—22no—
59Dic122—22no—
60C8×C61—22no—
61C8×C61—42no—
62#92418—41no—
63C22×C61—41no—
64C22×C61#12111yescharacteristic
65C22×C61#12312yes—
66C2×D61—42no—
67C2×D61—82no—
68C4×C61#12011yescharacteristic
69C4×C61#12112yes—
70C4×C61#12411yescharacteristic
71Dic61—22no—
72Dic61—41no—
73Dic61—42no—
74#2050—611nomaximal, Sylow
75C2×C61—21no—
76C2×C61—22no—
77C2×C61#39411yescharacteristic
78D61—82no—
79#575—611no—
80#423—611no—
81C2×#104—612no—
82#413—612no—
83#338D6111yescharacteristic, complemented
84C61#205011yescharacteristic, complemented, Sylow
85C2×#41—612no—
86#137—1222no—
87AGL(1,ℤ/8)—1222no—
88#135—1222no—
89C2×M16—611no—
90C2×M16C2×D6112yes—
91C2×M16C2×D6111yescharacteristic
92C2×C42—611no—
93C4⋊C8—1222no—
94#104—1222no—
95#104—1222no—
96#101—1222no—
97#100—1222no—
98#41—1222no—
99#41—1222no—
100#41—1222no—
101#41—1222no—
102C2×Q8—612no—
103C2×D4—612no—
104C2×D4—1222no—
105C22×C4—1221no—
106C22×C4—1222no—
107C22×C4C22×D6111yescharacteristic
108Q16—1222no—
109SD16—1224no—
110D8—1222no—
111M16—22no—
112M16—22no—
113M16—22no—
114M16—1222no—
115C2×C8—22no—
116C2×C8—1221no—
117C2×C8D24412yes—
118C42—611no—
119C42—611no—
120C42—1221no—
121C23—1222no—
122C23#1175822611yescharacteristic
123Q8—1222no—
124Q8—1222no—
125D4—1222no—
126D4—1222no—
127D4—2442no—
128D4—2442no—
129C2×C4—1221no—
130C2×C4—1221no—
131C2×C4—1222no—
132C2×C4—2442no—
133C2×C4—2442no—
134C2×C4—2442no—
135C2×C4C2×D24411yescharacteristic
136C2×C4#1175822212yes—
137C2×C4D4×D6112yes—
138C2×C4D4×D6111yescharacteristic
139C8—22no—
140C8—42no—
141C8—2441no—
142C22—41no—
143C22—4882no—
144C22—2442no—
145C22#1451975211yescharacteristic
146C22#1451976212yes—
147C4—1222no—
148C4—2441no—
149C4—2442no—
150C4#1451974711yescharacteristic
151C4#1451975012yes—
152C4#1451976511yescharacteristic
153C2—21no—
154C2—22no—
155C2—4882no—
156C2#1683968011yescharacteristic
subgroupG/H
centerC4#14519765
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#338C2
socleC2×C61#394
hypercenter#338D61
hypocenterC61#2050
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
2. #16839785C2semidirect
3. C2×#14519703C2semidirect
4. #16839744C2semidirect
5. C61×#338C2semidirect
83. #338D61semidirect
84. C61#2050semidirect