Finite Group Databasebeta

← #21447103

Subgroups — #21447103

Order 7808.

266 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 67 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#16839785C211yesmaximal, characteristic, complemented
2C2×#14519704C212yesmaximal, complemented
3#16839746C212yesmaximal, complemented
4#16839520C211yesmaximal, characteristic, complemented
5C61×#575C211yesmaximal, characteristic
6C2×#11758194C2211yescharacteristic
7C2×#11758194C2212yes—
8C2×C4×Dic61C2211yescharacteristic
9#14519706—22no—
10#14519704—22no—
11#14519704—22no—
12#14519696—22no—
13#14519694—22no—
14C2×#41×C61C2212yes—
15#137×C61—22no—
16AGL(1,ℤ/8)×C61—22no—
17#135×C61—22no—
18C2×M16×C61C2211yescharacteristic
19#41×C61—22no—
20#41×C61—22no—
21#41×C61—22no—
22#41×C61—22no—
23C2×Q8×C61D412yes—
24C2×D4×C61—22no—
25C2×D4×C61D412yes—
26C22×C4×C61—22no—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29Q16×C61—22no—
30SD16×C61—24no—
31D8×C61—22no—
32M16×C61—22no—
33C2×C8×C61D412yes—
34C4×Dic61—21no—
35C4×Dic61D411yescharacteristic
36C4×Dic61D411yescharacteristic
37#11758194—22no—
38#11758194—22no—
39#11758194—22no—
40C2×#92418—21no—
41C2×#92418—22no—
42C23×C61—22no—
43C23×C61#4111yescharacteristic
44Q8×C61—22no—
45Q8×C61—22no—
46D4×C61—22no—
47D4×C61—22no—
48D4×C61—42no—
49D4×C61—42no—
50C2×C4×C61—22no—
51C2×C4×C61—42no—
52C2×C4×C61—42no—
53C2×C4×C61C2×D412yes—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61#4112yes—
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—42no—
60C8×C61—22no—
61#92418—41no—
62#92418—42no—
63C22×C61—41no—
64C22×C61—42no—
65C22×C61—82no—
66C22×C61#12111yescharacteristic
67C22×C61#12312yes—
68C4×C61—42no—
69C4×C61#12011yescharacteristic
70C4×C61#12112yes—
71C4×C61#12411yescharacteristic
72Dic61—22no—
73Dic61—41no—
74#2050—611nomaximal, Sylow
75C2×C61—21no—
76C2×C61—22no—
77C2×C61—82no—
78C2×C61#39411yescharacteristic
79#575D6111yescharacteristic
80#423—611no—
81C2×#104—612no—
82#413—612no—
83#338—611no—
84C61#205011yescharacteristic, complemented, Sylow
85C2×#41C2×D6112yes—
86#137—22no—
87AGL(1,ℤ/8)—22no—
88#135—22no—
89C2×M16—612no—
90C2×M16—611no—
91C2×M16C2×D6111yescharacteristic
92C2×C42—611no—
93C4⋊C8—1222no—
94#104—1222no—
95#104—1222no—
96#101—1222no—
97#100—1222no—
98#41—22no—
99#41—22no—
100#41—22no—
101#41—22no—
102C2×Q8C22⋊D6112yes—
103C2×D4—22no—
104C2×D4C22⋊D6112yes—
105C22×C4—22no—
106C22×C4—1221no—
107C22×C4C22×D6111yescharacteristic
108Q16—22no—
109SD16—24no—
110D8—22no—
111M16—22no—
112M16—1222no—
113M16—1222no—
114M16—1222no—
115C2×C8—1222no—
116C2×C8—1221no—
117C2×C8C22⋊D6112yes—
118C42—611no—
119C42—611no—
120C42—1221no—
121C23—22no—
122C23#1175822411yescharacteristic
123Q8—22no—
124Q8—22no—
125D4—22no—
126D4—22no—
127D4—42no—
128D4—42no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—1221no—
133C2×C4—1221no—
134C2×C4—2442no—
135C2×C4D4×D6111yescharacteristic
136C2×C4#1175822412yes—
137C2×C4C2×C22⋊D6112yes—
138C2×C4C2×C22⋊D6111yescharacteristic
139C8—22no—
140C8—2441no—
141C8—2442no—
142C22—41no—
143C22—42no—
144C22—82no—
145C22#1451974811yescharacteristic
146C22#1451975812yes—
147C4—42no—
148C4—1222no—
149C4—2441no—
150C4#1451974611yescharacteristic
151C4#1451974912yes—
152C4#1451976411yescharacteristic
153C2—21no—
154C2—22no—
155C2—82no—
156C2#1683967611yescharacteristic
subgroupG/H
centerC4#14519764
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#575C2
socleC2×C61#394
hypercenter#575D61
hypocenterC61#2050
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #16839785C2semidirect
2. C2×#14519704C2semidirect
3. #16839746C2semidirect
4. #16839520C2semidirect
84. C61#2050semidirect