Finite Group Databasebeta

← #21447759

Subgroups — #21447759

Order 7808.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14519723C211yesmaximal, characteristic, complemented
2C2×#14519721C211yesmaximal, characteristic, complemented
3#16840003C211yesmaximal, characteristic, complemented
4#16839566C211yesmaximal, characteristic, complemented
5#16839563C211yesmaximal, characteristic, complemented
6C22⋊#11758185C211yesmaximal, characteristic, complemented
7C2×#135×C61C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9#14519756—21no—
10#14519723—22no—
11#14519721—22no—
12C2×#11758185C2211yescharacteristic
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519702—21no—
16C2×#41×C61—21no—
17#135×C61—22no—
18#135×C61—22no—
19C2×Q16×C61C2211yescharacteristic
20C2×SD16×C61—21no—
21C2×D8×C61C2211yescharacteristic
22C22×C8×C61C2211yescharacteristic
23#41×C61—24no—
24#41×C61—42no—
25C2×Q8×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—41no—
28C22×C4×C61—41no—
29C22×C4×C61D411yescharacteristic
30C2×Dic122—21no—
31Q16×C61—21no—
32Q16×C61D412yes—
33SD16×C61—24no—
34D8×C61—21no—
35D8×C61D412yes—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61D411yescharacteristic
39C2×C8×C61C2311yescharacteristic
40C22⋊Dic61—41no—
41C4⋊Dic61—21no—
42#11758196—41no—
43Dic244—21no—
44Dic244—21no—
45#11758185—21no—
46#11758185—21no—
47C23×C61—41no—
48C23×C61D811yescharacteristic
49Q8×C61—22no—
50Q8×C61—41no—
51D4×C61—22no—
52D4×C61—44no—
53D4×C61—41no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—44no—
57C2×C4×C61—41no—
58C2×C4×C61D811yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×Dic61—41no—
61C2×Dic61—41no—
62Dic122—41no—
63Dic122—41no—
64C8×C61—21no—
65C8×C61C2×D411yescharacteristic
66C8×C61C2×D411yescharacteristic
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—42no—
71C22×C61—81no—
72C22×C61—81no—
73C22×C61C2×D811yescharacteristic
74C4×C61—21no—
75C4×C61—42no—
76C4×C61#12011yescharacteristic
77C4×C61AGL(1,ℤ/8)11yescharacteristic
78Dic61—81no—
79Dic61—81no—
80#2189—611nomaximal, Sylow
81C2×C61—41no—
82C2×C61—82no—
83C2×C61#44711yescharacteristic
84C2×C61#50811yescharacteristic
85C2×C61#51011yescharacteristic
86C2×#135D6111yescharacteristic
87C2×Q32—611no—
88C2×SD32—611no—
89#467—611no—
90#358—611no—
91#357—611no—
92C22⋊C16—611no—
93C61#218911yescharacteristic, complemented, Sylow
94C2×#41—21no—
95#135—22no—
96#135—22no—
97C2×Q16—611no—
98C2×Q16C2×D6111yescharacteristic
99C2×SD16—21no—
100C2×D8C2×D6111yescharacteristic
101C22×C8C2×D6111yescharacteristic
102C22⋊Q8—1221no—
103Q32—1222no—
104SD32—1222no—
105C2×C16—611no—
106C2×C16—611no—
107#107—611no—
108#103—1221no—
109#41—24no—
110#41—42no—
111C2×Q8—21no—
112C2×Q8—1221no—
113C2×D4—21no—
114C2×D4—41no—
115C22×C4—41no—
116C22×C4C22⋊D6111yescharacteristic
117Q16—21no—
118Q16—1221no—
119Q16—1221no—
120Q16C22⋊D6112yes—
121SD16—24no—
122D8—21no—
123D8C22⋊D6112yes—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8C22⋊D6111yescharacteristic
127C2×C8C22×D6111yescharacteristic
128C4⋊C4—1221no—
129C4⋊C4—2441no—
130C22⋊C4—2441no—
131C16—1221no—
132C16—1221no—
133C23—41no—
134C23#1175819911yescharacteristic
135Q8—22no—
136Q8—41no—
137Q8—2441no—
138Q8—2441no—
139D4—22no—
140D4—44no—
141D4—41no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—44no—
145C2×C4—41no—
146C2×C4—2441no—
147C2×C4—2441no—
148C2×C4#1175819911yescharacteristic
149C2×C4C2×C22⋊D6111yescharacteristic
150C8—21no—
151C8C2×C22⋊D6111yescharacteristic
152C8C2×C22⋊D6111yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—42no—
157C22—81no—
158C22—81no—
159C22C2×#1175819911yescharacteristic
160C4—21no—
161C4—42no—
162C4—4881no—
163C4—4881no—
164C4#1451974611yescharacteristic
165C4#1451980311yescharacteristic
166C2—41no—
167C2—82no—
168C2#1683989611yescharacteristic
169C2#1684019211yescharacteristic
170C2#1684020211yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×#135×C61C2
socleC22×C61C2×D8
hypercenterC2×#135D61
hypocenterC61#2189
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14519723C2semidirect
2. C2×#14519721C2semidirect
3. #16840003C2semidirect
4. #16839566C2semidirect
5. #16839563C2semidirect
6. C22⋊#11758185C2semidirect
93. C61#2189semidirect