Finite Group Databasebeta

← #21456355

Subgroups — #21456355

Order 7808.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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#16840393C212yesmaximal
2#16840170C214yesmaximal, complemented
3#16840166C212yesmaximal, complemented
4#16840163C212yesmaximal, complemented
5#16839802C212yesmaximal
6#16839800C211yesmaximal, characteristic
7#16839717C211yesmaximal, characteristic
8C2×#107×C61C211yesmaximal, characteristic
9C2×#11758194C2211yescharacteristic
10#14519776—22no—
11#14519776C2214yes—
12#14519768—22no—
13#14519768C2214yes—
14#14519756—24no—
15#14519736C2212yes—
16#14519736C2211yescharacteristic
17#14519711C2211yescharacteristic
18#14519711C2211yescharacteristic
19#14519710C2214yes—
20#14519709C2212yes—
21#14519708C2214yes—
22#14519687C2212yes—
23C8×Dic61C2212yes—
24C22×C8×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2212yes—
26#107×C61C2212yes—
27#107×C61C2212yes—
28C22×C4×C61—22no—
29C22×C4×C61C2311yescharacteristic
30C2×Dic122—24no—
31C2×C8×C61Q814yescomplemented
32C2×C8×C61C2311yescharacteristic
33C2×C8×C61C2311yescharacteristic
34C4⋊C4×C61—22no—
35C4⋊C4×C61C2314yes—
36C22⋊Dic61—22no—
37C22⋊Dic61D412yes—
38C4⋊Dic61—24no—
39C4⋊Dic61D411yescharacteristic
40C4⋊Dic61D411yescharacteristic
41C4⋊Dic61C2312yes—
42C4⋊Dic61C2312yes—
43#11758196—24no—
44#11758196—24no—
45C4×Dic61—22no—
46C4×Dic61C2312yes—
47#11758194Q814yescomplemented
48C2×#92418C2312yes—
49C23×C61C2×D411yescharacteristic
50C2×C4×C61—24no—
51C2×C4×C61—82no—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×Q812yes—
54C2×C4×C61C2×Q812yes—
55C2×C4×C61C2411yescharacteristic
56C2×Dic61—22no—
57C2×Dic61—22no—
58C2×Dic61C2×D412yes—
59C2×Dic61C2×D412yes—
60Dic122—84no—
61C8×C61C2×Q812yes—
62C8×C61C2×Q812yes—
63#92418C2×Q814yes—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61C4⋊Q812yes—
67C22×C61C22×D411yescharacteristic
68C4×C61—44no—
69C4×C61C4⋊Q812yes—
70C4×C61C22×Q811yescharacteristic
71C4×C61C22×Q811yescharacteristic
72Dic61—22no—
73Dic61—22no—
74Dic61—42no—
75Dic61—42no—
76#3164—611nomaximal, Sylow
77C2×C61—22no—
78C2×C61C2×C4⋊Q811yescharacteristic
79C2×C61#57611yescharacteristic
80C2×C61#57811yescharacteristic
81#544—612no—
82#501—614no—
83#500—612no—
84#499—612no—
85#428—612no—
86#427—611no—
87C2×#107D6111yescharacteristic
88#405—611no—
89C61#316411yescharacteristic, complemented, Sylow
90C2×M16—611no—
91C22×C8C2×D6111yescharacteristic
92C4⋊Q8—614no—
93C4⋊Q8—1222no—
94#125—614no—
95#125—1222no—
96C22⋊Q8—1224no—
97#117—611no—
98#117—612no—
99C2×C4⋊C4C2×D6112yes—
100#107—611no—
101#107—611no—
102#107—614no—
103#107C2×D6112yes—
104#107C2×D6112yes—
105#106—612no—
106#106—614no—
107#97—612no—
108C4×C8—612no—
109C2×Q8—1224no—
110C22×C4—22no—
111C22×C4C22×D6111yescharacteristic
112M16—614no—
113C2×C8—612no—
114C2×C8Dic12214yescomplemented
115C2×C8C22×D6111yescharacteristic
116C2×C8C22×D6111yescharacteristic
117C4⋊C4—22no—
118C4⋊C4—611no—
119C4⋊C4—611no—
120C4⋊C4—612no—
121C4⋊C4—612no—
122C4⋊C4—1224no—
123C4⋊C4—1224no—
124C4⋊C4—1224no—
125C4⋊C4C22×D6114yes—
126C22⋊C4—612no—
127C22⋊C4—1222no—
128C42—612no—
129C42—1222no—
130C23D4×D6111yescharacteristic
131Q8—4884no—
132C2×C4—24no—
133C2×C4—82no—
134C2×C4—612no—
135C2×C4—612no—
136C2×C4—1222no—
137C2×C4—1222no—
138C2×C4C2×Dic12212yes—
139C2×C4D4×D6111yescharacteristic
140C2×C4Q8×D6112yes—
141C2×C4C23×D6111yescharacteristic
142C8—614no—
143C8C2×Dic12212yes—
144C8C2×Dic12212yes—
145C22—21no—
146C22—21no—
147C22#1451977612yes—
148C22C2×D4×D6111yescharacteristic
149C4—44no—
150C4—1222no—
151C4—1222no—
152C4—2442no—
153C4—2442no—
154C4#1451977612yes—
155C4C2×Q8×D6111yescharacteristic
156C4C22×Dic12211yescharacteristic
157C2—22no—
158C2C2×#1451977611yescharacteristic
159C2#1684056311yescharacteristic
160C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#107×C61C2
socleC22×C61C22×D4
hypercenterC2×#107D61
hypocenterC61#3164
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #16840170C2semidirect
3. #16840166C2semidirect
4. #16840163C2semidirect
31. C2×C8×C61Q8semidirect
47. #11758194Q8semidirect
89. C61#3164semidirect
114. C2×C8Dic122semidirect