Finite Group Databasebeta

← #21461937

Subgroups — #21461937

Order 7808.

196 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840773C212yesmaximal
2C2×#14519846C211yesmaximal, characteristic
3#16840725C211yesmaximal, characteristic
4#16840641C212yesmaximal
5#108×D61C211yesmaximal, characteristic
6D61⋊M16C2211yescharacteristic
7#14519856C2211yescharacteristic
8C2×C4⋊#6923C2212yes—
9#14519846—22no—
10#14519846—21no—
11#14519846—21no—
12#14519845—22no—
13#14519831—21no—
14C8×#6923—21no—
15M16×D61C2212yes—
16C2×C8×D61C2211yescharacteristic
17#14519713C411yescharacteristic, complemented
18#14519712C412yescomplemented
19#108×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×C4×D61C2311yescharacteristic
22C22⋊#6923—21no—
23#11758217Q812yes—
24C4⋊#6923—22no—
25C4⋊#6923—22no—
26C4⋊#6923D411yescharacteristic
27C4⋊#6923D411yescharacteristic
28C4×#6923—21no—
29#11758213—21no—
30D61⋊C8—21no—
31M16×C61C2×C412yes—
32C2×C8×C61C2×C411yescharacteristic
33#11758194C2×C412yes—
34C2×#92418C2×C411yescharacteristic
35#11758189—22no—
36C8×D61—22no—
37C8×D61D411yescharacteristic
38C8×D61D411yescharacteristic
39C8×D61Q811yescharacteristic
40C8×D61Q811yescharacteristic
41C22×D61#4111yescharacteristic
42C2×#6923—21no—
43C2×#6923—21no—
44C2×#6923—42no—
45C2×#6923—82no—
46C2×C4×C61C22×C411yescharacteristic
47C2×Dic61C2×Q811yescharacteristic
48C4×D61C2×D411yescharacteristic
49C4×D61C2×D411yescharacteristic
50C4×D61C2×Q811yescharacteristic
51C4×D61#4111yescharacteristic
52#92420—22no—
53C8×C61—22no—
54C8×C61C4⋊C411yescharacteristic
55C8×C61C4⋊C411yescharacteristic
56#92418—22no—
57#92418C4⋊C411yescharacteristic
58#92418C4⋊C411yescharacteristic
59C22×C61C4×Q811yescharacteristic
60C2×D61—21no—
61C2×D61—21no—
62C2×D61#12111yescharacteristic
63C2×D61#12511yescharacteristic
64#6923—41no—
65#6923—41no—
66#6923—82no—
67C4×C61C2×C4⋊C411yescharacteristic
68C4×C61C4×D411yescharacteristic
69Dic61C22⋊Q811yescharacteristic
70Dic61C4⋊Q811yescharacteristic
71#1952—611nomaximal, Sylow
72C2×C61—21no—
73C2×C61#38911yescharacteristic
74D61—21no—
75D61#47211yescharacteristic
76D61#47311yescharacteristic
77C2×#108—611no—
78#428—612no—
79C2×#107—611no—
80#405—611no—
81#343—612no—
82C61#195211yescharacteristic, complemented, Sylow
83C2×M16—611no—
84C2×M16—612no—
85C22×C8—611no—
86#117—611no—
87C2×C4⋊C4—612no—
88#108—612no—
89#108—611no—
90#108#692311yescharacteristic, complemented
91#107—1222no—
92#107—1221no—
93#107—1221no—
94#106—1222no—
95#97—1221no—
96C4×C8—1221no—
97C22×C4—611no—
98C22×C4—1222no—
99M16—612no—
100M16—612no—
101M16—1222no—
102M16—1221no—
103M16C2×#692312yes—
104C2×C8—611no—
105C2×C8—611no—
106C2×C8—611no—
107C2×C8—611no—
108C2×C8—611no—
109C2×C8—1222no—
110C2×C8—1221no—
111C2×C8C2×#692311yescharacteristic
112C4⋊C4—611no—
113C4⋊C4—611no—
114C4⋊C4—1222no—
115C4⋊C4—1222no—
116C22⋊C4—1221no—
117C42—1221no—
118C23—611no—
119C2×C4—611no—
120C2×C4—611no—
121C2×C4—611no—
122C2×C4—611no—
123C2×C4—611no—
124C2×C4—1221no—
125C2×C4—1221no—
126C2×C4—4882no—
127C2×C4—2442no—
128C2×C4C22×#692311yescharacteristic
129C8—22no—
130C8—611no—
131C8—611no—
132C8—1222no—
133C8—1222no—
134C8C4⋊#692311yescharacteristic
135C8C4⋊#692311yescharacteristic
136C22—611no—
137C22—611no—
138C22—1221no—
139C22—1221no—
140C22Q8×#692311yescharacteristic
141C4—611no—
142C4—611no—
143C4—4882no—
144C4—2441no—
145C4—2441no—
146C4C2×C4⋊#692311yescharacteristic
147C4D4×#692311yescharacteristic
148C2—21no—
149C2—611no—
150C2—611no—
151C2—1221no—
152C2#1684071311yescharacteristic
subgroupG/H
centerC2#16840713
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#108×C61C4
socleC2×C61#389
hypercenter#108#6923
hypocenterC61#1952
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
17. #14519713C4semidirect
18. #14519712C4semidirect
19. #108×C61C4semidirect
82. C61#1952semidirect
90. #108#6923semidirect