Finite Group Databasebeta

← #22626048

Subgroups — #22626048

Order 9344.

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#17989598C212yesmaximal
2C2×#14556659C211yesmaximal, characteristic
3#17989550C211yesmaximal, characteristic
4#17989466C212yesmaximal
5#108×D73C211yesmaximal, characteristic
6D73⋊M16C2211yescharacteristic
7#14556670C2211yescharacteristic
8C2×C4⋊#64408C2212yes—
9#14556660—22no—
10#14556659—22no—
11#14556659—21no—
12#14556659—21no—
13#14556645—21no—
14C8×#64408—21no—
15M16×D73C2212yes—
16C2×C8×D73C2211yescharacteristic
17#14556527C411yescharacteristic, complemented
18#14556526C412yescomplemented
19#108×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924038—21no—
22#11924037Q812yes—
23#11924036—21no—
24C4⋊#64408—22no—
25C4⋊#64408—22no—
26C4⋊#64408D412yes—
27C22⋊#64408—21no—
28C4×#64408—21no—
29C2×C4×D73C2311yescharacteristic
30#11924012C2×C412yes—
31#11924011—22no—
32C2×#10596831C2×C411yescharacteristic
33C8×D73—22no—
34C8×D73D411yescharacteristic
35C8×D73D411yescharacteristic
36C8×D73Q811yescharacteristic
37C8×D73Q811yescharacteristic
38M16×C73C2×C412yes—
39C2×C8×C73C2×C411yescharacteristic
40C22×D73#4111yescharacteristic
41C2×#64408—22no—
42C2×#64408—42no—
43C2×#64408—82no—
44C2×C4×C73C22×C411yescharacteristic
45C2×Dic73C2×Q811yescharacteristic
46C4×D73C2×D411yescharacteristic
47C4×D73C2×D411yescharacteristic
48C4×D73C2×Q811yescharacteristic
49C4×D73#4111yescharacteristic
50#10596833—22no—
51C8×C73—22no—
52C8×C73C4⋊C411yescharacteristic
53C8×C73C4⋊C411yescharacteristic
54#10596831—22no—
55#10596831C4⋊C411yescharacteristic
56#10596831C4⋊C411yescharacteristic
57C22×C73C4×Q811yescharacteristic
58C2×D73—22no—
59C2×D73#12111yescharacteristic
60C2×D73#12511yescharacteristic
61#64408—42no—
62#64408—82no—
63C4×C73C2×C4⋊C411yescharacteristic
64C4×C73C4×D411yescharacteristic
65Dic73C22⋊Q811yescharacteristic
66Dic73C4⋊Q811yescharacteristic
67C2×C73—21no—
68C2×C73#38911yescharacteristic
69D73—21no—
70D73#47112yes—
71#1951—731nomaximal, Sylow
72C73#195111yescharacteristic, complemented, Sylow
73C2×#108—731no—
74#428—732no—
75C2×#106—731no—
76#405—731no—
77#343—732no—
78C2×M16—731no—
79C2×M16—732no—
80C22×C8—731no—
81#117—731no—
82C2×C4⋊C4—732no—
83#108—732no—
84#108—731no—
85#108#6440811yescharacteristic, complemented
86#107—1462no—
87#106—1462no—
88#106—1461no—
89#106—1461no—
90#97—1461no—
91C4×C8—1461no—
92C22×C4—731no—
93C22×C4—1462no—
94M16—732no—
95M16—732no—
96M16—1462no—
97M16—1461no—
98M16C2×#6440812yes—
99C2×C8—731no—
100C2×C8—731no—
101C2×C8—731no—
102C2×C8—731no—
103C2×C8—731no—
104C2×C8—1462no—
105C2×C8—1461no—
106C2×C8C2×#6440811yescharacteristic
107C4⋊C4—732no—
108C4⋊C4—1462no—
109C4⋊C4—1462no—
110C22⋊C4—1461no—
111C42—1461no—
112C23—731no—
113C2×C4—2922no—
114C2×C4—5842no—
115C2×C4—731no—
116C2×C4—731no—
117C2×C4—731no—
118C2×C4—731no—
119C2×C4—731no—
120C2×C4—1462no—
121C2×C4C22×#6440811yescharacteristic
122C8—22no—
123C8—731no—
124C8—731no—
125C8—1462no—
126C8—1462no—
127C8C4⋊#6440811yescharacteristic
128C8C4⋊#6440811yescharacteristic
129C22—731no—
130C22—731no—
131C22—1462no—
132C22Q8×#6440811yescharacteristic
133C4—2922no—
134C4—5842no—
135C4—731no—
136C4—731no—
137C4C2×C4⋊#6440811yescharacteristic
138C4D4×#6440811yescharacteristic
139C2—21no—
140C2—732no—
141C2—1461no—
142C2#1798953811yescharacteristic
subgroupG/H
centerC2#17989538
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#108×C73C4
socleC2×C73#389
hypercenter#108#64408
hypocenterC73#1951
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
17. #14556527C4semidirect
18. #14556526C4semidirect
19. #108×C73C4semidirect
72. C73#1951semidirect
85. #108#64408semidirect