Finite Group Databasebeta

← #22626037

Subgroups — #22626037

Order 9344.

240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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×#14556660C211yesmaximal, characteristic
2C2×#14556645C211yesmaximal, characteristic
3#17989538C212yesmaximal
4#17989460C212yesmaximal
5#106×D73C211yesmaximal, characteristic
6C2×#11924036C2211yescharacteristic
7C2×C4⋊#64408—22no—
8C2×C4⋊#64408C2212yes—
9C2×C4×#64408C2211yescharacteristic
10#14556660—22no—
11#14556645—22no—
12(C2×#64408)⋊C4—22no—
13C2×C8×D73C2211yescharacteristic
14C4⋊C4×D73C2212yes—
15#14556523C411yescharacteristic, complemented
16#14556522C412yescomplemented
17#106×C73C411yescharacteristic, complemented
18C22×#64408—22no—
19C22×#64408D411yescharacteristic
20C22×#64408D411yescharacteristic
21#11924036—21no—
22#11924036Q812yes—
23C2×#10596833—21no—
24C4⋊#64408—22no—
25C4⋊#64408—22no—
26C4⋊#64408—44no—
27C4×#64408—21no—
28C4×#64408—21no—
29C2×C4×D73—22no—
30C2×C4×D73C2311yescharacteristic
31C2×#10596831C2×C411yescharacteristic
32C8×D73D412yes—
33C8×D73Q812yes—
34C4⋊Dic73C2×C412yes—
35#11924007—22no—
36C2×C8×C73C2×C411yescharacteristic
37C4⋊C4×C73C2×C412yes—
38C22×D73C2×D411yescharacteristic
39C2×#64408—21no—
40C2×#64408—21no—
41C2×#64408—22no—
42C2×#64408—22no—
43C2×#64408—42no—
44C2×#64408—42no—
45C2×#64408—42no—
46C2×C4×C73—22no—
47C2×C4×C73C22×C411yescharacteristic
48C2×Dic73—22no—
49C2×Dic73#4111yescharacteristic
50C4×D73—42no—
51C4×D73—42no—
52C4×D73C2×D411yescharacteristic
53C4×D73C2×Q811yescharacteristic
54C4×D73C2×Q811yescharacteristic
55C4×D73#4111yescharacteristic
56#10596833—22no—
57C8×C73C4⋊C412yescomplemented
58#10596831C4⋊C412yescomplemented
59C22×C73C4×D411yescharacteristic
60C2×D73#12111yescharacteristic
61C2×D73C4⋊Q811yescharacteristic
62C2×D73AGL(1,ℤ/8)12yes—
63C2×D73#13712yes—
64#64408—41no—
65#64408—41no—
66#64408—82no—
67C4×C73—42no—
68C4×C73C2×C4⋊C411yescharacteristic
69C4×C73C4×Q811yescharacteristic
70Dic73—42no—
71Dic73C22⋊Q811yescharacteristic
72Dic73#12511yescharacteristic
73C2×C73#38911yescharacteristic
74C2×C73#44012yes—
75D73#46911yescharacteristic
76D73#47011yescharacteristic
77D73#50112yes—
78#1944—731nomaximal, Sylow
79C73#194411yescharacteristic, complemented, Sylow
80C2×#107—731no—
81C2×#106—731no—
82C2×#97—731no—
83#389—732no—
84#340—732no—
85C22×C8—731no—
86C22×C8—731no—
87C2×C4⋊C4—732no—
88C2×C4⋊C4—732no—
89C2×C4⋊C4—1462no—
90C2×C42—731no—
91#107—1462no—
92#106—731no—
93#106—732no—
94#106#6440811yescharacteristic, complemented
95#97—1462no—
96#95—1462no—
97C22×C4—731no—
98C22×C4—731no—
99C22×C4—731no—
100C22×C4—1462no—
101C22×C4—1462no—
102C2×C8—731no—
103C2×C8—732no—
104C2×C8—732no—
105C2×C8—732no—
106C2×C8—1461no—
107C2×C8—1461no—
108C2×C8C2×#6440811yescharacteristic
109C4⋊C4—2924no—
110C4⋊C4—732no—
111C4⋊C4—1462no—
112C4⋊C4—1462no—
113C4⋊C4—1462no—
114C4⋊C4C2×#6440812yes—
115C42—1461no—
116C42—1461no—
117C23—731no—
118C2×C4—22no—
119C2×C4—2922no—
120C2×C4—2922no—
121C2×C4—2922no—
122C2×C4—2922no—
123C2×C4—2922no—
124C2×C4—731no—
125C2×C4—731no—
126C2×C4—731no—
127C2×C4—731no—
128C2×C4—731no—
129C2×C4—1461no—
130C2×C4—1461no—
131C2×C4—1462no—
132C2×C4—1462no—
133C2×C4—1462no—
134C2×C4C22×#6440811yescharacteristic
135C8—732no—
136C8—1462no—
137C8C4⋊#6440812yescomplemented
138C22—731no—
139C22—731no—
140C22—732no—
141C22—732no—
142C22D4×#6440811yescharacteristic
143C4—42no—
144C4—2921no—
145C4—2921no—
146C4—2922no—
147C4—5842no—
148C4—731no—
149C4—731no—
150C4C2×C4⋊#6440811yescharacteristic
151C4Q8×#6440811yescharacteristic
152C2—731no—
153C2—731no—
154C2—732no—
155C2#1798953811yescharacteristic
156C2#1798962612yes—
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#106×C73C4
socleC22×C73C4×D4
hypercenter#106#64408
hypocenterC73#1944
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
15. #14556523C4semidirect
16. #14556522C4semidirect
17. #106×C73C4semidirect
57. C8×C73C4⋊C4semidirect
58. #10596831C4⋊C4semidirect
79. C73#1944semidirect
94. #106#64408semidirect
137. C8C4⋊#64408semidirect