Finite Group Databasebeta

← #22626036

Subgroups — #22626036

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×#14556659C211yesmaximal, characteristic
2C2×#14556645C211yesmaximal, characteristic
3#17989538C212yesmaximal
4#17989460C212yesmaximal
5#107×D73C211yesmaximal, characteristic
6C2×#11924036C2211yescharacteristic
7C2×C4⋊#64408—22no—
8C2×C4⋊#64408C2212yes—
9C2×C4×#64408C2211yescharacteristic
10#14556659—22no—
11#14556645—22no—
12(C2×#64408)⋊C4—22no—
13C2×C8×D73C2211yescharacteristic
14C4⋊C4×D73C2212yes—
15#14556525C411yescharacteristic, complemented
16#14556524C412yescomplemented
17#107×C73C411yescharacteristic, complemented
18C22×#64408—22no—
19C22×#64408D412yes—
20#11924036—21no—
21#11924036Q812yes—
22C2×#10596833—21no—
23C4⋊#64408—22no—
24C4⋊#64408—22no—
25C4⋊#64408—44no—
26C4×#64408—21no—
27C4×#64408—21no—
28C2×C4×D73—22no—
29C2×C4×D73C2311yescharacteristic
30C2×#10596831C2×C411yescharacteristic
31C8×D73D412yes—
32C8×D73Q812yes—
33C4⋊Dic73C2×C412yes—
34#11924007—22no—
35C2×C8×C73C2×C411yescharacteristic
36C4⋊C4×C73C2×C412yes—
37C22×D73C2×D411yescharacteristic
38C2×#64408—22no—
39C2×#64408—22no—
40C2×#64408—22no—
41C2×#64408—42no—
42C2×#64408—42no—
43C2×#64408—42no—
44C2×C4×C73—22no—
45C2×C4×C73C22×C411yescharacteristic
46C2×Dic73—22no—
47C2×Dic73#4111yescharacteristic
48C4×D73—42no—
49C4×D73—42no—
50C4×D73C2×D411yescharacteristic
51C4×D73C2×Q811yescharacteristic
52C4×D73C2×Q811yescharacteristic
53C4×D73#4111yescharacteristic
54#10596833—22no—
55C8×C73C4⋊C412yescomplemented
56#10596831C4⋊C412yescomplemented
57C22×C73C4×D411yescharacteristic
58C2×D73#12111yescharacteristic
59C2×D73C4⋊Q811yescharacteristic
60C2×D73AGL(1,ℤ/8)12yes—
61C2×D73#13712yes—
62#64408—42no—
63#64408—82no—
64C4×C73—42no—
65C4×C73C2×C4⋊C411yescharacteristic
66C4×C73C4×Q811yescharacteristic
67Dic73—42no—
68Dic73C22⋊Q811yescharacteristic
69Dic73#12511yescharacteristic
70C2×C73#38911yescharacteristic
71C2×C73#44111yescharacteristic
72C2×C73#44211yescharacteristic
73D73#46812yes—
74D73#50112yes—
75#1943—731nomaximal, Sylow
76C73#194311yescharacteristic, complemented, Sylow
77C2×#107—731no—
78C2×#106—731no—
79C2×#97—731no—
80#389—732no—
81#340—732no—
82C22×C8—731no—
83C22×C8—731no—
84C2×C4⋊C4—732no—
85C2×C4⋊C4—732no—
86C2×C4⋊C4—1462no—
87C2×C42—731no—
88#107—731no—
89#107—732no—
90#107#6440811yescharacteristic, complemented
91#106—1462no—
92#97—1462no—
93#95—1462no—
94C22×C4—731no—
95C22×C4—732no—
96C22×C4—1462no—
97C22×C4—1462no—
98C2×C8—731no—
99C2×C8—732no—
100C2×C8—732no—
101C2×C8—732no—
102C2×C8—1461no—
103C2×C8—1461no—
104C2×C8C2×#6440811yescharacteristic
105C4⋊C4—2924no—
106C4⋊C4—732no—
107C4⋊C4—1462no—
108C4⋊C4—1462no—
109C4⋊C4—1462no—
110C4⋊C4C2×#6440812yes—
111C42—1461no—
112C42—1461no—
113C23—731no—
114C2×C4—22no—
115C2×C4—2922no—
116C2×C4—2922no—
117C2×C4—2922no—
118C2×C4—2922no—
119C2×C4—2922no—
120C2×C4—731no—
121C2×C4—731no—
122C2×C4—731no—
123C2×C4—731no—
124C2×C4—731no—
125C2×C4—1462no—
126C2×C4—1462no—
127C2×C4—1462no—
128C2×C4—1462no—
129C2×C4C22×#6440811yescharacteristic
130C8—732no—
131C8—1462no—
132C8C4⋊#6440812yescomplemented
133C22—731no—
134C22—731no—
135C22—732no—
136C22—732no—
137C22D4×#6440811yescharacteristic
138C4—42no—
139C4—2922no—
140C4—2922no—
141C4—5842no—
142C4—731no—
143C4—731no—
144C4C2×C4⋊#6440811yescharacteristic
145C4Q8×#6440811yescharacteristic
146C2—732no—
147C2—732no—
148C2#1798953811yescharacteristic
149C2#1798962711yescharacteristic
150C2#1798962811yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#107×C73C4
socleC22×C73C4×D4
hypercenter#107#64408
hypocenterC73#1943
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
15. #14556525C4semidirect
16. #14556524C4semidirect
17. #107×C73C4semidirect
55. C8×C73C4⋊C4semidirect
56. #10596831C4⋊C4semidirect
76. C73#1943semidirect
90. #107#64408semidirect
132. C8C4⋊#64408semidirect