Finite Group Databasebeta

← #22626059

Subgroups — #22626059

Order 9344.

436 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14556653C214yesmaximal, complemented
2C4×#11924036C211yesmaximal, characteristic, complemented
3#17989533C211yesmaximal, characteristic, complemented
4#127×D73C211yesmaximal, characteristic
5C2×#11924036C2212yes—
6C2×C4⋊#64408—22no—
7C2×C4⋊#64408C2212yes—
8#14556653—28no—
9C4×#10596833—22no—
10C2×D4×D73—22no—
11C2×D4×D73C2212yes—
12#14556588C411yescharacteristic, complemented
13#14556587—22no—
14#14556587C412yescomplemented
15C42×D73C2211yescharacteristic
16#127×C73C411yescharacteristic, complemented
17C22×#64408—22no—
18#11924036—22no—
19#11924036D414yescomplemented
20C2×#10596833—22no—
21C4⋊#64408—24no—
22C4⋊#64408—44no—
23C23×D73—22no—
24C2×D292—22no—
25C2×D292C2×C412yes—
26C2×C22⋊D73—24no—
27C2×C22⋊D73—22no—
28D4×D73—24no—
29D4×D73—24no—
30D4×D73—44no—
31D4×D73—44no—
32C2×C4×D73D412yes—
33C2×C4×D73C2311yescharacteristic
34C4×Dic73C2×C411yescharacteristic
35C4×Dic73D412yes—
36C2×D4×C73—22no—
37C2×D4×C73C2×C412yes—
38C42×C73C2×C411yescharacteristic
39C23×C73—22no—
40C22×D73—22no—
41C22×D73—42no—
42C22×D73—42no—
43C22×D73—44no—
44C22×D73—44no—
45C22×D73C2×D411yescharacteristic
46C2×#64408—42no—
47C2×#64408—44no—
48D4×C73—24no—
49D4×C73—44no—
50C2×C4×C73C22⋊C412yes—
51C2×C4×C73C22×C411yescharacteristic
52C22⋊D73—48no—
53C22⋊D73—44no—
54C2×Dic73C22⋊C412yes—
55C2×Dic73C2×D411yescharacteristic
56D292—24no—
57D292—44no—
58C4×D73D814yes—
59C4×D73SD1614yes—
60C4×D73C2×D412yes—
61C4×D73#4112yes—
62#10596833—24no—
63C22×C73—42no—
64C22×C73—44no—
65C22×C73C2×C22⋊C411yescharacteristic
66C2×D73—42no—
67C2×D73—44no—
68C2×D73—84no—
69C2×D73—82no—
70C2×D73—82no—
71C2×D73#12411yescharacteristic
72C2×D73#12711yescharacteristic
73C2×D73C2×D812yes—
74C2×D73C2×SD1612yes—
75#64408—82no—
76C4×C73#10214yescomplemented
77C4×C73C4×D412yes—
78Dic73#10214yescomplemented
79Dic73#12112yes—
80C2×C73—82no—
81C2×C73#39011yescharacteristic
82C2×C73C2×#10212yes—
83D73—82no—
84D73#48612yes—
85D73#49211yescharacteristic
86D73#49311yescharacteristic
87#1957—731nomaximal, Sylow
88C73#195711yescharacteristic, complemented, Sylow
89C2×#127—731no—
90C2×#102—734no—
91C2×C4×C8—731no—
92#384—731no—
93C22×D4—732no—
94C22×D4—1462no—
95C22×C8—732no—
96#127—732no—
97#127—731no—
98#127—1462no—
99#127#6440811yescharacteristic, complemented
100C2×C4⋊C4—732no—
101C2×C4⋊C4—1462no—
102C2×C42—731no—
103#102—1468no—
104C4×C8—1462no—
105C24—1462no—
106C2×D4—22no—
107C2×D4—2924no—
108C2×D4—2924no—
109C2×D4—732no—
110C2×D4—1464no—
111C2×D4—1464no—
112C2×D4—1464no—
113C2×D4—1462no—
114C2×D4—1462no—
115C2×D4C2×#6440812yes—
116C22×C4—732no—
117C22×C4—731no—
118C22×C4—1462no—
119C2×C8—734no—
120C2×C8—1462no—
121C2×C8—1462no—
122C4⋊C4—2924no—
123C4⋊C4—1464no—
124C42—732no—
125C42—731no—
126C42C2×#6440811yescharacteristic
127C23—22no—
128C23—2924no—
129C23—2924no—
130C23—2922no—
131C23—2922no—
132C23—731no—
133C23—1462no—
134D4—24no—
135D4—44no—
136D4—2928no—
137D4—2924no—
138D4—2924no—
139D4—1464no—
140C2×C4—2924no—
141C2×C4—2922no—
142C2×C4—731no—
143C2×C4—732no—
144C2×C4—734no—
145C2×C4—734no—
146C2×C4—732no—
147C2×C4—732no—
148C2×C4C22⋊#6440812yes—
149C2×C4C22×#6440811yescharacteristic
150C8—1464no—
151C22—42no—
152C22—44no—
153C22—2922no—
154C22—2924no—
155C22—5842no—
156C22—5844no—
157C22—5842no—
158C22—731no—
159C22—731no—
160C22—732no—
161C22—732no—
162C22C2×C22⋊#6440811yescharacteristic
163C4—5842no—
164C4—732no—
165C4—734no—
166C4#1455665314yescomplemented
167C4D4×#6440812yes—
168C2—82no—
169C2—5842no—
170C2—731no—
171C2—732no—
172C2—731no—
173C2#1798953911yescharacteristic
174C2C2×#1455665312yes—
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#127×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#127#64408
hypocenterC73#1957
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#14556653C2semidirect
2. C4×#11924036C2semidirect
3. #17989533C2semidirect
12. #14556588C4semidirect
14. #14556587C4semidirect
16. #127×C73C4semidirect
19. #11924036D4semidirect
76. C4×C73#102semidirect
78. Dic73#102semidirect
88. C73#1957semidirect
99. #127#64408semidirect
166. C4#14556653semidirect