Finite Group Databasebeta

← #22626209

Subgroups — #22626209

Order 9344.

286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D73⋊#99C212yesmaximal, complemented
2#17989493C212yesmaximal, complemented
3#17989492C212yesmaximal, complemented
4#17989155C211yesmaximal, characteristic
5C2×C22⋊#64408—22no—
6#14556650C2214yes—
7#14556649—22no—
8C2×#11924029C411yescharacteristic, complemented
9C2×D4×D73C2211yescharacteristic
10#14556588C2211yescharacteristic
11#14556587C411yescharacteristic, complemented
12#14556580C2211yescharacteristic
13#14556564—22no—
14#14556561—22no—
15#14556548C411yescharacteristic, complemented
16#124×C73C411yescharacteristic, complemented
17C22×#64408—42no—
18C22⋊#64408—24no—
19C22⋊#64408—42no—
20C23×D73D412yes—
21#11924029—42no—
22C2×D292—21no—
23C2×D292—22no—
24C2×D292C2×C411yescharacteristic, complemented
25C2×D292C2311yescharacteristic
26C2×C22⋊D73—22no—
27C2×C22⋊D73D412yes—
28D4×D73—42no—
29C2×C4×D73—21no—
30C2×C4×D73C2×C411yescharacteristic
31#11924007—21no—
32#11924005—21no—
33#11924005—22no—
34C4×Dic73C2×C411yescharacteristic, complemented
35C2×Q8×C73C2×C411yescharacteristic, complemented
36C2×D4×C73C2×C411yescharacteristic
37C22⋊C4×C73—22no—
38C42×C73C2×C411yescharacteristic, complemented
39C23×C73C22⋊C412yes—
40C22×D73—22no—
41C22×D73—22no—
42C22×D73—21no—
43C22×D73—82no—
44C22×D73C22⋊C411yescharacteristic
45C22×D73C2×D412yes—
46C2×#64408—44no—
47C2×#64408—84no—
48Q8×C73—41no—
49D4×C73—41no—
50C2×C4×C73—21no—
51C2×C4×C73—21no—
52C2×C4×C73C22×C411yescharacteristic
53C22⋊D73—42no—
54C22⋊D73—82no—
55C2×Dic73—21no—
56C2×Dic73C22⋊C411yescharacteristic
57D292—41no—
58D292—41no—
59D292—42no—
60D292—82no—
61C4×D73—22no—
62C4×D73—42no—
63C22×C73—22no—
64C22×C73—42no—
65C22×C73C2×C22⋊C411yescharacteristic
66C2×D73—22no—
67C2×D73—41no—
68C2×D73—44no—
69C2×D73—42no—
70C2×D73—42no—
71C2×D73—41no—
72C2×D73—82no—
73C2×D73#9912yes—
74#64408—84no—
75C4×C73—21no—
76C4×C73—41no—
77C4×C73—41no—
78Dic73—21no—
79Dic73—41no—
80C2×C73—21no—
81C2×C73—42no—
82C2×C73C2×#9911yescharacteristic
83D73—22no—
84D73—42no—
85D73—81no—
86#2127—731nomaximal, Sylow
87C73#212711yescharacteristic, complemented, Sylow
88#535—731no—
89C2×#99—732no—
90#354—732no—
91#353—732no—
92C2×#41—731no—
93C22×D4—731no—
94#127—731no—
95#127—731no—
96#124—731no—
97#124#6440811yescharacteristic, complemented
98#121—1462no—
99#120—1462no—
100#117—731no—
101C2×C22⋊C4—1462no—
102#99—734no—
103#99—1462no—
104C24—732no—
105#41—2922no—
106C2×Q8C2×#6440811yescharacteristic, complemented
107C2×D4—2922no—
108C2×D4—732no—
109C2×D4—731no—
110C2×D4—731no—
111C2×D4—1461no—
112C2×D4—1462no—
113C2×D4—1462no—
114C2×D4C2×#6440811yescharacteristic
115C22×C4—2922no—
116C22×C4—731no—
117C22×C4—1461no—
118C4⋊C4—1461no—
119C22⋊C4—22no—
120C22⋊C4—2922no—
121C22⋊C4—1461no—
122C22⋊C4—1462no—
123C22⋊C4—1464no—
124C42—731no—
125C42C2×#6440811yescharacteristic, complemented
126C23—5842no—
127C23—731no—
128C23—732no—
129C23—1462no—
130C23—1462no—
131C23—1461no—
132C23C22⋊#6440812yes—
133Q8—41no—
134D4—41no—
135D4—2921no—
136D4—2921no—
137D4—2922no—
138D4—2922no—
139D4—5842no—
140D4—5842no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—2922no—
144C2×C4—2924no—
145C2×C4—5844no—
146C2×C4—731no—
147C2×C4—1462no—
148C2×C4—1461no—
149C2×C4C22×#6440811yescharacteristic
150C22—22no—
151C22—42no—
152C22—2922no—
153C22—2922no—
154C22—2921no—
155C22—2924no—
156C22—2921no—
157C22—5842no—
158C22—732no—
159C22—1462no—
160C22C2×C22⋊#6440811yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—2921no—
165C4—5844no—
166C4—1461no—
167C2—21no—
168C2—42no—
169C2—2922no—
170C2—5841no—
171C2—1462no—
172C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC2×C73C2×#99
hypercenter#124#64408
hypocenterC73#2127
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D73⋊#99C2semidirect
2. #17989493C2semidirect
3. #17989492C2semidirect
8. C2×#11924029C4semidirect
11. #14556587C4semidirect
15. #14556548C4semidirect
16. #124×C73C4semidirect
24. C2×D292C2×C4semidirect
34. C4×Dic73C2×C4semidirect
35. C2×Q8×C73C2×C4semidirect
38. C42×C73C2×C4semidirect
87. C73#2127semidirect
97. #124#64408semidirect
106. C2×Q8C2×#64408semidirect
125. C42C2×#64408semidirect