Finite Group Databasebeta

← #22608271

Subgroups — #22608271

Order 9344.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×D292C211yesmaximal, characteristic
2#17988644C211yesmaximal, characteristic, complemented
3#17988310C214yesmaximal, complemented
4#432×C73C211yesmaximal, characteristic, complemented
5C22×D292C411yescharacteristic
6C22×C4×D73C412yes—
7C4×D292—21no—
8C4×D292—21no—
9C4×D292—21no—
10C4×D292—21no—
11C2×C4⋊Dic73C411yescharacteristic
12C2×#11924005C2212yes—
13C4⋊#10596831—21no—
14C22⋊#10596831C2212yes—
15#14556502—21no—
16C2×C42×C73C2211yescharacteristic
17C4⋊C8×C73—21no—
18C22⋊C8×C73C2212yes—
19#97×C73—21no—
20C23×D73C2×C412yes—
21C2×D292—24no—
22C2×D292—21no—
23C2×D292—21no—
24C22×Dic73C2×C412yes—
25C2×C4×D73—22no—
26C2×C4×D73—22no—
27C2×C4×D73—44no—
28C2×#10596831—22no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31#11924005—22no—
32#11924005—22no—
33C22×C4×C73C2×C411yescharacteristic
34C22×C4×C73C2×C411yescharacteristic
35C22×C4×C73C2311yescharacteristic
36C2×C8×C73—22no—
37C42×C73D411yescharacteristic
38C42×C73D411yescharacteristic
39C42×C73D411yescharacteristic
40C42×C73D411yescharacteristic
41C23×C73C22×C411yescharacteristic
42C22×D73—22no—
43C22×D73—22no—
44C22×D73—42no—
45C22×D73—42no—
46C22×D73M1614yes—
47C2×C4×C73—22no—
48C2×C4×C73—22no—
49C2×C4×C73—41no—
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C22⋊C411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×Dic73—22no—
57C2×Dic73—42no—
58D292—24no—
59D292—24no—
60C4×D73—44no—
61C4×D73—44no—
62C8×C73—42no—
63#10596831—42no—
64C22×C73—21no—
65C22×C73—21no—
66C22×C73C2×C22⋊C411yescharacteristic
67C22×C73C2×M1612yes—
68C2×D73—24no—
69C2×D73—44no—
70C2×D73—42no—
71C2×D73—42no—
72C2×D73—44no—
73C4×C73—21no—
74C4×C73—21no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73#10012yes—
79Dic73—42no—
80C2×C73—22no—
81C2×C73#40711yescharacteristic
82C2×C73#41011yescharacteristic
83C2×C73C2×#10011yescharacteristic
84D73—44no—
85#1466—731nomaximal, Sylow
86C73#146611yescharacteristic, complemented, Sylow
87C2×C4×D4—731no—
88#432—731no—
89#432D7311yescharacteristic, complemented
90#323—734no—
91C22×D4—731no—
92C23×C4—732no—
93C4×D4—1461no—
94C4×D4—1461no—
95C4×D4—1461no—
96C4×D4—1461no—
97C2×C4⋊C4—731no—
98C2×C22⋊C4—732no—
99C2×C42C2×D7311yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—1461no—
102C22⋊C8—732no—
103C22⋊C8C2×D7312yes—
104#97—21no—
105#97—1461no—
106C24—732no—
107C2×D4—1464no—
108C2×D4—1461no—
109C2×D4—1461no—
110C22×C4—2924no—
111C22×C4—732no—
112C22×C4—1462no—
113C22×C4—1462no—
114C22×C4C4×D7311yescharacteristic
115C22×C4C4×D7311yescharacteristic
116C22×C4C22×D7311yescharacteristic
117C2×C8—22no—
118C2×C8—1462no—
119C4⋊C4—1461no—
120C4⋊C4—1461no—
121C22⋊C4—1462no—
122C22⋊C4—1462no—
123C42D29211yescharacteristic
124C42D29211yescharacteristic
125C42C22⋊D7311yescharacteristic
126C42C22⋊D7311yescharacteristic
127C23—2922no—
128C23—2922no—
129C23—734no—
130C23—1462no—
131C23—1462no—
132C23C2×C4×D7311yescharacteristic
133D4—1464no—
134D4—1464no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—2924no—
139C2×C4—2924no—
140C2×C4—2922no—
141C2×C4—1462no—
142C2×C4#1192400511yescharacteristic
143C2×C4#1192400511yescharacteristic
144C2×C4#1192400511yescharacteristic
145C2×C4#1192400511yescharacteristic
146C2×C4C2×C22⋊D7311yescharacteristic
147C2×C4C2×D29211yescharacteristic
148C8—42no—
149C8—2922no—
150C22—21no—
151C22—21no—
152C22—2924no—
153C22—2924no—
154C22—2922no—
155C22—2922no—
156C22—1464no—
157C22C2×#1192400511yescharacteristic
158C22M16×D7312yes—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—21no—
164C4—2922no—
165C4#1455650712yes—
166C2—22no—
167C2—2924no—
168C2#1798855011yescharacteristic
169C2#1798856011yescharacteristic
170C2C2×#1455650711yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#432×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#432D73
hypocenterC73#1466
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #17988644C2semidirect
3. #17988310C2semidirect
4. #432×C73C2semidirect
86. C73#1466semidirect
89. #432D73semidirect