Finite Group Databasebeta

← #22608383

Subgroups — #22608383

Order 9344.

276 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#17989137C211yesmaximal, characteristic
2#17988611C211yesmaximal, characteristic, complemented
3#17988316C214yesmaximal, complemented
4C2×C4×C8×C73C211yesmaximal, characteristic, complemented
5C2×#11924028—21no—
6C2×#11924012—21no—
7#14556591C411yescharacteristic
8#14556588C411yescharacteristic
9#14556579—21no—
10#14556565—21no—
11#14556565C412yes—
12C4×D292—21no—
13C4×D292C2212yes—
14C4⋊#10596831—21no—
15C4⋊#10596831C2212yes—
16C22×C8×C73—21no—
17C2×C42×C73C2211yescharacteristic
18C4×C8×C73—21no—
19C4×C8×C73C2212yes—
20#11924028—42no—
21#11924028—42no—
22C2×Dic146—21no—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292C2×C412yes—
26C2×C22⋊D73—22no—
27C2×C4×D73—22no—
28#11924012—42no—
29C2×#10596831—22no—
30C4⋊Dic73—21no—
31C4⋊Dic73C2×C412yes—
32#11924005—22no—
33#11924005—22no—
34C22×C4×C73C2×C411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C22×C4×C73D411yescharacteristic
37C2×C8×C73—24no—
38C2×C8×C73—22no—
39C42×C73C2×C411yescharacteristic
40C42×C73D411yescharacteristic
41C42×C73D411yescharacteristic
42C42×C73C2311yescharacteristic
43C23×C73C22⋊C411yescharacteristic
44C22×D73—22no—
45C2×C4×C73—22no—
46C2×C4×C73—22no—
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22⋊C411yescharacteristic
49C2×C4×C73C22⋊C411yescharacteristic
50C2×C4×C73D812yes—
51C2×C4×C73SD1612yes—
52C2×C4×C73C22×C411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C22⋊D73—44no—
56C2×Dic73—22no—
57D292—24no—
58D292—42no—
59D292—42no—
60C4×D73—42no—
61C4×D73—42no—
62Dic146—42no—
63C8×C73—24no—
64#10596831—42no—
65C22×C73—21no—
66C22×C73—21no—
67C22×C73#10212yes—
68C22×C73C2×C22⋊C411yescharacteristic
69C2×D73—42no—
70C2×D73—42no—
71C2×D73—42no—
72C4×C73—21no—
73C4×C73—21no—
74C4×C73#10212yes—
75C4×C73#10412yes—
76C4×C73#13112yes—
77C4×C73C2×D811yescharacteristic
78C4×C73C2×SD1611yescharacteristic
79Dic73—42no—
80C2×C73—22no—
81C2×C73#40811yescharacteristic
82C2×C73C2×#10211yescharacteristic
83C2×C73C2×#10411yescharacteristic
84D73—82no—
85#1492—731nomaximal, Sylow
86C73#149211yescharacteristic, complemented, Sylow
87#532—731no—
88#423—731no—
89C2×C4×C8D7311yescharacteristic, complemented
90D4⋊C8—734no—
91C2×#41—1461no—
92C2×M16—1461no—
93C22×C8—21no—
94C4⋊Q8—731no—
95#127—731no—
96#124—1461no—
97#121—732no—
98#121—1461no—
99C4×D4—732no—
100C4×D4—1461no—
101C2×C42C2×D7311yescharacteristic
102C4⋊C8—732no—
103C4⋊C8—1461no—
104C4×C8—21no—
105C4×C8C2×D7312yes—
106#41—2922no—
107#41—2922no—
108C2×Q8—1461no—
109C2×D4—732no—
110C2×D4—1462no—
111C2×D4—1461no—
112C2×D4—1461no—
113C22×C4—1462no—
114C22×C4C4×D7311yescharacteristic
115C22×C4D29211yescharacteristic
116C22×C4C22⋊D7311yescharacteristic
117M16—2922no—
118C2×C8—24no—
119C2×C8—22no—
120C2×C8—1462no—
121C4⋊C4—732no—
122C4⋊C4—1461no—
123C22⋊C4—1462no—
124C22⋊C4—1462no—
125C42C4×D7311yescharacteristic
126C42D29211yescharacteristic
127C42C22⋊D7311yescharacteristic
128C42C22×D7311yescharacteristic
129C23—1462no—
130C23#1192400511yescharacteristic
131Q8—2922no—
132D4—2924no—
133D4—2922no—
134D4—2922no—
135D4—1464no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—2922no—
139C2×C4—2922no—
140C2×C4—1462no—
141C2×C4#1192400511yescharacteristic
142C2×C4#1192400511yescharacteristic
143C2×C4#1192400511yescharacteristic
144C2×C4D58412yes—
145C2×C4#1192401712yes—
146C2×C4C2×C4×D7311yescharacteristic
147C2×C4C2×C22⋊D7311yescharacteristic
148C2×C4C2×D29211yescharacteristic
149C8—24no—
150C8—2922no—
151C22—21no—
152C22—21no—
153C22—2922no—
154C22—2922no—
155C22—2922no—
156C22#1455651312yes—
157C22C2×#1192400511yescharacteristic
158C4—21no—
159C4—21no—
160C4—2922no—
161C4#1455651312yes—
162C4#1455651912yes—
163C4#1455659712yes—
164C4C2×D58411yescharacteristic
165C4C2×#1192401711yescharacteristic
166C2—22no—
167C2—5842no—
168C2#1798855311yescharacteristic
169C2C2×#1455651311yescharacteristic
170C2C2×#1455651911yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
FittingC2×C4×C8×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC2×C4×C8D73
hypocenterC73#1492
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #17988611C2semidirect
3. #17988316C2semidirect
4. C2×C4×C8×C73C2semidirect
86. C73#1492semidirect
89. C2×C4×C8D73semidirect