Finite Group Databasebeta

← #22610906

Subgroups — #22610906

Order 9344.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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#17989140C211yesmaximal, characteristic
2#17988610C211yesmaximal, characteristic
3C42×Dic73C211yesmaximal, characteristic
4#17988348C211yesmaximal, characteristic
5#17988347C211yesmaximal, characteristic
6#17988346C211yesmaximal, characteristic
7#339×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556590C412yescomplemented
10#14556582C412yescomplemented
11#14556568—22no—
12C4×Dic146—22no—
13#14556550C2211yescharacteristic
14C2×C4×Dic73—22no—
15C2×C4×Dic73C2211yescharacteristic
16C2×C4×Dic73C2211yescharacteristic
17#14556520—22no—
18C2×M16×C73C2211yescharacteristic
19#117×C73C2211yescharacteristic
20C2×C42×C73C2211yescharacteristic
21C2×Dic146—22no—
22C22×Dic73—21no—
23C22×Dic73D412yes—
24#11924012—21no—
25#11924012—21no—
26C2×#10596831—21no—
27C4⋊Dic73—22no—
28C4⋊Dic73C2×C412yes—
29#11924007—22no—
30#11924007—22no—
31C22⋊Dic73—21no—
32C4×Dic73—28no—
33C4×Dic73—21no—
34C4×Dic73—21no—
35C4×Dic73C2×C411yescharacteristic
36C4×Dic73C2×C411yescharacteristic
37C4×Dic73D412yes—
38C4×Dic73Q812yescomplemented
39C22×C4×C73—21no—
40C22×C4×C73C2311yescharacteristic
41M16×C73—21no—
42M16×C73—21no—
43C2×C8×C73—21no—
44C4⋊C4×C73C2×C412yes—
45C22⋊C4×C73—21no—
46C42×C73—21no—
47C42×C73—21no—
48C42×C73Q812yescomplemented
49C23×C73C2×D411yescharacteristic
50C2×C4×C73—24no—
51C2×C4×C73—22no—
52C2×C4×C73—22no—
53C2×C4×C73C22×C411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×Q811yescharacteristic
56C2×C4×C73C2×Q811yescharacteristic
57C2×C4×C73#4111yescharacteristic
58C2×C4×C73#4111yescharacteristic
59C2×Dic73—24no—
60C2×Dic73—22no—
61C2×Dic73—24no—
62C2×Dic73—22no—
63C2×Dic73C22⋊C412yes—
64C2×Dic73C22⋊C412yes—
65Dic146—44no—
66C8×C73—41no—
67#10596831—41no—
68C22×C73—22no—
69C22×C73C2×C22⋊C411yescharacteristic
70C22×C73C22⋊Q811yescharacteristic
71C22×C73C22⋊Q811yescharacteristic
72C4×C73—24no—
73C4×C73—42no—
74C4×C73C4×Q811yescharacteristic
75C4×C73C4×Q811yescharacteristic
76C4×C73#12411yescharacteristic
77C4×C73C4⋊Q811yescharacteristic
78Dic73—24no—
79Dic73—22no—
80Dic73—42no—
81Dic73#10414yes—
82C2×C73—21no—
83C2×C73—21no—
84C2×C73#39111yescharacteristic
85C2×C73C2×#10412yes—
86#1994—731nomaximal, Sylow
87C73#199411yescharacteristic, complemented, Sylow
88#533—731no—
89#423—731no—
90C43—731no—
91#339—731no—
92#339—731no—
93#339—731no—
94#339D7311yescharacteristic
95C2×M16—731no—
96C2×M16C2×D7311yescharacteristic
97C4⋊Q8—732no—
98#125—732no—
99C22⋊Q8—1462no—
100C4×Q8—1462no—
101#117—731no—
102#117C2×D7311yescharacteristic
103C2×C42—731no—
104C2×C42—731no—
105C2×C42—1462no—
106C2×C42C2×D7311yescharacteristic
107C4⋊C8—1462no—
108C2×Q8—1462no—
109C22×C4—21no—
110C22×C4—732no—
111C22×C4—1461no—
112C22×C4C22×D7311yescharacteristic
113M16—21no—
114M16—21no—
115M16—1461no—
116M16—1461no—
117C2×C8—21no—
118C2×C8—1461no—
119C4⋊C4—732no—
120C4⋊C4—1462no—
121C4⋊C4—1462no—
122C4⋊C4—1462no—
123C4⋊C4C4×D7312yes—
124C22⋊C4—21no—
125C22⋊C4—1461no—
126C42—21no—
127C42—21no—
128C42—731no—
129C42—731no—
130C42—732no—
131C42—732no—
132C42—1468no—
133C42—1461no—
134C42—1461no—
135C42Dic14612yescomplemented
136C23D4×D7311yescharacteristic
137Q8—2924no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—732no—
142C2×C4—732no—
143C2×C4—1462no—
144C2×C4—1464no—
145C2×C4—1464no—
146C2×C4—1462no—
147C2×C4C2×C4×D7311yescharacteristic
148C2×C4D4×D7311yescharacteristic
149C2×C4Q8×D7311yescharacteristic
150C2×C4C2×Dic14611yescharacteristic
151C2×C4#1192402711yescharacteristic
152C2×C4#1192402811yescharacteristic
153C8—41no—
154C8—2921no—
155C22—22no—
156C22C22⋊C4×D7311yescharacteristic
157C22#1455656811yescharacteristic
158C22#1455656911yescharacteristic
159C4—24no—
160C4—42no—
161C4—2922no—
162C4—734no—
163C4—1464no—
164C4—1462no—
165C4#1455655611yescharacteristic
166C4C4×Dic14611yescharacteristic
167C4#1455657711yescharacteristic
168C4#1455659011yescharacteristic
169C2—21no—
170C2—21no—
171C2#1798849111yescharacteristic
172C2#104×D7312yes—
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#339×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#339D73
hypocenterC73#1994
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14556590C4semidirect
10. #14556582C4semidirect
38. C4×Dic73Q8semidirect
48. C42×C73Q8semidirect
87. C73#1994semidirect
135. C42Dic146semidirect