Finite Group Databasebeta

← #22626227

Subgroups — #22626227

Order 9344.

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

normal subgroups only

This group has 230 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⋊#101C212yesmaximal, complemented
2#17989498C212yesmaximal, complemented
3#17989495C212yesmaximal, complemented
4#17989157C211yesmaximal, characteristic
5D73⋊M16—22no—
6#14556652—22no—
7#14556652C2214yes—
8C2×#11924027C411yescharacteristic
9C2×Q8×D73C2211yescharacteristic
10#14556591C2211yescharacteristic
11#14556589C411yescharacteristic
12#14556578C2211yescharacteristic
13#14556573—22no—
14#14556568—22no—
15#14556548C411yescharacteristic
16#124×C73C411yescharacteristic
17#11924038—42no—
18#11924037—24no—
19#11924036—42no—
20#11924027—42no—
21C2×Dic146C2×C411yescharacteristic
22C2×Dic146D412yes—
23C2×Dic146C2311yescharacteristic
24Q8×D73—42no—
25C2×C22⋊D73—21no—
26C22×Dic73—21no—
27C2×C4×D73C2×C411yescharacteristic
28C2×C4×D73D412yes—
29C4⋊Dic73—22no—
30#11924007—22no—
31#11924007—21no—
32C22⋊Dic73—22no—
33#11924005—21no—
34C4×Dic73C2×C411yescharacteristic
35C2×Q8×C73C2×C411yescharacteristic
36C2×D4×C73C2×C411yescharacteristic
37C22⋊C4×C73—22no—
38C42×C73C2×C411yescharacteristic
39C23×C73—21no—
40C22×D73C22⋊C411yescharacteristic
41Q8×C73—41no—
42D4×C73—41no—
43C2×C4×C73—21no—
44C2×C4×C73C22⋊C412yes—
45C2×C4×C73C22×C411yescharacteristic
46C22⋊D73—42no—
47C2×Dic73—21no—
48C2×Dic73—21no—
49C2×Dic73—42no—
50C2×Dic73C22⋊C411yescharacteristic
51C2×Dic73C2×D412yes—
52C4×D73—22no—
53C4×D73—22no—
54C4×D73—22no—
55Dic146—42no—
56Dic146—41no—
57Dic146—41no—
58#10596833—44no—
59C22×C73—42no—
60C22×C73—41no—
61C22×C73C2×C22⋊C411yescharacteristic
62C2×D73—41no—
63C2×D73#9912yes—
64C4×C73—21no—
65C4×C73—22no—
66C4×C73—41no—
67Dic73—22no—
68Dic73—21no—
69Dic73—41no—
70Dic73—41no—
71C2×C73—21no—
72C2×C73—81no—
73C2×C73C2×#9911yescharacteristic
74D73—22no—
75#2133—731nomaximal, Sylow
76C73#213311yescharacteristic, complemented, Sylow
77#536—731no—
78C2×#101—732no—
79#356—732no—
80#355—732no—
81C2×#41—731no—
82C22×Q8—731no—
83C2×M16—1462no—
84C4⋊Q8—731no—
85C4⋊Q8—731no—
86#124—731no—
87#124#6440811yescharacteristic
88#123—1462no—
89C22⋊Q8—1462no—
90#117—731no—
91#101—734no—
92#101—1462no—
93#41—2922no—
94C2×Q8—2922no—
95C2×Q8—732no—
96C2×Q8—731no—
97C2×Q8—731no—
98C2×Q8C2×#6440811yescharacteristic
99C2×D4—1461no—
100C2×D4C2×#6440811yescharacteristic
101C22×C4—732no—
102C22×C4—731no—
103C22×C4—1461no—
104M16—2922no—
105M16—1464no—
106C2×C8—2922no—
107C4⋊C4—1461no—
108C4⋊C4—1462no—
109C4⋊C4—1462no—
110C22⋊C4—22no—
111C22⋊C4—1461no—
112C22⋊C4—1462no—
113C42—731no—
114C42C2×#6440811yescharacteristic
115C23—21no—
116C23—731no—
117Q8—41no—
118Q8—2921no—
119Q8—2922no—
120Q8—2921no—
121D4—41no—
122D4—2922no—
123C2×C4—21no—
124C2×C4—2922no—
125C2×C4—732no—
126C2×C4—731no—
127C2×C4—1462no—
128C2×C4—1462no—
129C2×C4—1462no—
130C2×C4—1461no—
131C2×C4—1461no—
132C2×C4C22⋊#6440812yes—
133C2×C4C22×#6440811yescharacteristic
134C8—2924no—
135C22—42no—
136C22—41no—
137C22—2921no—
138C22—732no—
139C22C2×C22⋊#6440811yescharacteristic
140C4—22no—
141C4—21no—
142C4—41no—
143C4—2921no—
144C4—2921no—
145C4—1462no—
146C4—1461no—
147C2—21no—
148C2—81no—
149C2—1462no—
150C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC2×C73C2×#99
hypercenter#124#64408
hypocenterC73#2133
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D73⋊#101C2semidirect
2. #17989498C2semidirect
3. #17989495C2semidirect
76. C73#2133semidirect