Finite Group Databasebeta

← #22626222

Subgroups — #22626222

Order 9344.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#17989573C212yesmaximal, complemented
2#17989497C212yesmaximal, complemented
3#17989495C212yesmaximal, complemented
4#17989133C211yesmaximal, characteristic
5D73⋊M16—22no—
6#14556652C2214yes—
7#14556651—22no—
8C2×#11924028C2211yescharacteristic
9#14556589C2211yescharacteristic
10#14556587C411yescharacteristic
11#14556580C411yescharacteristic
12#14556578C2211yescharacteristic
13#14556563—22no—
14C4×C22⋊D73—22no—
15C2×C4×Dic73C411yescharacteristic
16C2×#41×C73C411yescharacteristic
17#11924038—42no—
18#11924037—24no—
19#11924036—42no—
20#11924028—41no—
21#11924028—41no—
22C2×Dic146C2311yescharacteristic
23C2×D292C2×C411yescharacteristic
24C2×C22⋊D73—22no—
25C2×C22⋊D73D412yes—
26C22×Dic73—21no—
27C2×C4×D73D412yes—
28#11924007—22no—
29C22⋊Dic73—22no—
30#11924005—22no—
31C4×Dic73—21no—
32C4×Dic73C2×C411yescharacteristic
33C4×Dic73C2×C411yescharacteristic
34#41×C73—41no—
35#41×C73—41no—
36C2×Q8×C73C2×C411yescharacteristic
37C2×D4×C73—21no—
38C2×D4×C73C2×C411yescharacteristic
39C22×C4×C73—21no—
40C22×C4×C73C2×C411yescharacteristic
41C23×C73—21no—
42C23×C73C22⋊C411yescharacteristic
43C22×D73C22⋊C412yes—
44Q8×C73—41no—
45D4×C73—41no—
46D4×C73—42no—
47C2×C4×C73—21no—
48C2×C4×C73—21no—
49C2×C4×C73—21no—
50C2×C4×C73—41no—
51C2×C4×C73—41no—
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C22×C411yescharacteristic
54C22⋊D73—42no—
55C22⋊D73—44no—
56C2×Dic73—21no—
57C2×Dic73—21no—
58C2×Dic73—42no—
59C2×Dic73C2×D412yes—
60D292—41no—
61C4×D73—22no—
62C4×D73—22no—
63Dic146—41no—
64#10596833—44no—
65C22×C73—21no—
66C22×C73—41no—
67C22×C73—42no—
68C22×C73—41no—
69C22×C73C2×C22⋊C411yescharacteristic
70C2×D73—22no—
71C2×D73—42no—
72C4×C73—21no—
73C4×C73—41no—
74C4×C73#9911yescharacteristic
75C4×C73#9911yescharacteristic
76Dic73—22no—
77Dic73—22no—
78Dic73—41no—
79C2×C73—21no—
80C2×C73—41no—
81C2×C73—81no—
82C2×C73C2×#9911yescharacteristic
83D73—42no—
84#2132—731nomaximal, Sylow
85C73#213211yescharacteristic, complemented, Sylow
86#532—731no—
87#413—732no—
88#356—732no—
89#355—732no—
90C2×#41—731no—
91C2×#41#6440811yescharacteristic
92C2×M16—1462no—
93C4⋊Q8—731no—
94#127—731no—
95#124—731no—
96#124—731no—
97#121—1462no—
98C4×D4—1462no—
99C2×C42—731no—
100#101—734no—
101#100—1462no—
102#41—41no—
103#41—41no—
104#41—2921no—
105#41—2921no—
106C2×Q8—731no—
107C2×Q8C2×#6440811yescharacteristic
108C2×D4—21no—
109C2×D4—732no—
110C2×D4—731no—
111C2×D4—1462no—
112C2×D4C2×#6440811yescharacteristic
113C22×C4—21no—
114C22×C4—732no—
115C22×C4—1461no—
116C22×C4C2×#6440811yescharacteristic
117M16—2922no—
118M16—1464no—
119C2×C8—2922no—
120C4⋊C4—1462no—
121C22⋊C4—1462no—
122C22⋊C4—1462no—
123C42—731no—
124C42—731no—
125C42—1461no—
126C23—21no—
127C23—732no—
128C23C22⋊#6440811yescharacteristic
129Q8—41no—
130Q8—2921no—
131D4—41no—
132D4—42no—
133D4—2921no—
134D4—2922no—
135D4—2924no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—2922no—
142C2×C4—732no—
143C2×C4—1461no—
144C2×C4—1461no—
145C2×C4—1462no—
146C2×C4—1462no—
147C2×C4C22⋊#6440811yescharacteristic
148C2×C4C22×#6440811yescharacteristic
149C8—2924no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—2922no—
155C22—1462no—
156C22C2×C22⋊#6440811yescharacteristic
157C4—21no—
158C4—41no—
159C4—2921no—
160C4—1462no—
161C4—1462no—
162C4#1455664911yescharacteristic
163C4#1455664911yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—2922no—
168C2C2×#1455664911yescharacteristic
subgroupG/H
centerC4#14556649
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×#41×C73C4
socleC2×C73C2×#99
hypercenterC2×#41#64408
hypocenterC73#2132
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #17989573C2semidirect
2. #17989497C2semidirect
3. #17989495C2semidirect
85. C73#2132semidirect