Finite Group Databasebeta

← #22625455

Subgroups — #22625455

Order 9344.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989607C211yesmaximal, characteristic, complemented
2#17989604C211yesmaximal, characteristic, complemented
3#17989446C212yesmaximal, complemented
4#17989445C212yesmaximal, complemented
5#17989132C211yesmaximal, characteristic
6#14556658C2212yes—
7#14556658C2212yes—
8C22⋊#10596833—21no—
9C22⋊#10596833—21no—
10#14556646—21no—
11C4×#10596833—21no—
12C2×#11924027—21no—
13#14556590C2211yescharacteristic
14#14556587C2211yescharacteristic
15#14556577—21no—
16#14556565C411yescharacteristic
17#14556563—21no—
18D4×Dic73C411yescharacteristic
19#14556553C411yescharacteristic
20#14556551—21no—
21C2×C4×Dic73C2211yescharacteristic
22#121×C73C411yescharacteristic
23C2×#10596833—22no—
24C2×#10596833—22no—
25#11924027—44no—
26C2×Dic146—21no—
27C2×D292C2×C411yescharacteristic
28C2×C22⋊D73—21no—
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C22×Dic73—21no—
32C22×Dic73D411yescharacteristic
33C22×Dic73D411yescharacteristic
34C2×C4×D73—21no—
35C4⋊Dic73C2×C411yescharacteristic
36#11924007—21no—
37C22⋊Dic73—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73C2311yescharacteristic
44C2×D4×C73—21no—
45C2×D4×C73C2×C411yescharacteristic
46C22×C4×C73C2×C411yescharacteristic
47C4⋊C4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C23×C73—21no—
50C23×C73C22⋊C411yescharacteristic
51C22×D73—21no—
52D4×C73—41no—
53D4×C73—42no—
54C2×C4×C73—21no—
55C2×C4×C73—41no—
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22×C411yescharacteristic
58C22⋊D73—42no—
59C22⋊D73—42no—
60C22⋊D73—42no—
61C2×Dic73—22no—
62C2×Dic73—22no—
63C2×Dic73—21no—
64C2×Dic73—42no—
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68C2×Dic73C2×D411yescharacteristic
69D292—41no—
70C4×D73—42no—
71Dic146—42no—
72#10596833—42no—
73#10596833—42no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73C2×C22⋊C411yescharacteristic
81C2×D73—41no—
82C2×D73—41no—
83C2×D73—41no—
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—41no—
87Dic73—21no—
88Dic73—21no—
89Dic73—41no—
90Dic73#13512yes—
91Dic73AGL(1,ℤ/8)12yes—
92C2×C73—41no—
93C2×C73—81no—
94C2×C73#41311yescharacteristic
95C2×C73#41611yescharacteristic
96C2×C73#41811yescharacteristic
97D73—81no—
98#1553—731nomaximal, Sylow
99C73#155311yescharacteristic, complemented, Sylow
100#532—731no—
101#432—731no—
102#431—731no—
103#332—732no—
104#331—732no—
105C2×#41—1461no—
106C4⋊Q8—731no—
107#127—731no—
108#124—1461no—
109#121—731no—
110#121—1461no—
111#121#6440811yescharacteristic
112C4×D4—731no—
113C4×D4—731no—
114C4×D4—1461no—
115C2×C42—731no—
116C4⋊C8—732no—
117C4⋊C8—732no—
118C22⋊C8—1461no—
119C22⋊C8—1461no—
120#97—1461no—
121C4×C8—1461no—
122#41—2924no—
123C2×Q8—1461no—
124C2×D4—21no—
125C2×D4—731no—
126C2×D4—1461no—
127C2×D4—1461no—
128C2×D4—1461no—
129C2×D4C2×#6440811yescharacteristic
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—1461no—
133C22×C4—1461no—
134C22×C4C2×#6440811yescharacteristic
135C2×C8—1462no—
136C2×C8—1462no—
137C4⋊C4—731no—
138C4⋊C4—1461no—
139C4⋊C4C2×#6440811yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—1461no—
142C22⋊C4—1461no—
143C22⋊C4—1461no—
144C42—731no—
145C42—731no—
146C42—731no—
147C42—731no—
148C23—21no—
149C23—1461no—
150C23C22⋊#6440811yescharacteristic
151Q8—2922no—
152D4—41no—
153D4—42no—
154D4—2921no—
155D4—2922no—
156D4—2922no—
157D4—2922no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—2922no—
161C2×C4—2922no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—731no—
165C2×C4—731no—
166C2×C4—1461no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4C22⋊#6440811yescharacteristic
170C2×C4C22×#6440811yescharacteristic
171C8—2922no—
172C8—2922no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—2921no—
180C22—2921no—
181C22—2921no—
182C22C2×C22⋊#6440811yescharacteristic
183C4—21no—
184C4—21no—
185C4—41no—
186C4—2921no—
187C4—732no—
188C4—732no—
189C4—1461no—
190C4—1461no—
191C2—41no—
192C2—81no—
193C2—5841no—
194C2#1798957411yescharacteristic
195C2#1798957711yescharacteristic
196C2#1798957911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1553
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #17989607C2semidirect
2. #17989604C2semidirect
3. #17989446C2semidirect
4. #17989445C2semidirect
99. C73#1553semidirect