Finite Group Databasebeta

← C2×D73⋊#101 #22626537

Subgroups — C2×D73⋊#101 #22626537

Order 9344.

736 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 210 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
1C2×D73⋊M16C212yesmaximal
2D73⋊#101C218yesmaximal, direct product factor
3C2×#14556652C214yesmaximal, complemented
4C22×Q8×D73C211yesmaximal, characteristic
5C2×#11924038—22no—
6D73⋊M16—24no—
7D73⋊M16C2218yes—
8C2×#11924037C2214yes—
9C2×#11924036—22no—
10#14556652C22116yescomplemented
11C22×Dic146C411yescharacteristic
12C22×Dic146C2212yes—
13C2×Q8×D73—22no—
14C2×Q8×D73—24no—
15C2×Q8×D73—22no—
16C2×Q8×D73C414yes—
17C2×Q8×D73C2214yes—
18C22×C4×D73C412yes—
19C22×C4×D73C2211yescharacteristic
20C22×Q8×C73C411yescharacteristic
21#11924038—28no—
22#11924037—24no—
23#11924037C2318yes—
24#11924036—28no—
25C2×#10596833—24no—
26C23×D73C2×C411yescharacteristic
27C2×Dic146—22no—
28C2×Dic146—22no—
29C2×Dic146—24no—
30C2×Dic146—24no—
31C2×Dic146C2×C414yes—
32C2×Dic146C2×C414yes—
33C2×Dic146C2314yes—
34Q8×D73—28no—
35Q8×D73—28no—
36Q8×D73—28no—
37Q8×D73—28no—
38C22×Dic73C2×C412yes—
39C22×Dic73C2311yescharacteristic
40C2×C4×D73—24no—
41C2×C4×D73—22no—
42C2×C4×D73—22no—
43C2×C4×D73C2×C418yes—
44C2×C4×D73C2×C412yes—
45C2×C4×D73D412yes—
46C2×C4×D73D414yes—
47C2×C4×D73D412yes—
48C2×C4×D73C2312yes—
49C2×Q8×C73—22no—
50C2×Q8×C73—22no—
51C2×Q8×C73C2×C414yes—
52C22×C4×C73C2×C412yes—
53C22×C4×C73C2×C411yescharacteristic
54C23×C73C22×C411yescharacteristic
55C22×D73—24no—
56C22×D73C22⋊C412yes—
57C22×D73C22⋊C411yescharacteristic
58C22×D73C22⋊C411yescharacteristic
59C22×D73C22×C412yes—
60Q8×C73—28no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73C22⋊C412yes—
64C2×C4×C73C22⋊C412yes—
65C2×C4×C73C22×C414yes—
66C2×C4×C73C22×C412yes—
67C2×Dic73—22no—
68C2×Dic73—22no—
69C2×Dic73C22×C414yes—
70C2×Dic73C22×C411yescharacteristic
71C2×Dic73C2×D412yes—
72C2×Dic73C2×D412yes—
73C2×Dic73C2411yescharacteristic
74C4×D73—28no—
75C4×D73—28no—
76C4×D73C22⋊C414yes—
77C4×D73C22⋊C414yes—
78C4×D73C2×D414yes—
79C4×D73C2×D414yes—
80Dic146—28no—
81Dic146—28no—
82Dic146—28no—
83#10596833—28no—
84C22×C73—22no—
85C22×C73C2×C22⋊C411yescharacteristic
86C22×C73C2×C22⋊C411yescharacteristic
87C22×C73C23×C411yescharacteristic
88C2×D73—22no—
89C2×D73—24no—
90C2×D73—24no—
91C2×D73#10114yescomplemented
92C2×D73C2×C22⋊C412yes—
93C2×D73C2×C22⋊C412yes—
94C4×C73—24no—
95C4×C73C2×C22⋊C414yes—
96Dic73—24no—
97Dic73C2×C22⋊C412yes—
98Dic73C22×D412yes—
99C2×C73—21no—
100C2×C73—21no—
101C2×C73C2×#10112yescomplemented
102C2×C73C22×C22⋊C411yescharacteristic
103D73—22no—
104D73C2×#10114yescomplemented
105C22×#101—731nomaximal, Sylow
106C73C22×#10111yescharacteristic, complemented, Sylow
107C23×Q8—731no—
108C22×M16—732no—
109C2×#101—734no—
110C2×#101—738no—
111C22×Q8—734no—
112C22×Q8—734no—
113C22×Q8—732no—
114C22×Q8—731no—
115C22×Q8—1462no—
116C22×Q8—1464no—
117C22×Q8—1462no—
118C22×Q8#6440811yescharacteristic
119C23×C4—731no—
120C23×C4—732no—
121C2×M16—734no—
122C2×M16—738no—
123C2×M16—1464no—
124C2×M16—1462no—
125C22×C8—1462no—
126#101—7316no—
127C24—731no—
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—734no—
131C2×Q8—734no—
132C2×Q8—734no—
133C2×Q8—1464no—
134C2×Q8—1464no—
135C2×Q8—1468no—
136C2×Q8—1468no—
137C2×Q8—1468no—
138C2×Q8—1468no—
139C2×Q8—1462no—
140C2×Q8—1462no—
141C2×Q8C2×#6440814yes—
142C22×C4—731no—
143C22×C4—732no—
144C22×C4—734no—
145C22×C4—732no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4—732no—
149C22×C4—738no—
150C22×C4—1464no—
151C22×C4—1462no—
152C22×C4—1462no—
153C22×C4C2×#6440812yes—
154C22×C4C2×#6440811yescharacteristic
155M16—738no—
156M16—1464no—
157M16—1468no—
158C2×C8—1464no—
159C2×C8—1468no—
160C23—731no—
161C23—732no—
162C23—732no—
163C23—731no—
164C23—1464no—
165C23C22×#6440811yescharacteristic
166Q8—28no—
167Q8—1468no—
168Q8—1468no—
169Q8—1468no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—731no—
173C2×C4—731no—
174C2×C4—732no—
175C2×C4—732no—
176C2×C4—734no—
177C2×C4—734no—
178C2×C4—734no—
179C2×C4—734no—
180C2×C4—734no—
181C2×C4—1468no—
182C2×C4—1468no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4C22⋊#6440812yes—
186C2×C4C22⋊#6440812yes—
187C2×C4C22×#6440814yes—
188C2×C4C22×#6440812yes—
189C8—1468no—
190C22—22no—
191C22—732no—
192C22—734no—
193C22—732no—
194C22—1464no—
195C22—1464no—
196C22—1462no—
197C22C2×C22⋊#6440811yescharacteristic
198C22C2×C22⋊#6440811yescharacteristic
199C22C23×#6440811yescharacteristic
200C4—24no—
201C4—732no—
202C4—732no—
203C4—1464no—
204C4C2×C22⋊#6440814yes—
205C2—21no—
206C2—21no—
207C2—734no—
208C2—1462no—
209C2D73⋊#10112yesdirect product factor
210C2C22×C22⋊#6440811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC22×C73C23×C4
FrattiniC22C23×#64408
FittingC22×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×Q8#64408
hypocenterC73C22×#101
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. D73⋊#101C2direct (N × H)
3. C2×#14556652C2semidirect
10. #14556652C22semidirect
91. C2×D73#101semidirect
101. C2×C73C2×#101semidirect
104. D73C2×#101semidirect
106. C73C22×#101semidirect
209. C2D73⋊#101direct (N × H)