Finite Group Databasebeta

← C2×#17988978 #22620368

Subgroups — C2×#17988978 #22620368

Order 9344.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×Dic292C211yesmaximal, characteristic, complemented
2C22×#11924018C211yesmaximal, characteristic, complemented
3C22×#11924016C211yesmaximal, characteristic
4C2×#14556589C211yesmaximal, characteristic, complemented
5C2×#14556578C211yesmaximal, characteristic
6#17988978C218yesmaximal, direct product factor
7C2×#14556501C211yesmaximal, characteristic, complemented
8C22×SD16×C73C211yesmaximal, characteristic
9C22×Dic146C2211yescharacteristic
10C22×Dic146C2211yescharacteristic
11C2×Dic292—24no—
12C2×Dic292C2214yescomplemented
13C2×#11924018—24no—
14C2×#11924018C2214yescomplemented
15C2×#11924016—24no—
16C2×#11924016C2214yes—
17C22×#10596831C2211yescharacteristic
18#14556589—22no—
19#14556589C2214yescomplemented
20#14556578—22no—
21#14556578C2214yes—
22C2×#11924007—22no—
23C2×C22⋊Dic73—22no—
24C2×C4×Dic73C2211yescharacteristic
25#14556501C2214yescomplemented
26C22×Q8×C73C2211yescharacteristic
27C22×D4×C73C2211yescharacteristic
28C2×SD16×C73—24no—
29C2×SD16×C73C2214yes—
30C22×C8×C73C2211yescharacteristic
31C2×Dic146—22no—
32C2×Dic146—22no—
33C2×Dic146—22no—
34C2×Dic146—22no—
35C2×Dic146—21no—
36C2×Dic146—21no—
37C2×Dic146C2312yes—
38C2×Dic146C2312yes—
39C22×Dic73—21no—
40C22×Dic73—21no—
41C22×Dic73D412yes—
42Dic292—28no—
43#11924018—28no—
44#11924016—28no—
45C2×#10596831D414yes—
46C2×#10596831C2312yes—
47#11924007—28no—
48C22⋊Dic73—28no—
49C4×Dic73D412yes—
50C4×Dic73C2312yes—
51C24×C73—21no—
52C2×Q8×C73—21no—
53C2×Q8×C73—22no—
54C2×Q8×C73—22no—
55C2×Q8×C73C2312yes—
56C2×D4×C73—22no—
57C2×D4×C73—22no—
58C2×D4×C73—21no—
59C2×D4×C73C2312yes—
60C22×C4×C73—21no—
61C22×C4×C73C2311yescharacteristic
62SD16×C73—28no—
63C2×C8×C73D414yes—
64C2×C8×C73C2312yes—
65C23×C73—22no—
66C23×C73—42no—
67C23×C73—44no—
68C23×C73C2×D411yescharacteristic
69Q8×C73—22no—
70Q8×C73—22no—
71Q8×C73—42no—
72D4×C73—22no—
73D4×C73—22no—
74D4×C73—42no—
75C2×C4×C73—22no—
76C2×C4×C73—42no—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D412yes—
79C2×C4×C73C2×D412yes—
80C2×C4×C73C2411yescharacteristic
81C2×Dic73—24no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—42no—
85C2×Dic73—42no—
86C2×Dic73C2×D414yes—
87Dic146—22no—
88Dic146—22no—
89Dic146—22no—
90Dic146—22no—
91Dic146—42no—
92Dic146—42no—
93C8×C73C2×D414yes—
94#10596831C2×D414yes—
95C22×C73—42no—
96C22×C73—44no—
97C22×C73—84no—
98C22×C73#12712yes—
99C22×C73#13714yes—
100C22×C73C22×D411yescharacteristic
101C4×C73—42no—
102C4×C73#12712yes—
103C4×C73C22×D411yescharacteristic
104C4×C73C22×D411yescharacteristic
105Dic73—24no—
106Dic73—42no—
107Dic73—42no—
108C2×C73—82no—
109C2×C73#49714yescomplemented
110C2×C73C2×#12711yescharacteristic
111C2×C73C2×#13712yes—
112C2×#497—731nomaximal, Sylow
113C73C2×#49711yescharacteristic, complemented, Sylow
114C22×Q16—731no—
115C22×Q16—731no—
116C22×SD16—731no—
117C22×SD16D7311yescharacteristic
118C2×C4⋊Q8—731no—
119C2×#124—731no—
120#497—738no—
121C2×#97—731no—
122C22×Q8—731no—
123C22×Q8—731no—
124C22×Q8C2×D7311yescharacteristic
125C22×D4C2×D7311yescharacteristic
126C2×Q16—734no—
127C2×Q16—734no—
128C2×Q16—1464no—
129C2×Q16—1464no—
130C2×SD16—24no—
131C2×SD16—734no—
132C2×SD16—1464no—
133C2×SD16C2×D7314yes—
134C22×C8—731no—
135C22×C8C2×D7311yescharacteristic
136C4⋊Q8—734no—
137C4⋊Q8—1462no—
138#124—734no—
139#124—1462no—
140C2×C4⋊C4—1462no—
141C2×C22⋊C4—1462no—
142C2×C42—731no—
143#97—734no—
144C24—21no—
145C2×Q8—21no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—732no—
149C2×Q8—732no—
150C2×Q8—1462no—
151C2×Q8—1462no—
152C2×Q8—1462no—
153C2×Q8—1462no—
154C2×Q8—1461no—
155C2×Q8—1461no—
156C2×Q8C22×D7312yes—
157C2×D4—22no—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4C22×D7312yes—
161C22×C4—21no—
162C22×C4—732no—
163C22×C4—1461no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166Q16—1468no—
167Q16—1468no—
168SD16—28no—
169SD16—1468no—
170C2×C8—734no—
171C2×C8—732no—
172C2×C8C22⋊D7314yes—
173C2×C8C22×D7312yes—
174C4⋊C4—1468no—
175C22⋊C4—1468no—
176C42—732no—
177C42—732no—
178C23—22no—
179C23—42no—
180C23—44no—
181C23D4×D7311yescharacteristic
182Q8—22no—
183Q8—22no—
184Q8—42no—
185Q8—2922no—
186Q8—2922no—
187Q8—1462no—
188Q8—1462no—
189Q8—1462no—
190Q8—1462no—
191D4—22no—
192D4—22no—
193D4—42no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4—734no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1464no—
202C2×C4D4×D7311yescharacteristic
203C2×C4D4×D7312yes—
204C2×C4C2×C22⋊D7312yes—
205C2×C4C23×D7311yescharacteristic
206C8—734no—
207C8C2×C22⋊D7314yes—
208C22—44no—
209C22—42no—
210C22—84no—
211C22#1455658712yes—
212C22#1455662014yes—
213C22C2×D4×D7311yescharacteristic
214C4—42no—
215C4—2922no—
216C4—2922no—
217C4—1464no—
218C4#1455658712yes—
219C4C2×D4×D7311yescharacteristic
220C4C22×C22⋊D7311yescharacteristic
221C2—82no—
222C2#1798897814yesdirect product factor
223C2C2×#1455658711yescharacteristic
224C2C2×#1455662012yes—
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC22×SD16×C73C2
socleC23×C73C2×D4
hypercenterC22×SD16D73
hypocenterC73C2×#497
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Dic292C2semidirect
2. C22×#11924018C2semidirect
4. C2×#14556589C2semidirect
6. #17988978C2direct (N × H)
7. C2×#14556501C2semidirect
12. C2×Dic292C22semidirect
14. C2×#11924018C22semidirect
19. #14556589C22semidirect
25. #14556501C22semidirect
109. C2×C73#497semidirect
113. C73C2×#497semidirect
222. C2#17988978direct (N × H)