Finite Group Databasebeta

← C2×#17989673 #22627042

Subgroups — C2×#17989673 #22627042

Order 9344.

328 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 79 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×C22⋊#10596842C212yesmaximal
2#17989673C214yesmaximal, direct product factor
3C22×C4⋊#64408C211yesmaximal, characteristic
4C22×#10596842—22no—
5C22⋊#10596842—22no—
6C22⋊#10596842C2214yes—
7C23×#64408C411yescharacteristic
8C23×#64408C2211yescharacteristic
9C2×C4⋊#64408—22no—
10C2×C4⋊#64408—22no—
11C2×C4⋊#64408C412yes—
12C2×C4⋊#64408C2212yes—
13C22×C4×D73C411yescharacteristic
14C2×#10596842—24no—
15C2×#10596842—44no—
16C22×#64408—21no—
17C22×#64408—21no—
18C22×#64408—42no—
19C22×#64408—42no—
20C22×#64408C2×C412yes—
21C22×#64408C2×C411yescharacteristic
22C22×#64408D412yes—
23C22×#64408D412yes—
24C22×#64408C2311yescharacteristic
25C4⋊#64408—24no—
26C4⋊#64408—24no—
27C23×D73C2×C411yescharacteristic
28C22×Dic73C811yescharacteristic, complemented
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—21no—
32C2×C4×D73—21no—
33C2×C4×D73C812yescomplemented
34C2×C4×D73C2×C412yes—
35C22×C4×C73C811yescharacteristic, complemented
36C23×C73C2×C811yescharacteristic
37C22×D73—22no—
38C22×D73—22no—
39C22×D73C22⋊C411yescharacteristic
40C22×D73C22⋊C411yescharacteristic
41C22×D73C2×C811yescharacteristic
42C22×D73M1611yescharacteristic
43C22×D73M1611yescharacteristic
44C22×D73C22×C411yescharacteristic
45C2×#64408—24no—
46C2×#64408—22no—
47C2×#64408—41no—
48C2×#64408—42no—
49C2×#64408—41no—
50C2×#64408—42no—
51C2×#64408—42no—
52C2×#64408—42no—
53C2×#64408C22⋊C412yes—
54C2×#64408C2×D412yes—
55#10596842—44no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73C2×C812yescomplemented
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73C2×C812yescomplemented
62C4×D73—22no—
63C4×D73—22no—
64C4×D73—22no—
65C4×D73—22no—
66C22×C73—22no—
67C22×C73C22⋊C811yescharacteristic
68C22×C73C22⋊C811yescharacteristic
69C22×C73C22×C811yescharacteristic
70C2×D73—22no—
71C2×D73—22no—
72C2×D73—22no—
73C2×D73—21no—
74C2×D73—21no—
75C2×D73—21no—
76C2×D73—21no—
77C2×D73C22⋊C811yescharacteristic
78C2×D73C22⋊C811yescharacteristic
79C2×D73#9912yes—
80C2×D73#10112yes—
81C2×D73C2×C22⋊C411yescharacteristic
82C2×D73C2×M1611yescharacteristic
83#64408—22no—
84#64408—22no—
85#64408—42no—
86C4×C73—22no—
87Dic73—22no—
88C2×C73—21no—
89C2×C73—21no—
90C2×C73#32412yescomplemented
91C2×C73C2×C22⋊C811yescharacteristic
92D73—21no—
93D73—21no—
94D73#32412yescomplemented
95D73C2×#9911yescharacteristic
96D73C2×#10111yescharacteristic
97C2×#324—731nomaximal, Sylow
98C73C2×#32411yescharacteristic, complemented, Sylow
99C22×C4⋊C4—731no—
100C2×C22⋊C8—732no—
101#324—734no—
102C23×C4—731no—
103C23×C4—731no—
104C23×C4—731no—
105C22×C8—1462no—
106C2×C4⋊C4—732no—
107C2×C4⋊C4—732no—
108C2×C4⋊C4—1462no—
109C2×C4⋊C4—1462no—
110C22⋊C8—734no—
111C22⋊C8—1462no—
112C24—731no—
113C22×C4—2922no—
114C22×C4—2922no—
115C22×C4—731no—
116C22×C4—732no—
117C22×C4—731no—
118C22×C4—732no—
119C22×C4—732no—
120C22×C4—731no—
121C22×C4—732no—
122C22×C4—732no—
123C22×C4—1461no—
124C22×C4—1461no—
125C22×C4—1461no—
126C22×C4—1461no—
127C22×C4—1461no—
128C22×C4—1461no—
129C22×C4#1059684211yescharacteristic, complemented
130C2×C8—2924no—
131C2×C8—1464no—
132C4⋊C4—1464no—
133C4⋊C4—1464no—
134C23—731no—
135C23—731no—
136C23—731no—
137C23—731no—
138C23—731no—
139C23—731no—
140C23—1462no—
141C23—1462no—
142C23C2×#1059684211yescharacteristic
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2922no—
146C2×C4—2922no—
147C2×C4—2922no—
148C2×C4—2921no—
149C2×C4—2922no—
150C2×C4—2921no—
151C2×C4—732no—
152C2×C4—732no—
153C2×C4—732no—
154C2×C4—1462no—
155C2×C4—1462no—
156C2×C4—1462no—
157C2×C4—1462no—
158C2×C4—1462no—
159C2×C4—1464no—
160C2×C4—1461no—
161C2×C4—1461no—
162C2×C4C2×#1059684212yescomplemented
163C8—2924no—
164C22—22no—
165C22—732no—
166C22—732no—
167C22—731no—
168C22—731no—
169C22—731no—
170C22—731no—
171C22—1461no—
172C22—1461no—
173C22—1462no—
174C22—1461no—
175C22—1462no—
176C22—1461no—
177C22—1462no—
178C22C22⋊#1059684211yescharacteristic
179C22C22⋊#1059684211yescharacteristic
180C22C22×#1059684211yescharacteristic
181C4—22no—
182C4—2922no—
183C4—1462no—
184C4—1462no—
185C4—1462no—
186C2—21no—
187C2—21no—
188C2—731no—
189C2—732no—
190C2—731no—
191C2—1461no—
192C2—1461no—
193C2#1798967312yesdirect product factor
194C2C2×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC22×C73C22×C8
FrattiniC22C22×#10596842
FittingC22×C4×C73C8
socleC22×C73C22⋊C8
hypercenterC22×C4#10596842
hypocenterC73C2×#324
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #17989673C2direct (N × H)
28. C22×Dic73C8semidirect
33. C2×C4×D73C8semidirect
35. C22×C4×C73C8semidirect
58. C2×C4×C73C2×C8semidirect
61. C2×Dic73C2×C8semidirect
90. C2×C73#324semidirect
94. D73#324semidirect
98. C73C2×#324semidirect
129. C22×C4#10596842semidirect
162. C2×C4C2×#10596842semidirect
193. C2#17989673direct (N × H)