Finite Group Databasebeta

← C2×#17989490 #22626181

Subgroups — C2×#17989490 #22626181

Order 9344.

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

normal subgroups only

This group has 278 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
1C2×#14556651C211yesmaximal, characteristic
2C2×#14556649C211yesmaximal, characteristic
3#17989490C214yesmaximal, direct product factor
4C2×#14556575C211yesmaximal, characteristic
5C2×#11924037—21no—
6C2×C22⋊#64408—21no—
7#14556651—21no—
8#14556651C2212yes—
9#14556649—21no—
10#14556649C2212yes—
11C22×C22⋊D73C2211yescharacteristic
12C23×Dic73C411yescharacteristic, complemented
13#14556575—21no—
14#14556575—21no—
15#14556575C412yescomplemented
16#14556575C2212yes—
17C2×C4⋊Dic73—21no—
18C2×#11924005—21no—
19C2×C22⋊C4×C73C411yescharacteristic, complemented
20C22×#64408—41no—
21#11924037—22no—
22#11924037—41no—
23C2×#10596833—41no—
24C22⋊#64408—22no—
25C22⋊#64408—41no—
26C23×D73D411yescharacteristic
27C2×C22⋊D73—41no—
28C2×C22⋊D73—41no—
29C2×C22⋊D73C2×C411yescharacteristic
30C2×C22⋊D73D411yescharacteristic
31C2×C22⋊D73D411yescharacteristic
32C2×C22⋊D73C2311yescharacteristic
33C22×Dic73—21no—
34C22×Dic73—21no—
35C22×Dic73—41no—
36C22×Dic73—41no—
37C22×Dic73C2×C412yescomplemented
38C22×Dic73D411yescharacteristic
39C4⋊Dic73—22no—
40C4⋊Dic73—22no—
41#11924005—22no—
42#11924005—22no—
43C24×C73C2×C411yescharacteristic
44C22×C4×C73—21no—
45C22⋊C4×C73—21no—
46C22⋊C4×C73C2×C412yescomplemented
47C23×C73—21no—
48C23×C73—21no—
49C23×C73—42no—
50C23×C73C22⋊C411yescharacteristic
51C23×C73C22⋊C411yescharacteristic
52C23×C73C22×C411yescharacteristic
53C22×D73—21no—
54C22×D73—21no—
55C22×D73—42no—
56C22×D73C22⋊C411yescharacteristic
57C22×D73C2×D411yescharacteristic
58C2×#64408—42no—
59C2×#64408—82no—
60C2×C4×C73—22no—
61C2×C4×C73—42no—
62C22⋊D73—41no—
63C22⋊D73—41no—
64C22⋊D73—41no—
65C22⋊D73—41no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—22no—
69C2×Dic73—42no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73—42no—
73C2×Dic73C22⋊C411yescharacteristic
74C2×Dic73C2×D411yescharacteristic
75#10596833—42no—
76C22×C73—22no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73—42no—
82C22×C73—42no—
83C22×C73#9911yescharacteristic
84C22×C73#9911yescharacteristic
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—42no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73—81no—
92#64408—82no—
93C4×C73—42no—
94Dic73—21no—
95Dic73—21no—
96Dic73—42no—
97C2×C73—21no—
98C2×C73—21no—
99C2×C73—41no—
100C2×C73—41no—
101C2×C73#35212yescomplemented
102C2×C73C2×#9911yescharacteristic
103D73—41no—
104D73—41no—
105C2×#352—731nomaximal, Sylow
106C73C2×#35211yescharacteristic, complemented, Sylow
107C2×#123—731no—
108C2×#100—731no—
109C2×#99—731no—
110#352—734no—
111C22×D4—731no—
112C23×C4—731no—
113C2×M16—1461no—
114#123—732no—
115#123—732no—
116#123—1461no—
117#123—1461no—
118C2×C4⋊C4—1461no—
119C2×C22⋊C4—1461no—
120C2×C22⋊C4—1461no—
121C2×C22⋊C4#6440811yescharacteristic, complemented
122#100—732no—
123#100—1461no—
124#99—732no—
125#99—1461no—
126C24—731no—
127C24C2×#6440811yescharacteristic
128C2×D4—2921no—
129C2×D4—2921no—
130C2×D4—731no—
131C2×D4—731no—
132C2×D4—731no—
133C2×D4—731no—
134C22×C4—21no—
135C22×C4—2921no—
136C22×C4—2921no—
137C22×C4—2921no—
138C22×C4—732no—
139C22×C4—731no—
140C22×C4—1461no—
141C22×C4—1461no—
142M16—2921no—
143M16—1462no—
144C2×C8—2921no—
145C4⋊C4—1462no—
146C4⋊C4—1462no—
147C22⋊C4—21no—
148C22⋊C4—2921no—
149C22⋊C4—1462no—
150C22⋊C4—1462no—
151C22⋊C4—1462no—
152C22⋊C4C2×#6440812yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—2922no—
157C23—731no—
158C23—731no—
159C23—1461no—
160C23—1461no—
161C23C22⋊#6440811yescharacteristic
162C23C22⋊#6440811yescharacteristic
163C23C22×#6440811yescharacteristic
164D4—2921no—
165D4—2921no—
166D4—2921no—
167D4—2921no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—2922no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—2922no—
174C2×C4—2922no—
175C2×C4—5842no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4—1462no—
179C2×C4—1461no—
180C2×C4—1461no—
181C8—2922no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—2921no—
190C22—2921no—
191C22—2922no—
192C22—5841no—
193C22—1461no—
194C22—1461no—
195C22#1455665011yescharacteristic
196C22#1455665011yescharacteristic
197C22C2×C22⋊#6440811yescharacteristic
198C4—42no—
199C4—2922no—
200C4—5842no—
201C4—1461no—
202C4—1461no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—2921no—
208C2—2921no—
209C2#1798949012yesdirect product factor
210C2C2×#1455665011yescharacteristic
subgroupG/H
centerC22#14556650
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73#99
hypercenterC2×C22⋊C4#64408
hypocenterC73C2×#352
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #17989490C2direct (N × H)
12. C23×Dic73C4semidirect
15. #14556575C4semidirect
19. C2×C22⋊C4×C73C4semidirect
37. C22×Dic73C2×C4semidirect
46. C22⋊C4×C73C2×C4semidirect
101. C2×C73#352semidirect
106. C73C2×#352semidirect
121. C2×C22⋊C4#64408semidirect
152. C22⋊C4C2×#64408semidirect
209. C2#17989490direct (N × H)