Finite Group Databasebeta

← C2×#14272066 #16835742

Subgroups — C2×#14272066 #16835742

Order 3712.

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×#11745229C211yesmaximal, characteristic
2C2×#11745227C211yesmaximal, characteristic
3#14272066C214yesmaximal, direct product factor
4C2×#11745248C211yesmaximal, characteristic
5C22×C22⋊D29C2211yescharacteristic
6C23×Dic29C411yescharacteristic, complemented
7C2×C22⋊#1181—21no—
8C2×#90800—21no—
9C2×C22⋊C4×C29C411yescharacteristic, complemented
10C2×#90781—21no—
11C2×C4⋊Dic29—21no—
12#11745248—21no—
13#11745248—21no—
14#11745248C412yescomplemented
15#11745248C2212yes—
16#11745229—21no—
17#11745229C2212yes—
18#11745227—21no—
19#11745227C2212yes—
20C24×C29C2×C411yescharacteristic
21C23×D29D411yescharacteristic
22C22×#1181—41no—
23C22×C4×C29—21no—
24C2×C22⋊D29—41no—
25C2×C22⋊D29—41no—
26C2×C22⋊D29C2×C411yescharacteristic
27C2×C22⋊D29D411yescharacteristic
28C2×C22⋊D29D411yescharacteristic
29C2×C22⋊D29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C22×Dic29—41no—
33C22×Dic29—41no—
34C22×Dic29C2×C412yescomplemented
35C22×Dic29D411yescharacteristic
36C22⋊#1181—22no—
37C22⋊#1181—41no—
38#90800—22no—
39#90800—41no—
40C2×#6599—41no—
41C22⋊C4×C29—21no—
42C22⋊C4×C29C2×C412yescomplemented
43#90781—22no—
44#90781—22no—
45C4⋊Dic29—22no—
46C4⋊Dic29—22no—
47C23×C29—21no—
48C23×C29—21no—
49C23×C29—42no—
50C23×C29C22⋊C411yescharacteristic
51C23×C29C22⋊C411yescharacteristic
52C23×C29C22×C411yescharacteristic
53C22×D29—21no—
54C22×D29—21no—
55C22×D29—42no—
56C22×D29C22⋊C411yescharacteristic
57C22×D29C2×D411yescharacteristic
58C2×#1181—42no—
59C2×#1181—82no—
60C2×C4×C29—22no—
61C2×C4×C29—42no—
62C22⋊D29—41no—
63C22⋊D29—41no—
64C22⋊D29—41no—
65C22⋊D29—41no—
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29—22no—
69C2×Dic29—42no—
70C2×Dic29—41no—
71C2×Dic29—41no—
72C2×Dic29—42no—
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C2×D411yescharacteristic
75#6599—42no—
76C2×#352—291nomaximal, Sylow
77C22×C29—22no—
78C22×C29—21no—
79C22×C29—21no—
80C22×C29—41no—
81C22×C29—41no—
82C22×C29—42no—
83C22×C29—42no—
84C22×C29#9911yescharacteristic
85C22×C29#9911yescharacteristic
86C22×C29C2×C22⋊C411yescharacteristic
87C2×D29—21no—
88C2×D29—21no—
89C2×D29—42no—
90C2×D29—41no—
91C2×D29—41no—
92C2×D29—81no—
93#1181—82no—
94C4×C29—42no—
95Dic29—21no—
96Dic29—21no—
97Dic29—42no—
98C2×#123—291no—
99C2×#100—291no—
100C2×#99—291no—
101#352—294no—
102C2×C29—21no—
103C2×C29—21no—
104C2×C29—41no—
105C2×C29—41no—
106C2×C29#35212yescomplemented
107C2×C29C2×#9911yescharacteristic
108D29—41no—
109D29—41no—
110C22×D4—291no—
111C23×C4—291no—
112C2×M16—581no—
113#123—292no—
114#123—292no—
115#123—581no—
116#123—581no—
117C2×C4⋊C4—581no—
118C2×C22⋊C4—581no—
119C2×C22⋊C4—581no—
120C2×C22⋊C4#118111yescharacteristic, complemented
121#100—292no—
122#100—581no—
123#99—292no—
124#99—581no—
125C29C2×#35211yescharacteristic, complemented, Sylow
126C24—291no—
127C24C2×#118111yescharacteristic
128C2×D4—291no—
129C2×D4—291no—
130C2×D4—291no—
131C2×D4—291no—
132C2×D4—1161no—
133C2×D4—1161no—
134C22×C4—21no—
135C22×C4—291no—
136C22×C4—292no—
137C22×C4—581no—
138C22×C4—581no—
139C22×C4—1161no—
140C22×C4—1161no—
141C22×C4—1161no—
142M16—582no—
143M16—1161no—
144C2×C8—1161no—
145C4⋊C4—582no—
146C4⋊C4—582no—
147C22⋊C4—21no—
148C22⋊C4—582no—
149C22⋊C4—582no—
150C22⋊C4—582no—
151C22⋊C4—1161no—
152C22⋊C4C2×#118112yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—291no—
157C23—291no—
158C23—581no—
159C23—581no—
160C23—1162no—
161C23C22⋊#118111yescharacteristic
162C23C22⋊#118111yescharacteristic
163C23C22×#118111yescharacteristic
164D4—1161no—
165D4—1161no—
166D4—1161no—
167D4—1161no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—291no—
171C2×C4—291no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—582no—
175C2×C4—1162no—
176C2×C4—1161no—
177C2×C4—1161no—
178C2×C4—1162no—
179C2×C4—1162no—
180C2×C4—2322no—
181C8—1162no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—581no—
190C22—581no—
191C22—1161no—
192C22—1161no—
193C22—1162no—
194C22—2321no—
195C22#1174521511yescharacteristic
196C22#1174521511yescharacteristic
197C22C2×C22⋊#118111yescharacteristic
198C4—42no—
199C4—581no—
200C4—581no—
201C4—1162no—
202C4—2322no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—1161no—
208C2—1161no—
209C2#1427206612yesdirect product factor
210C2C2×#1174521511yescharacteristic
subgroupG/H
centerC22#11745215
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29#99
prime radicalC22×C22⋊D29C22
cosocleC2×C22⋊D29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29C2×#352
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14272066C2direct (N × H)
6. C23×Dic29C4semidirect
9. C2×C22⋊C4×C29C4semidirect
14. #11745248C4semidirect
34. C22×Dic29C2×C4semidirect
42. C22⋊C4×C29C2×C4semidirect
106. C2×C29#352semidirect
120. C2×C22⋊C4#1181semidirect
125. C29C2×#352semidirect
152. C22⋊C4C2×#1181semidirect
209. C2#14272066direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117452292
C2×#117452272
#142720662
C2×#117452482
C2×#35229