Finite Group Databasebeta

← C2×C23×#352 #15669738

Subgroups — C2×C23×#352 #15669738

Order 2944.

278 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 88 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×C23×#123C211yesmaximal, characteristic
2C2×C23×#100C211yesmaximal, characteristic
3C2×C23×#99C211yesmaximal, characteristic
4C23×#352C214yesmaximal, direct product factor
5C22×D4×C23C2211yescharacteristic
6C23×C4×C23C411yescharacteristic, complemented
7C2×M16×C23—21no—
8C23×#123—21no—
9C23×#123—21no—
10C23×#123C412yescomplemented
11C23×#123C2212yes—
12C2×C4⋊C4×C23—21no—
13C2×C22⋊C4×C23—21no—
14C2×C22⋊C4×C23—21no—
15C2×C22⋊C4×C23C411yescharacteristic, complemented
16C23×#100—21no—
17C23×#100C2212yes—
18C23×#99—21no—
19C23×#99C2212yes—
20C24×C23C2×C411yescharacteristic
21C24×C23D411yescharacteristic
22C2×D4×C23—41no—
23C2×D4×C23—41no—
24C2×D4×C23C2×C411yescharacteristic
25C2×D4×C23D411yescharacteristic
26C2×D4×C23D411yescharacteristic
27C2×D4×C23C2311yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23—21no—
30C22×C4×C23—21no—
31C22×C4×C23—41no—
32C22×C4×C23—41no—
33C22×C4×C23—41no—
34C22×C4×C23C2×C412yescomplemented
35C22×C4×C23D411yescharacteristic
36M16×C23—22no—
37M16×C23—41no—
38C2×C8×C23—41no—
39C4⋊C4×C23—22no—
40C4⋊C4×C23—22no—
41C22⋊C4×C23—22no—
42C22⋊C4×C23—21no—
43C22⋊C4×C23—22no—
44C22⋊C4×C23—22no—
45C22⋊C4×C23—41no—
46C22⋊C4×C23C2×C412yescomplemented
47C23×C23—21no—
48C23×C23—21no—
49C23×C23—21no—
50C23×C23—21no—
51C23×C23—42no—
52C23×C23—42no—
53C23×C23C22⋊C411yescharacteristic
54C23×C23C22⋊C411yescharacteristic
55C23×C23C22⋊C411yescharacteristic
56C23×C23C22×C411yescharacteristic
57C23×C23C2×D411yescharacteristic
58D4×C23—41no—
59D4×C23—41no—
60D4×C23—41no—
61D4×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—22no—
65C2×C4×C23—22no—
66C2×C4×C23—42no—
67C2×C4×C23—42no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23—42no—
71C2×C4×C23—42no—
72C2×C4×C23—82no—
73C2×C4×C23C22⋊C411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C8×C23—42no—
76C2×#352C2311yesmaximal, characteristic, direct product factor, Sylow
77C22×C23—22no—
78C22×C23—21no—
79C22×C23—21no—
80C22×C23—21no—
81C22×C23—21no—
82C22×C23—41no—
83C22×C23—41no—
84C22×C23—41no—
85C22×C23—41no—
86C22×C23—42no—
87C22×C23—42no—
88C22×C23—42no—
89C22×C23—81no—
90C22×C23#9911yescharacteristic
91C22×C23#9911yescharacteristic
92C22×C23C2×C22⋊C411yescharacteristic
93C4×C23—21no—
94C4×C23—21no—
95C4×C23—42no—
96C4×C23—42no—
97C4×C23—82no—
98C2×#123C2×C2311yescharacteristic
99C2×#100C2×C2311yescharacteristic
100C2×#99C2×C2311yescharacteristic
101#352C2×C2314yesdirect product factor
102C2×C23—21no—
103C2×C23—21no—
104C2×C23—41no—
105C2×C23—41no—
106C2×C23—41no—
107C2×C23—41no—
108C2×C23#35212yesdirect product factor
109C2×C23C2×#9911yescharacteristic
110C22×D4C22×C2311yescharacteristic
111C23×C4C4×C2311yescharacteristic, complemented
112C2×M16—21no—
113#123—21no—
114#123—21no—
115#123C4×C2312yescomplemented
116#123C22×C2312yes—
117C2×C4⋊C4—21no—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4C4×C2311yescharacteristic, complemented
121#100—21no—
122#100C22×C2312yes—
123#99—21no—
124#99C22×C2312yes—
125C23C2×#35211yescharacteristic, direct product factor, Sylow
126C24C2×C4×C2311yescharacteristic
127C24D4×C2311yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×C4×C2311yescharacteristic
131C2×D4D4×C2311yescharacteristic
132C2×D4D4×C2311yescharacteristic
133C2×D4C23×C2311yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4C2×C4×C2312yescomplemented
141C22×C4D4×C2311yescharacteristic
142M16—22no—
143M16—41no—
144C2×C8—41no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C22⋊C4—22no—
150C22⋊C4—22no—
151C22⋊C4—41no—
152C22⋊C4C2×C4×C2312yescomplemented
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23C22⋊C4×C2311yescharacteristic
160C23C22⋊C4×C2311yescharacteristic
161C23C22⋊C4×C2311yescharacteristic
162C23C22×C4×C2311yescharacteristic
163C23C2×D4×C2311yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—82no—
179C2×C4C22⋊C4×C2311yescharacteristic
180C2×C4C2×D4×C2311yescharacteristic
181C8—42no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22C23×#9911yescharacteristic
196C22C23×#9911yescharacteristic
197C22C2×C22⋊C4×C2311yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2C23×#35212yesdirect product factor
210C2C2×C23×#9911yescharacteristic
subgroupG/H
center, socleC22×C23#99
commutatorC23C22×C4×C23
Frattini, cosocleC2×D4C23×C23
prime radicalC22×D4×C23C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C23 ◁ C22×D4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
4. C23×#352C2direct (N × H)
6. C23×C4×C23C4semidirect
10. C23×#123C4semidirect
15. C2×C22⋊C4×C23C4semidirect
34. C22×C4×C23C2×C4semidirect
46. C22⋊C4×C23C2×C4semidirect
76. C2×#352C23direct (N × H)
101. #352C2×C23direct (N × H)
108. C2×C23#352direct (N × H)
111. C23×C4C4×C23semidirect
115. #123C4×C23semidirect
120. C2×C22⋊C4C4×C23semidirect
125. C23C2×#352direct (N × H)
140. C22×C4C2×C4×C23semidirect
152. C22⋊C4C2×C4×C23semidirect
209. C2C23×#352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#1232
C2×C23×#1002
C2×C23×#992
C23×#3522
C2×#35223