Finite Group Databasebeta

← C2×C23×#2987 #19207873

Subgroups — C2×C23×#2987 #19207873

Order 5888.

1706 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#533C211yesmaximal, characteristic
2C23×#2987C2116yesmaximal, direct product factor
3C2×C23×#446C218yesmaximal, complemented
4C2×C23×#433C214yesmaximal
5C2×C23×#432C212yesmaximal
6C23×#533C418yes—
7C23×#533C2218yes—
8C2×C23×C4⋊Q8C412yes—
9C2×C23×#125C412yes—
10C2×C23×C22⋊Q8C414yes—
11C2×C4×Q8×C23C2214yes—
12C2×C23×#117C2212yes—
13C22×C42×C23C2211yescharacteristic
14C23×#446C22164yescomplemented
15C23×#433C22132yes—
16C23×#432C22116yes—
17C2×C23×C4⋊C8C2214yes—
18C2×C23×C4⋊C8C2218yes—
19C2×C23×C22⋊C8C2214yes—
20C2×C23×#97C2214yes—
21C2×C23×#97C2214yes—
22C2×C4×C8×C23C2214yes—
23C22×Q8×C23C2×C414yes—
24C23×C4×C23C2×C412yes—
25C23×C4×C23C2311yescharacteristic
26C22×C8×C23C2318yes—
27C23×C4⋊Q8C2×C4116yes—
28C23×#125C2×C4116yes—
29C23×C22⋊Q8C2×C4132yes—
30C4×Q8×C23C2×C4116yes—
31C4×Q8×C23C23116yes—
32C23×#117C2×C418yes—
33C23×#117C2318yes—
34C2×C4⋊C4×C23C2×C414yes—
35C2×C4⋊C4×C23C2×C418yes—
36C2×C4⋊C4×C23C2×C414yes—
37C2×C22⋊C4×C23C2×C414yes—
38C2×C42×C23C2×C411yescharacteristic
39C2×C42×C23C2×C411yescharacteristic
40C2×C42×C23C2×C414yes—
41C2×C42×C23C2314yes—
42C2×C42×C23C2314yes—
43C2×C42×C23C2312yes—
44C23×C4⋊C8C23116yes—
45C23×C4⋊C8C23132yes—
46C23×C22⋊C8C23116yes—
47C23×#97C23116yes—
48C23×#97C23116yes—
49C4×C8×C23C23116yes—
50C24×C23C22×C411yescharacteristic
51C2×Q8×C23—48no—
52C2×Q8×C23C22×C4116yes—
53C22×C4×C23—24no—
54C22×C4×C23—44no—
55C22×C4×C23C22×C411yescharacteristic
56C22×C4×C23C22×C412yes—
57C22×C4×C23C22×C412yes—
58C22×C4×C23C22×C412yes—
59C22×C4×C23C22×C418yes—
60C22×C4×C23C22×C418yes—
61C22×C4×C23C2412yes—
62C22×C4×C23C2411yescharacteristic
63C2×C8×C23—216no—
64C2×C8×C23C24116yes—
65C4⋊C4×C23C22×C4116yes—
66C4⋊C4×C23C22×C4132yes—
67C4⋊C4×C23C22×C4116yes—
68C22⋊C4×C23C22×C4116yes—
69C42×C23C22×C414yes—
70C42×C23C22×C414yes—
71C42×C23C22×C414yes—
72C42×C23C22×C418yes—
73C42×C23C2414yes—
74C42×C23C2418yes—
75C2×#2987C2311yesmaximal, characteristic, direct product factor, Sylow
76C23×C23—22no—
77C23×C23—24no—
78C23×C23C23×C412yes—
79C23×C23C23×C411yescharacteristic
80Q8×C23—416no—
81C2×C4×C23—22no—
82C2×C4×C23—24no—
83C2×C4×C23—24no—
84C2×C4×C23—216no—
85C2×C4×C23—24no—
86C2×C4×C23—24no—
87C2×C4×C23—48no—
88C2×C4×C23C23×C412yes—
89C2×C4×C23C23×C414yes—
90C2×C4×C23C23×C414yes—
91C2×C4×C23C23×C4116yes—
92C2×C4×C23C23×C411yescharacteristic
93C2×C4×C232−1+414yes—
94C2×C4×C23C2511yescharacteristic
95C8×C23—216no—
96C2×#533C2×C2311yescharacteristic
97#2987C2×C23116yesdirect product factor
98C2×#446C2×C2318yescomplemented
99C2×#433C2×C2314yes—
100C2×#432C2×C2312yes—
101C22×C23—22no—
102C22×C23—24no—
103C22×C23—44no—
104C22×C23#51912yes—
105C22×C23#56814yes—
106C22×C23C24×C411yescharacteristic
107C4×C23—22no—
108C4×C23—24no—
109C4×C23—24no—
110C4×C23—216no—
111C4×C23#51912yes—
112C4×C23C2×2−1+412yes—
113#533C4×C2318yes—
114#533C22×C2318yes—
115C2×C4⋊Q8C4×C2312yes—
116C2×#125C4×C2312yes—
117C2×C22⋊Q8C4×C2314yes—
118C2×C4×Q8C22×C2314yes—
119C2×#117C22×C2312yes—
120C22×C42C22×C2311yescharacteristic
121#446C22×C23164yescomplemented
122#433C22×C23132yes—
123#432C22×C23116yes—
124C2×C4⋊C8C22×C2314yes—
125C2×C4⋊C8C22×C2318yes—
126C2×C22⋊C8C22×C2314yes—
127C2×#97C22×C2314yes—
128C2×#97C22×C2314yes—
129C2×C4×C8C22×C2314yes—
130C2×C23—42no—
131C2×C23#298714yesdirect product factor
132C2×C23C2×#51911yescharacteristic
133C2×C23C2×#56812yes—
134C22×Q8C2×C4×C2314yes—
135C23×C4C2×C4×C2312yes—
136C23×C4C23×C2311yescharacteristic
137C22×C8C23×C2318yes—
138C4⋊Q8C2×C4×C23116yes—
139#125C2×C4×C23116yes—
140C22⋊Q8C2×C4×C23132yes—
141C4×Q8C2×C4×C23116yes—
142C4×Q8C23×C23116yes—
143#117C2×C4×C2318yes—
144#117C23×C2318yes—
145C2×C4⋊C4C2×C4×C2314yes—
146C2×C4⋊C4C2×C4×C2318yes—
147C2×C4⋊C4C2×C4×C2314yes—
148C2×C22⋊C4C2×C4×C2314yes—
149C2×C42C2×C4×C2311yescharacteristic
150C2×C42C2×C4×C2311yescharacteristic
151C2×C42C2×C4×C2314yes—
152C2×C42C23×C2314yes—
153C2×C42C23×C2312yes—
154C2×C42C23×C2314yes—
155C4⋊C8C23×C23116yes—
156C4⋊C8C23×C23132yes—
157C22⋊C8C23×C23116yes—
158#97C23×C23116yes—
159#97C23×C23116yes—
160C4×C8C23×C23116yes—
161C23C2×#298711yescharacteristic, direct product factor, Sylow
162C24C22×C4×C2311yescharacteristic
163C2×Q8—48no—
164C2×Q8C22×C4×C23116yes—
165C22×C4—24no—
166C22×C4—44no—
167C22×C4C22×C4×C2311yescharacteristic
168C22×C4C22×C4×C2312yes—
169C22×C4C22×C4×C2312yes—
170C22×C4C22×C4×C2312yes—
171C22×C4C22×C4×C2318yes—
172C22×C4C22×C4×C2318yes—
173C22×C4C24×C2312yes—
174C22×C4C24×C2311yescharacteristic
175C2×C8—216no—
176C2×C8C24×C23116yes—
177C4⋊C4C22×C4×C23116yes—
178C4⋊C4C22×C4×C23132yes—
179C4⋊C4C22×C4×C23116yes—
180C22⋊C4C22×C4×C23116yes—
181C42C22×C4×C2314yes—
182C42C22×C4×C2314yes—
183C42C22×C4×C2314yes—
184C42C22×C4×C2318yes—
185C42C24×C2318yes—
186C42C24×C2314yes—
187C23—24no—
188C23—22no—
189C23C23×C4×C2312yes—
190C23C23×C4×C2311yescharacteristic
191Q8—416no—
192C2×C4—24no—
193C2×C4—24no—
194C2×C4—216no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—48no—
199C2×C4C23×C4×C2312yes—
200C2×C4C23×C4×C2314yes—
201C2×C4C23×C4×C2314yes—
202C2×C4C23×C4×C23116yes—
203C2×C4C23×C4×C2311yescharacteristic
204C2×C4C23×2−1+414yes—
205C2×C4C25×C2311yescharacteristic
206C8—216no—
207C22—22no—
208C22—24no—
209C22—44no—
210C22C23×#51912yes—
211C22C23×#56814yes—
212C22C24×C4×C2311yescharacteristic
213C4—22no—
214C4—24no—
215C4—24no—
216C4—216no—
217C4C23×#51912yes—
218C4C2×C23×2−1+412yes—
219C2—42no—
220C2C23×#298714yesdirect product factor
221C2C2×C23×#51911yescharacteristic
222C2C2×C23×#56812yes—
subgroupG/H
centerC22×C4×C23C24
commutatorC22C24×C4×C23
Frattini, cosocleC2×C4C25×C23
socleC23×C23C23×C4
prime radicalC24×C23C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2987C2direct (N × H)
3. C2×C23×#446C2semidirect
14. C23×#446C22semidirect
75. C2×#2987C23direct (N × H)
97. #2987C2×C23direct (N × H)
98. C2×#446C2×C23semidirect
121. #446C22×C23semidirect
131. C2×C23#2987direct (N × H)
161. C23C2×#2987direct (N × H)
220. C2C23×#2987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#5332
C23×#29872
C2×C23×#4462
C2×C23×#4332
C2×C23×#4322
C2×#298723