Finite Group Databasebeta

← C23×#2655 #15670274

Subgroups — C23×#2655 #15670274

Order 2944.

344 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#401C211yesmaximal, characteristic
2C23×#400C211yesmaximal, characteristic
3C23×#400C211yesmaximal, characteristic
4C23×#400C211yesmaximal, characteristic
5C23×#400C211yesmaximal, characteristic
6C23×#398C211yesmaximal, characteristic
7C23×#398C211yesmaximal, characteristic
8C23×#398C211yesmaximal, characteristic
9C23×#389C211yesmaximal, characteristic
10C23×#387C211yesmaximal, characteristic
11C23×#387C211yesmaximal, characteristic
12C23×#387C211yesmaximal, characteristic
13C23×#387C211yesmaximal, characteristic
14C23×#387C211yesmaximal, characteristic
15C4×C4⋊C4×C23C211yesmaximal, characteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18C2×C4⋊C4×C23C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20C2×C4⋊C4×C23C2211yescharacteristic
21C2×C4⋊C4×C23C2211yescharacteristic
22C2×C4⋊C4×C23C2211yescharacteristic
23C2×C4⋊C4×C23C2211yescharacteristic
24C2×C4⋊C4×C23C2211yescharacteristic
25C2×C4⋊C4×C23C2211yescharacteristic
26C2×C4⋊C4×C23C2211yescharacteristic
27C2×C4⋊C4×C23C2211yescharacteristic
28C2×C42×C23C2211yescharacteristic
29C2×C42×C23C2211yescharacteristic
30C2×C42×C23C2211yescharacteristic
31C23×#95C2211yescharacteristic
32C23×#95C2211yescharacteristic
33C23×#95C2211yescharacteristic
34C23×#95C2211yescharacteristic
35C23×#95C2211yescharacteristic
36C23×#95C2211yescharacteristic
37C23×#95C2211yescharacteristic
38C23×#95C2211yescharacteristic
39C23×#95C2211yescharacteristic
40C23×#95C2211yescharacteristic
41C23×#95C2211yescharacteristic
42C23×#95C2211yescharacteristic
43C23×#95C2211yescharacteristic
44C23×#95C2211yescharacteristic
45C23×#95C2211yescharacteristic
46C23×#95C2211yescharacteristic
47C23×#95C2211yescharacteristic
48C23×#95C2211yescharacteristic
49C23×#95C2211yescharacteristic
50C23×#95C2211yescharacteristic
51C22×C4×C23C2311yescharacteristic
52C22×C4×C23C2311yescharacteristic
53C22×C4×C23C2311yescharacteristic
54C22×C4×C23C2311yescharacteristic
55C22×C4×C23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C22×C4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C4⋊C4×C23—22no—
67C4⋊C4×C23—22no—
68C4⋊C4×C23—22no—
69C4⋊C4×C23—22no—
70C4⋊C4×C23—22no—
71C4⋊C4×C23—22no—
72C4⋊C4×C23—22no—
73C4⋊C4×C23—22no—
74C4⋊C4×C23—41no—
75C4⋊C4×C23—41no—
76C4⋊C4×C23—41no—
77C4⋊C4×C23—41no—
78C42×C23—22no—
79C42×C23—41no—
80C42×C23—41no—
81C23×C23C2411yescharacteristic
82C2×C4×C23—21no—
83C2×C4×C23—21no—
84C2×C4×C23—21no—
85C2×C4×C23—21no—
86C2×C4×C23—21no—
87C2×C4×C23—21no—
88C2×C4×C23—21no—
89C2×C4×C23—21no—
90C2×C4×C23—21no—
91C2×C4×C23—21no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—21no—
96C2×C4×C23—21no—
97C2×C4×C23—21no—
98C2×C4×C23—21no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
105C2×C4×C23—21no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23#4112yes—
125C2×C4×C23#4112yes—
126C2×C4×C23#4112yes—
127#2655C2311yesmaximal, characteristic, direct product factor, Sylow
128C22×C23C2×#4111yescharacteristic
129C22×C23C2×#4111yescharacteristic
130C22×C23C2×#4111yescharacteristic
131C22×C23H(5,𝔽2)11yescharacteristic
132C22×C232−1+411yescharacteristic
133C22×C232−1+411yescharacteristic
134C22×C232−1+411yescharacteristic
135C4×C23—22no—
136C4×C23—22no—
137C4×C23—22no—
138C4×C23—41no—
139C4×C23—41no—
140C4×C23—41no—
141C4×C23—41no—
142C4×C23—41no—
143C4×C23—41no—
144C4×C23—41no—
145C4×C23—41no—
146C4×C23—41no—
147C4×C23—41no—
148C4×C23—41no—
149C4×C23—41no—
150#401C2×C2311yescharacteristic
151#400C2×C2311yescharacteristic
152#400C2×C2311yescharacteristic
153#400C2×C2311yescharacteristic
154#400C2×C2311yescharacteristic
155#398C2×C2311yescharacteristic
156#398C2×C2311yescharacteristic
157#398C2×C2311yescharacteristic
158#389C2×C2311yescharacteristic
159#387C2×C2311yescharacteristic
160#387C2×C2311yescharacteristic
161#387C2×C2311yescharacteristic
162#387C2×C2311yescharacteristic
163#387C2×C2311yescharacteristic
164C4×C4⋊C4C2×C2311yescharacteristic
165C2×C23#52911yescharacteristic
166C2×C23#53911yescharacteristic
167C2×C23#53911yescharacteristic
168C2×C23#54111yescharacteristic
169C2×C23#54111yescharacteristic
170C2×C23#54111yescharacteristic
171C2×C23#54211yescharacteristic
172C2×C4⋊C4C22×C2311yescharacteristic
173C2×C4⋊C4C22×C2311yescharacteristic
174C2×C4⋊C4C22×C2311yescharacteristic
175C2×C4⋊C4C22×C2311yescharacteristic
176C2×C4⋊C4C22×C2311yescharacteristic
177C2×C4⋊C4C22×C2311yescharacteristic
178C2×C4⋊C4C22×C2311yescharacteristic
179C2×C4⋊C4C22×C2311yescharacteristic
180C2×C4⋊C4C22×C2311yescharacteristic
181C2×C4⋊C4C22×C2311yescharacteristic
182C2×C4⋊C4C22×C2311yescharacteristic
183C2×C4⋊C4C22×C2311yescharacteristic
184C2×C42C22×C2311yescharacteristic
185C2×C42C22×C2311yescharacteristic
186C2×C42C22×C2311yescharacteristic
187#95C22×C2311yescharacteristic
188#95C22×C2311yescharacteristic
189#95C22×C2311yescharacteristic
190#95C22×C2311yescharacteristic
191#95C22×C2311yescharacteristic
192#95C22×C2311yescharacteristic
193#95C22×C2311yescharacteristic
194#95C22×C2311yescharacteristic
195#95C22×C2311yescharacteristic
196#95C22×C2311yescharacteristic
197#95C22×C2311yescharacteristic
198#95C22×C2311yescharacteristic
199#95C22×C2311yescharacteristic
200#95C22×C2311yescharacteristic
201#95C22×C2311yescharacteristic
202#95C22×C2311yescharacteristic
203#95C22×C2311yescharacteristic
204#95C22×C2311yescharacteristic
205#95C22×C2311yescharacteristic
206#95C22×C2311yescharacteristic
207C23#265511yescharacteristic, direct product factor, Sylow
208C22×C4C23×C2311yescharacteristic
209C22×C4C23×C2311yescharacteristic
210C22×C4C23×C2311yescharacteristic
211C22×C4C23×C2311yescharacteristic
212C22×C4C23×C2311yescharacteristic
213C22×C4C23×C2311yescharacteristic
214C22×C4C23×C2311yescharacteristic
215C22×C4C23×C2311yescharacteristic
216C22×C4C23×C2311yescharacteristic
217C22×C4C23×C2311yescharacteristic
218C22×C4C23×C2311yescharacteristic
219C22×C4C23×C2311yescharacteristic
220C22×C4C23×C2311yescharacteristic
221C22×C4C23×C2311yescharacteristic
222C22×C4C23×C2311yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C42—22no—
236C42—41no—
237C42—41no—
238C23C24×C2311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4#41×C2312yes—
282C2×C4#41×C2312yes—
283C2×C4#41×C2312yes—
284C22C2×#41×C2311yescharacteristic
285C22C2×#41×C2311yescharacteristic
286C22C2×#41×C2311yescharacteristic
287C22C23×H(5,𝔽2)11yescharacteristic
288C22C23×2−1+411yescharacteristic
289C22C23×2−1+411yescharacteristic
290C22C23×2−1+411yescharacteristic
291C4—22no—
292C4—22no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C2C23×#52911yescharacteristic
307C2C23×#53911yescharacteristic
308C2C23×#53911yescharacteristic
309C2C23×#54111yescharacteristic
310C2C23×#54111yescharacteristic
311C2C23×#54111yescharacteristic
312C2C23×#54211yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C23C24
commutator, Frattini, cosocleC23C24×C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

Complements

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

NH ≅ G/Ntype
127. #2655C23direct (N × H)
207. C23#2655direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#4012
C23×#4002
C23×#3982
C23×#3892
C23×#3872
C4×C4⋊C4×C232
#265523