Finite Group Databasebeta

← C23×#10441 #19158067

Subgroups — C23×#10441 #19158067

Order 5888.

492 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#459C211yesmaximal, characteristic
2C23×#1800C211yesmaximal, characteristic, complemented
3C23×#1570C211yesmaximal, characteristic, complemented
4C23×#1545C211yesmaximal, characteristic, complemented
5C23×#1545C211yesmaximal, characteristic, complemented
6C23×#1478C211yesmaximal, characteristic, complemented
7C23×#1301C211yesmaximal, characteristic, complemented
8C22×D8×C23—21no—
9C2×C23×#127C2211yescharacteristic
10C2×C4×D4×C23C2211yescharacteristic
11C23×#459—22no—
12C23×#459—22no—
13C23×#431C2211yescharacteristic
14C23×#431C2211yescharacteristic
15C23×#423C2211yescharacteristic
16C23×#423C2211yescharacteristic
17C2×C23×C4⋊C8C2211yescharacteristic
18C2×C23×#102—21no—
19C2×C23×#100—21no—
20C23×#343—21no—
21C23×#334—22no—
22C23×#331—22no—
23C23×#331—22no—
24C23×D4⋊C8—22no—
25C22×D4×C23—21no—
26C22×D4×C23—21no—
27C22×D4×C23—21no—
28C22×D4×C23D411yescharacteristic
29C23×C4×C23—21no—
30C2×D8×C23—24no—
31C2×D8×C23—42no—
32C2×D8×C23—42no—
33C2×M16×C23—21no—
34C2×M16×C23—21no—
35C22×C8×C23—21no—
36C23×#127—21no—
37C23×#127—21no—
38C23×#127—21no—
39C23×#127D412yes—
40C4×D4×C23—21no—
41C4×D4×C23—21no—
42C4×D4×C23—21no—
43C4×D4×C23—21no—
44C2×C4⋊C4×C23D411yescharacteristic
45C2×C22⋊C4×C23—21no—
46C2×C42×C23C2311yescharacteristic
47C23×C4⋊C8—21no—
48C23×C4⋊C8—21no—
49C23×C4⋊C8—21no—
50C23×C4⋊C8—21no—
51C23×C4⋊C8—21no—
52C23×C4⋊C8—21no—
53C23×C4⋊C8D412yes—
54C23×C4⋊C8D412yes—
55C23×#102—24no—
56C23×#100—42no—
57C23×C22⋊C8—21no—
58C23×C22⋊C8—21no—
59C4×C8×C23—21no—
60C4×C8×C23—21no—
61C24×C23—21no—
62C24×C23—41no—
63C2×D4×C23—21no—
64C2×D4×C23—22no—
65C2×D4×C23—21no—
66C2×D4×C23—22no—
67C2×D4×C23—22no—
68C2×D4×C23—21no—
69C2×D4×C23—21no—
70C2×D4×C23—21no—
71C2×D4×C23—41no—
72C2×D4×C23—41no—
73C2×D4×C23—41no—
74C2×D4×C23—41no—
75C2×D4×C23—41no—
76C2×D4×C23—41no—
77C2×D4×C23—41no—
78C2×D4×C23—82no—
79C2×D4×C23—82no—
80C2×D4×C23SD1612yes—
81C22×C4×C23—21no—
82C22×C4×C23—41no—
83C22×C4×C23—41no—
84C22×C4×C23—82no—
85C22×C4×C23C2×D411yescharacteristic
86C22×C4×C23#4111yescharacteristic
87C22×C4×C23#4111yescharacteristic
88D8×C23—48no—
89M16×C23—41no—
90M16×C23—41no—
91M16×C23—41no—
92M16×C23—41no—
93C2×C8×C23—22no—
94C2×C8×C23—22no—
95C2×C8×C23—41no—
96C2×C8×C23—41no—
97C2×C8×C23—41no—
98C2×C8×C23—41no—
99C2×C8×C23—41no—
100C4⋊C4×C23—21no—
101C4⋊C4×C23—21no—
102C22⋊C4×C23—41no—
103C22⋊C4×C23—41no—
104C42×C23C2×D411yescharacteristic
105C42×C23C2×D411yescharacteristic
106C42×C23C2×D411yescharacteristic
107C42×C23#4111yescharacteristic
108#10441C2311yesmaximal, characteristic, direct product factor, Sylow
109C23×C23—22no—
110C23×C23—41no—
111C23×C23—41no—
112C23×C23—42no—
113C23×C23—81no—
114C23×C23—81no—
115C23×C23—82no—
116C23×C23—82no—
117C23×C23—81no—
118C23×C23—81no—
119C23×C23#12311yescharacteristic
120D4×C23—22no—
121D4×C23—22no—
122D4×C23—41no—
123D4×C23—42no—
124D4×C23—42no—
125D4×C23—41no—
126D4×C23—82no—
127D4×C23—82no—
128D4×C23—82no—
129D4×C23—81no—
130D4×C23—81no—
131D4×C23—82no—
132C2×C4×C23—22no—
133C2×C4×C23—41no—
134C2×C4×C23—41no—
135C2×C4×C23—82no—
136C2×C4×C23—82no—
137C2×C4×C23—81no—
138C2×C4×C23#12011yescharacteristic
139C2×C4×C23#12111yescharacteristic
140C2×C4×C23#12111yescharacteristic
141C2×C4×C23#12111yescharacteristic
142C2×C4×C23#12311yescharacteristic
143C2×C4×C23#12411yescharacteristic
144C2×C4×C23C2×SD1611yescharacteristic
145C2×C4×C23#13511yescharacteristic
146C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
148C8×C23—42no—
149C8×C23—42no—
150C8×C23—81no—
151C8×C23—81no—
152C8×C23—81no—
153C2×#459C2×C2311yescharacteristic
154#1800C2×C2311yescharacteristic, complemented
155#1570C2×C2311yescharacteristic, complemented
156#1545C2×C2311yescharacteristic, complemented
157#1545C2×C2311yescharacteristic, complemented
158#1478C2×C2311yescharacteristic, complemented
159#1301C2×C2311yescharacteristic, complemented
160C22×C23—21no—
161C22×C23—21no—
162C22×C23—42no—
163C22×C23—82no—
164C22×C23—82no—
165C22×C23—81no—
166C22×C23—81no—
167C22×C23—82no—
168C22×C23—82no—
169C22×C23—82no—
170C22×C23—162no—
171C22×C23—162no—
172C22×C23#39411yescharacteristic
173C22×C23#48111yescharacteristic
174C22×C23#48211yescharacteristic
175C4×C23—21no—
176C4×C23—21no—
177C4×C23—21no—
178C4×C23—81no—
179C4×C23#44911yescharacteristic
180C4×C23#45011yescharacteristic
181C4×C23#46511yescharacteristic
182C4×C23#46911yescharacteristic
183C4×C23#47212yes—
184C22×D8—21no—
185C2×#127C22×C2311yescharacteristic
186C2×C4×D4C22×C2311yescharacteristic
187#459—22no—
188#459—22no—
189#431C22×C2311yescharacteristic
190#431C22×C2311yescharacteristic
191#423C22×C2311yescharacteristic
192#423C22×C2311yescharacteristic
193C2×C4⋊C8C22×C2311yescharacteristic
194C2×#102—21no—
195C2×#100—21no—
196#343—21no—
197#334—22no—
198#331—22no—
199#331—22no—
200D4⋊C8—22no—
201C2×C23—21no—
202C2×C23—21no—
203C2×C23—82no—
204C2×C23—162no—
205C2×C23#203411yescharacteristic
206C2×C23#204511yescharacteristic
207C2×C23#204811yescharacteristic
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4D4×C2311yescharacteristic
212C23×C4—21no—
213C2×D8—24no—
214C2×D8—42no—
215C2×D8—42no—
216C2×M16—21no—
217C2×M16—21no—
218C22×C8—21no—
219#127—21no—
220#127—21no—
221#127—21no—
222#127D4×C2312yes—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C2×C4⋊C4D4×C2311yescharacteristic
228C2×C22⋊C4—21no—
229C2×C42C23×C2311yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8D4×C2312yes—
237C4⋊C8D4×C2312yes—
238#102—24no—
239#100—42no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C4×C8—21no—
243C4×C8—21no—
244C23#1044111yescharacteristic, direct product factor, Sylow
245C24—21no—
246C24—41no—
247C2×D4—21no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—82no—
263C2×D4—82no—
264C2×D4SD16×C2312yes—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—82no—
269C22×C4C2×D4×C2311yescharacteristic
270C22×C4#41×C2311yescharacteristic
271C22×C4#41×C2311yescharacteristic
272D8—48no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42C2×D4×C2311yescharacteristic
289C42C2×D4×C2311yescharacteristic
290C42C2×D4×C2311yescharacteristic
291C42#41×C2311yescharacteristic
292C23—22no—
293C23—41no—
294C23—41no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—82no—
299C23—82no—
300C23—81no—
301C23—81no—
302C23C23×#12311yescharacteristic
303D4—22no—
304D4—22no—
305D4—41no—
306D4—42no—
307D4—42no—
308D4—41no—
309D4—82no—
310D4—82no—
311D4—82no—
312D4—81no—
313D4—81no—
314D4—82no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—81no—
321C2×C4C23×#12011yescharacteristic
322C2×C4C23×#12111yescharacteristic
323C2×C4C23×#12111yescharacteristic
324C2×C4C23×#12111yescharacteristic
325C2×C4C23×#12311yescharacteristic
326C2×C4C23×#12411yescharacteristic
327C2×C4C2×SD16×C2311yescharacteristic
328C2×C4C23×#13511yescharacteristic
329C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
330C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
331C8—42no—
332C8—42no—
333C8—81no—
334C8—81no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22—81no—
342C22—81no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—162no—
347C22—162no—
348C22C23×#39411yescharacteristic
349C22C23×#48111yescharacteristic
350C22C23×#48211yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—81no—
355C4C23×#44911yescharacteristic
356C4C23×#45011yescharacteristic
357C4C23×#46511yescharacteristic
358C4C23×#46911yescharacteristic
359C4C23×#47212yes—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—162no—
364C2C23×#203411yescharacteristic
365C2C23×#204511yescharacteristic
366C2C23×#204811yescharacteristic
subgroupG/H
center, socleC22×C23#394
commutator, Frattini, cosocleC2×C42C23×C23
prime radicalC2×C23×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#1800C2semidirect
3. C23×#1570C2semidirect
4. C23×#1545C2semidirect
5. C23×#1545C2semidirect
6. C23×#1478C2semidirect
7. C23×#1301C2semidirect
108. #10441C23direct (N × H)
154. #1800C2×C23semidirect
155. #1570C2×C23semidirect
156. #1545C2×C23semidirect
157. #1545C2×C23semidirect
158. #1478C2×C23semidirect
159. #1301C2×C23semidirect
244. C23#10441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#4592
C23×#18002
C23×#15702
C23×#15452
C23×#14782
C23×#13012
#1044123