Finite Group Databasebeta

← C23×#9086 #19156712

Subgroups — C23×#9086 #19156712

Order 5888.

604 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#432C211yesmaximal, characteristic
2C2×C23×#387C211yesmaximal, characteristic
3C23×#1817C211yesmaximal, characteristic
4C2×C23×#324C212yesmaximal
5C23×#1280C212yesmaximal
6C22×C4⋊C4×C23C411yescharacteristic
7C22×C4⋊C4×C23C2211yescharacteristic
8C22×C42×C23C2211yescharacteristic
9C23×#432—24no—
10C2×C23×C4⋊C8—21no—
11C2×C23×C22⋊C8C2212yes—
12C2×C23×C22⋊C8C2212yes—
13C2×C23×#97—21no—
14C23×#387—21no—
15C23×#387—21no—
16C23×#387—21no—
17C23×#387—21no—
18C2×C23×#95C411yescharacteristic
19C2×C23×#95C411yescharacteristic
20C2×C23×#95C411yescharacteristic
21C2×C23×#95C2211yescharacteristic
22C23×#336—21no—
23C23×#336—21no—
24C23×#324—24no—
25C23×C4×C23C2×C411yescharacteristic
26C23×C4×C23C2×C411yescharacteristic
27C23×C4×C23C2×C411yescharacteristic
28C23×C4×C23C2×C411yescharacteristic
29C23×C4×C23C2×C411yescharacteristic
30C23×C4×C23C2×C411yescharacteristic
31C23×C4×C23C2311yescharacteristic
32C22×C8×C23—22no—
33C22×C8×C23—22no—
34C2×C4⋊C4×C23—21no—
35C2×C4⋊C4×C23—21no—
36C2×C4⋊C4×C23—22no—
37C2×C4⋊C4×C23—22no—
38C2×C4⋊C4×C23—22no—
39C2×C4⋊C4×C23—21no—
40C2×C4⋊C4×C23—21no—
41C2×C4⋊C4×C23—22no—
42C2×C42×C23—22no—
43C2×C42×C23—22no—
44C2×C42×C23D411yescharacteristic
45C2×C42×C23D411yescharacteristic
46C2×C42×C23D411yescharacteristic
47C2×C42×C23D411yescharacteristic
48C23×C4⋊C8—24no—
49C23×C22⋊C8—22no—
50C23×C22⋊C8—22no—
51C23×C22⋊C8—22no—
52C23×C22⋊C8D414yes—
53C23×#97—24no—
54C23×#95—21no—
55C23×#95—21no—
56C23×#95—21no—
57C23×#95—21no—
58C23×#95—21no—
59C23×#95—21no—
60C23×#95—21no—
61C23×#95—21no—
62C24×C23C22×C411yescharacteristic
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C22×C4×C23—22no—
66C22×C4×C23—22no—
67C22×C4×C23—22no—
68C22×C4×C23—21no—
69C22×C4×C23—21no—
70C22×C4×C23—21no—
71C22×C4×C23—21no—
72C22×C4×C23—22no—
73C22×C4×C23—22no—
74C22×C4×C23—22no—
75C22×C4×C23—21no—
76C22×C4×C23—21no—
77C22×C4×C23—22no—
78C22×C4×C23—22no—
79C22×C4×C23—41no—
80C22×C4×C23—41no—
81C22×C4×C23—41no—
82C22×C4×C23—41no—
83C22×C4×C23—41no—
84C22×C4×C23—41no—
85C22×C4×C23—41no—
86C22×C4×C23—41no—
87C22×C4×C23—41no—
88C22×C4×C23C22⋊C411yescharacteristic
89C22×C4×C23C22⋊C411yescharacteristic
90C22×C4×C23C22⋊C411yescharacteristic
91C22×C4×C23C22⋊C411yescharacteristic
92C22×C4×C23M1612yes—
93C22×C4×C23M1612yes—
94C22×C4×C23C2×D411yescharacteristic
95C22×C4×C23C2×D411yescharacteristic
96C22×C4×C23C2×D412yes—
97C22×C4×C23#4112yes—
98C2×C8×C23—24no—
99C2×C8×C23—42no—
100C2×C8×C23—42no—
101C2×C8×C23—42no—
102C2×C8×C23—42no—
103C2×C8×C23—42no—
104C4⋊C4×C23—24no—
105C4⋊C4×C23—24no—
106C4⋊C4×C23—41no—
107C4⋊C4×C23—42no—
108C4⋊C4×C23—41no—
109C42×C23—21no—
110C42×C23—21no—
111C42×C23—22no—
112C42×C23—22no—
113C42×C23—21no—
114C42×C23—21no—
115#9086C2311yesmaximal, characteristic, direct product factor, Sylow
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23C2×C22⋊C411yescharacteristic
121C23×C23C4×D412yes—
122C23×C23C2×M1611yescharacteristic
123C23×C23C2×M1611yescharacteristic
124C23×C23#13112yes—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—22no—
137C2×C4×C23—22no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—24no—
143C2×C4×C23—42no—
144C2×C4×C23—42no—
145C2×C4×C23—44no—
146C2×C4×C23—42no—
147C2×C4×C23—41no—
148C2×C4×C23—41no—
149C2×C4×C23—41no—
150C2×C4×C23—41no—
151C2×C4×C23—42no—
152C2×C4×C23—42no—
153C2×C4×C23—42no—
154C2×C4×C23—42no—
155C2×C4×C23—41no—
156C2×C4×C23—41no—
157C2×C4×C23—41no—
158C2×C4×C23—41no—
159C2×C4×C23—41no—
160C2×C4×C23—41no—
161C2×C4×C23—82no—
162C2×C4×C23—82no—
163C2×C4×C23#10112yes—
164C2×C4×C23#12011yescharacteristic
165C2×C4×C23#12112yes—
166C2×C4×C23#12311yescharacteristic
167C8×C23—44no—
168C8×C23—82no—
169C2×#432C2×C2311yescharacteristic
170C2×#387C2×C2311yescharacteristic
171#1817C2×C2311yescharacteristic
172C2×#324C2×C2312yes—
173#1280C2×C2312yes—
174C22×C23—22no—
175C22×C23—22no—
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—21no—
180C22×C23—22no—
181C22×C23—22no—
182C22×C23#38611yescharacteristic
183C22×C23#40711yescharacteristic
184C22×C23#40811yescharacteristic
185C22×C23#41011yescharacteristic
186C22×C23#41011yescharacteristic
187C22×C23C2×#10111yescharacteristic
188C22×C23#41311yescharacteristic
189C22×C23#43512yes—
190C22×C23#43612yes—
191C4×C23—21no—
192C4×C23—22no—
193C4×C23—21no—
194C4×C23—22no—
195C4×C23—41no—
196C4×C23—41no—
197C4×C23—42no—
198C4×C23—41no—
199C4×C23—42no—
200C4×C23—81no—
201C4×C23—81no—
202C22×C4⋊C4C4×C2311yescharacteristic
203C22×C4⋊C4C22×C2311yescharacteristic
204C22×C42C22×C2311yescharacteristic
205#432—24no—
206C2×C4⋊C8—21no—
207C2×C22⋊C8C22×C2312yes—
208C2×C22⋊C8C22×C2312yes—
209C2×#97—21no—
210#387—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214C2×#95C4×C2311yescharacteristic
215C2×#95C4×C2311yescharacteristic
216C2×#95C4×C2311yescharacteristic
217C2×#95C22×C2311yescharacteristic
218#336—21no—
219#336—21no—
220#324—24no—
221C2×C23—22no—
222C2×C23—22no—
223C2×C23#146411yescharacteristic
224C2×C23#146711yescharacteristic
225C2×C23#147011yescharacteristic
226C2×C23#147311yescharacteristic
227C2×C23#187011yescharacteristic
228C2×C23#189911yescharacteristic
229C2×C23#190111yescharacteristic
230C23×C4C2×C4×C2311yescharacteristic
231C23×C4C2×C4×C2311yescharacteristic
232C23×C4C2×C4×C2311yescharacteristic
233C23×C4C2×C4×C2311yescharacteristic
234C23×C4C2×C4×C2311yescharacteristic
235C23×C4C2×C4×C2311yescharacteristic
236C23×C4C23×C2311yescharacteristic
237C22×C8—22no—
238C22×C8—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42D4×C2311yescharacteristic
250C2×C42D4×C2311yescharacteristic
251C2×C42D4×C2311yescharacteristic
252C2×C42D4×C2311yescharacteristic
253C4⋊C8—24no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8D4×C2314yes—
258#97—24no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267C23#908611yescharacteristic, direct product factor, Sylow
268C24C22×C4×C2311yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C22⋊C4×C2311yescharacteristic
295C22×C4C22⋊C4×C2311yescharacteristic
296C22×C4C22⋊C4×C2311yescharacteristic
297C22×C4C22⋊C4×C2311yescharacteristic
298C22×C4M16×C2312yes—
299C22×C4M16×C2312yes—
300C22×C4C2×D4×C2311yescharacteristic
301C22×C4C2×D4×C2311yescharacteristic
302C22×C4C2×D4×C2312yes—
303C22×C4#41×C2312yes—
304C2×C8—24no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C22⋊C4×C2311yescharacteristic
326C23C4×D4×C2312yes—
327C23C2×M16×C2311yescharacteristic
328C23C2×M16×C2311yescharacteristic
329C23C23×#13112yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4C23×#10112yes—
369C2×C4C23×#12011yescharacteristic
370C2×C4C23×#12112yes—
371C2×C4C23×#12311yescharacteristic
372C8—44no—
373C8—82no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22C23×#38611yescharacteristic
383C22C23×#40711yescharacteristic
384C22C23×#40811yescharacteristic
385C22C23×#41011yescharacteristic
386C22C23×#41011yescharacteristic
387C22C2×C23×#10111yescharacteristic
388C22C23×#41311yescharacteristic
389C22C23×#43512yes—
390C22C23×#43612yes—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—41no—
396C4—42no—
397C4—41no—
398C4—41no—
399C4—42no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2C23×#146411yescharacteristic
405C2C23×#146711yescharacteristic
406C2C23×#147011yescharacteristic
407C2C23×#147311yescharacteristic
408C2C23×#187011yescharacteristic
409C2C23×#189911yescharacteristic
410C2C23×#190111yescharacteristic
subgroupG/H
center, socleC23×C23C2×C22⋊C4
commutatorC24C22×C4×C23
Frattini, cosocleC23×C4C23×C23
prime radicalC24×C23C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C22×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
115. #9086C23direct (N × H)
267. C23#9086direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#4322
C2×C23×#3872
C23×#18172
C2×C23×#3242
C23×#12802
#908623