Finite Group Databasebeta

← C23×#8562 #19156188

Subgroups — C23×#8562 #19156188

Order 5888.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#387C211yesmaximal, characteristic
2C23×#1797C211yesmaximal, characteristic
3C23×#1797C211yesmaximal, characteristic
4C2×C23×#324C212yesmaximal
5C23×#1280C212yesmaximal
6C22×C4⋊C4×C23C411yescharacteristic
7C22×C4⋊C4×C23C2211yescharacteristic
8C22×C42×C23C2211yescharacteristic
9C2×C23×C4⋊C8—21no—
10C2×C23×C4⋊C8—21no—
11C2×C23×C22⋊C8C2212yes—
12C2×C23×C22⋊C8C2212yes—
13C23×#387—21no—
14C23×#387—21no—
15C23×#387—21no—
16C23×#387—21no—
17C2×C23×#95C411yescharacteristic
18C2×C23×#95C411yescharacteristic
19C2×C23×#95C411yescharacteristic
20C2×C23×#95C2211yescharacteristic
21C23×#336—21no—
22C23×#336—21no—
23C23×#324—24no—
24C23×C4×C23C2×C411yescharacteristic
25C23×C4×C23C2×C411yescharacteristic
26C23×C4×C23C2×C411yescharacteristic
27C23×C4×C23C2×C411yescharacteristic
28C23×C4×C23C2×C411yescharacteristic
29C23×C4×C23C2×C411yescharacteristic
30C23×C4×C23C2311yescharacteristic
31C22×C8×C23—22no—
32C22×C8×C23—22no—
33C2×C4⋊C4×C23—21no—
34C2×C4⋊C4×C23—21no—
35C2×C4⋊C4×C23—21no—
36C2×C4⋊C4×C23—21no—
37C2×C4⋊C4×C23—21no—
38C2×C4⋊C4×C23—21no—
39C2×C4⋊C4×C23—42no—
40C2×C4⋊C4×C23D412yes—
41C2×C4⋊C4×C23Q812yes—
42C2×C42×C23—42no—
43C2×C42×C23D411yescharacteristic
44C2×C42×C23D411yescharacteristic
45C2×C42×C23D411yescharacteristic
46C2×C42×C23D411yescharacteristic
47C23×C4⋊C8—42no—
48C23×C4⋊C8—42no—
49C23×C22⋊C8—22no—
50C23×C22⋊C8—22no—
51C23×C22⋊C8—22no—
52C23×C22⋊C8—22no—
53C23×#95—21no—
54C23×#95—21no—
55C23×#95—21no—
56C23×#95—21no—
57C23×#95—21no—
58C23×#95—21no—
59C23×#95—21no—
60C23×#95—21no—
61C24×C23C22×C411yescharacteristic
62C22×C4×C23—21no—
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C22×C4×C23—21no—
66C22×C4×C23—22no—
67C22×C4×C23—22no—
68C22×C4×C23—22no—
69C22×C4×C23—22no—
70C22×C4×C23—22no—
71C22×C4×C23—22no—
72C22×C4×C23—21no—
73C22×C4×C23—21no—
74C22×C4×C23—22no—
75C22×C4×C23—22no—
76C22×C4×C23—41no—
77C22×C4×C23—41no—
78C22×C4×C23—41no—
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×C23C22⋊C411yescharacteristic
87C22×C4×C23C22⋊C411yescharacteristic
88C22×C4×C23C22⋊C411yescharacteristic
89C22×C4×C23C22⋊C411yescharacteristic
90C22×C4×C23C4⋊C412yes—
91C22×C4×C23C4⋊C412yes—
92C22×C4×C23C2×D411yescharacteristic
93C22×C4×C23C2×D411yescharacteristic
94C22×C4×C23C2×D411yescharacteristic
95C22×C4×C23C2×Q811yescharacteristic
96C22×C4×C23#4111yescharacteristic
97C22×C4×C23#4111yescharacteristic
98C2×C8×C23—42no—
99C2×C8×C23—42no—
100C2×C8×C23—42no—
101C2×C8×C23—42no—
102C2×C8×C23—42no—
103C2×C8×C23—42no—
104C4⋊C4×C23—22no—
105C4⋊C4×C23—22no—
106C4⋊C4×C23—22no—
107C4⋊C4×C23—22no—
108C4⋊C4×C23—42no—
109C4⋊C4×C23—42no—
110C42×C23—22no—
111C42×C23—22no—
112C42×C23—41no—
113C42×C23—41no—
114#8562C2311yesmaximal, characteristic, direct product factor, Sylow
115C23×C23—21no—
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23C2×C22⋊C411yescharacteristic
120C23×C23C2×C4⋊C411yescharacteristic
121C23×C23#11711yescharacteristic
122C23×C23#13112yes—
123C23×C23#13112yes—
124C2×C4×C23—21no—
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—22no—
133C2×C4×C23—22no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—24no—
141C2×C4×C23—41no—
142C2×C4×C23—41no—
143C2×C4×C23—41no—
144C2×C4×C23—41no—
145C2×C4×C23—44no—
146C2×C4×C23—44no—
147C2×C4×C23—42no—
148C2×C4×C23—41no—
149C2×C4×C23—41no—
150C2×C4×C23—41no—
151C2×C4×C23—41no—
152C2×C4×C23—42no—
153C2×C4×C23—42no—
154C2×C4×C23—41no—
155C2×C4×C23—41no—
156C2×C4×C23—41no—
157C2×C4×C23—41no—
158C2×C4×C23—41no—
159C2×C4×C23—41no—
160C2×C4×C23—82no—
161C2×C4×C23—82no—
162C2×C4×C23#9912yes—
163C2×C4×C23#10112yes—
164C2×C4×C23#12111yescharacteristic
165C2×C4×C23#12111yescharacteristic
166C2×C4×C23C22⋊Q811yescharacteristic
167C2×C4×C23C22⋊Q811yescharacteristic
168C8×C23—82no—
169C8×C23—82no—
170C2×#387C2×C2311yescharacteristic
171#1797C2×C2311yescharacteristic
172#1797C2×C2311yescharacteristic
173C2×#324C2×C2312yes—
174#1280C2×C2312yes—
175C22×C23—21no—
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—22no—
180C22×C23—22no—
181C22×C23—22no—
182C22×C23—22no—
183C22×C23#38011yescharacteristic
184C22×C23#40811yescharacteristic
185C22×C23#40811yescharacteristic
186C22×C23C2×#9911yescharacteristic
187C22×C23#41011yescharacteristic
188C22×C23C2×#10111yescharacteristic
189C22×C23#41311yescharacteristic
190C22×C23#42412yes—
191C22×C23#43312yes—
192C4×C23—21no—
193C4×C23—21no—
194C4×C23—21no—
195C4×C23—21no—
196C4×C23—22no—
197C4×C23—22no—
198C4×C23—42no—
199C4×C23—42no—
200C4×C23—41no—
201C4×C23—41no—
202C4×C23—81no—
203C4×C23—81no—
204C22×C4⋊C4C4×C2311yescharacteristic
205C22×C4⋊C4C22×C2311yescharacteristic
206C22×C42C22×C2311yescharacteristic
207C2×C4⋊C8—21no—
208C2×C4⋊C8—21no—
209C2×C22⋊C8C22×C2312yes—
210C2×C22⋊C8C22×C2312yes—
211#387—21no—
212#387—21no—
213#387—21no—
214#387—21no—
215C2×#95C4×C2311yescharacteristic
216C2×#95C4×C2311yescharacteristic
217C2×#95C4×C2311yescharacteristic
218C2×#95C22×C2311yescharacteristic
219#336—21no—
220#336—21no—
221#324—24no—
222C2×C23—22no—
223C2×C23—22no—
224C2×C23#146811yescharacteristic
225C2×C23#147011yescharacteristic
226C2×C23#147211yescharacteristic
227C2×C23#147311yescharacteristic
228C2×C23#179811yescharacteristic
229C2×C23#179911yescharacteristic
230C2×C23#180111yescharacteristic
231C23×C4C2×C4×C2311yescharacteristic
232C23×C4C2×C4×C2311yescharacteristic
233C23×C4C2×C4×C2311yescharacteristic
234C23×C4C2×C4×C2311yescharacteristic
235C23×C4C2×C4×C2311yescharacteristic
236C23×C4C2×C4×C2311yescharacteristic
237C23×C4C23×C2311yescharacteristic
238C22×C8—22no—
239C22×C8—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4D4×C2312yes—
248C2×C4⋊C4Q8×C2312yes—
249C2×C42—42no—
250C2×C42D4×C2311yescharacteristic
251C2×C42D4×C2311yescharacteristic
252C2×C42D4×C2311yescharacteristic
253C2×C42D4×C2311yescharacteristic
254C4⋊C8—42no—
255C4⋊C8—42no—
256C22⋊C8—22no—
257C22⋊C8—22no—
258C22⋊C8—22no—
259C22⋊C8—22no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268C23#856211yescharacteristic, direct product factor, Sylow
269C24C22×C4×C2311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
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×C4C4⋊C4×C2312yes—
299C22×C4C4⋊C4×C2312yes—
300C22×C4C2×D4×C2311yescharacteristic
301C22×C4C2×D4×C2311yescharacteristic
302C22×C4C2×D4×C2311yescharacteristic
303C22×C4C2×Q8×C2311yescharacteristic
304C22×C4#41×C2311yescharacteristic
305C22×C4#41×C2311yescharacteristic
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×C22⋊C4×C2311yescharacteristic
327C23C2×C4⋊C4×C2311yescharacteristic
328C23C23×#11711yescharacteristic
329C23C23×#13112yes—
330C23C23×#13112yes—
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—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4C23×#9912yes—
370C2×C4C23×#10112yes—
371C2×C4C23×#12111yescharacteristic
372C2×C4C23×#12111yescharacteristic
373C2×C4C23×C22⋊Q811yescharacteristic
374C2×C4C23×C22⋊Q811yescharacteristic
375C8—82no—
376C8—82no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22C23×#38011yescharacteristic
386C22C23×#40811yescharacteristic
387C22C23×#40811yescharacteristic
388C22C2×C23×#9911yescharacteristic
389C22C23×#41011yescharacteristic
390C22C2×C23×#10111yescharacteristic
391C22C23×#41311yescharacteristic
392C22C23×#42412yes—
393C22C23×#43312yes—
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C2—22no—
407C2—22no—
408C2C23×#146811yescharacteristic
409C2C23×#147011yescharacteristic
410C2C23×#147211yescharacteristic
411C2C23×#147311yescharacteristic
412C2C23×#179811yescharacteristic
413C2C23×#179911yescharacteristic
414C2C23×#180111yescharacteristic
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
114. #8562C23direct (N × H)
268. C23#8562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3872
C23×#17972
C2×C23×#3242
C23×#12802
#856223