Finite Group Databasebeta

← C23×#9081 #19156707

Subgroups — C23×#9081 #19156707

Order 5888.

964 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×C22⋊C8C211yesmaximal, characteristic
2C2×C23×#385C211yesmaximal, characteristic
3C23×#1779C211yesmaximal, characteristic
4C2×C23×#324C212yesmaximal, complemented
5C23×#1280C212yesmaximal, complemented
6C24×C4×C23C2211yescharacteristic
7C23×C8×C23—21no—
8C22×C4⋊C4×C23C411yescharacteristic
9C22×C4⋊C4×C23C2211yescharacteristic
10C22×C22⋊C4×C23C411yescharacteristic
11C22×C22⋊C4×C23C411yescharacteristic
12C2×C23×C22⋊C8—24no—
13C2×C23×C22⋊C8—21no—
14C2×C23×C22⋊C8—21no—
15C2×C23×C22⋊C8—21no—
16C2×C23×C22⋊C8C2212yes—
17C2×C23×C22⋊C8C2212yes—
18C23×#385—21no—
19C23×#385—21no—
20C23×#385—21no—
21C23×#385—21no—
22C2×C23×#95C411yescharacteristic
23C2×C23×#95C2211yescharacteristic
24C23×#324—24no—
25C25×C23C2×C411yescharacteristic
26C23×C4×C23—22no—
27C23×C4×C23—22no—
28C23×C4×C23—42no—
29C23×C4×C23—42no—
30C23×C4×C23C2×C411yescharacteristic
31C23×C4×C23C2×C411yescharacteristic
32C23×C4×C23C2×C411yescharacteristic
33C23×C4×C23C2×C411yescharacteristic
34C23×C4×C23C2×C411yescharacteristic
35C23×C4×C23D411yescharacteristic
36C23×C4×C23D411yescharacteristic
37C23×C4×C23D411yescharacteristic
38C23×C4×C23D411yescharacteristic
39C23×C4×C23C2311yescharacteristic
40C22×C8×C23—24no—
41C22×C8×C23—22no—
42C22×C8×C23—22no—
43C22×C8×C23—42no—
44C22×C8×C23—42no—
45C2×C4⋊C4×C23—21no—
46C2×C4⋊C4×C23—21no—
47C2×C4⋊C4×C23—22no—
48C2×C4⋊C4×C23—21no—
49C2×C4⋊C4×C23—21no—
50C2×C4⋊C4×C23—22no—
51C2×C4⋊C4×C23—42no—
52C2×C22⋊C4×C23—21no—
53C2×C22⋊C4×C23—21no—
54C2×C22⋊C4×C23—22no—
55C2×C22⋊C4×C23—21no—
56C2×C22⋊C4×C23—21no—
57C2×C22⋊C4×C23—42no—
58C2×C22⋊C4×C23C814yescomplemented
59C23×C22⋊C8—24no—
60C23×C22⋊C8—22no—
61C23×C22⋊C8—22no—
62C23×C22⋊C8—22no—
63C23×C22⋊C8—42no—
64C23×C22⋊C8—42no—
65C23×C22⋊C8D414yes—
66C23×#95—21no—
67C23×#95—21no—
68C23×#95—21no—
69C23×#95—21no—
70C24×C23—22no—
71C24×C23—22no—
72C24×C23—22no—
73C24×C23—22no—
74C24×C23—41no—
75C24×C23—41no—
76C24×C23C22⋊C411yescharacteristic
77C24×C23C22⋊C411yescharacteristic
78C24×C23C2×C812yes—
79C24×C23M1612yes—
80C24×C23C22×C411yescharacteristic
81C22×C4×C23—22no—
82C22×C4×C23—22no—
83C22×C4×C23—21no—
84C22×C4×C23—21no—
85C22×C4×C23—22no—
86C22×C4×C23—21no—
87C22×C4×C23—21no—
88C22×C4×C23—22no—
89C22×C4×C23—22no—
90C22×C4×C23—21no—
91C22×C4×C23—21no—
92C22×C4×C23—22no—
93C22×C4×C23—22no—
94C22×C4×C23—22no—
95C22×C4×C23—21no—
96C22×C4×C23—22no—
97C22×C4×C23—22no—
98C22×C4×C23—21no—
99C22×C4×C23—21no—
100C22×C4×C23—21no—
101C22×C4×C23—22no—
102C22×C4×C23—22no—
103C22×C4×C23—41no—
104C22×C4×C23—41no—
105C22×C4×C23—41no—
106C22×C4×C23—41no—
107C22×C4×C23—41no—
108C22×C4×C23—41no—
109C22×C4×C23—41no—
110C22×C4×C23—48no—
111C22×C4×C23—48no—
112C22×C4×C23—41no—
113C22×C4×C23—41no—
114C22×C4×C23—41no—
115C22×C4×C23—41no—
116C22×C4×C23—41no—
117C22×C4×C23—41no—
118C22×C4×C23C22⋊C411yescharacteristic
119C22×C4×C23C22⋊C411yescharacteristic
120C22×C4×C23C2×C812yescomplemented
121C22×C4×C23C2×C812yescomplemented
122C22×C4×C23C2×D411yescharacteristic
123C22×C4×C23C2×D411yescharacteristic
124C22×C4×C23C2×D412yes—
125C22×C4×C23#4112yes—
126C2×C8×C23—24no—
127C2×C8×C23—48no—
128C2×C8×C23—42no—
129C2×C8×C23—42no—
130C2×C8×C23—42no—
131C2×C8×C23—42no—
132C2×C8×C23—42no—
133C4⋊C4×C23—42no—
134C4⋊C4×C23—42no—
135C4⋊C4×C23—41no—
136C4⋊C4×C23—42no—
137C4⋊C4×C23—41no—
138C22⋊C4×C23—24no—
139C22⋊C4×C23—24no—
140C22⋊C4×C23—42no—
141C22⋊C4×C23—42no—
142#9081C2311yesmaximal, characteristic, direct product factor, Sylow
143C23×C23—21no—
144C23×C23—21no—
145C23×C23—21no—
146C23×C23—21no—
147C23×C23—21no—
148C23×C23—21no—
149C23×C23—21no—
150C23×C23—21no—
151C23×C23—24no—
152C23×C23—24no—
153C23×C23—21no—
154C23×C23—21no—
155C23×C23—21no—
156C23×C23—21no—
157C23×C23—21no—
158C23×C23—21no—
159C23×C23—24no—
160C23×C23—24no—
161C23×C23—42no—
162C23×C23—42no—
163C23×C23—44no—
164C23×C23—44no—
165C23×C23—44no—
166C23×C23—44no—
167C23×C23C22⋊C812yes—
168C23×C23C22⋊C812yes—
169C23×C23#9912yes—
170C23×C23#10112yes—
171C23×C23C2×C22⋊C411yescharacteristic
172C23×C23C4×D412yes—
173C23×C23C22×C811yescharacteristic
174C23×C23C2×M1611yescharacteristic
175C23×C23#13112yes—
176C2×C4×C23—24no—
177C2×C4×C23—24no—
178C2×C4×C23—21no—
179C2×C4×C23—21no—
180C2×C4×C23—21no—
181C2×C4×C23—21no—
182C2×C4×C23—21no—
183C2×C4×C23—21no—
184C2×C4×C23—21no—
185C2×C4×C23—22no—
186C2×C4×C23—22no—
187C2×C4×C23—21no—
188C2×C4×C23—21no—
189C2×C4×C23—24no—
190C2×C4×C23—42no—
191C2×C4×C23—42no—
192C2×C4×C23—44no—
193C2×C4×C23—44no—
194C2×C4×C23—44no—
195C2×C4×C23—42no—
196C2×C4×C23—42no—
197C2×C4×C23—42no—
198C2×C4×C23—41no—
199C2×C4×C23—41no—
200C2×C4×C23—41no—
201C2×C4×C23—41no—
202C2×C4×C23—42no—
203C2×C4×C23—42no—
204C2×C4×C23—41no—
205C2×C4×C23—41no—
206C2×C4×C23—41no—
207C2×C4×C23—41no—
208C2×C4×C23—41no—
209C2×C4×C23—41no—
210C2×C4×C23—82no—
211C2×C4×C23—82no—
212C2×C4×C23#9912yes—
213C2×C4×C23#12011yescharacteristic
214C2×C4×C23#12112yes—
215C2×C4×C23#12311yescharacteristic
216C8×C23—44no—
217C8×C23—82no—
218C22×C22⋊C8C2×C2311yescharacteristic
219C2×#385C2×C2311yescharacteristic
220#1779C2×C2311yescharacteristic
221C2×#324C2×C2312yescomplemented
222#1280C2×C2312yescomplemented
223C22×C23—22no—
224C22×C23—22no—
225C22×C23—22no—
226C22×C23—22no—
227C22×C23—22no—
228C22×C23—21no—
229C22×C23—21no—
230C22×C23—21no—
231C22×C23—21no—
232C22×C23—22no—
233C22×C23—22no—
234C22×C23—22no—
235C22×C23—22no—
236C22×C23—22no—
237C22×C23—22no—
238C22×C23—22no—
239C22×C23—22no—
240C22×C23—48no—
241C22×C23—48no—
242C22×C23—41no—
243C22×C23—41no—
244C22×C23—41no—
245C22×C23—41no—
246C22×C23#32414yescomplemented
247C22×C23#38611yescharacteristic
248C22×C23C2×C22⋊C811yescharacteristic
249C22×C23#40811yescharacteristic
250C22×C23C2×#9911yescharacteristic
251C22×C23C2×#9911yescharacteristic
252C22×C23C2×#10111yescharacteristic
253C22×C23#41311yescharacteristic
254C22×C23C8×D412yes—
255C22×C23#43512yes—
256C4×C23—21no—
257C4×C23—22no—
258C4×C23—22no—
259C4×C23—21no—
260C4×C23—42no—
261C4×C23—41no—
262C4×C23—42no—
263C4×C23—81no—
264C4×C23—81no—
265C24×C4C22×C2311yescharacteristic
266C23×C8—21no—
267C22×C4⋊C4C4×C2311yescharacteristic
268C22×C4⋊C4C22×C2311yescharacteristic
269C22×C22⋊C4C4×C2311yescharacteristic
270C22×C22⋊C4C4×C2311yescharacteristic
271C2×C22⋊C8—21no—
272C2×C22⋊C8—24no—
273C2×C22⋊C8—21no—
274C2×C22⋊C8—21no—
275C2×C22⋊C8C22×C2312yes—
276C2×C22⋊C8C22×C2312yes—
277#385—21no—
278#385—21no—
279#385—21no—
280#385—21no—
281C2×#95C4×C2311yescharacteristic
282C2×#95C22×C2311yescharacteristic
283#324—24no—
284C2×C23—24no—
285C2×C23—22no—
286C2×C23—22no—
287C2×C23—42no—
288C2×C23C2×#32411yescharacteristic
289C2×C23#145911yescharacteristic
290C2×C23#146811yescharacteristic
291C2×C23#147211yescharacteristic
292C2×C23#186911yescharacteristic
293C2×C23#189811yescharacteristic
294C2×C23#190111yescharacteristic
295C25C2×C4×C2311yescharacteristic
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×C4×C2311yescharacteristic
301C23×C4C2×C4×C2311yescharacteristic
302C23×C4C2×C4×C2311yescharacteristic
303C23×C4C2×C4×C2311yescharacteristic
304C23×C4C2×C4×C2311yescharacteristic
305C23×C4D4×C2311yescharacteristic
306C23×C4D4×C2311yescharacteristic
307C23×C4D4×C2311yescharacteristic
308C23×C4D4×C2311yescharacteristic
309C23×C4C23×C2311yescharacteristic
310C22×C8—24no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—42no—
314C22×C8—42no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—42no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4C8×C2314yescomplemented
329C22⋊C8—24no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332C22⋊C8—22no—
333C22⋊C8—42no—
334C22⋊C8—42no—
335C22⋊C8D4×C2314yes—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340C23#908111yescharacteristic, direct product factor, Sylow
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—41no—
346C24—41no—
347C24C22⋊C4×C2311yescharacteristic
348C24C22⋊C4×C2311yescharacteristic
349C24C2×C8×C2312yes—
350C24M16×C2312yes—
351C24C22×C4×C2311yescharacteristic
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—48no—
382C22×C4—48no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4C22⋊C4×C2311yescharacteristic
390C22×C4C22⋊C4×C2311yescharacteristic
391C22×C4C2×C8×C2312yescomplemented
392C22×C4C2×C8×C2312yescomplemented
393C22×C4C2×D4×C2311yescharacteristic
394C22×C4C2×D4×C2311yescharacteristic
395C22×C4C2×D4×C2312yes—
396C22×C4#41×C2312yes—
397C2×C8—24no—
398C2×C8—48no—
399C2×C8—42no—
400C2×C8—42no—
401C2×C8—42no—
402C2×C8—42no—
403C2×C8—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—42no—
408C4⋊C4—41no—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—24no—
422C23—24no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—24no—
430C23—24no—
431C23—42no—
432C23—42no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23C23×C22⋊C812yes—
438C23C23×C22⋊C812yes—
439C23C23×#9912yes—
440C23C23×#10112yes—
441C23C2×C22⋊C4×C2311yescharacteristic
442C23C4×D4×C2312yes—
443C23C22×C8×C2311yescharacteristic
444C23C2×M16×C2311yescharacteristic
445C23C23×#13112yes—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4C23×#9912yes—
483C2×C4C23×#12011yescharacteristic
484C2×C4C23×#12112yes—
485C2×C4C23×#12311yescharacteristic
486C8—44no—
487C8—82no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—48no—
506C22—48no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22C23×#32414yescomplemented
512C22C23×#38611yescharacteristic
513C22C2×C23×C22⋊C811yescharacteristic
514C22C23×#40811yescharacteristic
515C22C2×C23×#9911yescharacteristic
516C22C2×C23×#9911yescharacteristic
517C22C2×C23×#10111yescharacteristic
518C22C23×#41311yescharacteristic
519C22C8×D4×C2312yes—
520C22C23×#43512yes—
521C4—21no—
522C4—22no—
523C4—22no—
524C4—21no—
525C4—41no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—81no—
530C2—24no—
531C2—22no—
532C2—22no—
533C2—42no—
534C2C2×C23×#32411yescharacteristic
535C2C23×#145911yescharacteristic
536C2C23×#146811yescharacteristic
537C2C23×#147211yescharacteristic
538C2C23×#186911yescharacteristic
539C2C23×#189811yescharacteristic
540C2C23×#190111yescharacteristic
subgroupG/H
center, socleC23×C23C2×C22⋊C4
commutatorC23C22×C8×C23
Frattini, cosocleC23×C4C23×C23
prime radicalC25×C23C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C24×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C23×#324C2semidirect
5. C23×#1280C2semidirect
58. C2×C22⋊C4×C23C8semidirect
120. C22×C4×C23C2×C8semidirect
121. C22×C4×C23C2×C8semidirect
142. #9081C23direct (N × H)
221. C2×#324C2×C23semidirect
222. #1280C2×C23semidirect
246. C22×C23#324semidirect
328. C2×C22⋊C4C8×C23semidirect
340. C23#9081direct (N × H)
391. C22×C4C2×C8×C23semidirect
392. C22×C4C2×C8×C23semidirect
511. C22C23×#324semidirect

Maximal subgroups

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

subgroupindex
C22×C23×C22⋊C82
C2×C23×#3852
C23×#17792
C2×C23×#3242
C23×#12802
#908123