Finite Group Databasebeta

← C23×#10960 #19158586

Subgroups — C23×#10960 #19158586

Order 5888.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×#99C212yesmaximal
2C2×C23×#386C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
4C2×C23×#342C212yesmaximal, complemented
5C23×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C23C2211yescharacteristic
7C24×C4×C23C2211yescharacteristic
8C22×C22⋊C4×C23C412yescomplemented
9C22×C22⋊C4×C23C2211yescharacteristic
10C22×C22⋊C4×C23C2212yes—
11C22×C22⋊C4×C23C2212yes—
12C22×C42×C23—21no—
13C2×C23×#99—24no—
14C2×C23×#99—24no—
15C2×C23×#99C418yescomplemented
16C23×#386—21no—
17C23×#386—22no—
18C23×#386—21no—
19C4×C22⋊C4×C23—24no—
20C2×C23×#95—21no—
21C2×C23×#95—22no—
22C2×C23×#95C412yescomplemented
23C23×#342—24no—
24C25×C23C2×C411yescharacteristic
25C25×C23C2311yescharacteristic
26C22×D4×C23—21no—
27C22×D4×C23—21no—
28C22×D4×C23—22no—
29C22×D4×C23—22no—
30C22×D4×C23—22no—
31C22×D4×C23—22no—
32C22×D4×C23—22no—
33C22×D4×C23C2×C414yes—
34C23×C4×C23—22no—
35C23×C4×C23—22no—
36C23×C4×C23—22no—
37C23×C4×C23—22no—
38C23×C4×C23—44no—
39C23×C4×C23C2×C411yescharacteristic
40C23×C4×C23C2×C412yes—
41C23×C4×C23C2×C412yes—
42C23×C4×C23D411yescharacteristic
43C23×C4×C23D412yes—
44C23×C4×C23D411yescharacteristic
45C2×C22⋊C4×C23—22no—
46C2×C22⋊C4×C23—22no—
47C2×C22⋊C4×C23—22no—
48C2×C22⋊C4×C23—22no—
49C2×C22⋊C4×C23—22no—
50C2×C22⋊C4×C23—22no—
51C2×C22⋊C4×C23—22no—
52C2×C22⋊C4×C23—22no—
53C2×C22⋊C4×C23—21no—
54C2×C22⋊C4×C23—21no—
55C2×C22⋊C4×C23—22no—
56C2×C22⋊C4×C23—22no—
57C2×C22⋊C4×C23—22no—
58C2×C22⋊C4×C23—22no—
59C2×C22⋊C4×C23—44no—
60C2×C22⋊C4×C23C2×C414yes—
61C2×C22⋊C4×C23C2×C414yes—
62C2×C22⋊C4×C23D414yes—
63C2×C22⋊C4×C23D414yes—
64C2×C42×C23—24no—
65C2×C42×C23—44no—
66C23×#99—216no—
67C23×#95—24no—
68C23×#95—22no—
69C23×#95—22no—
70C23×#95—44no—
71C24×C23—21no—
72C24×C23—21no—
73C24×C23—22no—
74C24×C23—22no—
75C24×C23—42no—
76C24×C23—42no—
77C24×C23—42no—
78C24×C23—42no—
79C24×C23C4212yescomplemented
80C24×C23C22×C411yescharacteristic
81C24×C23C22×C412yes—
82C24×C23C2×D411yescharacteristic
83C24×C23C2×D411yescharacteristic
84C24×C23C2×D412yes—
85C24×C23C2×D412yes—
86C24×C23#4112yes—
87C24×C23#4112yes—
88C24×C23#4112yes—
89C2×D4×C23—24no—
90C2×D4×C23—24no—
91C2×D4×C23—24no—
92C2×D4×C23—24no—
93C2×D4×C23—24no—
94C2×D4×C23—24no—
95C2×D4×C23—41no—
96C2×D4×C23—42no—
97C2×D4×C23—42no—
98C2×D4×C23—42no—
99C2×D4×C23—41no—
100C2×D4×C23—42no—
101C2×D4×C23—42no—
102C2×D4×C23—41no—
103C2×D4×C23—42no—
104C2×D4×C23—41no—
105C22×C4×C23—21no—
106C22×C4×C23—21no—
107C22×C4×C23—24no—
108C22×C4×C23—21no—
109C22×C4×C23—21no—
110C22×C4×C23—24no—
111C22×C4×C23—24no—
112C22×C4×C23—22no—
113C22×C4×C23—22no—
114C22×C4×C23—24no—
115C22×C4×C23—21no—
116C22×C4×C23—24no—
117C22×C4×C23—24no—
118C22×C4×C23—21no—
119C22×C4×C23—24no—
120C22×C4×C23—24no—
121C22×C4×C23—22no—
122C22×C4×C23—24no—
123C22×C4×C23—24no—
124C22×C4×C23—42no—
125C22×C4×C23—42no—
126C22×C4×C23—42no—
127C22×C4×C23—48no—
128C22×C4×C23—48no—
129C22×C4×C23—44no—
130C22×C4×C23—44no—
131C22×C4×C23—44no—
132C22×C4×C23—44no—
133C22×C4×C23—42no—
134C22×C4×C23—42no—
135C22×C4×C23—42no—
136C22×C4×C23—42no—
137C22×C4×C23C4212yescomplemented
138C22×C4×C23C22⋊C412yes—
139C22×C4×C23C22⋊C412yes—
140C22⋊C4×C23—24no—
141C22⋊C4×C23—24no—
142C22⋊C4×C23—24no—
143C22⋊C4×C23—24no—
144C22⋊C4×C23—24no—
145C22⋊C4×C23—44no—
146C22⋊C4×C23—42no—
147C22⋊C4×C23—42no—
148C22⋊C4×C23—42no—
149C22⋊C4×C23—41no—
150C22⋊C4×C23—41no—
151C22⋊C4×C23—44no—
152C22⋊C4×C23C22⋊C418yescomplemented
153C42×C23—48no—
154#10960C2311yesmaximal, characteristic, direct product factor, Sylow
155C23×C23—22no—
156C23×C23—22no—
157C23×C23—22no—
158C23×C23—22no—
159C23×C23—22no—
160C23×C23—22no—
161C23×C23—22no—
162C23×C23—24no—
163C23×C23—42no—
164C23×C23—42no—
165C23×C23—44no—
166C23×C23—42no—
167C23×C23—44no—
168C23×C23—42no—
169C23×C23—44no—
170C23×C23—44no—
171C23×C23—44no—
172C23×C23—44no—
173C23×C23—41no—
174C23×C23—42no—
175C23×C23—41no—
176C23×C23—42no—
177C23×C23—42no—
178C23×C23—82no—
179C23×C23—82no—
180C23×C23—84no—
181C23×C23C2×C4211yescharacteristic
182C23×C23C2×C22⋊C412yes—
183C23×C23C2×C22⋊C411yescharacteristic
184C23×C23#11711yescharacteristic
185C23×C23#11712yes—
186C23×C23C4×D412yes—
187C23×C23C4×D412yes—
188C23×C23C4×D412yes—
189C23×C23C4×D412yes—
190C23×C23C4×D412yes—
191C23×C23C4×D412yes—
192C23×C23#12011yescharacteristic
193C23×C23#12112yes—
194C23×C23#12112yes—
195C23×C23#12112yes—
196C23×C23#12311yescharacteristic
197C23×C23#12312yes—
198C23×C23#12411yescharacteristic
199C23×C23#12412yes—
200C23×C23#12612yes—
201C23×C23#12711yescharacteristic
202D4×C23—44no—
203D4×C23—44no—
204D4×C23—44no—
205D4×C23—44no—
206C2×C4×C23—24no—
207C2×C4×C23—24no—
208C2×C4×C23—22no—
209C2×C4×C23—22no—
210C2×C4×C23—24no—
211C2×C4×C23—22no—
212C2×C4×C23—28no—
213C2×C4×C23—22no—
214C2×C4×C23—22no—
215C2×C4×C23—22no—
216C2×C4×C23—48no—
217C2×C4×C23—48no—
218C2×C4×C23—44no—
219C2×C4×C23—44no—
220C2×C4×C23—48no—
221C2×C4×C23—48no—
222C2×C4×C23—42no—
223C2×C4×C23—42no—
224C2×C4×C23—41no—
225C2×C4×C23—42no—
226C2×C4×C23—41no—
227C2×C4×C23—48no—
228C2×C4×C23—44no—
229C2×C4×C23—42no—
230C2×C4×C23—42no—
231C2×C4×C23—42no—
232C2×C4×C23—82no—
233C2×C4×C23—82no—
234C2×C4×C23—84no—
235C2×C4×C23—84no—
236C2×C4×C23#9914yescomplemented
237C22×#99C2×C2312yes—
238C2×#386C2×C2311yescharacteristic
239C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
240C2×#342C2×C2312yescomplemented
241C22⋊#95C2×C2311yescharacteristic, complemented
242C22×C23—21no—
243C22×C23—21no—
244C22×C23—22no—
245C22×C23—22no—
246C22×C23—21no—
247C22×C23—22no—
248C22×C23—22no—
249C22×C23—21no—
250C22×C23—24no—
251C22×C23—22no—
252C22×C23—24no—
253C22×C23—22no—
254C22×C23—24no—
255C22×C23—24no—
256C22×C23—22no—
257C22×C23—22no—
258C22×C23—42no—
259C22×C23—42no—
260C22×C23—42no—
261C22×C23—42no—
262C22×C23—42no—
263C22×C23—42no—
264C22×C23—42no—
265C22×C23—42no—
266C22×C23—42no—
267C22×C23—44no—
268C22×C23—84no—
269C22×C23—84no—
270C22×C23—81no—
271C22×C23—81no—
272C22×C23—82no—
273C22×C23C4×C22⋊C412yes—
274C22×C23C4×C22⋊C411yescharacteristic
275C22×C23#38612yes—
276C22×C23#38611yescharacteristic
277C22×C23#38812yes—
278C22×C23#38812yes—
279C22×C23#38812yes—
280C22×C23#39012yes—
281C22×C23#39011yescharacteristic
282C22×C23C2×#9912yes—
283C22×C23#41012yes—
284C4×C23—24no—
285C4×C23—48no—
286C4×C23—42no—
287C4×C23—42no—
288C4×C23—84no—
289C4×C23—82no—
290C23×D4C22×C2311yescharacteristic
291C24×C4C22×C2311yescharacteristic
292C22×C22⋊C4C4×C2312yescomplemented
293C22×C22⋊C4C22×C2311yescharacteristic
294C22×C22⋊C4C22×C2312yes—
295C22×C22⋊C4C22×C2312yes—
296C22×C42—21no—
297C2×#99—24no—
298C2×#99—24no—
299C2×#99C4×C2318yescomplemented
300#386—21no—
301#386—22no—
302#386—21no—
303C4×C22⋊C4—24no—
304C2×#95—21no—
305C2×#95—22no—
306C2×#95C4×C2312yescomplemented
307#342—24no—
308C2×C23—22no—
309C2×C23—22no—
310C2×C23—22no—
311C2×C23—22no—
312C2×C23—22no—
313C2×C23—22no—
314C2×C23—82no—
315C2×C23#143711yescharacteristic
316C2×C23C4×#9912yes—
317C2×C23#189811yescharacteristic
318C2×C23#189911yescharacteristic
319C2×C23#196412yes—
320C25C2×C4×C2311yescharacteristic
321C25C23×C2311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4C2×C4×C2314yes—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—44no—
335C23×C4C2×C4×C2311yescharacteristic
336C23×C4C2×C4×C2312yes—
337C23×C4C2×C4×C2312yes—
338C23×C4D4×C2311yescharacteristic
339C23×C4D4×C2312yes—
340C23×C4D4×C2311yescharacteristic
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×C4×C2314yes—
357C2×C22⋊C4C2×C4×C2314yes—
358C2×C22⋊C4D4×C2314yes—
359C2×C22⋊C4D4×C2314yes—
360C2×C42—24no—
361C2×C42—44no—
362#99—216no—
363#95—24no—
364#95—22no—
365#95—22no—
366#95—44no—
367C23#1096011yescharacteristic, direct product factor, Sylow
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C2312yescomplemented
377C24C22×C4×C2311yescharacteristic
378C24C22×C4×C2312yes—
379C24C2×D4×C2311yescharacteristic
380C24C2×D4×C2311yescharacteristic
381C24C2×D4×C2312yes—
382C24C2×D4×C2312yes—
383C24#41×C2312yes—
384C24#41×C2312yes—
385C24#41×C2312yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C2312yescomplemented
435C22×C4C22⋊C4×C2312yes—
436C22×C4C22⋊C4×C2312yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C2318yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—41no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C2311yescharacteristic
478C23C2×C22⋊C4×C2312yes—
479C23C2×C22⋊C4×C2311yescharacteristic
480C23C23×#11711yescharacteristic
481C23C23×#11712yes—
482C23C4×D4×C2312yes—
483C23C4×D4×C2312yes—
484C23C4×D4×C2312yes—
485C23C4×D4×C2312yes—
486C23C4×D4×C2312yes—
487C23C4×D4×C2312yes—
488C23C23×#12011yescharacteristic
489C23C23×#12112yes—
490C23C23×#12112yes—
491C23C23×#12112yes—
492C23C23×#12311yescharacteristic
493C23C23×#12312yes—
494C23C23×#12411yescharacteristic
495C23C23×#12412yes—
496C23C23×#12612yes—
497C23C23×#12711yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4C23×#9914yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—44no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C2312yes—
565C22C4×C22⋊C4×C2311yescharacteristic
566C22C23×#38612yes—
567C22C23×#38611yescharacteristic
568C22C23×#38812yes—
569C22C23×#38812yes—
570C22C23×#38812yes—
571C22C23×#39012yes—
572C22C23×#39011yescharacteristic
573C22C2×C23×#9912yes—
574C22C23×#41012yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2C23×#143711yescharacteristic
589C2C4×C23×#9912yes—
590C2C23×#189811yescharacteristic
591C2C23×#189911yescharacteristic
592C2C23×#196412yes—
subgroupG/H
center, socleC23×C23C2×C22⋊C4
commutatorC23C2×C42×C23
Frattini, cosocleC25C23×C23
prime radicalC23×D4×C23C22
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
3. C2×C4×C22⋊C4×C23C2semidirect
4. C2×C23×#342C2semidirect
5. C23×C22⋊#95C2semidirect
8. C22×C22⋊C4×C23C4semidirect
15. C2×C23×#99C4semidirect
22. C2×C23×#95C4semidirect
79. C24×C23C42semidirect
137. C22×C4×C23C42semidirect
152. C22⋊C4×C23C22⋊C4semidirect
154. #10960C23direct (N × H)
236. C2×C4×C23#99semidirect
239. C2×C4×C22⋊C4C2×C23semidirect
240. C2×#342C2×C23semidirect
241. C22⋊#95C2×C23semidirect
292. C22×C22⋊C4C4×C23semidirect
299. C2×#99C4×C23semidirect
306. C2×#95C4×C23semidirect
367. C23#10960direct (N × H)
376. C24C42×C23semidirect
434. C22×C4C42×C23semidirect
449. C22⋊C4C22⋊C4×C23semidirect
532. C2×C4C23×#99semidirect

Maximal subgroups

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

subgroupindex
C22×C23×#992
C2×C23×#3862
C2×C4×C22⋊C4×C232
C2×C23×#3422
C23×C22⋊#952
#1096023