Finite Group Databasebeta

← C23×#9079 #19156705

Subgroups — C23×#9079 #19156705

Order 5888.

1136 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×C22⋊C8C211yesmaximal, characteristic, complemented
2C2×C23×#386C211yesmaximal, characteristic
3C23×#1779C211yesmaximal, characteristic, complemented
4C2×C23×#323C212yesmaximal, complemented
5C23×#1280C212yesmaximal, complemented
6C23×D4×C23C411yescharacteristic
7C24×C4×C23C2211yescharacteristic
8C23×C8×C23—21no—
9C22×C22⋊C4×C23C411yescharacteristic
10C22×C22⋊C4×C23C411yescharacteristic
11C22×C22⋊C4×C23C2211yescharacteristic
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×#386—21no—
19C23×#386—21no—
20C23×#386—21no—
21C23×#386—21no—
22C2×C23×#95C411yescharacteristic
23C2×C23×#95C2211yescharacteristic
24C23×#323—24no—
25C25×C23C2×C411yescharacteristic
26C25×C23C2×C411yescharacteristic
27C22×D4×C23—21no—
28C22×D4×C23—21no—
29C22×D4×C23—22no—
30C22×D4×C23—42no—
31C22×D4×C23—42no—
32C22×D4×C23C814yescomplemented
33C23×C4×C23—22no—
34C23×C4×C23—22no—
35C23×C4×C23—42no—
36C23×C4×C23—42no—
37C23×C4×C23C2×C411yescharacteristic
38C23×C4×C23C2×C411yescharacteristic
39C23×C4×C23C2×C411yescharacteristic
40C23×C4×C23C2×C411yescharacteristic
41C23×C4×C23D411yescharacteristic
42C23×C4×C23D411yescharacteristic
43C23×C4×C23D411yescharacteristic
44C23×C4×C23D411yescharacteristic
45C23×C4×C23C2311yescharacteristic
46C22×C8×C23—24no—
47C22×C8×C23—22no—
48C22×C8×C23—22no—
49C22×C8×C23—42no—
50C22×C8×C23—42no—
51C2×C22⋊C4×C23—21no—
52C2×C22⋊C4×C23—21no—
53C2×C22⋊C4×C23—21no—
54C2×C22⋊C4×C23—21no—
55C2×C22⋊C4×C23—22no—
56C2×C22⋊C4×C23—21no—
57C2×C22⋊C4×C23—21no—
58C2×C22⋊C4×C23—22no—
59C2×C22⋊C4×C23—42no—
60C2×C22⋊C4×C23—42no—
61C23×C22⋊C8—24no—
62C23×C22⋊C8—22no—
63C23×C22⋊C8—22no—
64C23×C22⋊C8—22no—
65C23×C22⋊C8—42no—
66C23×C22⋊C8—42no—
67C23×C22⋊C8D414yescomplemented
68C23×#95—21no—
69C23×#95—21no—
70C23×#95—21no—
71C23×#95—21no—
72C24×C23—22no—
73C24×C23—22no—
74C24×C23—22no—
75C24×C23—22no—
76C24×C23—21no—
77C24×C23—21no—
78C24×C23—22no—
79C24×C23—22no—
80C24×C23—41no—
81C24×C23—41no—
82C24×C23—41no—
83C24×C23—41no—
84C24×C23—41no—
85C24×C23—41no—
86C24×C23C22⋊C411yescharacteristic
87C24×C23C22⋊C411yescharacteristic
88C24×C23C2×C812yes—
89C24×C23C2×C812yescomplemented
90C24×C23M1612yes—
91C24×C23C22×C411yescharacteristic
92C2×D4×C23—24no—
93C2×D4×C23—24no—
94C2×D4×C23—48no—
95C2×D4×C23—42no—
96C2×D4×C23—42no—
97C2×D4×C23—42no—
98C2×D4×C23—42no—
99C2×D4×C23—48no—
100C22×C4×C23—22no—
101C22×C4×C23—22no—
102C22×C4×C23—21no—
103C22×C4×C23—21no—
104C22×C4×C23—22no—
105C22×C4×C23—21no—
106C22×C4×C23—22no—
107C22×C4×C23—21no—
108C22×C4×C23—22no—
109C22×C4×C23—22no—
110C22×C4×C23—21no—
111C22×C4×C23—22no—
112C22×C4×C23—22no—
113C22×C4×C23—21no—
114C22×C4×C23—21no—
115C22×C4×C23—21no—
116C22×C4×C23—22no—
117C22×C4×C23—22no—
118C22×C4×C23—41no—
119C22×C4×C23—41no—
120C22×C4×C23—41no—
121C22×C4×C23—41no—
122C22×C4×C23—41no—
123C22×C4×C23—41no—
124C22×C4×C23—41no—
125C22×C4×C23—48no—
126C22×C4×C23—48no—
127C22×C4×C23—41no—
128C22×C4×C23—41no—
129C22×C4×C23—41no—
130C22×C4×C23—41no—
131C22×C4×C23—41no—
132C22×C4×C23—41no—
133C22×C4×C23C22⋊C411yescharacteristic
134C22×C4×C23C22⋊C411yescharacteristic
135C22×C4×C23C2×C812yescomplemented
136C22×C4×C23C2×D411yescharacteristic
137C22×C4×C23C2×D411yescharacteristic
138C22×C4×C23C2×D412yes—
139C22×C4×C23#4112yes—
140C2×C8×C23—24no—
141C2×C8×C23—48no—
142C2×C8×C23—42no—
143C2×C8×C23—42no—
144C2×C8×C23—42no—
145C2×C8×C23—42no—
146C2×C8×C23—42no—
147C22⋊C4×C23—42no—
148C22⋊C4×C23—42no—
149C22⋊C4×C23—42no—
150C22⋊C4×C23—42no—
151C22⋊C4×C23—41no—
152C22⋊C4×C23—42no—
153C22⋊C4×C23—41no—
154#9079C2311yesmaximal, characteristic, direct product factor, Sylow
155C23×C23—21no—
156C23×C23—21no—
157C23×C23—21no—
158C23×C23—21no—
159C23×C23—21no—
160C23×C23—21no—
161C23×C23—21no—
162C23×C23—21no—
163C23×C23—24no—
164C23×C23—24no—
165C23×C23—21no—
166C23×C23—21no—
167C23×C23—21no—
168C23×C23—21no—
169C23×C23—21no—
170C23×C23—21no—
171C23×C23—24no—
172C23×C23—24no—
173C23×C23—22no—
174C23×C23—24no—
175C23×C23—42no—
176C23×C23—42no—
177C23×C23—44no—
178C23×C23—44no—
179C23×C23—44no—
180C23×C23—44no—
181C23×C23—42no—
182C23×C23—42no—
183C23×C23—42no—
184C23×C23—42no—
185C23×C23—41no—
186C23×C23—41no—
187C23×C23—41no—
188C23×C23—41no—
189C23×C23—41no—
190C23×C23—41no—
191C23×C23—42no—
192C23×C23—82no—
193C23×C23—82no—
194C23×C23—82no—
195C23×C23—82no—
196C23×C23C22⋊C812yes—
197C23×C23C22⋊C812yes—
198C23×C23#9912yes—
199C23×C23#10012yes—
200C23×C23C2×C22⋊C411yescharacteristic
201C23×C23C4×D412yes—
202C23×C23C22×C811yescharacteristic
203C23×C23C2×M1611yescharacteristic
204C23×C23#13112yes—
205D4×C23—48no—
206D4×C23—48no—
207C2×C4×C23—24no—
208C2×C4×C23—24no—
209C2×C4×C23—21no—
210C2×C4×C23—21no—
211C2×C4×C23—21no—
212C2×C4×C23—21no—
213C2×C4×C23—21no—
214C2×C4×C23—21no—
215C2×C4×C23—21no—
216C2×C4×C23—22no—
217C2×C4×C23—21no—
218C2×C4×C23—21no—
219C2×C4×C23—42no—
220C2×C4×C23—42no—
221C2×C4×C23—44no—
222C2×C4×C23—44no—
223C2×C4×C23—44no—
224C2×C4×C23—42no—
225C2×C4×C23—42no—
226C2×C4×C23—42no—
227C2×C4×C23—41no—
228C2×C4×C23—41no—
229C2×C4×C23—42no—
230C2×C4×C23—41no—
231C2×C4×C23—41no—
232C2×C4×C23—41no—
233C2×C4×C23—41no—
234C2×C4×C23—41no—
235C2×C4×C23—41no—
236C2×C4×C23—82no—
237C2×C4×C23—82no—
238C2×C4×C23#9912yes—
239C2×C4×C23#12011yescharacteristic
240C2×C4×C23#12112yes—
241C2×C4×C23#12311yescharacteristic
242C8×C23—44no—
243C8×C23—82no—
244C22×C22⋊C8C2×C2311yescharacteristic, complemented
245C2×#386C2×C2311yescharacteristic
246#1779C2×C2311yescharacteristic, complemented
247C2×#323C2×C2312yescomplemented
248#1280C2×C2312yescomplemented
249C22×C23—22no—
250C22×C23—22no—
251C22×C23—22no—
252C22×C23—22no—
253C22×C23—22no—
254C22×C23—21no—
255C22×C23—21no—
256C22×C23—21no—
257C22×C23—21no—
258C22×C23—22no—
259C22×C23—22no—
260C22×C23—22no—
261C22×C23—22no—
262C22×C23—22no—
263C22×C23—22no—
264C22×C23—22no—
265C22×C23—22no—
266C22×C23—48no—
267C22×C23—48no—
268C22×C23—41no—
269C22×C23—41no—
270C22×C23—41no—
271C22×C23—41no—
272C22×C23—42no—
273C22×C23—42no—
274C22×C23—42no—
275C22×C23—84no—
276C22×C23—84no—
277C22×C23—81no—
278C22×C23—81no—
279C22×C23—81no—
280C22×C23—81no—
281C22×C23#32314yescomplemented
282C22×C23#38611yescharacteristic
283C22×C23C2×C22⋊C811yescharacteristic
284C22×C23#40811yescharacteristic
285C22×C23C2×#9911yescharacteristic
286C22×C23C2×#9911yescharacteristic
287C22×C23C2×#10011yescharacteristic
288C22×C23#41311yescharacteristic
289C22×C23C8×D412yes—
290C22×C23#43512yes—
291C4×C23—21no—
292C4×C23—22no—
293C4×C23—22no—
294C4×C23—21no—
295C4×C23—41no—
296C4×C23—42no—
297C4×C23—81no—
298C4×C23—81no—
299C23×D4C4×C2311yescharacteristic
300C24×C4C22×C2311yescharacteristic
301C23×C8—21no—
302C22×C22⋊C4C4×C2311yescharacteristic
303C22×C22⋊C4C4×C2311yescharacteristic
304C22×C22⋊C4C22×C2311yescharacteristic
305C2×C22⋊C8—21no—
306C2×C22⋊C8—24no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C2312yes—
310C2×C22⋊C8C22×C2312yes—
311#386—21no—
312#386—21no—
313#386—21no—
314#386—21no—
315C2×#95C4×C2311yescharacteristic
316C2×#95C22×C2311yescharacteristic
317#323—24no—
318C2×C23—22no—
319C2×C23—22no—
320C2×C23—24no—
321C2×C23—42no—
322C2×C23—82no—
323C2×C23C2×#32311yescharacteristic
324C2×C23#145911yescharacteristic
325C2×C23#146811yescharacteristic
326C2×C23#147111yescharacteristic
327C2×C23#186911yescharacteristic
328C2×C23#189811yescharacteristic
329C2×C23#190011yescharacteristic
330C25C2×C4×C2311yescharacteristic
331C25C2×C4×C2311yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4C8×C2314yescomplemented
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4C2×C4×C2311yescharacteristic
343C23×C4C2×C4×C2311yescharacteristic
344C23×C4C2×C4×C2311yescharacteristic
345C23×C4C2×C4×C2311yescharacteristic
346C23×C4D4×C2311yescharacteristic
347C23×C4D4×C2311yescharacteristic
348C23×C4D4×C2311yescharacteristic
349C23×C4D4×C2311yescharacteristic
350C23×C4C23×C2311yescharacteristic
351C22×C8—24no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—42no—
355C22×C8—42no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C22⋊C8—24no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8D4×C2314yescomplemented
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377C23#907911yescharacteristic, direct product factor, Sylow
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24C22⋊C4×C2311yescharacteristic
393C24C22⋊C4×C2311yescharacteristic
394C24C2×C8×C2312yes—
395C24C2×C8×C2312yescomplemented
396C24M16×C2312yes—
397C24C22×C4×C2311yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—48no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C2311yescharacteristic
440C22×C4C22⋊C4×C2311yescharacteristic
441C22×C4C2×C8×C2312yescomplemented
442C22×C4C2×D4×C2311yescharacteristic
443C22×C4C2×D4×C2311yescharacteristic
444C22×C4C2×D4×C2312yes—
445C22×C4#41×C2312yes—
446C2×C8—24no—
447C2×C8—48no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—24no—
469C23—24no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—42no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23C23×C22⋊C812yes—
502C23C23×C22⋊C812yes—
503C23C23×#9912yes—
504C23C23×#10012yes—
505C23C2×C22⋊C4×C2311yescharacteristic
506C23C4×D4×C2312yes—
507C23C22×C8×C2311yescharacteristic
508C23C2×M16×C2311yescharacteristic
509C23C23×#13112yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C23×#9912yes—
544C2×C4C23×#12011yescharacteristic
545C2×C4C23×#12112yes—
546C2×C4C23×#12311yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—48no—
567C22—48no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—84no—
576C22—84no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C23×#32314yescomplemented
582C22C23×#38611yescharacteristic
583C22C2×C23×C22⋊C811yescharacteristic
584C22C23×#40811yescharacteristic
585C22C2×C23×#9911yescharacteristic
586C22C2×C23×#9911yescharacteristic
587C22C2×C23×#10011yescharacteristic
588C22C23×#41311yescharacteristic
589C22C8×D4×C2312yes—
590C22C23×#43512yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—42no—
603C2—82no—
604C2C2×C23×#32311yescharacteristic
605C2C23×#145911yescharacteristic
606C2C23×#146811yescharacteristic
607C2C23×#147111yescharacteristic
608C2C23×#186911yescharacteristic
609C2C23×#189811yescharacteristic
610C2C23×#190011yescharacteristic
subgroupG/H
center, socleC23×C23C2×C22⋊C4
commutatorC23C22×C8×C23
Frattini, cosocleC23×C4C23×C23
prime radicalC23×D4×C23C4
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
1. C22×C23×C22⋊C8C2semidirect
3. C23×#1779C2semidirect
4. C2×C23×#323C2semidirect
5. C23×#1280C2semidirect
32. C22×D4×C23C8semidirect
67. C23×C22⋊C8D4semidirect
89. C24×C23C2×C8semidirect
135. C22×C4×C23C2×C8semidirect
154. #9079C23direct (N × H)
244. C22×C22⋊C8C2×C23semidirect
246. #1779C2×C23semidirect
247. C2×#323C2×C23semidirect
248. #1280C2×C23semidirect
281. C22×C23#323semidirect
337. C22×D4C8×C23semidirect
372. C22⋊C8D4×C23semidirect
377. C23#9079direct (N × H)
395. C24C2×C8×C23semidirect
441. C22×C4C2×C8×C23semidirect
581. C22C23×#323semidirect

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×#3862
C23×#17792
C2×C23×#3232
C23×#12802
#907923