Finite Group Databasebeta

← C23×#24405 #19172031

Subgroups — C23×#24405 #19172031

Order 5888.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3484C211yesmaximal, characteristic
2C2×C23×#458C211yesmaximal, characteristic, complemented
3C22×C23×#99C211yesmaximal, characteristic, complemented
4C23×#2412C212yesmaximal, complemented
5C23×#2405C211yesmaximal, characteristic, complemented
6C23×#2044C212yesmaximal, complemented
7C23×#2022C212yesmaximal, complemented
8C23×#1898C212yesmaximal, complemented
9C23×#1890C211yesmaximal, characteristic, complemented
10C23×#1867C211yesmaximal, characteristic, complemented
11C23×#1790C211yesmaximal, characteristic, complemented
12C2×C23×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C23C2211yescharacteristic
14C23×#546—22no—
15C23×#546—22no—
16D42×C23—22no—
17D42×C23—22no—
18C23×#535—21no—
19C23×#534—21no—
20C23×#534C2212yes—
21C23×#525—21no—
22C2×C23×#123C2211yescharacteristic
23C2×C23×#123C2212yescomplemented
24C2×C23×#123C2211yescharacteristic, complemented
25C2×C23×#120—21no—
26C2×C23×#120C2212yes—
27C23×#518C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic, complemented
29C22×C22⋊C4×C23C2212yescomplemented
30C23×#458—24no—
31C2×C23×#99—24no—
32C2×C23×#99C2211yescharacteristic
33C2×C23×#99C2211yescharacteristic
34C2×C23×#99C2212yescomplemented
35C2×C23×#99C2212yescomplemented
36C2×C23×#99C2212yescomplemented
37C23×#397—22no—
38C23×#394—21no—
39C23×#394—21no—
40C23×#394—22no—
41C23×#386—22no—
42C23×#386C2211yescharacteristic
43C23×#386C2211yescharacteristic, complemented
44C23×#386C2212yescomplemented
45C23×#385—21no—
46C23×#385C2212yescomplemented
47C23×#381C2212yescomplemented
48C23×#380—22no—
49C23×#379—21no—
50C23×#379C2211yescharacteristic, complemented
51C23×#342C2212yescomplemented
52C23×#342C2212yescomplemented
53C25×C23D411yescharacteristic
54C25×C23C2311yescharacteristic
55C23×H(5,𝔽2)—22no—
56C23×H(5,𝔽2)—22no—
57C23×H(5,𝔽2)—42no—
58C2×#41×C23—21no—
59C2×#41×C23—22no—
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—21no—
63C22×D4×C23—22no—
64C22×D4×C23—21no—
65C22×D4×C23—21no—
66C22×D4×C23—22no—
67C22×D4×C23—22no—
68C22×D4×C23—42no—
69C22×D4×C23D411yescharacteristic
70C22×D4×C23D411yescharacteristic
71C22×D4×C23D412yes—
72C22×D4×C23D412yes—
73C22×D4×C23C2311yescharacteristic
74C22×D4×C23C2312yes—
75C22×D4×C23C2311yescharacteristic
76C23×C4×C23—22no—
77C23×C4×C23D411yescharacteristic
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
80C23×#127—22no—
81C23×#124—22no—
82C23×#123—22no—
83C23×#123—22no—
84C23×#123—22no—
85C23×#123—22no—
86C23×#123—22no—
87C23×#123—24no—
88C23×#123—42no—
89C23×#123—42no—
90C23×C22⋊Q8—21no—
91C23×C22⋊Q8—21no—
92C23×#121—21no—
93C23×#121—21no—
94C23×#121—22no—
95C23×#121—22no—
96C23×#121—22no—
97C23×#121—22no—
98C23×#121—22no—
99C23×#121—22no—
100C23×#120—22no—
101C23×#120—22no—
102C23×#120—22no—
103C23×#120—22no—
104C23×#120—22no—
105C23×#120—22no—
106C23×#120—22no—
107C23×#120—22no—
108C23×#120—22no—
109C4×D4×C23—22no—
110C4×D4×C23—22no—
111C4×D4×C23—22no—
112C4×D4×C23—22no—
113C23×#117—21no—
114C2×C4⋊C4×C23—22no—
115C2×C4⋊C4×C23—21no—
116C2×C4⋊C4×C23—21no—
117C2×C4⋊C4×C23—22no—
118C2×C22⋊C4×C23—21no—
119C2×C22⋊C4×C23—21no—
120C2×C22⋊C4×C23—21no—
121C2×C22⋊C4×C23—24no—
122C2×C22⋊C4×C23—21no—
123C2×C22⋊C4×C23—21no—
124C2×C22⋊C4×C23—21no—
125C2×C22⋊C4×C23—21no—
126C2×C22⋊C4×C23—22no—
127C2×C22⋊C4×C23—22no—
128C2×C22⋊C4×C23—21no—
129C2×C22⋊C4×C23—22no—
130C2×C22⋊C4×C23—22no—
131C2×C22⋊C4×C23—21no—
132C2×C22⋊C4×C23—21no—
133C2×C22⋊C4×C23—21no—
134C2×C22⋊C4×C23—22no—
135C2×C22⋊C4×C23—42no—
136C2×C22⋊C4×C23D412yes—
137C2×C22⋊C4×C23D412yes—
138C2×C22⋊C4×C23C2311yescharacteristic
139C2×C22⋊C4×C23C2311yescharacteristic
140C2×C22⋊C4×C23C2312yes—
141C2×C22⋊C4×C23C2312yes—
142C2×C22⋊C4×C23C2312yes—
143C23×#99—22no—
144C23×#99—24no—
145C23×#99—24no—
146C23×#99—42no—
147C23×#99D414yescomplemented
148C23×#95—22no—
149C23×#95—22no—
150C23×#95—22no—
151C23×#95—21no—
152C23×#95—21no—
153C23×#95—22no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—22no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—22no—
161C24×C23—41no—
162C24×C23—42no—
163C24×C23—42no—
164C24×C23—81no—
165C24×C23—81no—
166C24×C23C2×D411yescharacteristic
167C24×C23C2×D412yes—
168C24×C23C2×D411yescharacteristic
169C24×C23C2×D412yes—
170C24×C23C2×D412yes—
171C24×C23C2×D411yescharacteristic
172C24×C23C2×D411yescharacteristic
173C24×C23C2411yescharacteristic
174#41×C23—44no—
175#41×C23—44no—
176#41×C23—42no—
177#41×C23—42no—
178C2×Q8×C23—21no—
179C2×D4×C23—22no—
180C2×D4×C23—22no—
181C2×D4×C23—22no—
182C2×D4×C23—21no—
183C2×D4×C23—22no—
184C2×D4×C23—22no—
185C2×D4×C23—22no—
186C2×D4×C23—22no—
187C2×D4×C23—22no—
188C2×D4×C23—21no—
189C2×D4×C23—22no—
190C2×D4×C23—22no—
191C2×D4×C23—22no—
192C2×D4×C23—22no—
193C2×D4×C23—21no—
194C2×D4×C23—22no—
195C2×D4×C23—22no—
196C2×D4×C23—22no—
197C2×D4×C23—22no—
198C2×D4×C23—22no—
199C2×D4×C23—22no—
200C2×D4×C23—22no—
201C2×D4×C23—22no—
202C2×D4×C23—22no—
203C2×D4×C23—41no—
204C2×D4×C23—41no—
205C2×D4×C23—44no—
206C2×D4×C23—44no—
207C2×D4×C23—44no—
208C2×D4×C23—44no—
209C2×D4×C23—44no—
210C2×D4×C23—44no—
211C2×D4×C23—42no—
212C2×D4×C23—42no—
213C2×D4×C23—44no—
214C2×D4×C23—82no—
215C2×D4×C23—82no—
216C2×D4×C23—82no—
217C2×D4×C23C2×D412yes—
218C2×D4×C23#4112yes—
219C22×C4×C23—21no—
220C22×C4×C23—22no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—22no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—22no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—22no—
232C22×C4×C23—22no—
233C22×C4×C23—22no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—22no—
237C22×C4×C23—41no—
238C22×C4×C23—44no—
239C22×C4×C23—44no—
240C22×C4×C23—81no—
241C22×C4×C23—82no—
242C22×C4×C23C2×D412yes—
243C22×C4×C23C2×D411yescharacteristic
244C22×C4×C23C2×D411yescharacteristic
245C22×C4×C23C2×D412yes—
246C22×C4×C23C2×D412yes—
247C4⋊C4×C23—21no—
248C4⋊C4×C23—21no—
249C4⋊C4×C23—22no—
250C4⋊C4×C23—22no—
251C4⋊C4×C23—44no—
252C4⋊C4×C23—42no—
253C4⋊C4×C23—42no—
254C4⋊C4×C23—82no—
255C22⋊C4×C23—22no—
256C22⋊C4×C23—22no—
257C22⋊C4×C23—22no—
258C22⋊C4×C23—22no—
259C22⋊C4×C23—22no—
260C22⋊C4×C23—22no—
261C22⋊C4×C23—22no—
262C22⋊C4×C23—22no—
263C22⋊C4×C23—22no—
264C22⋊C4×C23—22no—
265C22⋊C4×C23—22no—
266C22⋊C4×C23—22no—
267C22⋊C4×C23—22no—
268C22⋊C4×C23—21no—
269C22⋊C4×C23—21no—
270C22⋊C4×C23—22no—
271C22⋊C4×C23—22no—
272C22⋊C4×C23—44no—
273C22⋊C4×C23—44no—
274C22⋊C4×C23—42no—
275C22⋊C4×C23—42no—
276C22⋊C4×C23—41no—
277C22⋊C4×C23—42no—
278C22⋊C4×C23—41no—
279C22⋊C4×C23—42no—
280C22⋊C4×C23—81no—
281C22⋊C4×C23—81no—
282C22⋊C4×C23—81no—
283C22⋊C4×C23—82no—
284C22⋊C4×C23C2×D414yescomplemented
285C42×C23—22no—
286#24405C2311yesmaximal, characteristic, direct product factor, Sylow
287C23×C23—21no—
288C23×C23—21no—
289C23×C23—21no—
290C23×C23—22no—
291C23×C23—22no—
292C23×C23—22no—
293C23×C23—24no—
294C23×C23—21no—
295C23×C23—21no—
296C23×C23—21no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—21no—
300C23×C23—22no—
301C23×C23—21no—
302C23×C23—21no—
303C23×C23—22no—
304C23×C23—22no—
305C23×C23—42no—
306C23×C23—41no—
307C23×C23—41no—
308C23×C23—41no—
309C23×C23—41no—
310C23×C23—42no—
311C23×C23—42no—
312C23×C23—41no—
313C23×C23—42no—
314C23×C23—42no—
315C23×C23—41no—
316C23×C23—41no—
317C23×C23—41no—
318C23×C23—41no—
319C23×C23—42no—
320C23×C23—42no—
321C23×C23—42no—
322C23×C23—42no—
323C23×C23—42no—
324C23×C23—81no—
325C23×C23—81no—
326C23×C23—82no—
327C23×C23—82no—
328C23×C23—84no—
329C23×C23—81no—
330C23×C23—81no—
331C23×C23—84no—
332C23×C23—84no—
333C23×C23#12011yescharacteristic
334C23×C23#12012yes—
335C23×C23#12011yescharacteristic
336C23×C23#12112yes—
337C23×C23C22×D411yescharacteristic
338C23×C23C22×D412yes—
339C23×C23C22×D411yescharacteristic
340C23×C23C2×#4111yescharacteristic
341C23×C23H(5,𝔽2)12yes—
342Q8×C23—42no—
343D4×C23—24no—
344D4×C23—24no—
345D4×C23—44no—
346D4×C23—42no—
347D4×C23—44no—
348D4×C23—44no—
349D4×C23—44no—
350D4×C23—42no—
351D4×C23—42no—
352D4×C23—42no—
353D4×C23—42no—
354D4×C23—42no—
355D4×C23—42no—
356D4×C23—44no—
357D4×C23—82no—
358D4×C23—82no—
359D4×C23—82no—
360D4×C23—82no—
361C2×C4×C23—21no—
362C2×C4×C23—21no—
363C2×C4×C23—22no—
364C2×C4×C23—22no—
365C2×C4×C23—22no—
366C2×C4×C23—21no—
367C2×C4×C23—21no—
368C2×C4×C23—21no—
369C2×C4×C23—24no—
370C2×C4×C23—22no—
371C2×C4×C23—22no—
372C2×C4×C23—42no—
373C2×C4×C23—42no—
374C2×C4×C23—44no—
375C2×C4×C23—42no—
376C2×C4×C23—42no—
377C2×C4×C23—42no—
378C2×C4×C23—42no—
379C2×C4×C23—42no—
380C2×C4×C23—41no—
381C2×C4×C23—41no—
382C2×C4×C23—41no—
383C2×C4×C23—41no—
384C2×C4×C23—42no—
385C2×C4×C23—42no—
386C2×C4×C23—41no—
387C2×C4×C23—41no—
388C2×C4×C23—42no—
389C2×C4×C23—42no—
390C2×C4×C23—41no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—41no—
394C2×C4×C23—41no—
395C2×C4×C23—41no—
396C2×C4×C23—42no—
397C2×C4×C23—42no—
398C2×C4×C23—42no—
399C2×C4×C23—81no—
400C2×C4×C23—81no—
401C2×C4×C23—88no—
402C2×C4×C23#12112yes—
403#3484C2×C2311yescharacteristic
404C2×#458C2×C2311yescharacteristic, complemented
405C22×#99C2×C2311yescharacteristic, complemented
406#2412C2×C2312yescomplemented
407#2405C2×C2311yescharacteristic, complemented
408#2044C2×C2312yescomplemented
409#2022C2×C2312yescomplemented
410#1898C2×C2312yescomplemented
411#1890C2×C2311yescharacteristic, complemented
412#1867C2×C2311yescharacteristic, complemented
413#1790C2×C2311yescharacteristic, complemented
414C22×C23—21no—
415C22×C23—22no—
416C22×C23—21no—
417C22×C23—22no—
418C22×C23—21no—
419C22×C23—21no—
420C22×C23—21no—
421C22×C23—22no—
422C22×C23—22no—
423C22×C23—22no—
424C22×C23—21no—
425C22×C23—21no—
426C22×C23—22no—
427C22×C23—41no—
428C22×C23—41no—
429C22×C23—42no—
430C22×C23—44no—
431C22×C23—44no—
432C22×C23—42no—
433C22×C23—42no—
434C22×C23—42no—
435C22×C23—42no—
436C22×C23—41no—
437C22×C23—41no—
438C22×C23—42no—
439C22×C23—41no—
440C22×C23—42no—
441C22×C23—41no—
442C22×C23—42no—
443C22×C23—41no—
444C22×C23—82no—
445C22×C23—81no—
446C22×C23—81no—
447C22×C23—81no—
448C22×C23—82no—
449C22×C23—84no—
450C22×C23—82no—
451C22×C23—82no—
452C22×C23—81no—
453C22×C23—84no—
454C22×C23—162no—
455C22×C23#45812yescomplemented
456C22×C23C2×#12011yescharacteristic
457C22×C23C2×#12111yescharacteristic
458C22×C23#53411yescharacteristic
459C22×C23D4212yes—
460C22×C23#54612yes—
461C4×C23—22no—
462C4×C23—44no—
463C4×C23—41no—
464C4×C23—42no—
465C4×C23—42no—
466C4×C23—42no—
467C4×C23—81no—
468C4×C23—81no—
469C4×C23—82no—
470C4×C23—81no—
471C4×C23—81no—
472C2×H(5,𝔽2)C22×C2311yescharacteristic
473C23×D4C22×C2311yescharacteristic
474#546—22no—
475#546—22no—
476D42—22no—
477D42—22no—
478#535—21no—
479#534—21no—
480#534C22×C2312yes—
481#525—21no—
482C2×#123C22×C2311yescharacteristic
483C2×#123C22×C2312yescomplemented
484C2×#123C22×C2311yescharacteristic, complemented
485C2×#120—21no—
486C2×#120C22×C2312yes—
487#518C22×C2311yescharacteristic
488C22×C22⋊C4C22×C2311yescharacteristic, complemented
489C22×C22⋊C4C22×C2312yescomplemented
490#458—24no—
491C2×#99—24no—
492C2×#99C22×C2311yescharacteristic
493C2×#99C22×C2311yescharacteristic
494C2×#99C22×C2312yescomplemented
495C2×#99C22×C2312yescomplemented
496C2×#99C22×C2312yescomplemented
497#397—22no—
498#394—21no—
499#394—21no—
500#394—22no—
501#386—22no—
502#386C22×C2311yescharacteristic
503#386C22×C2311yescharacteristic, complemented
504#386C22×C2312yescomplemented
505#385—21no—
506#385C22×C2312yescomplemented
507#381C22×C2312yescomplemented
508#380—22no—
509#379—21no—
510#379C22×C2311yescharacteristic, complemented
511#342C22×C2312yescomplemented
512#342C22×C2312yescomplemented
513C2×C23—22no—
514C2×C23—21no—
515C2×C23—21no—
516C2×C23—22no—
517C2×C23—22no—
518C2×C23—42no—
519C2×C23—41no—
520C2×C23—42no—
521C2×C23—81no—
522C2×C23—82no—
523C2×C23#241011yescharacteristic
524C2×C23C2×#45811yescharacteristic
525C2×C23#302611yescharacteristic
526C25D4×C2311yescharacteristic
527C25C23×C2311yescharacteristic
528H(5,𝔽2)—22no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—42no—
531C2×#41—21no—
532C2×#41—22no—
533C22×D4—21no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—42no—
542C22×D4D4×C2311yescharacteristic
543C22×D4D4×C2311yescharacteristic
544C22×D4D4×C2312yes—
545C22×D4D4×C2312yes—
546C22×D4C23×C2312yes—
547C22×D4C23×C2311yescharacteristic
548C22×D4C23×C2311yescharacteristic
549C23×C4—22no—
550C23×C4D4×C2311yescharacteristic
551C23×C4C23×C2311yescharacteristic
552C23×C4C23×C2311yescharacteristic
553#127—22no—
554#124—22no—
555#123—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—24no—
561#123—42no—
562#123—42no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565#121—21no—
566#121—21no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#120—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586#117—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4D4×C2312yes—
610C2×C22⋊C4D4×C2312yes—
611C2×C22⋊C4C23×C2312yes—
612C2×C22⋊C4C23×C2311yescharacteristic
613C2×C22⋊C4C23×C2311yescharacteristic
614C2×C22⋊C4C23×C2312yes—
615C2×C22⋊C4C23×C2312yes—
616#99—22no—
617#99—24no—
618#99—24no—
619#99—42no—
620#99D4×C2314yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—21no—
625#95—21no—
626#95—22no—
627C23#2440511yescharacteristic, direct product factor, Sylow
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C2311yescharacteristic
641C24C2×D4×C2312yes—
642C24C2×D4×C2311yescharacteristic
643C24C2×D4×C2312yes—
644C24C2×D4×C2312yes—
645C24C2×D4×C2311yescharacteristic
646C24C2×D4×C2311yescharacteristic
647C24C24×C2311yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C2312yes—
692C2×D4#41×C2312yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C2312yes—
717C22×C4C2×D4×C2311yescharacteristic
718C22×C4C2×D4×C2311yescharacteristic
719C22×C4C2×D4×C2312yes—
720C22×C4C2×D4×C2312yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C2314yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23C23×#12011yescharacteristic
807C23C23×#12012yes—
808C23C23×#12011yescharacteristic
809C23C23×#12112yes—
810C23C22×D4×C2311yescharacteristic
811C23C22×D4×C2312yes—
812C23C22×D4×C2311yescharacteristic
813C23C2×#41×C2311yescharacteristic
814C23C23×H(5,𝔽2)12yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4C23×#12112yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C23×#45812yescomplemented
918C22C2×C23×#12011yescharacteristic
919C22C2×C23×#12111yescharacteristic
920C22C23×#53411yescharacteristic
921C22D42×C2312yes—
922C22C23×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C23×#241011yescharacteristic
945C2C2×C23×#45811yescharacteristic
946C2C23×#302611yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C25×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C23×#458C2semidirect
3. C22×C23×#99C2semidirect
4. C23×#2412C2semidirect
5. C23×#2405C2semidirect
6. C23×#2044C2semidirect
7. C23×#2022C2semidirect
8. C23×#1898C2semidirect
9. C23×#1890C2semidirect
10. C23×#1867C2semidirect
11. C23×#1790C2semidirect
23. C2×C23×#123C22semidirect
24. C2×C23×#123C22semidirect
28. C22×C22⋊C4×C23C22semidirect
29. C22×C22⋊C4×C23C22semidirect
34. C2×C23×#99C22semidirect
35. C2×C23×#99C22semidirect
36. C2×C23×#99C22semidirect
43. C23×#386C22semidirect
44. C23×#386C22semidirect
46. C23×#385C22semidirect
47. C23×#381C22semidirect
50. C23×#379C22semidirect
51. C23×#342C22semidirect
52. C23×#342C22semidirect
147. C23×#99D4semidirect
284. C22⋊C4×C23C2×D4semidirect
286. #24405C23direct (N × H)
404. C2×#458C2×C23semidirect
405. C22×#99C2×C23semidirect
406. #2412C2×C23semidirect
407. #2405C2×C23semidirect
408. #2044C2×C23semidirect
409. #2022C2×C23semidirect
410. #1898C2×C23semidirect
411. #1890C2×C23semidirect
412. #1867C2×C23semidirect
413. #1790C2×C23semidirect
455. C22×C23#458semidirect
483. C2×#123C22×C23semidirect
484. C2×#123C22×C23semidirect
488. C22×C22⋊C4C22×C23semidirect
489. C22×C22⋊C4C22×C23semidirect
494. C2×#99C22×C23semidirect
495. C2×#99C22×C23semidirect
496. C2×#99C22×C23semidirect
503. #386C22×C23semidirect
504. #386C22×C23semidirect
506. #385C22×C23semidirect
507. #381C22×C23semidirect
510. #379C22×C23semidirect
511. #342C22×C23semidirect
512. #342C22×C23semidirect
620. #99D4×C23semidirect
627. C23#24405direct (N × H)
758. C22⋊C4C2×D4×C23semidirect
917. C22C23×#458semidirect

Maximal subgroups

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

subgroupindex
C23×#34842
C2×C23×#4582
C22×C23×#992
C23×#24122
C23×#24052
C23×#20442
C23×#20222
C23×#18982
C23×#18902
C23×#18672
C23×#17902
#2440523