Finite Group Databasebeta

← C23×#33556 #19181182

Subgroups — C23×#33556 #19181182

Order 5888.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3540C211yesmaximal, characteristic, complemented
2C23×#3028C211yesmaximal, characteristic, complemented
3C23×#3025C211yesmaximal, characteristic, complemented
4C23×#3021C211yesmaximal, characteristic, complemented
5C23×#2200C214yesmaximal, complemented
6C23×#2198C214yesmaximal, complemented
7C23×#2128C211yesmaximal, characteristic, complemented
8C23×#2123C211yesmaximal, characteristic, complemented
9C23×#2120C211yesmaximal, characteristic, complemented
10C23×#585C2211yescharacteristic
11C2×C23×AGL(1,ℤ/8)—21no—
12C23×H(3,𝔽4)—21no—
13C23×#560C2212yescomplemented
14C23×#559C2212yescomplemented
15C23×#556—21no—
16C23×#555—21no—
17C23×#551—21no—
18C23×#548—21no—
19C23×#546—21no—
20C23×#542—22no—
21C23×#542—21no—
22C23×#538—22no—
23C23×#536—21no—
24C23×#536C2211yescharacteristic
25C23×#535C2211yescharacteristic
26C23×#525—21no—
27C23×#525—21no—
28C23×#525C2211yescharacteristic
29C23×#458—21no—
30C23×#458—22no—
31C23×#458C2212yescomplemented
32C23×#458C2214yescomplemented
33C23×B(4,𝔽2)—21no—
34C23×B(4,𝔽2)C2212yescomplemented
35C23×#454—22no—
36C23×#453C2214yes—
37C23×#421—21no—
38C23×#413C2211yescharacteristic
39C23×#410—21no—
40C23×#410—21no—
41C23×#410C2211yescharacteristic
42C23×#410C2211yescharacteristic
43C23×#353C2214yescomplemented
44C23×#352C2212yescomplemented
45C23×#352C2214yescomplemented
46C23×AΣL(1,𝔽16)C2212yescomplemented
47C23×2−1+4—21no—
48C23×2−1+4—41no—
49C23×H(5,𝔽2)—21no—
50C23×H(5,𝔽2)—21no—
51C23×H(5,𝔽2)—41no—
52C23×H(5,𝔽2)C2312yes—
53C2×#41×C23—21no—
54C2×#41×C23—21no—
55C2×#41×C23—21no—
56C2×#41×C23—21no—
57C2×#41×C23—42no—
58C2×#41×C23C2311yescharacteristic
59C22×Q8×C23D411yescharacteristic, complemented
60C22×D4×C23D411yescharacteristic, complemented
61C23×C4×C23D411yescharacteristic
62C23×AGL(1,ℤ/8)—24no—
63C23×AGL(1,ℤ/8)—42no—
64C2×SD16×C23—41no—
65C2×D8×C23—41no—
66C2×M16×C23—21no—
67C23×C4⋊Q8—21no—
68C23×C4⋊Q8—21no—
69C23×C4⋊Q8—41no—
70C23×#127C2312yes—
71C23×#126—22no—
72C23×#126—22no—
73C23×#126—22no—
74C23×#124—22no—
75C23×#124—21no—
76C23×#124—22no—
77C23×#124—22no—
78C23×#124—21no—
79C23×#124—22no—
80C23×#124—22no—
81C23×#124—41no—
82C23×#124D412yescomplemented
83C23×#123—22no—
84C23×#123—22no—
85C23×#123—22no—
86C23×#123—22no—
87C23×#123—24no—
88C23×#123D411yescharacteristic
89C23×#123D412yescomplemented
90C23×#123C2311yescharacteristic
91C23×#123C2312yes—
92C23×C22⋊Q8—22no—
93C23×C22⋊Q8—21no—
94C23×C22⋊Q8—22no—
95C23×C22⋊Q8—21no—
96C23×C22⋊Q8—21no—
97C23×C22⋊Q8—21no—
98C23×C22⋊Q8—42no—
99C23×C22⋊Q8—41no—
100C23×#121—21no—
101C23×#121—22no—
102C23×#121—21no—
103C23×#121—21no—
104C23×#121—22no—
105C23×#121—21no—
106C23×#121—22no—
107C23×#121—41no—
108C23×#120—22no—
109C23×#120—22no—
110C23×#120—21no—
111C23×#120—21no—
112C23×#120—22no—
113C23×#120D411yescharacteristic
114C23×#120C2311yescharacteristic
115C4×Q8×C23—21no—
116C4×Q8×C23—22no—
117C4×D4×C23—21no—
118C4×D4×C23—22no—
119C4×D4×C23—21no—
120C4×D4×C23—22no—
121C4×D4×C23—22no—
122C4×D4×C23—21no—
123C4×D4×C23—42no—
124C23×#117—22no—
125C23×#117—21no—
126C23×#117—21no—
127C23×#117—21no—
128C23×#117D411yescharacteristic
129C23×#117D411yescharacteristic, complemented
130C23×#117D411yescharacteristic, complemented
131C2×C22⋊C4×C23—22no—
132C23×#104—24no—
133C23×#101—21no—
134C23×#100C2312yes—
135C23×#99—21no—
136C23×#99—21no—
137C23×#99—22no—
138C23×#99—22no—
139C23×#99—24no—
140C23×#99C2312yes—
141C23×#99C2312yes—
142C24×C23—21no—
143C24×C23C2×D411yescharacteristic
144#41×C23—22no—
145#41×C23—22no—
146#41×C23—41no—
147#41×C23—41no—
148#41×C23—42no—
149#41×C23—41no—
150#41×C23—41no—
151#41×C23—41no—
152#41×C23—41no—
153#41×C23—41no—
154#41×C23—42no—
155#41×C23—42no—
156#41×C23—42no—
157#41×C23—41no—
158#41×C23—41no—
159#41×C23—41no—
160#41×C23—81no—
161#41×C23—81no—
162C2×Q8×C23—21no—
163C2×Q8×C23—21no—
164C2×Q8×C23—22no—
165C2×Q8×C23—21no—
166C2×Q8×C23—21no—
167C2×Q8×C23—21no—
168C2×Q8×C23—41no—
169C2×Q8×C23—41no—
170C2×Q8×C23—42no—
171C2×Q8×C23C2×D411yescharacteristic
172C2×D4×C23—21no—
173C2×D4×C23—21no—
174C2×D4×C23—21no—
175C2×D4×C23—22no—
176C2×D4×C23—22no—
177C2×D4×C23—22no—
178C2×D4×C23—22no—
179C2×D4×C23—21no—
180C2×D4×C23—22no—
181C2×D4×C23—22no—
182C2×D4×C23—21no—
183C2×D4×C23—21no—
184C2×D4×C23—41no—
185C2×D4×C23—41no—
186C2×D4×C23—42no—
187C2×D4×C23—42no—
188C2×D4×C23—42no—
189C2×D4×C23—41no—
190C2×D4×C23—42no—
191C2×D4×C23C2×D411yescharacteristic
192C2×D4×C23C2×D411yescharacteristic
193C2×D4×C23C2×D412yes—
194C2×D4×C23C2411yescharacteristic
195C22×C4×C23—22no—
196C22×C4×C23—22no—
197C22×C4×C23—22no—
198C22×C4×C23—22no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—41no—
202C22×C4×C23—41no—
203C22×C4×C23—41no—
204C22×C4×C23C2×D411yescharacteristic
205C22×C4×C23C2×D411yescharacteristic
206C22×C4×C23C2×D411yescharacteristic
207C22×C4×C23C2×D411yescharacteristic
208C22×C4×C23C2×D412yes—
209SD16×C23—44no—
210D8×C23—44no—
211M16×C23—22no—
212M16×C23—41no—
213C2×C8×C23—41no—
214C4⋊C4×C23—22no—
215C4⋊C4×C23—22no—
216C4⋊C4×C23—22no—
217C4⋊C4×C23—21no—
218C4⋊C4×C23—21no—
219C4⋊C4×C23—22no—
220C4⋊C4×C23—21no—
221C4⋊C4×C23—21no—
222C4⋊C4×C23—21no—
223C4⋊C4×C23—22no—
224C4⋊C4×C23—41no—
225C4⋊C4×C23—41no—
226C4⋊C4×C23—42no—
227C4⋊C4×C23—44no—
228C22⋊C4×C23—22no—
229C22⋊C4×C23—22no—
230C22⋊C4×C23—22no—
231C22⋊C4×C23—22no—
232C22⋊C4×C23—22no—
233C22⋊C4×C23—22no—
234C22⋊C4×C23—21no—
235C22⋊C4×C23—22no—
236C22⋊C4×C23—21no—
237C22⋊C4×C23—21no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—22no—
240C22⋊C4×C23—22no—
241C22⋊C4×C23—21no—
242C22⋊C4×C23—21no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—22no—
245C22⋊C4×C23—42no—
246C22⋊C4×C23—42no—
247C22⋊C4×C23—44no—
248C22⋊C4×C23C2×D411yescharacteristic
249C22⋊C4×C23C2×D411yescharacteristic
250C22⋊C4×C23C2×D412yes—
251C42×C23—22no—
252C42×C23—22no—
253C42×C23—21no—
254C42×C23—21no—
255C42×C23—41no—
256C42×C23—41no—
257C42×C23C2×D412yes—
258#33556C2311yesmaximal, characteristic, direct product factor, Sylow
259C23×C23—22no—
260C23×C23—22no—
261C23×C23—21no—
262C23×C23—22no—
263C23×C23—41no—
264C23×C23—41no—
265C23×C23—81no—
266C23×C23—81no—
267C23×C23—82no—
268C23×C23#12011yescharacteristic
269C23×C23C22×D411yescharacteristic
270C23×C23C22×D411yescharacteristic
271Q8×C23—22no—
272Q8×C23—41no—
273Q8×C23—41no—
274Q8×C23—41no—
275Q8×C23—41no—
276Q8×C23—41no—
277Q8×C23—41no—
278Q8×C23—81no—
279Q8×C23—82no—
280D4×C23—22no—
281D4×C23—41no—
282D4×C23—41no—
283D4×C23—41no—
284D4×C23—42no—
285D4×C23—41no—
286D4×C23—41no—
287D4×C23—42no—
288D4×C23—42no—
289D4×C23—42no—
290D4×C23—42no—
291D4×C23—41no—
292D4×C23—41no—
293D4×C23—41no—
294D4×C23—81no—
295D4×C23—82no—
296D4×C23—82no—
297D4×C23—82no—
298D4×C23—81no—
299D4×C23—82no—
300D4×C23—84no—
301C2×C4×C23—21no—
302C2×C4×C23—21no—
303C2×C4×C23—21no—
304C2×C4×C23—21no—
305C2×C4×C23—21no—
306C2×C4×C23—21no—
307C2×C4×C23—22no—
308C2×C4×C23—22no—
309C2×C4×C23—21no—
310C2×C4×C23—22no—
311C2×C4×C23—22no—
312C2×C4×C23—21no—
313C2×C4×C23—22no—
314C2×C4×C23—21no—
315C2×C4×C23—42no—
316C2×C4×C23—42no—
317C2×C4×C23—42no—
318C2×C4×C23—41no—
319C2×C4×C23—42no—
320C2×C4×C23—41no—
321C2×C4×C23—41no—
322C2×C4×C23—41no—
323C2×C4×C23—42no—
324C2×C4×C23—42no—
325C2×C4×C23—42no—
326C2×C4×C23—81no—
327C2×C4×C23—82no—
328C2×C4×C23—82no—
329C2×C4×C23#12011yescharacteristic
330C2×C4×C23#12011yescharacteristic
331C2×C4×C23#12011yescharacteristic
332C2×C4×C23C22×D411yescharacteristic
333C8×C23—42no—
334#3540C2×C2311yescharacteristic, complemented
335#3028C2×C2311yescharacteristic, complemented
336#3025C2×C2311yescharacteristic, complemented
337#3021C2×C2311yescharacteristic, complemented
338#2200C2×C2314yescomplemented
339#2198C2×C2314yescomplemented
340#2128C2×C2311yescharacteristic, complemented
341#2123C2×C2311yescharacteristic, complemented
342#2120C2×C2311yescharacteristic, complemented
343C22×C23—21no—
344C22×C23—21no—
345C22×C23—21no—
346C22×C23—41no—
347C22×C23—41no—
348C22×C23—41no—
349C22×C23—42no—
350C22×C23—41no—
351C22×C23—41no—
352C22×C23—42no—
353C22×C23—42no—
354C22×C23—42no—
355C22×C23—41no—
356C22×C23—42no—
357C22×C23—82no—
358C22×C23—82no—
359C22×C23—81no—
360C22×C23—161no—
361C22×C23—162no—
362C22×C23C2×#12011yescharacteristic
363C4×C23—21no—
364C4×C23—21no—
365C4×C23—21no—
366C4×C23—41no—
367C4×C23—42no—
368C4×C23—42no—
369C4×C23—41no—
370C4×C23—42no—
371C4×C23—41no—
372C4×C23—42no—
373C4×C23—82no—
374C4×C23—82no—
375C4×C23B(4,𝔽2)11yescharacteristic
376C4×C23B(4,𝔽2)11yescharacteristic
377#585C22×C2311yescharacteristic
378C2×AGL(1,ℤ/8)—21no—
379H(3,𝔽4)—21no—
380#560C22×C2312yescomplemented
381#559C22×C2312yescomplemented
382#556—21no—
383#555—21no—
384#551—21no—
385#548—21no—
386#546—21no—
387#542—22no—
388#542—21no—
389#538—22no—
390#536—21no—
391#536C22×C2311yescharacteristic
392#535C22×C2311yescharacteristic
393#525—21no—
394#525—21no—
395#525C22×C2311yescharacteristic
396#458—21no—
397#458—22no—
398#458C22×C2312yescomplemented
399#458C22×C2314yescomplemented
400B(4,𝔽2)—21no—
401B(4,𝔽2)C22×C2312yescomplemented
402#454—22no—
403#453C22×C2314yes—
404#421—21no—
405#413C22×C2311yescharacteristic
406#410—21no—
407#410—21no—
408#410C22×C2311yescharacteristic
409#410C22×C2311yescharacteristic
410#353C22×C2314yescomplemented
411#352C22×C2312yescomplemented
412#352C22×C2314yescomplemented
413AΣL(1,𝔽16)C22×C2312yescomplemented
414C2×C23—21no—
415C2×C23—41no—
416C2×C23—41no—
417C2×C23—41no—
418C2×C23—81no—
419C2×C23—82no—
420C2×C23—82no—
421C2×C23C2×B(4,𝔽2)11yescharacteristic
4222−1+4—21no—
4232−1+4—41no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—41no—
427H(5,𝔽2)C23×C2312yes—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—42no—
433C2×#41C23×C2311yescharacteristic
434C22×Q8D4×C2311yescharacteristic, complemented
435C22×D4D4×C2311yescharacteristic, complemented
436C23×C4D4×C2311yescharacteristic
437AGL(1,ℤ/8)—24no—
438AGL(1,ℤ/8)—42no—
439C2×SD16—41no—
440C2×D8—41no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—41no—
445#127C23×C2312yes—
446#126—22no—
447#126—22no—
448#126—22no—
449#124—22no—
450#124—21no—
451#124—22no—
452#124—22no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—41no—
457#124D4×C2312yescomplemented
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462#123—24no—
463#123D4×C2311yescharacteristic
464#123D4×C2312yescomplemented
465#123C23×C2311yescharacteristic
466#123C23×C2312yes—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474C22⋊Q8—41no—
475#121—21no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—22no—
482#121—41no—
483#120—22no—
484#120—22no—
485#120—21no—
486#120—21no—
487#120—22no—
488#120D4×C2311yescharacteristic
489#120C23×C2311yescharacteristic
490C4×Q8—21no—
491C4×Q8—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—42no—
499#117—21no—
500#117—22no—
501#117—21no—
502#117—21no—
503#117D4×C2311yescharacteristic
504#117D4×C2311yescharacteristic, complemented
505#117D4×C2311yescharacteristic, complemented
506C2×C22⋊C4—22no—
507#104—24no—
508#101—21no—
509#100C23×C2312yes—
510#99—21no—
511#99—21no—
512#99—22no—
513#99—22no—
514#99—24no—
515#99C23×C2312yes—
516#99C23×C2312yes—
517C23#3355611yescharacteristic, direct product factor, Sylow
518C24—21no—
519C24C2×D4×C2311yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C2311yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C2311yescharacteristic
568C2×D4C2×D4×C2311yescharacteristic
569C2×D4C2×D4×C2312yes—
570C2×D4C24×C2311yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C2311yescharacteristic
581C22×C4C2×D4×C2311yescharacteristic
582C22×C4C2×D4×C2311yescharacteristic
583C22×C4C2×D4×C2311yescharacteristic
584C22×C4C2×D4×C2312yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C2311yescharacteristic
625C22⋊C4C2×D4×C2311yescharacteristic
626C22⋊C4C2×D4×C2312yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C2312yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23C23×#12011yescharacteristic
644C23C22×D4×C2311yescharacteristic
645C23C22×D4×C2311yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4C23×#12011yescharacteristic
705C2×C4C23×#12011yescharacteristic
706C2×C4C23×#12011yescharacteristic
707C2×C4C22×D4×C2311yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×C23×#12011yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C23×B(4,𝔽2)11yescharacteristic
742C4C23×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×C23×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C23C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3540C2semidirect
2. C23×#3028C2semidirect
3. C23×#3025C2semidirect
4. C23×#3021C2semidirect
5. C23×#2200C2semidirect
6. C23×#2198C2semidirect
7. C23×#2128C2semidirect
8. C23×#2123C2semidirect
9. C23×#2120C2semidirect
13. C23×#560C22semidirect
14. C23×#559C22semidirect
31. C23×#458C22semidirect
32. C23×#458C22semidirect
34. C23×B(4,𝔽2)C22semidirect
43. C23×#353C22semidirect
44. C23×#352C22semidirect
45. C23×#352C22semidirect
46. C23×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C23D4semidirect
60. C22×D4×C23D4semidirect
82. C23×#124D4semidirect
89. C23×#123D4semidirect
129. C23×#117D4semidirect
130. C23×#117D4semidirect
258. #33556C23direct (N × H)
334. #3540C2×C23semidirect
335. #3028C2×C23semidirect
336. #3025C2×C23semidirect
337. #3021C2×C23semidirect
338. #2200C2×C23semidirect
339. #2198C2×C23semidirect
340. #2128C2×C23semidirect
341. #2123C2×C23semidirect
342. #2120C2×C23semidirect
380. #560C22×C23semidirect
381. #559C22×C23semidirect
398. #458C22×C23semidirect
399. #458C22×C23semidirect
401. B(4,𝔽2)C22×C23semidirect
410. #353C22×C23semidirect
411. #352C22×C23semidirect
412. #352C22×C23semidirect
413. AΣL(1,𝔽16)C22×C23semidirect
434. C22×Q8D4×C23semidirect
435. C22×D4D4×C23semidirect
457. #124D4×C23semidirect
464. #123D4×C23semidirect
504. #117D4×C23semidirect
505. #117D4×C23semidirect
517. C23#33556direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35402
C23×#30282
C23×#30252
C23×#30212
C23×#22002
C23×#21982
C23×#21282
C23×#21232
C23×#21202
#3355623