Finite Group Databasebeta

← C23×#33560 #19181186

Subgroups — C23×#33560 #19181186

Order 5888.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3551C211yesmaximal, characteristic, complemented
2C23×#3028C211yesmaximal, characteristic, complemented
3C23×#3027C211yesmaximal, characteristic, complemented
4C23×#3018C211yesmaximal, characteristic, complemented
5C23×#2200C214yesmaximal, complemented
6C23×#2197C214yesmaximal, complemented
7C23×#2126C211yesmaximal, characteristic, complemented
8C23×#2123C211yesmaximal, characteristic, complemented
9C23×#2122C211yesmaximal, characteristic, complemented
10C23×#585C2211yescharacteristic
11C23×#575—21no—
12C23×#563—21no—
13C23×#560C2212yescomplemented
14C23×#555—21no—
15C23×#553—21no—
16C23×#552—21no—
17C23×#551C2212yescomplemented
18C23×#548—21no—
19C23×#546—21no—
20C23×#540—22no—
21C23×#538—22no—
22C23×#537—21no—
23C23×#536—21no—
24C23×#536C2211yescharacteristic
25C23×#535—21no—
26C23×#535C2211yescharacteristic
27C23×#532C2211yescharacteristic
28C23×#529—21no—
29C23×#458—22no—
30C23×#458C2214yes—
31C23×B(4,𝔽2)—22no—
32C23×B(4,𝔽2)C2214yes—
33C23×#456—21no—
34C23×#455C2212yes—
35C23×#454—21no—
36C23×#453C2212yes—
37C2×C23×#104—21no—
38C23×#413C2211yescharacteristic
39C23×#410—21no—
40C23×#410—21no—
41C23×#410C2211yescharacteristic
42C23×#410C2211yescharacteristic
43C23×#354C2212yescomplemented
44C23×#353C2212yescomplemented
45C23×#352C2214yescomplemented
46C23×AΣL(1,𝔽16)C2214yescomplemented
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×C23D411yescharacteristic, complemented
59C2×#41×C23C2311yescharacteristic
60C22×Q8×C23D411yescharacteristic, complemented
61C22×D4×C23D411yescharacteristic
62C23×#137—22no—
63C23×#137—41no—
64C23×AGL(1,ℤ/8)—22no—
65C23×AGL(1,ℤ/8)—41no—
66C23×#135—42no—
67C2×M16×C23—21no—
68C23×C4⋊Q8—21no—
69C23×C4⋊Q8—41no—
70C23×C4⋊Q8D411yescharacteristic, complemented
71C23×#127—21no—
72C23×#127—41no—
73C23×#127C2311yescharacteristic
74C23×#126—22no—
75C23×#126—22no—
76C23×#126—22no—
77C23×#125—21no—
78C23×#125—22no—
79C23×#124—22no—
80C23×#124—21no—
81C23×#124—21no—
82C23×#124—21no—
83C23×#124—41no—
84C23×#124—41no—
85C23×#124D411yescharacteristic, complemented
86C23×#124C2311yescharacteristic
87C23×#123—22no—
88C23×#123—22no—
89C23×#123—22no—
90C23×#123—22no—
91C23×#123—24no—
92C23×#123D412yescomplemented
93C23×#123C2312yes—
94C23×C22⋊Q8—21no—
95C23×C22⋊Q8—22no—
96C23×C22⋊Q8—22no—
97C23×C22⋊Q8—21no—
98C23×C22⋊Q8—21no—
99C23×C22⋊Q8—42no—
100C23×#121—21no—
101C23×#121—22no—
102C23×#121—22no—
103C23×#121—22no—
104C23×#121—22no—
105C23×#121—21no—
106C23×#121—21no—
107C23×#121—21no—
108C23×#121—22no—
109C23×#121—21no—
110C23×#121—22no—
111C23×#121—42no—
112C23×#120—22no—
113C23×#120—24no—
114C23×#120D412yes—
115C23×#120C2312yes—
116C4×Q8×C23—21no—
117C4×D4×C23—22no—
118C4×D4×C23—21no—
119C4×D4×C23—22no—
120C4×D4×C23—22no—
121C4×D4×C23—21no—
122C4×D4×C23—21no—
123C23×#117—22no—
124C23×#117—22no—
125C23×#117—21no—
126C23×#117—21no—
127C23×#117D411yescharacteristic
128C23×#117D411yescharacteristic, complemented
129C2×C4⋊C4×C23—21no—
130C2×C22⋊C4×C23—22no—
131C2×C42×C23D411yescharacteristic, complemented
132C23×#104—22no—
133C23×#104—22no—
134C23×#101—21no—
135C23×#100C2312yes—
136C23×#99—21no—
137C23×#99—21no—
138C23×#99—24no—
139C23×#99—24no—
140C23×#99C2312yes—
141C23×#99C2312yes—
142C24×C23C2×D412yes—
143#41×C23—22no—
144#41×C23—22no—
145#41×C23—41no—
146#41×C23—41no—
147#41×C23—42no—
148#41×C23—41no—
149#41×C23—41no—
150#41×C23—41no—
151#41×C23—41no—
152#41×C23—41no—
153#41×C23—42no—
154#41×C23—42no—
155#41×C23—41no—
156#41×C23—41no—
157#41×C23—42no—
158#41×C23—41no—
159#41×C23—41no—
160#41×C23—41no—
161#41×C23—81no—
162#41×C23—81no—
163C2×Q8×C23—21no—
164C2×Q8×C23—21no—
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×Q8×C23C2×D411yescharacteristic
173C2×D4×C23—21no—
174C2×D4×C23—21no—
175C2×D4×C23—21no—
176C2×D4×C23—22no—
177C2×D4×C23—22no—
178C2×D4×C23—22no—
179C2×D4×C23—22no—
180C2×D4×C23—22no—
181C2×D4×C23—21no—
182C2×D4×C23—21no—
183C2×D4×C23—22no—
184C2×D4×C23—21no—
185C2×D4×C23—21no—
186C2×D4×C23—21no—
187C2×D4×C23—41no—
188C2×D4×C23—41no—
189C2×D4×C23—42no—
190C2×D4×C23—42no—
191C2×D4×C23—42no—
192C2×D4×C23—41no—
193C2×D4×C23—44no—
194C2×D4×C23C2×D411yescharacteristic
195C2×D4×C23C2×D411yescharacteristic
196C2×D4×C23C2×D411yescharacteristic
197C2×D4×C23C2411yescharacteristic
198C22×C4×C23—22no—
199C22×C4×C23—22no—
200C22×C4×C23—22no—
201C22×C4×C23—22no—
202C22×C4×C23—22no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—41no—
206C22×C4×C23C2×D411yescharacteristic
207C22×C4×C23C2×D411yescharacteristic
208C22×C4×C23C2×D411yescharacteristic
209C22×C4×C23C2×D412yes—
210Q16×C23—42no—
211SD16×C23—42no—
212SD16×C23—42no—
213D8×C23—42no—
214M16×C23—22no—
215M16×C23—41no—
216C2×C8×C23—41no—
217C4⋊C4×C23—22no—
218C4⋊C4×C23—22no—
219C4⋊C4×C23—22no—
220C4⋊C4×C23—22no—
221C4⋊C4×C23—22no—
222C4⋊C4×C23—22no—
223C4⋊C4×C23—21no—
224C4⋊C4×C23—21no—
225C4⋊C4×C23—21no—
226C4⋊C4×C23—21no—
227C4⋊C4×C23—22no—
228C4⋊C4×C23—41no—
229C4⋊C4×C23—41no—
230C4⋊C4×C23—44no—
231C22⋊C4×C23—22no—
232C22⋊C4×C23—22no—
233C22⋊C4×C23—22no—
234C22⋊C4×C23—22no—
235C22⋊C4×C23—22no—
236C22⋊C4×C23—22no—
237C22⋊C4×C23—21no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—21no—
240C22⋊C4×C23—21no—
241C22⋊C4×C23—21no—
242C22⋊C4×C23—22no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—22no—
245C22⋊C4×C23—22no—
246C22⋊C4×C23—44no—
247C22⋊C4×C23—44no—
248C22⋊C4×C23C2×D412yes—
249C22⋊C4×C23C2×D412yes—
250C42×C23—22no—
251C42×C23—21no—
252C42×C23—21no—
253C42×C23—21no—
254C42×C23—41no—
255C42×C23—41no—
256C42×C23C2×D411yescharacteristic
257C42×C23C2×D411yescharacteristic
258#33560C2311yesmaximal, characteristic, direct product factor, Sylow
259C23×C23—22no—
260C23×C23—22no—
261C23×C23—22no—
262C23×C23—21no—
263C23×C23—41no—
264C23×C23—42no—
265C23×C23—82no—
266C23×C23#12011yescharacteristic
267C23×C23C22×D411yescharacteristic
268C23×C23C22×D411yescharacteristic
269Q8×C23—22no—
270Q8×C23—41no—
271Q8×C23—41no—
272Q8×C23—41no—
273Q8×C23—41no—
274Q8×C23—41no—
275Q8×C23—41no—
276Q8×C23—41no—
277Q8×C23—81no—
278D4×C23—22no—
279D4×C23—41no—
280D4×C23—41no—
281D4×C23—41no—
282D4×C23—41no—
283D4×C23—41no—
284D4×C23—41no—
285D4×C23—42no—
286D4×C23—42no—
287D4×C23—42no—
288D4×C23—42no—
289D4×C23—41no—
290D4×C23—41no—
291D4×C23—41no—
292D4×C23—81no—
293D4×C23—81no—
294D4×C23—82no—
295D4×C23—82no—
296D4×C23—82no—
297D4×C23—81no—
298D4×C23—81no—
299D4×C23—82no—
300D4×C23—164no—
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—21no—
312C2×C4×C23—22no—
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—42no—
323C2×C4×C23—42no—
324C2×C4×C23—42no—
325C2×C4×C23—82no—
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#3551C2×C2311yescharacteristic, complemented
335#3028C2×C2311yescharacteristic, complemented
336#3027C2×C2311yescharacteristic, complemented
337#3018C2×C2311yescharacteristic, complemented
338#2200C2×C2314yescomplemented
339#2197C2×C2314yescomplemented
340#2126C2×C2311yescharacteristic, complemented
341#2123C2×C2311yescharacteristic, complemented
342#2122C2×C2311yescharacteristic, complemented
343C22×C23—21no—
344C22×C23—21no—
345C22×C23—21no—
346C22×C23—41no—
347C22×C23—41no—
348C22×C23—41no—
349C22×C23—41no—
350C22×C23—42no—
351C22×C23—41no—
352C22×C23—42no—
353C22×C23—42no—
354C22×C23—41no—
355C22×C23—42no—
356C22×C23—82no—
357C22×C23—84no—
358C22×C23—82no—
359C22×C23—161no—
360C22×C23C2×#12011yescharacteristic
361C4×C23—21no—
362C4×C23—21no—
363C4×C23—21no—
364C4×C23—41no—
365C4×C23—42no—
366C4×C23—42no—
367C4×C23—41no—
368C4×C23—42no—
369C4×C23—41no—
370C4×C23—42no—
371C4×C23—82no—
372C4×C23—82no—
373C4×C23B(4,𝔽2)11yescharacteristic
374C4×C23B(4,𝔽2)11yescharacteristic
375#585C22×C2311yescharacteristic
376#575—21no—
377#563—21no—
378#560C22×C2312yescomplemented
379#555—21no—
380#553—21no—
381#552—21no—
382#551C22×C2312yescomplemented
383#548—21no—
384#546—21no—
385#540—22no—
386#538—22no—
387#537—21no—
388#536—21no—
389#536C22×C2311yescharacteristic
390#535—21no—
391#535C22×C2311yescharacteristic
392#532C22×C2311yescharacteristic
393#529—21no—
394#458—22no—
395#458C22×C2314yes—
396B(4,𝔽2)—22no—
397B(4,𝔽2)C22×C2314yes—
398#456—21no—
399#455C22×C2312yes—
400#454—21no—
401#453C22×C2312yes—
402C2×#104—21no—
403#413C22×C2311yescharacteristic
404#410—21no—
405#410—21no—
406#410C22×C2311yescharacteristic
407#410C22×C2311yescharacteristic
408#354C22×C2312yescomplemented
409#353C22×C2312yescomplemented
410#352C22×C2314yescomplemented
411AΣL(1,𝔽16)C22×C2314yescomplemented
412C2×C23—21no—
413C2×C23—41no—
414C2×C23—41no—
415C2×C23—41no—
416C2×C23—81no—
417C2×C23—82no—
418C2×C23—82no—
419C2×C23C2×B(4,𝔽2)11yescharacteristic
4202−1+4—21no—
4212−1+4—41no—
422H(5,𝔽2)—21no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—41no—
425H(5,𝔽2)C23×C2312yes—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—42no—
431C2×#41D4×C2311yescharacteristic, complemented
432C2×#41C23×C2311yescharacteristic
433C22×Q8D4×C2311yescharacteristic, complemented
434C22×D4D4×C2311yescharacteristic
435#137—22no—
436#137—41no—
437AGL(1,ℤ/8)—22no—
438AGL(1,ℤ/8)—41no—
439#135—42no—
440C2×M16—21no—
441C4⋊Q8—21no—
442C4⋊Q8—41no—
443C4⋊Q8D4×C2311yescharacteristic, complemented
444#127—21no—
445#127—41no—
446#127C23×C2311yescharacteristic
447#126—22no—
448#126—22no—
449#126—22no—
450#125—21no—
451#125—22no—
452#124—21no—
453#124—22no—
454#124—21no—
455#124—21no—
456#124—41no—
457#124—41no—
458#124D4×C2311yescharacteristic, complemented
459#124C23×C2311yescharacteristic
460#123—22no—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—24no—
465#123D4×C2312yescomplemented
466#123C23×C2312yes—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—42no—
473#121—22no—
474#121—22no—
475#121—21no—
476#121—22no—
477#121—21no—
478#121—21no—
479#121—22no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—22no—
484#121—42no—
485#120—22no—
486#120—24no—
487#120D4×C2312yes—
488#120C23×C2312yes—
489C4×Q8—21no—
490C4×D4—22no—
491C4×D4—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—22no—
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117D4×C2311yescharacteristic
501#117D4×C2311yescharacteristic, complemented
502C2×C4⋊C4—21no—
503C2×C22⋊C4—22no—
504C2×C42D4×C2311yescharacteristic, complemented
505#104—22no—
506#104—22no—
507#101—21no—
508#100C23×C2312yes—
509#99—21no—
510#99—21no—
511#99—24no—
512#99—24no—
513#99C23×C2312yes—
514#99C23×C2312yes—
515C23#3356011yescharacteristic, direct product factor, Sylow
516C24C2×D4×C2312yes—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—81no—
536#41—81no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—42no—
545C2×Q8C2×D4×C2311yescharacteristic
546C2×Q8C2×D4×C2311yescharacteristic
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—44no—
568C2×D4C2×D4×C2311yescharacteristic
569C2×D4C2×D4×C2311yescharacteristic
570C2×D4C2×D4×C2311yescharacteristic
571C2×D4C24×C2311yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C2311yescharacteristic
581C22×C4C2×D4×C2311yescharacteristic
582C22×C4C2×D4×C2311yescharacteristic
583C22×C4C2×D4×C2312yes—
584Q16—42no—
585SD16—42no—
586SD16—42no—
587D8—42no—
588M16—22no—
589M16—41no—
590C2×C8—41no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—44no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4C2×D4×C2312yes—
623C22⋊C4C2×D4×C2312yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C2311yescharacteristic
631C42C2×D4×C2311yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23C23×#12011yescharacteristic
640C23C22×D4×C2311yescharacteristic
641C23C22×D4×C2311yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—82no—
671D4—81no—
672D4—81no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4C23×#12011yescharacteristic
703C2×C4C23×#12011yescharacteristic
704C2×C4C23×#12011yescharacteristic
705C2×C4C22×D4×C2311yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×C23×#12011yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C23×B(4,𝔽2)11yescharacteristic
738C4C23×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×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×#3551C2semidirect
2. C23×#3028C2semidirect
3. C23×#3027C2semidirect
4. C23×#3018C2semidirect
5. C23×#2200C2semidirect
6. C23×#2197C2semidirect
7. C23×#2126C2semidirect
8. C23×#2123C2semidirect
9. C23×#2122C2semidirect
13. C23×#560C22semidirect
17. C23×#551C22semidirect
43. C23×#354C22semidirect
44. C23×#353C22semidirect
45. C23×#352C22semidirect
46. C23×AΣL(1,𝔽16)C22semidirect
58. C2×#41×C23D4semidirect
60. C22×Q8×C23D4semidirect
70. C23×C4⋊Q8D4semidirect
85. C23×#124D4semidirect
92. C23×#123D4semidirect
128. C23×#117D4semidirect
131. C2×C42×C23D4semidirect
258. #33560C23direct (N × H)
334. #3551C2×C23semidirect
335. #3028C2×C23semidirect
336. #3027C2×C23semidirect
337. #3018C2×C23semidirect
338. #2200C2×C23semidirect
339. #2197C2×C23semidirect
340. #2126C2×C23semidirect
341. #2123C2×C23semidirect
342. #2122C2×C23semidirect
378. #560C22×C23semidirect
382. #551C22×C23semidirect
408. #354C22×C23semidirect
409. #353C22×C23semidirect
410. #352C22×C23semidirect
411. AΣL(1,𝔽16)C22×C23semidirect
431. C2×#41D4×C23semidirect
433. C22×Q8D4×C23semidirect
443. C4⋊Q8D4×C23semidirect
458. #124D4×C23semidirect
465. #123D4×C23semidirect
501. #117D4×C23semidirect
504. C2×C42D4×C23semidirect
515. C23#33560direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35512
C23×#30282
C23×#30272
C23×#30182
C23×#22002
C23×#21972
C23×#21262
C23×#21232
C23×#21222
#3356023