Finite Group Databasebeta

← C23×#33555 #19181181

Subgroups — C23×#33555 #19181181

Order 5888.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3540C211yesmaximal, characteristic, complemented
2C23×#3027C211yesmaximal, characteristic, complemented
3C23×#3025C211yesmaximal, characteristic, complemented
4C23×#3022C211yesmaximal, characteristic, complemented
5C23×#2199C214yesmaximal, complemented
6C23×#2197C214yesmaximal, complemented
7C23×#2129C211yesmaximal, characteristic, complemented
8C23×#2122C211yesmaximal, characteristic, complemented
9C23×#2120C211yesmaximal, characteristic, complemented
10C23×#585C2211yescharacteristic
11C2×C23×#137—21no—
12C23×H(3,𝔽4)C2212yescomplemented
13C23×#560—21no—
14C23×#559—21no—
15C23×#556—21no—
16C23×#555—21no—
17C23×#551C2212yescomplemented
18C23×#548—21no—
19C23×#546—21no—
20C23×#542—22no—
21C23×#542—21no—
22C23×#538—22no—
23C23×#536C2211yescharacteristic
24C23×#535—21no—
25C23×#535C2211yescharacteristic
26C23×#525—21no—
27C23×#525—21no—
28C23×#525C2211yescharacteristic
29C23×#458—21no—
30C23×#458C2212yes—
31C23×B(4,𝔽2)—21no—
32C23×B(4,𝔽2)—22no—
33C23×B(4,𝔽2)C2214yes—
34C23×B(4,𝔽2)C2212yes—
35C23×#456—22no—
36C23×#455C2214yes—
37C23×#421—21no—
38C23×#413C2211yescharacteristic
39C23×#410—21no—
40C23×#410—21no—
41C23×#410C2211yescharacteristic
42C23×#410C2211yescharacteristic
43C23×#354C2214yescomplemented
44C23×#352C2212yescomplemented
45C23×AΣL(1,𝔽16)C2214yescomplemented
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, complemented
62C23×#137—24no—
63C23×#137—42no—
64C2×Q16×C23—41no—
65C2×SD16×C23—41no—
66C2×M16×C23—21no—
67C23×C4⋊Q8—21no—
68C23×C4⋊Q8D412yescomplemented
69C23×#127—21no—
70C23×#127—41no—
71C23×#126—22no—
72C23×#126—22no—
73C23×#126—22no—
74C23×#124—21no—
75C23×#124—22no—
76C23×#124—22no—
77C23×#124—21no—
78C23×#124—22no—
79C23×#124—22no—
80C23×#124—22no—
81C23×#124—41no—
82C23×#124C2312yes—
83C23×#123—22no—
84C23×#123—22no—
85C23×#123—21no—
86C23×#123—21no—
87C23×#123—22no—
88C23×#123—22no—
89C23×#123D411yescharacteristic, complemented
90C23×#123C2311yescharacteristic
91C23×C22⋊Q8—21no—
92C23×C22⋊Q8—22no—
93C23×C22⋊Q8—22no—
94C23×C22⋊Q8—21no—
95C23×C22⋊Q8—21no—
96C23×C22⋊Q8—21no—
97C23×C22⋊Q8—41no—
98C23×#121—22no—
99C23×#121—22no—
100C23×#121—21no—
101C23×#121—22no—
102C23×#121—21no—
103C23×#121—21no—
104C23×#121—21no—
105C23×#121—42no—
106C23×#121—41no—
107C23×#120—22no—
108C23×#120—22no—
109C23×#120—22no—
110C23×#120—24no—
111C23×#120D411yescharacteristic, complemented
112C23×#120D412yescomplemented
113C23×#120C2312yes—
114C23×#120C2311yescharacteristic
115C4×Q8×C23—21no—
116C4×Q8×C23—22no—
117C4×D4×C23—22no—
118C4×D4×C23—21no—
119C4×D4×C23—22no—
120C4×D4×C23—21no—
121C4×D4×C23—22no—
122C4×D4×C23—21no—
123C4×D4×C23—42no—
124C23×#117—21no—
125C23×#117—22no—
126C23×#117—21no—
127C23×#117—21no—
128C23×#117D411yescharacteristic, complemented
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—24no—
138C23×#99—22no—
139C23×#99—22no—
140C23×#99C2312yes—
141C23×#99C2312yes—
142C24×C23C2×D412yes—
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—41no—
168C2×Q8×C23—41no—
169C2×Q8×C23—42no—
170C2×Q8×C23C2×D412yes—
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—21no—
182C2×D4×C23—22no—
183C2×D4×C23—21no—
184C2×D4×C23—21no—
185C2×D4×C23—41no—
186C2×D4×C23—41no—
187C2×D4×C23—42no—
188C2×D4×C23—42no—
189C2×D4×C23—42no—
190C2×D4×C23—41no—
191C2×D4×C23—42no—
192C2×D4×C23—44no—
193C2×D4×C23C2×D411yescharacteristic
194C2×D4×C23C2×D411yescharacteristic
195C2×D4×C23C2411yescharacteristic
196C22×C4×C23—22no—
197C22×C4×C23—22no—
198C22×C4×C23—22no—
199C22×C4×C23—22no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—41no—
204C22×C4×C23—41no—
205C22×C4×C23—41no—
206C22×C4×C23C2×D411yescharacteristic
207C22×C4×C23C2×D411yescharacteristic
208C22×C4×C23C2×D411yescharacteristic
209C22×C4×C23C2×D411yescharacteristic
210Q16×C23—44no—
211SD16×C23—44no—
212M16×C23—22no—
213M16×C23—41no—
214C2×C8×C23—41no—
215C4⋊C4×C23—22no—
216C4⋊C4×C23—22no—
217C4⋊C4×C23—22no—
218C4⋊C4×C23—21no—
219C4⋊C4×C23—21no—
220C4⋊C4×C23—22no—
221C4⋊C4×C23—22no—
222C4⋊C4×C23—21no—
223C4⋊C4×C23—21no—
224C4⋊C4×C23—21no—
225C4⋊C4×C23—41no—
226C4⋊C4×C23—41no—
227C4⋊C4×C23—42no—
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—21no—
236C22⋊C4×C23—21no—
237C22⋊C4×C23—22no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—21no—
240C22⋊C4×C23—22no—
241C22⋊C4×C23—22no—
242C22⋊C4×C23—21no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—22no—
245C22⋊C4×C23—42no—
246C22⋊C4×C23—44no—
247C22⋊C4×C23—42no—
248C22⋊C4×C23C2×D412yes—
249C22⋊C4×C23C2×D411yescharacteristic
250C22⋊C4×C23C2×D411yescharacteristic
251C42×C23—22no—
252C42×C23—22no—
253C42×C23—21no—
254C42×C23—21no—
255C42×C23—41no—
256C42×C23—41no—
257C42×C23C2×D412yes—
258#33555C2311yesmaximal, characteristic, direct product factor, Sylow
259C23×C23—22no—
260C23×C23—22no—
261C23×C23—22no—
262C23×C23—21no—
263C23×C23—41no—
264C23×C23—41no—
265C23×C23—42no—
266C23×C23—81no—
267C23×C23—82no—
268C23×C23#12011yescharacteristic
269C23×C23C22×D411yescharacteristic
270C23×C23C22×D411yescharacteristic
271Q8×C23—22no—
272Q8×C23—41no—
273Q8×C23—42no—
274Q8×C23—41no—
275Q8×C23—41no—
276Q8×C23—41no—
277Q8×C23—41no—
278Q8×C23—41no—
279Q8×C23—82no—
280D4×C23—22no—
281D4×C23—41no—
282D4×C23—41no—
283D4×C23—41no—
284D4×C23—41no—
285D4×C23—41no—
286D4×C23—42no—
287D4×C23—42no—
288D4×C23—42no—
289D4×C23—42no—
290D4×C23—41no—
291D4×C23—41no—
292D4×C23—41no—
293D4×C23—81no—
294D4×C23—81no—
295D4×C23—82no—
296D4×C23—82no—
297D4×C23—82no—
298D4×C23—81no—
299D4×C23—82no—
300D4×C23—84no—
301D4×C23—164no—
302C2×C4×C23—21no—
303C2×C4×C23—21no—
304C2×C4×C23—21no—
305C2×C4×C23—21no—
306C2×C4×C23—21no—
307C2×C4×C23—21no—
308C2×C4×C23—22no—
309C2×C4×C23—22no—
310C2×C4×C23—21no—
311C2×C4×C23—22no—
312C2×C4×C23—21no—
313C2×C4×C23—22no—
314C2×C4×C23—22no—
315C2×C4×C23—21no—
316C2×C4×C23—42no—
317C2×C4×C23—42no—
318C2×C4×C23—42no—
319C2×C4×C23—41no—
320C2×C4×C23—42no—
321C2×C4×C23—41no—
322C2×C4×C23—41no—
323C2×C4×C23—41no—
324C2×C4×C23—42no—
325C2×C4×C23—42no—
326C2×C4×C23—81no—
327C2×C4×C23—81no—
328C2×C4×C23—82no—
329C2×C4×C23—82no—
330C2×C4×C23#12011yescharacteristic
331C2×C4×C23#12011yescharacteristic
332C2×C4×C23#12011yescharacteristic
333C2×C4×C23C22×D411yescharacteristic
334C8×C23—42no—
335#3540C2×C2311yescharacteristic, complemented
336#3027C2×C2311yescharacteristic, complemented
337#3025C2×C2311yescharacteristic, complemented
338#3022C2×C2311yescharacteristic, complemented
339#2199C2×C2314yescomplemented
340#2197C2×C2314yescomplemented
341#2129C2×C2311yescharacteristic, complemented
342#2122C2×C2311yescharacteristic, complemented
343#2120C2×C2311yescharacteristic, complemented
344C22×C23—21no—
345C22×C23—21no—
346C22×C23—21no—
347C22×C23—41no—
348C22×C23—41no—
349C22×C23—41no—
350C22×C23—42no—
351C22×C23—41no—
352C22×C23—41no—
353C22×C23—42no—
354C22×C23—42no—
355C22×C23—42no—
356C22×C23—41no—
357C22×C23—42no—
358C22×C23—82no—
359C22×C23—82no—
360C22×C23—84no—
361C22×C23—81no—
362C22×C23—161no—
363C22×C23C2×#12011yescharacteristic
364C4×C23—21no—
365C4×C23—21no—
366C4×C23—21no—
367C4×C23—41no—
368C4×C23—42no—
369C4×C23—42no—
370C4×C23—41no—
371C4×C23—42no—
372C4×C23—41no—
373C4×C23—42no—
374C4×C23—82no—
375C4×C23—82no—
376C4×C23B(4,𝔽2)11yescharacteristic
377C4×C23B(4,𝔽2)11yescharacteristic
378#585C22×C2311yescharacteristic
379C2×#137—21no—
380H(3,𝔽4)C22×C2312yescomplemented
381#560—21no—
382#559—21no—
383#556—21no—
384#555—21no—
385#551C22×C2312yescomplemented
386#548—21no—
387#546—21no—
388#542—22no—
389#542—21no—
390#538—22no—
391#536C22×C2311yescharacteristic
392#535—21no—
393#535C22×C2311yescharacteristic
394#525—21no—
395#525—21no—
396#525C22×C2311yescharacteristic
397#458—21no—
398#458C22×C2312yes—
399B(4,𝔽2)—21no—
400B(4,𝔽2)—22no—
401B(4,𝔽2)C22×C2314yes—
402B(4,𝔽2)C22×C2312yes—
403#456—22no—
404#455C22×C2314yes—
405#421—21no—
406#413C22×C2311yescharacteristic
407#410—21no—
408#410—21no—
409#410C22×C2311yescharacteristic
410#410C22×C2311yescharacteristic
411#354C22×C2314yescomplemented
412#352C22×C2312yescomplemented
413AΣL(1,𝔽16)C22×C2312yescomplemented
414AΣL(1,𝔽16)C22×C2314yescomplemented
415C2×C23—21no—
416C2×C23—41no—
417C2×C23—41no—
418C2×C23—41no—
419C2×C23—81no—
420C2×C23—82no—
421C2×C23—82no—
422C2×C23C2×B(4,𝔽2)11yescharacteristic
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C2312yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C2311yescharacteristic
435C22×Q8D4×C2311yescharacteristic, complemented
436C22×D4D4×C2311yescharacteristic, complemented
437C23×C4D4×C2311yescharacteristic, complemented
438#137—24no—
439#137—42no—
440C2×Q16—41no—
441C2×SD16—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8D4×C2312yescomplemented
445#127—21no—
446#127—41no—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—21no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124C23×C2312yes—
459#123—22no—
460#123—22no—
461#123—21no—
462#123—21no—
463#123—22no—
464#123—22no—
465#123D4×C2311yescharacteristic, complemented
466#123C23×C2311yescharacteristic
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—41no—
474#121—21no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—42no—
482#121—41no—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—24no—
487#120D4×C2311yescharacteristic, complemented
488#120D4×C2312yescomplemented
489#120C23×C2311yescharacteristic
490#120C23×C2312yes—
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—22no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C2311yescharacteristic, complemented
505#117D4×C2311yescharacteristic, complemented
506#117D4×C2311yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C2312yes—
511#99—21no—
512#99—21no—
513#99—24no—
514#99—22no—
515#99—22no—
516#99C23×C2312yes—
517#99C23×C2312yes—
518C23#3355511yescharacteristic, direct product factor, Sylow
519C24C2×D4×C2312yes—
520C24C2×D4×C2311yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C2312yes—
548C2×Q8C2×D4×C2311yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C2311yescharacteristic
571C2×D4C2×D4×C2311yescharacteristic
572C2×D4C24×C2311yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C2311yescharacteristic
584C22×C4C2×D4×C2311yescharacteristic
585C22×C4C2×D4×C2311yescharacteristic
586C22×C4C2×D4×C2311yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C2312yes—
626C22⋊C4C2×D4×C2311yescharacteristic
627C22⋊C4C2×D4×C2311yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C2312yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23C23×#12011yescharacteristic
645C23C22×D4×C2311yescharacteristic
646C23C22×D4×C2311yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—81no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4C23×#12011yescharacteristic
707C2×C4C23×#12011yescharacteristic
708C2×C4C23×#12011yescharacteristic
709C2×C4C22×D4×C2311yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×C23×#12011yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4C23×B(4,𝔽2)11yescharacteristic
744C4C23×B(4,𝔽2)11yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3027C2semidirect
3. C23×#3025C2semidirect
4. C23×#3022C2semidirect
5. C23×#2199C2semidirect
6. C23×#2197C2semidirect
7. C23×#2129C2semidirect
8. C23×#2122C2semidirect
9. C23×#2120C2semidirect
12. C23×H(3,𝔽4)C22semidirect
17. C23×#551C22semidirect
43. C23×#354C22semidirect
44. C23×#352C22semidirect
45. C23×AΣL(1,𝔽16)C22semidirect
46. C23×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C23D4semidirect
60. C22×D4×C23D4semidirect
61. C23×C4×C23D4semidirect
68. C23×C4⋊Q8D4semidirect
89. C23×#123D4semidirect
111. C23×#120D4semidirect
112. C23×#120D4semidirect
128. C23×#117D4semidirect
129. C23×#117D4semidirect
130. C23×#117D4semidirect
258. #33555C23direct (N × H)
335. #3540C2×C23semidirect
336. #3027C2×C23semidirect
337. #3025C2×C23semidirect
338. #3022C2×C23semidirect
339. #2199C2×C23semidirect
340. #2197C2×C23semidirect
341. #2129C2×C23semidirect
342. #2122C2×C23semidirect
343. #2120C2×C23semidirect
380. H(3,𝔽4)C22×C23semidirect
385. #551C22×C23semidirect
411. #354C22×C23semidirect
412. #352C22×C23semidirect
413. AΣL(1,𝔽16)C22×C23semidirect
414. AΣL(1,𝔽16)C22×C23semidirect
435. C22×Q8D4×C23semidirect
436. C22×D4D4×C23semidirect
437. C23×C4D4×C23semidirect
444. C4⋊Q8D4×C23semidirect
465. #123D4×C23semidirect
487. #120D4×C23semidirect
488. #120D4×C23semidirect
504. #117D4×C23semidirect
505. #117D4×C23semidirect
506. #117D4×C23semidirect
518. C23#33555direct (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×#30272
C23×#30252
C23×#30222
C23×#21992
C23×#21972
C23×#21292
C23×#21222
C23×#21202
#3355523