Finite Group Databasebeta

← C2×C23×#2200 #19181174

Subgroups — C2×C23×#2200 #19181174

Order 5888.

1328 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#560C211yesmaximal, characteristic, complemented
2C2×C23×#458C211yesmaximal, characteristic, complemented
3C2×C23×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C2×C23×#453C211yesmaximal, characteristic, complemented
5C23×#2200C218yesmaximal, direct product factor
6C2×C23×#353C211yesmaximal, characteristic, complemented
7C2×C23×#352C211yesmaximal, characteristic, complemented
8C2×C23×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
9C2×C23×H(5,𝔽2)C2211yescharacteristic
10C2×C23×AGL(1,ℤ/8)—21no—
11C23×#560—22no—
12C23×#560—22no—
13C23×#560—22no—
14C23×#560C2214yescomplemented
15C2×C23×#127C2211yescharacteristic
16C2×C23×#126—21no—
17C2×C23×#123—21no—
18C2×C23×#123—21no—
19C2×C23×#123C2211yescharacteristic
20C2×C23×#121—21no—
21C2×C23×#121—21no—
22C2×C23×#121—21no—
23C2×C23×#120—21no—
24C2×C23×#120—21no—
25C2×C23×#120C2211yescharacteristic
26C23×#458—22no—
27C23×#458C2214yescomplemented
28C23×B(4,𝔽2)—22no—
29C23×B(4,𝔽2)C2214yescomplemented
30C23×#453—22no—
31C23×#453C2214yescomplemented
32C2×C23×#104—21no—
33C2×C23×#100C2211yescharacteristic
34C2×C23×#99—21no—
35C2×C23×#99—21no—
36C2×C23×#99C2211yescharacteristic
37C2×C23×#99C2211yescharacteristic
38C23×#353C2214yescomplemented
39C23×#352C2214yescomplemented
40C23×AΣL(1,𝔽16)C2214yescomplemented
41C25×C23D411yescharacteristic
42C23×H(5,𝔽2)—21no—
43C23×H(5,𝔽2)—21no—
44C23×H(5,𝔽2)—21no—
45C23×H(5,𝔽2)—42no—
46C23×H(5,𝔽2)C2312yes—
47C2×#41×C23—21no—
48C2×#41×C23—41no—
49C22×D4×C23—21no—
50C22×D4×C23—21no—
51C22×D4×C23—21no—
52C22×D4×C23—21no—
53C22×D4×C23—21no—
54C22×D4×C23—21no—
55C22×D4×C23—21no—
56C22×D4×C23—41no—
57C22×D4×C23—41no—
58C22×D4×C23D411yescharacteristic, complemented
59C22×D4×C23C2311yescharacteristic
60C23×C4×C23—21no—
61C23×C4×C23D411yescharacteristic, complemented
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×#127—21no—
68C23×#127—21no—
69C23×#127D412yescomplemented
70C23×#127C2312yes—
71C23×#126—24no—
72C23×#126—24no—
73C23×#123—24no—
74C23×#123—21no—
75C23×#123—21no—
76C23×#123—24no—
77C23×#123—24no—
78C23×#123—42no—
79C23×#123D412yescomplemented
80C23×#123C2312yes—
81C23×#121—24no—
82C23×#121—24no—
83C23×#121—24no—
84C23×#121—24no—
85C23×#121—24no—
86C23×#121—24no—
87C23×#120—24no—
88C23×#120—24no—
89C23×#120—21no—
90C23×#120—21no—
91C23×#120—24no—
92C23×#120—42no—
93C23×#120D412yes—
94C23×#120C2312yes—
95C2×C4⋊C4×C23—21no—
96C2×C4⋊C4×C23—21no—
97C2×C4⋊C4×C23—21no—
98C2×C4⋊C4×C23—41no—
99C2×C22⋊C4×C23—21no—
100C2×C22⋊C4×C23—21no—
101C2×C22⋊C4×C23—21no—
102C2×C22⋊C4×C23—21no—
103C2×C22⋊C4×C23—21no—
104C2×C22⋊C4×C23—21no—
105C2×C22⋊C4×C23—21no—
106C2×C22⋊C4×C23—41no—
107C2×C22⋊C4×C23—41no—
108C2×C22⋊C4×C23D411yescharacteristic
109C2×C22⋊C4×C23D411yescharacteristic, complemented
110C2×C42×C23D411yescharacteristic, complemented
111C23×#104—24no—
112C23×#100—21no—
113C23×#100C2312yes—
114C23×#99—21no—
115C23×#99—21no—
116C23×#99—24no—
117C23×#99—24no—
118C23×#99C2312yes—
119C23×#99C2312yes—
120C24×C23—21no—
121C24×C23—21no—
122C24×C23—21no—
123C24×C23—21no—
124C24×C23—21no—
125C24×C23—41no—
126C24×C23—41no—
127C24×C23—82no—
128C24×C23C2×D411yescharacteristic
129C24×C23C2×D411yescharacteristic
130C24×C23C2×D412yes—
131#41×C23—22no—
132#41×C23—22no—
133#41×C23—42no—
134#41×C23—41no—
135#41×C23—42no—
136#41×C23—42no—
137#41×C23—42no—
138#41×C23—41no—
139C2×Q8×C23—21no—
140C2×D4×C23—21no—
141C2×D4×C23—22no—
142C2×D4×C23—22no—
143C2×D4×C23—22no—
144C2×D4×C23—22no—
145C2×D4×C23—24no—
146C2×D4×C23—24no—
147C2×D4×C23—22no—
148C2×D4×C23—22no—
149C2×D4×C23—22no—
150C2×D4×C23—22no—
151C2×D4×C23—22no—
152C2×D4×C23—22no—
153C2×D4×C23—21no—
154C2×D4×C23—41no—
155C2×D4×C23—41no—
156C2×D4×C23—41no—
157C2×D4×C23—41no—
158C2×D4×C23—42no—
159C2×D4×C23—42no—
160C2×D4×C23—41no—
161C2×D4×C23—41no—
162C2×D4×C23—41no—
163C2×D4×C23—41no—
164C2×D4×C23—42no—
165C2×D4×C23—42no—
166C2×D4×C23—41no—
167C2×D4×C23—41no—
168C2×D4×C23—41no—
169C2×D4×C23—44no—
170C2×D4×C23—82no—
171C2×D4×C23—82no—
172C2×D4×C23—82no—
173C2×D4×C23—82no—
174C2×D4×C23—81no—
175C2×D4×C23—81no—
176C2×D4×C23—84no—
177C2×D4×C23C2×D411yescharacteristic
178C2×D4×C23C2×D411yescharacteristic
179C2×D4×C23C2×D411yescharacteristic
180C2×D4×C23C2×D412yescomplemented
181C2×D4×C23C2411yescharacteristic
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—24no—
189C22×C4×C23—21no—
190C22×C4×C23—41no—
191C22×C4×C23—41no—
192C22×C4×C23—41no—
193C22×C4×C23—41no—
194C22×C4×C23—41no—
195C22×C4×C23—82no—
196C22×C4×C23C2×D411yescharacteristic
197C22×C4×C23C2×D412yescomplemented
198SD16×C23—44no—
199D8×C23—44no—
200M16×C23—22no—
201M16×C23—41no—
202C2×C8×C23—41no—
203C4⋊C4×C23—24no—
204C4⋊C4×C23—24no—
205C4⋊C4×C23—22no—
206C4⋊C4×C23—22no—
207C4⋊C4×C23—44no—
208C22⋊C4×C23—24no—
209C22⋊C4×C23—24no—
210C22⋊C4×C23—24no—
211C22⋊C4×C23—22no—
212C22⋊C4×C23—21no—
213C22⋊C4×C23—21no—
214C22⋊C4×C23—22no—
215C22⋊C4×C23—22no—
216C22⋊C4×C23—22no—
217C22⋊C4×C23—22no—
218C22⋊C4×C23—22no—
219C22⋊C4×C23—44no—
220C22⋊C4×C23—41no—
221C22⋊C4×C23—41no—
222C22⋊C4×C23—44no—
223C22⋊C4×C23C2×D412yes—
224C22⋊C4×C23C2×D412yescomplemented
225C42×C23—21no—
226C42×C23C2×D412yescomplemented
227C2×#2200C2311yesmaximal, characteristic, direct product factor, Sylow
228C23×C23—21no—
229C23×C23—21no—
230C23×C23—21no—
231C23×C23—21no—
232C23×C23—22no—
233C23×C23—22no—
234C23×C23—22no—
235C23×C23—22no—
236C23×C23—42no—
237C23×C23—42no—
238C23×C23—42no—
239C23×C23—42no—
240C23×C23—42no—
241C23×C23—42no—
242C23×C23—42no—
243C23×C23—41no—
244C23×C23—41no—
245C23×C23—44no—
246C23×C23—41no—
247C23×C23—41no—
248C23×C23—41no—
249C23×C23—41no—
250C23×C23—41no—
251C23×C23—81no—
252C23×C23—82no—
253C23×C23—82no—
254C23×C23—82no—
255C23×C23—84no—
256C23×C23—82no—
257C23×C23—82no—
258C23×C23#12011yescharacteristic
259C23×C23#12011yescharacteristic
260C23×C23#12011yescharacteristic
261C23×C23C22×D411yescharacteristic
262C23×C23C22×D411yescharacteristic
263Q8×C23—22no—
264Q8×C23—41no—
265D4×C23—22no—
266D4×C23—41no—
267D4×C23—41no—
268D4×C23—41no—
269D4×C23—41no—
270D4×C23—42no—
271D4×C23—41no—
272D4×C23—42no—
273D4×C23—42no—
274D4×C23—42no—
275D4×C23—42no—
276D4×C23—42no—
277D4×C23—42no—
278D4×C23—81no—
279D4×C23—82no—
280D4×C23—82no—
281D4×C23—84no—
282D4×C23—82no—
283D4×C23—82no—
284D4×C23—82no—
285D4×C23—82no—
286D4×C23—84no—
287D4×C23—88no—
288C2×C4×C23—21no—
289C2×C4×C23—21no—
290C2×C4×C23—22no—
291C2×C4×C23—22no—
292C2×C4×C23—22no—
293C2×C4×C23—22no—
294C2×C4×C23—22no—
295C2×C4×C23—22no—
296C2×C4×C23—42no—
297C2×C4×C23—42no—
298C2×C4×C23—42no—
299C2×C4×C23—42no—
300C2×C4×C23—41no—
301C2×C4×C23—41no—
302C2×C4×C23—42no—
303C2×C4×C23—41no—
304C2×C4×C23—41no—
305C2×C4×C23—41no—
306C2×C4×C23—42no—
307C2×C4×C23—42no—
308C2×C4×C23—42no—
309C2×C4×C23—81no—
310C2×C4×C23—84no—
311C2×C4×C23—82no—
312C2×C4×C23—82no—
313C2×C4×C23#12011yescharacteristic
314C2×C4×C23C22×D411yescharacteristic
315C8×C23—42no—
316C2×#560C2×C2311yescharacteristic, complemented
317C2×#458C2×C2311yescharacteristic, complemented
318C2×B(4,𝔽2)C2×C2311yescharacteristic, complemented
319C2×#453C2×C2311yescharacteristic, complemented
320#2200C2×C2318yesdirect product factor
321C2×#353C2×C2311yescharacteristic, complemented
322C2×#352C2×C2311yescharacteristic, complemented
323C2×AΣL(1,𝔽16)C2×C2311yescharacteristic, complemented
324C22×C23—22no—
325C22×C23—21no—
326C22×C23—21no—
327C22×C23—21no—
328C22×C23—21no—
329C22×C23—41no—
330C22×C23—41no—
331C22×C23—41no—
332C22×C23—41no—
333C22×C23—42no—
334C22×C23—42no—
335C22×C23—42no—
336C22×C23—42no—
337C22×C23—42no—
338C22×C23—42no—
339C22×C23—44no—
340C22×C23—42no—
341C22×C23—42no—
342C22×C23—42no—
343C22×C23—81no—
344C22×C23—81no—
345C22×C23—82no—
346C22×C23—82no—
347C22×C23—82no—
348C22×C23—82no—
349C22×C23—82no—
350C22×C23—84no—
351C22×C23—82no—
352C22×C23—82no—
353C22×C23—82no—
354C22×C23—161no—
355C22×C23—161no—
356C22×C23B(4,𝔽2)11yescharacteristic
357C22×C23B(4,𝔽2)11yescharacteristic
358C22×C23C2×#12011yescharacteristic
359C4×C23—21no—
360C4×C23—21no—
361C4×C23—42no—
362C4×C23—42no—
363C4×C23—42no—
364C4×C23—42no—
365C4×C23—42no—
366C4×C23—82no—
367C4×C23—82no—
368C2×H(5,𝔽2)C22×C2311yescharacteristic
369C2×AGL(1,ℤ/8)—21no—
370#560—22no—
371#560—22no—
372#560—22no—
373#560C22×C2314yescomplemented
374C2×#127C22×C2311yescharacteristic
375C2×#126—21no—
376C2×#123—21no—
377C2×#123—21no—
378C2×#123C22×C2311yescharacteristic
379C2×#121—21no—
380C2×#121—21no—
381C2×#121—21no—
382C2×#120—21no—
383C2×#120—21no—
384C2×#120C22×C2311yescharacteristic
385#458—22no—
386#458C22×C2314yescomplemented
387B(4,𝔽2)—22no—
388B(4,𝔽2)C22×C2314yescomplemented
389#453—22no—
390#453C22×C2314yescomplemented
391C2×#104—21no—
392C2×#100C22×C2311yescharacteristic
393C2×#99—21no—
394C2×#99—21no—
395C2×#99C22×C2311yescharacteristic
396C2×#99C22×C2311yescharacteristic
397#353C22×C2314yescomplemented
398#352C22×C2314yescomplemented
399AΣL(1,𝔽16)C22×C2314yescomplemented
400C2×C23—21no—
401C2×C23—21no—
402C2×C23—41no—
403C2×C23—41no—
404C2×C23—41no—
405C2×C23—41no—
406C2×C23—82no—
407C2×C23—82no—
408C2×C23—82no—
409C2×C23#220012yesdirect product factor
410C2×C23C2×B(4,𝔽2)11yescharacteristic
411C25D4×C2311yescharacteristic
412H(5,𝔽2)—21no—
413H(5,𝔽2)—21no—
414H(5,𝔽2)—21no—
415H(5,𝔽2)—42no—
416H(5,𝔽2)C23×C2312yes—
417C2×#41—21no—
418C2×#41—41no—
419C22×D4—21no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—41no—
427C22×D4—41no—
428C22×D4D4×C2311yescharacteristic, complemented
429C22×D4C23×C2311yescharacteristic
430C23×C4—21no—
431C23×C4D4×C2311yescharacteristic, complemented
432AGL(1,ℤ/8)—24no—
433AGL(1,ℤ/8)—42no—
434C2×SD16—41no—
435C2×D8—41no—
436C2×M16—21no—
437#127—21no—
438#127—21no—
439#127D4×C2312yescomplemented
440#127C23×C2312yes—
441#126—24no—
442#126—24no—
443#123—24no—
444#123—21no—
445#123—21no—
446#123—24no—
447#123—24no—
448#123—42no—
449#123D4×C2312yescomplemented
450#123C23×C2312yes—
451#121—24no—
452#121—24no—
453#121—24no—
454#121—24no—
455#121—24no—
456#121—24no—
457#120—24no—
458#120—24no—
459#120—21no—
460#120—21no—
461#120—24no—
462#120—42no—
463#120D4×C2312yes—
464#120C23×C2312yes—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—41no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—41no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4D4×C2311yescharacteristic
479C2×C22⋊C4D4×C2311yescharacteristic, complemented
480C2×C42D4×C2311yescharacteristic, complemented
481#104—24no—
482#100—21no—
483#100C23×C2312yes—
484#99—21no—
485#99—21no—
486#99—24no—
487#99—24no—
488#99C23×C2312yes—
489#99C23×C2312yes—
490C23C2×#220011yescharacteristic, direct product factor, Sylow
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24—82no—
499C24C2×D4×C2311yescharacteristic
500C24C2×D4×C2311yescharacteristic
501C24C2×D4×C2312yes—
502#41—22no—
503#41—22no—
504#41—42no—
505#41—41no—
506#41—42no—
507#41—42no—
508#41—42no—
509#41—41no—
510C2×Q8—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—44no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—84no—
548C2×D4C2×D4×C2311yescharacteristic
549C2×D4C2×D4×C2311yescharacteristic
550C2×D4C2×D4×C2311yescharacteristic
551C2×D4C2×D4×C2312yescomplemented
552C2×D4C24×C2311yescharacteristic
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—82no—
567C22×C4C2×D4×C2311yescharacteristic
568C22×C4C2×D4×C2312yescomplemented
569SD16—44no—
570D8—44no—
571M16—22no—
572M16—41no—
573C2×C8—41no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—44no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—44no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—44no—
594C22⋊C4C2×D4×C2312yes—
595C22⋊C4C2×D4×C2312yescomplemented
596C42—21no—
597C42C2×D4×C2312yescomplemented
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—44no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—84no—
626C23—82no—
627C23—82no—
628C23C23×#12011yescharacteristic
629C23C23×#12011yescharacteristic
630C23C23×#12011yescharacteristic
631C23C22×D4×C2311yescharacteristic
632C23C22×D4×C2311yescharacteristic
633Q8—22no—
634Q8—41no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—84no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—84no—
657D4—88no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—81no—
680C2×C4—84no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4C23×#12011yescharacteristic
684C2×C4C22×D4×C2311yescharacteristic
685C8—42no—
686C22—22no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—84no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—161no—
717C22—161no—
718C22C23×B(4,𝔽2)11yescharacteristic
719C22C23×B(4,𝔽2)11yescharacteristic
720C22C2×C23×#12011yescharacteristic
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—82no—
729C4—82no—
730C2—21no—
731C2—21no—
732C2—41no—
733C2—41no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—82no—
739C2C23×#220012yesdirect product factor
740C2C2×C23×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C23B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C23 ◁ C22×D4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#560C2semidirect
2. C2×C23×#458C2semidirect
3. C2×C23×B(4,𝔽2)C2semidirect
4. C2×C23×#453C2semidirect
5. C23×#2200C2direct (N × H)
6. C2×C23×#353C2semidirect
7. C2×C23×#352C2semidirect
8. C2×C23×AΣL(1,𝔽16)C2semidirect
14. C23×#560C22semidirect
27. C23×#458C22semidirect
29. C23×B(4,𝔽2)C22semidirect
31. C23×#453C22semidirect
38. C23×#353C22semidirect
39. C23×#352C22semidirect
40. C23×AΣL(1,𝔽16)C22semidirect
58. C22×D4×C23D4semidirect
61. C23×C4×C23D4semidirect
69. C23×#127D4semidirect
79. C23×#123D4semidirect
109. C2×C22⋊C4×C23D4semidirect
110. C2×C42×C23D4semidirect
180. C2×D4×C23C2×D4semidirect
197. C22×C4×C23C2×D4semidirect
224. C22⋊C4×C23C2×D4semidirect
226. C42×C23C2×D4semidirect
227. C2×#2200C23direct (N × H)
316. C2×#560C2×C23semidirect
317. C2×#458C2×C23semidirect
318. C2×B(4,𝔽2)C2×C23semidirect
319. C2×#453C2×C23semidirect
320. #2200C2×C23direct (N × H)
321. C2×#353C2×C23semidirect
322. C2×#352C2×C23semidirect
323. C2×AΣL(1,𝔽16)C2×C23semidirect
373. #560C22×C23semidirect
386. #458C22×C23semidirect
388. B(4,𝔽2)C22×C23semidirect
390. #453C22×C23semidirect
397. #353C22×C23semidirect
398. #352C22×C23semidirect
399. AΣL(1,𝔽16)C22×C23semidirect
409. C2×C23#2200direct (N × H)
428. C22×D4D4×C23semidirect
431. C23×C4D4×C23semidirect
439. #127D4×C23semidirect
449. #123D4×C23semidirect
479. C2×C22⋊C4D4×C23semidirect
480. C2×C42D4×C23semidirect
490. C23C2×#2200direct (N × H)
551. C2×D4C2×D4×C23semidirect
568. C22×C4C2×D4×C23semidirect
595. C22⋊C4C2×D4×C23semidirect
597. C42C2×D4×C23semidirect
739. C2C23×#2200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#5602
C2×C23×#4582
C2×C23×B(4,𝔽2)2
C2×C23×#4532
C23×#22002
C2×C23×#3532
C2×C23×#3522
C2×C23×AΣL(1,𝔽16)2
C2×#220023