Finite Group Databasebeta

← C2×C23×#2197 #19181170

Subgroups — C2×C23×#2197 #19181170

Order 5888.

1320 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#551C211yesmaximal, characteristic, complemented
2C2×C23×#458C211yesmaximal, characteristic, complemented
3C2×C23×B(4,𝔽2)C211yesmaximal, characteristic
4C2×C23×#455C211yesmaximal, characteristic, complemented
5C23×#2197C218yesmaximal, direct product factor
6C2×C23×#354C211yesmaximal, characteristic, complemented
7C2×C23×#352C211yesmaximal, characteristic, complemented
8C2×C23×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
9C2×C23×H(5,𝔽2)C2211yescharacteristic
10C2×C23×#137—21no—
11C23×#551—22no—
12C23×#551—22no—
13C23×#551—22no—
14C23×#551C2214yescomplemented
15C2×C23×#126—21no—
16C2×C23×#124C2211yescharacteristic
17C2×C23×#123—21no—
18C2×C23×#123—21no—
19C2×C23×#123C2211yescharacteristic
20C2×C23×C22⋊Q8—21no—
21C2×C23×#120—21no—
22C2×C23×#120C2211yescharacteristic
23C2×C4×D4×C23—21no—
24C2×C23×#117—21no—
25C22×C22⋊C4×C23—21no—
26C23×#458—22no—
27C23×#458C2214yescomplemented
28C23×B(4,𝔽2)—22no—
29C23×B(4,𝔽2)C2214yes—
30C23×#455—22no—
31C23×#455C2214yescomplemented
32C2×C23×#104—21no—
33C2×C23×#100C2211yescharacteristic
34C2×C23×#99—21no—
35C2×C23×#99—21no—
36C2×C23×#99C2211yescharacteristic
37C2×C23×#99C2211yescharacteristic
38C23×#354C2214yescomplemented
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×Q8×C23D411yescharacteristic, complemented
50C22×D4×C23—21no—
51C22×D4×C23—21no—
52C22×D4×C23—21no—
53C22×D4×C23—41no—
54C22×D4×C23—41no—
55C22×D4×C23C2311yescharacteristic
56C23×C4×C23—21no—
57C23×C4×C23—21no—
58C23×C4×C23D411yescharacteristic, complemented
59C23×#137—24no—
60C23×#137—42no—
61C2×Q16×C23—41no—
62C2×SD16×C23—41no—
63C2×M16×C23—21no—
64C23×#126—24no—
65C23×#126—24no—
66C23×#124—21no—
67C23×#124—21no—
68C23×#124D412yescomplemented
69C23×#124C2312yes—
70C23×#123—24no—
71C23×#123—21no—
72C23×#123—21no—
73C23×#123—24no—
74C23×#123—24no—
75C23×#123—42no—
76C23×#123D412yescomplemented
77C23×#123C2312yes—
78C23×C22⋊Q8—24no—
79C23×C22⋊Q8—24no—
80C23×#120—21no—
81C23×#120—21no—
82C23×#120—24no—
83C23×#120—42no—
84C23×#120D412yes—
85C23×#120C2312yes—
86C4×D4×C23—24no—
87C4×D4×C23—24no—
88C23×#117—24no—
89C23×#117—24no—
90C2×C4⋊C4×C23—21no—
91C2×C4⋊C4×C23—21no—
92C2×C4⋊C4×C23—21no—
93C2×C4⋊C4×C23—21no—
94C2×C4⋊C4×C23—41no—
95C2×C22⋊C4×C23—24no—
96C2×C22⋊C4×C23—21no—
97C2×C22⋊C4×C23—21no—
98C2×C22⋊C4×C23—24no—
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—41no—
106C2×C22⋊C4×C23—41no—
107C2×C22⋊C4×C23D411yescharacteristic
108C2×C22⋊C4×C23D411yescharacteristic, complemented
109C2×C42×C23—21no—
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—41no—
125C24×C23—44no—
126C24×C23—41no—
127C24×C23C2×D411yescharacteristic
128C24×C23C2×D411yescharacteristic
129C24×C23C2×D412yes—
130#41×C23—22no—
131#41×C23—22no—
132#41×C23—42no—
133#41×C23—41no—
134#41×C23—42no—
135#41×C23—42no—
136#41×C23—42no—
137#41×C23—41no—
138C2×Q8×C23—21no—
139C2×Q8×C23—21no—
140C2×Q8×C23—41no—
141C2×Q8×C23—41no—
142C2×Q8×C23C2×D412yescomplemented
143C2×D4×C23—21no—
144C2×D4×C23—22no—
145C2×D4×C23—22no—
146C2×D4×C23—22no—
147C2×D4×C23—22no—
148C2×D4×C23—22no—
149C2×D4×C23—22no—
150C2×D4×C23—41no—
151C2×D4×C23—41no—
152C2×D4×C23—42no—
153C2×D4×C23—42no—
154C2×D4×C23—44no—
155C2×D4×C23—41no—
156C2×D4×C23—41no—
157C2×D4×C23—41no—
158C2×D4×C23—41no—
159C2×D4×C23—42no—
160C2×D4×C23—42no—
161C2×D4×C23—41no—
162C2×D4×C23—41no—
163C2×D4×C23—41no—
164C2×D4×C23—44no—
165C2×D4×C23—84no—
166C2×D4×C23C2×D411yescharacteristic
167C2×D4×C23C2×D411yescharacteristic
168C2×D4×C23C2×D411yescharacteristic
169C2×D4×C23C2411yescharacteristic
170C22×C4×C23—24no—
171C22×C4×C23—21no—
172C22×C4×C23—21no—
173C22×C4×C23—21no—
174C22×C4×C23—21no—
175C22×C4×C23—21no—
176C22×C4×C23—21no—
177C22×C4×C23—21no—
178C22×C4×C23—24no—
179C22×C4×C23—21no—
180C22×C4×C23—41no—
181C22×C4×C23—44no—
182C22×C4×C23—41no—
183C22×C4×C23—41no—
184C22×C4×C23—41no—
185C22×C4×C23—41no—
186C22×C4×C23—81no—
187C22×C4×C23—81no—
188C22×C4×C23C2×D411yescharacteristic
189C22×C4×C23C2×D412yescomplemented
190Q16×C23—44no—
191SD16×C23—44no—
192M16×C23—22no—
193M16×C23—41no—
194C2×C8×C23—41no—
195C4⋊C4×C23—24no—
196C4⋊C4×C23—24no—
197C4⋊C4×C23—24no—
198C4⋊C4×C23—22no—
199C4⋊C4×C23—22no—
200C4⋊C4×C23—44no—
201C22⋊C4×C23—24no—
202C22⋊C4×C23—24no—
203C22⋊C4×C23—22no—
204C22⋊C4×C23—22no—
205C22⋊C4×C23—22no—
206C22⋊C4×C23—21no—
207C22⋊C4×C23—21no—
208C22⋊C4×C23—22no—
209C22⋊C4×C23—22no—
210C22⋊C4×C23—22no—
211C22⋊C4×C23—22no—
212C22⋊C4×C23—22no—
213C22⋊C4×C23—22no—
214C22⋊C4×C23—22no—
215C22⋊C4×C23—44no—
216C22⋊C4×C23—41no—
217C22⋊C4×C23—41no—
218C22⋊C4×C23—44no—
219C22⋊C4×C23C2×D412yes—
220C22⋊C4×C23C2×D412yescomplemented
221C42×C23—24no—
222C42×C23—21no—
223C42×C23C2×D412yescomplemented
224C2×#2197C2311yesmaximal, characteristic, direct product factor, Sylow
225C23×C23—24no—
226C23×C23—22no—
227C23×C23—21no—
228C23×C23—21no—
229C23×C23—21no—
230C23×C23—21no—
231C23×C23—22no—
232C23×C23—22no—
233C23×C23—42no—
234C23×C23—42no—
235C23×C23—42no—
236C23×C23—42no—
237C23×C23—44no—
238C23×C23—44no—
239C23×C23—41no—
240C23×C23—41no—
241C23×C23—41no—
242C23×C23—41no—
243C23×C23—44no—
244C23×C23—41no—
245C23×C23—81no—
246C23×C23—84no—
247C23×C23—82no—
248C23×C23—82no—
249C23×C23—82no—
250C23×C23#12011yescharacteristic
251C23×C23#12011yescharacteristic
252C23×C23#12011yescharacteristic
253C23×C23C22×D411yescharacteristic
254C23×C23C22×D411yescharacteristic
255Q8×C23—22no—
256Q8×C23—42no—
257Q8×C23—41no—
258Q8×C23—81no—
259D4×C23—22no—
260D4×C23—41no—
261D4×C23—41no—
262D4×C23—41no—
263D4×C23—41no—
264D4×C23—41no—
265D4×C23—44no—
266D4×C23—44no—
267D4×C23—42no—
268D4×C23—42no—
269D4×C23—42no—
270D4×C23—42no—
271D4×C23—42no—
272D4×C23—42no—
273D4×C23—88no—
274C2×C4×C23—21no—
275C2×C4×C23—21no—
276C2×C4×C23—22no—
277C2×C4×C23—22no—
278C2×C4×C23—22no—
279C2×C4×C23—22no—
280C2×C4×C23—22no—
281C2×C4×C23—22no—
282C2×C4×C23—22no—
283C2×C4×C23—42no—
284C2×C4×C23—42no—
285C2×C4×C23—42no—
286C2×C4×C23—42no—
287C2×C4×C23—48no—
288C2×C4×C23—42no—
289C2×C4×C23—41no—
290C2×C4×C23—41no—
291C2×C4×C23—41no—
292C2×C4×C23—41no—
293C2×C4×C23—41no—
294C2×C4×C23—41no—
295C2×C4×C23—41no—
296C2×C4×C23—42no—
297C2×C4×C23—42no—
298C2×C4×C23—42no—
299C2×C4×C23—81no—
300C2×C4×C23—84no—
301C2×C4×C23—82no—
302C2×C4×C23—82no—
303C2×C4×C23#12011yescharacteristic
304C2×C4×C23C22×D411yescharacteristic
305C8×C23—42no—
306C2×#551C2×C2311yescharacteristic, complemented
307C2×#458C2×C2311yescharacteristic, complemented
308C2×B(4,𝔽2)C2×C2311yescharacteristic
309C2×#455C2×C2311yescharacteristic, complemented
310#2197C2×C2318yesdirect product factor
311C2×#354C2×C2311yescharacteristic, complemented
312C2×#352C2×C2311yescharacteristic, complemented
313C2×AΣL(1,𝔽16)C2×C2311yescharacteristic, complemented
314C22×C23—22no—
315C22×C23—24no—
316C22×C23—21no—
317C22×C23—21no—
318C22×C23—21no—
319C22×C23—21no—
320C22×C23—41no—
321C22×C23—41no—
322C22×C23—41no—
323C22×C23—41no—
324C22×C23—42no—
325C22×C23—44no—
326C22×C23—44no—
327C22×C23—42no—
328C22×C23—42no—
329C22×C23—44no—
330C22×C23—42no—
331C22×C23—42no—
332C22×C23—81no—
333C22×C23—81no—
334C22×C23—82no—
335C22×C23—84no—
336C22×C23—82no—
337C22×C23—82no—
338C22×C23—82no—
339C22×C23—161no—
340C22×C23—161no—
341C22×C23B(4,𝔽2)11yescharacteristic
342C22×C23B(4,𝔽2)11yescharacteristic
343C22×C23C2×#12011yescharacteristic
344C4×C23—21no—
345C4×C23—21no—
346C4×C23—42no—
347C4×C23—42no—
348C4×C23—42no—
349C4×C23—42no—
350C4×C23—42no—
351C4×C23—42no—
352C4×C23—82no—
353C4×C23—82no—
354C2×H(5,𝔽2)C22×C2311yescharacteristic
355C2×#137—21no—
356#551—22no—
357#551—22no—
358#551—22no—
359#551C22×C2314yescomplemented
360C2×#126—21no—
361C2×#124C22×C2311yescharacteristic
362C2×#123—21no—
363C2×#123—21no—
364C2×#123C22×C2311yescharacteristic
365C2×C22⋊Q8—21no—
366C2×#120—21no—
367C2×#120C22×C2311yescharacteristic
368C2×C4×D4—21no—
369C2×#117—21no—
370C22×C22⋊C4—21no—
371#458—22no—
372#458C22×C2314yescomplemented
373B(4,𝔽2)—22no—
374B(4,𝔽2)C22×C2314yes—
375#455—22no—
376#455C22×C2314yescomplemented
377C2×#104—21no—
378C2×#100C22×C2311yescharacteristic
379C2×#99—21no—
380C2×#99—21no—
381C2×#99C22×C2311yescharacteristic
382C2×#99C22×C2311yescharacteristic
383#354C22×C2314yescomplemented
384#352C22×C2314yescomplemented
385AΣL(1,𝔽16)C22×C2314yescomplemented
386C2×C23—21no—
387C2×C23—21no—
388C2×C23—41no—
389C2×C23—41no—
390C2×C23—44no—
391C2×C23—41no—
392C2×C23—41no—
393C2×C23—82no—
394C2×C23#219712yesdirect product factor
395C2×C23C2×B(4,𝔽2)11yescharacteristic
396C25D4×C2311yescharacteristic
397H(5,𝔽2)—21no—
398H(5,𝔽2)—21no—
399H(5,𝔽2)—21no—
400H(5,𝔽2)—42no—
401H(5,𝔽2)C23×C2312yes—
402C2×#41—21no—
403C2×#41—41no—
404C22×Q8D4×C2311yescharacteristic, complemented
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—41no—
409C22×D4—41no—
410C22×D4C23×C2311yescharacteristic
411C23×C4—21no—
412C23×C4—21no—
413C23×C4D4×C2311yescharacteristic, complemented
414#137—24no—
415#137—42no—
416C2×Q16—41no—
417C2×SD16—41no—
418C2×M16—21no—
419#126—24no—
420#126—24no—
421#124—21no—
422#124—21no—
423#124D4×C2312yescomplemented
424#124C23×C2312yes—
425#123—24no—
426#123—21no—
427#123—21no—
428#123—24no—
429#123—24no—
430#123—42no—
431#123D4×C2312yescomplemented
432#123C23×C2312yes—
433C22⋊Q8—24no—
434C22⋊Q8—24no—
435#120—21no—
436#120—21no—
437#120—24no—
438#120—42no—
439#120D4×C2312yes—
440#120C23×C2312yes—
441C4×D4—24no—
442C4×D4—24no—
443#117—24no—
444#117—24no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—41no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4D4×C2311yescharacteristic
463C2×C22⋊C4D4×C2311yescharacteristic, complemented
464C2×C42—21no—
465C2×C42D4×C2311yescharacteristic, complemented
466#104—24no—
467#100—21no—
468#100C23×C2312yes—
469#99—21no—
470#99—21no—
471#99—24no—
472#99—24no—
473#99C23×C2312yes—
474#99C23×C2312yes—
475C23C2×#219711yescharacteristic, direct product factor, Sylow
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—41no—
481C24—44no—
482C24—41no—
483C24C2×D4×C2311yescharacteristic
484C24C2×D4×C2311yescharacteristic
485C24C2×D4×C2312yes—
486#41—22no—
487#41—22no—
488#41—42no—
489#41—41no—
490#41—42no—
491#41—42no—
492#41—42no—
493#41—41no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8C2×D4×C2312yescomplemented
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—44no—
521C2×D4—84no—
522C2×D4C2×D4×C2311yescharacteristic
523C2×D4C2×D4×C2311yescharacteristic
524C2×D4C2×D4×C2311yescharacteristic
525C2×D4C24×C2311yescharacteristic
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4—44no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4C2×D4×C2311yescharacteristic
545C22×C4C2×D4×C2312yescomplemented
546Q16—44no—
547SD16—44no—
548M16—22no—
549M16—41no—
550C2×C8—41no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—44no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—44no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—44no—
575C22⋊C4C2×D4×C2312yes—
576C22⋊C4C2×D4×C2312yescomplemented
577C42—24no—
578C42—21no—
579C42C2×D4×C2312yescomplemented
580C23—24no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—22no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—44no—
593C23—44no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—44no—
599C23—41no—
600C23—81no—
601C23—84no—
602C23—82no—
603C23—82no—
604C23—82no—
605C23C23×#12011yescharacteristic
606C23C23×#12011yescharacteristic
607C23C23×#12011yescharacteristic
608C23C22×D4×C2311yescharacteristic
609C23C22×D4×C2311yescharacteristic
610Q8—22no—
611Q8—42no—
612Q8—41no—
613Q8—81no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—42no—
621D4—42no—
622D4—42no—
623D4—42no—
624D4—44no—
625D4—44no—
626D4—42no—
627D4—42no—
628D4—88no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—48no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—81no—
655C2×C4—84no—
656C2×C4—82no—
657C2×C4—82no—
658C2×C4C23×#12011yescharacteristic
659C2×C4C22×D4×C2311yescharacteristic
660C8—42no—
661C22—22no—
662C22—24no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—44no—
673C22—44no—
674C22—42no—
675C22—42no—
676C22—44no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—82no—
682C22—84no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—161no—
687C22—161no—
688C22C23×B(4,𝔽2)11yescharacteristic
689C22C23×B(4,𝔽2)11yescharacteristic
690C22C2×C23×#12011yescharacteristic
691C4—21no—
692C4—21no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—82no—
700C4—82no—
701C2—21no—
702C2—21no—
703C2—41no—
704C2—41no—
705C2—44no—
706C2—41no—
707C2—41no—
708C2—82no—
709C2C23×#219712yesdirect product factor
710C2C2×C23×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C23B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C23
prime radicalC2×C23×B(4,𝔽2)C2
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×#551C2semidirect
2. C2×C23×#458C2semidirect
4. C2×C23×#455C2semidirect
5. C23×#2197C2direct (N × H)
6. C2×C23×#354C2semidirect
7. C2×C23×#352C2semidirect
8. C2×C23×AΣL(1,𝔽16)C2semidirect
14. C23×#551C22semidirect
27. C23×#458C22semidirect
31. C23×#455C22semidirect
38. C23×#354C22semidirect
39. C23×#352C22semidirect
40. C23×AΣL(1,𝔽16)C22semidirect
49. C22×Q8×C23D4semidirect
58. C23×C4×C23D4semidirect
68. C23×#124D4semidirect
76. C23×#123D4semidirect
108. C2×C22⋊C4×C23D4semidirect
110. C2×C42×C23D4semidirect
142. C2×Q8×C23C2×D4semidirect
189. C22×C4×C23C2×D4semidirect
220. C22⋊C4×C23C2×D4semidirect
223. C42×C23C2×D4semidirect
224. C2×#2197C23direct (N × H)
306. C2×#551C2×C23semidirect
307. C2×#458C2×C23semidirect
309. C2×#455C2×C23semidirect
310. #2197C2×C23direct (N × H)
311. C2×#354C2×C23semidirect
312. C2×#352C2×C23semidirect
313. C2×AΣL(1,𝔽16)C2×C23semidirect
359. #551C22×C23semidirect
372. #458C22×C23semidirect
376. #455C22×C23semidirect
383. #354C22×C23semidirect
384. #352C22×C23semidirect
385. AΣL(1,𝔽16)C22×C23semidirect
394. C2×C23#2197direct (N × H)
404. C22×Q8D4×C23semidirect
413. C23×C4D4×C23semidirect
423. #124D4×C23semidirect
431. #123D4×C23semidirect
463. C2×C22⋊C4D4×C23semidirect
465. C2×C42D4×C23semidirect
475. C23C2×#2197direct (N × H)
498. C2×Q8C2×D4×C23semidirect
545. C22×C4C2×D4×C23semidirect
576. C22⋊C4C2×D4×C23semidirect
579. C42C2×D4×C23semidirect
709. C2C23×#2197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#5512
C2×C23×#4582
C2×C23×B(4,𝔽2)2
C2×C23×#4552
C23×#21972
C2×C23×#3542
C2×C23×#3522
C2×C23×AΣL(1,𝔽16)2
C2×#219723