Finite Group Databasebeta

← C23×#18175 #19165801

Subgroups — C23×#18175 #19165801

Order 5888.

988 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3505C211yesmaximal, characteristic
2C23×#3095C211yesmaximal, characteristic, complemented
3C23×#3094C211yesmaximal, characteristic, complemented
4C23×#2395C211yesmaximal, characteristic, complemented
5C23×#1618C212yesmaximal, complemented
6C23×#1615C212yesmaximal, complemented
7C23×#1612C212yesmaximal, complemented
8C23×#1609C212yesmaximal, complemented
9C23×#1508C211yesmaximal, characteristic, complemented
10C23×#1507C211yesmaximal, characteristic, complemented
11C23×#1465C211yesmaximal, characteristic, complemented
12C23×#553—22no—
13C23×#553—21no—
14C23×#552—21no—
15C23×#551—22no—
16C23×#548—21no—
17C23×#546—21no—
18C23×#539C2212yes—
19C23×#538C2212yes—
20C23×#534—21no—
21C23×#529—21no—
22C23×#525—21no—
23C2×C23×C22⋊Q8C2211yescharacteristic
24C2×C23×#121C2211yescharacteristic
25C23×#518—21no—
26C2×C4×D4×C23C2211yescharacteristic
27C2×C23×#117C2211yescharacteristic
28C23×#485—22no—
29C23×#484C2212yescomplemented
30C23×#483C2212yescomplemented
31C23×#482—22no—
32C23×#481C2212yes—
33C23×#480C2212yes—
34C23×#428—21no—
35C23×#428—21no—
36C23×#419—21no—
37C23×#418—21no—
38C23×#407C2211yescharacteristic
39C23×#407C2211yescharacteristic
40C23×#400C2211yescharacteristic, complemented
41C23×#399C2211yescharacteristic, complemented
42C23×#398C2211yescharacteristic, complemented
43C23×#397—21no—
44C23×#397C2211yescharacteristic, complemented
45C23×#394—21no—
46C4×C4⋊C4×C23—21no—
47C4×C22⋊C4×C23—21no—
48C4×C22⋊C4×C23C2211yescharacteristic
49C23×#328C2212yescomplemented
50C23×#328C2212yescomplemented
51C23×#327C2212yes—
52C23×#327C2212yes—
53C23×#324C2212yescomplemented
54C23×#323C2212yescomplemented
55C2×#41×C23—21no—
56C22×Q8×C23D411yescharacteristic
57C22×D4×C23—21no—
58C22×D4×C23D411yescharacteristic
59C22×D4×C23D411yescharacteristic
60C23×C4×C23D411yescharacteristic
61C23×C4×C23C2311yescharacteristic
62C2×M16×C23—21no—
63C2×M16×C23—21no—
64C23×#126—22no—
65C23×#126—22no—
66C23×#126—22no—
67C23×#125—21no—
68C23×#125—22no—
69C23×#124—21no—
70C23×#124—22no—
71C23×#123—22no—
72C23×#123—22no—
73C23×#123—22no—
74C23×#123—22no—
75C23×#123—22no—
76C23×C22⋊Q8—21no—
77C23×C22⋊Q8—22no—
78C23×C22⋊Q8—21no—
79C23×C22⋊Q8—21no—
80C23×C22⋊Q8D412yes—
81C23×C22⋊Q8C2312yes—
82C23×#121—22no—
83C23×#121—22no—
84C23×#121—21no—
85C23×#121—22no—
86C23×#121—21no—
87C23×#121—21no—
88C23×#121D412yes—
89C23×#121C2312yes—
90C23×#120—22no—
91C23×#120—22no—
92C4×Q8×C23—21no—
93C4×D4×C23—22no—
94C4×D4×C23—22no—
95C4×D4×C23—22no—
96C4×D4×C23—21no—
97C4×D4×C23—21no—
98C4×D4×C23—21no—
99C4×D4×C23—21no—
100C4×D4×C23—21no—
101C4×D4×C23—22no—
102C4×D4×C23—22no—
103C23×#117—22no—
104C23×#117—22no—
105C23×#117—21no—
106C23×#117—21no—
107C23×#117—21no—
108C23×#117—21no—
109C23×#117—21no—
110C2×C4⋊C4×C23—21no—
111C2×C4⋊C4×C23—21no—
112C2×C4⋊C4×C23—21no—
113C2×C4⋊C4×C23D411yescharacteristic
114C2×C4⋊C4×C23D411yescharacteristic
115C2×C4⋊C4×C23C2311yescharacteristic
116C2×C4⋊C4×C23C2311yescharacteristic
117C2×C4⋊C4×C23C2311yescharacteristic
118C2×C22⋊C4×C23—22no—
119C2×C22⋊C4×C23—21no—
120C2×C22⋊C4×C23—21no—
121C2×C22⋊C4×C23—21no—
122C2×C22⋊C4×C23—21no—
123C2×C22⋊C4×C23—21no—
124C2×C22⋊C4×C23—21no—
125C2×C22⋊C4×C23D411yescharacteristic
126C2×C22⋊C4×C23C2311yescharacteristic
127C2×C42×C23—21no—
128C2×C42×C23—21no—
129C2×C42×C23D411yescharacteristic
130C23×#107—22no—
131C23×#107—22no—
132C23×#106—22no—
133C23×#106—22no—
134C23×#103—22no—
135C23×#103—22no—
136C23×#102—22no—
137C23×#102—22no—
138C23×C22⋊C8—21no—
139C23×C22⋊C8—21no—
140C23×C22⋊C8C2312yes—
141C23×C22⋊C8C2312yes—
142C23×#95—21no—
143C23×#95—21no—
144C23×#95—21no—
145C23×#95—21no—
146C23×#95C2311yescharacteristic
147C23×#95C2311yescharacteristic
148C24×C23—21no—
149C24×C23C2×D411yescharacteristic
150C24×C23C2×D411yescharacteristic
151#41×C23—82no—
152C2×Q8×C23—21no—
153C2×Q8×C23—42no—
154C2×Q8×C23C2×D412yes—
155C2×D4×C23—21no—
156C2×D4×C23—21no—
157C2×D4×C23—22no—
158C2×D4×C23—22no—
159C2×D4×C23—22no—
160C2×D4×C23—22no—
161C2×D4×C23—21no—
162C2×D4×C23—41no—
163C2×D4×C23—41no—
164C2×D4×C23—42no—
165C2×D4×C23—42no—
166C2×D4×C23—42no—
167C2×D4×C23C2×D412yes—
168C22×C4×C23—21no—
169C22×C4×C23—21no—
170C22×C4×C23—22no—
171C22×C4×C23—22no—
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—21no—
179C22×C4×C23—42no—
180C22×C4×C23—42no—
181C22×C4×C23C2×D411yescharacteristic
182C22×C4×C23C2×D411yescharacteristic
183C22×C4×C23C2×D411yescharacteristic
184C22×C4×C23C2×D411yescharacteristic
185C22×C4×C23C2×D411yescharacteristic
186C22×C4×C23C2×D411yescharacteristic
187C22×C4×C23C2×D411yescharacteristic
188C22×C4×C23C2×D411yescharacteristic
189C22×C4×C23C2411yescharacteristic
190M16×C23—42no—
191M16×C23—42no—
192C2×C8×C23—22no—
193C2×C8×C23—22no—
194C4⋊C4×C23—22no—
195C4⋊C4×C23—22no—
196C4⋊C4×C23—22no—
197C4⋊C4×C23—22no—
198C4⋊C4×C23—22no—
199C4⋊C4×C23—21no—
200C4⋊C4×C23—21no—
201C4⋊C4×C23—22no—
202C4⋊C4×C23—21no—
203C4⋊C4×C23—21no—
204C4⋊C4×C23—21no—
205C4⋊C4×C23—21no—
206C4⋊C4×C23—21no—
207C4⋊C4×C23—21no—
208C4⋊C4×C23—42no—
209C4⋊C4×C23—42no—
210C4⋊C4×C23C2×D412yes—
211C4⋊C4×C23C2×D412yes—
212C22⋊C4×C23—22no—
213C22⋊C4×C23—22no—
214C22⋊C4×C23—22no—
215C22⋊C4×C23—22no—
216C22⋊C4×C23—22no—
217C22⋊C4×C23—22no—
218C22⋊C4×C23—21no—
219C22⋊C4×C23—22no—
220C22⋊C4×C23—21no—
221C22⋊C4×C23—22no—
222C22⋊C4×C23—22no—
223C22⋊C4×C23—22no—
224C22⋊C4×C23—21no—
225C22⋊C4×C23—21no—
226C22⋊C4×C23—42no—
227C22⋊C4×C23—42no—
228C22⋊C4×C23—42no—
229C22⋊C4×C23—41no—
230C22⋊C4×C23—41no—
231C42×C23—22no—
232C42×C23—22no—
233C42×C23—21no—
234C42×C23—21no—
235C42×C23—42no—
236C42×C23—41no—
237C42×C23—41no—
238#18175C2311yesmaximal, characteristic, direct product factor, Sylow
239C23×C23—21no—
240C23×C23—21no—
241C23×C23—21no—
242C23×C23—22no—
243C23×C23—21no—
244C23×C23—21no—
245C23×C23—41no—
246C23×C23—41no—
247C23×C23—41no—
248C23×C23—41no—
249C23×C23—42no—
250C23×C23—81no—
251C23×C23—81no—
252C23×C23#12011yescharacteristic
253C23×C23#12011yescharacteristic
254C23×C23C22×D411yescharacteristic
255Q8×C23—42no—
256Q8×C23—42no—
257D4×C23—42no—
258D4×C23—42no—
259D4×C23—42no—
260D4×C23—44no—
261D4×C23—42no—
262D4×C23—42no—
263D4×C23—42no—
264D4×C23—82no—
265D4×C23—82no—
266C2×C4×C23—22no—
267C2×C4×C23—22no—
268C2×C4×C23—22no—
269C2×C4×C23—22no—
270C2×C4×C23—21no—
271C2×C4×C23—21no—
272C2×C4×C23—22no—
273C2×C4×C23—21no—
274C2×C4×C23—22no—
275C2×C4×C23—22no—
276C2×C4×C23—21no—
277C2×C4×C23—21no—
278C2×C4×C23—41no—
279C2×C4×C23—41no—
280C2×C4×C23—41no—
281C2×C4×C23—41no—
282C2×C4×C23—42no—
283C2×C4×C23—41no—
284C2×C4×C23—42no—
285C2×C4×C23—41no—
286C2×C4×C23—41no—
287C2×C4×C23—41no—
288C2×C4×C23—41no—
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—81no—
297C2×C4×C23—81no—
298C2×C4×C23—81no—
299C2×C4×C23—82no—
300C2×C4×C23—82no—
301C2×C4×C23#12011yescharacteristic
302C2×C4×C23#12011yescharacteristic
303C2×C4×C23C22×D411yescharacteristic
304C2×C4×C23C22×D411yescharacteristic
305C8×C23—42no—
306C8×C23—42no—
307#3505C2×C2311yescharacteristic
308#3095C2×C2311yescharacteristic, complemented
309#3094C2×C2311yescharacteristic, complemented
310#2395C2×C2311yescharacteristic, complemented
311#1618C2×C2312yescomplemented
312#1615C2×C2312yescomplemented
313#1612C2×C2312yescomplemented
314#1609C2×C2312yescomplemented
315#1508C2×C2311yescharacteristic, complemented
316#1507C2×C2311yescharacteristic, complemented
317#1465C2×C2311yescharacteristic, complemented
318C22×C23—21no—
319C22×C23—21no—
320C22×C23—21no—
321C22×C23—21no—
322C22×C23—21no—
323C22×C23—21no—
324C22×C23—21no—
325C22×C23—21no—
326C22×C23—42no—
327C22×C23—41no—
328C22×C23—42no—
329C22×C23—42no—
330C22×C23—41no—
331C22×C23—41no—
332C22×C23—42no—
333C22×C23—81no—
334C22×C23—81no—
335C22×C23—81no—
336C22×C23—162no—
337C22×C23C2×#12011yescharacteristic
338C22×C23#57511yescharacteristic
339C22×C23#57511yescharacteristic
340C4×C23—21no—
341C4×C23—21no—
342C4×C23—21no—
343C4×C23—42no—
344C4×C23—41no—
345C4×C23—42no—
346C4×C23—41no—
347C4×C23—42no—
348C4×C23—41no—
349C4×C23—42no—
350C4×C23—81no—
351C4×C23—81no—
352C4×C23—81no—
353C4×C23#45812yes—
354#553—22no—
355#553—21no—
356#552—21no—
357#551—22no—
358#548—21no—
359#546—21no—
360#539C22×C2312yes—
361#538C22×C2312yes—
362#534—21no—
363#529—21no—
364#525—21no—
365C2×C22⋊Q8C22×C2311yescharacteristic
366C2×#121C22×C2311yescharacteristic
367#518—21no—
368C2×C4×D4C22×C2311yescharacteristic
369C2×#117C22×C2311yescharacteristic
370#485—22no—
371#484C22×C2312yescomplemented
372#483C22×C2312yescomplemented
373#482—22no—
374#481C22×C2312yes—
375#480C22×C2312yes—
376#428—21no—
377#428—21no—
378#419—21no—
379#418—21no—
380#407C22×C2311yescharacteristic
381#407C22×C2311yescharacteristic
382#400C22×C2311yescharacteristic, complemented
383#399C22×C2311yescharacteristic, complemented
384#398C22×C2311yescharacteristic, complemented
385#397—21no—
386#397C22×C2311yescharacteristic, complemented
387#394—21no—
388C4×C4⋊C4—21no—
389C4×C22⋊C4—21no—
390C4×C22⋊C4C22×C2311yescharacteristic
391#328C22×C2312yescomplemented
392#328C22×C2312yescomplemented
393#327C22×C2312yes—
394#327C22×C2312yes—
395#324C22×C2312yescomplemented
396#323C22×C2312yescomplemented
397C2×C23—21no—
398C2×C23—21no—
399C2×C23—41no—
400C2×C23—41no—
401C2×C23—81no—
402C2×C23—82no—
403C2×C23#300511yescharacteristic
404C2×C23#301811yescharacteristic
405C2×C23C2×#45811yescharacteristic
406C2×#41—21no—
407C22×Q8D4×C2311yescharacteristic
408C22×D4—21no—
409C22×D4D4×C2311yescharacteristic
410C22×D4D4×C2311yescharacteristic
411C23×C4D4×C2311yescharacteristic
412C23×C4C23×C2311yescharacteristic
413C2×M16—21no—
414C2×M16—21no—
415#126—22no—
416#126—22no—
417#126—22no—
418#125—21no—
419#125—22no—
420#124—21no—
421#124—22no—
422#123—22no—
423#123—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427C22⋊Q8—21no—
428C22⋊Q8—22no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8D4×C2312yes—
432C22⋊Q8C23×C2312yes—
433#121—21no—
434#121—22no—
435#121—22no—
436#121—22no—
437#121—21no—
438#121—21no—
439#121D4×C2312yes—
440#121C23×C2312yes—
441#120—22no—
442#120—22no—
443C4×Q8—21no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—22no—
453C4×D4—22no—
454#117—22no—
455#117—21no—
456#117—22no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4D4×C2311yescharacteristic
465C2×C4⋊C4D4×C2311yescharacteristic
466C2×C4⋊C4C23×C2311yescharacteristic
467C2×C4⋊C4C23×C2311yescharacteristic
468C2×C4⋊C4C23×C2311yescharacteristic
469C2×C22⋊C4—22no—
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⋊C4D4×C2311yescharacteristic
477C2×C22⋊C4C23×C2311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42D4×C2311yescharacteristic
481#107—22no—
482#107—22no—
483#106—22no—
484#106—22no—
485#103—22no—
486#103—22no—
487#102—22no—
488#102—22no—
489C22⋊C8—21no—
490C22⋊C8—21no—
491C22⋊C8C23×C2312yes—
492C22⋊C8C23×C2312yes—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95C23×C2311yescharacteristic
498#95C23×C2311yescharacteristic
499C23#1817511yescharacteristic, direct product factor, Sylow
500C24—21no—
501C24C2×D4×C2311yescharacteristic
502C24C2×D4×C2311yescharacteristic
503#41—82no—
504C2×Q8—21no—
505C2×Q8—42no—
506C2×Q8C2×D4×C2312yes—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4C2×D4×C2312yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4C2×D4×C2311yescharacteristic
534C22×C4C2×D4×C2311yescharacteristic
535C22×C4C2×D4×C2311yescharacteristic
536C22×C4C2×D4×C2311yescharacteristic
537C22×C4C2×D4×C2311yescharacteristic
538C22×C4C2×D4×C2311yescharacteristic
539C22×C4C2×D4×C2311yescharacteristic
540C22×C4C2×D4×C2311yescharacteristic
541C22×C4C24×C2311yescharacteristic
542M16—42no—
543M16—42no—
544C2×C8—22no—
545C2×C8—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4C2×D4×C2312yes—
563C4⋊C4C2×D4×C2312yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—21no—
571C22⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C42—22no—
584C42—22no—
585C42—21no—
586C42—21no—
587C42—42no—
588C42—41no—
589C42—41no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—21no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—81no—
602C23—81no—
603C23C23×#12011yescharacteristic
604C23C23×#12011yescharacteristic
605C23C22×D4×C2311yescharacteristic
606Q8—42no—
607Q8—42no—
608D4—42no—
609D4—42no—
610D4—42no—
611D4—44no—
612D4—42no—
613D4—42no—
614D4—42no—
615D4—82no—
616D4—82no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4C23×#12011yescharacteristic
653C2×C4C23×#12011yescharacteristic
654C2×C4C22×D4×C2311yescharacteristic
655C2×C4C22×D4×C2311yescharacteristic
656C8—42no—
657C8—42no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—42no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—41no—
671C22—41no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—162no—
677C22C2×C23×#12011yescharacteristic
678C22C23×#57511yescharacteristic
679C22C23×#57511yescharacteristic
680C4—21no—
681C4—21no—
682C4—21no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4C23×#45812yes—
694C2—21no—
695C2—21no—
696C2—41no—
697C2—41no—
698C2—81no—
699C2—82no—
700C2C23×#300511yescharacteristic
701C2C23×#301811yescharacteristic
702C2C2×C23×#45811yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC23×#3505C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#3095C2semidirect
3. C23×#3094C2semidirect
4. C23×#2395C2semidirect
5. C23×#1618C2semidirect
6. C23×#1615C2semidirect
7. C23×#1612C2semidirect
8. C23×#1609C2semidirect
9. C23×#1508C2semidirect
10. C23×#1507C2semidirect
11. C23×#1465C2semidirect
29. C23×#484C22semidirect
30. C23×#483C22semidirect
40. C23×#400C22semidirect
41. C23×#399C22semidirect
42. C23×#398C22semidirect
44. C23×#397C22semidirect
49. C23×#328C22semidirect
50. C23×#328C22semidirect
53. C23×#324C22semidirect
54. C23×#323C22semidirect
238. #18175C23direct (N × H)
308. #3095C2×C23semidirect
309. #3094C2×C23semidirect
310. #2395C2×C23semidirect
311. #1618C2×C23semidirect
312. #1615C2×C23semidirect
313. #1612C2×C23semidirect
314. #1609C2×C23semidirect
315. #1508C2×C23semidirect
316. #1507C2×C23semidirect
317. #1465C2×C23semidirect
371. #484C22×C23semidirect
372. #483C22×C23semidirect
382. #400C22×C23semidirect
383. #399C22×C23semidirect
384. #398C22×C23semidirect
386. #397C22×C23semidirect
391. #328C22×C23semidirect
392. #328C22×C23semidirect
395. #324C22×C23semidirect
396. #323C22×C23semidirect
499. C23#18175direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35052
C23×#30952
C23×#30942
C23×#23952
C23×#16182
C23×#16152
C23×#16122
C23×#16092
C23×#15082
C23×#15072
C23×#14652
#1817523