Finite Group Databasebeta

← C23×#33572 #19181198

Subgroups — C23×#33572 #19181198

Order 5888.

1108 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
1C23×#3551C211yesmaximal, characteristic, complemented
2C23×#3022C211yesmaximal, characteristic, complemented
3C23×#3021C211yesmaximal, characteristic, complemented
4C23×#3018C211yesmaximal, characteristic, complemented
5C23×#2204C214yesmaximal, complemented
6C23×#2203C214yesmaximal, complemented
7C23×#2135C211yesmaximal, characteristic, complemented
8C23×#2134C211yesmaximal, characteristic, complemented
9C23×#2132C211yesmaximal, characteristic, complemented
10C23×#585C2211yescharacteristic
11C23×#575—21no—
12C2×C23×#137—21no—
13C2×C23×AGL(1,ℤ/8)—21no—
14C23×#563C2212yescomplemented
15C23×#560—21no—
16C23×#555C2212yescomplemented
17C23×#553—21no—
18C23×#552—21no—
19C23×#551—21no—
20C23×#548—21no—
21C23×#546—21no—
22C23×#540—22no—
23C23×#538—22no—
24C23×#537—21no—
25C23×#536C2211yescharacteristic
26C23×#535C2211yescharacteristic
27C23×#532C2211yescharacteristic
28C23×#529—21no—
29C23×#456C2212yescomplemented
30C23×#456C2214yescomplemented
31C23×#455—21no—
32C23×#455—22no—
33C23×#454C2214yes—
34C23×#454C2212yescomplemented
35C23×#453—21no—
36C23×#453—22no—
37C23×#421—21no—
38C23×#421—21no—
39C2×C23×#104—21no—
40C23×#413C2211yescharacteristic
41C23×#413C2211yescharacteristic
42C23×#413C2211yescharacteristic
43C23×#356C2212yescomplemented
44C23×#356C2214yescomplemented
45C23×#355C2214yescomplemented
46C23×#355C2212yescomplemented
47C23×2−1+4—41no—
48C23×2−1+4C2312yes—
49C23×H(5,𝔽2)—21no—
50C23×H(5,𝔽2)—21no—
51C23×H(5,𝔽2)—21no—
52C23×H(5,𝔽2)—41no—
53C2×#41×C23—21no—
54C2×#41×C23—21no—
55C2×#41×C23—21no—
56C2×#41×C23—21no—
57C2×#41×C23—42no—
58C2×#41×C23D411yescharacteristic
59C2×#41×C23C2311yescharacteristic
60C22×Q8×C23D411yescharacteristic
61C22×D4×C23D411yescharacteristic
62C23×#137—24no—
63C23×#137—22no—
64C23×#137—41no—
65C23×#137—42no—
66C23×AGL(1,ℤ/8)—24no—
67C23×AGL(1,ℤ/8)—22no—
68C23×AGL(1,ℤ/8)—41no—
69C23×AGL(1,ℤ/8)—42no—
70C23×#135—42no—
71C2×Q16×C23—41no—
72C2×SD16×C23—41no—
73C2×SD16×C23—41no—
74C2×D8×C23—41no—
75C2×M16×C23—21no—
76C2×M16×C23—21no—
77C2×M16×C23—21no—
78C23×C4⋊Q8C2312yes—
79C23×C4⋊Q8C2311yescharacteristic
80C23×#127D411yescharacteristic
81C23×#127D412yes—
82C23×#126—22no—
83C23×#126—22no—
84C23×#126—22no—
85C23×#125—21no—
86C23×#125—22no—
87C23×#124—21no—
88C23×#124—22no—
89C23×#124D411yescharacteristic
90C23×#124D412yes—
91C23×#124C2311yescharacteristic
92C23×#124C2312yes—
93C23×#123—22no—
94C23×#123—22no—
95C23×#123—22no—
96C23×#123—21no—
97C23×#123—22no—
98C23×#123—21no—
99C23×C22⋊Q8—21no—
100C23×C22⋊Q8—22no—
101C23×C22⋊Q8—22no—
102C23×C22⋊Q8—21no—
103C23×C22⋊Q8—21no—
104C23×#121—22no—
105C23×#121—22no—
106C23×#121—21no—
107C23×#121—22no—
108C23×#121—22no—
109C23×#121—22no—
110C23×#121—22no—
111C23×#121—21no—
112C23×#121—21no—
113C23×#121—21no—
114C23×#121—21no—
115C23×#120—22no—
116C23×#120—21no—
117C23×#120—21no—
118C4×Q8×C23—21no—
119C4×D4×C23—22no—
120C4×D4×C23—21no—
121C4×D4×C23—22no—
122C4×D4×C23—21no—
123C4×D4×C23—21no—
124C4×D4×C23—22no—
125C23×#117—22no—
126C23×#117—22no—
127C23×#117D411yescharacteristic
128C23×#117D411yescharacteristic
129C2×C4⋊C4×C23—21no—
130C2×C22⋊C4×C23—22no—
131C2×C42×C23D411yescharacteristic
132C23×#104—22no—
133C23×#104—22no—
134C23×#104—24no—
135C23×#104—24no—
136C23×#101C2312yes—
137C23×#101C2312yes—
138C23×#101C2312yes—
139C23×#100—21no—
140C23×#100—21no—
141C23×#100—21no—
142C24×C23—21no—
143#41×C23—22no—
144#41×C23—22no—
145#41×C23—22no—
146#41×C23—22no—
147#41×C23—22no—
148#41×C23—22no—
149#41×C23—41no—
150#41×C23—41no—
151#41×C23—41no—
152#41×C23—41no—
153#41×C23—41no—
154#41×C23—41no—
155#41×C23—41no—
156#41×C23—42no—
157#41×C23—42no—
158#41×C23—42no—
159#41×C23—42no—
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—41no—
168C2×Q8×C23—41no—
169C2×Q8×C23—42no—
170C2×Q8×C23C2×D411yescharacteristic
171C2×Q8×C23C2×D412yes—
172C2×Q8×C23C2411yescharacteristic
173C2×D4×C23—21no—
174C2×D4×C23—21no—
175C2×D4×C23—21no—
176C2×D4×C23—22no—
177C2×D4×C23—22no—
178C2×D4×C23—21no—
179C2×D4×C23—22no—
180C2×D4×C23—22no—
181C2×D4×C23—21no—
182C2×D4×C23—21no—
183C2×D4×C23—21no—
184C2×D4×C23—41no—
185C2×D4×C23—41no—
186C2×D4×C23—42no—
187C2×D4×C23—42no—
188C2×D4×C23—42no—
189C2×D4×C23—41no—
190C2×D4×C23—41no—
191C2×D4×C23—41no—
192C2×D4×C23C2×D411yescharacteristic
193C2×D4×C23C2×D412yes—
194C2×D4×C23C2×D411yescharacteristic
195C2×D4×C23C2×D411yescharacteristic
196C2×D4×C23C2×D411yescharacteristic
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
209Q16×C23—44no—
210Q16×C23—42no—
211SD16×C23—44no—
212SD16×C23—42no—
213SD16×C23—44no—
214SD16×C23—42no—
215D8×C23—44no—
216D8×C23—42no—
217M16×C23—22no—
218M16×C23—22no—
219M16×C23—22no—
220M16×C23—41no—
221M16×C23—41no—
222M16×C23—41no—
223C2×C8×C23—41no—
224C2×C8×C23—41no—
225C2×C8×C23—41no—
226C4⋊C4×C23—22no—
227C4⋊C4×C23—22no—
228C4⋊C4×C23—22no—
229C4⋊C4×C23—22no—
230C4⋊C4×C23—22no—
231C4⋊C4×C23—21no—
232C4⋊C4×C23—21no—
233C4⋊C4×C23—22no—
234C4⋊C4×C23—22no—
235C4⋊C4×C23—21no—
236C4⋊C4×C23—21no—
237C22⋊C4×C23—22no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—22no—
240C22⋊C4×C23—22no—
241C22⋊C4×C23—22no—
242C22⋊C4×C23—21no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—21no—
245C22⋊C4×C23—21no—
246C22⋊C4×C23—21no—
247C22⋊C4×C23—22no—
248C22⋊C4×C23—21no—
249C22⋊C4×C23—22no—
250C22⋊C4×C23—21no—
251C22⋊C4×C23—22no—
252C42×C23—22no—
253C42×C23—21no—
254C42×C23C2×D411yescharacteristic
255C42×C23C2×D411yescharacteristic
256C42×C23C2×D412yes—
257C42×C23C2×D412yes—
258#33572C2311yesmaximal, characteristic, direct product factor, Sylow
259C23×C23—22no—
260C23×C23—21no—
261C23×C23—41no—
262C23×C23—41no—
263C23×C23—41no—
264C23×C23—81no—
265C23×C23—82no—
266C23×C23#12011yescharacteristic
267C23×C23#12011yescharacteristic
268C23×C23#12011yescharacteristic
269Q8×C23—22no—
270Q8×C23—22no—
271Q8×C23—22no—
272Q8×C23—41no—
273Q8×C23—42no—
274Q8×C23—41no—
275Q8×C23—41no—
276Q8×C23—41no—
277Q8×C23—41no—
278D4×C23—22no—
279D4×C23—22no—
280D4×C23—22no—
281D4×C23—41no—
282D4×C23—41no—
283D4×C23—41no—
284D4×C23—42no—
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—82no—
295D4×C23—82no—
296D4×C23—82no—
297D4×C23—81no—
298D4×C23—81no—
299D4×C23—82no—
300C2×C4×C23—21no—
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—21no—
309C2×C4×C23—22no—
310C2×C4×C23—22no—
311C2×C4×C23—21no—
312C2×C4×C23—42no—
313C2×C4×C23—42no—
314C2×C4×C23—42no—
315C2×C4×C23—41no—
316C2×C4×C23—41no—
317C2×C4×C23—41no—
318C2×C4×C23—41no—
319C2×C4×C23—41no—
320C2×C4×C23—42no—
321C2×C4×C23—81no—
322C2×C4×C23—82no—
323C2×C4×C23—81no—
324C2×C4×C23—82no—
325C2×C4×C23—82no—
326C2×C4×C23#12011yescharacteristic
327C2×C4×C23C22×D411yescharacteristic
328C2×C4×C23C22×D411yescharacteristic
329C2×C4×C23C22×D411yescharacteristic
330C8×C23—42no—
331C8×C23—42no—
332C8×C23—42no—
333#3551C2×C2311yescharacteristic, complemented
334#3022C2×C2311yescharacteristic, complemented
335#3021C2×C2311yescharacteristic, complemented
336#3018C2×C2311yescharacteristic, complemented
337#2204C2×C2314yescomplemented
338#2203C2×C2314yescomplemented
339#2135C2×C2311yescharacteristic, complemented
340#2134C2×C2311yescharacteristic, complemented
341#2132C2×C2311yescharacteristic, complemented
342C22×C23—21no—
343C22×C23—21no—
344C22×C23—21no—
345C22×C23—41no—
346C22×C23—41no—
347C22×C23—41no—
348C22×C23—41no—
349C22×C23—42no—
350C22×C23—41no—
351C22×C23—42no—
352C22×C23—42no—
353C22×C23—41no—
354C22×C23—42no—
355C22×C23—161no—
356C22×C23—161no—
357C22×C23—161no—
358C22×C23—162no—
359C22×C23C2×#12011yescharacteristic
360C4×C23—21no—
361C4×C23—21no—
362C4×C23—21no—
363C4×C23—41no—
364C4×C23—42no—
365C4×C23—42no—
366C4×C23—41no—
367C4×C23—41no—
368C4×C23—42no—
369C4×C23—42no—
370C4×C23B(4,𝔽2)11yescharacteristic
371C4×C23B(4,𝔽2)11yescharacteristic
372#585C22×C2311yescharacteristic
373#575—21no—
374C2×#137—21no—
375C2×AGL(1,ℤ/8)—21no—
376#563C22×C2312yescomplemented
377#560—21no—
378#555C22×C2312yescomplemented
379#553—21no—
380#552—21no—
381#551—21no—
382#548—21no—
383#546—21no—
384#540—22no—
385#538—22no—
386#537—21no—
387#536C22×C2311yescharacteristic
388#535C22×C2311yescharacteristic
389#532C22×C2311yescharacteristic
390#529—21no—
391#456C22×C2312yescomplemented
392#456C22×C2314yescomplemented
393#455—21no—
394#455—22no—
395#454C22×C2314yes—
396#454C22×C2312yescomplemented
397#453—21no—
398#453—22no—
399#421—21no—
400#421—21no—
401C2×#104—21no—
402#413C22×C2311yescharacteristic
403#413C22×C2311yescharacteristic
404#413C22×C2311yescharacteristic
405#356C22×C2312yescomplemented
406#356C22×C2314yescomplemented
407#355C22×C2312yescomplemented
408#355C22×C2314yescomplemented
409C2×C23—21no—
410C2×C23—41no—
411C2×C23—41no—
412C2×C23—41no—
413C2×C23—81no—
414C2×C23—82no—
415C2×C23—82no—
416C2×C23C2×B(4,𝔽2)11yescharacteristic
4172−1+4—41no—
4182−1+4C23×C2312yes—
419H(5,𝔽2)—21no—
420H(5,𝔽2)—21no—
421H(5,𝔽2)—21no—
422H(5,𝔽2)—41no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—42no—
428C2×#41D4×C2311yescharacteristic
429C2×#41C23×C2311yescharacteristic
430C22×Q8D4×C2311yescharacteristic
431C22×D4D4×C2311yescharacteristic
432#137—24no—
433#137—22no—
434#137—41no—
435#137—42no—
436AGL(1,ℤ/8)—24no—
437AGL(1,ℤ/8)—22no—
438AGL(1,ℤ/8)—41no—
439AGL(1,ℤ/8)—42no—
440#135—42no—
441C2×Q16—41no—
442C2×SD16—41no—
443C2×SD16—41no—
444C2×D8—41no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—21no—
448C4⋊Q8C23×C2311yescharacteristic
449C4⋊Q8C23×C2312yes—
450#127D4×C2311yescharacteristic
451#127D4×C2312yes—
452#126—22no—
453#126—22no—
454#126—22no—
455#125—21no—
456#125—22no—
457#124—21no—
458#124—22no—
459#124D4×C2311yescharacteristic
460#124D4×C2312yes—
461#124C23×C2311yescharacteristic
462#124C23×C2312yes—
463#123—22no—
464#123—22no—
465#123—22no—
466#123—21no—
467#123—21no—
468#123—22no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—21no—
484#121—21no—
485#120—22no—
486#120—21no—
487#120—21no—
488C4×Q8—21no—
489C4×D4—22no—
490C4×D4—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117D4×C2311yescharacteristic
498#117D4×C2311yescharacteristic
499C2×C4⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C42D4×C2311yescharacteristic
502#104—22no—
503#104—22no—
504#104—24no—
505#104—24no—
506#101C23×C2312yes—
507#101C23×C2312yes—
508#101C23×C2312yes—
509#100—21no—
510#100—21no—
511#100—21no—
512C23#3357211yescharacteristic, direct product factor, Sylow
513C24—21no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—42no—
530#41—42no—
531#41—41no—
532#41—81no—
533#41—81no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—42no—
541C2×Q8C2×D4×C2311yescharacteristic
542C2×Q8C2×D4×C2312yes—
543C2×Q8C24×C2311yescharacteristic
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4C2×D4×C2311yescharacteristic
564C2×D4C2×D4×C2312yes—
565C2×D4C2×D4×C2311yescharacteristic
566C2×D4C2×D4×C2311yescharacteristic
567C2×D4C2×D4×C2311yescharacteristic
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4C2×D4×C2311yescharacteristic
578C22×C4C2×D4×C2311yescharacteristic
579C22×C4C2×D4×C2311yescharacteristic
580Q16—44no—
581Q16—42no—
582SD16—44no—
583SD16—42no—
584SD16—44no—
585SD16—42no—
586D8—44no—
587D8—42no—
588M16—22no—
589M16—22no—
590M16—22no—
591M16—41no—
592M16—41no—
593M16—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C42—22no—
624C42—21no—
625C42C2×D4×C2311yescharacteristic
626C42C2×D4×C2311yescharacteristic
627C42C2×D4×C2312yes—
628C42C2×D4×C2312yes—
629C23—22no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—81no—
635C23—82no—
636C23C23×#12011yescharacteristic
637C23C23×#12011yescharacteristic
638C23C23×#12011yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—42no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—42no—
655D4—41no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—81no—
664D4—82no—
665D4—82no—
666D4—82no—
667D4—82no—
668D4—81no—
669D4—81no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—81no—
695C2×C4—82no—
696C2×C4C23×#12011yescharacteristic
697C2×C4C22×D4×C2311yescharacteristic
698C2×C4C22×D4×C2311yescharacteristic
699C2×C4C22×D4×C2311yescharacteristic
700C8—42no—
701C8—42no—
702C8—42no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—161no—
717C22—161no—
718C22—161no—
719C22—162no—
720C22C2×C23×#12011yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—41no—
725C4—42no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4C23×B(4,𝔽2)11yescharacteristic
732C4C23×B(4,𝔽2)11yescharacteristic
733C2—21no—
734C2—41no—
735C2—41no—
736C2—41no—
737C2—82no—
738C2—81no—
739C2—82no—
740C2C2×C23×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C23C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C23
LCSG ▷ C2×Q8 ▷ 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×#3022C2semidirect
3. C23×#3021C2semidirect
4. C23×#3018C2semidirect
5. C23×#2204C2semidirect
6. C23×#2203C2semidirect
7. C23×#2135C2semidirect
8. C23×#2134C2semidirect
9. C23×#2132C2semidirect
14. C23×#563C22semidirect
16. C23×#555C22semidirect
29. C23×#456C22semidirect
30. C23×#456C22semidirect
34. C23×#454C22semidirect
43. C23×#356C22semidirect
44. C23×#356C22semidirect
45. C23×#355C22semidirect
46. C23×#355C22semidirect
258. #33572C23direct (N × H)
333. #3551C2×C23semidirect
334. #3022C2×C23semidirect
335. #3021C2×C23semidirect
336. #3018C2×C23semidirect
337. #2204C2×C23semidirect
338. #2203C2×C23semidirect
339. #2135C2×C23semidirect
340. #2134C2×C23semidirect
341. #2132C2×C23semidirect
376. #563C22×C23semidirect
378. #555C22×C23semidirect
391. #456C22×C23semidirect
392. #456C22×C23semidirect
396. #454C22×C23semidirect
405. #356C22×C23semidirect
406. #356C22×C23semidirect
407. #355C22×C23semidirect
408. #355C22×C23semidirect
512. C23#33572direct (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×#30222
C23×#30212
C23×#30182
C23×#22042
C23×#22032
C23×#21352
C23×#21342
C23×#21322
#3357223