Finite Group Databasebeta

← C23×#24386 #19172012

Subgroups — C23×#24386 #19172012

Order 5888.

1548 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×C22⋊Q8C211yesmaximal, characteristic
2C2×C23×#470C212yesmaximal, complemented
3C2×C23×#451C211yesmaximal, characteristic, complemented
4C2×C23×#407C211yesmaximal, characteristic
5C23×#2848C211yesmaximal, characteristic
6C23×#2035C212yesmaximal, complemented
7C23×#2001C212yesmaximal, complemented
8C23×#1894C212yesmaximal, complemented
9C23×#1872C211yesmaximal, characteristic, complemented
10C23×#1853C211yesmaximal, characteristic, complemented
11C23×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C23C2211yescharacteristic
13C24×C4×C23C2211yescharacteristic
14C22×Q16×C23C2212yescomplemented
15C22×M16×C23C2212yes—
16C2×C23×C22⋊Q8—21no—
17C2×C23×C22⋊Q8—21no—
18C2×C23×C22⋊Q8—28no—
19C2×C23×C22⋊Q8C2212yes—
20C2×C23×C22⋊Q8C2211yescharacteristic
21C2×C23×C22⋊Q8C2211yescharacteristic
22C2×C23×C22⋊Q8C2212yes—
23C2×C23×C22⋊Q8C2211yescharacteristic
24C22×C4⋊C4×C23—21no—
25C22×C4⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23—21no—
27C23×#470—28no—
28C23×#451—24no—
29C2×C23×#106C2212yescomplemented
30C2×C23×#103C2212yescomplemented
31C2×C23×#103C2212yescomplemented
32C2×C23×#103C2212yescomplemented
33C2×C23×#103C2212yescomplemented
34C23×#407—24no—
35C2×C23×C22⋊C8C2212yes—
36C2×C23×C22⋊C8C2211yescharacteristic
37C2×C23×C22⋊C8C2211yescharacteristic
38C23×#385—21no—
39C23×#385—21no—
40C23×#385—21no—
41C23×#380C2211yescharacteristic
42C23×#380C2211yescharacteristic
43C23×#380C2211yescharacteristic
44C23×#379—21no—
45C23×#340C2212yescomplemented
46C23×#340C2212yescomplemented
47C25×C23D411yescharacteristic
48C22×Q8×C23—24no—
49C22×Q8×C23—21no—
50C22×Q8×C23—22no—
51C22×Q8×C23—22no—
52C22×Q8×C23—42no—
53C22×Q8×C23C2311yescharacteristic
54C22×Q8×C23C2312yes—
55C23×C4×C23—21no—
56C23×C4×C23—21no—
57C23×C4×C23—22no—
58C23×C4×C23—24no—
59C23×C4×C23—22no—
60C23×C4×C23—42no—
61C23×C4×C23D411yescharacteristic
62C23×C4×C23D411yescharacteristic
63C23×C4×C23D411yescharacteristic
64C23×C4×C23C2311yescharacteristic
65C23×C4×C23C2311yescharacteristic
66C23×C4×C23C2311yescharacteristic
67C2×Q16×C23—24no—
68C2×Q16×C23—24no—
69C2×Q16×C23—42no—
70C2×M16×C23—24no—
71C2×M16×C23—24no—
72C2×M16×C23—42no—
73C22×C8×C23C2312yes—
74C22×C8×C23C2312yes—
75C23×C22⋊Q8—28no—
76C23×C22⋊Q8—28no—
77C23×C22⋊Q8—24no—
78C23×C22⋊Q8—24no—
79C23×C22⋊Q8—24no—
80C23×C22⋊Q8—22no—
81C23×C22⋊Q8—24no—
82C23×C22⋊Q8—22no—
83C23×C22⋊Q8—42no—
84C23×C22⋊Q8D418yes—
85C2×C4⋊C4×C23—28no—
86C2×C4⋊C4×C23—22no—
87C2×C4⋊C4×C23—22no—
88C2×C4⋊C4×C23—21no—
89C2×C4⋊C4×C23—24no—
90C2×C4⋊C4×C23—21no—
91C2×C4⋊C4×C23—21no—
92C2×C4⋊C4×C23—21no—
93C2×C4⋊C4×C23C2311yescharacteristic
94C2×C4⋊C4×C23C2311yescharacteristic
95C2×C4⋊C4×C23C2311yescharacteristic
96C2×C4⋊C4×C23C2312yes—
97C2×C22⋊C4×C23—28no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
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—
106C23×#106—24no—
107C23×#103—24no—
108C23×#103—24no—
109C23×#103—24no—
110C23×#103—42no—
111C23×C22⋊C8—22no—
112C23×C22⋊C8—24no—
113C23×C22⋊C8D414yes—
114C23×#95—21no—
115C23×#95—21no—
116C23×#95—21no—
117C24×C23—22no—
118C24×C23—22no—
119C24×C23—22no—
120C24×C23—22no—
121C24×C23—22no—
122C24×C23—41no—
123C24×C23—41no—
124C24×C23C2×D411yescharacteristic
125C24×C23C2×D411yescharacteristic
126C24×C23C2×D411yescharacteristic
127C2×Q8×C23—24no—
128C2×Q8×C23—22no—
129C2×Q8×C23—22no—
130C2×Q8×C23—22no—
131C2×Q8×C23—21no—
132C2×Q8×C23—22no—
133C2×Q8×C23—21no—
134C2×Q8×C23—22no—
135C2×Q8×C23—22no—
136C2×Q8×C23—22no—
137C2×Q8×C23—48no—
138C2×Q8×C23—48no—
139C2×Q8×C23—42no—
140C2×Q8×C23—42no—
141C2×Q8×C23C2×D414yes—
142C22×C4×C23—22no—
143C22×C4×C23—21no—
144C22×C4×C23—21no—
145C22×C4×C23—22no—
146C22×C4×C23—22no—
147C22×C4×C23—24no—
148C22×C4×C23—24no—
149C22×C4×C23—22no—
150C22×C4×C23—22no—
151C22×C4×C23—22no—
152C22×C4×C23—22no—
153C22×C4×C23—22no—
154C22×C4×C23—22no—
155C22×C4×C23—22no—
156C22×C4×C23—22no—
157C22×C4×C23—22no—
158C22×C4×C23—21no—
159C22×C4×C23—21no—
160C22×C4×C23—22no—
161C22×C4×C23—21no—
162C22×C4×C23—21no—
163C22×C4×C23—21no—
164C22×C4×C23—21no—
165C22×C4×C23—41no—
166C22×C4×C23—41no—
167C22×C4×C23—41no—
168C22×C4×C23—48no—
169C22×C4×C23—48no—
170C22×C4×C23—42no—
171C22×C4×C23—42no—
172C22×C4×C23—42no—
173C22×C4×C23—42no—
174C22×C4×C23C2×D411yescharacteristic
175C22×C4×C23C2×D411yescharacteristic
176C22×C4×C23C2×D414yes—
177C22×C4×C23C2×D411yescharacteristic
178C22×C4×C23C2×D412yes—
179C22×C4×C23#4112yes—
180C22×C4×C23C2411yescharacteristic
181Q16×C23—48no—
182M16×C23—48no—
183C2×C8×C23—22no—
184C2×C8×C23—22no—
185C2×C8×C23—22no—
186C2×C8×C23—22no—
187C2×C8×C23—22no—
188C2×C8×C23C2×D414yes—
189C4⋊C4×C23—24no—
190C4⋊C4×C23—28no—
191C4⋊C4×C23—28no—
192C4⋊C4×C23—22no—
193C4⋊C4×C23—21no—
194C4⋊C4×C23—22no—
195C4⋊C4×C23—21no—
196C4⋊C4×C23—22no—
197C4⋊C4×C23—42no—
198C4⋊C4×C23—42no—
199C4⋊C4×C23—42no—
200C4⋊C4×C23C2×D414yes—
201C22⋊C4×C23—28no—
202C22⋊C4×C23—28no—
203C22⋊C4×C23—42no—
204C22⋊C4×C23—42no—
205C22⋊C4×C23—42no—
206C22⋊C4×C23—42no—
207C22⋊C4×C23—42no—
208C22⋊C4×C23—42no—
209#24386C2311yesmaximal, characteristic, direct product factor, Sylow
210C23×C23—21no—
211C23×C23—21no—
212C23×C23—21no—
213C23×C23—21no—
214C23×C23—28no—
215C23×C23—21no—
216C23×C23—21no—
217C23×C23—21no—
218C23×C23—21no—
219C23×C23—21no—
220C23×C23—21no—
221C23×C23—21no—
222C23×C23—21no—
223C23×C23—21no—
224C23×C23—21no—
225C23×C23—21no—
226C23×C23—21no—
227C23×C23—44no—
228C23×C23—44no—
229C23×C23—44no—
230C23×C23—44no—
231C23×C23—44no—
232C23×C23—44no—
233C23×C23#12012yes—
234C23×C23#12112yes—
235C23×C23#13712yes—
236C23×C23#13712yes—
237C23×C23#13712yes—
238C23×C23C22×D411yescharacteristic
239Q8×C23—24no—
240Q8×C23—24no—
241Q8×C23—48no—
242Q8×C23—42no—
243Q8×C23—42no—
244Q8×C23—42no—
245Q8×C23—42no—
246C2×C4×C23—21no—
247C2×C4×C23—21no—
248C2×C4×C23—21no—
249C2×C4×C23—21no—
250C2×C4×C23—24no—
251C2×C4×C23—24no—
252C2×C4×C23—24no—
253C2×C4×C23—24no—
254C2×C4×C23—24no—
255C2×C4×C23—24no—
256C2×C4×C23—21no—
257C2×C4×C23—21no—
258C2×C4×C23—21no—
259C2×C4×C23—44no—
260C2×C4×C23—44no—
261C2×C4×C23—44no—
262C2×C4×C23—48no—
263C2×C4×C23—48no—
264C2×C4×C23—42no—
265C2×C4×C23—42no—
266C2×C4×C23—42no—
267C2×C4×C23—42no—
268C2×C4×C23—42no—
269C2×C4×C23—42no—
270C2×C4×C23—41no—
271C2×C4×C23—41no—
272C2×C4×C23—41no—
273C2×C4×C23—41no—
274C2×C4×C23—41no—
275C2×C4×C23—41no—
276C2×C4×C23—41no—
277C2×C4×C23—41no—
278C2×C4×C23—41no—
279C2×C4×C23—41no—
280C2×C4×C23—41no—
281C2×C4×C23—41no—
282C2×C4×C23#12012yes—
283C2×C4×C23#12112yes—
284C2×C4×C23C22×D411yescharacteristic
285C2×C4×C23C22×D412yes—
286C2×C4×C23C2×#4111yescharacteristic
287C2×C4×C23H(5,𝔽2)12yes—
288C8×C23—24no—
289C8×C23—42no—
290C22×C22⋊Q8C2×C2311yescharacteristic
291C2×#470C2×C2312yescomplemented
292C2×#451C2×C2311yescharacteristic, complemented
293C2×#407C2×C2311yescharacteristic
294#2848C2×C2311yescharacteristic
295#2035C2×C2312yescomplemented
296#2001C2×C2312yescomplemented
297#1894C2×C2312yescomplemented
298#1872C2×C2311yescharacteristic, complemented
299#1853C2×C2311yescharacteristic, complemented
300#1787C2×C2311yescharacteristic, complemented
301C22×C23—22no—
302C22×C23—22no—
303C22×C23—22no—
304C22×C23—22no—
305C22×C23—22no—
306C22×C23—22no—
307C22×C23—22no—
308C22×C23—22no—
309C22×C23—22no—
310C22×C23—22no—
311C22×C23—22no—
312C22×C23—22no—
313C22×C23—416no—
314C22×C23—41no—
315C22×C23—41no—
316C22×C23—41no—
317C22×C23—41no—
318C22×C23—41no—
319C22×C23—41no—
320C22×C23—41no—
321C22×C23—41no—
322C22×C23#47014yescomplemented
323C22×C23C2×#12011yescharacteristic
324C22×C23C2×#12111yescharacteristic
325C22×C23#53411yescharacteristic
326C22×C23C2×#13711yescharacteristic
327C22×C23C2×#13711yescharacteristic
328C22×C23C2×#13711yescharacteristic
329C22×C23#57511yescharacteristic
330C4×C23—22no—
331C4×C23—22no—
332C4×C23—41no—
333C4×C23—44no—
334C4×C23—44no—
335C4×C23—81no—
336C4×C23—81no—
337C4×C23—81no—
338C4×C23—81no—
339C4×C23D4212yes—
340C4×C23#54612yes—
341C23×Q8C22×C2311yescharacteristic
342C24×C4C22×C2311yescharacteristic
343C22×Q16C22×C2312yescomplemented
344C22×M16C22×C2312yes—
345C2×C22⋊Q8—21no—
346C2×C22⋊Q8—21no—
347C2×C22⋊Q8—28no—
348C2×C22⋊Q8C22×C2311yescharacteristic
349C2×C22⋊Q8C22×C2311yescharacteristic
350C2×C22⋊Q8C22×C2312yes—
351C2×C22⋊Q8C22×C2312yes—
352C2×C22⋊Q8C22×C2311yescharacteristic
353C22×C4⋊C4—21no—
354C22×C4⋊C4C22×C2311yescharacteristic
355C22×C22⋊C4—21no—
356#470—28no—
357#451—24no—
358C2×#106C22×C2312yescomplemented
359C2×#103C22×C2312yescomplemented
360C2×#103C22×C2312yescomplemented
361C2×#103C22×C2312yescomplemented
362C2×#103C22×C2312yescomplemented
363#407—24no—
364C2×C22⋊C8C22×C2311yescharacteristic
365C2×C22⋊C8C22×C2312yes—
366C2×C22⋊C8C22×C2311yescharacteristic
367#385—21no—
368#385—21no—
369#385—21no—
370#380C22×C2311yescharacteristic
371#380C22×C2311yescharacteristic
372#380C22×C2311yescharacteristic
373#379—21no—
374#340C22×C2312yescomplemented
375#340C22×C2312yescomplemented
376C2×C23—24no—
377C2×C23—42no—
378C2×C23—42no—
379C2×C23#241011yescharacteristic
380C2×C23#300411yescharacteristic
381C2×C23#300711yescharacteristic
382C2×C23C2×#47011yescharacteristic
383C2×C23#305611yescharacteristic
384C2×C23#319511yescharacteristic
385C2×C23#319611yescharacteristic
386C25D4×C2311yescharacteristic
387C22×Q8—24no—
388C22×Q8—21no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—42no—
392C22×Q8C23×C2311yescharacteristic
393C22×Q8C23×C2312yes—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—42no—
400C23×C4D4×C2311yescharacteristic
401C23×C4D4×C2311yescharacteristic
402C23×C4D4×C2311yescharacteristic
403C23×C4C23×C2311yescharacteristic
404C23×C4C23×C2311yescharacteristic
405C23×C4C23×C2311yescharacteristic
406C2×Q16—24no—
407C2×Q16—24no—
408C2×Q16—42no—
409C2×M16—24no—
410C2×M16—24no—
411C2×M16—42no—
412C22×C8C23×C2312yes—
413C22×C8C23×C2312yes—
414C22⋊Q8—28no—
415C22⋊Q8—28no—
416C22⋊Q8—24no—
417C22⋊Q8—24no—
418C22⋊Q8—24no—
419C22⋊Q8—22no—
420C22⋊Q8—24no—
421C22⋊Q8—22no—
422C22⋊Q8—42no—
423C22⋊Q8D4×C2318yes—
424C2×C4⋊C4—28no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4C23×C2311yescharacteristic
433C2×C4⋊C4C23×C2311yescharacteristic
434C2×C4⋊C4C23×C2311yescharacteristic
435C2×C4⋊C4C23×C2312yes—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445#106—24no—
446#103—24no—
447#103—24no—
448#103—24no—
449#103—42no—
450C22⋊C8—22no—
451C22⋊C8—24no—
452C22⋊C8D4×C2314yes—
453#95—21no—
454#95—21no—
455#95—21no—
456C23#2438611yescharacteristic, direct product factor, Sylow
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—41no—
463C24—41no—
464C24C2×D4×C2311yescharacteristic
465C24C2×D4×C2311yescharacteristic
466C24C2×D4×C2311yescharacteristic
467C2×Q8—24no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8C2×D4×C2314yes—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4C2×D4×C2311yescharacteristic
515C22×C4C2×D4×C2311yescharacteristic
516C22×C4C2×D4×C2314yes—
517C22×C4C2×D4×C2311yescharacteristic
518C22×C4C2×D4×C2312yes—
519C22×C4#41×C2312yes—
520C22×C4C24×C2311yescharacteristic
521Q16—48no—
522M16—48no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8C2×D4×C2314yes—
529C4⋊C4—24no—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4C2×D4×C2314yes—
541C22⋊C4—28no—
542C22⋊C4—28no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—28no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23C23×#12012yes—
573C23C23×#12112yes—
574C23C23×#13712yes—
575C23C23×#13712yes—
576C23C23×#13712yes—
577C23C22×D4×C2311yescharacteristic
578Q8—24no—
579Q8—24no—
580Q8—48no—
581Q8—42no—
582Q8—42no—
583Q8—42no—
584Q8—42no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4C23×#12012yes—
622C2×C4C23×#12112yes—
623C2×C4C22×D4×C2311yescharacteristic
624C2×C4C22×D4×C2312yes—
625C2×C4C2×#41×C2311yescharacteristic
626C2×C4C23×H(5,𝔽2)12yes—
627C8—24no—
628C8—42no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—416no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22C23×#47014yescomplemented
651C22C2×C23×#12011yescharacteristic
652C22C2×C23×#12111yescharacteristic
653C22C23×#53411yescharacteristic
654C22C2×C23×#13711yescharacteristic
655C22C2×C23×#13711yescharacteristic
656C22C2×C23×#13711yescharacteristic
657C22C23×#57511yescharacteristic
658C4—22no—
659C4—22no—
660C4—41no—
661C4—44no—
662C4—44no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4D42×C2312yes—
668C4C23×#54612yes—
669C2—24no—
670C2—42no—
671C2—42no—
672C2C23×#241011yescharacteristic
673C2C23×#300411yescharacteristic
674C2C23×#300711yescharacteristic
675C2C2×C23×#47011yescharacteristic
676C2C23×#305611yescharacteristic
677C2C23×#319511yescharacteristic
678C2C23×#319611yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC25×C23D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C24×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C23×#470C2semidirect
3. C2×C23×#451C2semidirect
6. C23×#2035C2semidirect
7. C23×#2001C2semidirect
8. C23×#1894C2semidirect
9. C23×#1872C2semidirect
10. C23×#1853C2semidirect
11. C23×#1787C2semidirect
14. C22×Q16×C23C22semidirect
29. C2×C23×#106C22semidirect
30. C2×C23×#103C22semidirect
31. C2×C23×#103C22semidirect
32. C2×C23×#103C22semidirect
33. C2×C23×#103C22semidirect
45. C23×#340C22semidirect
46. C23×#340C22semidirect
209. #24386C23direct (N × H)
291. C2×#470C2×C23semidirect
292. C2×#451C2×C23semidirect
295. #2035C2×C23semidirect
296. #2001C2×C23semidirect
297. #1894C2×C23semidirect
298. #1872C2×C23semidirect
299. #1853C2×C23semidirect
300. #1787C2×C23semidirect
322. C22×C23#470semidirect
343. C22×Q16C22×C23semidirect
358. C2×#106C22×C23semidirect
359. C2×#103C22×C23semidirect
360. C2×#103C22×C23semidirect
361. C2×#103C22×C23semidirect
362. C2×#103C22×C23semidirect
374. #340C22×C23semidirect
375. #340C22×C23semidirect
456. C23#24386direct (N × H)
650. C22C23×#470semidirect

Maximal subgroups

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

subgroupindex
C22×C23×C22⋊Q82
C2×C23×#4702
C2×C23×#4512
C2×C23×#4072
C23×#28482
C23×#20352
C23×#20012
C23×#18942
C23×#18722
C23×#18532
C23×#17872
#2438623