Finite Group Databasebeta

← C23×#26748 #19174374

Subgroups — C23×#26748 #19174374

Order 5888.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2491C211yesmaximal, characteristic
2C23×#2362C211yesmaximal, characteristic, complemented
3C23×#2055C211yesmaximal, characteristic, complemented
4C23×#2036C211yesmaximal, characteristic, complemented
5C23×#2024C211yesmaximal, characteristic, complemented
6C23×#2000C211yesmaximal, characteristic
7C23×#1988C211yesmaximal, characteristic, complemented
8C23×#1936C211yesmaximal, characteristic, complemented
9C23×#1925C211yesmaximal, characteristic, complemented
10C23×#1924C211yesmaximal, characteristic, complemented
11C23×#1921C211yesmaximal, characteristic, complemented
12C23×#1880C211yesmaximal, characteristic, complemented
13C23×#1875C211yesmaximal, characteristic
14C23×#1825C211yesmaximal, characteristic, complemented
15C23×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C23C2211yescharacteristic
17C2×C23×C4⋊Q8C2211yescharacteristic
18C2×C23×#124—21no—
19C2×C23×C22⋊Q8C2211yescharacteristic
20C2×C23×#121C2211yescharacteristic
21C2×C4×Q8×C23C2211yescharacteristic
22C2×C23×#117C2211yescharacteristic
23C2×C23×#107C2211yescharacteristic
24C2×C23×C4⋊C8C2211yescharacteristic
25C2×C23×#103C2211yescharacteristic
26C2×C23×#103C2211yescharacteristic
27C2×C23×#103C2211yescharacteristic
28C2×C23×#102C2211yescharacteristic
29C2×C23×#102C2211yescharacteristic
30C2×C23×#102C2211yescharacteristic
31C2×C23×C22⋊C8C2211yescharacteristic
32C2×C23×C22⋊C8C2211yescharacteristic
33C2×C23×#97C2211yescharacteristic
34C23×#394—21no—
35C23×#393—21no—
36C23×#391C2211yescharacteristic
37C23×#390C2211yescharacteristic
38C23×#390C2211yescharacteristic
39C23×#389C2211yescharacteristic
40C23×#388—21no—
41C23×#388—21no—
42C23×#388—21no—
43C23×#387—21no—
44C23×#380C2211yescharacteristic
45C4×C4⋊C4×C23—21no—
46C4×C4⋊C4×C23C2211yescharacteristic
47C4×C4⋊C4×C23C2211yescharacteristic
48C4×C22⋊C4×C23C2211yescharacteristic
49C23×#340C2211yescharacteristic
50C23×#340C2211yescharacteristic
51C23×#340C2211yescharacteristic
52C23×#340C2211yescharacteristic
53C23×#340C2211yescharacteristic
54C23×#340C2211yescharacteristic
55C23×#340C2211yescharacteristic
56C23×#340C2211yescharacteristic
57C23×#336C2211yescharacteristic
58C23×#336C2211yescharacteristic
59C22×Q8×C23—21no—
60C22×Q8×C23C2311yescharacteristic
61C22×D4×C23—21no—
62C22×D4×C23C2311yescharacteristic
63C23×C4×C23C2311yescharacteristic
64C2×SD16×C23—22no—
65C2×SD16×C23—41no—
66C2×SD16×C23—41no—
67C22×C8×C23C2311yescharacteristic
68C22×C8×C23C2311yescharacteristic
69C22×C8×C23C2311yescharacteristic
70C22×C8×C23C2311yescharacteristic
71C23×C4⋊Q8—22no—
72C23×C4⋊Q8—41no—
73C23×#124—44no—
74C23×C22⋊Q8—22no—
75C23×C22⋊Q8—22no—
76C23×#121—22no—
77C23×#121—41no—
78C4×Q8×C23—22no—
79C4×Q8×C23—41no—
80C23×#117—22no—
81C23×#117—41no—
82C2×C4⋊C4×C23—21no—
83C2×C4⋊C4×C23—21no—
84C2×C4⋊C4×C23—21no—
85C2×C4⋊C4×C23—21no—
86C2×C4⋊C4×C23C2311yescharacteristic
87C2×C4⋊C4×C23C2311yescharacteristic
88C2×C4⋊C4×C23C2311yescharacteristic
89C2×C4⋊C4×C23C2311yescharacteristic
90C2×C4⋊C4×C23C2311yescharacteristic
91C2×C4⋊C4×C23C2311yescharacteristic
92C2×C22⋊C4×C23—21no—
93C2×C22⋊C4×C23—21no—
94C2×C22⋊C4×C23—21no—
95C2×C22⋊C4×C23—21no—
96C2×C22⋊C4×C23—21no—
97C2×C22⋊C4×C23—21no—
98C2×C22⋊C4×C23—21no—
99C2×C22⋊C4×C23—21no—
100C2×C22⋊C4×C23D411yescharacteristic
101C2×C22⋊C4×C23D411yescharacteristic
102C2×C42×C23—21no—
103C2×C42×C23—21no—
104C2×C42×C23—21no—
105C2×C42×C23—21no—
106C2×C42×C23C2311yescharacteristic
107C2×C42×C23C2311yescharacteristic
108C23×#107—22no—
109C23×C4⋊C8—41no—
110C23×#103—22no—
111C23×#103—22no—
112C23×#103—41no—
113C23×#102—22no—
114C23×#102—22no—
115C23×#102—41no—
116C23×C22⋊C8—41no—
117C23×C22⋊C8—41no—
118C23×#97—41no—
119C23×#95—21no—
120C23×#95—21no—
121C23×#95—21no—
122C23×#95—21no—
123C23×#95—21no—
124C23×#95—21no—
125C23×#95D411yescharacteristic
126C23×#95D411yescharacteristic
127C24×C23—21no—
128C24×C23C2×D411yescharacteristic
129C2×Q8×C23—21no—
130C2×Q8×C23—21no—
131C2×Q8×C23—21no—
132C2×Q8×C23—21no—
133C2×Q8×C23—21no—
134C2×Q8×C23—42no—
135C2×Q8×C23—42no—
136C2×Q8×C23—81no—
137C2×Q8×C23#4112yes—
138C2×D4×C23—21no—
139C2×D4×C23—21no—
140C2×D4×C23—21no—
141C2×D4×C23—21no—
142C2×D4×C23—21no—
143C2×D4×C23—21no—
144C2×D4×C23—42no—
145C2×D4×C23—42no—
146C2×D4×C23—81no—
147C22×C4×C23—21no—
148C22×C4×C23—21no—
149C22×C4×C23—21no—
150C22×C4×C23—21no—
151C22×C4×C23—21no—
152C22×C4×C23—21no—
153C22×C4×C23—21no—
154C22×C4×C23—21no—
155C22×C4×C23—21no—
156C22×C4×C23—21no—
157C22×C4×C23—21no—
158C22×C4×C23—21no—
159C22×C4×C23—21no—
160C22×C4×C23C2×D411yescharacteristic
161C22×C4×C23C2×D411yescharacteristic
162C22×C4×C23C2×D411yescharacteristic
163C22×C4×C23C2×D411yescharacteristic
164C22×C4×C23C2×D411yescharacteristic
165C22×C4×C23C2411yescharacteristic
166SD16×C23—44no—
167C2×C8×C23—21no—
168C2×C8×C23—21no—
169C2×C8×C23—21no—
170C2×C8×C23—21no—
171C2×C8×C23—21no—
172C2×C8×C23—21no—
173C2×C8×C23—21no—
174C2×C8×C23—21no—
175C2×C8×C23—21no—
176C2×C8×C23—21no—
177C2×C8×C23—21no—
178C2×C8×C23—21no—
179C4⋊C4×C23—24no—
180C4⋊C4×C23—21no—
181C4⋊C4×C23—21no—
182C4⋊C4×C23—21no—
183C4⋊C4×C23—21no—
184C4⋊C4×C23—21no—
185C4⋊C4×C23—21no—
186C4⋊C4×C23—21no—
187C4⋊C4×C23—21no—
188C4⋊C4×C23—21no—
189C4⋊C4×C23—42no—
190C4⋊C4×C23—42no—
191C4⋊C4×C23—42no—
192C4⋊C4×C23#4112yes—
193C4⋊C4×C23#4112yes—
194C4⋊C4×C23#4112yes—
195C22⋊C4×C23—24no—
196C22⋊C4×C23—22no—
197C22⋊C4×C23—41no—
198C22⋊C4×C23—42no—
199C22⋊C4×C23—42no—
200C22⋊C4×C23—42no—
201C22⋊C4×C23—42no—
202C22⋊C4×C23—42no—
203C22⋊C4×C23—42no—
204C22⋊C4×C23—81no—
205C42×C23—21no—
206C42×C23—21no—
207C42×C23—21no—
208C42×C23—21no—
209C42×C23—42no—
210C42×C23—42no—
211C42×C23—42no—
212C42×C23—42no—
213#26748C2311yesmaximal, characteristic, direct product factor, Sylow
214C23×C23—21no—
215C23×C23—21no—
216C23×C23—21no—
217C23×C23—21no—
218C23×C23—21no—
219C23×C23—21no—
220C23×C23—21no—
221C23×C23—41no—
222C23×C23—41no—
223C23×C23—41no—
224C23×C23—41no—
225C23×C23—41no—
226C23×C23—41no—
227C23×C23—41no—
228C23×C23C22×D411yescharacteristic
229Q8×C23—22no—
230Q8×C23—22no—
231Q8×C23—41no—
232Q8×C23—41no—
233Q8×C23—84no—
234D4×C23—41no—
235D4×C23—41no—
236D4×C23—41no—
237D4×C23—41no—
238D4×C23—84no—
239C2×C4×C23—21no—
240C2×C4×C23—21no—
241C2×C4×C23—22no—
242C2×C4×C23—22no—
243C2×C4×C23—21no—
244C2×C4×C23—21no—
245C2×C4×C23—21no—
246C2×C4×C23—21no—
247C2×C4×C23—22no—
248C2×C4×C23—21no—
249C2×C4×C23—21no—
250C2×C4×C23—22no—
251C2×C4×C23—21no—
252C2×C4×C23—21no—
253C2×C4×C23—21no—
254C2×C4×C23—21no—
255C2×C4×C23—21no—
256C2×C4×C23—21no—
257C2×C4×C23—41no—
258C2×C4×C23—41no—
259C2×C4×C23—41no—
260C2×C4×C23—41no—
261C2×C4×C23—41no—
262C2×C4×C23—41no—
263C2×C4×C23—41no—
264C2×C4×C23—41no—
265C2×C4×C23—41no—
266C2×C4×C23—41no—
267C2×C4×C23—41no—
268C2×C4×C23—41no—
269C2×C4×C23—41no—
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×C23AGL(1,ℤ/8)12yes—
279C2×C4×C23C2×#4111yescharacteristic
280C2×C4×C23C2×#4111yescharacteristic
281C2×C4×C23C2×#4111yescharacteristic
282C2×C4×C23C2×#4111yescharacteristic
283C2×C4×C23H(5,𝔽2)11yescharacteristic
284C2×C4×C23H(5,𝔽2)11yescharacteristic
285C8×C23—41no—
286C8×C23—41no—
287C8×C23—41no—
288C8×C23—41no—
289#2491C2×C2311yescharacteristic
290#2362C2×C2311yescharacteristic, complemented
291#2055C2×C2311yescharacteristic, complemented
292#2036C2×C2311yescharacteristic, complemented
293#2024C2×C2311yescharacteristic, complemented
294#2000C2×C2311yescharacteristic
295#1988C2×C2311yescharacteristic, complemented
296#1936C2×C2311yescharacteristic, complemented
297#1925C2×C2311yescharacteristic, complemented
298#1924C2×C2311yescharacteristic, complemented
299#1921C2×C2311yescharacteristic, complemented
300#1880C2×C2311yescharacteristic, complemented
301#1875C2×C2311yescharacteristic
302#1825C2×C2311yescharacteristic, complemented
303#1763C2×C2311yescharacteristic, complemented
304C22×C23—41no—
305C22×C23—41no—
306C22×C23—41no—
307C22×C23—41no—
308C22×C23—41no—
309C22×C23—41no—
310C22×C23—41no—
311C22×C23—81no—
312C22×C23—81no—
313C22×C23—81no—
314C22×C23—81no—
315C22×C23—81no—
316C22×C23—81no—
317C22×C23—81no—
318C22×C23#52511yescharacteristic
319C22×C23#54611yescharacteristic
320C22×C23#54611yescharacteristic
321C22×C23C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C23#57511yescharacteristic
323C22×C23#57711yescharacteristic
324C22×C23#57811yescharacteristic
325C4×C23—22no—
326C4×C23—41no—
327C4×C23—42no—
328C4×C23—42no—
329C4×C23—41no—
330C4×C23—42no—
331C4×C23—42no—
332C4×C23—41no—
333C4×C23—41no—
334C4×C23—81no—
335C4×C23—81no—
336C4×C23—81no—
337C4×C23#52911yescharacteristic
338C4×C23#53811yescharacteristic
339C4×C23#55511yescharacteristic
340C4×C23#55911yescharacteristic
341C22×SD16C22×C2311yescharacteristic
342C2×C4⋊Q8C22×C2311yescharacteristic
343C2×#124—21no—
344C2×C22⋊Q8C22×C2311yescharacteristic
345C2×#121C22×C2311yescharacteristic
346C2×C4×Q8C22×C2311yescharacteristic
347C2×#117C22×C2311yescharacteristic
348C2×#107C22×C2311yescharacteristic
349C2×C4⋊C8C22×C2311yescharacteristic
350C2×#103C22×C2311yescharacteristic
351C2×#103C22×C2311yescharacteristic
352C2×#103C22×C2311yescharacteristic
353C2×#102C22×C2311yescharacteristic
354C2×#102C22×C2311yescharacteristic
355C2×#102C22×C2311yescharacteristic
356C2×C22⋊C8C22×C2311yescharacteristic
357C2×C22⋊C8C22×C2311yescharacteristic
358C2×#97C22×C2311yescharacteristic
359#394—21no—
360#393—21no—
361#391C22×C2311yescharacteristic
362#390C22×C2311yescharacteristic
363#390C22×C2311yescharacteristic
364#389C22×C2311yescharacteristic
365#388—21no—
366#388—21no—
367#388—21no—
368#387—21no—
369#380C22×C2311yescharacteristic
370C4×C4⋊C4—21no—
371C4×C4⋊C4C22×C2311yescharacteristic
372C4×C4⋊C4C22×C2311yescharacteristic
373C4×C22⋊C4C22×C2311yescharacteristic
374#340C22×C2311yescharacteristic
375#340C22×C2311yescharacteristic
376#340C22×C2311yescharacteristic
377#340C22×C2311yescharacteristic
378#340C22×C2311yescharacteristic
379#340C22×C2311yescharacteristic
380#340C22×C2311yescharacteristic
381#340C22×C2311yescharacteristic
382#336C22×C2311yescharacteristic
383#336C22×C2311yescharacteristic
384C2×C23—81no—
385C2×C23—161no—
386C2×C23#245911yescharacteristic
387C2×C23#311511yescharacteristic
388C2×C23#312111yescharacteristic
389C2×C23#331011yescharacteristic
390C2×C23#331311yescharacteristic
391C2×C23#332111yescharacteristic
392C2×C23#333011yescharacteristic
393C22×Q8—21no—
394C22×Q8C23×C2311yescharacteristic
395C22×D4—21no—
396C22×D4C23×C2311yescharacteristic
397C23×C4C23×C2311yescharacteristic
398C2×SD16—22no—
399C2×SD16—41no—
400C2×SD16—41no—
401C22×C8C23×C2311yescharacteristic
402C22×C8C23×C2311yescharacteristic
403C22×C8C23×C2311yescharacteristic
404C22×C8C23×C2311yescharacteristic
405C4⋊Q8—22no—
406C4⋊Q8—41no—
407#124—44no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410#121—22no—
411#121—41no—
412C4×Q8—22no—
413C4×Q8—41no—
414#117—22no—
415#117—41no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4C23×C2311yescharacteristic
421C2×C4⋊C4C23×C2311yescharacteristic
422C2×C4⋊C4C23×C2311yescharacteristic
423C2×C4⋊C4C23×C2311yescharacteristic
424C2×C4⋊C4C23×C2311yescharacteristic
425C2×C4⋊C4C23×C2311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4D4×C2311yescharacteristic
435C2×C22⋊C4D4×C2311yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42C23×C2311yescharacteristic
441C2×C42C23×C2311yescharacteristic
442#107—22no—
443C4⋊C8—41no—
444#103—22no—
445#103—22no—
446#103—41no—
447#102—22no—
448#102—22no—
449#102—41no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452#97—41no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95D4×C2311yescharacteristic
460#95D4×C2311yescharacteristic
461C23#2674811yescharacteristic, direct product factor, Sylow
462C24—21no—
463C24C2×D4×C2311yescharacteristic
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8#41×C2312yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—81no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4C2×D4×C2311yescharacteristic
496C22×C4C2×D4×C2311yescharacteristic
497C22×C4C2×D4×C2311yescharacteristic
498C22×C4C2×D4×C2311yescharacteristic
499C22×C4C2×D4×C2311yescharacteristic
500C22×C4C24×C2311yescharacteristic
501SD16—44no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C4⋊C4—24no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4#41×C2312yes—
528C4⋊C4#41×C2312yes—
529C4⋊C4#41×C2312yes—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—41no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—42no—
546C42—42no—
547C42—42no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23C22×D4×C2311yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—84no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—84no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4C23×AGL(1,ℤ/8)12yes—
613C2×C4C2×#41×C2311yescharacteristic
614C2×C4C2×#41×C2311yescharacteristic
615C2×C4C2×#41×C2311yescharacteristic
616C2×C4C2×#41×C2311yescharacteristic
617C2×C4C23×H(5,𝔽2)11yescharacteristic
618C2×C4C23×H(5,𝔽2)11yescharacteristic
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C23×#52511yescharacteristic
638C22C23×#54611yescharacteristic
639C22C23×#54611yescharacteristic
640C22C2×C23×AGL(1,ℤ/8)11yescharacteristic
641C22C23×#57511yescharacteristic
642C22C23×#57711yescharacteristic
643C22C23×#57811yescharacteristic
644C4—22no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4C23×#52911yescharacteristic
657C4C23×#53811yescharacteristic
658C4C23×#55511yescharacteristic
659C4C23×#55911yescharacteristic
660C2—81no—
661C2—161no—
662C2C23×#245911yescharacteristic
663C2C23×#311511yescharacteristic
664C2C23×#312111yescharacteristic
665C2C23×#331011yescharacteristic
666C2C23×#331311yescharacteristic
667C2C23×#332111yescharacteristic
668C2C23×#333011yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC2×C23×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C4×C22⋊C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2362C2semidirect
3. C23×#2055C2semidirect
4. C23×#2036C2semidirect
5. C23×#2024C2semidirect
7. C23×#1988C2semidirect
8. C23×#1936C2semidirect
9. C23×#1925C2semidirect
10. C23×#1924C2semidirect
11. C23×#1921C2semidirect
12. C23×#1880C2semidirect
14. C23×#1825C2semidirect
15. C23×#1763C2semidirect
213. #26748C23direct (N × H)
290. #2362C2×C23semidirect
291. #2055C2×C23semidirect
292. #2036C2×C23semidirect
293. #2024C2×C23semidirect
295. #1988C2×C23semidirect
296. #1936C2×C23semidirect
297. #1925C2×C23semidirect
298. #1924C2×C23semidirect
299. #1921C2×C23semidirect
300. #1880C2×C23semidirect
302. #1825C2×C23semidirect
303. #1763C2×C23semidirect
461. C23#26748direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#24912
C23×#23622
C23×#20552
C23×#20362
C23×#20242
C23×#20002
C23×#19882
C23×#19362
C23×#19252
C23×#19242
C23×#19212
C23×#18802
C23×#18752
C23×#18252
C23×#17632
#2674823