Finite Group Databasebeta

← C23×#27071 #19174697

Subgroups — C23×#27071 #19174697

Order 5888.

802 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2512C211yesmaximal, characteristic, complemented
2C23×#2367C211yesmaximal, characteristic, complemented
3C23×#2094C211yesmaximal, characteristic, complemented
4C23×#2054C211yesmaximal, characteristic
5C23×#2042C211yesmaximal, characteristic, complemented
6C23×#2012C211yesmaximal, characteristic
7C23×#1968C211yesmaximal, characteristic, complemented
8C23×#1927C211yesmaximal, characteristic, complemented
9C23×#1926C211yesmaximal, characteristic, complemented
10C23×#1920C211yesmaximal, characteristic, complemented
11C23×#1916C211yesmaximal, characteristic, complemented
12C23×#1880C211yesmaximal, characteristic, complemented
13C23×#1879C211yesmaximal, characteristic
14C23×#1803C211yesmaximal, characteristic, complemented
15C4×C23×#102C211yesmaximal, characteristic, complemented
16C22×SD16×C23C2211yescharacteristic
17C22×D8×C23C2211yescharacteristic
18C2×C23×#126—21no—
19C2×C23×#124C2211yescharacteristic
20C2×C4×Q8×C23C2211yescharacteristic
21C2×C4×D4×C23C2211yescharacteristic
22C2×C23×#106C2211yescharacteristic
23C2×C23×#106C2211yescharacteristic
24C2×C23×C4⋊C8C2211yescharacteristic
25C2×C23×#103C2211yescharacteristic
26C2×C23×#103C2211yescharacteristic
27C2×C23×#103C2211yescharacteristic
28C2×C23×#102C2211yescharacteristic
29C2×C23×#102C2211yescharacteristic
30C2×C23×#102C2211yescharacteristic
31C2×C23×#102C2211yescharacteristic
32C2×C23×#102C2211yescharacteristic
33C2×C4×C8×C23C2211yescharacteristic
34C23×#397—21no—
35C23×#396—21no—
36C23×#391C2211yescharacteristic
37C23×#390C2211yescharacteristic
38C23×#390C2211yescharacteristic
39C23×#390C2211yescharacteristic
40C23×#390C2211yescharacteristic
41C23×#389C2211yescharacteristic
42C23×#388—21no—
43C23×#388—21no—
44C23×#388—21no—
45C23×#385—21no—
46C23×#384C2211yescharacteristic
47C4×C4⋊C4×C23C2211yescharacteristic
48C4×C4⋊C4×C23C2211yescharacteristic
49C4×C4⋊C4×C23C2211yescharacteristic
50C4×C22⋊C4×C23—21no—
51C23×#340C2211yescharacteristic
52C23×#340C2211yescharacteristic
53C23×#340C2211yescharacteristic
54C23×#340C2211yescharacteristic
55C23×#336C2211yescharacteristic
56C23×#336C2211yescharacteristic
57C23×#336C2211yescharacteristic
58C23×#336C2211yescharacteristic
59C22×Q8×C23C2311yescharacteristic
60C22×D4×C23C2311yescharacteristic
61C22×D4×C23C2311yescharacteristic
62C23×C4×C23—21no—
63C2×SD16×C23—22no—
64C2×SD16×C23—22no—
65C2×SD16×C23—41no—
66C2×D8×C23—22no—
67C2×D8×C23—41no—
68C2×D8×C23—41no—
69C22×C8×C23C2311yescharacteristic
70C22×C8×C23C2311yescharacteristic
71C22×C8×C23C2311yescharacteristic
72C22×C8×C23C2311yescharacteristic
73C23×#126—44no—
74C23×#124—22no—
75C23×#124—22no—
76C4×Q8×C23—22no—
77C4×Q8×C23—41no—
78C4×D4×C23—22no—
79C4×D4×C23—41no—
80C2×C4⋊C4×C23—21no—
81C2×C4⋊C4×C23—21no—
82C2×C4⋊C4×C23—21no—
83C2×C4⋊C4×C23—21no—
84C2×C4⋊C4×C23D411yescharacteristic
85C2×C4⋊C4×C23D411yescharacteristic
86C2×C4⋊C4×C23C2311yescharacteristic
87C2×C4⋊C4×C23C2311yescharacteristic
88C2×C4⋊C4×C23C2311yescharacteristic
89C2×C4⋊C4×C23C2311yescharacteristic
90C2×C4⋊C4×C23C2311yescharacteristic
91C2×C22⋊C4×C23—21no—
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×C23—21no—
101C2×C22⋊C4×C23—21no—
102C2×C42×C23—21no—
103C2×C42×C23—21no—
104C2×C42×C23—21no—
105C2×C42×C23C2311yescharacteristic
106C2×C42×C23C2311yescharacteristic
107C2×C42×C23C2311yescharacteristic
108C23×#106—22no—
109C23×#106—41no—
110C23×C4⋊C8—41no—
111C23×#103—22no—
112C23×#103—41no—
113C23×#103—41no—
114C23×#102—22no—
115C23×#102—22no—
116C23×#102—22no—
117C23×#102—41no—
118C23×#102—41no—
119C4×C8×C23—41no—
120C23×#95—21no—
121C23×#95—21no—
122C23×#95—21no—
123C23×#95—21no—
124C23×#95—21no—
125C23×#95D411yescharacteristic
126C23×#95D411yescharacteristic
127C24×C23—21no—
128C24×C23—21no—
129C2×Q8×C23—21no—
130C2×Q8×C23—21no—
131C2×Q8×C23—21no—
132C2×Q8×C23—21no—
133C2×Q8×C23—21no—
134C2×Q8×C23#4112yes—
135C2×D4×C23—21no—
136C2×D4×C23—21no—
137C2×D4×C23—21no—
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—21no—
145C2×D4×C23—21no—
146C2×D4×C23#4112yes—
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—42no—
154C22×C4×C23—42no—
155C22×C4×C23—81no—
156C22×C4×C23C2×D411yescharacteristic
157C22×C4×C23C2×D411yescharacteristic
158C22×C4×C23C2×D411yescharacteristic
159C22×C4×C23C2×D411yescharacteristic
160C22×C4×C23C2×D411yescharacteristic
161C22×C4×C23C2×D411yescharacteristic
162C22×C4×C23C2411yescharacteristic
163SD16×C23—44no—
164D8×C23—44no—
165C2×C8×C23—21no—
166C2×C8×C23—21no—
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#4112yes—
177C4⋊C4×C23—22no—
178C4⋊C4×C23—22no—
179C4⋊C4×C23—21no—
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—42no—
189C4⋊C4×C23—42no—
190C4⋊C4×C23—42no—
191C4⋊C4×C23—81no—
192C4⋊C4×C23#4112yes—
193C22⋊C4×C23—24no—
194C22⋊C4×C23—24no—
195C22⋊C4×C23—42no—
196C22⋊C4×C23—42no—
197C22⋊C4×C23—42no—
198C22⋊C4×C23—42no—
199C22⋊C4×C23—42no—
200C22⋊C4×C23—42no—
201C22⋊C4×C23—81no—
202C22⋊C4×C23—81no—
203C22⋊C4×C23—81no—
204C42×C23—21no—
205C42×C23—21no—
206C42×C23—21no—
207C42×C23—21no—
208C42×C23—21no—
209C42×C23—21no—
210C42×C23—42no—
211C42×C23—42no—
212C42×C23—81no—
213#27071C2311yesmaximal, characteristic, direct product factor, Sylow
214C23×C23—22no—
215C23×C23—41no—
216C23×C23—41no—
217C23×C23—41no—
218C23×C23—41no—
219C23×C23—41no—
220C23×C23—41no—
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—
233D4×C23—22no—
234D4×C23—22no—
235D4×C23—41no—
236D4×C23—41no—
237D4×C23—41no—
238D4×C23—41no—
239D4×C23—41no—
240D4×C23—41no—
241C2×C4×C23—21no—
242C2×C4×C23—21no—
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—21no—
258C2×C4×C23—21no—
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—84no—
276C2×C4×C23#13512yes—
277C2×C4×C23AGL(1,ℤ/8)12yes—
278C2×C4×C23C2×#4111yescharacteristic
279C2×C4×C23C2×#4111yescharacteristic
280C2×C4×C23C2×#4111yescharacteristic
281C2×C4×C23C2×#4111yescharacteristic
282C2×C4×C23H(5,𝔽2)11yescharacteristic
283C2×C4×C23H(5,𝔽2)11yescharacteristic
284C8×C23—22no—
285C8×C23—41no—
286C8×C23—41no—
287C8×C23—41no—
288#2512C2×C2311yescharacteristic, complemented
289#2367C2×C2311yescharacteristic, complemented
290#2094C2×C2311yescharacteristic, complemented
291#2054C2×C2311yescharacteristic
292#2042C2×C2311yescharacteristic, complemented
293#2012C2×C2311yescharacteristic
294#1968C2×C2311yescharacteristic, complemented
295#1927C2×C2311yescharacteristic, complemented
296#1926C2×C2311yescharacteristic, complemented
297#1920C2×C2311yescharacteristic, complemented
298#1916C2×C2311yescharacteristic, complemented
299#1880C2×C2311yescharacteristic, complemented
300#1879C2×C2311yescharacteristic
301#1803C2×C2311yescharacteristic, complemented
302C4×#102C2×C2311yescharacteristic, complemented
303C22×C23—42no—
304C22×C23—42no—
305C22×C23—42no—
306C22×C23—81no—
307C22×C23—81no—
308C22×C23—81no—
309C22×C23—81no—
310C22×C23—81no—
311C22×C23—81no—
312C22×C23—81no—
313C22×C23—81no—
314C22×C23—81no—
315C22×C23—81no—
316C22×C23—81no—
317C22×C23#52511yescharacteristic
318C22×C23#54611yescharacteristic
319C22×C23#55011yescharacteristic
320C22×C23C2×#13511yescharacteristic
321C22×C23C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C23#57711yescharacteristic
323C22×C23#57711yescharacteristic
324C4×C23—22no—
325C4×C23—22no—
326C4×C23—41no—
327C4×C23—41no—
328C4×C23—42no—
329C4×C23—41no—
330C4×C23—41no—
331C4×C23—42no—
332C4×C23—81no—
333C4×C23—81no—
334C4×C23—81no—
335C4×C23—81no—
336C4×C23#52911yescharacteristic
337C4×C23#53811yescharacteristic
338C4×C23#55111yescharacteristic
339C4×C23#55311yescharacteristic
340C22×SD16C22×C2311yescharacteristic
341C22×D8C22×C2311yescharacteristic
342C2×#126—21no—
343C2×#124C22×C2311yescharacteristic
344C2×C4×Q8C22×C2311yescharacteristic
345C2×C4×D4C22×C2311yescharacteristic
346C2×#106C22×C2311yescharacteristic
347C2×#106C22×C2311yescharacteristic
348C2×C4⋊C8C22×C2311yescharacteristic
349C2×#103C22×C2311yescharacteristic
350C2×#103C22×C2311yescharacteristic
351C2×#103C22×C2311yescharacteristic
352C2×#102C22×C2311yescharacteristic
353C2×#102C22×C2311yescharacteristic
354C2×#102C22×C2311yescharacteristic
355C2×#102C22×C2311yescharacteristic
356C2×#102C22×C2311yescharacteristic
357C2×C4×C8C22×C2311yescharacteristic
358#397—21no—
359#396—21no—
360#391C22×C2311yescharacteristic
361#390C22×C2311yescharacteristic
362#390C22×C2311yescharacteristic
363#390C22×C2311yescharacteristic
364#390C22×C2311yescharacteristic
365#389C22×C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#385—21no—
370#384C22×C2311yescharacteristic
371C4×C4⋊C4C22×C2311yescharacteristic
372C4×C4⋊C4C22×C2311yescharacteristic
373C4×C4⋊C4C22×C2311yescharacteristic
374C4×C22⋊C4—21no—
375#340C22×C2311yescharacteristic
376#340C22×C2311yescharacteristic
377#340C22×C2311yescharacteristic
378#340C22×C2311yescharacteristic
379#336C22×C2311yescharacteristic
380#336C22×C2311yescharacteristic
381#336C22×C2311yescharacteristic
382#336C22×C2311yescharacteristic
383C2×C23—82no—
384C2×C23—161no—
385C2×C23#246711yescharacteristic
386C2×C23#310611yescharacteristic
387C2×C23#312511yescharacteristic
388C2×C23#330111yescharacteristic
389C2×C23#330611yescharacteristic
390C2×C23#339411yescharacteristic
391C2×C23#339711yescharacteristic
392C22×Q8C23×C2311yescharacteristic
393C22×D4C23×C2311yescharacteristic
394C22×D4C23×C2311yescharacteristic
395C23×C4—21no—
396C2×SD16—22no—
397C2×SD16—22no—
398C2×SD16—41no—
399C2×D8—22no—
400C2×D8—41no—
401C2×D8—41no—
402C22×C8C23×C2311yescharacteristic
403C22×C8C23×C2311yescharacteristic
404C22×C8C23×C2311yescharacteristic
405C22×C8C23×C2311yescharacteristic
406#126—44no—
407#124—22no—
408#124—22no—
409C4×Q8—22no—
410C4×Q8—41no—
411C4×D4—22no—
412C4×D4—41no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4D4×C2311yescharacteristic
418C2×C4⋊C4D4×C2311yescharacteristic
419C2×C4⋊C4C23×C2311yescharacteristic
420C2×C4⋊C4C23×C2311yescharacteristic
421C2×C4⋊C4C23×C2311yescharacteristic
422C2×C4⋊C4C23×C2311yescharacteristic
423C2×C4⋊C4C23×C2311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
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⋊C4—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C2311yescharacteristic
439C2×C42C23×C2311yescharacteristic
440C2×C42C23×C2311yescharacteristic
441#106—22no—
442#106—41no—
443C4⋊C8—41no—
444#103—22no—
445#103—41no—
446#103—41no—
447#102—22no—
448#102—22no—
449#102—22no—
450#102—41no—
451#102—41no—
452C4×C8—41no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95D4×C2311yescharacteristic
459#95D4×C2311yescharacteristic
460C23#2707111yescharacteristic, direct product factor, Sylow
461C24—21no—
462C24—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8#41×C2312yes—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4#41×C2312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—81no—
490C22×C4C2×D4×C2311yescharacteristic
491C22×C4C2×D4×C2311yescharacteristic
492C22×C4C2×D4×C2311yescharacteristic
493C22×C4C2×D4×C2311yescharacteristic
494C22×C4C2×D4×C2311yescharacteristic
495C22×C4C2×D4×C2311yescharacteristic
496C22×C4C24×C2311yescharacteristic
497SD16—44no—
498D8—44no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
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#41×C2312yes—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—81no—
526C4⋊C4#41×C2312yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—81no—
536C22⋊C4—81no—
537C22⋊C4—81no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—42no—
546C42—81no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×D4×C2311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
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—84no—
609C2×C4C23×#13512yes—
610C2×C4C23×AGL(1,ℤ/8)12yes—
611C2×C4C2×#41×C2311yescharacteristic
612C2×C4C2×#41×C2311yescharacteristic
613C2×C4C2×#41×C2311yescharacteristic
614C2×C4C2×#41×C2311yescharacteristic
615C2×C4C23×H(5,𝔽2)11yescharacteristic
616C2×C4C23×H(5,𝔽2)11yescharacteristic
617C8—22no—
618C8—41no—
619C8—41no—
620C8—41no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22C23×#52511yescharacteristic
636C22C23×#54611yescharacteristic
637C22C23×#55011yescharacteristic
638C22C2×C23×#13511yescharacteristic
639C22C2×C23×AGL(1,ℤ/8)11yescharacteristic
640C22C23×#57711yescharacteristic
641C22C23×#57711yescharacteristic
642C4—22no—
643C4—22no—
644C4—42no—
645C4—41no—
646C4—41no—
647C4—42no—
648C4—41no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4C23×#52911yescharacteristic
655C4C23×#53811yescharacteristic
656C4C23×#55111yescharacteristic
657C4C23×#55311yescharacteristic
658C2—82no—
659C2—161no—
660C2C23×#246711yescharacteristic
661C2C23×#310611yescharacteristic
662C2C23×#312511yescharacteristic
663C2C23×#330111yescharacteristic
664C2C23×#330611yescharacteristic
665C2C23×#339411yescharacteristic
666C2C23×#339711yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC22×D8×C23C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C4×C4⋊C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#2512C2semidirect
2. C23×#2367C2semidirect
3. C23×#2094C2semidirect
5. C23×#2042C2semidirect
7. C23×#1968C2semidirect
8. C23×#1927C2semidirect
9. C23×#1926C2semidirect
10. C23×#1920C2semidirect
11. C23×#1916C2semidirect
12. C23×#1880C2semidirect
14. C23×#1803C2semidirect
15. C4×C23×#102C2semidirect
213. #27071C23direct (N × H)
288. #2512C2×C23semidirect
289. #2367C2×C23semidirect
290. #2094C2×C23semidirect
292. #2042C2×C23semidirect
294. #1968C2×C23semidirect
295. #1927C2×C23semidirect
296. #1926C2×C23semidirect
297. #1920C2×C23semidirect
298. #1916C2×C23semidirect
299. #1880C2×C23semidirect
301. #1803C2×C23semidirect
302. C4×#102C2×C23semidirect
460. C23#27071direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#25122
C23×#23672
C23×#20942
C23×#20542
C23×#20422
C23×#20122
C23×#19682
C23×#19272
C23×#19262
C23×#19202
C23×#19162
C23×#18802
C23×#18792
C23×#18032
C4×C23×#1022
#2707123