Finite Group Databasebeta

← C23×#14265 #19161891

Subgroups — C23×#14265 #19161891

Order 5888.

1782 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
1C2×C23×#385C211yesmaximal, characteristic
2C2×C23×#385C211yesmaximal, characteristic
3C22×C23×#95C211yesmaximal, characteristic
4C23×#1445C212yesmaximal, complemented
5C23×#1443C212yesmaximal, complemented
6C23×#1442C212yesmaximal, complemented
7C23×#1441C212yesmaximal, complemented
8C23×C22⋊#95C211yesmaximal, characteristic
9C23×C22⋊#95C211yesmaximal, characteristic
10C23×C22⋊#95C211yesmaximal, characteristic
11C23×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C23C2211yescharacteristic
13C24×C4×C23C2211yescharacteristic
14C24×C4×C23C2211yescharacteristic
15C22×C4⋊C4×C23C2211yescharacteristic
16C22×C4⋊C4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2212yes—
18C22×C22⋊C4×C23C2211yescharacteristic
19C22×C22⋊C4×C23C2211yescharacteristic
20C22×C22⋊C4×C23C2211yescharacteristic
21C22×C22⋊C4×C23C2211yescharacteristic
22C23×#385—24no—
23C23×#385C418yescomplemented
24C2×C23×#95—24no—
25C2×C23×#95C2212yes—
26C2×C23×#95C2212yes—
27C2×C23×#95C2211yescharacteristic
28C2×C23×#95C2211yescharacteristic
29C2×C23×#95C2212yes—
30C2×C23×#95C2212yes—
31C2×C23×#95C2212yes—
32C2×C23×#95C2212yes—
33C2×C23×#95C2212yes—
34C2×C23×#95C2212yes—
35C2×C23×#95C2212yes—
36C2×C23×#95C2212yes—
37C2×C23×#95C2212yes—
38C25×C23C2311yescharacteristic
39C23×C4×C23—22no—
40C23×C4×C23—22no—
41C23×C4×C23—22no—
42C23×C4×C23—22no—
43C23×C4×C23—22no—
44C23×C4×C23—22no—
45C23×C4×C23—42no—
46C23×C4×C23—42no—
47C23×C4×C23—42no—
48C23×C4×C23—42no—
49C23×C4×C23—42no—
50C23×C4×C23—42no—
51C23×C4×C23C2×C414yes—
52C23×C4×C23D414yes—
53C23×C4×C23Q814yes—
54C23×C4×C23C2311yescharacteristic
55C23×C4×C23C2312yes—
56C23×C4×C23C2311yescharacteristic
57C23×C4×C23C2312yes—
58C23×C4×C23C2311yescharacteristic
59C23×C4×C23C2312yes—
60C23×C4×C23C2311yescharacteristic
61C23×C4×C23C2311yescharacteristic
62C23×C4×C23C2311yescharacteristic
63C23×C4×C23C2312yes—
64C2×C4⋊C4×C23—22no—
65C2×C4⋊C4×C23—22no—
66C2×C4⋊C4×C23—42no—
67C2×C4⋊C4×C23—42no—
68C2×C4⋊C4×C23—42no—
69C2×C4⋊C4×C23—42no—
70C2×C4⋊C4×C23C2×C418yescomplemented
71C2×C22⋊C4×C23—22no—
72C2×C22⋊C4×C23—22no—
73C2×C22⋊C4×C23—22no—
74C2×C22⋊C4×C23—22no—
75C2×C22⋊C4×C23—22no—
76C2×C22⋊C4×C23—22no—
77C2×C22⋊C4×C23—22no—
78C2×C22⋊C4×C23—22no—
79C2×C22⋊C4×C23—22no—
80C2×C22⋊C4×C23—22no—
81C2×C22⋊C4×C23C2×C414yes—
82C2×C22⋊C4×C23C2×C414yes—
83C23×#95—24no—
84C23×#95—24no—
85C23×#95—22no—
86C23×#95—22no—
87C23×#95—42no—
88C23×#95—42no—
89C23×#95—42no—
90C23×#95—42no—
91C23×#95—42no—
92C23×#95—42no—
93C23×#95—42no—
94C23×#95—42no—
95C23×#95C2×C418yescomplemented
96C24×C23—22no—
97C24×C23—22no—
98C24×C23—22no—
99C24×C23—22no—
100C24×C23C22×C412yes—
101C24×C23C2×D412yes—
102C24×C23C2×Q812yes—
103C24×C23#4112yes—
104C24×C23#4112yes—
105C24×C23#4112yes—
106C24×C23#4112yes—
107C24×C23C2411yescharacteristic
108C22×C4×C23—28no—
109C22×C4×C23—28no—
110C22×C4×C23—28no—
111C22×C4×C23—21no—
112C22×C4×C23—21no—
113C22×C4×C23—22no—
114C22×C4×C23—22no—
115C22×C4×C23—22no—
116C22×C4×C23—22no—
117C22×C4×C23—21no—
118C22×C4×C23—21no—
119C22×C4×C23—22no—
120C22×C4×C23—22no—
121C22×C4×C23—21no—
122C22×C4×C23—21no—
123C22×C4×C23—21no—
124C22×C4×C23—21no—
125C22×C4×C23—22no—
126C22×C4×C23—22no—
127C22×C4×C23—22no—
128C22×C4×C23—22no—
129C22×C4×C23—22no—
130C22×C4×C23—22no—
131C22×C4×C23—22no—
132C22×C4×C23—22no—
133C22×C4×C23—22no—
134C22×C4×C23—22no—
135C22×C4×C23—22no—
136C22×C4×C23—22no—
137C22×C4×C23—22no—
138C22×C4×C23—22no—
139C22×C4×C23—22no—
140C22×C4×C23—22no—
141C22×C4×C23—22no—
142C22×C4×C23—22no—
143C22×C4×C23—22no—
144C22×C4×C23—22no—
145C22×C4×C23—21no—
146C22×C4×C23—21no—
147C22×C4×C23—21no—
148C22×C4×C23—21no—
149C22×C4×C23—21no—
150C22×C4×C23—21no—
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—22no—
159C22×C4×C23—22no—
160C22×C4×C23—22no—
161C22×C4×C23—22no—
162C22×C4×C23—48no—
163C22×C4×C23—44no—
164C22×C4×C23—44no—
165C22×C4×C23—48no—
166C22×C4×C23—44no—
167C22×C4×C23—44no—
168C22×C4×C23—44no—
169C22×C4×C23—44no—
170C22×C4×C23—48no—
171C22×C4×C23—48no—
172C22×C4×C23—48no—
173C22×C4×C23—48no—
174C22×C4×C23C22×C412yes—
175C22×C4×C23C22×C414yes—
176C22×C4×C23C22×C412yes—
177C22×C4×C23C22×C414yes—
178C22×C4×C23C2×D412yes—
179C22×C4×C23C2×D412yes—
180C22×C4×C23C2×Q814yes—
181C4⋊C4×C23—48no—
182C4⋊C4×C23—44no—
183C4⋊C4×C23—44no—
184C22⋊C4×C23—28no—
185C22⋊C4×C23—28no—
186C22⋊C4×C23—44no—
187C22⋊C4×C23—44no—
188#14265C2311yesmaximal, characteristic, direct product factor, Sylow
189C23×C23—24no—
190C23×C23—24no—
191C23×C23—22no—
192C23×C23—22no—
193C23×C23—22no—
194C23×C23—22no—
195C23×C23—24no—
196C23×C23—24no—
197C23×C23—24no—
198C23×C23—24no—
199C23×C23—24no—
200C23×C23—24no—
201C23×C23—24no—
202C23×C23—24no—
203C23×C23—24no—
204C23×C23—24no—
205C23×C23#11714yes—
206C23×C23C4×D414yes—
207C23×C23C4×Q814yes—
208C23×C23C22⋊Q814yes—
209C23×C23#12314yes—
210C23×C23#12514yes—
211C23×C23#12614yes—
212C23×C23C23×C411yescharacteristic
213C23×C23C22×D411yescharacteristic
214C23×C23C22×Q811yescharacteristic
215C23×C23C2×#4111yescharacteristic
216C23×C23C2×#4111yescharacteristic
217C23×C23C2×#4111yescharacteristic
218C23×C23C2×#4111yescharacteristic
219C23×C23H(5,𝔽2)12yes—
220C23×C23H(5,𝔽2)12yes—
221C23×C23H(5,𝔽2)12yes—
222C23×C232−1+412yes—
223C2×C4×C23—24no—
224C2×C4×C23—22no—
225C2×C4×C23—22no—
226C2×C4×C23—24no—
227C2×C4×C23—24no—
228C2×C4×C23—24no—
229C2×C4×C23—24no—
230C2×C4×C23—24no—
231C2×C4×C23—24no—
232C2×C4×C23—24no—
233C2×C4×C23—24no—
234C2×C4×C23—22no—
235C2×C4×C23—22no—
236C2×C4×C23—22no—
237C2×C4×C23—22no—
238C2×C4×C23—22no—
239C2×C4×C23—22no—
240C2×C4×C23—24no—
241C2×C4×C23—24no—
242C2×C4×C23—416no—
243C2×C4×C23—416no—
244C2×C4×C23—416no—
245C2×C4×C23—41no—
246C2×C4×C23—41no—
247C2×C4×C23—42no—
248C2×C4×C23—42no—
249C2×C4×C23—41no—
250C2×C4×C23—42no—
251C2×C4×C23—42no—
252C2×C4×C23—41no—
253C2×C4×C23—42no—
254C2×C4×C23—42no—
255C2×C4×C23—42no—
256C2×C4×C23—42no—
257C2×C4×C23—42no—
258C2×C4×C23—42no—
259C2×C4×C23—42no—
260C2×C4×C23—42no—
261C2×C4×C23—42no—
262C2×C4×C23—42no—
263C2×C4×C23—42no—
264C2×C4×C23—42no—
265C2×C4×C23—42no—
266C2×C4×C23—42no—
267C2×C4×C23—41no—
268C2×C4×C23—41no—
269C2×C4×C23—42no—
270C2×C4×C23—41no—
271C2×C4×C23—41no—
272C2×C4×C23—41no—
273C2×C4×C23—41no—
274C2×C4×C23—42no—
275C2×C4×C23—42no—
276C2×C4×C23—42no—
277C2×C4×C23—42no—
278C2×C4×C23—42no—
279C2×C4×C23—42no—
280C2×C4×C23—42no—
281C2×C4×C23—42no—
282C2×C4×C23—42no—
283C2×C4×C23—42no—
284C2×#385C2×C2311yescharacteristic
285C2×#385C2×C2311yescharacteristic
286C22×#95C2×C2311yescharacteristic
287#1445C2×C2312yescomplemented
288#1443C2×C2312yescomplemented
289#1442C2×C2312yescomplemented
290#1441C2×C2312yescomplemented
291C22⋊#95C2×C2311yescharacteristic
292C22⋊#95C2×C2311yescharacteristic
293C22⋊#95C2×C2311yescharacteristic
294C22⋊#95C2×C2311yescharacteristic
295C22×C23—28no—
296C22×C23—24no—
297C22×C23—24no—
298C22×C23—28no—
299C22×C23—24no—
300C22×C23—24no—
301C22×C23—24no—
302C22×C23—24no—
303C22×C23—28no—
304C22×C23—28no—
305C22×C23#38718yes—
306C22×C23C2×#11711yescharacteristic
307C22×C23C2×C4×D411yescharacteristic
308C22×C23C2×C4×Q811yescharacteristic
309C22×C23#51812yes—
310C22×C23#52012yes—
311C22×C23C2×C22⋊Q811yescharacteristic
312C22×C23C2×#12311yescharacteristic
313C22×C23C2×#12511yescharacteristic
314C22×C23C2×#12611yescharacteristic
315C22×C23#53411yescharacteristic
316C22×C23#53411yescharacteristic
317C22×C23#53511yescharacteristic
318C22×C23#53611yescharacteristic
319C22×C23#53812yes—
320C22×C23#53812yes—
321C22×C23#53812yes—
322C22×C23#53812yes—
323C22×C23#53912yes—
324C22×C23#53912yes—
325C22×C23#53912yes—
326C22×C23#53912yes—
327C22×C23#54312yes—
328C22×C23#54412yes—
329C4×C23—44no—
330C4×C23—42no—
331C4×C23—44no—
332C4×C23—42no—
333C4×C23—42no—
334C4×C23—42no—
335C4×C23—44no—
336C4×C23—81no—
337C4×C23—81no—
338C4×C23—82no—
339C24×C4C22×C2311yescharacteristic
340C24×C4C22×C2311yescharacteristic
341C24×C4C22×C2311yescharacteristic
342C22×C4⋊C4C22×C2311yescharacteristic
343C22×C4⋊C4C22×C2311yescharacteristic
344C22×C4⋊C4C22×C2312yes—
345C22×C22⋊C4C22×C2311yescharacteristic
346C22×C22⋊C4C22×C2311yescharacteristic
347C22×C22⋊C4C22×C2311yescharacteristic
348C22×C22⋊C4C22×C2311yescharacteristic
349#385—24no—
350#385C4×C2318yescomplemented
351C2×#95—24no—
352C2×#95C22×C2312yes—
353C2×#95C22×C2312yes—
354C2×#95C22×C2311yescharacteristic
355C2×#95C22×C2311yescharacteristic
356C2×#95C22×C2312yes—
357C2×#95C22×C2312yes—
358C2×#95C22×C2312yes—
359C2×#95C22×C2312yes—
360C2×#95C22×C2312yes—
361C2×#95C22×C2312yes—
362C2×#95C22×C2312yes—
363C2×#95C22×C2312yes—
364C2×#95C22×C2312yes—
365C2×C23—28no—
366C2×C23C2×#38711yescharacteristic
367C2×C23#231812yes—
368C2×C23#232111yescharacteristic
369C2×C23#232211yescharacteristic
370C2×C23#232912yes—
371C2×C23#262211yescharacteristic
372C2×C23#262311yescharacteristic
373C2×C23#262611yescharacteristic
374C2×C23#262711yescharacteristic
375C2×C23#264312yes—
376C2×C23#264612yes—
377C25C23×C2311yescharacteristic
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4C2×C4×C2314yes—
391C23×C4D4×C2314yes—
392C23×C4Q8×C2314yes—
393C23×C4C23×C2311yescharacteristic
394C23×C4C23×C2311yescharacteristic
395C23×C4C23×C2312yes—
396C23×C4C23×C2311yescharacteristic
397C23×C4C23×C2311yescharacteristic
398C23×C4C23×C2312yes—
399C23×C4C23×C2312yes—
400C23×C4C23×C2311yescharacteristic
401C23×C4C23×C2311yescharacteristic
402C23×C4C23×C2312yes—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4C2×C4×C2318yescomplemented
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4C2×C4×C2314yes—
421C2×C22⋊C4C2×C4×C2314yes—
422#95—24no—
423#95—24no—
424#95—22no—
425#95—22no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95C2×C4×C2318yescomplemented
435C23#1426511yescharacteristic, direct product factor, Sylow
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24C22×C4×C2312yes—
441C24C2×D4×C2312yes—
442C24C2×Q8×C2312yes—
443C24#41×C2312yes—
444C24#41×C2312yes—
445C24#41×C2312yes—
446C24#41×C2312yes—
447C24C24×C2311yescharacteristic
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—48no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—48no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4C22×C4×C2312yes—
515C22×C4C22×C4×C2314yes—
516C22×C4C22×C4×C2314yes—
517C22×C4C22×C4×C2312yes—
518C22×C4C2×D4×C2312yes—
519C22×C4C2×D4×C2312yes—
520C22×C4C2×Q8×C2314yes—
521C4⋊C4—48no—
522C4⋊C4—44no—
523C4⋊C4—44no—
524C22⋊C4—28no—
525C22⋊C4—28no—
526C22⋊C4—44no—
527C22⋊C4—44no—
528C23—24no—
529C23—24no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23C23×#11714yes—
545C23C4×D4×C2314yes—
546C23C4×Q8×C2314yes—
547C23C23×C22⋊Q814yes—
548C23C23×#12314yes—
549C23C23×#12514yes—
550C23C23×#12614yes—
551C23C23×C4×C2311yescharacteristic
552C23C22×D4×C2311yescharacteristic
553C23C22×Q8×C2311yescharacteristic
554C23C2×#41×C2311yescharacteristic
555C23C2×#41×C2311yescharacteristic
556C23C2×#41×C2311yescharacteristic
557C23C2×#41×C2311yescharacteristic
558C23C23×H(5,𝔽2)12yes—
559C23C23×H(5,𝔽2)12yes—
560C23C23×H(5,𝔽2)12yes—
561C23C23×2−1+412yes—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—416no—
582C2×C4—416no—
583C2×C4—416no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C22—28no—
624C22—24no—
625C22—24no—
626C22—28no—
627C22—24no—
628C22—24no—
629C22—24no—
630C22—24no—
631C22—28no—
632C22—28no—
633C22C23×#38718yes—
634C22C2×C23×#11711yescharacteristic
635C22C2×C4×D4×C2311yescharacteristic
636C22C2×C4×Q8×C2311yescharacteristic
637C22C23×#51812yes—
638C22C23×#52012yes—
639C22C2×C23×C22⋊Q811yescharacteristic
640C22C2×C23×#12311yescharacteristic
641C22C2×C23×#12511yescharacteristic
642C22C2×C23×#12611yescharacteristic
643C22C23×#53411yescharacteristic
644C22C23×#53411yescharacteristic
645C22C23×#53511yescharacteristic
646C22C23×#53611yescharacteristic
647C22C23×#53812yes—
648C22C23×#53812yes—
649C22C23×#53812yes—
650C22C23×#53812yes—
651C22C23×#53912yes—
652C22C23×#53912yes—
653C22C23×#53912yes—
654C22C23×#53912yes—
655C22C23×#54312yes—
656C22C23×#54412yes—
657C4—44no—
658C4—44no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—42no—
663C4—44no—
664C4—81no—
665C4—81no—
666C4—82no—
667C2—28no—
668C2C2×C23×#38711yescharacteristic
669C2C23×#231812yes—
670C2C23×#232111yescharacteristic
671C2C23×#232211yescharacteristic
672C2C23×#232912yes—
673C2C23×#262211yescharacteristic
674C2C23×#262311yescharacteristic
675C2C23×#262611yescharacteristic
676C2C23×#262711yescharacteristic
677C2C23×#264312yes—
678C2C23×#264612yes—
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC25×C23C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
4. C23×#1445C2semidirect
5. C23×#1443C2semidirect
6. C23×#1442C2semidirect
7. C23×#1441C2semidirect
23. C23×#385C4semidirect
70. C2×C4⋊C4×C23C2×C4semidirect
95. C23×#95C2×C4semidirect
188. #14265C23direct (N × H)
287. #1445C2×C23semidirect
288. #1443C2×C23semidirect
289. #1442C2×C23semidirect
290. #1441C2×C23semidirect
350. #385C4×C23semidirect
409. C2×C4⋊C4C2×C4×C23semidirect
434. #95C2×C4×C23semidirect
435. C23#14265direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3852
C22×C23×#952
C23×#14452
C23×#14432
C23×#14422
C23×#14412
C23×C22⋊#952
#1426523