Finite Group Databasebeta

← C23×#29120 #19176746

Subgroups — C23×#29120 #19176746

Order 5888.

850 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2628C211yesmaximal, characteristic, complemented
2C23×#2311C211yesmaximal, characteristic
3C23×#2074C211yesmaximal, characteristic, complemented
4C23×#2073C211yesmaximal, characteristic, complemented
5C23×#2024C211yesmaximal, characteristic, complemented
6C23×#2023C211yesmaximal, characteristic, complemented
7C23×#1936C211yesmaximal, characteristic, complemented
8C23×#1935C211yesmaximal, characteristic, complemented
9C23×#1934C211yesmaximal, characteristic, complemented
10C23×#1933C211yesmaximal, characteristic, complemented
11C23×#1824C211yesmaximal, characteristic, complemented
12C23×#1823C211yesmaximal, characteristic, complemented
13C23×#1788C211yesmaximal, characteristic
14C23×#1788C211yesmaximal, characteristic
15C23×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C23C2211yescharacteristic
17C2×C23×C4⋊Q8C2211yescharacteristic
18C2×C23×#117C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C2×C23×#103C2211yescharacteristic
21C2×C23×#103C2211yescharacteristic
22C2×C23×#103C2211yescharacteristic
23C2×C23×#103C2211yescharacteristic
24C2×C23×#102C2211yescharacteristic
25C2×C23×#102C2211yescharacteristic
26C2×C23×#102C2211yescharacteristic
27C2×C23×#102C2211yescharacteristic
28C2×C23×C22⋊C8C2211yescharacteristic
29C2×C23×C22⋊C8C2211yescharacteristic
30C2×C23×#97C2211yescharacteristic
31C2×C4×C8×C23C2211yescharacteristic
32C23×#400—21no—
33C23×#399—21no—
34C23×#395—21no—
35C23×#393—21no—
36C23×#391C2211yescharacteristic
37C23×#391C2211yescharacteristic
38C23×#390C2211yescharacteristic
39C23×#390C2211yescharacteristic
40C23×#389C2211yescharacteristic
41C23×#389C2211yescharacteristic
42C23×#386—21no—
43C23×#386—21no—
44C23×#382C2211yescharacteristic
45C23×#380—21no—
46C23×#380—21no—
47C23×#380C2211yescharacteristic
48C23×#380C2211yescharacteristic
49C23×#340C2211yescharacteristic
50C23×#340C2211yescharacteristic
51C23×#340C2211yescharacteristic
52C23×#340C2211yescharacteristic
53C23×#340C2211yescharacteristic
54C23×#340C2211yescharacteristic
55C23×#340C2211yescharacteristic
56C23×#340C2211yescharacteristic
57C23×#336C2211yescharacteristic
58C23×#336C2211yescharacteristic
59C2×#41×C23—22no—
60C2×#41×C23—22no—
61C2×#41×C23—22no—
62C2×#41×C23—22no—
63C2×#41×C23—41no—
64C2×#41×C23—41no—
65C22×Q8×C23—21no—
66C22×Q8×C23C2311yescharacteristic
67C22×D4×C23—21no—
68C22×D4×C23C2311yescharacteristic
69C23×C4×C23—21no—
70C23×C4×C23—21no—
71C23×C4×C23C2311yescharacteristic
72C22×C8×C23C2311yescharacteristic
73C22×C8×C23C2311yescharacteristic
74C22×C8×C23C2311yescharacteristic
75C22×C8×C23C2311yescharacteristic
76C23×C4⋊Q8—41no—
77C23×C4⋊Q8—41no—
78C23×#117—41no—
79C23×#117—41no—
80C2×C4⋊C4×C23—22no—
81C2×C4⋊C4×C23—22no—
82C2×C4⋊C4×C23—21no—
83C2×C4⋊C4×C23—21no—
84C2×C4⋊C4×C23—21no—
85C2×C4⋊C4×C23—21no—
86C2×C4⋊C4×C23D411yescharacteristic
87C2×C4⋊C4×C23D411yescharacteristic
88C2×C4⋊C4×C23C2311yescharacteristic
89C2×C4⋊C4×C23C2311yescharacteristic
90C2×C4⋊C4×C23C2311yescharacteristic
91C2×C4⋊C4×C23C2311yescharacteristic
92C2×C4⋊C4×C23C2311yescharacteristic
93C2×C4⋊C4×C23C2311yescharacteristic
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×C23C2311yescharacteristic
103C2×C42×C23C2311yescharacteristic
104C23×#103—22no—
105C23×#103—22no—
106C23×#103—41no—
107C23×#103—41no—
108C23×#102—22no—
109C23×#102—22no—
110C23×#102—41no—
111C23×#102—41no—
112C23×C22⋊C8—22no—
113C23×C22⋊C8—22no—
114C23×#97—41no—
115C4×C8×C23—41no—
116C23×#95—21no—
117C23×#95—21no—
118C23×#95—21no—
119C23×#95—21no—
120C23×#95—21no—
121C23×#95—21no—
122C23×#95—21no—
123C23×#95—21no—
124C23×#95—21no—
125C23×#95—21no—
126C24×C23—21no—
127C24×C23C2×D411yescharacteristic
128#41×C23—44no—
129#41×C23—44no—
130#41×C23—44no—
131#41×C23—44no—
132C2×Q8×C23—21no—
133C2×Q8×C23—21no—
134C2×Q8×C23—21no—
135C2×Q8×C23—21no—
136C2×Q8×C23—21no—
137C2×Q8×C23—42no—
138C2×Q8×C23—81no—
139C2×Q8×C23—81no—
140C2×Q8×C23#4112yes—
141C2×D4×C23—24no—
142C2×D4×C23—21no—
143C2×D4×C23—21no—
144C2×D4×C23—21no—
145C2×D4×C23—21no—
146C2×D4×C23—21no—
147C2×D4×C23—42no—
148C2×D4×C23—42no—
149C2×D4×C23#4112yes—
150C22×C4×C23—21no—
151C22×C4×C23—21no—
152C22×C4×C23—21no—
153C22×C4×C23—21no—
154C22×C4×C23—24no—
155C22×C4×C23—21no—
156C22×C4×C23—21no—
157C22×C4×C23—21no—
158C22×C4×C23—21no—
159C22×C4×C23—21no—
160C22×C4×C23—21no—
161C22×C4×C23—21no—
162C22×C4×C23—42no—
163C22×C4×C23—42no—
164C22×C4×C23—42no—
165C22×C4×C23—81no—
166C22×C4×C23—81no—
167C22×C4×C23C2×D411yescharacteristic
168C22×C4×C23C2×D411yescharacteristic
169C22×C4×C23C2×D411yescharacteristic
170C22×C4×C23C2×D411yescharacteristic
171C22×C4×C23C2×D411yescharacteristic
172C22×C4×C23#4112yes—
173C22×C4×C23#4112yes—
174C22×C4×C23C2411yescharacteristic
175C2×C8×C23—21no—
176C2×C8×C23—21no—
177C2×C8×C23—21no—
178C2×C8×C23—21no—
179C2×C8×C23—21no—
180C2×C8×C23—21no—
181C2×C8×C23—21no—
182C2×C8×C23—21no—
183C2×C8×C23—21no—
184C2×C8×C23—21no—
185C2×C8×C23—21no—
186C2×C8×C23—21no—
187C4⋊C4×C23—21no—
188C4⋊C4×C23—21no—
189C4⋊C4×C23—21no—
190C4⋊C4×C23—21no—
191C4⋊C4×C23—21no—
192C4⋊C4×C23—21no—
193C4⋊C4×C23—21no—
194C4⋊C4×C23—21no—
195C4⋊C4×C23—21no—
196C4⋊C4×C23—21no—
197C4⋊C4×C23—21no—
198C4⋊C4×C23—21no—
199C4⋊C4×C23—41no—
200C4⋊C4×C23—41no—
201C4⋊C4×C23—42no—
202C4⋊C4×C23—42no—
203C4⋊C4×C23—81no—
204C4⋊C4×C23—81no—
205C22⋊C4×C23—41no—
206C22⋊C4×C23—41no—
207C22⋊C4×C23—81no—
208C22⋊C4×C23—81no—
209C22⋊C4×C23—81no—
210C22⋊C4×C23—81no—
211C22⋊C4×C23—81no—
212C22⋊C4×C23—81no—
213C42×C23—21no—
214C42×C23—21no—
215C42×C23—21no—
216C42×C23—21no—
217#29120C2311yesmaximal, characteristic, direct product factor, Sylow
218C23×C23—21no—
219C23×C23—21no—
220C23×C23—21no—
221C23×C23—21no—
222C23×C23—21no—
223C23×C23—21no—
224C23×C23—22no—
225C23×C23—41no—
226C23×C23—41no—
227C23×C23—41no—
228C23×C23—41no—
229C23×C23—41no—
230C23×C23—41no—
231C23×C23#12412yes—
232C23×C23C22×D411yescharacteristic
233Q8×C23—22no—
234Q8×C23—22no—
235Q8×C23—41no—
236Q8×C23—41no—
237Q8×C23—84no—
238D4×C23—22no—
239D4×C23—22no—
240D4×C23—48no—
241D4×C23—41no—
242D4×C23—41no—
243C2×C4×C23—21no—
244C2×C4×C23—21no—
245C2×C4×C23—22no—
246C2×C4×C23—22no—
247C2×C4×C23—22no—
248C2×C4×C23—22no—
249C2×C4×C23—22no—
250C2×C4×C23—21no—
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—21no—
260C2×C4×C23—21no—
261C2×C4×C23—21no—
262C2×C4×C23—48no—
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×C23—41no—
279C2×C4×C23—41no—
280C2×C4×C23—41no—
281C2×C4×C23—41no—
282C2×C4×C23—41no—
283C2×C4×C23—84no—
284C2×C4×C23#12412yes—
285C2×C4×C23C2×#4111yescharacteristic
286C2×C4×C23C2×#4111yescharacteristic
287C2×C4×C23C2×#4111yescharacteristic
288C2×C4×C23C2×#4111yescharacteristic
289C2×C4×C23H(5,𝔽2)11yescharacteristic
290C2×C4×C23H(5,𝔽2)11yescharacteristic
291C8×C23—41no—
292C8×C23—41no—
293C8×C23—41no—
294C8×C23—41no—
295#2628C2×C2311yescharacteristic, complemented
296#2311C2×C2311yescharacteristic
297#2074C2×C2311yescharacteristic, complemented
298#2073C2×C2311yescharacteristic, complemented
299#2024C2×C2311yescharacteristic, complemented
300#2023C2×C2311yescharacteristic, complemented
301#1936C2×C2311yescharacteristic, complemented
302#1935C2×C2311yescharacteristic, complemented
303#1934C2×C2311yescharacteristic, complemented
304#1933C2×C2311yescharacteristic, complemented
305#1824C2×C2311yescharacteristic, complemented
306#1823C2×C2311yescharacteristic, complemented
307#1788C2×C2311yescharacteristic
308#1788C2×C2311yescharacteristic
309#1750C2×C2311yescharacteristic, complemented
310C22×C23—22no—
311C22×C23—22no—
312C22×C23—22no—
313C22×C23—41no—
314C22×C23—41no—
315C22×C23—41no—
316C22×C23—41no—
317C22×C23—42no—
318C22×C23—42no—
319C22×C23—42no—
320C22×C23—81no—
321C22×C23—81no—
322C22×C23—81no—
323C22×C23—81no—
324C22×C23#52511yescharacteristic
325C22×C23C2×#12411yescharacteristic
326C22×C23#53411yescharacteristic
327C22×C23#57611yescharacteristic
328C22×C23#57711yescharacteristic
329C22×C23#57711yescharacteristic
330C22×C23#57811yescharacteristic
331C4×C23—22no—
332C4×C23—42no—
333C4×C23—41no—
334C4×C23—41no—
335C4×C23—41no—
336C4×C23—41no—
337C4×C23—81no—
338C4×C23—81no—
339C4×C23—81no—
340C4×C23—81no—
341C4×C23—81no—
342C4×C23—81no—
343C4×C23#55111yescharacteristic
344C4×C23#55111yescharacteristic
345C4×C23#55111yescharacteristic
346C4×C23#55111yescharacteristic
347C22×#41C22×C2311yescharacteristic
348C2×C4⋊Q8C22×C2311yescharacteristic
349C2×#117C22×C2311yescharacteristic
350C22×C4⋊C4C22×C2311yescharacteristic
351C2×#103C22×C2311yescharacteristic
352C2×#103C22×C2311yescharacteristic
353C2×#103C22×C2311yescharacteristic
354C2×#103C22×C2311yescharacteristic
355C2×#102C22×C2311yescharacteristic
356C2×#102C22×C2311yescharacteristic
357C2×#102C22×C2311yescharacteristic
358C2×#102C22×C2311yescharacteristic
359C2×C22⋊C8C22×C2311yescharacteristic
360C2×C22⋊C8C22×C2311yescharacteristic
361C2×#97C22×C2311yescharacteristic
362C2×C4×C8C22×C2311yescharacteristic
363#400—21no—
364#399—21no—
365#395—21no—
366#393—21no—
367#391C22×C2311yescharacteristic
368#391C22×C2311yescharacteristic
369#390C22×C2311yescharacteristic
370#390C22×C2311yescharacteristic
371#389C22×C2311yescharacteristic
372#389C22×C2311yescharacteristic
373#386—21no—
374#386—21no—
375#382C22×C2311yescharacteristic
376#380—21no—
377#380—21no—
378#380C22×C2311yescharacteristic
379#380C22×C2311yescharacteristic
380#340C22×C2311yescharacteristic
381#340C22×C2311yescharacteristic
382#340C22×C2311yescharacteristic
383#340C22×C2311yescharacteristic
384#340C22×C2311yescharacteristic
385#340C22×C2311yescharacteristic
386#340C22×C2311yescharacteristic
387#340C22×C2311yescharacteristic
388#336C22×C2311yescharacteristic
389#336C22×C2311yescharacteristic
390C2×C23—42no—
391C2×C23—82no—
392C2×C23#256111yescharacteristic
393C2×C23#312411yescharacteristic
394C2×C23#312511yescharacteristic
395C2×C23#313611yescharacteristic
396C2×C23#313711yescharacteristic
397C2×C23#319811yescharacteristic
398C2×C23#320111yescharacteristic
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—41no—
404C2×#41—41no—
405C22×Q8—21no—
406C22×Q8C23×C2311yescharacteristic
407C22×D4—21no—
408C22×D4C23×C2311yescharacteristic
409C23×C4—21no—
410C23×C4—21no—
411C23×C4C23×C2311yescharacteristic
412C22×C8C23×C2311yescharacteristic
413C22×C8C23×C2311yescharacteristic
414C22×C8C23×C2311yescharacteristic
415C22×C8C23×C2311yescharacteristic
416C4⋊Q8—41no—
417C4⋊Q8—41no—
418#117—41no—
419#117—41no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4D4×C2311yescharacteristic
427C2×C4⋊C4D4×C2311yescharacteristic
428C2×C4⋊C4C23×C2311yescharacteristic
429C2×C4⋊C4C23×C2311yescharacteristic
430C2×C4⋊C4C23×C2311yescharacteristic
431C2×C4⋊C4C23×C2311yescharacteristic
432C2×C4⋊C4C23×C2311yescharacteristic
433C2×C4⋊C4C23×C2311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C2311yescharacteristic
441C2×C22⋊C4D4×C2311yescharacteristic
442C2×C42C23×C2311yescharacteristic
443C2×C42C23×C2311yescharacteristic
444#103—22no—
445#103—22no—
446#103—41no—
447#103—41no—
448#102—22no—
449#102—22no—
450#102—41no—
451#102—41no—
452C22⋊C8—22no—
453C22⋊C8—22no—
454#97—41no—
455C4×C8—41no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466C23#2912011yescharacteristic, direct product factor, Sylow
467C24—21no—
468C24C2×D4×C2311yescharacteristic
469#41—44no—
470#41—44no—
471#41—44no—
472#41—44no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—42no—
479C2×Q8—81no—
480C2×Q8—81no—
481C2×Q8#41×C2312yes—
482C2×D4—24no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4#41×C2312yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C2×D4×C2311yescharacteristic
509C22×C4C2×D4×C2311yescharacteristic
510C22×C4C2×D4×C2311yescharacteristic
511C22×C4C2×D4×C2311yescharacteristic
512C22×C4C2×D4×C2311yescharacteristic
513C22×C4#41×C2312yes—
514C22×C4#41×C2312yes—
515C22×C4C24×C2311yescharacteristic
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4—81no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C23×#12412yes—
572C23C22×D4×C2311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—84no—
578D4—22no—
579D4—22no—
580D4—48no—
581D4—41no—
582D4—41no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—48no—
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×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×C4—41no—
622C2×C4—41no—
623C2×C4—84no—
624C2×C4C23×#12412yes—
625C2×C4C2×#41×C2311yescharacteristic
626C2×C4C2×#41×C2311yescharacteristic
627C2×C4C2×#41×C2311yescharacteristic
628C2×C4C2×#41×C2311yescharacteristic
629C2×C4C23×H(5,𝔽2)11yescharacteristic
630C2×C4C23×H(5,𝔽2)11yescharacteristic
631C8—41no—
632C8—41no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C23×#52511yescharacteristic
650C22C2×C23×#12411yescharacteristic
651C22C23×#53411yescharacteristic
652C22C23×#57611yescharacteristic
653C22C23×#57711yescharacteristic
654C22C23×#57711yescharacteristic
655C22C23×#57811yescharacteristic
656C4—22no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4C23×#55111yescharacteristic
669C4C23×#55111yescharacteristic
670C4C23×#55111yescharacteristic
671C4C23×#55111yescharacteristic
672C2—42no—
673C2—82no—
674C2C23×#256111yescharacteristic
675C2C23×#312411yescharacteristic
676C2C23×#312511yescharacteristic
677C2C23×#313611yescharacteristic
678C2C23×#313711yescharacteristic
679C2C23×#319811yescharacteristic
680C2C23×#320111yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC22×#41×C23C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C23×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#2628C2semidirect
3. C23×#2074C2semidirect
4. C23×#2073C2semidirect
5. C23×#2024C2semidirect
6. C23×#2023C2semidirect
7. C23×#1936C2semidirect
8. C23×#1935C2semidirect
9. C23×#1934C2semidirect
10. C23×#1933C2semidirect
11. C23×#1824C2semidirect
12. C23×#1823C2semidirect
15. C23×#1750C2semidirect
217. #29120C23direct (N × H)
295. #2628C2×C23semidirect
297. #2074C2×C23semidirect
298. #2073C2×C23semidirect
299. #2024C2×C23semidirect
300. #2023C2×C23semidirect
301. #1936C2×C23semidirect
302. #1935C2×C23semidirect
303. #1934C2×C23semidirect
304. #1933C2×C23semidirect
305. #1824C2×C23semidirect
306. #1823C2×C23semidirect
309. #1750C2×C23semidirect
466. C23#29120direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#26282
C23×#23112
C23×#20742
C23×#20732
C23×#20242
C23×#20232
C23×#19362
C23×#19352
C23×#19342
C23×#19332
C23×#18242
C23×#18232
C23×#17882
C23×#17502
#2912023