Finite Group Databasebeta

← C23×#16573 #19164199

Subgroups — C23×#16573 #19164199

Order 5888.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C2×C23×#390C211yesmaximal, characteristic
3C23×#1442C211yesmaximal, characteristic, complemented
4C23×#1441C211yesmaximal, characteristic, complemented
5C23×#1440C211yesmaximal, characteristic, complemented
6C23×#1440C211yesmaximal, characteristic, complemented
7C23×#1440C211yesmaximal, characteristic, complemented
8C23×#1440C211yesmaximal, characteristic, complemented
9C23×#1440C211yesmaximal, characteristic, complemented
10C23×#1440C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1439C211yesmaximal, characteristic, complemented
13C23×#1438C211yesmaximal, characteristic
14C23×#1436C211yesmaximal, characteristic, complemented
15C23×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C22⋊C4×C23C2211yescharacteristic
21C22×C22⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C22⋊C4×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C23×#394—24no—
34C23×#390—24no—
35C2×C23×#95C2211yescharacteristic
36C2×C23×#95C2211yescharacteristic
37C2×C23×#95C2211yescharacteristic
38C2×C23×#95C2211yescharacteristic
39C2×C23×#95C2211yescharacteristic
40C2×C23×#95C2211yescharacteristic
41C2×C23×#95C2211yescharacteristic
42C2×C23×#95C2211yescharacteristic
43C2×C23×#95C2211yescharacteristic
44C2×C23×#95C2211yescharacteristic
45C2×C23×#95C2211yescharacteristic
46C2×C23×#95C2211yescharacteristic
47C2×C23×#95C2211yescharacteristic
48C2×C23×#95C2211yescharacteristic
49C2×C23×#95C2211yescharacteristic
50C2×C23×#95C2211yescharacteristic
51C2×C23×#95C2211yescharacteristic
52C2×C23×#95C2211yescharacteristic
53C25×C23C2311yescharacteristic
54C25×C23C2311yescharacteristic
55C22×D4×C23—22no—
56C22×D4×C23—22no—
57C22×D4×C23—41no—
58C22×D4×C23—41no—
59C22×D4×C23—41no—
60C22×D4×C23—41no—
61C22×D4×C23D414yes—
62C23×C4×C23C2311yescharacteristic
63C23×C4×C23C2311yescharacteristic
64C23×C4×C23C2311yescharacteristic
65C23×C4×C23C2311yescharacteristic
66C23×C4×C23C2311yescharacteristic
67C23×C4×C23C2311yescharacteristic
68C23×C4×C23C2311yescharacteristic
69C23×C4×C23C2311yescharacteristic
70C23×C4×C23C2311yescharacteristic
71C23×C4×C23C2311yescharacteristic
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C2×C4⋊C4×C23—22no—
76C2×C4⋊C4×C23—22no—
77C2×C4⋊C4×C23—22no—
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—41no—
81C2×C4⋊C4×C23—41no—
82C2×C4⋊C4×C23—41no—
83C2×C4⋊C4×C23—41no—
84C2×C22⋊C4×C23—22no—
85C2×C22⋊C4×C23—22no—
86C2×C22⋊C4×C23—22no—
87C2×C22⋊C4×C23—22no—
88C2×C22⋊C4×C23—22no—
89C2×C22⋊C4×C23—22no—
90C2×C22⋊C4×C23—22no—
91C2×C22⋊C4×C23—22no—
92C2×C22⋊C4×C23—22no—
93C2×C22⋊C4×C23—22no—
94C2×C22⋊C4×C23—22no—
95C2×C22⋊C4×C23—22no—
96C2×C22⋊C4×C23—22no—
97C2×C22⋊C4×C23—22no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
100C2×C22⋊C4×C23—41no—
101C2×C22⋊C4×C23—41no—
102C2×C22⋊C4×C23—41no—
103C2×C22⋊C4×C23—41no—
104C2×C22⋊C4×C23—41no—
105C2×C22⋊C4×C23—41no—
106C2×C22⋊C4×C23—41no—
107C2×C22⋊C4×C23—41no—
108C2×C22⋊C4×C23—41no—
109C2×C22⋊C4×C23—41no—
110C2×C22⋊C4×C23—41no—
111C2×C22⋊C4×C23—41no—
112C2×C22⋊C4×C23—41no—
113C2×C22⋊C4×C23—41no—
114C2×C22⋊C4×C23—41no—
115C2×C22⋊C4×C23—41no—
116C2×C22⋊C4×C23—41no—
117C2×C22⋊C4×C23—41no—
118C2×C22⋊C4×C23—41no—
119C2×C22⋊C4×C23—41no—
120C2×C42×C23—22no—
121C2×C42×C23—41no—
122C2×C42×C23—41no—
123C23×#95—22no—
124C23×#95—22no—
125C23×#95—22no—
126C23×#95—22no—
127C23×#95—22no—
128C23×#95—22no—
129C23×#95—41no—
130C23×#95—41no—
131C23×#95—41no—
132C23×#95—41no—
133C23×#95—41no—
134C23×#95—41no—
135C23×#95—41no—
136C23×#95—41no—
137C23×#95—41no—
138C23×#95—41no—
139C23×#95—41no—
140C23×#95—41no—
141C24×C23—21no—
142C24×C23—21no—
143C24×C23—21no—
144C24×C23—21no—
145C24×C23—21no—
146C24×C23—21no—
147C24×C23—21no—
148C24×C23—21no—
149C24×C23—21no—
150C24×C23—21no—
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—21no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—21no—
161C24×C23—21no—
162C24×C23—21no—
163C24×C23—21no—
164C24×C23—21no—
165C24×C23—21no—
166C24×C23—21no—
167C24×C23—21no—
168C24×C23—21no—
169C24×C23C2×D412yes—
170C24×C23C2×D412yes—
171C24×C23C2411yescharacteristic
172C2×D4×C23—28no—
173C2×D4×C23—44no—
174C2×D4×C23—44no—
175C2×D4×C23—44no—
176C2×D4×C23—44no—
177C2×D4×C23—44no—
178C2×D4×C23—44no—
179C22×C4×C23—21no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—21no—
247C22×C4×C23—21no—
248C22×C4×C23—21no—
249C22×C4×C23—21no—
250C22×C4×C23—21no—
251C22×C4×C23—21no—
252C22×C4×C23—21no—
253C22×C4×C23—21no—
254C22×C4×C23—21no—
255C22×C4×C23—21no—
256C22×C4×C23—21no—
257C22×C4×C23—21no—
258C22×C4×C23—21no—
259C22×C4×C23—21no—
260C22×C4×C23—21no—
261C22×C4×C23—21no—
262C22×C4×C23—21no—
263C22×C4×C23C2×D412yes—
264C22×C4×C23#4112yes—
265C22×C4×C23#4112yes—
266C22×C4×C23#4112yes—
267C22×C4×C23#4112yes—
268C22×C4×C23#4112yes—
269C22×C4×C23#4112yes—
270C4⋊C4×C23—44no—
271C4⋊C4×C23—44no—
272C4⋊C4×C23—44no—
273C22⋊C4×C23—44no—
274C22⋊C4×C23—44no—
275C22⋊C4×C23—44no—
276C22⋊C4×C23—44no—
277C22⋊C4×C23—44no—
278C22⋊C4×C23—44no—
279C22⋊C4×C23—44no—
280C22⋊C4×C23—44no—
281C22⋊C4×C23—44no—
282C22⋊C4×C23—44no—
283C22⋊C4×C23—44no—
284C22⋊C4×C23—44no—
285C42×C23—44no—
286#16573C2311yesmaximal, characteristic, direct product factor, Sylow
287C23×C23—22no—
288C23×C23—22no—
289C23×C23—22no—
290C23×C23—22no—
291C23×C23—22no—
292C23×C23—22no—
293C23×C23—22no—
294C23×C23—22no—
295C23×C23—22no—
296C23×C23—22no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—22no—
300C23×C23—22no—
301C23×C23—41no—
302C23×C23—41no—
303C23×C23—41no—
304C23×C23—41no—
305C23×C23—41no—
306C23×C23—41no—
307C23×C23—41no—
308C23×C23—41no—
309C23×C23—41no—
310C23×C23—41no—
311C23×C23—41no—
312C23×C23—41no—
313C23×C23—41no—
314C23×C23—41no—
315C23×C23—41no—
316C23×C23—41no—
317C23×C23—41no—
318C23×C23—41no—
319C23×C23—41no—
320C23×C23—41no—
321C23×C23—41no—
322C23×C23—41no—
323C23×C23—41no—
324C23×C23—41no—
325C23×C23—41no—
326C23×C23—41no—
327C23×C23—41no—
328C23×C23—41no—
329C23×C23—41no—
330C23×C23—41no—
331C23×C23—41no—
332C23×C23—41no—
333C23×C23—41no—
334C23×C23—41no—
335C23×C23—41no—
336C23×C23—41no—
337C23×C23—41no—
338C23×C23—41no—
339C23×C23—41no—
340C23×C23—41no—
341C23×C23—41no—
342C23×C23—41no—
343C23×C23—41no—
344C23×C23—41no—
345C23×C23—41no—
346C23×C23—41no—
347C23×C23—41no—
348C23×C23—41no—
349C23×C23—41no—
350C23×C23—41no—
351C23×C23—41no—
352C23×C23—41no—
353C23×C23—41no—
354C23×C23—41no—
355C23×C23—41no—
356C23×C23—41no—
357C23×C23C22×D411yescharacteristic
358C23×C23C2×#4111yescharacteristic
359C23×C23C2×#4111yescharacteristic
360C23×C23C2×#4111yescharacteristic
361C23×C23C2×#4111yescharacteristic
362C23×C23C2×#4111yescharacteristic
363C23×C23C2×#4111yescharacteristic
364C23×C23H(5,𝔽2)11yescharacteristic
365C23×C23H(5,𝔽2)11yescharacteristic
366C23×C23H(5,𝔽2)11yescharacteristic
367C23×C23H(5,𝔽2)11yescharacteristic
368C23×C23H(5,𝔽2)11yescharacteristic
369C23×C23H(5,𝔽2)11yescharacteristic
370C23×C23H(5,𝔽2)11yescharacteristic
371C23×C232−1+411yescharacteristic
372D4×C23—416no—
373C2×C4×C23—22no—
374C2×C4×C23—22no—
375C2×C4×C23—22no—
376C2×C4×C23—22no—
377C2×C4×C23—22no—
378C2×C4×C23—22no—
379C2×C4×C23—22no—
380C2×C4×C23—22no—
381C2×C4×C23—22no—
382C2×C4×C23—22no—
383C2×C4×C23—22no—
384C2×C4×C23—22no—
385C2×C4×C23—22no—
386C2×C4×C23—22no—
387C2×C4×C23—22no—
388C2×C4×C23—22no—
389C2×C4×C23—22no—
390C2×C4×C23—22no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—41no—
394C2×C4×C23—41no—
395C2×C4×C23—41no—
396C2×C4×C23—41no—
397C2×C4×C23—41no—
398C2×C4×C23—41no—
399C2×C4×C23—41no—
400C2×C4×C23—41no—
401C2×C4×C23—41no—
402C2×C4×C23—41no—
403C2×C4×C23—41no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—41no—
411C2×C4×C23—41no—
412C2×C4×C23—41no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23—41no—
421C2×C4×C23—41no—
422C2×C4×C23—41no—
423C2×C4×C23—41no—
424C2×C4×C23—41no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23—41no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—41no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23—41no—
435C2×C4×C23—41no—
436C2×C4×C23—41no—
437C2×C4×C23—41no—
438C2×C4×C23—41no—
439C2×C4×C23—41no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—41no—
443C2×C4×C23—41no—
444C2×C4×C23—41no—
445C2×C4×C23—41no—
446C2×C4×C23—41no—
447C2×C4×C23—41no—
448C2×C4×C23—41no—
449C2×C4×C23—41no—
450C2×C4×C23—41no—
451C2×C4×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—41no—
454C2×C4×C23—41no—
455C2×C4×C23—41no—
456C2×C4×C23—41no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—41no—
460C2×C4×C23—41no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23#12314yes—
464C2×#394C2×C2311yescharacteristic
465C2×#390C2×C2311yescharacteristic
466#1442C2×C2311yescharacteristic, complemented
467#1441C2×C2311yescharacteristic, complemented
468#1440C2×C2311yescharacteristic, complemented
469#1440C2×C2311yescharacteristic, complemented
470#1440C2×C2311yescharacteristic, complemented
471#1440C2×C2311yescharacteristic, complemented
472#1440C2×C2311yescharacteristic, complemented
473#1440C2×C2311yescharacteristic, complemented
474#1439C2×C2311yescharacteristic, complemented
475#1439C2×C2311yescharacteristic, complemented
476#1438C2×C2311yescharacteristic
477#1436C2×C2311yescharacteristic, complemented
478#1436C2×C2311yescharacteristic, complemented
479C22×C23—42no—
480C22×C23—42no—
481C22×C23—42no—
482C22×C23—42no—
483C22×C23—42no—
484C22×C23—42no—
485C22×C23—42no—
486C22×C23—42no—
487C22×C23—42no—
488C22×C23—42no—
489C22×C23—42no—
490C22×C23—42no—
491C22×C23—42no—
492C22×C23—42no—
493C22×C23—81no—
494C22×C23—81no—
495C22×C23—81no—
496C22×C23—81no—
497C22×C23—81no—
498C22×C23—81no—
499C22×C23—81no—
500C22×C23—81no—
501C22×C23—81no—
502C22×C23—81no—
503C22×C23—81no—
504C22×C23—81no—
505C22×C23—81no—
506C22×C23—81no—
507C22×C23—81no—
508C22×C23—81no—
509C22×C23C2×#12311yescharacteristic
510C22×C23#52911yescharacteristic
511C22×C23#52911yescharacteristic
512C22×C23#53411yescharacteristic
513C22×C23#53411yescharacteristic
514C22×C23#53811yescharacteristic
515C22×C23#53811yescharacteristic
516C22×C23#53811yescharacteristic
517C22×C23#53811yescharacteristic
518C22×C23#53811yescharacteristic
519C22×C23#53811yescharacteristic
520C22×C23#53811yescharacteristic
521C22×C23#53911yescharacteristic
522C22×C23#54011yescharacteristic
523C22×C23#54011yescharacteristic
524C22×C23#54011yescharacteristic
525C22×C23#54011yescharacteristic
526C22×C23#54211yescharacteristic
527C22×C23#54211yescharacteristic
528C22×C23#54611yescharacteristic
529C22×C23#54611yescharacteristic
530C22×C23#54611yescharacteristic
531C22×C23#54711yescharacteristic
532C22×C23#55311yescharacteristic
533C22×C23#55311yescharacteristic
534C22×C23#55311yescharacteristic
535C22×C23#55511yescharacteristic
536C22×C23#55511yescharacteristic
537C22×C23#55611yescharacteristic
538C22×C23#55911yescharacteristic
539C22×C23#55911yescharacteristic
540C22×C23#56011yescharacteristic
541C22×C23#56011yescharacteristic
542C22×C23#56211yescharacteristic
543C22×C23#56211yescharacteristic
544C4×C23—24no—
545C4×C23—42no—
546C4×C23—42no—
547C4×C23—42no—
548C4×C23—42no—
549C4×C23—81no—
550C4×C23—81no—
551C4×C23—81no—
552C4×C23—81no—
553C4×C23—81no—
554C4×C23—81no—
555C4×C23—81no—
556C4×C23—81no—
557C23×D4C22×C2311yescharacteristic
558C22×C4⋊C4C22×C2311yescharacteristic
559C22×C4⋊C4C22×C2311yescharacteristic
560C22×C4⋊C4C22×C2311yescharacteristic
561C22×C22⋊C4C22×C2311yescharacteristic
562C22×C22⋊C4C22×C2311yescharacteristic
563C22×C22⋊C4C22×C2311yescharacteristic
564C22×C22⋊C4C22×C2311yescharacteristic
565C22×C22⋊C4C22×C2311yescharacteristic
566C22×C22⋊C4C22×C2311yescharacteristic
567C22×C22⋊C4C22×C2311yescharacteristic
568C22×C22⋊C4C22×C2311yescharacteristic
569C22×C22⋊C4C22×C2311yescharacteristic
570C22×C22⋊C4C22×C2311yescharacteristic
571C22×C22⋊C4C22×C2311yescharacteristic
572C22×C22⋊C4C22×C2311yescharacteristic
573C22×C42C22×C2311yescharacteristic
574#394—24no—
575#390—24no—
576C2×#95C22×C2311yescharacteristic
577C2×#95C22×C2311yescharacteristic
578C2×#95C22×C2311yescharacteristic
579C2×#95C22×C2311yescharacteristic
580C2×#95C22×C2311yescharacteristic
581C2×#95C22×C2311yescharacteristic
582C2×#95C22×C2311yescharacteristic
583C2×#95C22×C2311yescharacteristic
584C2×#95C22×C2311yescharacteristic
585C2×#95C22×C2311yescharacteristic
586C2×#95C22×C2311yescharacteristic
587C2×#95C22×C2311yescharacteristic
588C2×#95C22×C2311yescharacteristic
589C2×#95C22×C2311yescharacteristic
590C2×#95C22×C2311yescharacteristic
591C2×#95C22×C2311yescharacteristic
592C2×#95C22×C2311yescharacteristic
593C2×#95C22×C2311yescharacteristic
594C2×C23—82no—
595C2×C23—82no—
596C2×C23#242011yescharacteristic
597C2×C23#244711yescharacteristic
598C2×C23#259311yescharacteristic
599C2×C23#262211yescharacteristic
600C2×C23#264811yescharacteristic
601C2×C23#265111yescharacteristic
602C2×C23#268611yescharacteristic
603C2×C23#268811yescharacteristic
604C2×C23#270811yescharacteristic
605C2×C23#270911yescharacteristic
606C2×C23#280011yescharacteristic
607C2×C23#280311yescharacteristic
608C2×C23#280311yescharacteristic
609C2×C23#280811yescharacteristic
610C2×C23#282911yescharacteristic
611C25C23×C2311yescharacteristic
612C25C23×C2311yescharacteristic
613C22×D4—22no—
614C22×D4—22no—
615C22×D4—41no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4—41no—
619C22×D4D4×C2314yes—
620C23×C4C23×C2311yescharacteristic
621C23×C4C23×C2311yescharacteristic
622C23×C4C23×C2311yescharacteristic
623C23×C4C23×C2311yescharacteristic
624C23×C4C23×C2311yescharacteristic
625C23×C4C23×C2311yescharacteristic
626C23×C4C23×C2311yescharacteristic
627C23×C4C23×C2311yescharacteristic
628C23×C4C23×C2311yescharacteristic
629C23×C4C23×C2311yescharacteristic
630C23×C4C23×C2311yescharacteristic
631C23×C4C23×C2311yescharacteristic
632C23×C4C23×C2311yescharacteristic
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C42—22no—
679C2×C42—41no—
680C2×C42—41no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699C23#1657311yescharacteristic, direct product factor, Sylow
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24C2×D4×C2312yes—
729C24C2×D4×C2312yes—
730C24C24×C2311yescharacteristic
731C2×D4—28no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4C2×D4×C2312yes—
823C22×C4#41×C2312yes—
824C22×C4#41×C2312yes—
825C22×C4#41×C2312yes—
826C22×C4#41×C2312yes—
827C22×C4#41×C2312yes—
828C22×C4#41×C2312yes—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C42—44no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23C22×D4×C2311yescharacteristic
916C23C2×#41×C2311yescharacteristic
917C23C2×#41×C2311yescharacteristic
918C23C2×#41×C2311yescharacteristic
919C23C2×#41×C2311yescharacteristic
920C23C2×#41×C2311yescharacteristic
921C23C2×#41×C2311yescharacteristic
922C23C23×H(5,𝔽2)11yescharacteristic
923C23C23×H(5,𝔽2)11yescharacteristic
924C23C23×H(5,𝔽2)11yescharacteristic
925C23C23×H(5,𝔽2)11yescharacteristic
926C23C23×H(5,𝔽2)11yescharacteristic
927C23C23×H(5,𝔽2)11yescharacteristic
928C23C23×H(5,𝔽2)11yescharacteristic
929C23C23×2−1+411yescharacteristic
930D4—416no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4C23×#12314yes—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22C2×C23×#12311yescharacteristic
1053C22C23×#52911yescharacteristic
1054C22C23×#52911yescharacteristic
1055C22C23×#53411yescharacteristic
1056C22C23×#53411yescharacteristic
1057C22C23×#53811yescharacteristic
1058C22C23×#53811yescharacteristic
1059C22C23×#53811yescharacteristic
1060C22C23×#53811yescharacteristic
1061C22C23×#53811yescharacteristic
1062C22C23×#53811yescharacteristic
1063C22C23×#53811yescharacteristic
1064C22C23×#53911yescharacteristic
1065C22C23×#54011yescharacteristic
1066C22C23×#54011yescharacteristic
1067C22C23×#54011yescharacteristic
1068C22C23×#54011yescharacteristic
1069C22C23×#54211yescharacteristic
1070C22C23×#54211yescharacteristic
1071C22C23×#54611yescharacteristic
1072C22C23×#54611yescharacteristic
1073C22C23×#54611yescharacteristic
1074C22C23×#54711yescharacteristic
1075C22C23×#55311yescharacteristic
1076C22C23×#55311yescharacteristic
1077C22C23×#55311yescharacteristic
1078C22C23×#55511yescharacteristic
1079C22C23×#55511yescharacteristic
1080C22C23×#55611yescharacteristic
1081C22C23×#55911yescharacteristic
1082C22C23×#55911yescharacteristic
1083C22C23×#56011yescharacteristic
1084C22C23×#56011yescharacteristic
1085C22C23×#56211yescharacteristic
1086C22C23×#56211yescharacteristic
1087C4—24no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C2—82no—
1101C2—82no—
1102C2C23×#242011yescharacteristic
1103C2C23×#244711yescharacteristic
1104C2C23×#259311yescharacteristic
1105C2C23×#262211yescharacteristic
1106C2C23×#264811yescharacteristic
1107C2C23×#265111yescharacteristic
1108C2C23×#268611yescharacteristic
1109C2C23×#268811yescharacteristic
1110C2C23×#270811yescharacteristic
1111C2C23×#270911yescharacteristic
1112C2C23×#280011yescharacteristic
1113C2C23×#280311yescharacteristic
1114C2C23×#280311yescharacteristic
1115C2C23×#280811yescharacteristic
1116C2C23×#282911yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
3. C23×#1442C2semidirect
4. C23×#1441C2semidirect
5. C23×#1440C2semidirect
6. C23×#1440C2semidirect
7. C23×#1440C2semidirect
8. C23×#1440C2semidirect
9. C23×#1440C2semidirect
10. C23×#1440C2semidirect
11. C23×#1439C2semidirect
12. C23×#1439C2semidirect
14. C23×#1436C2semidirect
15. C23×#1436C2semidirect
286. #16573C23direct (N × H)
466. #1442C2×C23semidirect
467. #1441C2×C23semidirect
468. #1440C2×C23semidirect
469. #1440C2×C23semidirect
470. #1440C2×C23semidirect
471. #1440C2×C23semidirect
472. #1440C2×C23semidirect
473. #1440C2×C23semidirect
474. #1439C2×C23semidirect
475. #1439C2×C23semidirect
477. #1436C2×C23semidirect
478. #1436C2×C23semidirect
699. C23#16573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3942
C2×C23×#3902
C23×#14422
C23×#14412
C23×#14402
C23×#14392
C23×#14382
C23×#14362
#1657323