Finite Group Databasebeta

← C23×#16533 #19164159

Subgroups — C23×#16533 #19164159

Order 5888.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#396C211yesmaximal, characteristic, complemented
2C2×C23×#394C211yesmaximal, characteristic
3C2×C23×#394C211yesmaximal, characteristic
4C2×C23×#388C211yesmaximal, characteristic, complemented
5C23×#1445C211yesmaximal, characteristic, complemented
6C23×#1444C211yesmaximal, characteristic, complemented
7C23×#1441C211yesmaximal, 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×#1437C211yesmaximal, characteristic, complemented
15C23×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊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×C22⋊C4×C23C2211yescharacteristic
33C22×C22⋊C4×C23C2211yescharacteristic
34C22×C42×C23C2211yescharacteristic
35C23×#396—24no—
36C23×#394—24no—
37C23×#394—24no—
38C23×#388—24no—
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
53C2×C23×#95C2211yescharacteristic
54C2×C23×#95C2211yescharacteristic
55C25×C23C2311yescharacteristic
56C25×C23C2311yescharacteristic
57C22×D4×C23—22no—
58C22×D4×C23—22no—
59C22×D4×C23—22no—
60C22×D4×C23—41no—
61C22×D4×C23—41no—
62C22×D4×C23—41no—
63C22×D4×C23—41no—
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
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C2×C4⋊C4×C23—22no—
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—22no—
81C2×C4⋊C4×C23—22no—
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—22no—
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—22no—
86C2×C4⋊C4×C23—41no—
87C2×C4⋊C4×C23—41no—
88C2×C4⋊C4×C23—41no—
89C2×C4⋊C4×C23—41no—
90C2×C4⋊C4×C23—41no—
91C2×C4⋊C4×C23—41no—
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—22no—
101C2×C22⋊C4×C23—22no—
102C2×C22⋊C4×C23—22no—
103C2×C22⋊C4×C23—22no—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—22no—
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×C22⋊C4×C23—41no—
121C2×C22⋊C4×C23—41no—
122C2×C22⋊C4×C23—41no—
123C2×C22⋊C4×C23—41no—
124C2×C22⋊C4×C23—41no—
125C2×C22⋊C4×C23—41no—
126C2×C22⋊C4×C23D414yes—
127C2×C22⋊C4×C23D414yes—
128C2×C42×C23—22no—
129C2×C42×C23—41no—
130C2×C42×C23—41no—
131C23×#95—22no—
132C23×#95—22no—
133C23×#95—22no—
134C23×#95—22no—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—41no—
140C23×#95—41no—
141C23×#95—41no—
142C23×#95—41no—
143C23×#95—41no—
144C23×#95—41no—
145C23×#95—41no—
146C23×#95—41no—
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×C23—21no—
170C24×C23—21no—
171C24×C23—21no—
172C24×C23—21no—
173C24×C23—21no—
174C24×C23—21no—
175C24×C23C2×D412yes—
176C24×C23C2×D412yes—
177C24×C23C2411yescharacteristic
178C2×D4×C23—44no—
179C2×D4×C23—44no—
180C2×D4×C23—44no—
181C2×D4×C23—44no—
182C2×D4×C23—44no—
183C2×D4×C23—44no—
184C2×D4×C23—44no—
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×C23—21no—
264C22×C4×C23—21no—
265C22×C4×C23—21no—
266C22×C4×C23—21no—
267C22×C4×C23C2×D412yes—
268C22×C4×C23C2×D412yes—
269C22×C4×C23C2×D412yes—
270C22×C4×C23C2×D412yes—
271C22×C4×C23#4112yes—
272C22×C4×C23#4112yes—
273C22×C4×C23#4112yes—
274C22×C4×C23#4112yes—
275C22×C4×C23#4112yes—
276C4⋊C4×C23—44no—
277C4⋊C4×C23—44no—
278C4⋊C4×C23—44no—
279C4⋊C4×C23—44no—
280C4⋊C4×C23—44no—
281C22⋊C4×C23—28no—
282C22⋊C4×C23—44no—
283C22⋊C4×C23—44no—
284C22⋊C4×C23—44no—
285C22⋊C4×C23—44no—
286C22⋊C4×C23—44no—
287C22⋊C4×C23—44no—
288C22⋊C4×C23—44no—
289C22⋊C4×C23—44no—
290C22⋊C4×C23—44no—
291C22⋊C4×C23—44no—
292C22⋊C4×C23—44no—
293C42×C23—44no—
294#16533C2311yesmaximal, characteristic, direct product factor, Sylow
295C23×C23—22no—
296C23×C23—22no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—22no—
300C23×C23—22no—
301C23×C23—22no—
302C23×C23—22no—
303C23×C23—22no—
304C23×C23—22no—
305C23×C23—22no—
306C23×C23—22no—
307C23×C23—22no—
308C23×C23—22no—
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×C23—41no—
358C23×C23—41no—
359C23×C23—41no—
360C23×C23—41no—
361C23×C23—41no—
362C23×C23—41no—
363C23×C23—41no—
364C23×C23—41no—
365C23×C23C22×D411yescharacteristic
366C23×C23C22×D411yescharacteristic
367C23×C23C2×#4111yescharacteristic
368C23×C23C2×#4111yescharacteristic
369C23×C23C2×#4111yescharacteristic
370C23×C23C2×#4111yescharacteristic
371C23×C23C2×#4111yescharacteristic
372C23×C23H(5,𝔽2)11yescharacteristic
373C23×C23H(5,𝔽2)11yescharacteristic
374C23×C23H(5,𝔽2)11yescharacteristic
375C23×C23H(5,𝔽2)11yescharacteristic
376C23×C23H(5,𝔽2)11yescharacteristic
377C23×C23H(5,𝔽2)11yescharacteristic
378C23×C232−1+411yescharacteristic
379C23×C232−1+411yescharacteristic
380D4×C23—416no—
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—22no—
392C2×C4×C23—22no—
393C2×C4×C23—22no—
394C2×C4×C23—22no—
395C2×C4×C23—22no—
396C2×C4×C23—22no—
397C2×C4×C23—22no—
398C2×C4×C23—22no—
399C2×C4×C23—22no—
400C2×C4×C23—22no—
401C2×C4×C23—22no—
402C2×C4×C23—22no—
403C2×C4×C23—22no—
404C2×C4×C23—22no—
405C2×C4×C23—22no—
406C2×C4×C23—22no—
407C2×C4×C23—22no—
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—41no—
464C2×C4×C23—41no—
465C2×C4×C23—41no—
466C2×C4×C23—41no—
467C2×C4×C23—41no—
468C2×C4×C23—41no—
469C2×C4×C23—41no—
470C2×C4×C23—41no—
471C2×C4×C23—41no—
472C2×#396C2×C2311yescharacteristic, complemented
473C2×#394C2×C2311yescharacteristic
474C2×#394C2×C2311yescharacteristic
475C2×#388C2×C2311yescharacteristic, complemented
476#1445C2×C2311yescharacteristic, complemented
477#1444C2×C2311yescharacteristic, complemented
478#1441C2×C2311yescharacteristic, complemented
479#1440C2×C2311yescharacteristic, complemented
480#1440C2×C2311yescharacteristic, complemented
481#1440C2×C2311yescharacteristic, complemented
482#1439C2×C2311yescharacteristic, complemented
483#1439C2×C2311yescharacteristic, complemented
484#1438C2×C2311yescharacteristic
485#1437C2×C2311yescharacteristic, complemented
486#1436C2×C2311yescharacteristic, complemented
487C22×C23—42no—
488C22×C23—42no—
489C22×C23—42no—
490C22×C23—42no—
491C22×C23—42no—
492C22×C23—42no—
493C22×C23—42no—
494C22×C23—42no—
495C22×C23—42no—
496C22×C23—42no—
497C22×C23—42no—
498C22×C23—42no—
499C22×C23—42no—
500C22×C23—42no—
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×C23—81no—
510C22×C23—81no—
511C22×C23—81no—
512C22×C23—81no—
513C22×C23—81no—
514C22×C23—81no—
515C22×C23—81no—
516C22×C23—81no—
517C22×C23#52511yescharacteristic
518C22×C23#52911yescharacteristic
519C22×C23#53211yescharacteristic
520C22×C23#53411yescharacteristic
521C22×C23#53411yescharacteristic
522C22×C23#53611yescharacteristic
523C22×C23#53711yescharacteristic
524C22×C23#53811yescharacteristic
525C22×C23#53811yescharacteristic
526C22×C23#53911yescharacteristic
527C22×C23#53911yescharacteristic
528C22×C23#54011yescharacteristic
529C22×C23#54011yescharacteristic
530C22×C23#54011yescharacteristic
531C22×C23#54211yescharacteristic
532C22×C23#54211yescharacteristic
533C22×C23#54211yescharacteristic
534C22×C23#54211yescharacteristic
535C22×C23#54211yescharacteristic
536C22×C23D4211yescharacteristic
537C22×C23#54611yescharacteristic
538C22×C23#54611yescharacteristic
539C22×C23#54611yescharacteristic
540C22×C23#54611yescharacteristic
541C22×C23#54611yescharacteristic
542C22×C23#54711yescharacteristic
543C22×C23#55311yescharacteristic
544C22×C23#55311yescharacteristic
545C22×C23#55311yescharacteristic
546C22×C23#55511yescharacteristic
547C22×C23#55611yescharacteristic
548C22×C23#56011yescharacteristic
549C22×C23#56011yescharacteristic
550C22×C23#56211yescharacteristic
551C22×C23#56211yescharacteristic
552C4×C23—42no—
553C4×C23—42no—
554C4×C23—42no—
555C4×C23—42no—
556C4×C23—42no—
557C4×C23—42no—
558C4×C23—42no—
559C4×C23—42no—
560C4×C23—42no—
561C4×C23—81no—
562C4×C23—81no—
563C4×C23—81no—
564C4×C23—81no—
565C23×D4C22×C2311yescharacteristic
566C22×C4⋊C4C22×C2311yescharacteristic
567C22×C4⋊C4C22×C2311yescharacteristic
568C22×C4⋊C4C22×C2311yescharacteristic
569C22×C4⋊C4C22×C2311yescharacteristic
570C22×C4⋊C4C22×C2311yescharacteristic
571C22×C22⋊C4C22×C2311yescharacteristic
572C22×C22⋊C4C22×C2311yescharacteristic
573C22×C22⋊C4C22×C2311yescharacteristic
574C22×C22⋊C4C22×C2311yescharacteristic
575C22×C22⋊C4C22×C2311yescharacteristic
576C22×C22⋊C4C22×C2311yescharacteristic
577C22×C22⋊C4C22×C2311yescharacteristic
578C22×C22⋊C4C22×C2311yescharacteristic
579C22×C22⋊C4C22×C2311yescharacteristic
580C22×C22⋊C4C22×C2311yescharacteristic
581C22×C22⋊C4C22×C2311yescharacteristic
582C22×C22⋊C4C22×C2311yescharacteristic
583C22×C42C22×C2311yescharacteristic
584#396—24no—
585#394—24no—
586#394—24no—
587#388—24no—
588C2×#95C22×C2311yescharacteristic
589C2×#95C22×C2311yescharacteristic
590C2×#95C22×C2311yescharacteristic
591C2×#95C22×C2311yescharacteristic
592C2×#95C22×C2311yescharacteristic
593C2×#95C22×C2311yescharacteristic
594C2×#95C22×C2311yescharacteristic
595C2×#95C22×C2311yescharacteristic
596C2×#95C22×C2311yescharacteristic
597C2×#95C22×C2311yescharacteristic
598C2×#95C22×C2311yescharacteristic
599C2×#95C22×C2311yescharacteristic
600C2×#95C22×C2311yescharacteristic
601C2×#95C22×C2311yescharacteristic
602C2×#95C22×C2311yescharacteristic
603C2×#95C22×C2311yescharacteristic
604C2×C23—82no—
605C2×C23—82no—
606C2×C23#246411yescharacteristic
607C2×C23#247411yescharacteristic
608C2×C23#255911yescharacteristic
609C2×C23#263011yescharacteristic
610C2×C23#265111yescharacteristic
611C2×C23#266311yescharacteristic
612C2×C23#266811yescharacteristic
613C2×C23#267211yescharacteristic
614C2×C23#269111yescharacteristic
615C2×C23#269911yescharacteristic
616C2×C23#270011yescharacteristic
617C2×C23#270111yescharacteristic
618C2×C23#279511yescharacteristic
619C2×C23#280011yescharacteristic
620C2×C23#282911yescharacteristic
621C25C23×C2311yescharacteristic
622C25C23×C2311yescharacteristic
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4—41no—
630C23×C4C23×C2311yescharacteristic
631C23×C4C23×C2311yescharacteristic
632C23×C4C23×C2311yescharacteristic
633C23×C4C23×C2311yescharacteristic
634C23×C4C23×C2311yescharacteristic
635C23×C4C23×C2311yescharacteristic
636C23×C4C23×C2311yescharacteristic
637C23×C4C23×C2311yescharacteristic
638C23×C4C23×C2311yescharacteristic
639C23×C4C23×C2311yescharacteristic
640C23×C4C23×C2311yescharacteristic
641C23×C4C23×C2311yescharacteristic
642C23×C4C23×C2311yescharacteristic
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4D4×C2314yes—
693C2×C22⋊C4D4×C2314yes—
694C2×C42—22no—
695C2×C42—41no—
696C2×C42—41no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713C23#1653311yescharacteristic, direct product factor, Sylow
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—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24C2×D4×C2312yes—
743C24C2×D4×C2312yes—
744C24C24×C2311yescharacteristic
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
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×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4C2×D4×C2312yes—
835C22×C4C2×D4×C2312yes—
836C22×C4C2×D4×C2312yes—
837C22×C4C2×D4×C2312yes—
838C22×C4#41×C2312yes—
839C22×C4#41×C2312yes—
840C22×C4#41×C2312yes—
841C22×C4#41×C2312yes—
842C22×C4#41×C2312yes—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C22⋊C4—28no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C42—44no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
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—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23C22×D4×C2311yescharacteristic
932C23C22×D4×C2311yescharacteristic
933C23C2×#41×C2311yescharacteristic
934C23C2×#41×C2311yescharacteristic
935C23C2×#41×C2311yescharacteristic
936C23C2×#41×C2311yescharacteristic
937C23C2×#41×C2311yescharacteristic
938C23C23×H(5,𝔽2)11yescharacteristic
939C23C23×H(5,𝔽2)11yescharacteristic
940C23C23×H(5,𝔽2)11yescharacteristic
941C23C23×H(5,𝔽2)11yescharacteristic
942C23C23×H(5,𝔽2)11yescharacteristic
943C23C23×H(5,𝔽2)11yescharacteristic
944C23C23×2−1+411yescharacteristic
945C23C23×2−1+411yescharacteristic
946D4—416no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
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×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22C23×#52511yescharacteristic
1069C22C23×#52911yescharacteristic
1070C22C23×#53211yescharacteristic
1071C22C23×#53411yescharacteristic
1072C22C23×#53411yescharacteristic
1073C22C23×#53611yescharacteristic
1074C22C23×#53711yescharacteristic
1075C22C23×#53811yescharacteristic
1076C22C23×#53811yescharacteristic
1077C22C23×#53911yescharacteristic
1078C22C23×#53911yescharacteristic
1079C22C23×#54011yescharacteristic
1080C22C23×#54011yescharacteristic
1081C22C23×#54011yescharacteristic
1082C22C23×#54211yescharacteristic
1083C22C23×#54211yescharacteristic
1084C22C23×#54211yescharacteristic
1085C22C23×#54211yescharacteristic
1086C22C23×#54211yescharacteristic
1087C22D42×C2311yescharacteristic
1088C22C23×#54611yescharacteristic
1089C22C23×#54611yescharacteristic
1090C22C23×#54611yescharacteristic
1091C22C23×#54611yescharacteristic
1092C22C23×#54611yescharacteristic
1093C22C23×#54711yescharacteristic
1094C22C23×#55311yescharacteristic
1095C22C23×#55311yescharacteristic
1096C22C23×#55311yescharacteristic
1097C22C23×#55511yescharacteristic
1098C22C23×#55611yescharacteristic
1099C22C23×#56011yescharacteristic
1100C22C23×#56011yescharacteristic
1101C22C23×#56211yescharacteristic
1102C22C23×#56211yescharacteristic
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C2—82no—
1117C2—82no—
1118C2C23×#246411yescharacteristic
1119C2C23×#247411yescharacteristic
1120C2C23×#255911yescharacteristic
1121C2C23×#263011yescharacteristic
1122C2C23×#265111yescharacteristic
1123C2C23×#266311yescharacteristic
1124C2C23×#266811yescharacteristic
1125C2C23×#267211yescharacteristic
1126C2C23×#269111yescharacteristic
1127C2C23×#269911yescharacteristic
1128C2C23×#270011yescharacteristic
1129C2C23×#270111yescharacteristic
1130C2C23×#279511yescharacteristic
1131C2C23×#280011yescharacteristic
1132C2C23×#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
1. C2×C23×#396C2semidirect
4. C2×C23×#388C2semidirect
5. C23×#1445C2semidirect
6. C23×#1444C2semidirect
7. C23×#1441C2semidirect
8. C23×#1440C2semidirect
9. C23×#1440C2semidirect
10. C23×#1440C2semidirect
11. C23×#1439C2semidirect
12. C23×#1439C2semidirect
14. C23×#1437C2semidirect
15. C23×#1436C2semidirect
294. #16533C23direct (N × H)
472. C2×#396C2×C23semidirect
475. C2×#388C2×C23semidirect
476. #1445C2×C23semidirect
477. #1444C2×C23semidirect
478. #1441C2×C23semidirect
479. #1440C2×C23semidirect
480. #1440C2×C23semidirect
481. #1440C2×C23semidirect
482. #1439C2×C23semidirect
483. #1439C2×C23semidirect
485. #1437C2×C23semidirect
486. #1436C2×C23semidirect
713. C23#16533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3962
C2×C23×#3942
C2×C23×#3882
C23×#14452
C23×#14442
C23×#14412
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
#1653323