Finite Group Databasebeta

← C23×#16476 #19164102

Subgroups — C23×#16476 #19164102

Order 5888.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#396C211yesmaximal, characteristic, complemented
2C2×C23×#386C211yesmaximal, characteristic
3C23×#1445C211yesmaximal, characteristic, complemented
4C23×#1443C211yesmaximal, characteristic, complemented
5C23×#1442C211yesmaximal, characteristic, complemented
6C23×#1441C211yesmaximal, characteristic, complemented
7C23×#1439C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1438C211yesmaximal, characteristic
13C23×#1438C211yesmaximal, characteristic
14C23×C22⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×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
33C23×#396—24no—
34C23×#386—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×C23Q814yes—
62C23×C4×C23—22no—
63C23×C4×C23—22no—
64C23×C4×C23—22no—
65C23×C4×C23—41no—
66C23×C4×C23—41no—
67C23×C4×C23—41no—
68C23×C4×C23—41no—
69C23×C4×C23C2311yescharacteristic
70C23×C4×C23C2311yescharacteristic
71C23×C4×C23C2311yescharacteristic
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
80C23×C4×C23C2311yescharacteristic
81C23×C4×C23C2311yescharacteristic
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—22no—
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—22no—
86C2×C4⋊C4×C23—22no—
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×C4⋊C4×C23—41no—
93C2×C4⋊C4×C23—41no—
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—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×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—
127C23×#95—22no—
128C23×#95—22no—
129C23×#95—22no—
130C23×#95—22no—
131C23×#95—22no—
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—
141C23×#95—41no—
142C23×#95—41no—
143C23×#95—41no—
144C23×#95—41no—
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×C23—21no—
170C24×C23—21no—
171C24×C23C2×D412yes—
172C24×C23C2×Q812yes—
173C24×C23C2×Q812yes—
174C24×C23#4112yes—
175C24×C23C2411yescharacteristic
176C2×D4×C23—28no—
177C2×D4×C23—44no—
178C2×D4×C23—44no—
179C2×D4×C23—44no—
180C2×D4×C23—44no—
181C2×D4×C23—44no—
182C2×D4×C23—44no—
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×C23—21no—
264C22×C4×C23—21no—
265C22×C4×C23—21no—
266C22×C4×C23—21no—
267C22×C4×C23—44no—
268C22×C4×C23—44no—
269C22×C4×C23—44no—
270C22×C4×C23—44no—
271C22×C4×C23—44no—
272C22×C4×C23—44no—
273C22×C4×C23—44no—
274C22×C4×C23C2×D412yes—
275C22×C4×C23C2×D412yes—
276C22×C4×C23C2×Q812yes—
277C22×C4×C23#4112yes—
278C22×C4×C23#4112yes—
279C22×C4×C23#4112yes—
280C22×C4×C23#4112yes—
281C4⋊C4×C23—44no—
282C4⋊C4×C23—44no—
283C4⋊C4×C23—44no—
284C4⋊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—
293C22⋊C4×C23—44no—
294C22⋊C4×C23—44no—
295C22⋊C4×C23—44no—
296#16476C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
310C23×C23—22no—
311C23×C23—22no—
312C23×C23—22no—
313C23×C23—22no—
314C23×C23—22no—
315C23×C23—22no—
316C23×C23—22no—
317C23×C23—22no—
318C23×C23—22no—
319C23×C23—22no—
320C23×C23—22no—
321C23×C23—22no—
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×C23—41no—
366C23×C23C22⋊Q814yes—
367C23×C23C22×D411yescharacteristic
368C23×C23C22×Q811yescharacteristic
369C23×C23C2×#4111yescharacteristic
370C23×C23C2×#4111yescharacteristic
371C23×C23C2×#4111yescharacteristic
372C23×C23C2×#4111yescharacteristic
373C23×C23C2×#4111yescharacteristic
374C23×C23H(5,𝔽2)11yescharacteristic
375C23×C23H(5,𝔽2)11yescharacteristic
376C23×C23H(5,𝔽2)11yescharacteristic
377C23×C23H(5,𝔽2)11yescharacteristic
378C23×C23H(5,𝔽2)11yescharacteristic
379C23×C23H(5,𝔽2)11yescharacteristic
380C23×C23H(5,𝔽2)11yescharacteristic
381C23×C23H(5,𝔽2)11yescharacteristic
382D4×C23—416no—
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—416no—
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—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×C4×C23—41no—
473C2×C4×C23—41no—
474C2×C4×C23—41no—
475C2×#396C2×C2311yescharacteristic, complemented
476C2×#386C2×C2311yescharacteristic
477#1445C2×C2311yescharacteristic, complemented
478#1443C2×C2311yescharacteristic, complemented
479#1442C2×C2311yescharacteristic, complemented
480#1441C2×C2311yescharacteristic, complemented
481#1439C2×C2311yescharacteristic, complemented
482#1439C2×C2311yescharacteristic, complemented
483#1439C2×C2311yescharacteristic, complemented
484#1439C2×C2311yescharacteristic, complemented
485#1439C2×C2311yescharacteristic, complemented
486#1438C2×C2311yescharacteristic
487#1438C2×C2311yescharacteristic
488C22⋊#95C2×C2311yescharacteristic, complemented
489C22⋊#95C2×C2311yescharacteristic, complemented
490C22×C23—24no—
491C22×C23—24no—
492C22×C23—24no—
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—42no—
502C22×C23—42no—
503C22×C23—42no—
504C22×C23—42no—
505C22×C23—42no—
506C22×C23—42no—
507C22×C23—42no—
508C22×C23—42no—
509C22×C23—42no—
510C22×C23—42no—
511C22×C23—42no—
512C22×C23—81no—
513C22×C23—81no—
514C22×C23—81no—
515C22×C23—81no—
516C22×C23—81no—
517C22×C23—81no—
518C22×C23—81no—
519C22×C23—81no—
520C22×C23C2×C22⋊Q811yescharacteristic
521C22×C23#52911yescharacteristic
522C22×C23#52911yescharacteristic
523C22×C23#53411yescharacteristic
524C22×C23#53511yescharacteristic
525C22×C23#53811yescharacteristic
526C22×C23#53811yescharacteristic
527C22×C23#53811yescharacteristic
528C22×C23#53811yescharacteristic
529C22×C23#53811yescharacteristic
530C22×C23#53811yescharacteristic
531C22×C23#53811yescharacteristic
532C22×C23#53811yescharacteristic
533C22×C23#54011yescharacteristic
534C22×C23#54011yescharacteristic
535C22×C23#54011yescharacteristic
536C22×C23#54011yescharacteristic
537C22×C23#54311yescharacteristic
538C22×C23#54311yescharacteristic
539C22×C23#54611yescharacteristic
540C22×C23#54611yescharacteristic
541C22×C23#54611yescharacteristic
542C22×C23#54611yescharacteristic
543C22×C23#55111yescharacteristic
544C22×C23#55311yescharacteristic
545C22×C23#55311yescharacteristic
546C22×C23#55411yescharacteristic
547C22×C23#55411yescharacteristic
548C22×C23#55411yescharacteristic
549C22×C23#55411yescharacteristic
550C22×C23#55511yescharacteristic
551C22×C23#56011yescharacteristic
552C22×C23#56011yescharacteristic
553C22×C23#56011yescharacteristic
554C22×C23#56011yescharacteristic
555C4×C23—42no—
556C4×C23—42no—
557C4×C23—42no—
558C4×C23—42no—
559C4×C23—42no—
560C4×C23—42no—
561C4×C23—42no—
562C4×C23—81no—
563C4×C23—81no—
564C4×C23—81no—
565C4×C23—81no—
566C4×C23—81no—
567C4×C23—81no—
568C23×D4C22×C2311yescharacteristic
569C24×C4C22×C2311yescharacteristic
570C22×C4⋊C4C22×C2311yescharacteristic
571C22×C4⋊C4C22×C2311yescharacteristic
572C22×C4⋊C4C22×C2311yescharacteristic
573C22×C4⋊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×C22⋊C4C22×C2311yescharacteristic
584C22×C22⋊C4C22×C2311yescharacteristic
585#396—24no—
586#386—24no—
587C2×#95C22×C2311yescharacteristic
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×#95C22×C2311yescharacteristic
605C2×C23—44no—
606C2×C23—82no—
607C2×C23#245011yescharacteristic
608C2×C23#245011yescharacteristic
609C2×C23#251811yescharacteristic
610C2×C23#262611yescharacteristic
611C2×C23#264811yescharacteristic
612C2×C23#264811yescharacteristic
613C2×C23#268511yescharacteristic
614C2×C23#268811yescharacteristic
615C2×C23#269911yescharacteristic
616C2×C23#270311yescharacteristic
617C2×C23#274811yescharacteristic
618C2×C23#278011yescharacteristic
619C2×C23#278011yescharacteristic
620C2×C23#278411yescharacteristic
621C2×C23#282511yescharacteristic
622C25C23×C2311yescharacteristic
623C25C23×C2311yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4Q8×C2314yes—
631C23×C4—22no—
632C23×C4—22no—
633C23×C4—22no—
634C23×C4—41no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4C23×C2311yescharacteristic
639C23×C4C23×C2311yescharacteristic
640C23×C4C23×C2311yescharacteristic
641C23×C4C23×C2311yescharacteristic
642C23×C4C23×C2311yescharacteristic
643C23×C4C23×C2311yescharacteristic
644C23×C4C23×C2311yescharacteristic
645C23×C4C23×C2311yescharacteristic
646C23×C4C23×C2311yescharacteristic
647C23×C4C23×C2311yescharacteristic
648C23×C4C23×C2311yescharacteristic
649C23×C4C23×C2311yescharacteristic
650C23×C4C23×C2311yescharacteristic
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
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—41no—
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⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4D4×C2314yes—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714C23#1647611yescharacteristic, direct product factor, Sylow
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—
741C24C2×D4×C2312yes—
742C24C2×Q8×C2312yes—
743C24C2×Q8×C2312yes—
744C24#41×C2312yes—
745C24C24×C2311yescharacteristic
746C2×D4—28no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
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×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4C2×D4×C2312yes—
845C22×C4C2×D4×C2312yes—
846C22×C4C2×Q8×C2312yes—
847C22×C4#41×C2312yes—
848C22×C4#41×C2312yes—
849C22×C4#41×C2312yes—
850C22×C4#41×C2312yes—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
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—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23C23×C22⋊Q814yes—
936C23C22×D4×C2311yescharacteristic
937C23C22×Q8×C2311yescharacteristic
938C23C2×#41×C2311yescharacteristic
939C23C2×#41×C2311yescharacteristic
940C23C2×#41×C2311yescharacteristic
941C23C2×#41×C2311yescharacteristic
942C23C2×#41×C2311yescharacteristic
943C23C23×H(5,𝔽2)11yescharacteristic
944C23C23×H(5,𝔽2)11yescharacteristic
945C23C23×H(5,𝔽2)11yescharacteristic
946C23C23×H(5,𝔽2)11yescharacteristic
947C23C23×H(5,𝔽2)11yescharacteristic
948C23C23×H(5,𝔽2)11yescharacteristic
949C23C23×H(5,𝔽2)11yescharacteristic
950C23C23×H(5,𝔽2)11yescharacteristic
951D4—416no—
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—416no—
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—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22C2×C23×C22⋊Q811yescharacteristic
1075C22C23×#52911yescharacteristic
1076C22C23×#52911yescharacteristic
1077C22C23×#53411yescharacteristic
1078C22C23×#53511yescharacteristic
1079C22C23×#53811yescharacteristic
1080C22C23×#53811yescharacteristic
1081C22C23×#53811yescharacteristic
1082C22C23×#53811yescharacteristic
1083C22C23×#53811yescharacteristic
1084C22C23×#53811yescharacteristic
1085C22C23×#53811yescharacteristic
1086C22C23×#53811yescharacteristic
1087C22C23×#54011yescharacteristic
1088C22C23×#54011yescharacteristic
1089C22C23×#54011yescharacteristic
1090C22C23×#54011yescharacteristic
1091C22C23×#54311yescharacteristic
1092C22C23×#54311yescharacteristic
1093C22C23×#54611yescharacteristic
1094C22C23×#54611yescharacteristic
1095C22C23×#54611yescharacteristic
1096C22C23×#54611yescharacteristic
1097C22C23×#55111yescharacteristic
1098C22C23×#55311yescharacteristic
1099C22C23×#55311yescharacteristic
1100C22C23×#55411yescharacteristic
1101C22C23×#55411yescharacteristic
1102C22C23×#55411yescharacteristic
1103C22C23×#55411yescharacteristic
1104C22C23×#55511yescharacteristic
1105C22C23×#56011yescharacteristic
1106C22C23×#56011yescharacteristic
1107C22C23×#56011yescharacteristic
1108C22C23×#56011yescharacteristic
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C2—44no—
1123C2—82no—
1124C2C23×#245011yescharacteristic
1125C2C23×#245011yescharacteristic
1126C2C23×#251811yescharacteristic
1127C2C23×#262611yescharacteristic
1128C2C23×#264811yescharacteristic
1129C2C23×#264811yescharacteristic
1130C2C23×#268511yescharacteristic
1131C2C23×#268811yescharacteristic
1132C2C23×#269911yescharacteristic
1133C2C23×#270311yescharacteristic
1134C2C23×#274811yescharacteristic
1135C2C23×#278011yescharacteristic
1136C2C23×#278011yescharacteristic
1137C2C23×#278411yescharacteristic
1138C2C23×#282511yescharacteristic
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
3. C23×#1445C2semidirect
4. C23×#1443C2semidirect
5. C23×#1442C2semidirect
6. C23×#1441C2semidirect
7. C23×#1439C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
14. C23×C22⋊#95C2semidirect
15. C23×C22⋊#95C2semidirect
296. #16476C23direct (N × H)
475. C2×#396C2×C23semidirect
477. #1445C2×C23semidirect
478. #1443C2×C23semidirect
479. #1442C2×C23semidirect
480. #1441C2×C23semidirect
481. #1439C2×C23semidirect
482. #1439C2×C23semidirect
483. #1439C2×C23semidirect
484. #1439C2×C23semidirect
485. #1439C2×C23semidirect
488. C22⋊#95C2×C23semidirect
489. C22⋊#95C2×C23semidirect
714. C23#16476direct (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×#3862
C23×#14452
C23×#14432
C23×#14422
C23×#14412
C23×#14392
C23×#14382
C23×C22⋊#952
#1647623