Finite Group Databasebeta

← C23×#14568 #19162194

Subgroups — C23×#14568 #19162194

Order 5888.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C2×C23×#390C211yesmaximal, characteristic
3C2×C23×#387C211yesmaximal, characteristic, complemented
4C23×#1440C211yesmaximal, characteristic, complemented
5C23×#1440C211yesmaximal, characteristic, complemented
6C23×#1439C211yesmaximal, characteristic, complemented
7C23×#1439C211yesmaximal, characteristic, complemented
8C23×#1438C211yesmaximal, characteristic
9C23×#1437C211yesmaximal, characteristic, complemented
10C23×#1437C211yesmaximal, characteristic, complemented
11C23×#1437C211yesmaximal, characteristic, complemented
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
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
33C22×C42×C23C2211yescharacteristic
34C22×C42×C23C2211yescharacteristic
35C23×#394C418yescomplemented
36C23×#390—24no—
37C23×#387—24no—
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
53C2×C23×#95C2211yescharacteristic
54C25×C23C2311yescharacteristic
55C25×C23C2311yescharacteristic
56C22×D4×C23—22no—
57C22×D4×C23—22no—
58C22×D4×C23—41no—
59C22×D4×C23—41no—
60C22×D4×C23—41no—
61C22×D4×C23—41no—
62C22×D4×C23C2×C414yes—
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
75C23×C4×C23C2311yescharacteristic
76C2×C4⋊C4×C23—22no—
77C2×C4⋊C4×C23—22no—
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—41no—
80C2×C4⋊C4×C23—41no—
81C2×C4⋊C4×C23—41no—
82C2×C4⋊C4×C23—41no—
83C2×C4⋊C4×C23C2×C414yes—
84C2×C4⋊C4×C23D414yes—
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—41no—
98C2×C22⋊C4×C23—41no—
99C2×C22⋊C4×C23—41no—
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×C23C2×C414yes—
118C2×C22⋊C4×C23C2×C414yes—
119C2×C22⋊C4×C23C2×C414yes—
120C2×C22⋊C4×C23C2×C414yes—
121C2×C42×C23—22no—
122C2×C42×C23—22no—
123C2×C42×C23—41no—
124C2×C42×C23—41no—
125C2×C42×C23—41no—
126C2×C42×C23—41no—
127C2×C42×C23—41no—
128C2×C42×C23—41no—
129C2×C42×C23—41no—
130C23×#95—22no—
131C23×#95—22no—
132C23×#95—22no—
133C23×#95—22no—
134C23×#95—22no—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—41no—
139C23×#95—41no—
140C23×#95—41no—
141C23×#95—41no—
142C23×#95—41no—
143C23×#95—41no—
144C23×#95—41no—
145C23×#95C2×C414yes—
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×C23—21no—
172C24×C23—21no—
173C24×C23—21no—
174C24×C23C22×C412yes—
175C24×C23C22×C412yes—
176C24×C23C2411yescharacteristic
177C2×D4×C23—28no—
178C2×D4×C23—44no—
179C2×D4×C23—44no—
180C2×D4×C23—44no—
181C2×D4×C23—44no—
182C2×D4×C23—44no—
183C2×D4×C23—44no—
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×C23C22×C412yes—
263C22×C4×C23C22×C412yes—
264C22×C4×C23C22×C412yes—
265C22×C4×C23C22×C412yes—
266C22×C4×C23C22×C412yes—
267C22×C4×C23C2×D412yes—
268C22×C4×C23C2×D412yes—
269C22×C4×C23C2×D412yes—
270C22×C4×C23#4112yes—
271C22×C4×C23#4112yes—
272C22×C4×C23#4112yes—
273C22×C4×C23#4112yes—
274C22×C4×C23#4112yes—
275C4⋊C4×C23—28no—
276C4⋊C4×C23—44no—
277C4⋊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—
285C22⋊C4×C23—44no—
286C22⋊C4×C23—44no—
287C22⋊C4×C23—44no—
288C22⋊C4×C23—44no—
289C22⋊C4×C23—44no—
290C42×C23—44no—
291C42×C23—44no—
292C42×C23—44no—
293#14568C2311yesmaximal, characteristic, direct product factor, Sylow
294C23×C23—22no—
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—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×C23—41no—
358C23×C23—41no—
359C23×C23—41no—
360C23×C23—41no—
361C23×C23—41no—
362C23×C23—41no—
363C23×C23—41no—
364C23×C23C23×C411yescharacteristic
365C23×C23C22×D411yescharacteristic
366C23×C23C2×#4111yescharacteristic
367C23×C23C2×#4111yescharacteristic
368C23×C23C2×#4111yescharacteristic
369C23×C23C2×#4111yescharacteristic
370C23×C23C2×#4111yescharacteristic
371C23×C23H(5,𝔽2)11yescharacteristic
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
379D4×C23—416no—
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—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—22no—
409C2×C4×C23—22no—
410C2×C4×C23—22no—
411C2×C4×C23—22no—
412C2×C4×C23—22no—
413C2×C4×C23—22no—
414C2×C4×C23—22no—
415C2×C4×C23—22no—
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×C23C4×D414yes—
471C2×#394C2×C2311yescharacteristic
472C2×#390C2×C2311yescharacteristic
473C2×#387C2×C2311yescharacteristic, complemented
474#1440C2×C2311yescharacteristic, complemented
475#1440C2×C2311yescharacteristic, complemented
476#1439C2×C2311yescharacteristic, complemented
477#1439C2×C2311yescharacteristic, complemented
478#1438C2×C2311yescharacteristic
479#1437C2×C2311yescharacteristic, complemented
480#1437C2×C2311yescharacteristic, complemented
481#1437C2×C2311yescharacteristic, complemented
482#1437C2×C2311yescharacteristic, complemented
483#1436C2×C2311yescharacteristic, complemented
484#1436C2×C2311yescharacteristic, complemented
485#1436C2×C2311yescharacteristic, complemented
486C22×C23—42no—
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—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×C23—81no—
510C22×C23—81no—
511C22×C23—81no—
512C22×C23—81no—
513C22×C23—81no—
514C22×C23—81no—
515C22×C23—81no—
516C22×C23C2×C4×D411yescharacteristic
517C22×C23C4×#4111yescharacteristic
518C22×C23C4×#4111yescharacteristic
519C22×C23#51811yescharacteristic
520C22×C23#51811yescharacteristic
521C22×C23#51811yescharacteristic
522C22×C23#52011yescharacteristic
523C22×C23#53411yescharacteristic
524C22×C23#53511yescharacteristic
525C22×C23#53811yescharacteristic
526C22×C23#53811yescharacteristic
527C22×C23#53811yescharacteristic
528C22×C23#53811yescharacteristic
529C22×C23#53811yescharacteristic
530C22×C23#53911yescharacteristic
531C22×C23#54011yescharacteristic
532C22×C23#54011yescharacteristic
533C22×C23#54011yescharacteristic
534C22×C23#54211yescharacteristic
535C22×C23#54611yescharacteristic
536C22×C23#54611yescharacteristic
537C22×C23#54811yescharacteristic
538C22×C23#55011yescharacteristic
539C22×C23#55111yescharacteristic
540C22×C23#55311yescharacteristic
541C22×C23#55311yescharacteristic
542C22×C23#55311yescharacteristic
543C22×C23#55511yescharacteristic
544C22×C23#55611yescharacteristic
545C22×C23#55911yescharacteristic
546C22×C23#55911yescharacteristic
547C22×C23#56011yescharacteristic
548C22×C23#56011yescharacteristic
549C22×C23#56211yescharacteristic
550C22×C23#56211yescharacteristic
551C4×C23—24no—
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—42no—
562C4×C23—81no—
563C4×C23—81no—
564C23×D4C22×C2311yescharacteristic
565C22×C4⋊C4C22×C2311yescharacteristic
566C22×C4⋊C4C22×C2311yescharacteristic
567C22×C4⋊C4C22×C2311yescharacteristic
568C22×C22⋊C4C22×C2311yescharacteristic
569C22×C22⋊C4C22×C2311yescharacteristic
570C22×C22⋊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×C42C22×C2311yescharacteristic
581C22×C42C22×C2311yescharacteristic
582C22×C42C22×C2311yescharacteristic
583#394C4×C2318yescomplemented
584#390—24no—
585#387—24no—
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×#95C22×C2311yescharacteristic
595C2×#95C22×C2311yescharacteristic
596C2×#95C22×C2311yescharacteristic
597C2×#95C22×C2311yescharacteristic
598C2×#95C22×C2311yescharacteristic
599C2×#95C22×C2311yescharacteristic
600C2×#95C22×C2311yescharacteristic
601C2×#95C22×C2311yescharacteristic
602C2×C23—82no—
603C2×C23—82no—
604C2×C23#232111yescharacteristic
605C2×C23#233311yescharacteristic
606C2×C23#233511yescharacteristic
607C2×C23#236311yescharacteristic
608C2×C23#236711yescharacteristic
609C2×C23#237411yescharacteristic
610C2×C23#237711yescharacteristic
611C2×C23#270911yescharacteristic
612C2×C23#271111yescharacteristic
613C2×C23#271411yescharacteristic
614C2×C23#273011yescharacteristic
615C2×C23#279711yescharacteristic
616C2×C23#280011yescharacteristic
617C2×C23#280311yescharacteristic
618C2×C23#280811yescharacteristic
619C25C23×C2311yescharacteristic
620C25C23×C2311yescharacteristic
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4—41no—
626C22×D4—41no—
627C22×D4C2×C4×C2314yes—
628C23×C4C23×C2311yescharacteristic
629C23×C4C23×C2311yescharacteristic
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
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4C2×C4×C2314yes—
649C2×C4⋊C4D4×C2314yes—
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—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
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×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4C2×C4×C2314yes—
683C2×C22⋊C4C2×C4×C2314yes—
684C2×C22⋊C4C2×C4×C2314yes—
685C2×C22⋊C4C2×C4×C2314yes—
686C2×C42—22no—
687C2×C42—22no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42—41no—
695#95—22no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95C2×C4×C2314yes—
711C23#1456811yescharacteristic, direct product factor, Sylow
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—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24C22×C4×C2312yes—
741C24C22×C4×C2312yes—
742C24C24×C2311yescharacteristic
743C2×D4—28no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
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×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4C22×C4×C2312yes—
829C22×C4C22×C4×C2312yes—
830C22×C4C22×C4×C2312yes—
831C22×C4C22×C4×C2312yes—
832C22×C4C22×C4×C2312yes—
833C22×C4C2×D4×C2312yes—
834C22×C4C2×D4×C2312yes—
835C22×C4C2×D4×C2312yes—
836C22×C4#41×C2312yes—
837C22×C4#41×C2312yes—
838C22×C4#41×C2312yes—
839C22×C4#41×C2312yes—
840C22×C4#41×C2312yes—
841C4⋊C4—28no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C42—44no—
857C42—44no—
858C42—44no—
859C23—22no—
860C23—22no—
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—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—
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—
929C23C23×C4×C2311yescharacteristic
930C23C22×D4×C2311yescharacteristic
931C23C2×#41×C2311yescharacteristic
932C23C2×#41×C2311yescharacteristic
933C23C2×#41×C2311yescharacteristic
934C23C2×#41×C2311yescharacteristic
935C23C2×#41×C2311yescharacteristic
936C23C23×H(5,𝔽2)11yescharacteristic
937C23C23×H(5,𝔽2)11yescharacteristic
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
943C23C23×2−1+411yescharacteristic
944D4—416no—
945C2×C4—22no—
946C2×C4—22no—
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—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
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×C4C4×D4×C2314yes—
1036C22—42no—
1037C22—42no—
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—81no—
1051C22—81no—
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—
1066C22C2×C4×D4×C2311yescharacteristic
1067C22C4×#41×C2311yescharacteristic
1068C22C4×#41×C2311yescharacteristic
1069C22C23×#51811yescharacteristic
1070C22C23×#51811yescharacteristic
1071C22C23×#51811yescharacteristic
1072C22C23×#52011yescharacteristic
1073C22C23×#53411yescharacteristic
1074C22C23×#53511yescharacteristic
1075C22C23×#53811yescharacteristic
1076C22C23×#53811yescharacteristic
1077C22C23×#53811yescharacteristic
1078C22C23×#53811yescharacteristic
1079C22C23×#53811yescharacteristic
1080C22C23×#53911yescharacteristic
1081C22C23×#54011yescharacteristic
1082C22C23×#54011yescharacteristic
1083C22C23×#54011yescharacteristic
1084C22C23×#54211yescharacteristic
1085C22C23×#54611yescharacteristic
1086C22C23×#54611yescharacteristic
1087C22C23×#54811yescharacteristic
1088C22C23×#55011yescharacteristic
1089C22C23×#55111yescharacteristic
1090C22C23×#55311yescharacteristic
1091C22C23×#55311yescharacteristic
1092C22C23×#55311yescharacteristic
1093C22C23×#55511yescharacteristic
1094C22C23×#55611yescharacteristic
1095C22C23×#55911yescharacteristic
1096C22C23×#55911yescharacteristic
1097C22C23×#56011yescharacteristic
1098C22C23×#56011yescharacteristic
1099C22C23×#56211yescharacteristic
1100C22C23×#56211yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—81no—
1113C4—81no—
1114C2—82no—
1115C2—82no—
1116C2C23×#232111yescharacteristic
1117C2C23×#233311yescharacteristic
1118C2C23×#233511yescharacteristic
1119C2C23×#236311yescharacteristic
1120C2C23×#236711yescharacteristic
1121C2C23×#237411yescharacteristic
1122C2C23×#237711yescharacteristic
1123C2C23×#270911yescharacteristic
1124C2C23×#271111yescharacteristic
1125C2C23×#271411yescharacteristic
1126C2C23×#273011yescharacteristic
1127C2C23×#279711yescharacteristic
1128C2C23×#280011yescharacteristic
1129C2C23×#280311yescharacteristic
1130C2C23×#280811yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C23×#387C2semidirect
4. C23×#1440C2semidirect
5. C23×#1440C2semidirect
6. C23×#1439C2semidirect
7. C23×#1439C2semidirect
9. C23×#1437C2semidirect
10. C23×#1437C2semidirect
11. C23×#1437C2semidirect
12. C23×#1437C2semidirect
13. C23×#1436C2semidirect
14. C23×#1436C2semidirect
15. C23×#1436C2semidirect
35. C23×#394C4semidirect
293. #14568C23direct (N × H)
473. C2×#387C2×C23semidirect
474. #1440C2×C23semidirect
475. #1440C2×C23semidirect
476. #1439C2×C23semidirect
477. #1439C2×C23semidirect
479. #1437C2×C23semidirect
480. #1437C2×C23semidirect
481. #1437C2×C23semidirect
482. #1437C2×C23semidirect
483. #1436C2×C23semidirect
484. #1436C2×C23semidirect
485. #1436C2×C23semidirect
583. #394C4×C23semidirect
711. C23#14568direct (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
C2×C23×#3872
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
#1456823