Finite Group Databasebeta

← C23×#14645 #19162271

Subgroups — C23×#14645 #19162271

Order 5888.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C23×#1445C211yesmaximal, characteristic, complemented
3C23×#1443C211yesmaximal, characteristic, complemented
4C23×#1441C211yesmaximal, characteristic, complemented
5C23×#1440C211yesmaximal, characteristic, complemented
6C23×#1440C211yesmaximal, characteristic, complemented
7C23×#1439C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic
12C23×#1438C211yesmaximal, characteristic
13C23×#1437C211yesmaximal, characteristic, complemented
14C23×#1437C211yesmaximal, 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×#394C418yescomplemented
34C2×C23×#95C2211yescharacteristic
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
52C25×C23C2311yescharacteristic
53C25×C23C2311yescharacteristic
54C22×D4×C23—41no—
55C22×D4×C23—41no—
56C22×D4×C23—41no—
57C22×D4×C23—41no—
58C22×D4×C23—41no—
59C22×D4×C23—41no—
60C22×D4×C23C2×C414yes—
61C23×C4×C23C2311yescharacteristic
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
74C2×C4⋊C4×C23—22no—
75C2×C4⋊C4×C23—41no—
76C2×C4⋊C4×C23—41no—
77C2×C4⋊C4×C23—41no—
78C2×C4⋊C4×C23—41no—
79C2×C4⋊C4×C23—41no—
80C2×C4⋊C4×C23—41no—
81C2×C4⋊C4×C23—41no—
82C2×C4⋊C4×C23C2×C414yes—
83C2×C22⋊C4×C23—22no—
84C2×C22⋊C4×C23—22no—
85C2×C22⋊C4×C23—22no—
86C2×C22⋊C4×C23—22no—
87C2×C22⋊C4×C23—41no—
88C2×C22⋊C4×C23—41no—
89C2×C22⋊C4×C23—41no—
90C2×C22⋊C4×C23—41no—
91C2×C22⋊C4×C23—41no—
92C2×C22⋊C4×C23—41no—
93C2×C22⋊C4×C23—41no—
94C2×C22⋊C4×C23—41no—
95C2×C22⋊C4×C23—41no—
96C2×C22⋊C4×C23—41no—
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×C23C2×C414yes—
116C2×C22⋊C4×C23C2×C414yes—
117C2×C22⋊C4×C23C2×C414yes—
118C2×C22⋊C4×C23C2×C414yes—
119C2×C42×C23—41no—
120C2×C42×C23—41no—
121C2×C42×C23—41no—
122C23×#95—22no—
123C23×#95—41no—
124C23×#95—41no—
125C23×#95—41no—
126C23×#95—41no—
127C23×#95—41no—
128C23×#95—41no—
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×#95C2×C414yes—
140C24×C23—21no—
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×C23C22×C412yes—
169C24×C23C22×C412yes—
170C24×C23C2411yescharacteristic
171C2×D4×C23—44no—
172C2×D4×C23—44no—
173C2×D4×C23—44no—
174C2×D4×C23—44no—
175C2×D4×C23—44no—
176C2×D4×C23—44no—
177C2×D4×C23—44no—
178C22×C4×C23—21no—
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×C23C22×C412yes—
263C22×C4×C23C22×C412yes—
264C22×C4×C23C22×C412yes—
265C22×C4×C23C22×C412yes—
266C22×C4×C23C22×C412yes—
267C22×C4×C23#4112yes—
268C22×C4×C23#4112yes—
269C4⋊C4×C23—44no—
270C4⋊C4×C23—44no—
271C4⋊C4×C23—44no—
272C22⋊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—
284C42×C23—44no—
285#14645C2311yesmaximal, characteristic, direct product factor, Sylow
286C23×C23—22no—
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—41no—
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×C23C23×C411yescharacteristic
357C23×C23C2×#4111yescharacteristic
358C23×C23C2×#4111yescharacteristic
359C23×C23H(5,𝔽2)11yescharacteristic
360C23×C23H(5,𝔽2)11yescharacteristic
361C23×C23H(5,𝔽2)11yescharacteristic
362C23×C23H(5,𝔽2)11yescharacteristic
363C23×C23H(5,𝔽2)11yescharacteristic
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×C232−1+411yescharacteristic
370C23×C232−1+411yescharacteristic
371D4×C23—416no—
372C2×C4×C23—22no—
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—22no—
392C2×C4×C23—22no—
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×#394C2×C2311yescharacteristic
464#1445C2×C2311yescharacteristic, complemented
465#1443C2×C2311yescharacteristic, complemented
466#1441C2×C2311yescharacteristic, complemented
467#1440C2×C2311yescharacteristic, complemented
468#1440C2×C2311yescharacteristic, complemented
469#1439C2×C2311yescharacteristic, complemented
470#1439C2×C2311yescharacteristic, complemented
471#1439C2×C2311yescharacteristic, complemented
472#1439C2×C2311yescharacteristic, complemented
473#1438C2×C2311yescharacteristic
474#1438C2×C2311yescharacteristic
475#1437C2×C2311yescharacteristic, complemented
476#1437C2×C2311yescharacteristic, complemented
477#1436C2×C2311yescharacteristic, complemented
478C22×C23—42no—
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—81no—
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×C23C4×#4111yescharacteristic
509C22×C23#51811yescharacteristic
510C22×C23#51811yescharacteristic
511C22×C23#51811yescharacteristic
512C22×C23#51811yescharacteristic
513C22×C23#52011yescharacteristic
514C22×C23#52011yescharacteristic
515C22×C23#53811yescharacteristic
516C22×C23#53811yescharacteristic
517C22×C23#53811yescharacteristic
518C22×C23#53811yescharacteristic
519C22×C23#53811yescharacteristic
520C22×C23#53911yescharacteristic
521C22×C23#54011yescharacteristic
522C22×C23#54011yescharacteristic
523C22×C23#54011yescharacteristic
524C22×C23#54211yescharacteristic
525C22×C23#54211yescharacteristic
526C22×C23#54211yescharacteristic
527C22×C23#56011yescharacteristic
528C22×C23#56011yescharacteristic
529C22×C23#56011yescharacteristic
530C22×C23#56011yescharacteristic
531C22×C23#56011yescharacteristic
532C22×C23#56011yescharacteristic
533C22×C23#56011yescharacteristic
534C22×C23#56011yescharacteristic
535C22×C23H(3,𝔽4)11yescharacteristic
536C22×C23#56211yescharacteristic
537C22×C23#56211yescharacteristic
538C22×C23#56211yescharacteristic
539C22×C23#56211yescharacteristic
540C22×C23#56211yescharacteristic
541C22×C23#56211yescharacteristic
542C22×C23#56311yescharacteristic
543C4×C23—42no—
544C4×C23—42no—
545C4×C23—42no—
546C4×C23—42no—
547C4×C23—42no—
548C4×C23—42no—
549C4×C23—42no—
550C4×C23—81no—
551C4×C23—81no—
552C4×C23—81no—
553C4×C23—81no—
554C4×C23—81no—
555C4×C23—81no—
556C23×D4C22×C2311yescharacteristic
557C22×C4⋊C4C22×C2311yescharacteristic
558C22×C4⋊C4C22×C2311yescharacteristic
559C22×C4⋊C4C22×C2311yescharacteristic
560C22×C22⋊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×C42C22×C2311yescharacteristic
573#394C4×C2318yescomplemented
574C2×#95C22×C2311yescharacteristic
575C2×#95C22×C2311yescharacteristic
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×C23—82no—
593C2×C23—82no—
594C2×C23#233311yescharacteristic
595C2×C23#233511yescharacteristic
596C2×C23#233711yescharacteristic
597C2×C23#237511yescharacteristic
598C2×C23#237611yescharacteristic
599C2×C23#237711yescharacteristic
600C2×C23#237711yescharacteristic
601C2×C23#282511yescharacteristic
602C2×C23#282611yescharacteristic
603C2×C23#282811yescharacteristic
604C2×C23#282911yescharacteristic
605C2×C23#282911yescharacteristic
606C2×C23#282911yescharacteristic
607C2×C23#283211yescharacteristic
608C2×C23#283711yescharacteristic
609C25C23×C2311yescharacteristic
610C25C23×C2311yescharacteristic
611C22×D4—41no—
612C22×D4—41no—
613C22×D4—41no—
614C22×D4—41no—
615C22×D4—41no—
616C22×D4—41no—
617C22×D4C2×C4×C2314yes—
618C23×C4C23×C2311yescharacteristic
619C23×C4C23×C2311yescharacteristic
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
631C2×C4⋊C4—22no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4C2×C4×C2314yes—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
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⋊C4C2×C4×C2314yes—
673C2×C22⋊C4C2×C4×C2314yes—
674C2×C22⋊C4C2×C4×C2314yes—
675C2×C22⋊C4C2×C4×C2314yes—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42—41no—
679#95—22no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
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#95C2×C4×C2314yes—
697C23#1464511yescharacteristic, direct product factor, Sylow
698C24—21no—
699C24—21no—
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—
726C24C22×C4×C2312yes—
727C24C22×C4×C2312yes—
728C24C24×C2311yescharacteristic
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C22×C4—21no—
737C22×C4—21no—
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×C4C22×C4×C2312yes—
821C22×C4C22×C4×C2312yes—
822C22×C4C22×C4×C2312yes—
823C22×C4C22×C4×C2312yes—
824C22×C4C22×C4×C2312yes—
825C22×C4#41×C2312yes—
826C22×C4#41×C2312yes—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C22⋊C4—44no—
831C22⋊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—
842C42—44no—
843C23—22no—
844C23—22no—
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—41no—
858C23—41no—
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—
913C23C23×C4×C2311yescharacteristic
914C23C2×#41×C2311yescharacteristic
915C23C2×#41×C2311yescharacteristic
916C23C23×H(5,𝔽2)11yescharacteristic
917C23C23×H(5,𝔽2)11yescharacteristic
918C23C23×H(5,𝔽2)11yescharacteristic
919C23C23×H(5,𝔽2)11yescharacteristic
920C23C23×H(5,𝔽2)11yescharacteristic
921C23C23×H(5,𝔽2)11yescharacteristic
922C23C23×H(5,𝔽2)11yescharacteristic
923C23C23×H(5,𝔽2)11yescharacteristic
924C23C23×H(5,𝔽2)11yescharacteristic
925C23C23×H(5,𝔽2)11yescharacteristic
926C23C23×2−1+411yescharacteristic
927C23C23×2−1+411yescharacteristic
928D4—416no—
929C2×C4—22no—
930C2×C4—22no—
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—22no—
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—
1020C22—42no—
1021C22—42no—
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—81no—
1035C22—81no—
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—
1050C22C4×#41×C2311yescharacteristic
1051C22C23×#51811yescharacteristic
1052C22C23×#51811yescharacteristic
1053C22C23×#51811yescharacteristic
1054C22C23×#51811yescharacteristic
1055C22C23×#52011yescharacteristic
1056C22C23×#52011yescharacteristic
1057C22C23×#53811yescharacteristic
1058C22C23×#53811yescharacteristic
1059C22C23×#53811yescharacteristic
1060C22C23×#53811yescharacteristic
1061C22C23×#53811yescharacteristic
1062C22C23×#53911yescharacteristic
1063C22C23×#54011yescharacteristic
1064C22C23×#54011yescharacteristic
1065C22C23×#54011yescharacteristic
1066C22C23×#54211yescharacteristic
1067C22C23×#54211yescharacteristic
1068C22C23×#54211yescharacteristic
1069C22C23×#56011yescharacteristic
1070C22C23×#56011yescharacteristic
1071C22C23×#56011yescharacteristic
1072C22C23×#56011yescharacteristic
1073C22C23×#56011yescharacteristic
1074C22C23×#56011yescharacteristic
1075C22C23×#56011yescharacteristic
1076C22C23×#56011yescharacteristic
1077C22C23×H(3,𝔽4)11yescharacteristic
1078C22C23×#56211yescharacteristic
1079C22C23×#56211yescharacteristic
1080C22C23×#56211yescharacteristic
1081C22C23×#56211yescharacteristic
1082C22C23×#56211yescharacteristic
1083C22C23×#56211yescharacteristic
1084C22C23×#56311yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C2—82no—
1099C2—82no—
1100C2C23×#233311yescharacteristic
1101C2C23×#233511yescharacteristic
1102C2C23×#233711yescharacteristic
1103C2C23×#237511yescharacteristic
1104C2C23×#237611yescharacteristic
1105C2C23×#237711yescharacteristic
1106C2C23×#237711yescharacteristic
1107C2C23×#282511yescharacteristic
1108C2C23×#282611yescharacteristic
1109C2C23×#282811yescharacteristic
1110C2C23×#282911yescharacteristic
1111C2C23×#282911yescharacteristic
1112C2C23×#282911yescharacteristic
1113C2C23×#283211yescharacteristic
1114C2C23×#283711yescharacteristic
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
2. C23×#1445C2semidirect
3. C23×#1443C2semidirect
4. C23×#1441C2semidirect
5. C23×#1440C2semidirect
6. C23×#1440C2semidirect
7. C23×#1439C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
13. C23×#1437C2semidirect
14. C23×#1437C2semidirect
15. C23×#1436C2semidirect
33. C23×#394C4semidirect
285. #14645C23direct (N × H)
464. #1445C2×C23semidirect
465. #1443C2×C23semidirect
466. #1441C2×C23semidirect
467. #1440C2×C23semidirect
468. #1440C2×C23semidirect
469. #1439C2×C23semidirect
470. #1439C2×C23semidirect
471. #1439C2×C23semidirect
472. #1439C2×C23semidirect
475. #1437C2×C23semidirect
476. #1437C2×C23semidirect
477. #1436C2×C23semidirect
573. #394C4×C23semidirect
697. C23#14645direct (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
C23×#14452
C23×#14432
C23×#14412
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
#1464523