Finite Group Databasebeta

← C23×#16432 #19164058

Subgroups — C23×#16432 #19164058

Order 5888.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C2×C23×#386C211yesmaximal, characteristic
3C23×#1443C211yesmaximal, characteristic, complemented
4C23×#1442C211yesmaximal, characteristic, complemented
5C23×#1442C211yesmaximal, characteristic, complemented
6C23×#1442C211yesmaximal, characteristic, complemented
7C23×#1440C211yesmaximal, characteristic, complemented
8C23×#1440C211yesmaximal, characteristic, complemented
9C23×#1440C211yesmaximal, characteristic, complemented
10C23×#1440C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1439C211yesmaximal, characteristic, complemented
13C23×#1438C211yesmaximal, characteristic
14C23×C22⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×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
31C23×#394—24no—
32C23×#386—24no—
33C2×C23×#95C2211yescharacteristic
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
52C2×C23×#95C2211yescharacteristic
53C25×C23C2311yescharacteristic
54C25×C23C2311yescharacteristic
55C22×D4×C23—22no—
56C22×D4×C23—22no—
57C22×D4×C23—41no—
58C22×D4×C23—41no—
59C22×D4×C23—41no—
60C22×D4×C23—41no—
61C22×D4×C23D414yes—
62C23×C4×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—41no—
84C2×C4⋊C4×C23—41no—
85C2×C4⋊C4×C23—41no—
86C2×C4⋊C4×C23—41no—
87C2×C4⋊C4×C23—41no—
88C2×C22⋊C4×C23—22no—
89C2×C22⋊C4×C23—22no—
90C2×C22⋊C4×C23—22no—
91C2×C22⋊C4×C23—22no—
92C2×C22⋊C4×C23—22no—
93C2×C22⋊C4×C23—22no—
94C2×C22⋊C4×C23—22no—
95C2×C22⋊C4×C23—22no—
96C2×C22⋊C4×C23—22no—
97C2×C22⋊C4×C23—22no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
100C2×C22⋊C4×C23—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—41no—
106C2×C22⋊C4×C23—41no—
107C2×C22⋊C4×C23—41no—
108C2×C22⋊C4×C23—41no—
109C2×C22⋊C4×C23—41no—
110C2×C22⋊C4×C23—41no—
111C2×C22⋊C4×C23—41no—
112C2×C22⋊C4×C23—41no—
113C2×C22⋊C4×C23—41no—
114C2×C22⋊C4×C23—41no—
115C2×C22⋊C4×C23—41no—
116C2×C22⋊C4×C23—41no—
117C2×C22⋊C4×C23—41no—
118C2×C22⋊C4×C23—41no—
119C2×C22⋊C4×C23—41no—
120C2×C22⋊C4×C23—41no—
121C23×#95—22no—
122C23×#95—22no—
123C23×#95—22no—
124C23×#95—22no—
125C23×#95—22no—
126C23×#95—22no—
127C23×#95—22no—
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×#95—41no—
140C23×#95—41no—
141C24×C23—21no—
142C24×C23—21no—
143C24×C23—21no—
144C24×C23—21no—
145C24×C23—21no—
146C24×C23—21no—
147C24×C23—21no—
148C24×C23—21no—
149C24×C23—21no—
150C24×C23—21no—
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—21no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—21no—
161C24×C23—21no—
162C24×C23—21no—
163C24×C23—21no—
164C24×C23—21no—
165C24×C23—21no—
166C24×C23—21no—
167C24×C23C2×D412yes—
168C24×C23C2×D412yes—
169C24×C23#4112yes—
170C24×C23#4112yes—
171C24×C23C2411yescharacteristic
172C2×D4×C23—28no—
173C2×D4×C23—44no—
174C2×D4×C23—44no—
175C2×D4×C23—44no—
176C2×D4×C23—44no—
177C2×D4×C23—44no—
178C2×D4×C23—44no—
179C22×C4×C23—21no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—21no—
247C22×C4×C23—21no—
248C22×C4×C23—21no—
249C22×C4×C23—21no—
250C22×C4×C23—21no—
251C22×C4×C23—21no—
252C22×C4×C23—21no—
253C22×C4×C23—21no—
254C22×C4×C23—21no—
255C22×C4×C23—21no—
256C22×C4×C23—21no—
257C22×C4×C23—21no—
258C22×C4×C23—21no—
259C22×C4×C23—21no—
260C22×C4×C23—21no—
261C22×C4×C23—21no—
262C22×C4×C23—21no—
263C22×C4×C23—21no—
264C22×C4×C23—21no—
265C22×C4×C23—44no—
266C22×C4×C23—44no—
267C22×C4×C23—44no—
268C22×C4×C23—44no—
269C22×C4×C23—44no—
270C22×C4×C23—44no—
271C22×C4×C23—44no—
272C22×C4×C23C2×D412yes—
273C22×C4×C23#4112yes—
274C22×C4×C23#4112yes—
275C22×C4×C23#4112yes—
276C22×C4×C23#4112yes—
277C4⋊C4×C23—44no—
278C4⋊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—
290#16432C2311yesmaximal, characteristic, direct product factor, Sylow
291C23×C23—22no—
292C23×C23—22no—
293C23×C23—22no—
294C23×C23—22no—
295C23×C23—22no—
296C23×C23—22no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—22no—
300C23×C23—22no—
301C23×C23—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—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#12314yes—
361C23×C23C22×D411yescharacteristic
362C23×C23C2×#4111yescharacteristic
363C23×C23C2×#4111yescharacteristic
364C23×C23C2×#4111yescharacteristic
365C23×C23C2×#4111yescharacteristic
366C23×C23C2×#4111yescharacteristic
367C23×C23C2×#4111yescharacteristic
368C23×C23H(5,𝔽2)11yescharacteristic
369C23×C23H(5,𝔽2)11yescharacteristic
370C23×C23H(5,𝔽2)11yescharacteristic
371C23×C23H(5,𝔽2)11yescharacteristic
372C23×C23H(5,𝔽2)11yescharacteristic
373C23×C23H(5,𝔽2)11yescharacteristic
374C23×C23H(5,𝔽2)11yescharacteristic
375C23×C232−1+411yescharacteristic
376D4×C23—416no—
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—416no—
393C2×C4×C23—41no—
394C2×C4×C23—41no—
395C2×C4×C23—41no—
396C2×C4×C23—41no—
397C2×C4×C23—41no—
398C2×C4×C23—41no—
399C2×C4×C23—41no—
400C2×C4×C23—41no—
401C2×C4×C23—41no—
402C2×C4×C23—41no—
403C2×C4×C23—41no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—41no—
411C2×C4×C23—41no—
412C2×C4×C23—41no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23—41no—
421C2×C4×C23—41no—
422C2×C4×C23—41no—
423C2×C4×C23—41no—
424C2×C4×C23—41no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23—41no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—41no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23—41no—
435C2×C4×C23—41no—
436C2×C4×C23—41no—
437C2×C4×C23—41no—
438C2×C4×C23—41no—
439C2×C4×C23—41no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—41no—
443C2×C4×C23—41no—
444C2×C4×C23—41no—
445C2×C4×C23—41no—
446C2×C4×C23—41no—
447C2×C4×C23—41no—
448C2×C4×C23—41no—
449C2×C4×C23—41no—
450C2×C4×C23—41no—
451C2×C4×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—41no—
454C2×C4×C23—41no—
455C2×C4×C23—41no—
456C2×C4×C23—41no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—41no—
460C2×C4×C23—41no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23—41no—
464C2×C4×C23—41no—
465C2×C4×C23—41no—
466C2×C4×C23—41no—
467C2×C4×C23—41no—
468C2×C4×C23—41no—
469C2×#394C2×C2311yescharacteristic
470C2×#386C2×C2311yescharacteristic
471#1443C2×C2311yescharacteristic, complemented
472#1442C2×C2311yescharacteristic, complemented
473#1442C2×C2311yescharacteristic, complemented
474#1442C2×C2311yescharacteristic, complemented
475#1440C2×C2311yescharacteristic, complemented
476#1440C2×C2311yescharacteristic, complemented
477#1440C2×C2311yescharacteristic, complemented
478#1440C2×C2311yescharacteristic, complemented
479#1439C2×C2311yescharacteristic, complemented
480#1439C2×C2311yescharacteristic, complemented
481#1438C2×C2311yescharacteristic
482C22⋊#95C2×C2311yescharacteristic, complemented
483C22⋊#95C2×C2311yescharacteristic, complemented
484C22×C23—24no—
485C22×C23—24no—
486C22×C23—24no—
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—42no—
502C22×C23—42no—
503C22×C23—42no—
504C22×C23—42no—
505C22×C23—42no—
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×C23C2×#12311yescharacteristic
515C22×C23#52911yescharacteristic
516C22×C23#52911yescharacteristic
517C22×C23#53411yescharacteristic
518C22×C23#53411yescharacteristic
519C22×C23#53811yescharacteristic
520C22×C23#53811yescharacteristic
521C22×C23#53811yescharacteristic
522C22×C23#53811yescharacteristic
523C22×C23#53811yescharacteristic
524C22×C23#53811yescharacteristic
525C22×C23#53811yescharacteristic
526C22×C23#53811yescharacteristic
527C22×C23#53911yescharacteristic
528C22×C23#53911yescharacteristic
529C22×C23#54011yescharacteristic
530C22×C23#54011yescharacteristic
531C22×C23#54011yescharacteristic
532C22×C23#54211yescharacteristic
533C22×C23#54611yescharacteristic
534C22×C23#54611yescharacteristic
535C22×C23#54611yescharacteristic
536C22×C23#54711yescharacteristic
537C22×C23#55111yescharacteristic
538C22×C23#55111yescharacteristic
539C22×C23#55211yescharacteristic
540C22×C23#55311yescharacteristic
541C22×C23#55311yescharacteristic
542C22×C23#55311yescharacteristic
543C22×C23#55311yescharacteristic
544C22×C23#55511yescharacteristic
545C22×C23#56011yescharacteristic
546C22×C23H(3,𝔽4)11yescharacteristic
547C22×C23#56211yescharacteristic
548C22×C23#56211yescharacteristic
549C4×C23—42no—
550C4×C23—42no—
551C4×C23—42no—
552C4×C23—42no—
553C4×C23—42no—
554C4×C23—81no—
555C4×C23—81no—
556C4×C23—81no—
557C4×C23—81no—
558C4×C23—81no—
559C4×C23—81no—
560C4×C23—81no—
561C4×C23—81no—
562C23×D4C22×C2311yescharacteristic
563C24×C4C22×C2311yescharacteristic
564C22×C4⋊C4C22×C2311yescharacteristic
565C22×C4⋊C4C22×C2311yescharacteristic
566C22×C22⋊C4C22×C2311yescharacteristic
567C22×C22⋊C4C22×C2311yescharacteristic
568C22×C22⋊C4C22×C2311yescharacteristic
569C22×C22⋊C4C22×C2311yescharacteristic
570C22×C22⋊C4C22×C2311yescharacteristic
571C22×C22⋊C4C22×C2311yescharacteristic
572C22×C22⋊C4C22×C2311yescharacteristic
573C22×C22⋊C4C22×C2311yescharacteristic
574C22×C22⋊C4C22×C2311yescharacteristic
575C22×C22⋊C4C22×C2311yescharacteristic
576C22×C22⋊C4C22×C2311yescharacteristic
577#394—24no—
578#386—24no—
579C2×#95C22×C2311yescharacteristic
580C2×#95C22×C2311yescharacteristic
581C2×#95C22×C2311yescharacteristic
582C2×#95C22×C2311yescharacteristic
583C2×#95C22×C2311yescharacteristic
584C2×#95C22×C2311yescharacteristic
585C2×#95C22×C2311yescharacteristic
586C2×#95C22×C2311yescharacteristic
587C2×#95C22×C2311yescharacteristic
588C2×#95C22×C2311yescharacteristic
589C2×#95C22×C2311yescharacteristic
590C2×#95C22×C2311yescharacteristic
591C2×#95C22×C2311yescharacteristic
592C2×#95C22×C2311yescharacteristic
593C2×#95C22×C2311yescharacteristic
594C2×#95C22×C2311yescharacteristic
595C2×#95C22×C2311yescharacteristic
596C2×#95C22×C2311yescharacteristic
597C2×#95C22×C2311yescharacteristic
598C2×#95C22×C2311yescharacteristic
599C2×C23—44no—
600C2×C23—82no—
601C2×C23#241911yescharacteristic
602C2×C23#244411yescharacteristic
603C2×C23#251811yescharacteristic
604C2×C23#262211yescharacteristic
605C2×C23#264811yescharacteristic
606C2×C23#264911yescharacteristic
607C2×C23#268411yescharacteristic
608C2×C23#269911yescharacteristic
609C2×C23#270111yescharacteristic
610C2×C23#270811yescharacteristic
611C2×C23#274111yescharacteristic
612C2×C23#275311yescharacteristic
613C2×C23#277811yescharacteristic
614C2×C23#278111yescharacteristic
615C2×C23#282411yescharacteristic
616C25C23×C2311yescharacteristic
617C25C23×C2311yescharacteristic
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—41no—
621C22×D4—41no—
622C22×D4—41no—
623C22×D4—41no—
624C22×D4D4×C2314yes—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—41no—
629C23×C4—41no—
630C23×C4—41no—
631C23×C4—41no—
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
643C23×C4C23×C2311yescharacteristic
644C23×C4C23×C2311yescharacteristic
645C2×C4⋊C4—22no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
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—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
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⋊C4—41no—
683C2×C22⋊C4—41no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704C23#1643211yescharacteristic, direct product factor, Sylow
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24C2×D4×C2312yes—
732C24C2×D4×C2312yes—
733C24#41×C2312yes—
734C24#41×C2312yes—
735C24C24×C2311yescharacteristic
736C2×D4—28no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4C2×D4×C2312yes—
837C22×C4#41×C2312yes—
838C22×C4#41×C2312yes—
839C22×C4#41×C2312yes—
840C22×C4#41×C2312yes—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C22⋊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—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
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—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
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—
923C23C23×#12314yes—
924C23C22×D4×C2311yescharacteristic
925C23C2×#41×C2311yescharacteristic
926C23C2×#41×C2311yescharacteristic
927C23C2×#41×C2311yescharacteristic
928C23C2×#41×C2311yescharacteristic
929C23C2×#41×C2311yescharacteristic
930C23C2×#41×C2311yescharacteristic
931C23C23×H(5,𝔽2)11yescharacteristic
932C23C23×H(5,𝔽2)11yescharacteristic
933C23C23×H(5,𝔽2)11yescharacteristic
934C23C23×H(5,𝔽2)11yescharacteristic
935C23C23×H(5,𝔽2)11yescharacteristic
936C23C23×H(5,𝔽2)11yescharacteristic
937C23C23×H(5,𝔽2)11yescharacteristic
938C23C23×2−1+411yescharacteristic
939D4—416no—
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—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—416no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×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—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—42no—
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—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22C2×C23×#12311yescharacteristic
1063C22C23×#52911yescharacteristic
1064C22C23×#52911yescharacteristic
1065C22C23×#53411yescharacteristic
1066C22C23×#53411yescharacteristic
1067C22C23×#53811yescharacteristic
1068C22C23×#53811yescharacteristic
1069C22C23×#53811yescharacteristic
1070C22C23×#53811yescharacteristic
1071C22C23×#53811yescharacteristic
1072C22C23×#53811yescharacteristic
1073C22C23×#53811yescharacteristic
1074C22C23×#53811yescharacteristic
1075C22C23×#53911yescharacteristic
1076C22C23×#53911yescharacteristic
1077C22C23×#54011yescharacteristic
1078C22C23×#54011yescharacteristic
1079C22C23×#54011yescharacteristic
1080C22C23×#54211yescharacteristic
1081C22C23×#54611yescharacteristic
1082C22C23×#54611yescharacteristic
1083C22C23×#54611yescharacteristic
1084C22C23×#54711yescharacteristic
1085C22C23×#55111yescharacteristic
1086C22C23×#55111yescharacteristic
1087C22C23×#55211yescharacteristic
1088C22C23×#55311yescharacteristic
1089C22C23×#55311yescharacteristic
1090C22C23×#55311yescharacteristic
1091C22C23×#55311yescharacteristic
1092C22C23×#55511yescharacteristic
1093C22C23×#56011yescharacteristic
1094C22C23×H(3,𝔽4)11yescharacteristic
1095C22C23×#56211yescharacteristic
1096C22C23×#56211yescharacteristic
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C2—44no—
1111C2—82no—
1112C2C23×#241911yescharacteristic
1113C2C23×#244411yescharacteristic
1114C2C23×#251811yescharacteristic
1115C2C23×#262211yescharacteristic
1116C2C23×#264811yescharacteristic
1117C2C23×#264911yescharacteristic
1118C2C23×#268411yescharacteristic
1119C2C23×#269911yescharacteristic
1120C2C23×#270111yescharacteristic
1121C2C23×#270811yescharacteristic
1122C2C23×#274111yescharacteristic
1123C2C23×#275311yescharacteristic
1124C2C23×#277811yescharacteristic
1125C2C23×#278111yescharacteristic
1126C2C23×#282411yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
3. C23×#1443C2semidirect
4. C23×#1442C2semidirect
5. C23×#1442C2semidirect
6. C23×#1442C2semidirect
7. C23×#1440C2semidirect
8. C23×#1440C2semidirect
9. C23×#1440C2semidirect
10. C23×#1440C2semidirect
11. C23×#1439C2semidirect
12. C23×#1439C2semidirect
14. C23×C22⋊#95C2semidirect
15. C23×C22⋊#95C2semidirect
290. #16432C23direct (N × H)
471. #1443C2×C23semidirect
472. #1442C2×C23semidirect
473. #1442C2×C23semidirect
474. #1442C2×C23semidirect
475. #1440C2×C23semidirect
476. #1440C2×C23semidirect
477. #1440C2×C23semidirect
478. #1440C2×C23semidirect
479. #1439C2×C23semidirect
480. #1439C2×C23semidirect
482. C22⋊#95C2×C23semidirect
483. C22⋊#95C2×C23semidirect
704. C23#16432direct (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×#3862
C23×#14432
C23×#14422
C23×#14402
C23×#14392
C23×#14382
C23×C22⋊#952
#1643223