Finite Group Databasebeta

← C23×#13998 #19161624

Subgroups — C23×#13998 #19161624

Order 5888.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×#121C211yesmaximal, characteristic
2C2×C23×#390C211yesmaximal, characteristic, complemented
3C2×C23×#390C211yesmaximal, characteristic, complemented
4C2×C23×#390C212yesmaximal, complemented
5C2×C23×#389C211yesmaximal, characteristic, complemented
6C2×C23×#380C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊C4×C23C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
9C23×#1439C212yesmaximal, complemented
10C23×#1438C212yesmaximal, complemented
11C23×#1437C212yesmaximal, complemented
12C23×D4×C23C2211yescharacteristic
13C23×D4×C23C2212yes—
14C24×C4×C23C2211yescharacteristic
15C2×C23×#121—24no—
16C2×C23×#121—24no—
17C2×C23×#121C418yescomplemented
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2212yes—
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2212yes—
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2212yes—
25C22×C22⋊C4×C23C2212yes—
26C22×C22⋊C4×C23C2212yes—
27C22×C22⋊C4×C23C2212yes—
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2212yes—
30C22×C42×C23C2211yescharacteristic
31C22×C42×C23C2212yes—
32C22×C42×C23C2211yescharacteristic
33C23×#390—24no—
34C23×#390—28no—
35C23×#390—24no—
36C23×#389—24no—
37C23×#380—24no—
38C4×C4⋊C4×C23—24no—
39C4×C22⋊C4×C23—24no—
40C2×C23×#95C2211yescharacteristic
41C2×C23×#95C2212yes—
42C2×C23×#95C2212yes—
43C2×C23×#95C2212yes—
44C2×C23×#95C2211yescharacteristic
45C25×C23C2312yes—
46C25×C23C2311yescharacteristic
47C22×D4×C23—24no—
48C22×D4×C23—24no—
49C22×D4×C23—22no—
50C22×D4×C23—22no—
51C22×D4×C23—24no—
52C22×D4×C23—24no—
53C22×D4×C23—22no—
54C22×D4×C23—22no—
55C22×D4×C23—22no—
56C22×D4×C23—22no—
57C22×D4×C23—42no—
58C22×D4×C23—42no—
59C22×D4×C23C2×C414yes—
60C22×D4×C23C2×C418yes—
61C23×C4×C23—22no—
62C23×C4×C23—22no—
63C23×C4×C23—22no—
64C23×C4×C23—22no—
65C23×C4×C23—22no—
66C23×C4×C23—22no—
67C23×C4×C23C2×C414yes—
68C23×C4×C23C2312yes—
69C23×C4×C23C2311yescharacteristic
70C23×C4×C23C2311yescharacteristic
71C23×C4×C23C2312yes—
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2312yes—
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×#121—232no—
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—22no—
81C2×C4⋊C4×C23—24no—
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—24no—
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—42no—
86C2×C4⋊C4×C23C2×C414yes—
87C2×C4⋊C4×C23D414yes—
88C2×C4⋊C4×C23D414yes—
89C2×C4⋊C4×C23D414yescomplemented
90C2×C22⋊C4×C23—22no—
91C2×C22⋊C4×C23—22no—
92C2×C22⋊C4×C23—22no—
93C2×C22⋊C4×C23—24no—
94C2×C22⋊C4×C23—24no—
95C2×C22⋊C4×C23—22no—
96C2×C22⋊C4×C23—22no—
97C2×C22⋊C4×C23—24no—
98C2×C22⋊C4×C23—24no—
99C2×C22⋊C4×C23—24no—
100C2×C22⋊C4×C23—24no—
101C2×C22⋊C4×C23—24no—
102C2×C22⋊C4×C23—24no—
103C2×C22⋊C4×C23—24no—
104C2×C22⋊C4×C23—24no—
105C2×C22⋊C4×C23—24no—
106C2×C22⋊C4×C23—24no—
107C2×C22⋊C4×C23—42no—
108C2×C22⋊C4×C23—42no—
109C2×C22⋊C4×C23—42no—
110C2×C22⋊C4×C23—42no—
111C2×C22⋊C4×C23—42no—
112C2×C22⋊C4×C23C2×C418yes—
113C2×C22⋊C4×C23D414yescomplemented
114C2×C42×C23—22no—
115C2×C42×C23—22no—
116C2×C42×C23—22no—
117C2×C42×C23—24no—
118C2×C42×C23—22no—
119C2×C42×C23—24no—
120C2×C42×C23—22no—
121C2×C42×C23—42no—
122C2×C42×C23D414yescomplemented
123C23×#95—22no—
124C23×#95—22no—
125C23×#95—24no—
126C23×#95—24no—
127C23×#95—24no—
128C24×C23—21no—
129C24×C23—21no—
130C24×C23—21no—
131C24×C23—21no—
132C24×C23—21no—
133C24×C23—21no—
134C24×C23—21no—
135C24×C23—21no—
136C24×C23—21no—
137C24×C23—21no—
138C24×C23—21no—
139C24×C23—21no—
140C24×C23—22no—
141C24×C23—22no—
142C24×C23—22no—
143C24×C23—22no—
144C24×C23—22no—
145C24×C23—22no—
146C24×C23—22no—
147C24×C23—22no—
148C24×C23—22no—
149C24×C23—22no—
150C24×C23—22no—
151C24×C23—22no—
152C24×C23—22no—
153C24×C23—22no—
154C24×C23C22×C414yes—
155C24×C23C22×C412yes—
156C24×C23C2×D412yes—
157C24×C23#4112yes—
158C24×C23C2411yescharacteristic
159C2×D4×C23—216no—
160C2×D4×C23—216no—
161C2×D4×C23—28no—
162C2×D4×C23—28no—
163C2×D4×C23—28no—
164C2×D4×C23—48no—
165C2×D4×C23—48no—
166C2×D4×C23—48no—
167C2×D4×C23—48no—
168C2×D4×C23—48no—
169C2×D4×C23—44no—
170C2×D4×C23—44no—
171C2×D4×C23—44no—
172C2×D4×C23—44no—
173C22×C4×C23—21no—
174C22×C4×C23—22no—
175C22×C4×C23—21no—
176C22×C4×C23—22no—
177C22×C4×C23—21no—
178C22×C4×C23—22no—
179C22×C4×C23—22no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—22no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—22no—
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—22no—
200C22×C4×C23—22no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—22no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—22no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—28no—
212C22×C4×C23—28no—
213C22×C4×C23—28no—
214C22×C4×C23—22no—
215C22×C4×C23—22no—
216C22×C4×C23—22no—
217C22×C4×C23—22no—
218C22×C4×C23—22no—
219C22×C4×C23—22no—
220C22×C4×C23—22no—
221C22×C4×C23—44no—
222C22×C4×C23—44no—
223C22×C4×C23—44no—
224C22×C4×C23—44no—
225C22×C4×C23C22×C412yes—
226C22×C4×C23C22×C414yes—
227C22×C4×C23C22×C412yes—
228C22×C4×C23C2×D412yes—
229C22×C4×C23C2×D414yes—
230C22×C4×C23C2×D412yes—
231C22×C4×C23C2×D414yes—
232C22×C4×C23C2×D414yes—
233C22×C4×C23C2×D412yes—
234C22×C4×C23C2×D412yes—
235C22×C4×C23C2×D412yes—
236C22×C4×C23C2×D412yes—
237C22×C4×C23C2×D412yes—
238C22×C4×C23C2×D412yes—
239C22×C4×C23#4112yes—
240C22×C4×C23#4112yes—
241C22×C4×C23#4112yes—
242C22×C4×C23#4112yes—
243C4⋊C4×C23—28no—
244C4⋊C4×C23—48no—
245C4⋊C4×C23—44no—
246C4⋊C4×C23C22⋊C4116yescomplemented
247C22⋊C4×C23—28no—
248C22⋊C4×C23—216no—
249C22⋊C4×C23—28no—
250C22⋊C4×C23—48no—
251C22⋊C4×C23—48no—
252C22⋊C4×C23—48no—
253C22⋊C4×C23—48no—
254C22⋊C4×C23—48no—
255C42×C23—28no—
256C42×C23—48no—
257C42×C23—44no—
258#13998C2311yesmaximal, characteristic, direct product factor, Sylow
259C23×C23—22no—
260C23×C23—22no—
261C23×C23—22no—
262C23×C23—22no—
263C23×C23—22no—
264C23×C23—22no—
265C23×C23—22no—
266C23×C23—22no—
267C23×C23—22no—
268C23×C23—22no—
269C23×C23—22no—
270C23×C23—22no—
271C23×C23—22no—
272C23×C23—22no—
273C23×C23—22no—
274C23×C23—22no—
275C23×C23—22no—
276C23×C23—22no—
277C23×C23—24no—
278C23×C23—24no—
279C23×C23—24no—
280C23×C23—24no—
281C23×C23—24no—
282C23×C23—24no—
283C23×C23—24no—
284C23×C23—41no—
285C23×C23—41no—
286C23×C23—41no—
287C23×C23—41no—
288C23×C23—41no—
289C23×C23—41no—
290C23×C23—41no—
291C23×C23—41no—
292C23×C23—41no—
293C23×C23—41no—
294C23×C23—41no—
295C23×C23—41no—
296C23×C23—41no—
297C23×C23—41no—
298C23×C23—41no—
299C23×C23—41no—
300C23×C23—42no—
301C23×C23—42no—
302C23×C23—42no—
303C23×C23—42no—
304C23×C23—42no—
305C23×C23—42no—
306C23×C23—42no—
307C23×C23—42no—
308C23×C23—42no—
309C23×C23—42no—
310C23×C23—42no—
311C23×C23—42no—
312C23×C23—42no—
313C23×C23—42no—
314C23×C23—42no—
315C23×C23—42no—
316C23×C23—42no—
317C23×C23—42no—
318C23×C23—42no—
319C23×C23—42no—
320C23×C23—42no—
321C23×C23—42no—
322C23×C23—42no—
323C23×C23—42no—
324C23×C23—42no—
325C23×C23—42no—
326C23×C23—42no—
327C23×C23—42no—
328C23×C23C4×D414yes—
329C23×C23C23×C411yescharacteristic
330C23×C23C22×D411yescharacteristic
331C23×C23C22×D411yescharacteristic
332C23×C23C22×D411yescharacteristic
333C23×C23C22×D411yescharacteristic
334C23×C23C22×D411yescharacteristic
335C23×C23C2×#4111yescharacteristic
336C23×C23C2×#4111yescharacteristic
337C23×C23C2×#4111yescharacteristic
338C23×C23C2×#4111yescharacteristic
339C23×C23C2×#4111yescharacteristic
340C23×C23H(5,𝔽2)11yescharacteristic
341C23×C23H(5,𝔽2)11yescharacteristic
342C23×C23H(5,𝔽2)11yescharacteristic
343C23×C232−1+411yescharacteristic
344D4×C23—432no—
345D4×C23—416no—
346C2×C4×C23—24no—
347C2×C4×C23—24no—
348C2×C4×C23—22no—
349C2×C4×C23—22no—
350C2×C4×C23—22no—
351C2×C4×C23—24no—
352C2×C4×C23—24no—
353C2×C4×C23—24no—
354C2×C4×C23—24no—
355C2×C4×C23—22no—
356C2×C4×C23—22no—
357C2×C4×C23—22no—
358C2×C4×C23—22no—
359C2×C4×C23—22no—
360C2×C4×C23—22no—
361C2×C4×C23—22no—
362C2×C4×C23—22no—
363C2×C4×C23—24no—
364C2×C4×C23—22no—
365C2×C4×C23—22no—
366C2×C4×C23—22no—
367C2×C4×C23—24no—
368C2×C4×C23—22no—
369C2×C4×C23—22no—
370C2×C4×C23—22no—
371C2×C4×C23—24no—
372C2×C4×C23—22no—
373C2×C4×C23—41no—
374C2×C4×C23—41no—
375C2×C4×C23—41no—
376C2×C4×C23—41no—
377C2×C4×C23—41no—
378C2×C4×C23—41no—
379C2×C4×C23—42no—
380C2×C4×C23—41no—
381C2×C4×C23—41no—
382C2×C4×C23—42no—
383C2×C4×C23—42no—
384C2×C4×C23—41no—
385C2×C4×C23—41no—
386C2×C4×C23—41no—
387C2×C4×C23—41no—
388C2×C4×C23—42no—
389C2×C4×C23—41no—
390C2×C4×C23—41no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—416no—
394C2×C4×C23—42no—
395C2×C4×C23—42no—
396C2×C4×C23—42no—
397C2×C4×C23—42no—
398C2×C4×C23—42no—
399C2×C4×C23—42no—
400C2×C4×C23—42no—
401C2×C4×C23C2×C22⋊C418yes—
402C2×C4×C23C2×C22⋊C414yes—
403C2×C4×C23C4×D414yes—
404C2×C4×C23C4×D414yes—
405C2×C4×C23#12114yes—
406C2×C4×C23#12114yes—
407C2×C4×C23#12114yescomplemented
408C2×C4×C23#12414yes—
409C2×C4×C23#12714yes—
410C22×#121C2×C2311yescharacteristic
411C2×#390C2×C2311yescharacteristic, complemented
412C2×#390C2×C2312yescomplemented
413C2×#390C2×C2311yescharacteristic, complemented
414C2×#389C2×C2311yescharacteristic, complemented
415C2×#380C2×C2311yescharacteristic, complemented
416C2×C4×C4⋊C4C2×C2311yescharacteristic, complemented
417C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
418#1439C2×C2312yescomplemented
419#1438C2×C2312yescomplemented
420#1437C2×C2312yescomplemented
421C22×C23—24no—
422C22×C23—24no—
423C22×C23—24no—
424C22×C23—42no—
425C22×C23—42no—
426C22×C23—42no—
427C22×C23—42no—
428C22×C23—42no—
429C22×C23—42no—
430C22×C23—42no—
431C22×C23—42no—
432C22×C23—42no—
433C22×C23—42no—
434C22×C23—42no—
435C22×C23—42no—
436C22×C23—44no—
437C22×C23—44no—
438C22×C23—44no—
439C22×C23—44no—
440C22×C23—44no—
441C22×C23—44no—
442C22×C23—44no—
443C22×C23—82no—
444C22×C23—82no—
445C22×C23—82no—
446C22×C23—82no—
447C22×C23—82no—
448C22×C23—82no—
449C22×C23—82no—
450C22×C23—82no—
451C22×C23C22×C22⋊C411yescharacteristic
452C22×C23C2×C4×D411yescharacteristic
453C22×C23C2×C4×D411yescharacteristic
454C22×C23C2×C4×D411yescharacteristic
455C22×C23C4×#4111yescharacteristic
456C22×C23#51811yescharacteristic
457C22×C23#52011yescharacteristic
458C22×C23C2×#12111yescharacteristic
459C22×C23C2×#12111yescharacteristic
460C22×C23C2×#12111yescharacteristic
461C22×C23#52511yescharacteristic
462C22×C23C2×#12411yescharacteristic
463C22×C23#52911yescharacteristic
464C22×C23C2×#12711yescharacteristic
465C22×C23#53211yescharacteristic
466C22×C23#53511yescharacteristic
467C22×C23#53711yescharacteristic
468C22×C23#54011yescharacteristic
469C22×C23#54211yescharacteristic
470C22×C23D4211yescharacteristic
471C22×C23D4211yescharacteristic
472C22×C23D4211yescharacteristic
473C22×C23#54611yescharacteristic
474C22×C23#54611yescharacteristic
475C22×C23#54611yescharacteristic
476C22×C23#54711yescharacteristic
477C22×C23#54811yescharacteristic
478C22×C23#54811yescharacteristic
479C22×C23#54811yescharacteristic
480C22×C23#55011yescharacteristic
481C22×C23#55011yescharacteristic
482C22×C23#55011yescharacteristic
483C22×C23#55311yescharacteristic
484C22×C23#55311yescharacteristic
485C22×C23#55511yescharacteristic
486C4×C23—28no—
487C4×C23—24no—
488C4×C23—42no—
489C4×C23—44no—
490C4×C23—42no—
491C4×C23—42no—
492C4×C23—42no—
493C4×C23—82no—
494C4×C23#39018yescomplemented
495C23×D4C22×C2311yescharacteristic
496C23×D4C22×C2312yes—
497C24×C4C22×C2311yescharacteristic
498C2×#121—24no—
499C2×#121—24no—
500C2×#121C4×C2318yescomplemented
501C22×C4⋊C4C22×C2311yescharacteristic
502C22×C4⋊C4C22×C2312yes—
503C22×C4⋊C4C22×C2311yescharacteristic
504C22×C4⋊C4C22×C2311yescharacteristic
505C22×C22⋊C4C22×C2312yes—
506C22×C22⋊C4C22×C2311yescharacteristic
507C22×C22⋊C4C22×C2312yes—
508C22×C22⋊C4C22×C2312yes—
509C22×C22⋊C4C22×C2312yes—
510C22×C22⋊C4C22×C2312yes—
511C22×C22⋊C4C22×C2311yescharacteristic
512C22×C22⋊C4C22×C2312yes—
513C22×C42C22×C2311yescharacteristic
514C22×C42C22×C2312yes—
515C22×C42C22×C2311yescharacteristic
516#390—24no—
517#390—28no—
518#390—24no—
519#389—24no—
520#380—24no—
521C4×C4⋊C4—24no—
522C4×C22⋊C4—24no—
523C2×#95C22×C2311yescharacteristic
524C2×#95C22×C2312yes—
525C2×#95C22×C2312yes—
526C2×#95C22×C2312yes—
527C2×#95C22×C2311yescharacteristic
528C2×C23—44no—
529C2×C23—84no—
530C2×C23C2×#39011yescharacteristic
531C2×C23C4×#12111yescharacteristic
532C2×C23#232411yescharacteristic
533C2×C23D4×C22⋊C411yescharacteristic
534C2×C23#234111yescharacteristic
535C2×C23#236111yescharacteristic
536C2×C23#236311yescharacteristic
537C2×C23#241411yescharacteristic
538C2×C23#241611yescharacteristic
539C2×C23#242611yescharacteristic
540C2×C23#242811yescharacteristic
541C2×C23#249011yescharacteristic
542C2×C23#249111yescharacteristic
543C2×C23#254011yescharacteristic
544C2×C23#254111yescharacteristic
545C25C23×C2312yes—
546C25C23×C2311yescharacteristic
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4—42no—
559C22×D4C2×C4×C2314yes—
560C22×D4C2×C4×C2318yes—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4C2×C4×C2314yes—
568C23×C4C23×C2312yes—
569C23×C4C23×C2311yescharacteristic
570C23×C4C23×C2311yescharacteristic
571C23×C4C23×C2312yes—
572C23×C4C23×C2311yescharacteristic
573C23×C4C23×C2311yescharacteristic
574C23×C4C23×C2312yes—
575C23×C4C23×C2311yescharacteristic
576C23×C4C23×C2311yescharacteristic
577#121—232no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—42no—
586C2×C4⋊C4C2×C4×C2314yes—
587C2×C4⋊C4D4×C2314yes—
588C2×C4⋊C4D4×C2314yes—
589C2×C4⋊C4D4×C2314yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4C2×C4×C2318yes—
613C2×C22⋊C4D4×C2314yescomplemented
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—24no—
618C2×C42—22no—
619C2×C42—24no—
620C2×C42—22no—
621C2×C42—42no—
622C2×C42D4×C2314yescomplemented
623#95—22no—
624#95—22no—
625#95—24no—
626#95—24no—
627#95—24no—
628C23#1399811yescharacteristic, direct product factor, Sylow
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24C22×C4×C2314yes—
656C24C22×C4×C2312yes—
657C24C2×D4×C2312yes—
658C24#41×C2312yes—
659C24C24×C2311yescharacteristic
660C2×D4—216no—
661C2×D4—216no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4C22×C4×C2312yes—
727C22×C4C22×C4×C2314yes—
728C22×C4C22×C4×C2312yes—
729C22×C4C2×D4×C2312yes—
730C22×C4C2×D4×C2314yes—
731C22×C4C2×D4×C2312yes—
732C22×C4C2×D4×C2314yes—
733C22×C4C2×D4×C2314yes—
734C22×C4C2×D4×C2312yes—
735C22×C4C2×D4×C2312yes—
736C22×C4C2×D4×C2312yes—
737C22×C4C2×D4×C2312yes—
738C22×C4C2×D4×C2312yes—
739C22×C4C2×D4×C2312yes—
740C22×C4#41×C2312yes—
741C22×C4#41×C2312yes—
742C22×C4#41×C2312yes—
743C22×C4#41×C2312yes—
744C4⋊C4—28no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4C22⋊C4×C23116yescomplemented
748C22⋊C4—28no—
749C22⋊C4—216no—
750C22⋊C4—28no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C42—48no—
758C42—44no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23C4×D4×C2314yes—
829C23C23×C4×C2311yescharacteristic
830C23C22×D4×C2311yescharacteristic
831C23C22×D4×C2311yescharacteristic
832C23C22×D4×C2311yescharacteristic
833C23C22×D4×C2311yescharacteristic
834C23C22×D4×C2311yescharacteristic
835C23C2×#41×C2311yescharacteristic
836C23C2×#41×C2311yescharacteristic
837C23C2×#41×C2311yescharacteristic
838C23C2×#41×C2311yescharacteristic
839C23C2×#41×C2311yescharacteristic
840C23C23×H(5,𝔽2)11yescharacteristic
841C23C23×H(5,𝔽2)11yescharacteristic
842C23C23×H(5,𝔽2)11yescharacteristic
843C23C23×2−1+411yescharacteristic
844D4—432no—
845D4—416no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—416no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4C2×C22⋊C4×C2318yes—
902C2×C4C2×C22⋊C4×C2314yes—
903C2×C4C4×D4×C2314yes—
904C2×C4C4×D4×C2314yes—
905C2×C4C23×#12114yes—
906C2×C4C23×#12114yes—
907C2×C4C23×#12114yescomplemented
908C2×C4C23×#12414yes—
909C2×C4C23×#12714yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C22×C22⋊C4×C2311yescharacteristic
941C22C2×C4×D4×C2311yescharacteristic
942C22C2×C4×D4×C2311yescharacteristic
943C22C2×C4×D4×C2311yescharacteristic
944C22C4×#41×C2311yescharacteristic
945C22C23×#51811yescharacteristic
946C22C23×#52011yescharacteristic
947C22C2×C23×#12111yescharacteristic
948C22C2×C23×#12111yescharacteristic
949C22C2×C23×#12111yescharacteristic
950C22C23×#52511yescharacteristic
951C22C2×C23×#12411yescharacteristic
952C22C23×#52911yescharacteristic
953C22C2×C23×#12711yescharacteristic
954C22C23×#53211yescharacteristic
955C22C23×#53511yescharacteristic
956C22C23×#53711yescharacteristic
957C22C23×#54011yescharacteristic
958C22C23×#54211yescharacteristic
959C22D42×C2311yescharacteristic
960C22D42×C2311yescharacteristic
961C22D42×C2311yescharacteristic
962C22C23×#54611yescharacteristic
963C22C23×#54611yescharacteristic
964C22C23×#54611yescharacteristic
965C22C23×#54711yescharacteristic
966C22C23×#54811yescharacteristic
967C22C23×#54811yescharacteristic
968C22C23×#54811yescharacteristic
969C22C23×#55011yescharacteristic
970C22C23×#55011yescharacteristic
971C22C23×#55011yescharacteristic
972C22C23×#55311yescharacteristic
973C22C23×#55311yescharacteristic
974C22C23×#55511yescharacteristic
975C4—24no—
976C4—28no—
977C4—42no—
978C4—44no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—82no—
983C4C23×#39018yescomplemented
984C2—44no—
985C2—84no—
986C2C2×C23×#39011yescharacteristic
987C2C4×C23×#12111yescharacteristic
988C2C23×#232411yescharacteristic
989C2D4×C22⋊C4×C2311yescharacteristic
990C2C23×#234111yescharacteristic
991C2C23×#236111yescharacteristic
992C2C23×#236311yescharacteristic
993C2C23×#241411yescharacteristic
994C2C23×#241611yescharacteristic
995C2C23×#242611yescharacteristic
996C2C23×#242811yescharacteristic
997C2C23×#249011yescharacteristic
998C2C23×#249111yescharacteristic
999C2C23×#254011yescharacteristic
1000C2C23×#254111yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC22×C23×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C23×#390C2semidirect
3. C2×C23×#390C2semidirect
4. C2×C23×#390C2semidirect
5. C2×C23×#389C2semidirect
6. C2×C23×#380C2semidirect
7. C2×C4×C4⋊C4×C23C2semidirect
8. C2×C4×C22⋊C4×C23C2semidirect
9. C23×#1439C2semidirect
10. C23×#1438C2semidirect
11. C23×#1437C2semidirect
17. C2×C23×#121C4semidirect
89. C2×C4⋊C4×C23D4semidirect
113. C2×C22⋊C4×C23D4semidirect
122. C2×C42×C23D4semidirect
246. C4⋊C4×C23C22⋊C4semidirect
258. #13998C23direct (N × H)
407. C2×C4×C23#121semidirect
411. C2×#390C2×C23semidirect
412. C2×#390C2×C23semidirect
413. C2×#390C2×C23semidirect
414. C2×#389C2×C23semidirect
415. C2×#380C2×C23semidirect
416. C2×C4×C4⋊C4C2×C23semidirect
417. C2×C4×C22⋊C4C2×C23semidirect
418. #1439C2×C23semidirect
419. #1438C2×C23semidirect
420. #1437C2×C23semidirect
494. C4×C23#390semidirect
500. C2×#121C4×C23semidirect
589. C2×C4⋊C4D4×C23semidirect
613. C2×C22⋊C4D4×C23semidirect
622. C2×C42D4×C23semidirect
628. C23#13998direct (N × H)
747. C4⋊C4C22⋊C4×C23semidirect
907. C2×C4C23×#121semidirect
983. C4C23×#390semidirect

Maximal subgroups

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

subgroupindex
C22×C23×#1212
C2×C23×#3902
C2×C23×#3892
C2×C23×#3802
C2×C4×C4⋊C4×C232
C2×C4×C22⋊C4×C232
C23×#14392
C23×#14382
C23×#14372
#1399823