Finite Group Databasebeta

← C23×#13967 #19161593

Subgroups — C23×#13967 #19161593

Order 5888.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×#120C211yesmaximal, characteristic
2C22×C4×D4×C23C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C23C211yesmaximal, characteristic, complemented
4C2×C23×#386C211yesmaximal, characteristic, complemented
5C2×C23×#386C212yesmaximal, complemented
6C2×C23×#379C211yesmaximal, characteristic, complemented
7C23×#1439C212yesmaximal, complemented
8C23×#1438C212yesmaximal, complemented
9C23×#1437C212yesmaximal, complemented
10C23×C22⋊#95C211yesmaximal, characteristic, complemented
11C23×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C23C2211yescharacteristic
13C23×D4×C23C2212yes—
14C23×D4×C23C2211yescharacteristic
15C24×C4×C23C2211yescharacteristic
16C24×C4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic, complemented
18C2×C23×#120—24no—
19C2×C23×#120—24no—
20C2×C23×#120C418yescomplemented
21C2×C4×D4×C23—24no—
22C2×C4×D4×C23—24no—
23C2×C4×D4×C23—24no—
24C22×C4⋊C4×C23C2211yescharacteristic, complemented
25C22×C22⋊C4×C23—24no—
26C22×C22⋊C4×C23—28no—
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2212yes—
29C22×C22⋊C4×C23C2212yes—
30C22×C22⋊C4×C23C2212yes—
31C22×C22⋊C4×C23C2211yescharacteristic
32C22×C22⋊C4×C23C2212yes—
33C22×C22⋊C4×C23C2211yescharacteristic
34C22×C22⋊C4×C23C2212yes—
35C22×C22⋊C4×C23C2211yescharacteristic, complemented
36C22×C22⋊C4×C23C2212yescomplemented
37C22×C42×C23C2211yescharacteristic, complemented
38C23×#386—24no—
39C23×#386—28no—
40C23×#379—24no—
41C2×C23×#95C2212yescomplemented
42C2×C23×#95C2212yescomplemented
43C2×C23×#95C2212yescomplemented
44C2×C23×#95C2212yescomplemented
45C2×C23×#95C2212yescomplemented
46C25×C23—24no—
47C25×C23—22no—
48C25×C23—24no—
49C25×C23—22no—
50C25×C23—22no—
51C25×C23—22no—
52C25×C23—22no—
53C25×C23—22no—
54C25×C23—42no—
55C25×C23—42no—
56C25×C23C2×C414yescomplemented
57C25×C23C2311yescharacteristic
58C25×C23C2312yes—
59C25×C23C2311yescharacteristic
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—22no—
63C22×D4×C23—22no—
64C22×D4×C23—24no—
65C22×D4×C23—24no—
66C22×D4×C23—24no—
67C22×D4×C23—24no—
68C22×D4×C23—42no—
69C22×D4×C23—42no—
70C22×D4×C23C2×C414yes—
71C22×D4×C23C2×C418yescomplemented
72C22×D4×C23D414yes—
73C22×D4×C23D414yes—
74C23×C4×C23—22no—
75C23×C4×C23—22no—
76C23×C4×C23—22no—
77C23×C4×C23—22no—
78C23×C4×C23—24no—
79C23×C4×C23—24no—
80C23×C4×C23—22no—
81C23×C4×C23—22no—
82C23×C4×C23—22no—
83C23×C4×C23—22no—
84C23×C4×C23—24no—
85C23×C4×C23—42no—
86C23×C4×C23—42no—
87C23×C4×C23—42no—
88C23×C4×C23D414yescomplemented
89C23×C4×C23C2312yes—
90C23×C4×C23C2312yes—
91C23×C4×C23C2312yes—
92C23×C4×C23C2311yescharacteristic
93C23×C4×C23C2311yescharacteristic
94C23×C4×C23C2311yescharacteristic
95C23×C4×C23C2311yescharacteristic
96C23×C4×C23C2311yescharacteristic
97C23×#120—232no—
98C4×D4×C23—232no—
99C2×C4⋊C4×C23—22no—
100C2×C4⋊C4×C23—22no—
101C2×C4⋊C4×C23—22no—
102C2×C22⋊C4×C23—232no—
103C2×C22⋊C4×C23—24no—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—24no—
110C2×C22⋊C4×C23—24no—
111C2×C22⋊C4×C23—24no—
112C2×C22⋊C4×C23—24no—
113C2×C22⋊C4×C23—24no—
114C2×C22⋊C4×C23—24no—
115C2×C22⋊C4×C23—22no—
116C2×C22⋊C4×C23—22no—
117C2×C22⋊C4×C23—22no—
118C2×C22⋊C4×C23—24no—
119C2×C22⋊C4×C23—22no—
120C2×C22⋊C4×C23—24no—
121C2×C22⋊C4×C23—24no—
122C2×C22⋊C4×C23—22no—
123C2×C22⋊C4×C23—24no—
124C2×C22⋊C4×C23—24no—
125C2×C22⋊C4×C23—24no—
126C2×C22⋊C4×C23—42no—
127C2×C22⋊C4×C23—42no—
128C2×C22⋊C4×C23—42no—
129C2×C22⋊C4×C23C2×C414yescomplemented
130C2×C22⋊C4×C23C2×C418yescomplemented
131C2×C22⋊C4×C23D414yescomplemented
132C2×C22⋊C4×C23D418yescomplemented
133C2×C42×C23—22no—
134C2×C42×C23—22no—
135C2×C42×C23—22no—
136C23×#95—24no—
137C23×#95—24no—
138C23×#95—24no—
139C23×#95—42no—
140C23×#95—42no—
141C24×C23—22no—
142C24×C23—22no—
143C24×C23—22no—
144C24×C23—22no—
145C24×C23—28no—
146C24×C23—28no—
147C24×C23—216no—
148C24×C23—28no—
149C24×C23—216no—
150C24×C23—22no—
151C24×C23—22no—
152C24×C23—22no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—22no—
156C24×C23—22no—
157C24×C23—22no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—22no—
161C24×C23—22no—
162C24×C23—22no—
163C24×C23—22no—
164C24×C23—22no—
165C24×C23—22no—
166C24×C23—22no—
167C24×C23—22no—
168C24×C23—22no—
169C24×C23—22no—
170C24×C23—28no—
171C24×C23—28no—
172C24×C23—48no—
173C24×C23—48no—
174C24×C23—48no—
175C24×C23—48no—
176C24×C23—48no—
177C24×C23—48no—
178C24×C23—48no—
179C24×C23—48no—
180C24×C23—48no—
181C24×C23—44no—
182C24×C23—44no—
183C24×C23—48no—
184C24×C23—44no—
185C24×C23—44no—
186C24×C23—44no—
187C24×C23—44no—
188C24×C23C22×C412yes—
189C24×C23C22×C414yes—
190C24×C23C22×C412yes—
191C24×C23C2×D412yes—
192C24×C23C2×D412yes—
193C24×C23C2×D414yes—
194C24×C23C2×D412yes—
195C24×C23C2×D412yes—
196C24×C23C2×D412yes—
197C24×C23C2×D412yes—
198C24×C23#4114yes—
199C24×C23#4112yes—
200C24×C23#4112yes—
201C24×C23C2411yescharacteristic
202C2×D4×C23—28no—
203C2×D4×C23—28no—
204C2×D4×C23—28no—
205C2×D4×C23—28no—
206C2×D4×C23—28no—
207C2×D4×C23—28no—
208C2×D4×C23—216no—
209C2×D4×C23—216no—
210C2×D4×C23—48no—
211C2×D4×C23—48no—
212C2×D4×C23—48no—
213C2×D4×C23—48no—
214C2×D4×C23—48no—
215C2×D4×C23C22⋊C4116yescomplemented
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—22no—
223C22×C4×C23—28no—
224C22×C4×C23—28no—
225C22×C4×C23—28no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—22no—
229C22×C4×C23—22no—
230C22×C4×C23—22no—
231C22×C4×C23—22no—
232C22×C4×C23—22no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—22no—
238C22×C4×C23—22no—
239C22×C4×C23—22no—
240C22×C4×C23—22no—
241C22×C4×C23—22no—
242C22×C4×C23—22no—
243C22×C4×C23—22no—
244C22×C4×C23—22no—
245C22×C4×C23—22no—
246C22×C4×C23—22no—
247C22×C4×C23—22no—
248C22×C4×C23—22no—
249C22×C4×C23—22no—
250C22×C4×C23—28no—
251C22×C4×C23—22no—
252C22×C4×C23—22no—
253C22×C4×C23—22no—
254C22×C4×C23—22no—
255C22×C4×C23—22no—
256C22×C4×C23—22no—
257C22×C4×C23—22no—
258C22×C4×C23—44no—
259C22×C4×C23—48no—
260C22×C4×C23—48no—
261C22×C4×C23—48no—
262C22×C4×C23—48no—
263C22×C4×C23—48no—
264C22×C4×C23—48no—
265C22×C4×C23—44no—
266C22×C4×C23—44no—
267C22×C4×C23—44no—
268C22×C4×C23—44no—
269C22×C4×C23C22×C414yes—
270C22×C4×C23C22×C412yes—
271C22×C4×C23C2×D412yes—
272C22×C4×C23C2×D412yes—
273C22×C4×C23C2×D412yes—
274C22×C4×C23C2×D414yes—
275C22×C4×C23C2×D412yes—
276C22×C4×C23C2×D412yes—
277C22×C4×C23C2×D412yes—
278C22×C4×C23C2×D414yes—
279C4⋊C4×C23—28no—
280C22⋊C4×C23—216no—
281C22⋊C4×C23—28no—
282C22⋊C4×C23—28no—
283C22⋊C4×C23—28no—
284C22⋊C4×C23—216no—
285C22⋊C4×C23—216no—
286C22⋊C4×C23—48no—
287C22⋊C4×C23—48no—
288C22⋊C4×C23—48no—
289C22⋊C4×C23—44no—
290C42×C23—28no—
291#13967C2311yesmaximal, characteristic, direct product factor, Sylow
292C23×C23—24no—
293C23×C23—24no—
294C23×C23—22no—
295C23×C23—22no—
296C23×C23—24no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—24no—
300C23×C23—24no—
301C23×C23—24no—
302C23×C23—24no—
303C23×C23—24no—
304C23×C23—24no—
305C23×C23—24no—
306C23×C23—24no—
307C23×C23—24no—
308C23×C23—232no—
309C23×C23—24no—
310C23×C23—24no—
311C23×C23—22no—
312C23×C23—22no—
313C23×C23—24no—
314C23×C23—24no—
315C23×C23—24no—
316C23×C23—24no—
317C23×C23—24no—
318C23×C23—24no—
319C23×C23—24no—
320C23×C23—22no—
321C23×C23—22no—
322C23×C23—22no—
323C23×C23—22no—
324C23×C23—24no—
325C23×C23—24no—
326C23×C23—24no—
327C23×C23—24no—
328C23×C23—24no—
329C23×C23—24no—
330C23×C23—24no—
331C23×C23—24no—
332C23×C23—24no—
333C23×C23—24no—
334C23×C23—24no—
335C23×C23—24no—
336C23×C23—24no—
337C23×C23—24no—
338C23×C23—24no—
339C23×C23—432no—
340C23×C23—432no—
341C23×C23—416no—
342C23×C23—416no—
343C23×C23—416no—
344C23×C23—416no—
345C23×C23—432no—
346C23×C23—432no—
347C23×C23—416no—
348C23×C23—41no—
349C23×C23—42no—
350C23×C23—42no—
351C23×C23—42no—
352C23×C23—42no—
353C23×C23—41no—
354C23×C23—42no—
355C23×C23—41no—
356C23×C23—42no—
357C23×C23—41no—
358C23×C23—42no—
359C23×C23—42no—
360C23×C23—42no—
361C23×C23—42no—
362C23×C23—42no—
363C23×C23—42no—
364C23×C23—42no—
365C23×C23—42no—
366C23×C23—42no—
367C23×C23—42no—
368C23×C23—42no—
369C23×C23—42no—
370C23×C23—42no—
371C23×C23—42no—
372C23×C23—42no—
373C23×C23—42no—
374C23×C23—416no—
375C23×C23C2×C22⋊C414yes—
376C23×C23C2×C22⋊C414yescomplemented
377C23×C23C4×D414yes—
378C23×C23C4×D414yes—
379C23×C23C4×D418yescomplemented
380C23×C23#12014yes—
381C23×C23#12114yes—
382C23×C23#12114yes—
383C23×C23#12314yes—
384C23×C23C23×C411yescharacteristic
385C23×C23C22×D411yescharacteristic
386C23×C23C22×D411yescharacteristic
387C23×C23C22×D411yescharacteristic
388C23×C23C22×D411yescharacteristic
389C23×C23C22×D412yes—
390C23×C23C2×#4111yescharacteristic
391C23×C23C2×#4111yescharacteristic
392C23×C23C2×#4112yes—
393C23×C23H(5,𝔽2)12yes—
394C23×C23H(5,𝔽2)12yes—
395D4×C23—232no—
396D4×C23—432no—
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—24no—
406C2×C4×C23—24no—
407C2×C4×C23—24no—
408C2×C4×C23—24no—
409C2×C4×C23—24no—
410C2×C4×C23—22no—
411C2×C4×C23—22no—
412C2×C4×C23—24no—
413C2×C4×C23—22no—
414C2×C4×C23—22no—
415C2×C4×C23—22no—
416C2×C4×C23—24no—
417C2×C4×C23—24no—
418C2×C4×C23—24no—
419C2×C4×C23—24no—
420C2×C4×C23—416no—
421C2×C4×C23—416no—
422C2×C4×C23—416no—
423C2×C4×C23—41no—
424C2×C4×C23—42no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23—42no—
429C2×C4×C23—42no—
430C2×C4×C23—42no—
431C2×C4×C23—42no—
432C2×C4×C23—42no—
433C2×C4×C23—42no—
434C2×C4×C23—42no—
435C2×C4×C23—42no—
436C2×C4×C23—42no—
437C2×C4×C23—42no—
438C2×C4×C23—42no—
439C2×C4×C23—42no—
440C2×C4×C23—42no—
441C2×C4×C23—42no—
442C2×C4×C23—42no—
443C2×C4×C23—42no—
444C2×C4×C23—42no—
445C2×C4×C23—42no—
446C2×C4×C23C2×C22⋊C414yescomplemented
447C2×C4×C23#12014yescomplemented
448C22×#120C2×C2311yescharacteristic
449C22×C4×D4C2×C2311yescharacteristic, complemented
450C23×C22⋊C4C2×C2311yescharacteristic, complemented
451C2×#386C2×C2312yescomplemented
452C2×#386C2×C2311yescharacteristic, complemented
453C2×#379C2×C2311yescharacteristic, complemented
454#1439C2×C2312yescomplemented
455#1438C2×C2312yescomplemented
456#1437C2×C2312yescomplemented
457C22⋊#95C2×C2311yescharacteristic, complemented
458C22⋊#95C2×C2311yescharacteristic, complemented
459C22×C23—24no—
460C22×C23—28no—
461C22×C23—28no—
462C22×C23—24no—
463C22×C23—24no—
464C22×C23—24no—
465C22×C23—28no—
466C22×C23—28no—
467C22×C23—24no—
468C22×C23—24no—
469C22×C23—28no—
470C22×C23—28no—
471C22×C23—28no—
472C22×C23—24no—
473C22×C23—28no—
474C22×C23—464no—
475C22×C23—42no—
476C22×C23—44no—
477C22×C23—44no—
478C22×C23—44no—
479C22×C23—44no—
480C22×C23—42no—
481C22×C23—44no—
482C22×C23—42no—
483C22×C23—44no—
484C22×C23—42no—
485C22×C23—44no—
486C22×C23—44no—
487C22×C23—44no—
488C22×C23—44no—
489C22×C23—44no—
490C22×C23—44no—
491C22×C23—44no—
492C22×C23—42no—
493C22×C23—44no—
494C22×C23—44no—
495C22×C23—42no—
496C22×C23#38618yescomplemented
497C22×C23C22×C22⋊C411yescharacteristic
498C22×C23C2×C4×D411yescharacteristic
499C22×C23C2×C4×D412yes—
500C22×C23C2×C4×D411yescharacteristic
501C22×C23#51812yes—
502C22×C23C2×#12011yescharacteristic
503C22×C23C2×#12011yescharacteristic
504C22×C23C2×#12111yescharacteristic
505C22×C23C2×#12111yescharacteristic
506C22×C23C2×#12311yescharacteristic
507C22×C23#52511yescharacteristic
508C22×C23#52512yes—
509C22×C23#53411yescharacteristic
510C22×C23#53511yescharacteristic
511C22×C23#53812yes—
512C22×C23D4212yes—
513C22×C23D4212yes—
514C22×C23D4212yes—
515C22×C23#54612yes—
516C22×C23#54612yes—
517C22×C23#54612yes—
518C22×C23#54612yes—
519C22×C23#55112yes—
520C4×C23—24no—
521C4×C23—24no—
522C4×C23—44no—
523C4×C23—42no—
524C4×C23—42no—
525C4×C23—42no—
526C4×C23—44no—
527C4×C23—82no—
528C26C22×C2311yescharacteristic
529C23×D4C22×C2312yes—
530C23×D4C22×C2311yescharacteristic
531C24×C4C22×C2311yescharacteristic
532C24×C4C22×C2311yescharacteristic
533C24×C4C22×C2311yescharacteristic, complemented
534C2×#120—24no—
535C2×#120—24no—
536C2×#120C4×C2318yescomplemented
537C2×C4×D4—24no—
538C2×C4×D4—24no—
539C2×C4×D4—24no—
540C22×C4⋊C4C22×C2311yescharacteristic, complemented
541C22×C22⋊C4—24no—
542C22×C22⋊C4—28no—
543C22×C22⋊C4C22×C2312yes—
544C22×C22⋊C4C22×C2311yescharacteristic
545C22×C22⋊C4C22×C2312yes—
546C22×C22⋊C4C22×C2312yes—
547C22×C22⋊C4C22×C2311yescharacteristic
548C22×C22⋊C4C22×C2312yes—
549C22×C22⋊C4C22×C2312yes—
550C22×C22⋊C4C22×C2311yescharacteristic
551C22×C22⋊C4C22×C2311yescharacteristic, complemented
552C22×C22⋊C4C22×C2312yescomplemented
553C22×C42C22×C2311yescharacteristic, complemented
554#386—24no—
555#386—28no—
556#379—24no—
557C2×#95C22×C2312yescomplemented
558C2×#95C22×C2312yescomplemented
559C2×#95C22×C2312yescomplemented
560C2×#95C22×C2312yescomplemented
561C2×#95C22×C2312yescomplemented
562C2×C23—28no—
563C2×C23—44no—
564C2×C23—48no—
565C2×C23C2×#38611yescharacteristic
566C2×C23C4×#12011yescharacteristic
567C2×C23#232111yescharacteristic
568C2×C23D4×C22⋊C412yes—
569C2×C23#235812yes—
570C2×C23#240311yescharacteristic
571C2×C23#240411yescharacteristic
572C2×C23#240811yescharacteristic
573C2×C23#241812yes—
574C2×C23#242412yes—
575C2×C23#253411yescharacteristic
576C25—24no—
577C25—22no—
578C25—24no—
579C25—22no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—42no—
585C25—42no—
586C25C2×C4×C2314yescomplemented
587C25C23×C2311yescharacteristic
588C25C23×C2312yes—
589C25C23×C2311yescharacteristic
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—24no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—42no—
599C22×D4—42no—
600C22×D4C2×C4×C2314yes—
601C22×D4C2×C4×C2318yescomplemented
602C22×D4D4×C2314yes—
603C22×D4D4×C2314yes—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—24no—
615C23×C4—42no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4D4×C2314yescomplemented
619C23×C4C23×C2312yes—
620C23×C4C23×C2312yes—
621C23×C4C23×C2311yescharacteristic
622C23×C4C23×C2311yescharacteristic
623C23×C4C23×C2311yescharacteristic
624C23×C4C23×C2312yes—
625C23×C4C23×C2311yescharacteristic
626C23×C4C23×C2311yescharacteristic
627#120—232no—
628C4×D4—232no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C22⋊C4—232no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—42no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4C2×C4×C2314yescomplemented
660C2×C22⋊C4C2×C4×C2318yescomplemented
661C2×C22⋊C4D4×C2318yescomplemented
662C2×C22⋊C4D4×C2314yescomplemented
663C2×C42—22no—
664C2×C42—22no—
665C2×C42—22no—
666#95—24no—
667#95—24no—
668#95—24no—
669#95—42no—
670#95—42no—
671C23#1396711yescharacteristic, direct product factor, Sylow
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C2312yes—
720C24C22×C4×C2314yes—
721C24C22×C4×C2312yes—
722C24C2×D4×C2312yes—
723C24C2×D4×C2312yes—
724C24C2×D4×C2314yes—
725C24C2×D4×C2312yes—
726C24C2×D4×C2312yes—
727C24C2×D4×C2312yes—
728C24C2×D4×C2312yes—
729C24#41×C2314yes—
730C24#41×C2312yes—
731C24#41×C2312yes—
732C24C24×C2311yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C23116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C2314yes—
801C22×C4C22×C4×C2312yes—
802C22×C4C2×D4×C2314yes—
803C22×C4C2×D4×C2312yes—
804C22×C4C2×D4×C2312yes—
805C22×C4C2×D4×C2312yes—
806C22×C4C2×D4×C2312yes—
807C22×C4C2×D4×C2312yes—
808C22×C4C2×D4×C2314yes—
809C22×C4C2×D4×C2312yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—22no—
826C23—22no—
827C23—24no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—22no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—432no—
875C23—432no—
876C23—416no—
877C23—416no—
878C23—42no—
879C23—42no—
880C23—416no—
881C23—41no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—41no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—41no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23C2×C22⋊C4×C2314yes—
906C23C2×C22⋊C4×C2314yescomplemented
907C23C4×D4×C2314yes—
908C23C4×D4×C2314yes—
909C23C4×D4×C2318yescomplemented
910C23C23×#12014yes—
911C23C23×#12114yes—
912C23C23×#12114yes—
913C23C23×#12314yes—
914C23C23×C4×C2311yescharacteristic
915C23C22×D4×C2311yescharacteristic
916C23C22×D4×C2311yescharacteristic
917C23C22×D4×C2311yescharacteristic
918C23C22×D4×C2311yescharacteristic
919C23C22×D4×C2312yes—
920C23C2×#41×C2311yescharacteristic
921C23C2×#41×C2312yes—
922C23C2×#41×C2311yescharacteristic
923C23C23×H(5,𝔽2)12yes—
924C23C23×H(5,𝔽2)12yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C2314yescomplemented
977C2×C4C23×#12014yescomplemented
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—42no—
995C22—44no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—42no—
1008C22—44no—
1009C22—42no—
1010C22—44no—
1011C22—42no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22C23×#38618yescomplemented
1016C22C22×C22⋊C4×C2311yescharacteristic
1017C22C2×C4×D4×C2311yescharacteristic
1018C22C2×C4×D4×C2311yescharacteristic
1019C22C2×C4×D4×C2312yes—
1020C22C23×#51812yes—
1021C22C2×C23×#12011yescharacteristic
1022C22C2×C23×#12011yescharacteristic
1023C22C2×C23×#12111yescharacteristic
1024C22C2×C23×#12111yescharacteristic
1025C22C2×C23×#12311yescharacteristic
1026C22C23×#52511yescharacteristic
1027C22C23×#52512yes—
1028C22C23×#53411yescharacteristic
1029C22C23×#53511yescharacteristic
1030C22C23×#53812yes—
1031C22D42×C2312yes—
1032C22D42×C2312yes—
1033C22D42×C2312yes—
1034C22C23×#54612yes—
1035C22C23×#54612yes—
1036C22C23×#54612yes—
1037C22C23×#54612yes—
1038C22C23×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—44no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C23×#38611yescharacteristic
1051C2C4×C23×#12011yescharacteristic
1052C2C23×#232111yescharacteristic
1053C2D4×C22⋊C4×C2312yes—
1054C2C23×#235812yes—
1055C2C23×#240311yescharacteristic
1056C2C23×#240411yescharacteristic
1057C2C23×#240811yescharacteristic
1058C2C23×#241812yes—
1059C2C23×#242412yes—
1060C2C23×#253411yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC22×C23×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C23C2semidirect
3. C23×C22⋊C4×C23C2semidirect
4. C2×C23×#386C2semidirect
5. C2×C23×#386C2semidirect
6. C2×C23×#379C2semidirect
7. C23×#1439C2semidirect
8. C23×#1438C2semidirect
9. C23×#1437C2semidirect
10. C23×C22⋊#95C2semidirect
11. C23×C22⋊#95C2semidirect
17. C24×C4×C23C22semidirect
20. C2×C23×#120C4semidirect
24. C22×C4⋊C4×C23C22semidirect
35. C22×C22⋊C4×C23C22semidirect
36. C22×C22⋊C4×C23C22semidirect
37. C22×C42×C23C22semidirect
41. C2×C23×#95C22semidirect
42. C2×C23×#95C22semidirect
43. C2×C23×#95C22semidirect
44. C2×C23×#95C22semidirect
45. C2×C23×#95C22semidirect
56. C25×C23C2×C4semidirect
71. C22×D4×C23C2×C4semidirect
88. C23×C4×C23D4semidirect
129. C2×C22⋊C4×C23C2×C4semidirect
130. C2×C22⋊C4×C23C2×C4semidirect
131. C2×C22⋊C4×C23D4semidirect
132. C2×C22⋊C4×C23D4semidirect
215. C2×D4×C23C22⋊C4semidirect
291. #13967C23direct (N × H)
376. C23×C23C2×C22⋊C4semidirect
379. C23×C23C4×D4semidirect
446. C2×C4×C23C2×C22⋊C4semidirect
447. C2×C4×C23#120semidirect
449. C22×C4×D4C2×C23semidirect
450. C23×C22⋊C4C2×C23semidirect
451. C2×#386C2×C23semidirect
452. C2×#386C2×C23semidirect
453. C2×#379C2×C23semidirect
454. #1439C2×C23semidirect
455. #1438C2×C23semidirect
456. #1437C2×C23semidirect
457. C22⋊#95C2×C23semidirect
458. C22⋊#95C2×C23semidirect
496. C22×C23#386semidirect
533. C24×C4C22×C23semidirect
536. C2×#120C4×C23semidirect
540. C22×C4⋊C4C22×C23semidirect
551. C22×C22⋊C4C22×C23semidirect
552. C22×C22⋊C4C22×C23semidirect
553. C22×C42C22×C23semidirect
557. C2×#95C22×C23semidirect
558. C2×#95C22×C23semidirect
559. C2×#95C22×C23semidirect
560. C2×#95C22×C23semidirect
561. C2×#95C22×C23semidirect
586. C25C2×C4×C23semidirect
601. C22×D4C2×C4×C23semidirect
618. C23×C4D4×C23semidirect
659. C2×C22⋊C4C2×C4×C23semidirect
660. C2×C22⋊C4C2×C4×C23semidirect
661. C2×C22⋊C4D4×C23semidirect
662. C2×C22⋊C4D4×C23semidirect
671. C23#13967direct (N × H)
746. C2×D4C22⋊C4×C23semidirect
906. C23C2×C22⋊C4×C23semidirect
909. C23C4×D4×C23semidirect
976. C2×C4C2×C22⋊C4×C23semidirect
977. C2×C4C23×#120semidirect
1015. C22C23×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C23×#1202
C22×C4×D4×C232
C23×C22⋊C4×C232
C2×C23×#3862
C2×C23×#3792
C23×#14392
C23×#14382
C23×#14372
C23×C22⋊#952
#1396723