Finite Group Databasebeta

← C43×#13967 #24933984

Subgroups — C43×#13967 #24933984

Order 11008.

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×#120×C43C211yesmaximal, characteristic
2C22×C4×D4×C43C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C43C211yesmaximal, characteristic, complemented
4C2×C43×#386C212yesmaximal, complemented
5C2×C43×#386C211yesmaximal, characteristic, complemented
6C2×C43×#379C211yesmaximal, characteristic, complemented
7C43×#1439C212yesmaximal, complemented
8C43×#1438C212yesmaximal, complemented
9C43×#1437C212yesmaximal, complemented
10C43×C22⋊#95C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C43C2211yescharacteristic
13C23×D4×C43C2212yes—
14C23×D4×C43C2211yescharacteristic
15C24×C4×C43C2211yescharacteristic
16C24×C4×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic, complemented
18C2×#120×C43—24no—
19C2×#120×C43—24no—
20C2×#120×C43C418yescomplemented
21C2×C4×D4×C43—24no—
22C2×C4×D4×C43—24no—
23C2×C4×D4×C43—24no—
24C22×C4⋊C4×C43C2211yescharacteristic, complemented
25C22×C22⋊C4×C43—24no—
26C22×C22⋊C4×C43—28no—
27C22×C22⋊C4×C43C2212yes—
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C22×C22⋊C4×C43C2212yes—
31C22×C22⋊C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2212yes—
33C22×C22⋊C4×C43C2212yes—
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2211yescharacteristic, complemented
36C22×C22⋊C4×C43C2212yescomplemented
37C22×C42×C43C2211yescharacteristic, complemented
38C43×#386—24no—
39C43×#386—28no—
40C43×#379—24no—
41C2×#95×C43C2212yescomplemented
42C2×#95×C43C2212yescomplemented
43C2×#95×C43C2212yescomplemented
44C2×#95×C43C2212yescomplemented
45C2×#95×C43C2212yescomplemented
46C25×C43—24no—
47C25×C43—22no—
48C25×C43—24no—
49C25×C43—22no—
50C25×C43—22no—
51C25×C43—22no—
52C25×C43—22no—
53C25×C43—22no—
54C25×C43—42no—
55C25×C43—42no—
56C25×C43C2×C414yescomplemented
57C25×C43C2311yescharacteristic
58C25×C43C2312yes—
59C25×C43C2311yescharacteristic
60C22×D4×C43—22no—
61C22×D4×C43—22no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—24no—
65C22×D4×C43—24no—
66C22×D4×C43—24no—
67C22×D4×C43—24no—
68C22×D4×C43—42no—
69C22×D4×C43—42no—
70C22×D4×C43C2×C414yes—
71C22×D4×C43C2×C418yescomplemented
72C22×D4×C43D414yes—
73C22×D4×C43D414yes—
74C23×C4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43—22no—
77C23×C4×C43—22no—
78C23×C4×C43—24no—
79C23×C4×C43—24no—
80C23×C4×C43—22no—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—24no—
85C23×C4×C43—42no—
86C23×C4×C43—42no—
87C23×C4×C43—42no—
88C23×C4×C43D414yescomplemented
89C23×C4×C43C2312yes—
90C23×C4×C43C2312yes—
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97#120×C43—232no—
98C4×D4×C43—232no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C22⋊C4×C43—232no—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43—24no—
110C2×C22⋊C4×C43—24no—
111C2×C22⋊C4×C43—24no—
112C2×C22⋊C4×C43—24no—
113C2×C22⋊C4×C43—24no—
114C2×C22⋊C4×C43—24no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—24no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—24no—
121C2×C22⋊C4×C43—24no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—24no—
124C2×C22⋊C4×C43—24no—
125C2×C22⋊C4×C43—24no—
126C2×C22⋊C4×C43—42no—
127C2×C22⋊C4×C43—42no—
128C2×C22⋊C4×C43—42no—
129C2×C22⋊C4×C43C2×C418yescomplemented
130C2×C22⋊C4×C43C2×C414yescomplemented
131C2×C22⋊C4×C43D418yescomplemented
132C2×C22⋊C4×C43D414yescomplemented
133C2×C42×C43—22no—
134C2×C42×C43—22no—
135C2×C42×C43—22no—
136#95×C43—24no—
137#95×C43—24no—
138#95×C43—24no—
139#95×C43—42no—
140#95×C43—42no—
141C24×C43—22no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—28no—
146C24×C43—28no—
147C24×C43—216no—
148C24×C43—28no—
149C24×C43—216no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—22no—
167C24×C43—22no—
168C24×C43—22no—
169C24×C43—22no—
170C24×C43—28no—
171C24×C43—28no—
172C24×C43—48no—
173C24×C43—48no—
174C24×C43—48no—
175C24×C43—48no—
176C24×C43—48no—
177C24×C43—48no—
178C24×C43—48no—
179C24×C43—48no—
180C24×C43—48no—
181C24×C43—44no—
182C24×C43—44no—
183C24×C43—48no—
184C24×C43—44no—
185C24×C43—44no—
186C24×C43—44no—
187C24×C43—44no—
188C24×C43C22×C412yes—
189C24×C43C22×C414yes—
190C24×C43C22×C412yes—
191C24×C43C2×D412yes—
192C24×C43C2×D412yes—
193C24×C43C2×D414yes—
194C24×C43C2×D412yes—
195C24×C43C2×D412yes—
196C24×C43C2×D412yes—
197C24×C43C2×D412yes—
198C24×C43#4114yes—
199C24×C43#4112yes—
200C24×C43#4112yes—
201C24×C43C2411yescharacteristic
202C2×D4×C43—216no—
203C2×D4×C43—28no—
204C2×D4×C43—28no—
205C2×D4×C43—216no—
206C2×D4×C43—28no—
207C2×D4×C43—28no—
208C2×D4×C43—28no—
209C2×D4×C43—28no—
210C2×D4×C43—48no—
211C2×D4×C43—48no—
212C2×D4×C43—48no—
213C2×D4×C43—48no—
214C2×D4×C43—48no—
215C2×D4×C43C22⋊C4116yescomplemented
216C22×C4×C43—28no—
217C22×C4×C43—28no—
218C22×C4×C43—28no—
219C22×C4×C43—28no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—22no—
225C22×C4×C43—22no—
226C22×C4×C43—22no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—22no—
233C22×C4×C43—22no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—22no—
239C22×C4×C43—22no—
240C22×C4×C43—22no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—22no—
244C22×C4×C43—22no—
245C22×C4×C43—22no—
246C22×C4×C43—22no—
247C22×C4×C43—22no—
248C22×C4×C43—22no—
249C22×C4×C43—22no—
250C22×C4×C43—22no—
251C22×C4×C43—22no—
252C22×C4×C43—22no—
253C22×C4×C43—22no—
254C22×C4×C43—22no—
255C22×C4×C43—22no—
256C22×C4×C43—22no—
257C22×C4×C43—22no—
258C22×C4×C43—44no—
259C22×C4×C43—48no—
260C22×C4×C43—48no—
261C22×C4×C43—48no—
262C22×C4×C43—48no—
263C22×C4×C43—48no—
264C22×C4×C43—44no—
265C22×C4×C43—48no—
266C22×C4×C43—44no—
267C22×C4×C43—44no—
268C22×C4×C43—44no—
269C22×C4×C43C22×C414yes—
270C22×C4×C43C22×C412yes—
271C22×C4×C43C2×D414yes—
272C22×C4×C43C2×D412yes—
273C22×C4×C43C2×D412yes—
274C22×C4×C43C2×D412yes—
275C22×C4×C43C2×D412yes—
276C22×C4×C43C2×D412yes—
277C22×C4×C43C2×D414yes—
278C22×C4×C43C2×D412yes—
279C4⋊C4×C43—28no—
280C22⋊C4×C43—216no—
281C22⋊C4×C43—28no—
282C22⋊C4×C43—216no—
283C22⋊C4×C43—216no—
284C22⋊C4×C43—28no—
285C22⋊C4×C43—28no—
286C22⋊C4×C43—48no—
287C22⋊C4×C43—48no—
288C22⋊C4×C43—48no—
289C22⋊C4×C43—44no—
290C42×C43—28no—
291C23×C43—24no—
292C23×C43—24no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—24no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—24no—
299C23×C43—24no—
300C23×C43—24no—
301C23×C43—24no—
302C23×C43—24no—
303C23×C43—24no—
304C23×C43—24no—
305C23×C43—24no—
306C23×C43—24no—
307C23×C43—232no—
308C23×C43—24no—
309C23×C43—24no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—24no—
313C23×C43—24no—
314C23×C43—24no—
315C23×C43—24no—
316C23×C43—24no—
317C23×C43—24no—
318C23×C43—24no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—24no—
324C23×C43—24no—
325C23×C43—24no—
326C23×C43—24no—
327C23×C43—24no—
328C23×C43—24no—
329C23×C43—24no—
330C23×C43—24no—
331C23×C43—24no—
332C23×C43—24no—
333C23×C43—24no—
334C23×C43—24no—
335C23×C43—24no—
336C23×C43—24no—
337C23×C43—24no—
338C23×C43—432no—
339C23×C43—432no—
340C23×C43—416no—
341C23×C43—416no—
342C23×C43—416no—
343C23×C43—416no—
344C23×C43—432no—
345C23×C43—432no—
346C23×C43—416no—
347C23×C43—41no—
348C23×C43—42no—
349C23×C43—42no—
350C23×C43—42no—
351C23×C43—42no—
352C23×C43—41no—
353C23×C43—42no—
354C23×C43—41no—
355C23×C43—42no—
356C23×C43—41no—
357C23×C43—42no—
358C23×C43—42no—
359C23×C43—42no—
360C23×C43—42no—
361C23×C43—42no—
362C23×C43—42no—
363C23×C43—42no—
364C23×C43—42no—
365C23×C43—42no—
366C23×C43—42no—
367C23×C43—42no—
368C23×C43—42no—
369C23×C43—42no—
370C23×C43—42no—
371C23×C43—42no—
372C23×C43—42no—
373C23×C43—416no—
374C23×C43C2×C22⋊C414yes—
375C23×C43C2×C22⋊C414yescomplemented
376C23×C43C4×D414yes—
377C23×C43C4×D414yes—
378C23×C43C4×D418yescomplemented
379C23×C43#12014yes—
380C23×C43#12114yes—
381C23×C43#12114yes—
382C23×C43#12314yes—
383C23×C43C23×C411yescharacteristic
384C23×C43C22×D411yescharacteristic
385C23×C43C22×D411yescharacteristic
386C23×C43C22×D411yescharacteristic
387C23×C43C22×D411yescharacteristic
388C23×C43C22×D412yes—
389C23×C43C2×#4111yescharacteristic
390C23×C43C2×#4111yescharacteristic
391C23×C43C2×#4112yes—
392C23×C43H(5,𝔽2)12yes—
393C23×C43H(5,𝔽2)12yes—
394D4×C43—232no—
395D4×C43—432no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—24no—
405C2×C4×C43—24no—
406C2×C4×C43—24no—
407C2×C4×C43—24no—
408C2×C4×C43—24no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—24no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—24no—
416C2×C4×C43—24no—
417C2×C4×C43—24no—
418C2×C4×C43—24no—
419C2×C4×C43—416no—
420C2×C4×C43—416no—
421C2×C4×C43—416no—
422C2×C4×C43—41no—
423C2×C4×C43—42no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—42no—
428C2×C4×C43—42no—
429C2×C4×C43—42no—
430C2×C4×C43—42no—
431C2×C4×C43—42no—
432C2×C4×C43—42no—
433C2×C4×C43—42no—
434C2×C4×C43—42no—
435C2×C4×C43—42no—
436C2×C4×C43—42no—
437C2×C4×C43—42no—
438C2×C4×C43—42no—
439C2×C4×C43—42no—
440C2×C4×C43—42no—
441C2×C4×C43—42no—
442C2×C4×C43—42no—
443C2×C4×C43—42no—
444C2×C4×C43—42no—
445C2×C4×C43C2×C22⋊C414yescomplemented
446C2×C4×C43#12014yescomplemented
447#13967C4311yesmaximal, characteristic, direct product factor, Sylow
448C22×C43—24no—
449C22×C43—28no—
450C22×C43—28no—
451C22×C43—24no—
452C22×C43—24no—
453C22×C43—24no—
454C22×C43—28no—
455C22×C43—28no—
456C22×C43—24no—
457C22×C43—24no—
458C22×C43—28no—
459C22×C43—28no—
460C22×C43—28no—
461C22×C43—24no—
462C22×C43—28no—
463C22×C43—464no—
464C22×C43—42no—
465C22×C43—44no—
466C22×C43—44no—
467C22×C43—44no—
468C22×C43—44no—
469C22×C43—44no—
470C22×C43—42no—
471C22×C43—42no—
472C22×C43—44no—
473C22×C43—42no—
474C22×C43—44no—
475C22×C43—44no—
476C22×C43—44no—
477C22×C43—44no—
478C22×C43—44no—
479C22×C43—44no—
480C22×C43—44no—
481C22×C43—42no—
482C22×C43—44no—
483C22×C43—44no—
484C22×C43—42no—
485C22×C43#38618yescomplemented
486C22×C43C22×C22⋊C411yescharacteristic
487C22×C43C2×C4×D411yescharacteristic
488C22×C43C2×C4×D412yes—
489C22×C43C2×C4×D411yescharacteristic
490C22×C43#51812yes—
491C22×C43C2×#12011yescharacteristic
492C22×C43C2×#12011yescharacteristic
493C22×C43C2×#12111yescharacteristic
494C22×C43C2×#12111yescharacteristic
495C22×C43C2×#12311yescharacteristic
496C22×C43#52511yescharacteristic
497C22×C43#52512yes—
498C22×C43#53411yescharacteristic
499C22×C43#53511yescharacteristic
500C22×C43#53812yes—
501C22×C43D4212yes—
502C22×C43D4212yes—
503C22×C43D4212yes—
504C22×C43#54612yes—
505C22×C43#54612yes—
506C22×C43#54612yes—
507C22×C43#54612yes—
508C22×C43#55112yes—
509C4×C43—24no—
510C4×C43—24no—
511C4×C43—44no—
512C4×C43—42no—
513C4×C43—42no—
514C4×C43—42no—
515C4×C43—44no—
516C4×C43—82no—
517C22×#120C2×C4311yescharacteristic
518C22×C4×D4C2×C4311yescharacteristic, complemented
519C23×C22⋊C4C2×C4311yescharacteristic, complemented
520C2×#386C2×C4312yescomplemented
521C2×#386C2×C4311yescharacteristic, complemented
522C2×#379C2×C4311yescharacteristic, complemented
523#1439C2×C4312yescomplemented
524#1438C2×C4312yescomplemented
525#1437C2×C4312yescomplemented
526C22⋊#95C2×C4311yescharacteristic, complemented
527C22⋊#95C2×C4311yescharacteristic, complemented
528C2×C43—28no—
529C2×C43—44no—
530C2×C43—48no—
531C2×C43C2×#38611yescharacteristic
532C2×C43C4×#12011yescharacteristic
533C2×C43#232111yescharacteristic
534C2×C43D4×C22⋊C412yes—
535C2×C43#235812yes—
536C2×C43#240311yescharacteristic
537C2×C43#240411yescharacteristic
538C2×C43#240811yescharacteristic
539C2×C43#241812yes—
540C2×C43#242412yes—
541C2×C43#253411yescharacteristic
542C26C22×C4311yescharacteristic
543C23×D4C22×C4312yes—
544C23×D4C22×C4311yescharacteristic
545C24×C4C22×C4311yescharacteristic
546C24×C4C22×C4311yescharacteristic
547C24×C4C22×C4311yescharacteristic, complemented
548C2×#120—24no—
549C2×#120—24no—
550C2×#120C4×C4318yescomplemented
551C2×C4×D4—24no—
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C22×C4⋊C4C22×C4311yescharacteristic, complemented
555C22×C22⋊C4—24no—
556C22×C22⋊C4—28no—
557C22×C22⋊C4C22×C4312yes—
558C22×C22⋊C4C22×C4311yescharacteristic
559C22×C22⋊C4C22×C4312yes—
560C22×C22⋊C4C22×C4312yes—
561C22×C22⋊C4C22×C4311yescharacteristic
562C22×C22⋊C4C22×C4312yes—
563C22×C22⋊C4C22×C4312yes—
564C22×C22⋊C4C22×C4311yescharacteristic
565C22×C22⋊C4C22×C4311yescharacteristic, complemented
566C22×C22⋊C4C22×C4312yescomplemented
567C22×C42C22×C4311yescharacteristic, complemented
568#386—24no—
569#386—28no—
570#379—24no—
571C2×#95C22×C4312yescomplemented
572C2×#95C22×C4312yescomplemented
573C2×#95C22×C4312yescomplemented
574C2×#95C22×C4312yescomplemented
575C2×#95C22×C4312yescomplemented
576C43#1396711yescharacteristic, direct product factor, Sylow
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C4314yescomplemented
588C25C23×C4311yescharacteristic
589C25C23×C4312yes—
590C25C23×C4311yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C4314yes—
602C22×D4C2×C4×C4318yescomplemented
603C22×D4D4×C4314yes—
604C22×D4D4×C4314yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C4314yescomplemented
620C23×C4C23×C4312yes—
621C23×C4C23×C4312yes—
622C23×C4C23×C4311yescharacteristic
623C23×C4C23×C4311yescharacteristic
624C23×C4C23×C4311yescharacteristic
625C23×C4C23×C4312yes—
626C23×C4C23×C4311yescharacteristic
627C23×C4C23×C4311yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C4314yescomplemented
661C2×C22⋊C4C2×C4×C4318yescomplemented
662C2×C22⋊C4D4×C4318yescomplemented
663C2×C22⋊C4D4×C4314yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
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×C4312yes—
720C24C22×C4×C4314yes—
721C24C22×C4×C4312yes—
722C24C2×D4×C4312yes—
723C24C2×D4×C4312yes—
724C24C2×D4×C4314yes—
725C24C2×D4×C4312yes—
726C24C2×D4×C4312yes—
727C24C2×D4×C4312yes—
728C24C2×D4×C4312yes—
729C24#41×C4314yes—
730C24#41×C4312yes—
731C24#41×C4312yes—
732C24C24×C4311yescharacteristic
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×C43116yescomplemented
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×C4314yes—
801C22×C4C22×C4×C4312yes—
802C22×C4C2×D4×C4314yes—
803C22×C4C2×D4×C4312yes—
804C22×C4C2×D4×C4312yes—
805C22×C4C2×D4×C4312yes—
806C22×C4C2×D4×C4312yes—
807C22×C4C2×D4×C4312yes—
808C22×C4C2×D4×C4314yes—
809C22×C4C2×D4×C4312yes—
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—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
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—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
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—416no—
875C23—432no—
876C23—432no—
877C23—416no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
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—416no—
905C23C2×C22⋊C4×C4314yes—
906C23C2×C22⋊C4×C4314yescomplemented
907C23C4×D4×C4314yes—
908C23C4×D4×C4314yes—
909C23C4×D4×C4318yescomplemented
910C23#120×C4314yes—
911C23#121×C4314yes—
912C23#121×C4314yes—
913C23#123×C4314yes—
914C23C23×C4×C4311yescharacteristic
915C23C22×D4×C4311yescharacteristic
916C23C22×D4×C4311yescharacteristic
917C23C22×D4×C4311yescharacteristic
918C23C22×D4×C4311yescharacteristic
919C23C22×D4×C4312yes—
920C23C2×#41×C4311yescharacteristic
921C23C2×#41×C4311yescharacteristic
922C23C2×#41×C4312yes—
923C23H(5,𝔽2)×C4312yes—
924C23H(5,𝔽2)×C4312yes—
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×C4314yescomplemented
977C2×C4#120×C4314yescomplemented
978C22—24no—
979C22—28no—
980C22—28no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—28no—
985C22—28no—
986C22—24no—
987C22—24no—
988C22—28no—
989C22—28no—
990C22—28no—
991C22—24no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22C43×#38618yescomplemented
1016C22C22×C22⋊C4×C4311yescharacteristic
1017C22C2×C4×D4×C4311yescharacteristic
1018C22C2×C4×D4×C4312yes—
1019C22C2×C4×D4×C4311yescharacteristic
1020C22C43×#51812yes—
1021C22C2×#120×C4311yescharacteristic
1022C22C2×#120×C4311yescharacteristic
1023C22C2×#121×C4311yescharacteristic
1024C22C2×#121×C4311yescharacteristic
1025C22C2×#123×C4311yescharacteristic
1026C22C43×#52511yescharacteristic
1027C22C43×#52512yes—
1028C22C43×#53411yescharacteristic
1029C22C43×#53511yescharacteristic
1030C22C43×#53812yes—
1031C22D42×C4312yes—
1032C22D42×C4312yes—
1033C22D42×C4312yes—
1034C22C43×#54612yes—
1035C22C43×#54612yes—
1036C22C43×#54612yes—
1037C22C43×#54612yes—
1038C22C43×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C43×#38611yescharacteristic
1051C2C4×#120×C4311yescharacteristic
1052C2C43×#232111yescharacteristic
1053C2D4×C22⋊C4×C4312yes—
1054C2C43×#235812yes—
1055C2C43×#240311yescharacteristic
1056C2C43×#240411yescharacteristic
1057C2C43×#240811yescharacteristic
1058C2C43×#241812yes—
1059C2C43×#242412yes—
1060C2C43×#253411yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC22×#120×C43C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C43C2semidirect
3. C23×C22⋊C4×C43C2semidirect
4. C2×C43×#386C2semidirect
5. C2×C43×#386C2semidirect
6. C2×C43×#379C2semidirect
7. C43×#1439C2semidirect
8. C43×#1438C2semidirect
9. C43×#1437C2semidirect
10. C43×C22⋊#95C2semidirect
11. C43×C22⋊#95C2semidirect
17. C24×C4×C43C22semidirect
20. C2×#120×C43C4semidirect
24. C22×C4⋊C4×C43C22semidirect
35. C22×C22⋊C4×C43C22semidirect
36. C22×C22⋊C4×C43C22semidirect
37. C22×C42×C43C22semidirect
41. C2×#95×C43C22semidirect
42. C2×#95×C43C22semidirect
43. C2×#95×C43C22semidirect
44. C2×#95×C43C22semidirect
45. C2×#95×C43C22semidirect
56. C25×C43C2×C4semidirect
71. C22×D4×C43C2×C4semidirect
88. C23×C4×C43D4semidirect
129. C2×C22⋊C4×C43C2×C4semidirect
130. C2×C22⋊C4×C43C2×C4semidirect
131. C2×C22⋊C4×C43D4semidirect
132. C2×C22⋊C4×C43D4semidirect
215. C2×D4×C43C22⋊C4semidirect
375. C23×C43C2×C22⋊C4semidirect
378. C23×C43C4×D4semidirect
445. C2×C4×C43C2×C22⋊C4semidirect
446. C2×C4×C43#120semidirect
447. #13967C43direct (N × H)
485. C22×C43#386semidirect
518. C22×C4×D4C2×C43semidirect
519. C23×C22⋊C4C2×C43semidirect
520. C2×#386C2×C43semidirect
521. C2×#386C2×C43semidirect
522. C2×#379C2×C43semidirect
523. #1439C2×C43semidirect
524. #1438C2×C43semidirect
525. #1437C2×C43semidirect
526. C22⋊#95C2×C43semidirect
527. C22⋊#95C2×C43semidirect
547. C24×C4C22×C43semidirect
550. C2×#120C4×C43semidirect
554. C22×C4⋊C4C22×C43semidirect
565. C22×C22⋊C4C22×C43semidirect
566. C22×C22⋊C4C22×C43semidirect
567. C22×C42C22×C43semidirect
571. C2×#95C22×C43semidirect
572. C2×#95C22×C43semidirect
573. C2×#95C22×C43semidirect
574. C2×#95C22×C43semidirect
575. C2×#95C22×C43semidirect
576. C43#13967direct (N × H)
587. C25C2×C4×C43semidirect
602. C22×D4C2×C4×C43semidirect
619. C23×C4D4×C43semidirect
660. C2×C22⋊C4C2×C4×C43semidirect
661. C2×C22⋊C4C2×C4×C43semidirect
662. C2×C22⋊C4D4×C43semidirect
663. C2×C22⋊C4D4×C43semidirect
746. C2×D4C22⋊C4×C43semidirect
906. C23C2×C22⋊C4×C43semidirect
909. C23C4×D4×C43semidirect
976. C2×C4C2×C22⋊C4×C43semidirect
977. C2×C4#120×C43semidirect
1015. C22C43×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C432
C22×C4×D4×C432
C23×C22⋊C4×C432
C2×C43×#3862
C2×C43×#3792
C43×#14392
C43×#14382
C43×#14372
C43×C22⋊#952
#1396743