Finite Group Databasebeta

← C43×#13873 #24933890

Subgroups — C43×#13873 #24933890

Order 11008.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C43C211yesmaximal, characteristic
2C2×C43×#388C212yesmaximal, complemented
3C2×C43×#380C211yesmaximal, characteristic, complemented
4C2×C43×#379C211yesmaximal, characteristic
5C2×C43×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
7C43×#1440C212yesmaximal, complemented
8C43×#1439C212yesmaximal, complemented
9C43×#1437C212yesmaximal, complemented
10C43×C22⋊#95C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C43C2211yescharacteristic
13C24×C4×C43C2211yescharacteristic
14C24×C4×C43C2211yescharacteristic
15C22×C4⋊C4×C43C2212yescomplemented
16C22×C22⋊C4×C43—28no—
17C22×C22⋊C4×C43C418yescomplemented
18C22×C22⋊C4×C43C2211yescharacteristic
19C22×C22⋊C4×C43C2211yescharacteristic
20C22×C22⋊C4×C43C2212yes—
21C22×C22⋊C4×C43C2212yes—
22C22×C22⋊C4×C43C2212yes—
23C22×C22⋊C4×C43C2212yes—
24C22×C22⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C42×C43C2212yescomplemented
31C43×#388—28no—
32C43×#380—24no—
33C43×#379—24no—
34C43×#379—24no—
35C4×C22⋊C4×C43—24no—
36C2×#95×C43C2212yescomplemented
37C2×#95×C43C2212yescomplemented
38C2×#95×C43C2212yescomplemented
39C2×#95×C43C2212yescomplemented
40C2×#95×C43C2212yescomplemented
41C2×#95×C43C2212yescomplemented
42C25×C43—24no—
43C25×C43—24no—
44C25×C43—22no—
45C25×C43—22no—
46C25×C43—22no—
47C25×C43—22no—
48C25×C43—22no—
49C25×C43—22no—
50C25×C43—42no—
51C25×C43—42no—
52C25×C43C2×C414yes—
53C25×C43C2311yescharacteristic
54C25×C43C2311yescharacteristic
55C25×C43C2311yescharacteristic
56C23×C4×C43—22no—
57C23×C4×C43—22no—
58C23×C4×C43—22no—
59C23×C4×C43—22no—
60C23×C4×C43—24no—
61C23×C4×C43—24no—
62C23×C4×C43—42no—
63C23×C4×C43—42no—
64C23×C4×C43C2×C414yes—
65C23×C4×C43C2×C414yes—
66C23×C4×C43C2312yes—
67C23×C4×C43C2312yes—
68C23×C4×C43C2311yescharacteristic
69C23×C4×C43C2311yescharacteristic
70C23×C4×C43C2312yes—
71C23×C4×C43C2312yes—
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C2×C4⋊C4×C43—24no—
75C2×C4⋊C4×C43—24no—
76C2×C4⋊C4×C43—42no—
77C2×C22⋊C4×C43—24no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—22no—
82C2×C22⋊C4×C43—24no—
83C2×C22⋊C4×C43—24no—
84C2×C22⋊C4×C43—232no—
85C2×C22⋊C4×C43—22no—
86C2×C22⋊C4×C43—22no—
87C2×C22⋊C4×C43—22no—
88C2×C22⋊C4×C43—24no—
89C2×C22⋊C4×C43—24no—
90C2×C22⋊C4×C43—24no—
91C2×C22⋊C4×C43—24no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—24no—
96C2×C22⋊C4×C43—24no—
97C2×C22⋊C4×C43—24no—
98C2×C22⋊C4×C43—24no—
99C2×C22⋊C4×C43—42no—
100C2×C22⋊C4×C43—42no—
101C2×C22⋊C4×C43—42no—
102C2×C22⋊C4×C43—42no—
103C2×C22⋊C4×C43C2×C414yes—
104C2×C22⋊C4×C43C2×C414yes—
105C2×C22⋊C4×C43C2×C414yes—
106C2×C22⋊C4×C43C2×C414yes—
107C2×C22⋊C4×C43D414yes—
108C2×C22⋊C4×C43D414yes—
109C2×C22⋊C4×C43D418yes—
110C2×C42×C43—24no—
111C2×C42×C43—24no—
112C2×C42×C43—42no—
113#95×C43—24no—
114#95×C43—24no—
115#95×C43—24no—
116#95×C43—24no—
117#95×C43—42no—
118#95×C43—42no—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43—22no—
122C24×C43—22no—
123C24×C43—216no—
124C24×C43—216no—
125C24×C43—28no—
126C24×C43—28no—
127C24×C43—28no—
128C24×C43—22no—
129C24×C43—21no—
130C24×C43—21no—
131C24×C43—21no—
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—21no—
135C24×C43—22no—
136C24×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—28no—
147C24×C43—28no—
148C24×C43—44no—
149C24×C43—44no—
150C24×C43—48no—
151C24×C43—48no—
152C24×C43—48no—
153C24×C43—48no—
154C24×C43—48no—
155C24×C43—48no—
156C24×C43—48no—
157C24×C43—48no—
158C24×C43—48no—
159C24×C43—48no—
160C24×C43—44no—
161C24×C43—44no—
162C24×C43—44no—
163C24×C43—44no—
164C24×C43C22×C412yes—
165C24×C43C22×C412yes—
166C24×C43C22×C412yes—
167C24×C43C2×D414yes—
168C24×C43C2×D412yes—
169C24×C43C2×D412yes—
170C24×C43#4114yes—
171C24×C43#4112yes—
172C24×C43#4112yes—
173C24×C43#4112yes—
174C24×C43#4112yes—
175C24×C43C2411yescharacteristic
176C22×C4×C43—28no—
177C22×C4×C43—28no—
178C22×C4×C43—28no—
179C22×C4×C43—28no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—44no—
221C22×C4×C43—44no—
222C22×C4×C43—48no—
223C22×C4×C43—48no—
224C22×C4×C43—48no—
225C22×C4×C43—48no—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C22×C412yes—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C2×D414yes—
231C22×C4×C43C2×D414yes—
232C22×C4×C43C2×D414yes—
233C22×C4×C43C2×D414yes—
234C4⋊C4×C43—48no—
235C22⋊C4×C43—28no—
236C22⋊C4×C43—28no—
237C22⋊C4×C43—28no—
238C22⋊C4×C43—28no—
239C22⋊C4×C43—28no—
240C22⋊C4×C43—48no—
241C22⋊C4×C43—48no—
242C22⋊C4×C43—48no—
243C22⋊C4×C43—48no—
244C22⋊C4×C43—44no—
245C22⋊C4×C43—44no—
246C22⋊C4×C43C22⋊C4116yescomplemented
247C42×C43—48no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—24no—
253C23×C43—24no—
254C23×C43—24no—
255C23×C43—24no—
256C23×C43—24no—
257C23×C43—24no—
258C23×C43—24no—
259C23×C43—24no—
260C23×C43—24no—
261C23×C43—24no—
262C23×C43—24no—
263C23×C43—24no—
264C23×C43—232no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—24no—
278C23×C43—24no—
279C23×C43—24no—
280C23×C43—24no—
281C23×C43—24no—
282C23×C43—24no—
283C23×C43—24no—
284C23×C43—24no—
285C23×C43—24no—
286C23×C43—24no—
287C23×C43—24no—
288C23×C43—24no—
289C23×C43—416no—
290C23×C43—416no—
291C23×C43—416no—
292C23×C43—416no—
293C23×C43—416no—
294C23×C43—432no—
295C23×C43—432no—
296C23×C43—432no—
297C23×C43—432no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43—416no—
319C23×C43C2×C22⋊C414yes—
320C23×C43#11714yes—
321C23×C43#11714yes—
322C23×C43C4×D414yes—
323C23×C43C4×D414yes—
324C23×C43#12114yes—
325C23×C43#12314yes—
326C23×C43#12414yes—
327C23×C43#12614yes—
328C23×C43C23×C411yescharacteristic
329C23×C43C22×D412yes—
330C23×C43C22×D411yescharacteristic
331C23×C43C22×D411yescharacteristic
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4112yes—
335C23×C43C2×#4111yescharacteristic
336C23×C43C2×#4111yescharacteristic
337C23×C43H(5,𝔽2)12yes—
338C23×C43H(5,𝔽2)12yes—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—24no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—24no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—24no—
354C2×C4×C43—24no—
355C2×C4×C43—24no—
356C2×C4×C43—24no—
357C2×C4×C43—24no—
358C2×C4×C43—24no—
359C2×C4×C43—416no—
360C2×C4×C43—416no—
361C2×C4×C43—42no—
362C2×C4×C43—42no—
363C2×C4×C43—42no—
364C2×C4×C43—42no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—42no—
370C2×C4×C43—42no—
371C2×C4×C43—42no—
372C2×C4×C43—42no—
373C2×C4×C43—42no—
374C2×C4×C43—42no—
375C2×C4×C43—42no—
376C2×C4×C43—42no—
377C2×C4×C43—42no—
378C2×C4×C43—42no—
379C2×C4×C43—42no—
380C2×C4×C43—42no—
381C2×C4×C43—42no—
382C2×C4×C43—42no—
383C2×C4×C43—42no—
384C2×C4×C43—42no—
385C2×C4×C43—42no—
386C2×C4×C43—42no—
387C2×C4×C43C2×C22⋊C414yes—
388C2×C4×C43C2×C22⋊C414yes—
389#13873C4311yesmaximal, characteristic, direct product factor, Sylow
390C22×C43—24no—
391C22×C43—24no—
392C22×C43—24no—
393C22×C43—24no—
394C22×C43—24no—
395C22×C43—28no—
396C22×C43—28no—
397C22×C43—28no—
398C22×C43—28no—
399C22×C43—24no—
400C22×C43—24no—
401C22×C43—24no—
402C22×C43—24no—
403C22×C43—24no—
404C22×C43—24no—
405C22×C43—24no—
406C22×C43—464no—
407C22×C43—42no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—44no—
414C22×C43—44no—
415C22×C43—44no—
416C22×C43—44no—
417C22×C43—44no—
418C22×C43—44no—
419C22×C43—44no—
420C22×C43—44no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43#38818yescomplemented
424C22×C43C22×C22⋊C411yescharacteristic
425C22×C43C2×#11711yescharacteristic
426C22×C43C2×#11711yescharacteristic
427C22×C43C2×C4×D411yescharacteristic
428C22×C43C2×C4×D411yescharacteristic
429C22×C43#51811yescharacteristic
430C22×C43#51811yescharacteristic
431C22×C43C2×#12111yescharacteristic
432C22×C43C2×#12311yescharacteristic
433C22×C43#52512yes—
434C22×C43#52512yes—
435C22×C43C2×#12411yescharacteristic
436C22×C43C2×#12611yescharacteristic
437C22×C43#53812yes—
438C22×C43#53812yes—
439C22×C43D4212yes—
440C22×C43D4212yes—
441C22×C43#54612yes—
442C22×C43#54612yes—
443C22×C43#54612yes—
444C22×C43#54612yes—
445C22×C43#55112yes—
446C22×C43#55112yes—
447C4×C43—24no—
448C4×C43—24no—
449C4×C43—42no—
450C4×C43—42no—
451C4×C43—44no—
452C4×C43—44no—
453C4×C43—82no—
454C4×C43—82no—
455C23×C22⋊C4C2×C4311yescharacteristic
456C2×#388C2×C4312yescomplemented
457C2×#380C2×C4311yescharacteristic, complemented
458C2×#379C2×C4311yescharacteristic
459C2×#379C2×C4311yescharacteristic
460C2×C4×C22⋊C4C2×C4311yescharacteristic, complemented
461#1440C2×C4312yescomplemented
462#1439C2×C4312yescomplemented
463#1437C2×C4312yescomplemented
464C22⋊#95C2×C4311yescharacteristic, complemented
465C22⋊#95C2×C4311yescharacteristic, complemented
466C2×C43—28no—
467C2×C43—44no—
468C2×C43—44no—
469C2×C43#228011yescharacteristic
470C2×C43C2×#38811yescharacteristic
471C2×C43#231211yescharacteristic
472C2×C43D4×C22⋊C411yescharacteristic
473C2×C43D4×C22⋊C411yescharacteristic
474C2×C43#234211yescharacteristic
475C2×C43#234211yescharacteristic
476C2×C43#241812yes—
477C2×C43#242412yes—
478C2×C43#247212yes—
479C2×C43#248012yes—
480C26C22×C4311yescharacteristic
481C24×C4C22×C4311yescharacteristic
482C24×C4C22×C4311yescharacteristic
483C22×C4⋊C4C22×C4312yescomplemented
484C22×C22⋊C4—28no—
485C22×C22⋊C4C4×C4318yescomplemented
486C22×C22⋊C4C22×C4311yescharacteristic
487C22×C22⋊C4C22×C4311yescharacteristic
488C22×C22⋊C4C22×C4312yes—
489C22×C22⋊C4C22×C4312yes—
490C22×C22⋊C4C22×C4312yes—
491C22×C22⋊C4C22×C4312yes—
492C22×C22⋊C4C22×C4311yescharacteristic
493C22×C22⋊C4C22×C4311yescharacteristic
494C22×C22⋊C4C22×C4311yescharacteristic
495C22×C22⋊C4C22×C4311yescharacteristic
496C22×C22⋊C4C22×C4311yescharacteristic
497C22×C22⋊C4C22×C4311yescharacteristic
498C22×C42C22×C4312yescomplemented
499#388—28no—
500#380—24no—
501#379—24no—
502#379—24no—
503C4×C22⋊C4—24no—
504C2×#95C22×C4312yescomplemented
505C2×#95C22×C4312yescomplemented
506C2×#95C22×C4312yescomplemented
507C2×#95C22×C4312yescomplemented
508C2×#95C22×C4312yescomplemented
509C2×#95C22×C4312yescomplemented
510C43#1387311yescharacteristic, direct product factor, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C4314yes—
522C25C23×C4311yescharacteristic
523C25C23×C4311yescharacteristic
524C25C23×C4311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C4314yes—
534C23×C4C2×C4×C4314yes—
535C23×C4C23×C4312yes—
536C23×C4C23×C4312yes—
537C23×C4C23×C4311yescharacteristic
538C23×C4C23×C4311yescharacteristic
539C23×C4C23×C4312yes—
540C23×C4C23×C4312yes—
541C23×C4C23×C4311yescharacteristic
542C23×C4C23×C4311yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C4314yes—
573C2×C22⋊C4C2×C4×C4314yes—
574C2×C22⋊C4C2×C4×C4314yes—
575C2×C22⋊C4C2×C4×C4314yes—
576C2×C22⋊C4D4×C4314yes—
577C2×C22⋊C4D4×C4314yes—
578C2×C22⋊C4D4×C4318yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C4312yes—
634C24C22×C4×C4312yes—
635C24C22×C4×C4312yes—
636C24C2×D4×C4314yes—
637C24C2×D4×C4312yes—
638C24C2×D4×C4312yes—
639C24#41×C4314yes—
640C24#41×C4312yes—
641C24#41×C4312yes—
642C24#41×C4312yes—
643C24#41×C4312yes—
644C24C24×C4311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C4312yes—
696C22×C4C22×C4×C4312yes—
697C22×C4C22×C4×C4312yes—
698C22×C4C22×C4×C4312yes—
699C22×C4C2×D4×C4314yes—
700C22×C4C2×D4×C4314yes—
701C22×C4C2×D4×C4314yes—
702C22×C4C2×D4×C4314yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C43116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—416no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C4314yes—
789C23#117×C4314yes—
790C23#117×C4314yes—
791C23C4×D4×C4314yes—
792C23C4×D4×C4314yes—
793C23#121×C4314yes—
794C23#123×C4314yes—
795C23#124×C4314yes—
796C23#126×C4314yes—
797C23C23×C4×C4311yescharacteristic
798C23C22×D4×C4312yes—
799C23C22×D4×C4311yescharacteristic
800C23C22×D4×C4311yescharacteristic
801C23C2×#41×C4311yescharacteristic
802C23C2×#41×C4311yescharacteristic
803C23C2×#41×C4312yes—
804C23C2×#41×C4311yescharacteristic
805C23C2×#41×C4311yescharacteristic
806C23H(5,𝔽2)×C4312yes—
807C23H(5,𝔽2)×C4312yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C4314yes—
857C2×C4C2×C22⋊C4×C4314yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—28no—
863C22—28no—
864C22—28no—
865C22—28no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22C43×#38818yescomplemented
892C22C22×C22⋊C4×C4311yescharacteristic
893C22C2×#117×C4311yescharacteristic
894C22C2×#117×C4311yescharacteristic
895C22C2×C4×D4×C4311yescharacteristic
896C22C2×C4×D4×C4311yescharacteristic
897C22C43×#51811yescharacteristic
898C22C43×#51811yescharacteristic
899C22C2×#121×C4311yescharacteristic
900C22C2×#123×C4311yescharacteristic
901C22C43×#52512yes—
902C22C43×#52512yes—
903C22C2×#124×C4311yescharacteristic
904C22C2×#126×C4311yescharacteristic
905C22C43×#53812yes—
906C22C43×#53812yes—
907C22D42×C4312yes—
908C22D42×C4312yes—
909C22C43×#54612yes—
910C22C43×#54612yes—
911C22C43×#54612yes—
912C22C43×#54612yes—
913C22C43×#55112yes—
914C22C43×#55112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C43×#228011yescharacteristic
927C2C2×C43×#38811yescharacteristic
928C2C43×#231211yescharacteristic
929C2D4×C22⋊C4×C4311yescharacteristic
930C2D4×C22⋊C4×C4311yescharacteristic
931C2C43×#234211yescharacteristic
932C2C43×#234211yescharacteristic
933C2C43×#241812yes—
934C2C43×#242412yes—
935C2C43×#247212yes—
936C2C43×#248012yes—
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC26×C43C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#388C2semidirect
3. C2×C43×#380C2semidirect
6. C2×C4×C22⋊C4×C43C2semidirect
7. C43×#1440C2semidirect
8. C43×#1439C2semidirect
9. C43×#1437C2semidirect
10. C43×C22⋊#95C2semidirect
11. C43×C22⋊#95C2semidirect
15. C22×C4⋊C4×C43C22semidirect
17. C22×C22⋊C4×C43C4semidirect
30. C22×C42×C43C22semidirect
36. C2×#95×C43C22semidirect
37. C2×#95×C43C22semidirect
38. C2×#95×C43C22semidirect
39. C2×#95×C43C22semidirect
40. C2×#95×C43C22semidirect
41. C2×#95×C43C22semidirect
246. C22⋊C4×C43C22⋊C4semidirect
389. #13873C43direct (N × H)
423. C22×C43#388semidirect
456. C2×#388C2×C43semidirect
457. C2×#380C2×C43semidirect
460. C2×C4×C22⋊C4C2×C43semidirect
461. #1440C2×C43semidirect
462. #1439C2×C43semidirect
463. #1437C2×C43semidirect
464. C22⋊#95C2×C43semidirect
465. C22⋊#95C2×C43semidirect
483. C22×C4⋊C4C22×C43semidirect
485. C22×C22⋊C4C4×C43semidirect
498. C22×C42C22×C43semidirect
504. C2×#95C22×C43semidirect
505. C2×#95C22×C43semidirect
506. C2×#95C22×C43semidirect
507. C2×#95C22×C43semidirect
508. C2×#95C22×C43semidirect
509. C2×#95C22×C43semidirect
510. C43#13873direct (N × H)
715. C22⋊C4C22⋊C4×C43semidirect
891. C22C43×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C432
C2×C43×#3882
C2×C43×#3802
C2×C43×#3792
C2×C4×C22⋊C4×C432
C43×#14402
C43×#14392
C43×#14372
C43×C22⋊#952
#1387343