Finite Group Databasebeta

← C43×#24909 #24944926

Subgroups — C43×#24909 #24944926

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#447C211yesmaximal, characteristic
2C2×C43×#442C211yesmaximal, characteristic, complemented
3C43×#2420C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
5C43×#2092C211yesmaximal, characteristic, complemented
6C43×#2077C211yesmaximal, characteristic, complemented
7C43×#2054C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1936C211yesmaximal, characteristic, complemented
10C43×#1924C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1879C211yesmaximal, characteristic, complemented
13C43×#1862C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic, complemented
23C22×C22⋊C4×C43—21no—
24C43×#447—24no—
25C43×#442—24no—
26C2×#107×C43C2211yescharacteristic, complemented
27C2×#106×C43C2211yescharacteristic, complemented
28C2×C4⋊C8×C43C2211yescharacteristic, complemented
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic, complemented
36C2×#102×C43C2211yescharacteristic, complemented
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#97×C43C2211yescharacteristic, complemented
40C43×#397—21no—
41C43×#394—21no—
42C43×#390C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic, complemented
45C43×#389C2211yescharacteristic, complemented
46C43×#386—21no—
47C43×#386—21no—
48C43×#386—21no—
49C43×#382C2211yescharacteristic, complemented
50C43×#381—21no—
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#379—21no—
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C25×C43—21no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—41no—
69C22×D4×C43—41no—
70C22×D4×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C23×C4×C43—21no—
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C2×D8×C43—22no—
78C2×D8×C43—22no—
79C2×D8×C43—22no—
80C2×D8×C43—22no—
81C2×D8×C43—41no—
82C2×D8×C43D414yes—
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87#121×C43—22no—
88#121×C43—41no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C4×D4×C43—41no—
93C4×D4×C43—41no—
94C4×D4×C43—41no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—44no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#107×C43—41no—
119#106×C43—22no—
120C4⋊C8×C43—41no—
121#102×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—41no—
128#102×C43—41no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—41no—
131#97×C43—22no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—42no—
147C24×C43—81no—
148C24×C43—81no—
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—24no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43—44no—
171C2×D4×C43—42no—
172C2×D4×C43—81no—
173C2×D4×C43C2×D412yes—
174C2×D4×C43C2×D412yes—
175C2×D4×C43#4112yes—
176C2×D4×C43#4112yes—
177C2×D4×C43#4112yes—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43—81no—
196C22×C4×C43—81no—
197C22×C4×C43—81no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204D8×C43—28no—
205D8×C43—44no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C2×D412yes—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—81no—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—41no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—81no—
239C22⋊C4×C43—81no—
240C22⋊C4×C43—81no—
241C22⋊C4×C43—81no—
242C22⋊C4×C43—81no—
243C42×C43—21no—
244C42×C43—21no—
245C42×C43—21no—
246C42×C43—21no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—48no—
259C23×C43—48no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43AGL(1,ℤ/8)12yes—
282C23×C43C22×D411yescharacteristic
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—48no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—84no—
296D4×C43#12314yes—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—84no—
332C2×C4×C43—84no—
333C2×C4×C43—84no—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C2×C4×C43H(5,𝔽2)11yescharacteristic
340C8×C43—22no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344#24909C4311yesmaximal, characteristic, direct product factor, Sylow
345C22×C43—22no—
346C22×C43—24no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43—41no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—41no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—816no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43#52511yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C43#57511yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57611yescharacteristic
381C4×C43—41no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43—81no—
390C4×C43—81no—
391C4×C43C2×#12311yescharacteristic
392C4×C43#53811yescharacteristic
393C4×C43#54611yescharacteristic
394C4×C43#55111yescharacteristic
395C2×#447C2×C4311yescharacteristic
396C2×#442C2×C4311yescharacteristic, complemented
397#2420C2×C4311yescharacteristic, complemented
398D4×C22⋊C4C2×C4311yescharacteristic, complemented
399#2092C2×C4311yescharacteristic, complemented
400#2077C2×C4311yescharacteristic, complemented
401#2054C2×C4311yescharacteristic, complemented
402#2033C2×C4311yescharacteristic, complemented
403#1936C2×C4311yescharacteristic, complemented
404#1924C2×C4311yescharacteristic, complemented
405#1879C2×C4311yescharacteristic, complemented
406#1879C2×C4311yescharacteristic, complemented
407#1862C2×C4311yescharacteristic, complemented
408#1804C2×C4311yescharacteristic, complemented
409#1786C2×C4311yescharacteristic, complemented
410C2×C43—42no—
411C2×C43—44no—
412C2×C43—82no—
413C2×C43—82no—
414C2×C43#241811yescharacteristic
415C2×C43#311411yescharacteristic
416C2×C43#312211yescharacteristic
417C2×C43#326411yescharacteristic
418C2×C43#327311yescharacteristic
419C2×C43#331811yescharacteristic
420C2×C43#331911yescharacteristic
421C23×D4C22×C4311yescharacteristic
422C22×D8C22×C4311yescharacteristic
423C22×D8C22×C4311yescharacteristic
424C2×#121C22×C4311yescharacteristic
425C2×C4×D4C22×C4311yescharacteristic
426C2×C4×D4C22×C4311yescharacteristic
427C2×C4×D4C22×C4311yescharacteristic, complemented
428C22×C22⋊C4—21no—
429#447—24no—
430#442—24no—
431C2×#107C22×C4311yescharacteristic, complemented
432C2×#106C22×C4311yescharacteristic, complemented
433C2×C4⋊C8C22×C4311yescharacteristic, complemented
434C2×#102C22×C4311yescharacteristic
435C2×#102C22×C4311yescharacteristic
436C2×#102C22×C4311yescharacteristic
437C2×#102C22×C4311yescharacteristic
438C2×#102C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic, complemented
441C2×#102C22×C4311yescharacteristic, complemented
442C2×C22⋊C8C22×C4311yescharacteristic
443C2×C22⋊C8C22×C4311yescharacteristic
444C2×#97C22×C4311yescharacteristic, complemented
445#397—21no—
446#394—21no—
447#390C22×C4311yescharacteristic
448#390C22×C4311yescharacteristic
449#390C22×C4311yescharacteristic, complemented
450#389C22×C4311yescharacteristic, complemented
451#386—21no—
452#386—21no—
453#386—21no—
454#382C22×C4311yescharacteristic, complemented
455#381—21no—
456#380C22×C4311yescharacteristic
457#380C22×C4311yescharacteristic
458#379—21no—
459C4×C22⋊C4C22×C4311yescharacteristic
460#340C22×C4311yescharacteristic, complemented
461#340C22×C4311yescharacteristic, complemented
462#340C22×C4311yescharacteristic, complemented
463#340C22×C4311yescharacteristic, complemented
464#336C22×C4311yescharacteristic, complemented
465#336C22×C4311yescharacteristic, complemented
466C43#2490911yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C4311yescharacteristic
477C22×D4C23×C4311yescharacteristic
478C22×D4C23×C4311yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C4311yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C4314yes—
489C22×C8C23×C4311yescharacteristic
490C22×C8C23×C4311yescharacteristic
491C22×C8C23×C4311yescharacteristic
492C22×C8C23×C4311yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C4311yescharacteristic
503C2×C4⋊C4C23×C4311yescharacteristic
504C2×C4⋊C4C23×C4311yescharacteristic
505C2×C4⋊C4C23×C4311yescharacteristic
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—44no—
520C2×C22⋊C4D4×C4311yescharacteristic
521C2×C22⋊C4D4×C4311yescharacteristic
522C2×C42C23×C4311yescharacteristic
523C2×C42C23×C4311yescharacteristic
524#107—41no—
525#106—22no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537#97—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C4311yescharacteristic
544#95D4×C4311yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C4311yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C4312yes—
580C2×D4C2×D4×C4312yes—
581C2×D4#41×C4312yes—
582C2×D4#41×C4312yes—
583C2×D4#41×C4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C4311yescharacteristic
605C22×C4C2×D4×C4311yescharacteristic
606C22×C4C2×D4×C4311yescharacteristic
607C22×C4C2×D4×C4311yescharacteristic
608C22×C4C2×D4×C4311yescharacteristic
609C22×C4C24×C4311yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×D4×C4312yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—81no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23AGL(1,ℤ/8)×C4312yes—
688C23C22×D4×C4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C4314yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4C22×D4×C4311yescharacteristic
741C2×C4C2×#41×C4311yescharacteristic
742C2×C4C2×#41×C4311yescharacteristic
743C2×C4C2×#41×C4311yescharacteristic
744C2×C4H(5,𝔽2)×C4311yescharacteristic
745C2×C4H(5,𝔽2)×C4311yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C43×#52511yescharacteristic
780C22D42×C4311yescharacteristic
781C22C43×#54611yescharacteristic
782C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
783C22C43×#57511yescharacteristic
784C22C43×#57611yescharacteristic
785C22C43×#57611yescharacteristic
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C4311yescharacteristic
797C4C43×#53811yescharacteristic
798C4C43×#54611yescharacteristic
799C4C43×#55111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2C43×#241811yescharacteristic
805C2C43×#311411yescharacteristic
806C2C43×#312211yescharacteristic
807C2C43×#326411yescharacteristic
808C2C43×#327311yescharacteristic
809C2C43×#331811yescharacteristic
810C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#442C2semidirect
3. C43×#2420C2semidirect
4. D4×C22⋊C4×C43C2semidirect
5. C43×#2092C2semidirect
6. C43×#2077C2semidirect
7. C43×#2054C2semidirect
8. C43×#2033C2semidirect
9. C43×#1936C2semidirect
10. C43×#1924C2semidirect
11. C43×#1879C2semidirect
12. C43×#1879C2semidirect
13. C43×#1862C2semidirect
14. C43×#1804C2semidirect
15. C43×#1786C2semidirect
22. C2×C4×D4×C43C22semidirect
26. C2×#107×C43C22semidirect
27. C2×#106×C43C22semidirect
28. C2×C4⋊C8×C43C22semidirect
35. C2×#102×C43C22semidirect
36. C2×#102×C43C22semidirect
39. C2×#97×C43C22semidirect
44. C43×#390C22semidirect
45. C43×#389C22semidirect
49. C43×#382C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
344. #24909C43direct (N × H)
396. C2×#442C2×C43semidirect
397. #2420C2×C43semidirect
398. D4×C22⋊C4C2×C43semidirect
399. #2092C2×C43semidirect
400. #2077C2×C43semidirect
401. #2054C2×C43semidirect
402. #2033C2×C43semidirect
403. #1936C2×C43semidirect
404. #1924C2×C43semidirect
405. #1879C2×C43semidirect
406. #1879C2×C43semidirect
407. #1862C2×C43semidirect
408. #1804C2×C43semidirect
409. #1786C2×C43semidirect
427. C2×C4×D4C22×C43semidirect
431. C2×#107C22×C43semidirect
432. C2×#106C22×C43semidirect
433. C2×C4⋊C8C22×C43semidirect
440. C2×#102C22×C43semidirect
441. C2×#102C22×C43semidirect
444. C2×#97C22×C43semidirect
449. #390C22×C43semidirect
450. #389C22×C43semidirect
454. #382C22×C43semidirect
460. #340C22×C43semidirect
461. #340C22×C43semidirect
462. #340C22×C43semidirect
463. #340C22×C43semidirect
464. #336C22×C43semidirect
465. #336C22×C43semidirect
466. C43#24909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4472
C2×C43×#4422
C43×#24202
D4×C22⋊C4×C432
C43×#20922
C43×#20772
C43×#20542
C43×#20332
C43×#19362
C43×#19242
C43×#18792
C43×#18622
C43×#18042
C43×#17862
#2490943