Finite Group Databasebeta

← C43×#22868 #24942885

Subgroups — C43×#22868 #24942885

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 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
3C2×C43×#418C211yesmaximal, characteristic, complemented
4C43×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
6C43×#1970C211yesmaximal, characteristic, complemented
7C43×#1936C211yesmaximal, characteristic, complemented
8C43×#1926C211yesmaximal, characteristic, complemented
9C43×#1895C211yesmaximal, characteristic, complemented
10C43×#1879C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1862C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C43C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×C4×D4×C43C2211yescharacteristic, complemented
24C2×#117×C43C2211yescharacteristic
25C22×C22⋊C4×C43—21no—
26C43×#447C418yescomplemented
27C43×#442—24no—
28C2×#107×C43C2211yescharacteristic, complemented
29C2×#106×C43C2211yescharacteristic, complemented
30C43×#418—24no—
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic, complemented
38C2×#102×C43C2211yescharacteristic, complemented
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic, complemented
41C2×C4×C8×C43C2211yescharacteristic, complemented
42C43×#390—21no—
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic, complemented
46C43×#389C2211yescharacteristic, complemented
47C43×#388—21no—
48C43×#386—21no—
49C43×#386—21no—
50C43×#386—21no—
51C43×#380C2211yescharacteristic
52C43×#379—21no—
53C4×C4⋊C4×C43C2211yescharacteristic, complemented
54C4×C22⋊C4×C43—21no—
55C4×C22⋊C4×C43C2211yescharacteristic
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C25×C43—21no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—22no—
68C22×D4×C43—41no—
69C22×D4×C43—41no—
70C22×D4×C43C2×C414yescomplemented
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43—21no—
77C23×C4×C43C2311yescharacteristic
78C2×D8×C43—22no—
79C2×D8×C43—22no—
80C2×D8×C43—41no—
81C2×D8×C43—41no—
82C2×D8×C43C2×C414yes—
83C2×D8×C43C2×C414yescomplemented
84C2×M16×C43—22no—
85C2×M16×C43—22no—
86C2×M16×C43—41no—
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91#121×C43—22no—
92#121×C43C2×C414yescomplemented
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—41no—
97C4×D4×C43—41no—
98C4×D4×C43—41no—
99#117×C43—22no—
100#117×C43—41no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
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—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—44no—
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126#107×C43—41no—
127#106×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#102×C43—22no—
132#102×C43—41no—
133#102×C43C2×C414yescomplemented
134#102×C43C2×C414yescomplemented
135#102×C43D414yescomplemented
136C22⋊C8×C43C2×C414yescomplemented
137#97×C43—22no—
138C4×C8×C43—41no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—24no—
148C24×C43—42no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—42no—
152C24×C43—81no—
153C24×C43—81no—
154C24×C43C2×D411yescharacteristic
155C2×D4×C43—24no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—24no—
162C2×D4×C43—28no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—44no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C22×C412yes—
180C2×D4×C43C22×C412yes—
181C2×D4×C43C2×D412yes—
182C2×D4×C43#4112yes—
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—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43—81no—
199C22×C4×C43—81no—
200C22×C4×C43—81no—
201C22×C4×C43C22×C412yes—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43#4112yes—
208C22×C4×C43C2411yescharacteristic
209D8×C43—28no—
210D8×C43—44no—
211M16×C43—44no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43C22×C412yes—
222C2×C8×C43C22×C412yes—
223C2×C8×C43C2×D412yes—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—81no—
233C4⋊C4×C43C22×C412yes—
234C4⋊C4×C43C2×D412yes—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—41no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—42no—
243C22⋊C4×C43—42no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—81no—
247C22⋊C4×C43—81no—
248C22⋊C4×C43—81no—
249C42×C43—21no—
250C42×C43—21no—
251C42×C43—21no—
252C42×C43—21no—
253C42×C43—42no—
254C42×C43—81no—
255C23×C43—22no—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—48no—
267C23×C43—48no—
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—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—84no—
285C23×C43—84no—
286C23×C43—84no—
287C23×C43—84no—
288C23×C43—84no—
289C23×C43C4×D412yes—
290C23×C43C22×D411yescharacteristic
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—48no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—84no—
304D4×C43C4×D414yes—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
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—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—84no—
338C2×C4×C43—84no—
339C2×C4×C43—84no—
340C2×C4×C43C4×D412yes—
341C2×C4×C43AGL(1,ℤ/8)12yes—
342C2×C4×C43C23×C411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C8×C43—22no—
349C8×C43—22no—
350C8×C43—22no—
351C8×C43—41no—
352#22868C4311yesmaximal, characteristic, direct product factor, Sylow
353C22×C43—24no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—41no—
360C22×C43—42no—
361C22×C43—41no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—816no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43C2×C4×D411yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C43#57511yescharacteristic
387C22×C43#57611yescharacteristic
388C22×C43#57611yescharacteristic
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—42no—
392C4×C43—41no—
393C4×C43—42no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—81no—
397C4×C43—81no—
398C4×C43—81no—
399C4×C43C2×C4×D411yescharacteristic
400C4×C43#51811yescharacteristic
401C4×C43#54611yescharacteristic
402C4×C43#55111yescharacteristic
403C2×#447C2×C4311yescharacteristic
404C2×#442C2×C4311yescharacteristic, complemented
405C2×#418C2×C4311yescharacteristic, complemented
406#2363C2×C4311yescharacteristic, complemented
407D4×C22⋊C4C2×C4311yescharacteristic, complemented
408#1970C2×C4311yescharacteristic, complemented
409#1936C2×C4311yescharacteristic, complemented
410#1926C2×C4311yescharacteristic, complemented
411#1895C2×C4311yescharacteristic, complemented
412#1879C2×C4311yescharacteristic, complemented
413#1879C2×C4311yescharacteristic, complemented
414#1862C2×C4311yescharacteristic, complemented
415#1854C2×C4311yescharacteristic, complemented
416C4×#102C2×C4311yescharacteristic, complemented
417#1753C2×C4311yescharacteristic, complemented
418C2×C43—42no—
419C2×C43—44no—
420C2×C43—82no—
421C2×C43—82no—
422C2×C43#235811yescharacteristic
423C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C43#294811yescharacteristic
425C2×C43#327311yescharacteristic
426C2×C43#327411yescharacteristic
427C2×C43#331811yescharacteristic
428C2×C43#331911yescharacteristic
429C23×D4C22×C4311yescharacteristic
430C22×D8C22×C4311yescharacteristic
431C22×D8C22×C4311yescharacteristic
432C22×M16C22×C4311yescharacteristic
433C2×#121C22×C4311yescharacteristic
434C2×C4×D4C22×C4311yescharacteristic
435C2×C4×D4C22×C4311yescharacteristic
436C2×C4×D4C22×C4311yescharacteristic, complemented
437C2×#117C22×C4311yescharacteristic
438C22×C22⋊C4—21no—
439#447C4×C4318yescomplemented
440#442—24no—
441C2×#107C22×C4311yescharacteristic, complemented
442C2×#106C22×C4311yescharacteristic, complemented
443#418—24no—
444C2×#102C22×C4311yescharacteristic
445C2×#102C22×C4311yescharacteristic
446C2×#102C22×C4311yescharacteristic
447C2×#102C22×C4311yescharacteristic
448C2×#102C22×C4311yescharacteristic
449C2×#102C22×C4311yescharacteristic
450C2×#102C22×C4311yescharacteristic, complemented
451C2×#102C22×C4311yescharacteristic, complemented
452C2×C22⋊C8C22×C4311yescharacteristic
453C2×#97C22×C4311yescharacteristic, complemented
454C2×C4×C8C22×C4311yescharacteristic, complemented
455#390—21no—
456#390C22×C4311yescharacteristic
457#390C22×C4311yescharacteristic
458#390C22×C4311yescharacteristic, complemented
459#389C22×C4311yescharacteristic, complemented
460#388—21no—
461#386—21no—
462#386—21no—
463#386—21no—
464#380C22×C4311yescharacteristic
465#379—21no—
466C4×C4⋊C4C22×C4311yescharacteristic, complemented
467C4×C22⋊C4—21no—
468C4×C22⋊C4C22×C4311yescharacteristic
469#340C22×C4311yescharacteristic, complemented
470#340C22×C4311yescharacteristic, complemented
471#340C22×C4311yescharacteristic, complemented
472#340C22×C4311yescharacteristic, complemented
473#336C22×C4311yescharacteristic, complemented
474#336C22×C4311yescharacteristic, complemented
475C43#2286811yescharacteristic, direct product factor, Sylow
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C4314yescomplemented
485C22×D4C23×C4311yescharacteristic
486C22×D4C23×C4311yescharacteristic
487C22×D4C23×C4311yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C4311yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C4314yes—
497C2×D8C2×C4×C4314yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C4311yescharacteristic
502C22×C8C23×C4311yescharacteristic
503C22×C8C23×C4311yescharacteristic
504C22×C8C23×C4311yescharacteristic
505#121—22no—
506#121C2×C4×C4314yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C4311yescharacteristic
517C2×C4⋊C4C23×C4311yescharacteristic
518C2×C4⋊C4C23×C4311yescharacteristic
519C2×C4⋊C4C23×C4311yescharacteristic
520C2×C4⋊C4C23×C4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C4311yescharacteristic
535C2×C22⋊C4D4×C4311yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C4311yescharacteristic
539C2×C42C23×C4311yescharacteristic
540#107—41no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C4314yescomplemented
548#102C2×C4×C4314yescomplemented
549#102D4×C4314yescomplemented
550C22⋊C8C2×C4×C4314yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C4311yescharacteristic
557#95D4×C4311yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C4311yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C4312yes—
593C2×D4C22×C4×C4312yes—
594C2×D4C22×C4×C4312yes—
595C2×D4C2×D4×C4312yes—
596C2×D4#41×C4312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C4312yes—
616C22×C4C2×D4×C4311yescharacteristic
617C22×C4C2×D4×C4311yescharacteristic
618C22×C4C2×D4×C4311yescharacteristic
619C22×C4C2×D4×C4311yescharacteristic
620C22×C4C2×D4×C4311yescharacteristic
621C22×C4#41×C4312yes—
622C22×C4C24×C4311yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C4312yes—
636C2×C8C22×C4×C4312yes—
637C2×C8C2×D4×C4312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C4312yes—
648C4⋊C4C2×D4×C4312yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C4312yes—
704C23C22×D4×C4311yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C4314yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C4312yes—
755C2×C4AGL(1,ℤ/8)×C4312yes—
756C2×C4C23×C4×C4311yescharacteristic
757C2×C4C22×D4×C4311yescharacteristic
758C2×C4C2×#41×C4311yescharacteristic
759C2×C4C2×#41×C4311yescharacteristic
760C2×C4H(5,𝔽2)×C4311yescharacteristic
761C2×C4H(5,𝔽2)×C4311yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C4311yescharacteristic
796C22D42×C4311yescharacteristic
797C22C43×#54611yescharacteristic
798C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
799C22C43×#57511yescharacteristic
800C22C43×#57611yescharacteristic
801C22C43×#57611yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C4311yescharacteristic
813C4C43×#51811yescharacteristic
814C4C43×#54611yescharacteristic
815C4C43×#55111yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C43×#235811yescharacteristic
821C2C4×AGL(1,ℤ/8)×C4311yescharacteristic
822C2C43×#294811yescharacteristic
823C2C43×#327311yescharacteristic
824C2C43×#327411yescharacteristic
825C2C43×#331811yescharacteristic
826C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C2×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. C2×C43×#418C2semidirect
4. C43×#2363C2semidirect
5. D4×C22⋊C4×C43C2semidirect
6. C43×#1970C2semidirect
7. C43×#1936C2semidirect
8. C43×#1926C2semidirect
9. C43×#1895C2semidirect
10. C43×#1879C2semidirect
11. C43×#1879C2semidirect
12. C43×#1862C2semidirect
13. C43×#1854C2semidirect
14. C4×#102×C43C2semidirect
15. C43×#1753C2semidirect
23. C2×C4×D4×C43C22semidirect
26. C43×#447C4semidirect
28. C2×#107×C43C22semidirect
29. C2×#106×C43C22semidirect
37. C2×#102×C43C22semidirect
38. C2×#102×C43C22semidirect
40. C2×#97×C43C22semidirect
41. C2×C4×C8×C43C22semidirect
45. C43×#390C22semidirect
46. C43×#389C22semidirect
53. C4×C4⋊C4×C43C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#336C22semidirect
61. C43×#336C22semidirect
70. C22×D4×C43C2×C4semidirect
83. C2×D8×C43C2×C4semidirect
92. #121×C43C2×C4semidirect
133. #102×C43C2×C4semidirect
134. #102×C43C2×C4semidirect
135. #102×C43D4semidirect
136. C22⋊C8×C43C2×C4semidirect
352. #22868C43direct (N × H)
404. C2×#442C2×C43semidirect
405. C2×#418C2×C43semidirect
406. #2363C2×C43semidirect
407. D4×C22⋊C4C2×C43semidirect
408. #1970C2×C43semidirect
409. #1936C2×C43semidirect
410. #1926C2×C43semidirect
411. #1895C2×C43semidirect
412. #1879C2×C43semidirect
413. #1879C2×C43semidirect
414. #1862C2×C43semidirect
415. #1854C2×C43semidirect
416. C4×#102C2×C43semidirect
417. #1753C2×C43semidirect
436. C2×C4×D4C22×C43semidirect
439. #447C4×C43semidirect
441. C2×#107C22×C43semidirect
442. C2×#106C22×C43semidirect
450. C2×#102C22×C43semidirect
451. C2×#102C22×C43semidirect
453. C2×#97C22×C43semidirect
454. C2×C4×C8C22×C43semidirect
458. #390C22×C43semidirect
459. #389C22×C43semidirect
466. C4×C4⋊C4C22×C43semidirect
469. #340C22×C43semidirect
470. #340C22×C43semidirect
471. #340C22×C43semidirect
472. #340C22×C43semidirect
473. #336C22×C43semidirect
474. #336C22×C43semidirect
475. C43#22868direct (N × H)
484. C22×D4C2×C4×C43semidirect
497. C2×D8C2×C4×C43semidirect
506. #121C2×C4×C43semidirect
547. #102C2×C4×C43semidirect
548. #102C2×C4×C43semidirect
549. #102D4×C43semidirect
550. C22⋊C8C2×C4×C43semidirect

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
C2×C43×#4182
C43×#23632
D4×C22⋊C4×C432
C43×#19702
C43×#19362
C43×#19262
C43×#18952
C43×#18792
C43×#18622
C43×#18542
C4×#102×C432
C43×#17532
#2286843